PE Chemical Reference Handbook Version 1.1
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[email protected]. PO Box 1686 Clemson, SC 29633 800-250-3196 www.ncees.org Second printing July 2017
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CONTENTS PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 1 GENERAL INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Terms, Symbols, and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. Constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2. Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1. Metric Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2. Base and Derived SI Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.3. Unit Conversion Tables (U.S. and Metric) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 General Engineering Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.3.1. Measures of Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.3.2. Density Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.4 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.4.1. Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.4.2. Geometry and Trigonometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1.4.3. Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 1.4.4. Statistics and Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.5 Chemistry and Physical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 1.5.1. Periodic Table of the Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 1.5.2. Relative Atomic Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 1.5.3. Oxidation Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 1.5.4. Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 1.5.5. Industrial Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2 MASS/ENERGY BALANCES AND THERMODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.2 Material Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2.2.1. Material Balances With No Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2.2.2. Material Balances With Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2.3 State Functions and Thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 2.3.1. Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 ©2017 NCEES
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2.3.2. Properties of State Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 2.4 First Law of Thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.4.1. Closed Thermodynamic Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.4.2. Open Thermodynamic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 2.4.3. Steady-Flow Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.5 Behavior of Single-Component Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.5.1. Ideal Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.5.2. Nonideal Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 2.5.3. Phase Equilibrium for a Pure Component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.6 Behavior of Multicomponent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 2.6.1. Ideal Mixtures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 2.6.2. Nonideal Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 2.6.3. Phase Equilibrium for Multicomponent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 2.7 Power Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3 HEAT TRANSFER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.2 Heat-Transfer Mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.2.1. Heat Transfer Without Phase Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.2.2. Heat Transfer With Phase Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 3.3 Heat-Transfer Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 3.3.1. Heat-Exchange Equipment Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 3.3.2. Heat-Exchange Equipment Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 3.4 Tables and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 3.4.1. Tables of Heat-Transfer Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 3.4.2. Charts with Heat-Transfer Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 3.4.3. Heat-Exchanger Design Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 3.4.4. F-Factor Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 4 KINETICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 4.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 4.1.1. Reaction Parameters – Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.1.2. Temperature Dependence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.1.3. Reaction Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 ©2017 NCEES
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4.2 Rate Equations in Differential Form for Irreversible Reactions. . . . . . . . . . . . . . . . . . . . . 175 4.2.1. Zero-Order (A " R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 4.2.2. First-Order ^A " R h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 4.2.3. Second-Order ^2A " R h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 4.2.4. Second-Order ^A + bB " R h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
4.3 Chemical Equilibrium Constants from Rate Constants for Reversible Reactions . . . . . . . 175 4.3.1. Gaseous Phase Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 4.3.2. Liquid Phase Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 4.3.3. Effect of Temperature on Chemical Equilibrium Constants . . . . . . . . . . . . . . . . . . . 176 4.3.4. Relationship Between Gibbs Free Energy and the Equilibrium Constant . . . . . . . . . 176 4.4 Reactor Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 4.4.1. Batch Reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 4.4.2. Half-Life. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 4.4.3. Flow Reactors, Steady State (Space Time, Space Velocity) . . . . . . . . . . . . . . . . . . . 178 4.5 Integrated Reactor Equations for Irreversible Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . 179 4.5.1. Zero-Order Reactions _A " R, − rA = k i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 4.5.2. First-Order Reactions _ A " R, − rA = k C A i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 4.5.3. Second-Order Reactions `2 A " R, − rA = k C 2A j . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 4.5.4. Second-Order Reactions _A + bB " R, − rA = k C A C B i . . . . . . . . . . . . . . . . . . . . . . . 181
4.6 Complex Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 k1
4.6.1. First-Order Reversible Reactions f A E R p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 k2
4.6.2. Reactions of Shifting Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 4.6.3. Plug-Flow Reactors With Recycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 4.7 Yield and Selectivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 4.7.1. Two Irreversible Reactions in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 4.7.2. Two First-Order Irreversible Reactions in Series . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 4.8 Catalytic and Surface Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4.8.1. Key Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4.8.2. Surface Reaction Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4.8.3. Langmuir Adsorption Isotherm (Adsorption without Reaction). . . . . . . . . . . . . . . . 184 4.9 Enzyme Kinetics: Michaelis-Menten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 4.9.1. Michaelis-Menten Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 ©2017 NCEES
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4.9.2. Estimation of KM and Vmax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 4.9.3. Single-Substrate Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5 FLUIDS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 5.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 5.2 Mechanical-Energy Balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 5.2.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 5.2.2. Conservation of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 5.3 Flow Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 5.3.1. Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 5.3.2. Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 5.3.3. Friction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 5.3.4. Laminar Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 5.3.5. Turbulent Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 5.3.6. Particle Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 5.3.7. Two-Phase Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 5.3.8. Jet Propulsion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 5.3.9. Open-Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 5.3.10. Compressible Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 5.4 Flow Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 5.4.1. Pumps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 5.4.2. Fans, Compressors, and Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 5.4.3. Control Valves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 5.4.4. Mixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 5.4.5. Air Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 5.4.6. Solids Handling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 5.4.7. Cyclone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 5.4.8. Special Flow Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 5.5 Flow and Pressure Measurement Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 5.5.1. Manometers and Barometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 5.5.2. Flow Measurement Devices (Summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 5.5.3. Orifice, Nozzle, and Venturi Meters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 5.6 Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 ©2017 NCEES
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6 MASS TRANSFER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 6.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 6.2 Phase Equilibria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 6.2.1. Phase Equilibrium Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 6.2.2. Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 6.3 Continuous Vapor-Liquid Contactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6.3.1. Material and Energy Balances for Trayed and Packed Units. . . . . . . . . . . . . . . . . . . 285 6.3.2. Design Parameters for Trayed Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 6.3.3. Nontrayed Continuous Contact Columns (Packed Towers) . . . . . . . . . . . . . . . . . . . 318 6.4 Miscellaneous Mass Transfer Processes (Continuous, Batch, and Semicontinuous). . . . . 338 6.4.1. Membrane Separation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 6.4.2. Liquid-Liquid Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 6.4.3. Adsorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 6.4.4. Leaching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 6.4.5. Batch Distillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 6.4.6. Crystallization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 6.4.7. Filtration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 6.4.8. Drying of Solids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 6.4.9. Adiabatic Humidification and Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 7 PLANT DESIGN AND OPERATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 7.1 Terms and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 7.2 Economic Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 7.2.1. Cost Estimation and Project Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 7.3 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 7.3.1. Process Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 7.3.2. Process Equipment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 7.3.3. Siting Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 7.3.4. Instrumentation and Process Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 7.3.5. Materials of Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432 7.4 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 7.4.1. Process and Equipment Reliability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 7.4.2. Process Improvement and Troubleshooting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 ©2017 NCEES
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7.5 Safety, Health, and Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 7.5.1. General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 7.5.2. Protection Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 7.5.3. Industrial Hygiene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 7.5.4. Hazard Identification and Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 7.5.5. Environmental Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 7.6. Flammability Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536 8 PHYSICAL PROPERTIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 8.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 8.2 Physical Properties of Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540 8.2.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540 8.2.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541 8.3 Physical Properties of Plastics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542 8.3.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542 8.3.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 8.3.3. Chemical Resistance of Plastics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 8.4 Physical Properties of Liquids and Gases—Temperature-Independent Properties . . . . . . . 545 8.4.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 8.4.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 8.5 Physical Properties of Liquids and Gases—Temperature-Dependent Properties . . . . . . . . 549 8.5.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 8.5.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 8.6 Physical Properties of Air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 8.6.1. Dry Atmospheric Air Composition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 8.6.2. Dry Atmospheric Air Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 8.6.3. Temperature-Dependent Properties of Air (U.S. Customary Units) . . . . . . . . . . . . . 558 8.6.4. Temperature-Dependent Properties of Air (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . 559 8.6.5. Psychrometric Chart (U.S. Customary Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 8.6.6. Psychrometric Chart (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 8.7 Physical Properties of Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 8.7.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 8.7.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564 ©2017 NCEES
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8.7.3. Properties of Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566 8.8 Steam Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567 8.8.1. Properties of Saturated Steam (U.S. Customary Units). . . . . . . . . . . . . . . . . . . . . . . 567 8.8.2. Saturated Steam (SI Units). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 8.8.3. Superheated Steam (U.S. Customary Units). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 8.8.4. Superheated Steam (SI Units). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580 8.9 Diagrams for Water and Steam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584
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PREFACE About the Handbook The Principles and Practice of Engineering (PE) Chemical exam is computer-based, and the PE Chemical Reference Handbook is the only resource material you can use during the exam. Reviewing it before exam day will help you become familiar with the charts, formulas, tables, and other reference information provided. You will not be allowed to bring your personal copy of the PE Chemical Reference Handbook into the exam room. Instead, the computer-based exam will include a PDF version of the handbook for your use. No printed copies of the handbook will be allowed in the exam room. The PDF version of the PE Chemical Reference Handbook that you use on exam day will be very similar to this one. However, pages not needed to solve exam questions—such as the cover, introductory material, and exam specifications—will not be included in the exam version. In addition, NCEES will periodically revise and update the handbook, and each PE Chemical exam will be administered using the updated version. The PE Chemical Reference Handbook does not contain all the information required to answer every question on the exam. Theories, conversions, formulas, and definitions that examinees are expected to know have not been included. The handbook is intended solely for use on the NCEES PE Chemical exam.
Updates on Exam Content and Procedures NCEES.org is our home on the web. Visit us there for updates on everything exam-related, including specifications, exam-day policies, scoring, and practice tests.
Errata To report errata in this book, send your correction using our chat feature on NCEES.org. Examinees are not penalized for any errors in the Handbook that affect an exam question.
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1 GENERAL INFORMATION 1.1 Terms, Symbols, and Definitions Symbols Symbol
Description
A
Area or surface area
a
Acceleration
ci
Molar concentration
cp
Heat capacity
D
Diameter
DAB
Mass diffusivity Distance or diameter or diagonal
f
Moody friction factor
f
Frequency
g
Gravitational acceleration
h
Height
h
Convection heat-transfer coefficient
hm
Mass-transfer coefficient
Dhvap ©2017 NCEES
Units (SI)
ft2 ft sec 2 lb mole ft 3
m2 m s2 mol m3
Btu lbm-cF ft or in.
J = m2 kg : K s 2 : K m
ft 2 hr
m2 s m
ft or in.
d
Dhfusion
Units (U.S.)
dimensionless 1 sec ft sec 2 ft or in.
1 s m s2
Btu hr-ft 2-cF ft hr
W = kg m 2 : K s3 : K m s
Latent heat of fusion
Btu lbm
J = m2 kg s 2
Latent heat of vaporization
Btu lbm
J = m2 kg s 2
1
m
Chapter 1: General Information Symbols (cont'd) Symbol
Description
Units (U.S.)
Units (SI)
W = kg : m m : K s3 : K m
k
Thermal conductivity
Btu hr-ft-cF
L
Length
ft or in.
MW
Molecular weight
lbm lb mole
N
Number of moles
lb mole
kg mol mol
n
Impeller speed (revolutions per time)
1 sec
1 s
m
Mass
lbm
kg
P
Power
Btu hr
P
Pressure
lbf in 2
kg : m 2 s3 kg N = Pa = 2 m m : s2
P
Perimeter
ft or in.
m
P
Probability
r, R R
dimensionless ft or in.
m
psi-ft 3 Btu lb mole -cR or lb mole -cR
J mol : K
Radius Universal gas constant
W=
RD
Relative density
dimensionless
SG
Specific gravity
dimensionless
T t
Temperature Time
u
Velocity
usound
°F or °R hr or sec
°C or K s m s m s
ft sec ft sec ft3
Local speed of sound
m3
V
Volume
Wi
Mass ratio
dimensionless
wi
Mass fraction or weight fraction
dimensionless
Xi
Molar ratio
dimensionless
xi
Mole fraction
dimensionless
x a, b, q, f, j
Thermal diffusivity
β
Coefficient of thermal expansion
m
degree or radians
Angle
a
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ft or in.
Distance
ft 2 hr 1 cR
2
m2 s 1 K
Chapter 1: General Information Symbols (cont'd) Symbol
1.1.1
Description
Units (U.S.)
Units (SI)
gi
Mass concentration
lbm ft 3
kg m3
g
Surface tension
lbf in.
λ
Molecular mean free path
N kg m = s2 m
μ
Dynamic viscosity
n
Kinematic viscosity
ft 2 hr
m2 s
r
Density
lbm ft3
kg m3
t
Shear stress
lbf in 2
N = kg m2 m : s2
ji
Volume fraction
fi
Volume concentration
ft or in. cP or
kg Pa : s = m : s
lbf -sec ft 2
dimensionless ft 3 ft 3
m3 m3
Constants Physical Constants Symbol
co
Value
Units
6.706 • 108
miles hr m s
2.998 • 108 3.44 • 10–8
G 6.674 •
g gc
9.8067 32.174 5.66 • 10–24
k
NA
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N : m2 kg 2
10–11
32.174
1.3806 •
ft 4 lbf -sec 4
10–23
ft sec 2 m s2 lbm-ft lbf -sec 2 ft-lbf cR 2 J = kg : m K s2 : K
2.731 • 1026
1 lb mole
6.022 • 1023
1 mol 3
Description
Speed of light
Gravitational constant
Gravitational acceleration (earth) Gravitational conversion factor Boltzmann constant
Avogadro's Number
Chapter 1: General Information Physical Constants (cont'd) Symbol
Value
Units
8.314
3 J = m : Pa mol : K mol : K
83.14
cm 3 : bar mol : K
8314
m 3 : Pa kmol : K
82.06
cm 3 : atm mol : K liter : atm mol : K liter : Torr mol : K
0.0821 R
62.36
Description
Universal gas constant
62,360
cm 3 : Torr mol : K
10.73
psi-ft3 lb mole-cR Btu = cal lb mole-cR mol : K
1.987 1545
ft-lbf lb mole-cR
0.7302
atm-ft3 lb mole- cR
1.71 • 10–9
Btu ft - hr -cR 4
5.67 • 10–8
W = kg m2 : K4 s3 : K4
v
2
Stefan-Boltzmann constant (radiation)
Mathematical Constants
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Symbol
Value
p e g
3.14159 2.71828 0.57722
Description
Archimedes constant (Pi) Base of the natural log Euler's constant
4
Chapter 1: General Information Standard Values Note: The definitions for STP (standard temperature and pressure) vary between industries. The table below contains several conditions as specified. Property Conditions U.S. Units SI Units P = 1 atm = 14.696 psia T = 0°C = 32°F
Molar standard volume, ideal gas (STP)
m3 0.0224 mol liter 22.41 mol
3
ft 359 lb mole
m3 0.02365 mol liter 23.645 mol
Molar standard volume, ideal gas (ambient)
P = 1 atm = 14.696 psia T = 15°C = 59°F
Standard cubic foot (scf)
P = 1 atm = 14.696 psia T = 15.56°C = 60°F
Density of air (STP)
P = 1 atm = 14.696 psia T = 0°C = 32°F
0.0805
lbm ft3
1.29
Density of air (ambient)
P = 1 atm = 14.696 psia T = 15.6°C = 60°F
0.0764
lbm ft3
1.22
Density of air (ambient)
P = 1 atm = 14.696 psia T = 20°C = 68°F
0.0749
lbm ft3
Density of mercury
P = 1 atm = 14.696 psia T = 20°C = 68°F
848
lbm ft 3
Density of water
P = 1 atm= 14.696 psia T = 4°C = 39.2°F
62.4
lbm ft 3
Density of water
P = 1 atm= 14.696 psia T = 15.6°C = 60°F
62.37
lbm ft 3
kg m3 kg 999.0 3 m
Sea level
14.696
lbm in 2
1.013 : 105 Pa
Atmospheric pressure Triple point of water Speed of sound in air (STP) Speed of sound in air (ambient) Energy of visible light
P = 1 atm= 14.696 psia T = 0°C = 32°F P = 1 atm= 14.696 psia T = 20°C = 69°F Wavelength: 555 nm
ft 3 379.49 lb mole kg m3
kg m3 kg 1.20 3 m
13, 579
kg m3
1000
32.02cF 0.0887 psia
0.01109cC 0.6123 kPa
ft 1090 sec
m 330 s
ft 1130 sec
m 343 s
1 cd : sr = 4.98 : 10
−3
Btu * hr
1 cd : sr = 1.46 : 10
−3
W
* cd • sr = candela steradian; see derived SI units for definition
1.1.2
Dimensional Analysis
A dimensionally homogeneous equation has the same dimensions on the left and the right sides of the equation. Dimensional analysis involves the development of equations that relate dimensionless groups of variables to describe physical phenomena.
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Chapter 1: General Information 1.1.2.1 Buckingham Pi Theorem The number of independent dimensionless groups that may be used to describe a phenomenon known to involve n variables is equal to the number (n-r ), where r is the number of basic dimensions (e.g., mass, length, time) needed to express the variables dimensionally.
1.1.2.2 Similitude To use a model to simulate the conditions of the prototype, the model must be geometrically, kinematically, and dynamically similar to the system that is modeled. Systems that have the same dimensionless numbers are similar.
Dimensionless Numbers1 Symbol
Ar
Name
Definition g Dp3 tf `t p − tf j n
2p
f
Bi
hL hV k or k A
Bim
hm L DAB
Bm
x y gc L nu
Bo
(t1 - tv) g L2 c
Br Cf
n u2 k DT x 1 2 2tu
Archimedes Biot Biot (mass transfer)
Description
Ratio of buoyancy forces to viscous forces for a particle (p) in a fluid (f) Ratio of internal thermal resistance of a solid body to its surface thermal resistance (used for heat transfer) Ratio of the internal species transfer resistance to the boundary layer species transfer resistance (used for mass transfer)
Bingham
Ratio of yield stress (τy) to viscous stress for Bingham fluids in laminar flow
Bond
Ratio of buoyancy force to surface tension (used for boiling and condensation)
Brinkman
Ratio of viscous dissipation to enthalpy change (for use in high-speed flow)
Drag or friction Ratio of surface shear stress to free-stream kinetic energy; coefficient dimensionless surface shear stress
n u We c = Re
Capillary
Ratio of viscous forces to surface tension (for use in two-phase flow)
u2 = Ma 2
Cauchy
Ratio of inertia forces to compression forces (for use in compressible flow)
Ca
Pref - Pvap 1 2 2 tu
Cavitation
Ratio of pressure forces to inertia forces for pumps (special case of Euler number) with Pref local absolute reference pressure
Ec
u2 c p DT
Eckert
Kinetic energy of flow relative to boundary-layer enthalpy difference (for use in high-speed flow)
Eu
DP t u2
Euler
Ratio of pressure to inertia force
Fourier
Dimensionless time; ratio of rate of heat conduction to rate of internal energy storage in a solid (for use in transient heat transfer problems)
Ca Ca
Fo Fom
2 usound
DAB t L2 at L2
Fr
u2 gL
f
DP L 1 2 Dt2u
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Fourier (mass transfer) Froude Friction factor
Dimensionless time; ratio of rate of heat conduction to rate of internal energy storage in a solid (for use in transient mass transfer problems) Ratio of flow inertia to gravitational forces (for flow with a free surface) Ratio of shear force to inertia force; dimensionless pressure drop for internal flow
6
Chapter 1: General Information Dimensionless Numbers (cont'd) Symbol
Definition
Ga
g L3 v2
Gr Gz
g b DT L3 v2 Re Pr = u L x x aD D
Jal
cp.l DT Dhvap
Jav
cp.v DT Dhvap
jH
St Pr 3
jm
Stm Sc 3
Ka
g n4 t c3
2
2
Name
Galilei
Ratio of gravitational forces to viscous forces
Grashoff
Ratio of buoyancy to viscous forces (for use in natural convection)
Graetz
Ratio of enthalpy flow rate to axial heat conduction
Jakob
Ratio of sensible heat to latent heat (for use in film condensation and boiling)
Colburn factor (heat) Colburn factor (mass)
Knudsen
Ratio of mean free path to a characteristic length (for use in noncontinuum flow)
Lewis
Ratio of molecular thermal diffusivity to mass diffusivity
Ma
u usound
Nu
hL k
Np
P t n3 D5
Pe
u3 L a = Re Pr
Peclet
Pem
u3 L = DAB Re Sc
Peclet (mass transfer)
Pr
cp n k
Ra
g b DT L3 Pr v2
Sc Sh ©2017 NCEES
tu D n v DAB hm L DAB
Dimensionless mass-transfer coefficient Ratio of surface tension forces to viscous forces (used for waves on a liquid film)
Le
Re
Dimensionless heat-transfer coefficient
Kapitza
m L a DAB
Kn
Description
Mach Nusselt Power number
Prandtl
Rayleigh Reynolds Schmidt Sherwood
Dimensionless velocity; ratio of velocity to speed of sound (for use in compressible flow) Dimensionless heat-transfer coefficient; ratio of convection heat transfer to conduction in a fluid layer of thickness L (for use in convective heat transfer) Ratio of drag force to inertial force for power consumption calculation of a mixing impeller Ratio of enthalpy flow rate to heat conduction rate (for use in forced convection heat transfer) Ratio of enthalpy flow rate to heat conduction rate (for use in forced convection mass transfer) Relative effectiveness of molecular transport of momentum and energy within the boundary layer; ratio of molecular momentum diffusivity to thermal conductivity (for use in convective heat transfer) Product of Grashoff and Prandtl numbers (for use in natural convection) Ratio of inertia and viscous forces (for use in forced convection and fluid flow) Ratio of molecular momentum diffusivity to mass diffusivity (for use in convective mass transfer) Ratio of convection mass transfer to diffusion in a slab of thickness L (for use in convective mass transfer) 7
Chapter 1: General Information Dimensionless Numbers (cont'd) Symbol
Definition
Name
Sk
DP L nu
Stokes
St
Nu = h Re Pr t u c p
Stanton
Stm
Sh = hm Re Sc u
Stanton (mass)
Ste
c p DT Dhfusion
Stefan
Ratio of sensible heat to latent heat for the solid/liquid transition (for use in melting and solidification)
Sr
Lf u
Strouhal
Time characteristics of fluid flow (for use in oscillating flow)
We
t u2 L c
Weber
Ratio of inertial to surface tension forces (for use in liquid/vapor phase change)
1Verify
Description
Ratio of pressure force to viscous force Dimensionless heat-transfer coefficient, ratio of actual convection heat flux to enthalpy energy heat flux (for use in forced convection heat transfer) Dimensionless mass-transfer coefficient (for use in forced convection mass transfer)
whether gravitational conversion factor (gc) is required before using.
1.2 Units of Measurement 1.2.1
Metric Prefixes Metric Prefixes and Their Symbols Multiple
Prefix
Symbol
10–18 10–12
atto femto pico
a f p
10–9 10–6 10–3 10–2 10–1 101 102 103 106 109 1012 1015 1018
nano micro milli centi deci deka hecto kilo mega giga tera peta exa
n μ m c d da h k M G T P E
10–15
©2017 NCEES
8
Chapter 1: General Information
1.2.2
Base and Derived SI Units Base SI Units Quantity
Name
Length Mass Time Electric current Temperature Amount of a substance Luminous intensity
Symbol
meter kilogram second ampere Kelvin mol candela
m kg s A K mol cd
Derived SI Units With Special Names Quantity Name
Unit Symbol
Name
Symbol
Electric capacitance
C
farad
F
C A2 : s2 A2 : s4 F= V = J = kg : m 2
Electric charge
Q
coulomb
C
C = A:s
Electric conductance
G
siemens
S
S=
Energy or work or heat
H
joule
J
J = N:m =
Force
F
newton
N
Frequency
f
hertz
Hz
Inductance
L
henry
H
2 V : s kg : m H = X:s = A = 2 2 A :s
Electric potential
E
volt
V
kg : m 2 J V = A:s = 2 3 A :s
Power or energy flux
P
watt
W
2 J N : m kg : m W= s = s = s3
Pressure or stress
P
pascal
Pa
Pa =
Electric resistance
R
ohm
Ω
2 V kg : m X= A = 2 3 A :s
lux
lx
lx =
Illuminance
Definition
1 = A = A 2 : s = A 2 : s3 J X V kg : m 2 kg : m 2 s2
kg : m s2 1 Hz = s N=
N = kg m2 m : s2
lm = cd : sr m2 m2
Luminous flux
UV
lumen
lm
lm = cd : sr
Magnetic flux
UE
weber
Wb
Wb = V : s =
tesla
T
Magnetic flux density
T=
kg : m 2 s2 : A
Wb = V : s = kg m2 m2 s2 : A
Note: Steradian or square radian (sr) is dimensionless and represents a solid angle in three-dimensional space (angle at the tip of a cone). ©2017 NCEES
9
Chapter 1: General Information
1.2.3
Unit Conversion Tables (U.S. and Metric) Time
Time 1 sec = 1 min = 1 hr = 1 day = 1 week = 1 year =
Second (sec)
Minute (min)
1 60 3600 8.6400E+04 6.0480E+05 3.1536E+07
0.01667 1 60 1440 1.0080E+04 5.2560E+05
Hour (hr) 2.7778E–04 0.01667 1 24 168 8760
Day 1.1574E–05 6.9444E–04 0.04167 1 7 365
Week 1.6534E–06 9.9206E–05 5.9524E–03 0.14286 1 52.143
Year 3.1710E–08 1.9026E–06 1.1416E–04 2.7397E–03 0.01918 1
Additional Unit Conversions for Time 1 fortnight = 3.4560 • 105 sec = 14 days 1.2.3.1 Angle Conversion Table for the Most Commonly Used Units of an Angle Angle 1° =
Degree (°)
rad 0.01745 1 2.9089E–04 4.8481E–06 6.2832
1 57.296 0.01667 2.7778E–04 360
1 rad = 1' = 1" = 1 rev =
Minute (')
Second (")
60 3437.7 1 0.01667 2.1600E+04
3600 2.0626E+05 60 1 1.2960E+06
Revolution 2.7778E–03 0.15915 4.6296E–05 7.7161E–07 1
1.2.3.2 Length Conversion Table for the Most Commonly Used Units of Length Length 1m= 1 in = 1 ft = 1 yd = 1 mile = 1 mil =
©2017 NCEES
m
in
ft
yd
mile
mil
1 0.0254 0.3048 0.9144 1609.4 2.5400E–05
39.370 1 12 36 6.3362E+04 0.001
3.2808 0.0833 1 3 5280.2 8.3333E–05
1.0936 0.02778 0.3333 1 1760.1 2.7778E–05
6.2135E–04 1.5782E–05 1.8939E–04 5.6816E–04 1 1.5782E–08
3.9370E+04 1000 1.2000E+04 3.6000E+04 6.3362E+07 1
10
Chapter 1: General Information Additional Unit Conversions for Length 1 league = 4828.2 m = 3 miles –6 1 m (micron) = 1 • 10 m = 3.937 • 10–5 in. 1 mile (nautical) = 1853.3 m = 1.1515 miles 1 nautical league = 5559.9 m = 3 nautical miles 1 furlong
=
201.17 m
=
1 8 mile
1 perch = 1 rod = 1 pole
=
5.292 m
=
1 fathom 1 cable length (U.S. Survey) 1 chain (U.S. Survey) 1 link
= = = =
1.8288 m 219.456 m 20.117 m 0.2012 m
= = = =
1 5.5 yds = 4 chain 6 ft = 2 yds 120 fathoms = 240 yd 0.1 furlong 0.001 furlong
1 cubit
=
0.4572 m
=
1 bolt 1 skein 1 span 1 hand (horses)
= = = =
36.576 m 109.728 m 0.2286 m 0.1016 m
= = = =
1 caliber
=
2.54 • 10–4 m
=
1 Å (Angström) 1 fermi 1 astronomical unit 1 light year 1 mm 1 cm 1 km
= = = = = = =
1 • 10–10 m 1 • 10–15 m 1.496 •1011 m 9.4605 • 1015 m 0.001 m 0.01 m 1000 m
= = = = = = =
1 2 yard = 18 in. 40 yd 120 yd 9 in. 4 in. 1 100 in. 3.937 • 10–9 in. 3.937 • 10–14 in. 9.2954 • 107 miles 5.8783 • 1012 miles 0.03937 in. 0.3937 in. 0.62135 mile
1.2.3.3 Area Conversion Table for the Most Commonly Used Units of Area Area 1 m2 = 1
in2
=
1
ft2
=
1
yd2
=
1 acre = 1 sq mile =
©2017 NCEES
m2
in2
ft2
yd2
acre
sq mile
1 6.4516E–04 0.09290 0.83613 4046.9 2.5900E+06
1550 1 144 1296 6.2727E+06 4.0145E+09
10.764 6.9444E–03 1 9 4.3560E+04 2.7879E+07
1.196 7.7160E–04 0.1111 1 4840 3.0976E+06
2.4710E–04 1.5942E–07 2.2957E–05 2.0661E–04 1 640
3.8610E–09 2.4910E–12 3.5870E–10 3.2283E–09 1.5625E–05 1
11
Chapter 1: General Information
1 circ mil 1 circ inch 1 ha (hectare) 1 township 1 homestead 1 rood 1 sq rod 1 section 1 barn (bn) 1 are 1 centiare 1 mm2 1 cm2 1 km2
Additional Unit Conversions for Area r –7 2 = 5.067 • 10–10 m2 = 4 sq.mil = 7.8539 • 10 in r 2 2 = 5.0671 • 10–4 m2 = 4 in = 0.78539 in = 1 • 104 m2 = 2.471 acres 7 2 = 9.324 • 10 m = 144 homesteads = 6.475 • 105 m2 = 160 acres 2 = 1011.725 m = 0.25 acre 2 = 25.2926 m = 30.25 sq. yd 8 2 = 2.59 • 10 m = 1 sq. mile –28 2 = 1 • 10 m = 100 fm2 (femtometer) = 100 m2 = 119.6 sq. yd = 1 m2 = 10.764 ft2 –6 2 = 1 • 10 m = 1.55 • 10–3 in2 = 1 • 10–4 m2 = 0.155 in2 = 1 • 106 m2 = 0.3861 sq. mile
1.2.3.4 Volume Conversion Table for the Most Commonly Used Units of Volume Volume 1 m3 = 1 in3 = 1 ft3 = 1 gal = 1 barrel = 1 liter =
©2017 NCEES
m3
in3
ft3
gal
barrel (oil)
liter
1 1.6387E–05 0.02832 3.7850E–03 0.15898 0.001
6.1024E+04 1 1728 231 9701.6 61.024
35.314 5.7870E–04 1 0.13367 5.6143 0.03531
264.20 4.3295E–03 7.4814 1 42.0 0.2642
6.2901 1.0308E–04 0.17812 0.02381 1 6.2901E–03
1000 0.01639 28.317 3.7850 158.98 1
12
Chapter 1: General Information Additional Unit Conversions for Volume = 0.7646 m3 = 27 ft3 3 = 2.8317 m = 100 ft3 = 4.405 • 10–3 m3 = 1.164 gal (U.S.) 3 = 0.0353 m = 8 dry gal (U.S.) = 9.31 gal (U.S.) 1 quart (U.S.) = 9.4625 • 10–4 m3 = 1 gal (U.S.) 4 1 pint (U.S.) = 4.7313 • 10–4 m3 = 1 gal (U.S.) = 1 quart (U.S.) 8 2 1 cup (U.S.) = 2.3656 • 10–4 m3 = 1 pint = 1 gal (U.S.) 2 16 1 gill (U.S.) = 1.1828 • 10–4 m3 = 1 pint = 1 gal (U.S.) 4 32 1 fl oz (U.S.) = 2.9570 • 10–5 m3 = 1 cup = 1 gal (U.S.) 8 128 1 fl dram (U.S.) = 3.6963 • 10–6 m3 = 1 fl oz = 1 gal (U.S.) 8 1024 1 1 1 minim (U.S.) = 6.1605 • 10–8 m3 = 60 dram = 480 fl oz 1 cm3 = 1 ml = 1 • 10–6 m3 = 0.06102 in3 1 mm3 = 1 • 10–9 m3 = 6.1024 • 10–5 in3 3 1 hectoliter = 0.1 m = 26.42 gal (U.S.) 3 1 hogshead = 0.2385 m = 63 gal (U.S.) 3 1 UK bushel = 0.0364 m = 8 dry gal (UK) 3 1 Imperial gal (UK) = 0.0045 m = 1.201 gal (U.S.) 1 quarter (UK) = 0.291 m3 = 64 gal (UK) 3 1 peck (UK) = 0.0091 m = 2 gal (UK) 1 quart (UK) = 0.0011 m3 = 1 gal (UK) 4 1 pint (UK) = 5.6826 • 10–4 m3 = 1 gal (UK) 8 3 1 barrel (UK) = 0.1637 m = 36 gal (UK) = 43 gal (U.S.) 3 1 barrel (U.S. liq) = 0.1192 m = 31.503 gal (U.S.) = 26 gal (UK) 3 1 barrel (U.S. dry) = 0.1156 m = 30.55 gal (U.S.) 3 1 cord (lumber) = 3.625 m = 128 ft3 1 stere (lumber) = 1 m3 = 1.308 yd3 1 3 1 boardfoot (lumber) = 2.3597 • 10–6 m3 = 12 ft 1 yd3 1 register ton 1 dry gal (U.S.) 1 U.S. bushel
U.S. Conversion for Liquid Volume 1 gal (U.S.) = 4 quarts 1 quart = 2 pints 1 pint = 2 cups 1 cup = 8 fl oz
©2017 NCEES
13
Chapter 1: General Information U.S. Conversion for Dry Volume 1 cup = 16 tablespoons (Tbsp) 1 Tbsp = 3 teaspoons (tsp) 1 tsp = 8 pinches 1 pinch = 2 dashes 1.2.3.5 Mass Conversion Table for the Most Commonly Used Units of Mass Mass 1 kg = 1 lbm = 1 oz = 1 ton (short) = 1 ton (long) = 1 slug =
kg
lbm
oz
ton (short)
ton (long)
slug
1 0.45359 0.02835 907.18 1016.1 14.594
2.2046 1 0.0625 2000 2240 32.174
35.273 16 1 3.1999E+04 3.5840E+04 514.78
1.1023E–03 5.0000E–04 3.1251E–05 1 1.12 0.01608
9.8420E–04 4.4642E–04 2.7902E–05 0.89285 1 0.014363
0.06852 0.03108 1.9426E–03 0.62162 69.622 1
1 hundredweight (short) = 1 hundredweight (long) = 1 tonne (metric) 1 centner 1 dram 1 grain 1 carat 1 atomic mass unit
= = = = = =
Additional Unit Conversions for Mass 45.3592 kg = 100 lbm 50.8023 kg = 112 lbm 1000 kg = 2204.6 lbm 100 kg = 220.5 lbm –3 1.7719 • 10 kg = 0.0625 oz –5 6.4799 • 10 kg = 2.2857 • 10–3 oz 2.0000 • 10–4 kg = 7.0547 • 10–3 oz 1.6605 • 10–27 kg = 3.6608 • 10–27 lbm
kgf : s 2 = 9.8067 kg m 1 stone = 6.3503 kg
=
21.62 lbm
=
14 lbm
1 firkin = 40.8231 kg
=
90 lbm
1 lb (apothecary/troy) = 0.3732 kg
=
13.166 oz = 12 oz (ap/troy) = 0.8229 lbm
1 oz (apothecary/troy) = 3.1103 • 10–2 kg
=
1.0971 oz
1 dram (apothecary) = 3.8879 • 10–3 kg
=
0.13714 oz
1 scruple (apothecary) = 1.2960 • 10–3 kg
=
0.04571 oz
1 grain (apothecary/troy) = 6.4799 • 10–5 kg
=
2.2857 • 10–3 oz = 1.4286 • 10–4 lbm
1 carat (troy) = 2.0500 • 10–4 kg
=
7.231 • 10–3 oz
1 pennyweight (troy) = 1.5552 • 10–3 kg
=
0.05486 oz
kg
=
1.1428 • 10–4 oz
1 doite (troy) = 1.3500 • 10–7 kg
=
4.7618 • 10–6 oz
1
1 mite (troy) = 3.2400 •
©2017 NCEES
10–6
14
Chapter 1: General Information Apothecary Measures 1 lb = 373.242 grain 1 lb = 12 oz 1 oz = 8 drams 1 dram = 3 scruples 1 scruple = 20 grains Troy Measures 1 lb = 373.242 grain 1 lb = 12 oz (ozt) 1 ozt = 20 pennyweight (dwt) 1 dwt = 24 grains 1 grain = 20 mites 1 mite = 24 doites 1.2.3.6 Density Conversion Table for the Most Commonly Used Units of Density Density
kg m3
lbm ft 3
lbm gal
kg liter
lbm in 3
ton yd 3
1
kg = m3
1
0.06243
8.3452E–03
0.001
3.6128E–05
7.5250E–04
1
lbm = ft 3
16.018
1
0.13367
0.01618
5.7870E–04
0.01205
lbm 1 gal =
119.83
7.481
1
0.11983
4.3292E–03
0.09017
kg 1 liter =
1000
62.43
8.3452
1
0.036128
0.7525
1
lbm = in 3
2.7679E+04
1728
231
27.679
1
20.829
1
ton = yd 3
1328.9
82.963
11.09
1.3289
0.048011
1
©2017 NCEES
15
Chapter 1: General Information Additional Unit Conversions for Density slug kg lbm = 515.379 3 = 32.175 3 1 3 ft ft m g lbm 1 liter = 1 kg3 = 0.06243 3 ft m oz 1 gal
=
7.4906
kg m3
=
grain ft3
=
0.0023
kg m3
= 1.4286 : 10
lbm 1 UK gal
=
99.978
kg m3
=
1
0.46764
6.2416
lbm ft 3 -4
lbm ft 3
lbm ft 3
Specific gravity (also called relative density): The ratio of the density of a substance to the density of water at 4°C (39°F): t t = SG = kg lbm 1000 3 62.4 3 ft m API gravity: 141.5 − 141.5 API = SG 131.5 ; SG60cF = API + 131.5 60cF
1.2.3.7 Specific Volume Conversion Table for the Most Commonly Used Units of Specific Volume Specific Volume
m3 kg
liter kg
ft 3 lbm
gal lbm
in 3 lbm
ft 3 kg
1
1000
16.018
119.76
2.7680E+04
35.314
0.001
1
0.01602
0.11976
27.68
0.03531
ft 3 1 lbm =
0.06243
62.428
1
7.4764
1728
2.2046
gal 1 lbm =
8.3500E–03
8.35
0.13375
1
231
0.29488
in 3 1 lbm =
3.6127E–05
0.03613
5.7870E–04
4.3266E–03
1
1.2758E–03
0.02832
28.317
0.45359
3.3913
783.81
1
m3 1 kg = liter 1 kg =
ft 3 1 kg =
©2017 NCEES
16
Chapter 1: General Information 1.2.3.8 Velocity Conversion Table for the Most Commonly Used Units of Velocity m s
ft min
miles hr
km hr
knots
m 1 s =
ft sec
1
3.2808
196.85
2.2369
3.6
1.9423
ft 1 sec =
0.3048
1
60
0.68182
1.0973
0.592
ft 1 min =
5.0800E–03
0.01667
1
0.01136
0.018288
9.8667E–03
mile 1 hr = km 1 hr = 1 knot =
0.44704
1.4667
88
1
1.6093
0.86827
0.27778
0.91134
54.681
0.62137
1
0.53952
0.51486
1.6892
101.35
1.1517
1.8535
1
Velocity
1.2.3.9 Acceleration Conversion Table for the Most Commonly Used Units of Acceleration m s2
ft sec 2
in. sec 2
cm s2
g
km hr : s
1
3.2808
39.37
0.01
0.10197
3.569
0.3048
1
12
3.0480E–03
0.03108
1.0878
0.0254
0.08333
1
2.5400E–04
2.5901E–03
0.09065
100
328.08
3937
1
10.197
356.9
1g=
9.8067
32.174
386.09
0.09807
1
35
km 1 hr : s =
0.28019
0.91926
11.031
2.8019E–03
0.02857
1
Acceleration 1
m= s2
1
ft = sec 2
in. = sec 2 cm 1 2 = s 1
©2017 NCEES
17
Chapter 1: General Information 1.2.3.10 Volumetric Flow Volumetric Flow
Conversion Table for the Most Commonly Used Units of Volumetric Flow MMgal ** barrel * gal m3 ft 3 day day min s hr
ft 3 sec
m3 1 s =
1
1.5851E+04
1.2713E+05
5.4345E+05
22.8
35.314
gal 1 min =
6.3089E–05
1
8.0207
34.286
1.4384E–03
2.2280E–03
ft 3 1 hr =
7.8658E–06
0.12468
1
4.2747
1.7934E–04
2.7778E–04
barrel 1 day =
1.8401E–06
0.02917
0.23394
1
4.1954E–05
6.4982E–05
0.04386
695.2
5576
2.3835E+04
1
1.5489
0.02832
448.84
3600
1.5389E+04
0.64563
1
1
MMgal = day
ft 3 1 sec =
* 1 barrel of oil = 42 gallons
** million gallons
Additional Unit Conversions for Volumetric Flow ft3 1 min gal 1 hr UK gal 1 min UK gal 1 hr 1
4.7195 : 10
-4
m3 s
=
3
=
m3 s
=
3
=
= 1.0515 : 10 -6 m s =
7.5766 : 10
-5
= 1.2628 : 10 -6 m s
U.S.gal min U.S.gal 0.01667 min U.S. gal 1.201 min U.S. gal 0.02 min 7.4807
MM gal (UK) day
=
m3 0.0526 s
=
834.01
m3 1 hr
=
=
5.7062 : 10 7
liter 1 s
=
m3 3600 hr m3 0.001 s
liter 1 min
=
m3 0.06 s
=
15.851
nliter s
= 10 -9 m s
3
=
1.5851 : 10
mliter s
= 10 -6 m s
3
1 1
©2017 NCEES
=
=
=
18
U.S. gal min
U.S. gal min U.S. gal 951.04 min U.S. gal min
U.S. gal min U.S. gal 0.01585 min -5
Chapter 1: General Information 1.2.3.11 Mass Flow
Mass Flow
kg 1 s =
Conversion Table for the Most Commonly Used Units of Mass Flow kg kg MMlbm * lbm lbm year s hr hr min
ton (short) day
1
7936.5
132.28
3600
69.524
95.238
lbm 1 hr =
1.2600E–04
1
0.01667
0.4536
8.7600E–03
0.012
lbm 1 min =
7.5600E–03
60
1
27.216
0.5256
0.72
kg 1 hr =
2.7778E–04
2.2046
0.03674
1
0.01931
0.02646
1
MMlbm = year
0.01438
114.16
1.9026
51.781
1
1.3699
1
ton (short) = day
0.0105
83.33
1.3889
37.8
0.73
1
* million pounds
Additional Unit Conversions for Mass Flow
©2017 NCEES
1
ton (long) day
=
kg 0.0118 s
=
lbm 930, 333 hr
1
ton (short) hr
=
kg 0.2520 s
=
lbm 2000 hr
1
ton (long) hr
=
kg 0.2822 s
=
lbm 2240 hr
slug 1 hr
=
4.0539 : 10
=
lbm 32.174 hr
lbm 1 sec
=
kg 0.4536 s
=
lbm 3600 hr
19
-3
kg s
Chapter 1: General Information 1.2.3.12 Mass Flux Conversion Table for the Most Commonly Used Units of Mass Flux Mass Flux
kg s : m2
kg hr : m 2
g s : cm 2
lbm hr -ft 2
lbm sec -ft 2
lbm sec - in 2
1
kg = s : m2
1
3600
0.1
737.35
0.20482
1.4223E–03
1
kg = hr : m 2
2.7778E–04
1
2.7778E–05
0.20482
5.6894E–05
3.9510E–07
1
g = s : cm 2
10
3.6000E+04
1
7373.5
2.0482
0.01422
1
lbm = hr -ft 2
1.3562E–03
4.8823
1.3562E–04
1
2.7777E–04
1.9290E–06
1
lbm = sec -ft 2
4.8824
1.7577E+04
0.48824
3600
1
6.9444E–03
1
lbm = sec - in 2
703.07
2.5310E+06
70.307
5.1841E+05
144
1
1.2.3.13 Force
Force
1N= 1 lbf = 1 pdl = 1 dyne = 1 kgf = 1 ozf =
Conversion Table for the Most Commonly Used Units of Force g : cm kg : m lbm -ft dyne = pdl = lbf kgf = kilopond (kp) ozf N= s2 sec 2 s2 1 0.22481 7.233 1.0000E+05 0.10197 3.5969 4.4482 1 32.174 4.4482E+05 0.45359 16 0.13825 0.03108 1 1.3825E+04 0.01410 0.4973 1.0000E–05 2.2481E–06 7.2330E–05 1 1.0197E–06 3.5969E–05 9.8067 2.2046 70.932 9.8067E+05 1 35.274 0.27801 0.0625 2.0109 2.7801E+04 0.02835 1 Additional Unit Conversions for Force 1
kg : m = 1 dyne = 1 N s2 1 dyne = 1 : 10 -5 N
=
= 9964 N
= 2240 lbf
1 tonf (short)
= 8896.44 N
= 2000 lbf
20
-
0.22481 : 10 5 lbf
1 tonf (long)
1 kip = 1 kilo lbf = 4448.2 N 1 pond = 1 p = 0.0098 N
©2017 NCEES
= 0.22481 lbf
= 1000 lbf = 2.2046 • 10–3 lbf
Chapter 1: General Information 1.2.3.14 Pressure/Stress Conversion Table for the Most Commonly Used Units of Pressure Pressure 1 Pa =
Pa =
kg m : s2
psi =
lbf * in 2
Torr = mmHg
in w. c.**
bar
atm
1 bar =
1 6894.8 133.32 249.08 1.0000E+05
1.4504E–04 1 0.01934 0.03613 14.504
7.5008E–03 51.716 1 1.8683 750.08
4.0148E–03 27.681 0.53525 1 401.48
1.0000E–05 0.06895 1.3332E–03 2.4908E–03 1
9.8717E–06 0.06806 1.3161E–03 2.4588E–03 0.98717
1 atm =
1.0130E+05
14.696
759.83
406.7
1.013
1
1 psi*= 1 Torr = 1 in w. c.** =
*0 psig (gauge) = 14.696 psia (absolute) = 1 atm = 1.013 • 105 Pa ** inches water column
Additional Unit Conversions for Pressure and Stress kg N = 1 m2 m : s2 1 in Hg lbf 1 2 ft kgf 1 at = 1 2 cm kgf 1 mm w. c. = 1 2 m 1 ft w. c. dyne 1 cm 2 pdl 1 2 ft pdl 1 2 m tonf (long) 1 in 2 1
1
tonf (short) in 2 N cm 2 lbm -g 1 ft 2 1
= 1 Pa
=
1.4504 • 10–4 psi
= 3386.6 Pa
=
0.49118 psi
= 47.8803 Pa
=
6.9444 • 10–3 psi
= 9.8067 • 104 Pa
=
14.223 psi
= 9.8067 Pa
=
1.4223 • 10–3 psi
= 2988.98 Pa
=
0.4335 psi
= 0.1 Pa
=
1.4504 • 10–5 psi
= 1.4882 Pa
=
2.1584 • 10–4 psi
= 0.1383 Pa
=
2.0052 • 10–5 psi
= 1.5444 • 107 Pa
=
2240 psi
= 1.3790 • 107 Pa
=
2000 psi
= 1 • 104 Pa
=
1.4504 psi
= 47.88 Pa
=
6.9444 • 10–3 psi
=
0.98692 atm
1 bar = 1 : 10 6
©2017 NCEES
21
dyne cm 2
Chapter 1: General Information 1.2.3.15 Energy and Torque Conversion Table for the Most Commonly Used Units of Energy (Work or Heat) Energy 1J= 1 Btu = 1 kcal = 1 kWh = 1 ft-lbf = 1 hp-hr =
kg : m 2 s2 1 1055.1 4186.8 3.6000E+06
Btu
kcal
kWh
ft-lbf
hp-hr
9.4778E–04 1 3.9682 3412
2.3885E–04 0.25201 1 859.85
2.7778E–07 2.9308E–04 1.1630E–03 1
0.73757 778.21 3088.1 2.6553E+06
3.7251E–07 3.9303E–04 1.5596E–03 1.341
1.3558 2.6845E+06
1.2850E–03 2544.3
3.2383E–04 641.19
3.7661E–07 0.7457
1 1.9800E+06
5.0504E–07 1
J=
Additional Unit Conversions for Energy (Work or Heat) and Torque kg : m 2 1 = 1= N : m 1W : s s2 1 therm 1 cal = 0.001 kcal 1 CHU 1 ton-hr (refrigeration) 1 PS • hr (metric) 1 kgf • m 1 dyne • cm = 1 erg 1 dyne • m 1 lbf -in 1 ft-pdl 1 ton (explosives) 1 eV 1 hp-hr (UK) 1 psi-ft3 1 atm • cm3
©2017 NCEES
= 1J
= 9.4778 • 10–4 Btu
= = = = = = = = = = = = = = =
= = = = = = = = = = = = = = =
1.0551 • 108 J 4.1868 J 1899.1 J 1.2661 • 107 J 2.6478 • 106 J 9.8067 J 1 • 10–7 J 1J 0.113 J 0.0421 J 4.1840 • 109 J 1.6022 • 10–19 J 2.5645 • 106 J 195.2401 J 0.1013 J
22
105 Btu 3.9682 • 10–3 Btu 1.8 Btu 1.2 • 104 Btu 2509.5 Btu 9.2946 • 10–3 Btu 9.4778 • 10–11 Btu 9.4778 • 10–4 Btu 1.0708 • 10–4 Btu 3.9938 • 10–5 Btu 3.9655 • 106 Btu 1.5185 • 10–22 Btu 2430.6 Btu 0.18504 Btu 9.601 • 10–5 Btu
Chapter 1: General Information 1.2.3.16 Specific Enthalpy Specific Enthalpy
J 1 kg =
Conversion Table for the Most Commonly Used Units of Specific Enthalpy hp-hr J Btu kcal kWh kg lbm kg kg lbm
lbf -ft lbm
1
4.2992E–04
2.3885E–04
1.6897E–07
2.7778E–07
0.33456
Btu 1 lbm =
2326
1
0.55556
3.9301E–04
6.4611E–04
778.18
kcal 1 kg =
4186.8
1.8
1
7.0743E–04
1.1630E–03
1400.7
5.9184E+06
2544.4
1413.6
1
1.644
1.9800E+06
3.6000E+06
1547.7
859.85
0.60828
1
1.2044E+06
2.989
1.2851E–03
7.1392E–04
5.0505E–07
8.3029E–07
1
hp-hr 1 lbm = kWh 1 kg = lbf -ft 1 lbm =
Additional Unit Conversions for Specific Enthalpy Btu kcal = CHU cal = = 1.8 lbm 1 kg 1 lbm 1 g = 4186.8 J kg Btu kgf : m J = 9.8067 kg = 4.2161 • 10–3 lbm 1 kg psi -ft 3 = 1 lbm 1
atm : cm 3 = g
J 430.4329 kg
=
Btu 0.18505 lbm
J 101.3 kg
=
Btu 0.04355 lbm
1.2.3.17 Calorific Value Calorific Value
J = m3 Btu 1 3 = ft kcal 1 3 = m therm = 1 ft 3 therm 1 gal = 1
1
CHU = ft 3
©2017 NCEES
Conversion Table for the Most Commonly Used Units of Calorific Value therm J Btu kcal therm gal m3 ft 3 m3 ft 3
CHU ft 3
1
2.6838E–05
2.3885E–04
2.6838E–10
3.5971E–11
1.4910E–05
3.7260E+04
1
8.8994
1.0000E–05
1.3403E–06
0.55556
4186.8
0.11237
1
1.1237E–06
1.5060E–07
0.06243
3.7260E+09
1.0000E+05
8.8994E+05
1
0.13403
5.5556E+04
2.7800E+10
7.4611E+05
6.6399E+06
7.4611
1
4.1451E+05
6.7067E+04
1.8
16.019
1.8000E–05
2.4125E–06
1
23
Chapter 1: General Information 1.2.3.18 Entropy
Entropy
Conversion Table for the Most Common Units of Entropy kcal = Btu J CHU Clausius K cC cF cC
J 1K =
kcal cF
1
5.2654E–04
2.3885E–04
5.2654E–04
4.2992E–04
Btu 1 oF =
1899.2
1
0.45361
1
0.8165
kcal 1 oC =
4186.8
2.2045
1
2.2045
1.8
1
CHU = oC
1899.2
1
0.45361
1
0.8165
1
kcal = o F
2326.0
1.2247
0.5556
1.2247
1
1.2.3.19 Power
Power
Conversion Table for the Most Commonly Used Units of Power Btu kcal therm W hp hr hr hr
ton refrigeration
1
3.4120
0.85985
1.3404E–03
3.4120E–05
2.8434E–04
Btu 1 hr = kcal 1 hr =
0.29308
1
0.252
3.9285E–04
1.0000E–05
8.3335E–05
1.1630
3.9682
1
1.5589E–03
3.9682E–05
3.3069E–04
1 hp =
746.04
2545.5
641.48
1
0.02546
0.21213
2.9308E+04
1.0000E+05
2.5200E+04
39.285
1
8.3335
3516.9
1.2000E+04
3024.0
4.7141
0.12
1
1W=
1
therm = hr
1 ton refrigeration =
©2017 NCEES
24
Chapter 1: General Information Additional Unit Conversions for Power kg : m 2 J = 1 s V= :A s3 kgf : m 1 s 1
atm : m 3 hr
= 1W
Btu = 3.412 hr
= 9.8067 W
= 33.461 Btu hr
= 28.15 W
Btu = 96.049 hr
1 PS (metric) = 735.48 W erg 1 s
= 2509.5 Btu hr
= 1 • 10–7 W
= 3.412 • 10–7 Btu hr
CHU 1 hr lbf -ft 1 min lbf -ft 1 sec
= 0.5275 W
= 1.8 Btu hr
= 0.0226 W
pdl-ft 1 sec
= 0.0421 W
= 0.0771 Btu hr = 4.626 Btu hr = 0.14378 Btu hr
= 1.3558 W
1 hp (British) = 756.7 W
= 2581.9 Btu hr
1 hp (Boiler) = 9809.5 W
= 3.347 • 104 Btu hr
1.2.3.20 Heat Flux
Heat Flux
W = m2 Btu = 1 2 ft -hr kcal = 1 2 m : hr cal = 1 cm 2 : s kcal = 1 2 ft -hr CHU = 1 2 ft -hr 1
©2017 NCEES
Conversion Table for the Most Commonly Used Units of Heat Flux W Btu kcal cal kcal m2 ft 2-hr m 2 : hr cm 2 : s ft 2-hr
CHU ft 2-hr
1
0.317
0.85985
2.3885E–05
0.07989
0.17611
3.1546
1
2.7125
7.5346E–05
0.25201
0.55554
1.163
0.36867
1
2.7778E–05
0.09291
0.20481
4.1868E+04
1.3272E+04
3.6000E+04
1
3344.6
7372.2
12.518
3.9682
10.764
2.9899E–04
1
2.2045
5.6784
1.8
4.8825
1.3563E–04
0.45362
1
25
Chapter 1: General Information 1.2.3.21 Dynamic Viscosity Viscosity (dynamic)
1 Pa • s = 1 cP = 1 Poise = lbf - sec = ft 2 lbf - sec = 1 in 2 1
lbm 1 ft -sec =
Conversion Table for the Most Commonly Used Units of Dynamic Viscosity lbf -sec lbf -sec Pa • s cP Poise ft 2 in 2 1 1000 10 0.02089 1.4504E–04
lbm ft -sec 0.67195
0.001
1
0.01
2.0885E–05
1.4504E–07
6.7195E–04
0.1
100
1
2.0885E–03
1.4504E–05
0.06720
47.88
4.7880E+04
478.8
1
6.9444E–03
32.173
6894.8
6.8948E+06
6.8948E+04
144
1
4633
1.4882
1488.2
14.882
0.03108
2.1585E–04
1
Additional Unit Conversions for Dynamic Viscosity g dyne : s 1= Poise 1= cm : s 1 cm 2 lbf -sec = slug 1 1 ft -s ft 2 lbm pdl - s 1 ft - s = ft 2 lbm 1 ft - hr kgf : s 1 m2 kgf : hr 1 m2 kg 1 ft : hr
©2017 NCEES
lbf -sec ft 2
= 0.1 Pa • s
=
2.0885 • 10–3
= 47.8803 Pa • s
=
1
= 1.4882 Pa • s
=
0.03108
= 4.1338 • 10–4 Pa • s
=
8.6336 • 10–6
= 9.8067 Pa • s
=
= 3.5320 • 10–4 Pa • s
=
7.3767 • 10–6
lbf -sec ft 2
= 9.1134 • 10–4 Pa • s
=
1.9034 • 10–5
lbf -sec ft 2
26
lbf -sec ft 2 lbf -sec ft 2
lbf -sec ft 2 lbf -sec 0.20482 ft 2
Chapter 1: General Information 1.2.3.22 Diffusion Coefficient, Thermal Diffusivity, and Kinematic Viscosity Conversion Table for the Most Commonly Used Units of the Diffusion Coefficient, T hermal Diffusivity, and Kinematic Viscosity 2 * liter m ft 2 in 2 ft 2 cm 2 Diffusivity = St in.-hr s sec sec hr s m2 1 s =
1
1.0000E+04
10.764
3.8751E+04
1550
9.1441E+04
1.0000E–04
1
1.0764E–03
3.8751
0.155
9.1441
ft 2 1 sec =
0.09290
929.03
1
3600
144
8495.2
ft 2 1 hr =
2.5806E–05
0.25806
2.7777E–04
1
0.04
2.3597
in 2 1 sec =
6.4516E–04
6.4516
6.9444E–03
25
1
58.994
liter 1 in.-hr =
1.0936E–05
0.10936
1.1771E–04
0.42378
0.01695
1
*
cm 2 = 1 St = s
* St = Stokes
1.2.3.23 Heat Capacity and Specific Entropy Conversion Table for the Most Commonly Used Units of Heat Capacity and S pecific Entropy Btu W lbf -ft = Heat Capacity m:K lbm-cF lbm-cR W 1 2.3885E–04 0.18586 1m :k = Btu 4186.8 1 778.17 1 lbm-cF = lbf -ft 5.3803 1.2851E–03 1 1 lbm-cR = Btu kcal cal = CHU = 1= lbm- cF 1 kg : cC 1 g : cC 1 lbm-cC
©2017 NCEES
27
Chapter 1: General Information 1.2.3.24 Thermal Conductivity Conversion Table for the Most Commonly Used Units of Thermal Conductivity Btu kcal cal W Btu- in m:K hr - ft -cF hr : m : cC s : cm : cC hr - ft 2-cF
Thermal Conductivity
W 1m:K =
Btu 1 hr - ft -cF = Btu- in = hr - ft 2-cF kcal 1 hr : m : cC = cal 1 s : cm : cC = 1
1
0.57777
6.9334
0.85985
2.3885E–03
1.7308
1
12
1.4882
4.1339E–03
0.14423
0.08333
1
0.12402
3.4449E–04
1.163
0.67194
8.0635
1
2.7778E–03
418.68
241.9
2902.9
360
1
Btu CHU 1 hr - ft -cF = 1 hr - ft -cC
1.2.3.25 Heat-Transfer Coefficient Conversion Table for the Most Commonly Used Units of the Heat-Transfer Coefficient Heat-Transfer W Btu Btu kcal cal kcal Coefficient m2 : K hr - ft 2-cF sec - ft 2-cF hr : m 2 : cC s : cm 2 : cC hr - ft 2- cC W = 1 0.1761 4.8919E–05 0.85985 2.3885E–05 0.07989 1 2 m :K Btu = 1 5.6785 1 2.7779E–04 4.8826 1.3563E–04 0.45363 hr - ft 2- cF Btu = 2.0442E+04 3599.8 1 1.7577E+04 0.48824 1633 1 sec - ft 2-cF kcal = 1.1630 0.20481 5.6893E–05 1 2.7778E–05 0.09291 1 hr : m 2 : cC cal = 4.1868E+04 7373.1 2.0482 3.6000E+04 1 3344.6 1 s : m 2 : cC kcal = 1 12.518 2.2045 6.1237E–04 10.764 2.9899E–04 1 hr - ft 2- cC 1
©2017 NCEES
Btu = 1 CHU hr - ft 2-cC hr - ft 2- cF
28
Chapter 1: General Information 1.2.3.26 Surface Tension Surface Tension
Conversion Table for the Most Commonly Used Units of Surface Tension g N pdl dyne lbf lbf cm m in. ft cm in.
N 1m =
1
5.7101E–03
4.7585E–04
1.0197
1000
0.18372
lbf 1 in. =
175.13
1
0.08333
178.58
1.7513E+05
32.174
2101.5
12
1
2143
2.1015E+06
386.09
0.98067
5.5997E–03
4.6665E–04
1
980.67
0.18017
dyne 1 cm =
0.001
5.7101E–06
4.7585E–07
1.0197E–03
1
1.8372E–04
pdl 1 in. =
5.4431
0.03108
2.5901E–03
5.5504
5443.1
1
lbf 1 ft = g 1 cm =
1.2.3.27 Cubic Expansion Coefficient Conversion Table for the Most Commonly Used Units of Cubic Expansion g Cubic kg lbm 3 3 3 Expansion cm : cC m -cF m :K kg = m3 : K lbm = 1 3 m -cF g = 1 cm 3 : cC
1
1
0.03468
0.001
28.833
1
0.02883
1000
34.682
1
1.2.3.28 Temperature Conversion Table for Temperature Units
©2017 NCEES
Kelvin (K)
Celsius (°C)
Rankine (°R)
Fahrenheit (°F)
T(K) =
T(K)
T(°C) + 273.15
5 9 T(°R)
5 9 T(°F) + 255.37
T(°C) =
T(K) – 273.15
T(°C)
5 9 T(°R) – 273.15
5 9 T(°F) – 17.78
T(°R) =
9 5 T(K)
T(°R)
T(°F) + 459.67
T(°F) =
9 5 T(K) + 459.67
9 5 T(°C) + 491.67°R 9 5 T(°C) + 32
T(°R) – 459.67
T(°F)
29
Chapter 1: General Information
1.3 General Engineering Relations 1.3.1
Measures of Composition
1.3.1.1 Fractions Mole Fraction (or mole%): xi N x A = NA
For binary systems: N x A = N +aN = A B
1 N 1 + NB a
N=
/i Ni /i xi = 1
1 N A = c x − 1 m N B x A + x B = 1 B
Mass Fractions (Weight Fraction or wt%): wi m w A = mA m = For binary systems: m 1 w A = m +Am = m A B 1 + mB A
/i mi /i wi = 1
1 m A = c w − 1 m m B w A + w B = 1 B
Conversion Between Mole Fraction and Mass Fraction m MWA = N A m A = N A MWA A = xA
mA = A / i mi MW MW i
wA = wA A / i wi MW MWi
NA = MWi / i Ni MW A
m N A = MWA A
xA MWi / i xi MW A
For binary systems: xA =
mA
MW m A + m B MWA B
=
1 MW 1 1 + c w − 1 m MWA A B
wA =
NA
MW N A + N B MWB A
=
1 MW 1 1 + c x − 1 m MWB A A
Volume Fraction (%vol): {i {i =
V i* V*
where V [ = / i V i[
/i { i = 1
Volume fraction is the volume of a constituent of a mixture prior to mixing `V i[ j divided by the sum of volumes of all constituents prior to mixing `V [ j . For mixtures of ideal gases:
φi = xi
For ideal solutions (no volume change due to mixing):
©2017 NCEES
t { i = wi t
i
30
Chapter 1: General Information Density and Average Molecular Weight (MW) of a Mixture: MW = / i xi MWi For ideal solutions (no change in volume due to mixing):
1 = / wi i ti t
For solutions of components with similar densities (assume volume of the solution is proportional to the mass): t = / i wi t i
1.3.1.2 Ratios or Loading Mole Ratio: Xi Ratios are used primarily for dilute solution or when one component is not affected by the process. For solutions with a solvent it is also called "solute-free basis" and for combustion gases "dry basis." Note: Component A is the basis (the solvent, the inert, or the predominant component). Ni xi N = = Xi N x A / i ! A Xi = N A − 1 X A = 1 A For binary systems (A: Solvent, B: Solute): x 1 = 1 − X B = 1 − Bx = 1 x A 1 B − 1 xB For dilute systems with xA→1:
xB =
1 1 1+ X B
1 xA = 1 + X
B
Xi→xi
Mass Ratio: Wi mi w = = w i Wi m A A
/ i ! A Wi = mmA − 1
WA = 1
For binary systems (A: Solvent, B: Solute): wB = 1 = w1 − 1 WB = 1 − w 1 − A B wB 1 For dilute systems with wA→1:
wB =
Wi→wi
Conversion Between Mole Ratio and Mass Ratio MW Wi = Xi MW i A
MW Xi = Wi MWA i
1.3.1.3 Concentrations Molar Concentration: ci or [i] N ci = V i For ideal gases:
©2017 NCEES
p ci = xi RT
31
1 1 1+W B
1 wA = 1 + W
B
Chapter 1: General Information Mass Concentration: γi = ci
mi = V wi t
Volume Concentration: φi V[ z i = Vi Volume fraction is the volume of a constituent of a mixture prior to mixing V i* divided by the volume of the mixture (V). For mixtures in which volume decreases on mixing:
/i V i* 2 Vmix
/i z i 2 1
Ideal solution (no volume change due to mixing): t z=i {=i wi t i
/i z i = 1
(ideal solutions only)
1.3.1.4 Molarity and Molality Molarity (M) moles of solute Molarity = Liters of solution Note that molarity is temperature-dependent. Molality (m) moles of solute Molality = kg of solvent Note that molality is temperature-independent.
©2017 NCEES
32
Chapter 1: General Information 1.3.1.5 Special Measures of Composition Normality (N) Normality =
equivalent grams of the solute liters of solution
Gram equivalent weight is a measure of the reactive capacity of a given molecule and thus is reaction-dependent. Note that normality is temperature-dependent. pH and pOH
pH =− log10 7H +A or pOH =− log10 7OH −A
pH =− log10 8H 3 O +B
and
pK = pH + pOH =− log10 K For water at 20cC : K = 10
−14
where and pK = 14
Note that all concentrations are in moles/liter. Proof (for Alcohol Content) = 2= Proof abv 200
ml of pure ethanol ml of solution
abv = alcohol % by volume (volume concentration) For Dilute Solution (Can Be Based on Mass, Molar, or Volume) ppm = parts per million = 10–6 ppb = parts per billion = 10–9 ppt = parts per trillion = 10–12 Percent: 1% = 10,000 ppm Permil: 1a = 1000 ppm
©2017 NCEES
33
K = 8H 3 O +B 7OH −A
©2017 NCEES
wi wA
xi MWA x A MWi
Mass Ration
xi MWi t MW
/ j x j MW j
MW x MW / j j ti j
Mass concentration gi =
Avg. MW MW =
Avg.* Density r=
ci =
Molar concentration
Wi =
Xi =
34
/ j!A X j
1 w
/ j t jj
/j
/ j ! AWj
wi c A
Wi c A MWi
Wj 1 + MWA / j ! A X j MW j
*Ideal solutions only
1 + / j!A X j
MWA + / j ! A X j MW j
1
Xi c A
Wi
MW Xi MW i A
1 + / j ! AWj
Wi
Wi MWi MWi + MWA / j ! A W j MW j
MW Wi MWA i
Xi MWi c A
wj MW j
Wi
Mass Ratio
Xi
Xi MWi + MWA / j ! A X j MW j
1+
Xi
Xi
Mole Ratio
wi t
wi t MWi
wi MWi w A MWA
xi xA
Mole Ratio
wi =
xi t MW
wi
xi MW / j x j MWij
Mass Fraction
xi =
MWi / j w j MW j
wi
wi
Mass Fraction
xi
Mole Fraction
xi
Mole Fraction
Multicomponent Systems
1.3.1.6 Conversion Table Between Different Measures of Concentration
ci MWi
ci
gi
ci MWi
ci cA
c i MWA c A MWi
ci cA ci MWi c A MWA
ci t
c i MW t MWi
Mass concentration gi
ci MWi t
ci MW t
ci
Molar concentration
Chapter 1: General Information
©2017 NCEES
35
Avg.* Density r=
Avg. MW MW =
cB = Mass concentration gB =
Molar concentration
WB =
wB t
x B MWB t MW
w B + _1 − w B i
tB
MW t X B + MWA t B B A
B
*Ideal solutions only
tB tA
MW t B d MW + X B n
MWA + X B MWB 1 + XB
X B c A MWB
XB cA
_1 + WB i t B tB WB + t A
1 + WB 1 + WB MWA MWB
wB c A
WB c A MWB
WB
MW WB MWA B
WB 1 + WB
WB MWB + MWA WB
WB
Mass Ratio
c B MWB
cB
c B MWB c A MWA
cB cA
c B MWB t
c B MW t
cB
Molar concentration
Note: For mole and mass ratios, "A" is the basis component (e.g., the solvent).
MW t B MW B MWA t B x B + _1 − x B i MW t A B
MWB MWB − + 1 x _ i x B MWB B MWA w + _1 − w i B MW B
wB t MWB
MW X B MWB A
wB 1 - wB
x B MWB 1 - x B MWA
Mass Ratio
XB =
xB t MW
XB
w B MWA 1 - w B MWB
wB = xB 1 - xB
XB MWA + MWB X B
XB 1 + XB
Mole Ratio
A
MW w B + _1 − w B i MWB A
wB
XB
Mole Ratio
wB
xB
xB
wB
Mass Fraction
MW x B + _1 − x B i MWA B
Mass Fraction
xB =
Mole Fraction
xB
Mole Fraction
Binary Systems
gB
cB MWB
cB cA
c B MWA c A MWB
cB t
c B MW t MWB
Mass concentration gB
Chapter 1: General Information
Chapter 1: General Information
1.3.2
Density Definitions
1.3.2.1 Density and Relative Density Density is m t=V Relative density is t RD = t ref where
tref = density of a reference material
1.3.2.2 Specific Gravity Specific Gravity (Relative Density) of Gas tgas SG = t air at ref temp, press The reference temperatures are commonly either 0°C or 60°F and the reference pressure is commonly 14.696 psia (101,325 Pa). For ideal gas: MWgas SG = MW = air
MWgas g 28.96 mol
Specific Gravity (Relative Density) of Liquid t SG = t H2 O at ref temp where
kg lbm = = t H 2 O, ref 62.4 1000 3 3 ft m
The reference temperatures are commonly either 4°C or 60°F. Specific Gravity (Relative Density) in Baumé
140 For liquids lighter than water, using degrees Baumé or B°: SG = 130 + Bc 145 For liquids heavier than water, using degrees Baumé or B°: SG = 145 − Bc Specific Gravity (Relative Density) for Hydrocarbon Liquid 141.5 SG60cF = 131.5 + API
141.5 − API = SG 131.5 60cF
where API = American Petroleum Institute gravity or API gravity
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Chapter 1: General Information Specific Gravity (Relative Density) for Slurries Bulk density and specific gravity of solids and liquid mixtures (slurries) are 1 1 1 1 tbulk = tliquid + \solids d tsolids − tliquid n 1 − 1 1 = 1 + e o SGbulk SGliquid \solids SGsolids SGliquid
1.4 Mathematics 1.4.1
Algebra
1.4.1.1 Linear Algebra Straight Line General form:
Ax+By+C=0
Standard form:
y=mx+b
Point-slope form:
y - y1 = m (x - x1) y − y1 y 2 − y1 = x − x1 x 2 − x1
Two-point form: Intercept form:
x + y − = x0 y0 1 0 , where intercepts x0 ≠ 0, y0 ≠ 0
y −y Slope: m = x 2 − x1 2 1 Angle between lines with slopes m1 and m2:
m − m1 o a = arctan e +2 1 m 2 m1
Distance between two points (two-dimensional space): d = ` y 2 − y1 j + _ x 2 − x1 i b −b m b −m b Intersection of two straight lines: xi = m2 − m1 yi = 1m2 − m 2 1 1 2 1 2 2
1.4.1.2 Polynomials Quadratic Equation Standard form:
a x2 + b x + c = 0
x2 + p x + q = 0 −b ! b2 − 4 a c 4ac −b Roots: x 1, 2 = 2a d1 ! 1 − 2 n = 2a b Normal form:
p x 1, 2 = 2 !
Vieta's Rule:
p = – (x1 + x2)
p2 − 4 q q = x1 x2
If (b2 – 4 a c) > 0, the roots are real and unequal. If (b2 – 4 a c) = 0, the roots are real and equal. If (b2 – 4 a c) < 0, the roots are imaginary and unequal. If (b2 – 4 a c) = n2 (perfect square), the roots are rational and unequal. ©2017 NCEES
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2
Chapter 1: General Information Expansion of General Algebraic Expressions (a ± b)2 = a2 ± 2 a b + b2 (a ± b)3 = a3 ± 3 a2 b + 3 a ∙ b2 ± b3 (a ± b)4 = a4 ± 4 a3 b + 6 a2 b2 ± 4 a b3 + b4 a2 – b2 = (a + b) (a – b) a3 + b3 = (a + b) (a2 – a b + b2) a3 – b3 = (a – b) (a2 + a b + b2) a4 + b4 = (a2 + b2) (a2 – b2) = (a2 + a b 2 + b2) (a2 – a b
2 + b2)
Quadratic Surface (Sphere) Standard form:
(x – h)2 + (y – k)2 + (z – m)2 = r2
d = _ x 2 − x1 i + ` y 2 − y1 j + _ z 2 − z1 i 2
Distance between two points in three-dimensional space:
1.4.1.3 Logarithms, Exponents, and Roots Logarithms General definition: logb(x) = c
where: x = bc
Natural logarithm: ln(x) = c
where: x = ec (base: e = 2.71828)
Base 10 logarithm: log(x) = c where: x = 10c (base: 10) To change from one base to another: log (x) logb (x) = loga (b) a log10 (x) = = 2.302585 log10 (x) ln (x) log 10 (e) ln (x) = = 0.4343 ln (x) log (x) ln (10) Identities: logb(1) = 0 logb(b) = 1 logb(bn) = n logb(xc) = c logb(x) 1 − log b c x c m = log b (x c) = − c log b (x) = c log b c 1x m 1 1 c c xi = = log log b_ b 8(x) B c log b (x)
log b (x y) = log b (x) + log b (y) logb d xy n = logb (x) − logb (y) ©2017 NCEES
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2
2
Chapter 1: General Information b n log b (x) = x n b
log b (x) n
1
= xn
Rules for Exponents and Radicals a0 = 1 a1 = a Identities: p an ± q an = (p ± q) an an am = an+m an = n − m a am (= a m) n (= a n) m a n m a
−n
n = 1n = c 1 m a a
an bn = (a b)n n an = c a m n b b 1
(a) n = n a n m n j = `= a (a) n a
m
m
nx
n am x = am
p ` n a j + q ` n a j = ( p + q) ` n a j
`m a j `n a j = n + m a n
ab = n a + n b
n a = n b
1
a c a mn = b b
n
1.4.1.4 Proportions c
Directly proportional (4th proportional): x\c
a
a:b=c:x bc x= a b
a c a+b c+x If b = x then: b = x
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and
a−b = c−x x b 39
and
a−b = c−x a+b c+x
x
Chapter 1: General Information Square proportional (3rd proportional):
90°
x \ b2 a:b=b:x
b
2
b x= a
a
x
Mean proportional: 90°
x\ b
x
a:x=x:b x = ab a
Inversely proportional: 1 x\ b Inversely square proportional: x\
1 b2
1.4.1.5 Complex Numbers Rectangular form: z = a + i b where
i = -1 a = real component b = imaginary component
Polar form: z = c+i = c _cos i + i sin i i = c e i i c = a2 + b2 − i = tan 1 c ba m a = c cos i b = c sin i Addition and Subtraction (in rectangular form): z1 ! z 2 = (a1 ! a 2) + i _b1 ! b 2 i Multiplication and Division (in polar form): z1 z 2 = _c1 c 2 i + _i1 + i 2 i z1 c1 − z 2 = d c 2 n + _i1 i 2 i
n z n = _ a + i b i = c n + ^n i h
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b
Chapter 1: General Information Complex Conjugate: z) = a − i b z z) = a 2 + b 2 Euler's Identity: e i i = cos i + i sin i − e i i = cos i − i sin i 1 cos i = 2 _e i i + e −i i i 1 sin i = 2 i _e i i − e −i i i
1.4.2
Geometry and Trigonometry
1.4.2.1 Circular Transcendental Functions Trigonometric functions are defined using a right triangle:
sin
r
y
θ x
y = arcsin c r m i= , arccsc d ry n i = arccos b rx l i= , arcsec c rx m i y = arctan c x m i= , arccot d xy n i Law of Sines a b c = = sin A sin B sin C
c
B
Law of Cosines
a
a2 = b2 + c2 – 2bc cos A b2 = a2 + c2 – 2ac cos B c2 = a2 + b2 – 2ab cos C
A b
Law of Tangents
1 a − b = tan 2 (A − B) 1 a+b tan 2 (A + B) 1 b − c = tan 2 (B − C) b + c tan 1 (B + C) 2 1 a − c = tan 2 (A − C) a + c tan 1 (A + C) 2
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C
Chapter 1: General Information
sec
θ
Trigonometric Functions in a Unit Circle
(0, 1)
cot θ tan θ
csc
θ
cos θ
θ
sin θ
(1,0)
Trigonometric Identities
sin (–θ) = –sin θ cos (–θ) = cos θ tan (–θ) = –tan θ r r cos i = sin ci + 2 m =− sin ci − 2 m
r r sin i = cos ci − 2 m =− cos ci + 2 m 1 sin i 1 sec i = cos i sin i tan i = cos i 1 cot i = tan i csc i =
sin 2 i + cos 2 i = 1 tan 2 i + 1 = sec 2 i cot 2 i + 1 = csc 2 i
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Chapter 1: General Information Double-Angle Formulas sin 2a = 2 sin a cos a cos 2a = cos 2 a − sin 2 a = 1 − 2 sin 2 a = 2 cos 2 a − 1 tan 2a =
2 tan a 1 − tan 2 a
cot 2 a − 1 cot 2a = 2 cot a Two-Angle Formulas sin (a + b) = sin a cos b + cos a sin b cos (a + b) = cos a cos b − sin a sin b tan (a + b) =
(tan a + tan b) (1 − tan a tan b)
cot (a + b) =
(cot a cot b − 1) (cot a + cot b)
sin (a − b) = sin a cos b − cos a sin b cos (a − b) = cos a cos b + sin a sin b tan (a − b) =
(tan a − tan b) (1 + tan a tan b)
cot (a − b) =
(cot a cot b + 1) (cot b − cot a)
Half-Angle Formulas
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a sin c 2 m = !
(1 − cos a) 2
a cos c 2 m = !
(1 + cos a) 2
a tan c 2 m = !
(1 − cos a) (1 + cos a)
a cot c 2 m = !
(1 + cos a) (1 − cos a)
43
Chapter 1: General Information Combination of the Trigonometric Functions of Different Angles 1 sin a sin b = 2 8cos (a − b) − cos (a + b)B 1 cos a cos b = 2 8cos (a − b) + cos (a + b)B 1 sin a cos b = 2 8sin (a + b) + sin (a − b)B 1 1 sin a + sin b = 2 sin
1 − cos 2i 2
1 1 cos i = cos 2 c 2 i m − sin 2 c 2 i m =
1 + cos 2i 2
1 2 tan c 2 i m
1 1 2 c 2 i m cos c 2 i m = tan i = 1 1 1 1 − tan 2 c 2 i m cos 2 c 2 i m − sin 2 c 2 i m tan i =
cot i =
cot i =
1 − cos 2i = sin 2i = 1 − cos 2i 1 + cos 2i 1 + cos 2i sin 2i 1 cot 2 c 2 i m − 1 1 2 cot c 2 i m
=
1 1 cos 2 c 2 i m − sin 2 c 2 i m 1 1 2 c 2 i m cos c 2 i m
1 + cos 2i = 1 + cos 2i = sin 2i 1 − cos 2i sin 2i 1 − cos 2i
1.4.2.2 Planar Geometry—Area and Perimeter A
= area
P
= perimeter (circumference)
a,b,c = lengths of sides d
= diagonal(s) or diameter
h = height
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Chapter 1: General Information Square A = a2
d
a
P=4a d=a 2 Rectangle A=ab
b
d
P = 2 (a + b) d = a2 + b2 a
Parallelogram A = a h = a b sin a
h P = 2 (a + b) = 2 c a + sin a m
h
d1 d2
b
d1 = (a + h cot a) 2 + h 2
α
d 2 = (a − h cot a) 2 + h 2 d12 + d 22 = 2 (a 2 + b 2)
a a
h
Trapezoid a+b A = 2 h = mh a+b m= 2
m b
Triangle (oblique) P = a+b+c 2a 2b 2c ri = c1 − P m c1 − P m c1 − P m 1 1 A = 2 a h = 2 r1 P 1 A = 2 P (P − 2a) (P − 2b) (P − 2c)
h
b
c
ri a
Triangle (equilateral)
h
a
P = 3a a2 3 1 = A = 4 2 a h a 3 h= 2
a
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Chapter 1: General Information Triangle (right) P = a+b+h 1 A = 2 ah b = a2 + h2
b
h
a
Regular Polygon (n equal sides) P = na nr a A= 2 z a = 2 r =tan c mG 2 2r z= n r (n − 2 ) i= n
φ
r
a θ
Circle = P 2= rr rd r d2 = A r= r2 4 d = 2r d
r
Annulus r r A = 4 (D 2 − d 2) = 4 (D + d ) (D − d ) = r b (b + d ) D−d b= 2
b d
D
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Chapter 1: General Information Sector of a Circle
s
2
r z sr A= 2 = 2 s = rz P = 2 r + s = r (2 + z )
φ r
Segment of a Circle
b
z b = 2 r sin c m 2 − s z = r = 2 arccos c r r d m r 2 (z − sin z) A= 2 d A = 6 d (3 d 2 + 4 b 2) d b2 r = 2 + 8h z z b d = r =1 − cos c mG = 2 tan c m 2 4 z P = s + b = r =z + 2 sin c mG 2
s A d
Ellipse Papprox = 2 r A = rab
φ
r
a2 + b2 2
y'
a
b
(h, k)
Parabola 2bh Ai = 3 bh Ao = 3
b
Ai h Ao
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x'
Chapter 1: General Information 1.4.2.3 Cubic Geometry—Volume and Surface Area A
= surface area
V
= volume
a,b,c = lengths of sides d
= diagonal(s) or diameter
h
= height
Cube V = a3 A = 6 a2 d=a 3
d
σ
a α
Cuboid V = abc A = 2 (a b + a c + b c) d = a2 + b2 + c2
c
d b a
Parallelepiped V = Abase h h A base
Pyramid A h V = base 3 h
A base
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Chapter 1: General Information Frustum of Pyramid
A2
h V = 3 _ A1 + A2 + A1 A2 i A +A V . h 1 2 2 for A1 . A2
h
A1
Right Circular Cylinder r V = 4 d2 h Amantle = 2 r r h A = 2 r r ( r + h)
r h
d
Hollow Cylinder r V = 4 h (D 2 − d 2)
h
d
D
Right Circular Cone r r V = 3 r 2 h = 12 d 2 h Amantle = r r m A = r r (r + m )
h
m = h2 + r2 A1: A2 = x 2: h 2
A2
x m
A1
r
Frustum of Cone r V = 12 h (D 2 + D d + d 2)
h
r Amantle = 2 m (D + d) = 2 r p m m=
d
− 2 h2 + c D 2 d m
p d
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m — 2 m
49
Chapter 1: General Information Sphere 4 3 1 3 = V 3= rr 6 rd = r r2 r d2 A 4=
Zone of a Sphere r V = 6 h (3 a 2 + 3 b 2 + h 2) Amantle = 2 r r h A = r (2 r h + a 2 + b 2)
a h
r
b
Segment of a Sphere (Spherical Cap) r 3 h V = 6 h c 4 s2 + h2 m = r h2 c r − 3 m r Acap = 2 r r h = 4 (s 2 + 4 h 2) Acap = 2 r r 2 (1 − cos i0) s = 2 h (2 r − h )
h
s
r
q0 is the angle of the cutout, rotated from the center of the radius. Sector of a Sphere 2 V = 3 r r2 h r A = 2 r (4 h + s )
r h s
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Chapter 1: General Information Sphere with Cylindrical Boring r V = 6 h3 A = 2 r h (R + r ) h = R2 − r2
h
R
r Sphere with Conical Boring 2 V = 3 r R2 h D A = 2 r h (R + 2 ) D = 2 R2 − h2
h
R
D
Torus r2 V = 4 D d2 A = r2 D d
d D
Sliced Cylinder r V = 4 d2 h
h
d Ungula 2 V = 3 r2 h Amantle = 2 r h h r A = r 2 >2 r + 2 e1 +
1+
h
h 2 oH r2
r
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Chapter 1: General Information Barrel r V . 12 h (2 D 2 + d 2) h
D
d
Prismoid h V = 6 (A1 + A2 + 4 A)
A2 h h/2 A
A1
Regular Polyhedra Name Tetrahedron
No. of Faces
4
Form of Faces Equilateral triangle
Cube
6
Square
Octahedron
8
Dodecahedron Icosahedron
Total Surface Area
Volume
2
6 a2
0.1179 a3 a3
Equilateral triangle
3.4641 a 2
0.4714 a3
12
Regular pentagon
20.6457 a 2
7.6631 a3
20
Equilateral Triangle
8.6603 a 2
2.1817 a3
1.7321 a
The radius of a sphere inscribed within a regular polyhedron is: 3V r= A Paraboloid of Revolution r V = 8 h d2
d
h
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Chapter 1: General Information
1.4.3
Calculus
1.4.3.1 Differentiation
dy = D= = l For any function y = f(x), the derivative x y dx y Dy yl = limit d n Dx " 0 Dx = limit * Dx " 0
8 f _ x + Dx i - f ^ x hB
^Dx h
4
where yl = the slope of the curve f ^ x h Test for a Maximum
y = f ^ x h is a maximum for x = a, if f l^a h = 0 and f m^a h 1 0
Test for Minimum
y = f ^ x h is a minimum for x = a, if f l^a h = 0 and f m^a h 2 0
Test for a Point of Inflection
y = f(x) has a point of inflection at x = a, if f m^a h = 0, and if f m^ x h changes sign as x increases through x = a
L'Hôpital's Rule If the fractional function limit x"a
f^ xh g^ xh
f^ xh 3 0 assumes one of the indeterminate forms 0 or 3 (where a is finite or infinite), then: g^ xh
is equal to the first of the expressions limit x"a
f l^ x h g l^ x h
limit x"a
f m^ x h g m^ x h
limit x"a
f n^ x h g n^ x h
which is not indeterminate, provided such first indicated limit exists. Curvature K of a Function The curvature K of a curve at point P is the limit of its average curvature for the arc PQ as Q approaches P. This is also expressed as:
y = f (x) Q
Y Δs
The curvature of a curve at a given point is the rate of change of its inclination with respect to its arc length.
P
Da da = = K lim it ds Ds " 0 Ds α O
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=Δ α
α + Δα X
Chapter 1: General Information Curvature in Rectangular Coordinates ym K= 3 91 + _ yli2C2
When it may be easier to differentiate the function with respect to y rather than x, the notation xl will be used for the derivative. dx xl = dy − xm K= 3 81 + ^ xlh2B2 Radius of Curvature The radius of curvature R at any point on a curve is defined as the absolute value of the reciprocal of the curvature K at that point. R=
_ K ! 0i
1 K 3
2 2 R = 91 + _ yli C ym
_ ym ! 0i
List of Derivatives u, v, and w represent functions of x. a, c, and n represent constants. Arguments of trigonometric functions are in radians. The following definitions are used: arcsin u = sin-1 (u),
− ^sin uh 1 = 1 sin u
dc 1. dx = 0 dx 2. dx = 1
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3.
d ^cu h = c du dx dx
4.
d _u + v − w i du dv dw = + − dx dx dx dx
5.
d ^uv h = u dv + v du dx dx dx
6.
d ^uvw h = u v dw + u w dv + v w du dx dx dx dx
7.
d c uv m
8.
d _u n i = n u n − 1 du dx dx
du dv v dx − u dx = dx v2
54
Chapter 1: General Information
9.
d 7 f ^u hA 7 f ^u hA du = )d 3 dx dx du
du 1 10. dx = dx c m du 11. 12. 13. 14. 15.
d _loga u i = _loga e i 1u du dx dx
d ^ln u h 1 du =u dx dx
d _a u i = ^ln a h a u du dx dx d _e u i = e u du dx dx
d _u v i = vu v − 1 du + ^ln u h u v dv dx dx dx
16.
d ^sin u h = cos u du dx dx
17.
d ^cos u h = − sin u du dx dx
18.
d ^tan u h = sec 2 u du dx dx
19.
d ^cot u h = − csc 2 u du dx dx
20.
d ^sec u h = sec u tan u du dx dx
21.
d ^csc u h = − csc u cot u du dx dx
d _sin −1 u i 1 du = 2 dx dx 1−u d _cos −1 u i du =− 1 23. dx 1 − u 2 dx 22.
24. 25.
d _ tan −1 u i = 1 2 du dx 1 + u dx d _cot −1 u i = − 1 2 du dx 1 + u dx
d _sec −1 u i 1 du = 2 dx u u − 1 dx d _csc −1 u i 1 du =− 27. dx u u 2 − 1 dx 26.
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c - r # sin -1 u # r m 2 2
_0 # cos -1 u # r i c - r 1 tan -1 u 1 r m 2 2
_0 1 cot -1 u 1 r i c 0 1 sec -1 u # r m and c - r # sec -1 u - r m 2 2 c 0 1 csc -1 u # r m and c - r 1 csc -1 u # - r m 2 2
55
Chapter 1: General Information Parametric Form of the Derivative dy dy dt yo = hi = yl_ x ^ t = dx dt dx xo y m_ x ^ t hi =
d2y xo yp − yo xp 2 = xp ^dxh
where dy yo = dt d2y yp = 2 dt Derivative of Inverse Functions
The equation y = f(x) solved for x gives the inverse function x = { _ y i . f l^ x h =
1.4.3.2 Integration
1 {l _ y i
The indefinite integral F(x) is a function such that F l] xg = f ] xg .
#
f ^ x h dx = F ^ x h + C
C is an unknown constant which disappears on differentiation. The definite integral: n
limit n"3
/ f_ xiiDxi = #a
i=1
b
f ^ x h dx = F (x) ba = F ^b h − F ^a h
Also, Dxi " 0 for all i. To find the integral: Use the list of indefinite integrals (below), integration by parts (equation #6 in the list), integration by substitution, and separation of rational fractions into partial fractions. List of Indefinite Integrals u, v, and w represent functions of x. a, c, and n represent constants. Arguments of trigonometric functions are in radians. The following definitions are used: − arc sin u = sin 1 ^u h,
− ^sin u h 1 = 1 sin u
Note: A constant of integration should be added to the integrals. 1. 2. 3. 4.
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# d f^ xh = f^ xh # dx = x # a f^ xhdx = a # f^ xhdx # 7u^ xh ! v^ xhAdx = # u^ xhdx ! # v^ xhdx 56
Chapter 1: General Information m+1
_m ! - 1 i
5.
# xm dx = mx + 1
6.
# u^ xhdv^ xh = u^ xhv^ xh - # v^ xhdu^ xh
7. 8.
# #
dx = 1 ln + ax + b a ax b dx 2 x x
11. 12.
# sin2 x dx = 2x - sin42x
13.
# cos2 x dx = 2x + sin42x
14.
# x sin x dx = sin x - x cos x
15.
# x cos x dx = cos x + x sin x
16.
# sin x
17.
# sin a x
10.
#
dx = x ln x
x
# a x dx = lna a # sin x dx = - cos x # cos x dx = sin x
9.
for a = 1 and b = 0:
cos x dx =
sin 2 x 2
cos b x dx = -
cos _a − b i x cos _a + b i x 2_a − b i 2_a + b i
_a 2 ! b 2 i
#
18. = tan x dx -= ln cos x ln sec x
#
19. = cot x dx -= ln csc x ln sin x 20. 21. 22. 23. 24. 25. 26.
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# tan2 x dx = tan x - x # cot2 x dx = - cot x − x # eax dx = c 1a meax # xeax dx = e ea2 o^ax - 1h ax
# ln x dx = x8ln ^ xh − 1B ^ x 2 0h # a2dx+ x2 = 1a tan−1 ax _a ! 0i = # axdx 2 +c
1 − tan 1 c x ac
a m _a 2 0, c 2 0 i c
57
Chapter 1: General Information
27a.
# ax2 +dxbx + c =
+ − 2 tan 1 2ax b 2 2 4ac − b 4ac − b
_4ac - b 2 2 0 i
27b.
# ax2 +dxbx + c =
2ax + b - b 2 - 4ac 1 ln 2ax + b + b 2 - 4ac b 2 − 4ac
_b 2 - 4ac 2 0 i
27c. #
dx = - 2+ _b 2 - 4ac = 0 i 2ax b ax 2 + bx + c
1.4.3.3 Multivariable Calculus Partial Derivatives In a function of two independent variables x and y, a derivative with respect to one of the variables may be found if the other variable is assumed to remain constant. If y is kept fixed, the function z = f _ x, y i becomes a function of the single variable x, and its derivative (if it exists) can be found. This derivative is called the partial derivative of z with respect to x. The partial derivative with respect to x is denoted as follows: 2z = 2f (x, y) 2x 2x Total Derivative Given f(x,y), then the total derivative df is 2f 2f df = d n dx + e o dy 2x y 2y x Chain Rule
Given f _ x, y i where x = g ^ t h and y = h ^ t h , then df 2f 2f dy = d n dx + e o dt 2x y dt 2y x dt Identities in Partial Derivatives c 2x m = 1 2x z c 2x m = 0 2z x
Implicit Differentiation
If f (x,y,z) cannot be converted to an explicit expression in the form of z = f )_ x, y i , then 2f 2f −e o n 2y x, z 2 x y, z c 2z m = d 2z n = and 2y x 2x y 2f 2f d n d n 2z x, y 2z x, y −d
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Chapter 1: General Information Rules for changing the constant or the variable on a partial derivative: Given f (x,y,z) = constant, then d
2f 2f 2f 2y n = d n +e o d n 2x z 2x y 2y x 2x z
d
2f 2f 2y n =e o d n 2z x 2y x 2z x
1.4.3.4 Differential Equations A common class of ordinary linear differential equations is dy ^ x h d n y^ xh + ... + b1 + b 0 y^ xh = f^ xh bn dx dx n where bn, ... , bi, ... , b1, b0 are constants. When the equation is a homogeneous differential equation, f(x) = 0, the solution is y h ^ x h = C1 e r1 x + C 2 e r2 x + . . . + C i e ri x + C n e rn x where rn is the nth distinct root of the characteristic polynomial P(x) with P ^rh = b n r n + b n − 1 r n
−1
+ b1 r + b 0
If the root r1 = r2, then C 2 e r2 x is replaced with C 2 xe r1 x . Higher orders of multiplicity imply higher powers of x. The complete solution for the differential equation is y(x) = yh(x) + yp(x) where yp(x) is any particular solution with f(x) present. If f(x) has e rnx terms, then resonance is manifested. Furthermore, specific f(x) forms result in specific yp(x) forms, some of which are f(x) A
yp(x) B
Aeax
Beax, a ! rn
A1 sin ~x + A2 cos ~x
B1 sin ~x + B2 cos ~x
Common First-Order Differential Equations and Their Solutions Form
Solution
Linear, homogeneous ODE with constant coefficients yl + a y = 0 Linear, homogeneous ODE yl + p ^ x h
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y=0
−ax
C is a constant that satisfies the initial condition.
− # p(x)dx)
C is a constant that satisfies the initial condition.
y (x) = C e
y (x) = C e(
59
Substitution/Conditions
Chapter 1: General Information Common First-Order Differential Equations and Their Solutions (cont'd) Form
Solution
Substitution/Conditions
At 1 01 y (t) = KA + (KB − KA) a1 = − e− x k p (t) '= y (0) K A Bt20 = = x time constan t, K gain t KB − KA x = ln e KB − y o t
Linear, inhomogeneous ODE with constant coefficients x yl + y = K p (t)
Comment: Solution is for a step function.
x = f _ yli
Substitution: yl = p
x = f (p) y = # p f (p) dp + C
Implicit ODE, no y term
Comment: Elimination of p leads to a solution in parametric form. f (p) p dp + C y = f (p)
x= #
Implicit ODE, no x term y = f _ yli
yl = p
Comment: Elimination of p leads to a solution in parametric form.
Separable ODE dy f^ xh = = yl dx g_ yi
Similarity ODE y yl = f c x m
# g_ y idy = #
f ^ x h dx + C
Comment: The variables x and y can be separated into the left and right sides of the equation. y Substitution: u = x dx = du + C du x ^ u f h− u yl = u + x dx
#
#
y Comment: Check whether it is possible to transform to f c m . x
Common Second-Order Differential Equations and Their Solutions Form
ODE, y and y' terms missing ym = f^ xh ODE, y term missing y m + p1 ^ x h f _ yli = 0 ODE, x term missing y m = f (y, yl )
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Solution
y (x) = C1 + C2 x +
# ;#
Substitution
f ^ x h dxE dx
Comment: Start the calculation with the inner integral.
#
du = − f ^u h y=
#
p1 ^ x h dx + C1
# udx + C2
du u dy = f _ y, u i dy +C x= # u_ yi
60
Substitution: u = y' du = = y m dx f _ yli f ^u h Substitution: u = yl du = = u du = f (y, u) y m dx dy dy Then substitute yl = dx for u. = where u u= (y) and y y (x)
Chapter 1: General Information Common Second-Order Differential Equations and Their Solutions Form
Solution
Substitution
Solution depends on the values of a and b.
1 r1, 2 = 2 `− a ! a 2 − 4b j
y (x) = C1 e r1x + C2 e r2x
a 2 2 4b (overdamped)
y (x) = (C1 + C2 x) e r 1x
a 2 = 4b (critically damped)
y (x) = ea x [C1 cos (b x) + C2 sin (b x)] 1 1 a =− 2a b = 2 4b − a 2
a 2 1 4b (underdamped)
Linear, homogeneous ODE with constant coefficients y m + a yl + b y = 0
1.4.3.5 The Fourier Transform and Its Inverse X_ f i =
#− 3+ 3 x^t he −j2rft dt +3 x ^t h = # X _ f i e j2rft df −3
We say that x(t) and X(f) form a Fourier transform pair: x^ t h * X_ f i Fourier Transform Pairs x(t)
Fourier Transform Pairs X(f)
d_ f i
1 d^ t h
1
u^ t h
1 _ f i+ 1 2d j 2r f
P c xt m
x sinc _xf i
sinc ^ Bt h
1 dfn BP B
K c xt m
x sinc 2 _xf i
e at u ^ t h
1 a + j2rf
te at u ^ t h
2a 2 a 2 + _2rf i
-
-
e e
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2a 2 a 2 + _2rf i
-a t
a20 a20 a20 2
r - c rf m a e a
-^at h2
61
Chapter 1: General Information Fourier Transform Pairs (cont'd) X(f) 1 9 ji ` f − f j + −ji ` f + f jC cos `2rf0t + i j e d 0 0 2 e d x(t)
1 9 ji ` − j − −ji ` + jC 2j e d f f0 e d f f0
sin `2rf0t + i j n =+ 3
/ d_t − nTsi
fs
n =− 3
k =+ 3
/ d` f − kfsj
k =− 3
1 fs = T s
Fourier Transform Theorems
Fourier Transform Theorems Linearity
aX _ f i + bY _ f i
Scale change
x ^at h
1 cfm X a a
Time reversal
x_- t i
X`- f j
Duality Time shift Frequency shift Modulation Multiplication Convolution Differentiation Integration
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ax ^ t h + by ^ t h
x`- f j
X^ t h
x _t - t0 j
x^ t he
X_ f ie
-j2rft
0
X ` f - f0 j
-j2rf t 0
x ^ t h cos 2rf0t
1 ` f − f j+ 1 ` f + f j 0 0 2X 2X
x^ t h * y^ t h
X_ f i : Y_ f i
X_ f i * Y_ f i
x^ t h : y^ t h dn x^ t h dt n
_ j2rf i X _ f i
#- 3t x (m) d m
1 _ f i + 1 X ^0 h d _ f i 2 j2rf X
n
62
Chapter 1: General Information 1.4.3.6 Laplace Transforms The unilateral Laplace transform pair: F^ s h =
#0 3 f^ t he−st dt
1 f ^ t h = 2rj where
v + j3
#v − j3
F ^ s h e st ds
s = s + jw
represents a powerful tool for the transient and frequency response of linear time invariant systems. Some useful Laplace transform pairs are
Laplace Transform Pairs f(t) d(t), Impulse at t = 0
F(s) 1
u(t), Step at t = 0
1 s
t[u(t)], Ramp at t = 0
1 s2
e
te
e
_ s + ai
1 2 _ s + ai
-at
- at
sin bt
- at
cos bt
e
1
-at
b
9_ s + a i2 + b 2C _ s + ai
9_ s + a i2 + b 2C
d n f ^t h dt n
sn F^ s h −
/ sn − m − 1 d dtf ^m0 h
n−1
m
m=0
#0 t f^x hdx
c 1 mF^ s h s
#0 t x_t - xih^x hdx
H^ s hX^ s h
f _t - x i u _t - x i
e
lim it t " 3 f^ t h
- xs
F^ s h
limit ^ h s " 0 sF s
limit ^ h t"0 f t
limit s " 3 sF ^ s h
The last two transforms represent the Final Value Theorem (F.V.T.) and Initial Value Theorem (I.V.T.), respectively. It is assumed that the limits exist.
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63
Chapter 1: General Information
1.4.4
Statistics and Probability
1.4.4.1 Mean, Median, and Mode If X1, X2, ... , Xn represents the values of a discrete random sample of n items or observations, the arithmetic mean of these items or observations, denoted X , is defined as X = c 1n m_ X1 + X 2 + ... + X n j = c 1n m
n
/X
i
i−1
X " n for sufficiently large values of n. The weighted arithmetic mean is /w X X w = /wi i i where Xi = the value of the ith observation and wi = the weight applied to Xi. The variance of the population is the arithmetic mean of the squared deviations from the population mean. If m is the arithmetic mean of a discrete population of size N, the population variance is defined by 2 2 2 1 v 2 = c N m:_ X1 − n i + _ X2 − n i + ... + ` XN − n j D
=c1 m N
N
/ _ Xi − nj
2
i=1
Standard deviation formulas are
c 1 m / _ Xi − n j N
2
spopulation = ssum =
v12 + v 22 + ... + v 2n
sseries = v n smean = sproduct =
v n
A 2 v 2b + B 2 va2
The sample variance is
s2
==
1 G _n − 1 i
n
/_X − X j
2
i
i=1
The sample standard deviation is =
n
2 c 1− m / _ Xi − X j n 1 = i 1
The sample coefficient of variation is CV = The sample geometric mean is
n
s X
X1 X 2 X3 ...X n
The sample root-mean-square value is
c 1 m /Xi2 n
+ th When the discrete data are rearranged in increasing order and n is odd, the median is the value of the c n 1 m 2 item. th n th n When n is even, the median is the avarage of the c 2 m and c 2 + 1 m items.
The mode of a set of data is the value that occurs with greatest frequency. The sample range R is the largest sample value minus the smallest sample value. ©2017 NCEES
64
Chapter 1: General Information 1.4.4.2 Permutations and Combinations A permutation is a particular sequence of a given set of objects. A combination is the set itself without reference to order. The number of different permutations of n distinct objects taken r at a time is: P _ n, r i =
n!
_n − r i!
An alternative notation for P(n,r) is nPr. The number of different combinations of n distinct objects taken r at a time is: P _ n, r i n! C _n, r i = r! = 8r! _ n − r i !B nCr and b nr l are alternative notations for C(n,r).
The number of different permutations of n objects taken n at a time, given that ni are of type i, where i= 1, 2, ..., k and /ni = n, is n! P _n; n1, n2, ..., nk i = n !n !...n ! 1 2 k
1.4.4.3 Probabilities Property 1. General Character of Probability The probability P(E) of an event E is a real number in the range of 0 to 1. The probability of an impossible event is 0 and that of an event certain to occur is 1. Property 2. Law of Total Probability where
P ^ A + B h = P ^ Ah + P ^ Bh − P _ A, B i
P(A+B) = the probability that either A or B occurs alone or that both occur together
P(A)
= the probability that A occurs
P(B)
= the probability that B occurs
P(A,B) = the probability that both A and B occur simultaneously Property 3. Law of Compound or Joint Probability If neither P(A) nor P(B) is zero, then P(A, B) = P(A) P(B | A) = P(B) P(A | B) where P(B | A) = the probability that B occurs given the fact that A has occurred P(A | B) = the probability that A occurs given the fact that B has occurred If either P(A) or P(B) is zero, then P(A, B) = 0.
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65
Chapter 1: General Information Bayes' Theorem: P` B j j P` A | B j j
P` B j | Aj =
n
/ P _ A | Bi i P _ Bi i
i=1
P(Aj ) is the probability of event Aj within the population of A
where
P(Bj ) is the probability of event Bj within the population of B
1.4.4.4 Distributions and Expected Values A random variable X has a probability associated with each of its possible values. The probability is termed a discrete probability if X can assume only discrete values, or X = x1, x2, x3, ..., xn The discrete probability of any single event X = xi occurring is defined as P(xi) while the probability mass function of the random variable X is defined by f _ xk i = P _ X = xk j,
k = 1, 2, ..., n
Probability Density Function If X is continuous, the probability density function, f, is defined such that P ^a # X # b h =
b
#
a
f ^ x h dx
See the table of probability and density functions. Cumulative Distribution Function The cumulative distribution function, F, of a discrete random variable, X, that has a probability distribution described by P(xi) is defined as m
= F _ xm i
= / P _ xk i
k=1
P _ X # xm i,
m = 1, 2, ..., n
If X is continous, the cumulative distribution function F is defined by F^ xh =
x
#
−3
f ^ t h dt
which implies that F(a) is the probability that X # a . Expected Values Let X be a discrete random variable having probability mass function: f _ xk i, k = 1, 2, ..., n The expected value of X is defined as = 6X @ n E=
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/ xk f ^ xk h n
k=1
66
Chapter 1: General Information The variance of X is defined as v2 = V6X @ =
n
/ _ xk − nj2 f_ xk i
k=1
Let X be a continuous random variable having a density function f(X) and let Y = g(X) be some general function. The expected value of Y is E 6Y @ = E 7g ^ X hA =
3
#
−3
g ^ x h f ^ x h dx
The mean or expected value of the random variable X is now defined as n = E6X @ =
3
#
−3
xf ^ x h dx
while the variance is v 2 = V 6 X @ = E :_ X − n i D =
3
2
#
−3
_ x − n i f ^ x h dx 2
The standard deviation is v = V 6 X @ .
v The coefficient of variation is defined as n . Combinations of Random Variables Y = a1 X1 + a2 X2 + ... + an Xn
The expected value of Y is n y = E ^Y h = a1 E _ X1 i + a2 E _ X2 i + ... + an E _ Xn i . If the random variables are statistically independent, then the variance of Y is v 2y = V ^Y h = a12 V _ X1 i + a 22 V _ X2 i + ... + a n2 V _ Xn i = a12 v12 + a 22 v 22 + ... + a n2 v 2n
Also, the standard deviation of Y is v y = v 2y . When Y = f(X1,X2,...,Xn) and Xi are independent, the standard deviation of Y is expressed as vy =
e
2
2
2
2f 2f 2f o +e o + ... + e o 2X1 vx1 2X2 vx2 2Xn vxn
Normal Distribution (Gaussian Distribution) This is a unimodal distribution, the mode being x = µ, with two points of inflection (each located at a distance σ to either side of the mode). The averages of n observations tend to become normally distributed as n increases. The variate x is said to be normally distributed if its density function f (x) is given by an expression of the form f^ xh =
2
x−n n 1 −1d e 2 v v 2r
where µ = the population mean σ = the standard deviation of the population -3 # x # 3
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67
Chapter 1: General Information When µ = 0 and σ2 = σ = 1, the distribution is called a standardized or unit normal distribution. Then f^ xh =
where
1 −x 2 /2 e 2r -3 # x # 3
It is noted that Z =
x- n v follows a standardized normal distribution function.
A unit normal distribution table is included at the end of this section. In the table, the following notations are used: F(x) = the area under the curve from –∞ to x R(x) = the area under the curve from x to ∞ W(x) = the area under the curve between –x and x F(-x) = 1 - F(x)
1.4.4.5 Confidence Intervals Confidence Interval for the Mean n of a Normal Distribution When standard deviation v is known: v v # n # X + Za/2 n n When standard deviation v is not known: X - Za/2
s s # n # X + ta/2 n n where ta/2 corresponds to n - 1 degrees of freedom. X - ta/2
Confidence Interval for the Difference Between Two Means m1 and m2 When standard deviations s1 and s2 are known: X1 - X 2 - Za/2
v12 v 22 n1 + n 2 # n1 - n 2 # X1 - X 2 + Za/2
v12 v 22 n1 + n 2
When standard deviations s1 and s2 are not known: X1 - X 2 - ta/2
c n1 + n1 m8_n1 - 1 i s12 + ^n2 - 1h s 22B 1 2 # n1 - n 2 # n1 + n 2 - 2
X1 - X 2 + ta/2
c n1 + n1 m8_n1 - 1 i s12 + ^n2 - 1h s 22B 1 2 n1 + n 2 − 2
where ta/2 corresponds to n1 + n2 - 2 degrees of freedom. Confidence Intervals for the Variance v2 of a Normal Distribution
^n - 1 h s 2 ^n - 1 h s 2 2 # v # xa2/2, n - 1 x12- a/2, n - 1 Sample Size z=
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X-n v n
2
vz n = e −a/2 o xr n
68
Chapter 1: General Information The Central Limit Theorem Let X1, X2,...,Xn be a sequence of independent and identically distributed random variables having mean m and variance s2.Then for a large n, the Central Limit Theorem asserts that the sum Y = X1 + X2 + ... + Xn is approximately normal n yr = n and the standard deviation is v yr =
Kind of Distribution
General (continuous)
General (discrete)
Uniform
v . n
Probability and Density Functions Form of the Density Expected Mean (m), Probability Density Function f(x) Function Mean (x), Variance (s2) Distribution Function F(x) Comment: General distribution for continuous values f (x) F (x) =
#− 33 x f (x) dx 3 v 2 = # x 2 f (x) dx − n 2 −3 x=
#− 3 f (t) dt x
Comment: General distribution for discrete values: n is the number in a random sample, xi is the discrete value of the random variable, and Pi is the probability. Pi F (x) =
/in= 1 (xi Pi) n v 2 = / i = 1 (xi2 Pi − n 2) x=
/i < x Pi
Comment: Random variable x = 0 only within the interval
, where each value is of equal probability. Use when only maximum and minimum values are known but no other information about the distribution in between. Z] 1 f(x) ]] for a # x # b f (x) = [] b − a ]] 0 a+b for outside x= 2 \]Z 1 ]] 0 for − 3 1 x 1 a 2 b-a ]] − _ i − b a v 2 = 12 F (x) = ][ x − a for a # x # b ]] b a o ]] 1 for b 1 x 1 3 a μ b x \ Comment: If P(k) is the probability that in n random samples exactly k errors will occur, the error probability is p. Lot size is assumed to be 3. P(k)
Binomial
n−k n P (k) = c k m p k `1 − p j
F (x) =
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0.3
x=np v 2 = n p (1 − p)
/ nx pk `1 − pjn − k
k
0.2 0.1 0
69
n = 20 p = 0.1 p = 0.2 p = 0.5
5
10
15 k
Chapter 1: General Information Probability and Density Functions (cont'd) Kind of Distribution
Probability Density Function f(x) Distribution Function F(x)
Form of the Density Function
Expected Mean (m), Mean (x), Variance (s2)
Comment: Often obtained in practice as measured values with a bell-shaped distribution occurring around a mean value. Special case of the binomial distribution with n " 3 and p = 0.5. f(x)
Normal (Gaussian)
f (x) = F (x) =
2
1 exp >− 1 d x − n n H 2 v v 2r
σ = 0.5
μ =0
m
0.5
σ =1 σ =2
v2
2
#− 3x v 12r exp >− 12 d t −vn n Hdt
–2 –1
0
1
2
x
Comment: Special case of the Normal (Gaussian) distribution. A unit normal table is included below. Standardized (unit normal)
2 1 exp d − x n 2 2r 2 x 1 exp d − t n dt F (x) = 2 − 3 2r
f (x) =
n=0 v2 = 1
#
---
Comment: Sample of dichotomous population (population of two types, e.g., defective/ not defective parts) without replacement. N is lot size, pN is number of defective parts in the lot, P is the probability that in n random samples k will be defective.
Hypergeometric
pN N (1 − p) G n= k n−k P (k) = cNm n pN N (1 − p) G d n= k n−k = F (x) k#x cNm n d
/
0.4
x=np
N−n v 2 = n p N − 1 (1 − p)
P(k)
p = 0.04 p = 0.1
0.3
p = 0.2
0.2
N = 100 n = 20
0.1 0
5
10
15
k
Comment: P(k) is the probability that in n random samples k errors will occur. Used for curves in a random sampling valuation. Conditions: large value of random samples with a small value for proportion defective. P(k)
Poisson
(n p) k −n $ p k! e (n p) k −n $ p F (x) = k! e k#x
0.3
P (k) =
x=np v2 = n p
/
70
n.p = 5 n.p = 10
0.2 0.1 0
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n.p = 1
5
10
15
k
Chapter 1: General Information Probability and Density Functions (cont'd) Kind of Distribution
Probability Density Function f(x) Distribution Function F(x)
Form of the Density Function
Expected Mean (m), Mean (x), Variance (s2)
Comment: Special case of the Poisson distribution for x = 0 that gives the probability without error. When used for reliability calculations, replace ^a $ xh with failure rate r multiplied by control time t. 2
Exponential
1 x=a
−
f (x) = a e a x a20 x$0 − F (x) = 1 − e a x
v2 =
1 a2
f(x) a =2 a =1
1
a = 0.5
0.5 0
0.5
1
2 x
Comment: Describes the number of trials needed to get the first success, with p as the success parameter. Geometric
f (x, p) = p (1 − p) x
−1
1 n= p 1−p v2 = 2 p
x
F (x) =
/ p ( 1 − p) n − 1
n=1
---
Comment: Describes the trial number of the kth success, with k as the stopping parameter and p as the success probability. Negative Binomial
− − P (k) = c n − 1 m p k (1 − p) n k k 1 F (x) =
1 x=k p
x
/ c nk −− 11 m pk (1 − p) n − k
k
v2 = k
`1 − p j
---
p2
Comment: Gamma distribution is widely used to model physical quantities that take positive values. The Gamma function is defined as C (k) = Gamma
1 − − x k 1 e x/b b k C (k) x C c k, b m where k > 0 F (x) = b>0 C (k) f (x) =
#0 3 xk − 1 e−x dx where k $ 0, x $ 0 x = bk v2 = b2 k
---
Comment: Note that when k = 1, the Weibull distribution reduces to the exponential distribution with parameter 1. Weibull
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f (t) =
1 x = b C c1 + k m
k
k k − 1 −c bt m t e bk
2 v 2 = b 2
k
− F (t) = 1 − e c b m where 0 < t < 3 t
1 2 C 2 c1 + k m G
71
---
Chapter 1: General Information Probability and Density Functions (cont'd) Kind of Distribution
Triangular
Probability Density Function f(x) Distribution Function F(x)
Expected Mean (m), Mean (x), Variance (s2)
Form of the Density Function
Comment: The triangular distribution is based on a simple geometric shape. The distribution arises naturally when uniformly distributed random variables are transformed in various ways. ]]Z 2 ]] a # x # a + p~ (x − a) , ] p ~2 f (x) = [] ]] 2 a + p~ # x # a + w ]] p ~ 2 (a + ~ − x) , \ ~ x = a + 3 (1 + p) ]]Z 1 2 ]] a # x # a + p~ (x − a) 2 , 2 ] p ~2 = ~ [1 − p (1 − p)] v = [ 18 F (x) ] 1 ]] − 2 ]]1 ~ 2 (1 − p) (a + ~ − x) , a + p~ # x # a + w \ Comment: The semicircular distribution is based on the shape of a semicircle with center a (location parameter) and radius r (scale parameter). 2 r 2 − (x − a ) 2 r r2 x=a 1 x−a 2− − 2+ F (x) = 2 + r (x a ) 2 rr r2 v2 = 4 1 x−a r arcsin c r m where a − r # x # a + r Comment: f(x) is symmetric about m. f (x) =
Semicircle
U-Power Distribution
f (x) =
2k
2k + 1 d x − n n 2c c
x=n
2k + 1 1 F (x) = 2 >1 + d x − n n H c
2k + 1 v = c 2k + 3 2
where n − c # x # n − c
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72
2
---
Chapter 1: General Information Normal Distribution Table
©2017 NCEES
x
f(x)
F(x)
R(x)
2 R(x)
W(x)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0.3989 0.3970 0.3910 0.3814 0.3683 0.3521 0.3332 0.3123 0.2897 0.2661 0.2420 0.2179 0.1942 0.1714 0.1497 0.1295 0.1109 0.0940 0.0790 0.0656 0.0540 0.0440 0.0355 0.0283 0.0224 0.0175 0.0136 0.0104 0.0079 0.0060 0.0044
0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.9987
0.5000 0.4602 0.4207 0.3821 0.3446 0.3085 0.2743 0.2420 0.2119 0.1841 0.1587 0.1357 0.1151 0.0968 0.0808 0.0668 0.0548 0.0446 0.0359 0.0287 0.0228 0.0179 0.0139 0.0107 0.0082 0.0062 0.0047 0.0035 0.0026 0.0019 0.0013
1.0000 0.9203 0.8415 0.7642 0.6892 0.6171 0.5485 0.4839 0.4237 0.3681 0.3173 0.2713 0.2301 0.1936 0.1615 0.1336 0.1096 0.0891 0.0719 0.0574 0.0455 0.0357 0.0278 0.0214 0.0164 0.0124 0.0093 0.0069 0.0051 0.0037 0.0027
0.0000 0.0797 0.1585 0.2358 0.3108 0.3829 0.4515 0.5161 0.5763 0.6319 0.6827 0.7287 0.7699 0.8064 0.8385 0.8664 0.8904 0.9109 0.9281 0.9426 0.9545 0.9643 0.9722 0.9786 0.9836 0.9876 0.9907 0.9931 0.9949 0.9963 0.9973
73
Chapter 1: General Information Normal Distribution Table (cont'd) x
f(x)
F(x)
1.2816 1.6449 1.9600 2.0537 2.3263 2.5758
0.1755 0.1031 0.0584 0.0484 0.0267 0.0145
0.9000 0.9500 0.9750 0.9800 0.9900 0.9950
R(x) Fractiles
0.1000 0.0500 0.0250 0.0200 0.0100 0.0050
1.4.4.6 Linear Regression and Goodness of Fit Least Squares t y = at + bx where tr y-intercept = at = yr - bx Sxy slope = bt = S xx Sxy = Sxx =
where
n
n
/ xi yi − c 1n mf / xi pf / yi p n
i=1
i=1
n
n
i−1
2
/ xi2 − c 1n mf / xi p i=1
i=1
n
yr = c 1n mf
i=1
/ yi p
xr = c 1n mf
/ xi p
n
i=1
n = sample size Sxx = sum of squares of x Syy = sum of squares of y Sxy = sum of x-y products 2 Standard Error Estimate S e
where
2 2 SxxSyy − S xy = Se = MSE Sxx _ n − 2 i
S yy =
©2017 NCEES
n
/
i=1
yi2
n
2
− c 1 mf yi p n i=1
/
74
2 R(x)
W(x)
0.2000 0.1000 0.0500 0.0400 0.0200 0.0100
0.8000 0.9000 0.9500 0.9600 0.9800 0.9900
Chapter 1: General Information Confidence Interval for Intercept at at ! ta/2,n − 2
2 e 1n + xr o MSE Sxx
Confidence Interval for Slope bt MSE bt ! ta/2,n - 2 Sxx Sample Correlation Coefficient R and Coefficient of Determination R2 R=
Sxy SxxSyy
2 S xy R2 = S S xx yy
1.4.4.7 Test Statistics The following definitions apply: X-n X - no Z var = v o t var = s n n where Zvar = the standard normal Z score tvar = the sample distribution test statistic v = known standard deviation n o = population mean X = hypothesized mean or sample mean n
= sample size
s
= computed sample standard deviation
The Z score is applicable when the standard deviations are known. The test statistic is applicable when the standard deviations are computed at time of sampling. Za corresponds to the appropriate probability under the normal probability curve for a given Zvar. ta, n-1 corresponds to the appropriate probability under the t distribution with n-1 degrees of freedom for a given tvar.
Values of Za/2
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Confidence Interval
Za/2
80% 90% 95% 96% 98% 99%
1.2816 1.6449 1.9600 2.0537 2.3263 2.5758
75
©2017 NCEES
21
76
39
89**
Ac
Be
9.0122
12
Mg
24.305
20
Ca
40.078
38
Sr
87.62
56
Ba
137.33
88
Ra
226.02
Li
6.941
11
Na
22.990
19
K
39.098
37
Rb
85.468
55
Cs
132.91
87
Fr
(223)
**Actinide Series
*Lanthanide Series
44.956
4
3
227.03
138.91
La
57*
88.906
Y
Sc
II
1.0079
22
23
91 Pa 231.04
Th 232.04
140.91
140.12 90
59 Pr
58
(262)
Ha
105
180.95
Ta
73
92.906
Nb
41
50.941
V
Ce
(261)
Rf
104
178.49
Hf
72
91.224
Zr
40
47.88
Ti
238.03
U
92
144.24
Nd
60
183.85
W
74
95.94
Mo
42
51.996
Cr
24
237.05
Np
93
(145)
Pm
61
186.21
Re
75
(98)
Tc
43
54.938
Mn
25
(244)
Pu
94
150.36
Sm
62
190.2
Os
76
101.07
Ru
44
55.847
Fe
26
(243)
Am
95
151.96
Eu
63
192.22
Ir
77
102.91
Rh
45
58.933
Co
27
29
158.92 97 Bk (247)
96 Cm (247)
Tb
65
196.97
Au
79
107.87
Ag
47
63.546
Cu
157.25
Gd
64
195.08
Pt
78
106.42
Pd
46
58.69
Ni
28
Atomic Weight
Symbol
Atomic Number
30
(251)
Cf
98
162.50
Dy
66
200.59
Hg
80
112.41
Cd
48
65.39
Zn
(252)
Es
99
164.93
Ho
67
204.38
Tl
81
114.82
In
49
69.723
Ga
31
26.981
Al
13
10.811
(257)
Fm
100
167.26
Er
68
207.2
Pb
82
118.71
Sn
50
72.61
Ge
32
28.086
Si
14
12.011
C
6
5 B
IV
III
V
(258)
Md
101
168.93
Tm
69
208.98
Bi
83
121.75
Sb
51
74.921
As
33
30.974
P
15
14.007
N
7
VI
(259)
No
102
173.04
Yb
70
(209)
Po
84
127.60
Te
52
78.96
Se
34
32.066
S
16
15.999
O
8
VII
(260)
Lr
103
174.97
Lu
71
(210)
At
85
126.90
I
53
79.904
Br
35
35.453
Cl
17
18.998
F
9
(222)
Rn
86
131.29
Xe
54
83.80
Kr
36
39.948
Ar
18
20.179
Ne
10
4.0026
2 He
H
VIII
1.5.1
1
I
Periodic Table of Elements
Periodic Table of the Elements
Chapter 1: General Information
1.5 Chemistry and Physical Properties Periodic Table of the Elements
Chapter 1: General Information
1.5.2
Relative Atomic Mass Table of Relative Atomic Mass (Atomic Weight)
Name Actinium Aluminum Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Boron Bromine Cadmium Calcium Californium Carbon Cerium Cesium Chlorine Chromium Cobalt Copper Curium Dysprosium Einsteinium Erbium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium Gold Hafnium Helium
©2017 NCEES
Symbol
Atomic Number
Atomic Mass
Ac Al Am Sb Ar As At Ba Bk Be Bi B Br Cd Ca Cf C Ce Cs Cl Cr Co Cu Cm Dy Es Er Eu Fm F Fr Gd Ga Ge Au Hf He
89 13 95 51 18 33 85 56 97 4 83 5 35 48 20 98 6 58 55 17 24 27 29 96 66 99 68 63 100 9 87 64 31 32 79 72 2
---* 26.9815 ---* 121.75 39.948 74.9216 ---* 137.34 ---* 9.0122 208.980 10.811 79.904 112.40 40.08 ---* 12.01115 140.12 132.905 35.453 51.996 58.9332 63.546 ---* 162.50 ---* 167.26 151.96 ---* 18.9984 ---* 157.25 69.72 72.59 196.967 178.49 4.0026
Name Holmium Hydrogen Indium Iodine Iridium Iron Krypton Lanthanum Lead Lithium Lutetium Magnesium Manganese Mendelevium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Polonium Potassium Praseodymium Promethium Protactinium Radium Radon Rhenium
77
Symbol
Atomic Number
Atomic Mass
Ho H In I Ir Fe Kr La Pb Li Lu Mg Mn Md Hg Mo Nd Ne Np Ni Nb N No Os O Pd P Pt Pu Po K Pr Pm Pa Ra Rn Re
67 1 49 53 77 26 36 57 82 3 71 12 25 101 80 42 60 10 93 28 41 7 102 76 8 46 15 78 94 84 19 59 61 91 88 86 75
164.930 1.00797 114.82 126.9044 192.2 55.847 83.80 138.91 207.19 6.939 174.97 24.312 54.9380 ---* 200.59 95.94 144.24 20.183 ---* 58.71 92.906 14.0067 ---* 190.2 15.9994 106.4 30.9738 195.09 ---* ---* 39.102 140.907 ---* ---* ---* ---* 186.2
Chapter 1: General Information Table of Relative Atomic Mass (Atomic Weight) (cont'd) Name Rhodium Rubidium Ruthenium Samarium Scandium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium
Symbol
Atomic Number
Atomic Mass
Rh Rb Ru Sm Sc Se Si Ag Na Sr S Ta Tc Te
45 37 44 62 21 34 14 47 11 38 16 73 43 52
102.905 85.47 101.07 150.35 44.956 78.96 28.086 107.868 22.9898 87.62 32.064 180.948 ---* 127.60
Name Terbium Thallium Thorium Thulium Tin Titanium Tungsten Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium
* Multiple isotopes
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78
Symbol
Atomic Number
Atomic Mass
Tb Tl Th Tm Sn Ti W U V Xe Yb Y Zn Zr
65 81 90 69 50 22 74 92 23 54 70 39 30 40
158.924 204.37 232.038 168.934 118.69 47.90 183.85 238.03 50.942 131.30 173.04 88.905 65.37 91.22
Chapter 1: General Information
1.5.3
Oxidation Number Oxidation Number or Charge Number Name Acetate Aluminum Ammonium Barium Borate Boron Bromine Calcium Carbon Carbonate Chlorate Chlorine Chlorite Chromate Chromium Copper Cyanide Dichromate Fluorine Gold Hydrogen Hydroxide Hypochlorite
©2017 NCEES
Symbol C2H3O2 Al NH4 Ba BO3 B Br Ca C
Charge
CO3 ClO3 Cl ClO2 CrO4 Cr Cu CN Cr2O7 F Au H OH ClO
–2 –1 –1 –1 –2 +2, +3, +6 +1, +2 –1 –2 –1 +1, +3 +1 –1 –1
Name Iron
–1 +3 +1 +2 –3 +3 –1 +2 +4, –4
Lead Lithium Magnesium Mercury Nickel Nitrate Nitrite Nitrogen Oxygen Perchlorate Permanganate Phosphate Phosphorus Potassium Silicon Silver Sodium Sulfate Sulfite Sulfur Tin Zinc
79
Symbol
Charge
Fe Pb Li Mg Hg Ni NO3 NO2 N
+2, +3 +2, +4 +1 +2 +1, +2 +2, +3 –1 –1 –3, +1, +2, +3, +4, +5 –2 –1 –1 –3 –3, +3, +5 +1 +4, –4 +1 +1 –2 –2 –2, +4, +6 +2, +4 +2
O ClO4 MnO4 PO4 P K Si Ag Na SO4 SO3 S Sn Zn
Chapter 1: General Information
1.5.4
Organic Compounds Families of Organic Compounds Specific Example
IUPAC Name
Common Name
General Formula
Functional Group
CH3CH3
Ethane
Ethane
RH
C–H and C–C bonds
Alkene
H2C = CH2
Ethene or ethylene
Ethylene
RCH = CH2 RCH = CHR R2C = CHR R2C = CR2
C =C
Alkyne
HC = CH
Ethyne or acetylene
Acetylene
RC = CH RC = CR
– C =C –
Benzene
Benzene
ArH
Aromatic ring
RX
C X
FAMILY Alkane
Arene
Haloalkane
CH3CH2Cl
Alcohol
CH3CH2OH
Ethanol
Ethyl alcohol
ROH
C OH
Ether
CH3OCH3
Methoxymethane
Dimethyl ether
ROR
C O C
Amine
CH3NH2
Methanamine
Methylamine
RNH2 R2NH R3N
C N
Ethanal
Acetaldehyde
Acetone
Dimethyl ketone
Ethanoic acid
Acetic acid
Methyl ethanoate
Methyl acetate
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CH3COH O
CH3COCH3
80
=
=
=
=
R1CR2
C
O
RCOH O
RCOR
O
=
O
O
=
=
=
CH3CCH3
O
C H
RCH
C OH
O
=
Ester
O
O
O
=
Carboxylic Acid
CH3CH
=
Ketone
O
=
Aldehyde
Chloroethane Ethyl chloride
C O C
Chapter 1: General Information
1.5.5
Industrial Chemicals Common Names of Industrial Chemicals Common Name Acetone
Chemical Name
Molecular Formula
Acetone Acetylene Ammonia Ammonium hydroxide Titanium dioxide Aminobenzene Sodium bicarbonate Sulfuric acid
(CH3)2CO C2H2 NH3 NH4OH TiO2 C6H5NH2 NaHCO3 H2SO4
Aluminum oxide Hydrated aluminum oxide
Al2O3 Al2O3 : 2H2O
Borane
Calcium hypochloride Borane
Ca(ClO)2
Borax
Sodium tetraborate
Na2B4O7 : 10H2O
Sodium chloride (solution) Calcium carbide Phenol Carbon dioxide Silicon carbide Sodium hydroxide Calcium carbonate Chlorite ion Chlorate ion
NaCl CaC2 C6H5OH CO2 SiC NaOH CaCO3 ClO2–1
Mercuric sulfide Isopropyl benzene
HgS
Acetylene Ammonia Ammonium Anatase/rutile Aniline Baking soda Battery acid Bauxite Bleach
Brine, salt Carbide Carbolic acid Carbon dioxide Carborundum Caustic soda/lye Chalk Chlorite Chlorate Cinnabar Cumene Deuterium Dichromate Dolomite Epsom salt Ether Ethylene oxide Eyewash Formic acid Glauber's salt Glycerine Grain alcohol Graphite Gypsum
©2017 NCEES
BH3
ClO3–1 C6H5CH(CH3)2
Deuterium Dichromate ion Magnesium carbonate Magnesium sulfate Diethyl ether
(C2H3)2O
Ethylene oxide
C2H4O
Boric acid (solution) Methanoic acid Decahydrated sodium sulfate
H3BO3 HCOOH
Glycerine Ethanol Crystalline carbon Calcium sulfate
81
H2 Cr2O7-2 MgCO3 MgSO4
Na2SO4 : 10H2O C3H5(OH)3 C2H5OH C CaSO4 : 2H2O
Chapter 1: General Information Common Names of Industrial Chemicals (cont'd) Common Name Heavy water Hydronium Hydroquinone Hypochlorite Iron chloride Laughing gas Limestone Magnesia Magnetite Marsh gas Muriate of potash Muriatic acid Neopentane Niter Niter cake Oleum Ozone Perchlorate Permanganate Phosgene Potash Prussic acid Pyrite, Fool's Gold Pyrolusite Quicklime Quicksilver Sal soda/washing soda Salammoniac Salt/halite Salt cake Sand/silica Silane Slaked lime Soda ash Styrene Sugar Stannous chloride Superphosphate
©2017 NCEES
Chemical Name
Molecular Formula
Deuterium oxide Hydronium ion P-dihydroxybenzene Hypochlorite ion Ferrous chloride
(H2)2O H3O+1 C6H4(OH)2 OCl–1
Nitrous oxide Calcium carbonate Magnesium oxide Ferrous/ferric oxide Methane Potassium chloride Hydrochloric acid 2,2-dimethylpropane Sodium nitrate Sodium bisulfate Fuming sulfuric acid Ozone Perchlorate ion Permanganate ion Phosgene Potassium carbonate Hydrogen cyanide Ferrous sulfide Manganese dioxide Calcium oxide Mercury Decahydrated sodium carbonate Ammonium chloride Sodium chloride Sodium sulfate (crude) Silicon dioxide Silane Calcium hydroxide Sodium carbonate Vinyl benzene Sucrose
FeCl 2 : 4H 2 O N2O CaCO3 MgO Fe3O4 CH4 KCl HCl CH3C(CH3)2CH3 NaNO3 NaHSO4 SO3 in H2SO4 O3 ClO4–1 MnO4–1 COCl2 K2CO3 HCN FeS MnO2 CaO Hg Na 2 CO3 : 10H 2 O NH4Cl NaCl Na2SO4 SiO2 SiH4 Ca(OH)2 Na2CO3 C6H5CH=CH2 C12H22O11
Stannous chloride
SnCl 2 : 2H 2 O
Monohydrated primary calcium phosphate
Ca ^H 2 PO 4h2 : H 2 O
82
Chapter 1: General Information Common Names of Industrial Chemicals (cont'd) Common Name Toluene Trilene Tritium Urea Vinegar (acetic acid) Vinyl alcohol Vinyl chloride Wood alcohol Wolfram Xylene Zinc blende
©2017 NCEES
Chemical Name
Molecular Formula
Methyl benzene Tricholormethylene Tritium Urea Ethanoic acid Vinyl alcohol Vinyl chloride Methanol Tungsten Dimethyl benzene Zinc sulfide
C6H5CH3 C2HCl3 H3 (NH2)2CO CH2COOH CH2=CHOH CH2=CHCl CH3OH W C6H4(CH3)2 ZiS
83
Chapter 1: General Information
©2017 NCEES
84
2 MASS/ENERGY BALANCES AND THERMODYNAMICS 2.1 Symbols and Definitions Symbols Symbol
cP, cv
Specific heat capacity†
Units (U.S.)
Units (SI)
Btu lbm -cF
J = m2 kg : K s 2 : K
f
Fugacity of a pure component
lbf in 2
= Pa
kg N = m2 m : s2
fti
Fugacity of component i in a mixture
lbf in 2
= Pa
kg N = 2 m m : s2
G
Gibbs free energy
Btu
g
Specific Gibbs free energy†
Btu lbm
J = m2 kg s 2
H
Enthalpy
Btu
J
H
Henry's Law constant
lbf in 2
h
Specific enthalpy
Btu lbm
J = m2 kg s 2
lbm lb mole
kg mol
lbm
kg
lb mole
mol
MW
©2017 NCEES
Description
Molecular weight (molar mass)
J=
= Pa
kg : m 2 s2
kg N = 2 m m : s2
m
Mass
n
Number of moles
P
Pressure
lbf or psi in 2
= Pa
kg N = m2 m : s2
Pc
Critical pressure
lbf = psia in 2
= Pa
kg N = 2 m m : s2
85
Chapter 2: Mass/Energy Balances and Thermodynamics Symbols (cont'd) Symbol
Description
Units (U.S.)
Units (SI)
dimensionless
Pr
Reduced pressure
Psat
Saturation pressure, or vapor pressure
lbf in 2
p
Partial pressure
lbf in 2
/
Poynting correction factor
Q
Heat
Btu
J
S
Entropy
Btu oR
J K
kg N = m2 m : s2 kg N = Pa = 2 m m : s2 dimensionless = Pa
SG
Specific gravity
s
Specific entropy†
Btu lbm-o R
J kg : K
T
Temperature
°R or °F
K or °C
Tc
Critical temperature
°R or °F
K or °C
Tr
Reduced temperature
t
Time
U
dimensionless hr
s
Internal energy
Btu
J
u
Specific internal energy†
V
Volume
Btu lbm ft3
v
Velocity
ft sec
J kg m3 m s
v
Specific volume†
ft 3 lbm
m3 kg
W
Work
Btu or lbf-ft
J
w
Weight fraction
dimensionless
x
Mole fraction
dimensionless
y
Mole fraction
dimensionless
Z
Compressibility factor
dimensionless
aij
Relative volatility for components i and j
dimensionless
g
Activity coefficient
dimensionless
h
Efficiency
dimensionless
m
Dynamic viscosity
r
Density †
©2017 NCEES
dimensionless
lbm cP or ft-sec
kg Pa : s = m : s
lbm ft 3
kg m3
Property values on molar basis are denoted by ^. For example, molar volume is vt .
86
Chapter 2: Mass/Energy Balances and Thermodynamics
2.2 Material Balances General balance equation: Accumulation = Input – Output + Generation – Consumption
2.2.1
Material Balances With No Reaction
Balanced equation at steady state with no reaction: Input = Output
2.2.2
Material Balances With Reaction
2.2.2.1 General Balanced equation at steady state with reaction: Input + Generation = Output + Consumption
Common Flow Configurations
PROCESS WITH BYPASS
PROCESS WITH RECYCLE
PROCESS WITH PURGE
PROCESS WITH RECYCLE AND PURGE
2.2.2.2 Combustion Reactions Theoretical (stoichiometric) air is the air required for complete combustion. Moles of air A Molar air-fuel ratio c F m = Moles of fuel cAm F Actual # 100 Percent theoretical air = cAm F Theoretical
−c Am cAm F Actual F Theoretical = # 100 Percent excess air A c m F Theoretical
Gross or higher heating value (HHV) is the heat of combustion assuming all water generated is condensed as a liquid. Net or lower heating value (LHV) is the heat of combustion assuming that no water is condensed.
©2017 NCEES
87
Chapter 2: Mass/Energy Balances and Thermodynamics Major Components of Air Element
Volume, %
Nitrogen Oxygen Argon
78.09 20.94 0.93
Selected Properties of Air Property
Amount
lbm 28.965 lb mole
Molecular weight of air Absolute viscosity (µ) at 80°F
lbm 0.045 hr -ft
at 100°F
lbm 0.047 hr -ft
Density lbm ft 3 lbm 0.0708 3 ft
at 80°F
0.0734
at 100°F
The dry adiabatic lapse rate ΓAD is 0.98°C per 100 m (5.4°F per 1000 ft). This is the rate at which dry air cools adiabatically with altitude. The actual (environmental) lapse rate Γ is compared to ΓAD to determine stability.
Stability of Adiabatic Lapse Rate Lapse Rate
Stability Condition
G > GAD G = GAD G < GAD
Unstable Neutral Stable
2.2.2.3 Heat of Reaction Calculate standard state heat of reaction Dht R0 from standard heat of formation Dht f0 at 298 K (25°C) and 1 atm, using Dht R0 =
/ Dht f0
products
−
/ Dht f0
reactants
Calculate Dht R at temperature T using Dht R = Dht R0 +
/ Dht products
where
©2017 NCEES
f
+
/ Dht
f
reactants
Dht f includes the sensible and latent heat changes between T and 298K
88
Chapter 2: Mass/Energy Balances and Thermodynamics 2.2.2.4 Standard Heat of Formation and Combustion The standard heat of formation and combustion at 25°C are shown in the tables below. The products of combustion are H2O (l) and CO2 (g). Solids are listed as s in the tables below.
Alkanes Name
Methane Ethane n-Propane Isobutane n-Butane n-Pentane n-Pentane Cyclohexane Cyclohexane n-Hexane n-Hexane Methylcyclohexane Methylcyclohexane n-Heptane n-Heptane n-Octane n-Octane n-Nonane n-Nonane n-Decane n-Decane
©2017 NCEES
Formula
CH4 C2H6 C3H8 C4H10 C4H10 C5H12 C5H12 C6H12 C6H12 C6H14 C6H14 C7H14 C7H14 C7H16 C7H16 C8H18 C8H18 C9H20 C9H20 C10H22 C10H22
Dht f0
Phase
kJ mol –74.6 –84.00 –104.6 –134.3 –125.5 –146.9 –173.5 –124.0 –157.0 –167.2 –198.8 –154.78 –190.2 –187.9 –225.0 –208.4 –250.0 –228.3 –274.7 –249.7 –301.0
g g g g g g l g l g l g l g l g l g l g l
89
Btu lb mol –32,070 –36,110 –44,970 –57,740 –53,960 –63,160 –74,600 –53,310 –67,500 –71,890 –85,470 –66,540 –81,760 –80,790 –96,740 –89,600 –107,500 –98,160 –118,100 –107,400 –129,400
− Dht c0 HHV kJ mol 890.7 1560 2219 2868 2877 3535 3509 — 3930 4199 4163 4601 4565 — 4817 — 5430 — 6125 — 6779
Btu lb mol 382,900 670,700 954,100 1,233,000 1,237,000 1,520,000 1,507,000 — 1,690,000 1,805,000 1,790,000 1,978,000 1,963,000 — 2,071,000 — 2,335,000 — 2,633,000 — 2,915,000
Chapter 2: Mass/Energy Balances and Thermodynamics
Alkenes and Alkynes
Name
Acetylene Ethylene Propylene 1,3-Butadiene 1,3-Butadiene 1-Butene 1-Pentene 1-Pentene 1-Hexene 1-Hexene
Formula
C2H2 C2H4 C3H6 C4H6 C4H6 C4H8 C5H10 C5H10 C6H12 C6H12
Phase
g g g g l g g l g l
− Dht c0
Dht f0 kJ mol 226.8 52.3 20.4 109 91 –0.630 –22 –49 –42 –73
HHV
Btu lb mol 97,510 22,500 8770 46,900 39,100 –270 –9500 –21,000 –18,000 –31,000
kJ mol — 1411 2058 2540 2522 2717 — 3350 — —
Btu lb mol — 606,600 884,800 1,092,000 1,084,000 1,168,000 — 1,440,000 — —
Aromatics Name
Formula
Phase
Benzene Benzene Toluene Toluene Styrene Styrene Ethylbenzene Ethylbenzene p-Xylene p-Xylene
C6H6 C6H6 C7H8 C7H8 C8H8 C8H8 C8H10 C8H10 C8H12 C8H12
g l g l g l g l g l
kJ mol 82.9 49 50 12 147 103 49 6.8 17.9 –24.4
o-Xylene o-Xylene
C8H12 C8H12
g l
19 –24.4
©2017 NCEES
− Dht c0
Dht f0
90
HHV Btu lb mol 35,600 21,000 21,000 5200 63,200 44,300 21,000 2900 7700 –10,500
kJ mol — 3270 — 3920 — 4390 — 4567 — 4552
Btu lb mol — 1,406,000 — 1,685,000 — 1,887,000 — 1,964,000 — 1,957,000
8200 –10,500
— 4552
— 1,957,000
Chapter 2: Mass/Energy Balances and Thermodynamics
Other Organic Compounds
Name
Methanol Methanol Acetaldehyde Acetaldehyde Ethylene oxide Ethylene oxide Acetic Acid Ethanol Ethanol Ethylene glycol
Formula
CH4O CH4O C2H4O C2H4O C2H4O C2H4O C2H4O2 C2H6O C2H6O C2H6O2
− Dht c0
Dht f0
Phase
kJ mol –205 –239 –171 –196 –53 –96 –484 –234 –276 –460
g l g l g l l g l l
HHV
Btu lb mol –88,100 –103,000 –73,500 –84,300 –22,700 –41,200 –208,000 –100,600 –119,000 –197,800
kJ mol 764 726 — — 1306 1263 875 1366 1367 1190
Btu lb mol 328,500 312,100 — — 561,500 543,000 376,000 587,300 587,700 511,600
Inorganic Compounds Name
Ammonia Calcium carbide Calcium carbonate Calcium chloride Calcium chloride Calcium hydroxide Calcium oxide Carbon Carbon monoxide Carbon dioxide Hydrochloric acid Hydrogen Hydrogen sulfide Iron oxide Iron oxide Iron oxide Nitric acid Nitric oxide Nitrogen dioxide Nitrogen trioxide Sodium carbonate ©2017 NCEES
Formula
NH3 CaC2 CaCO3 CaCl2 CaCl2 6H2O Ca(OH)2 CaO C, graphite CO CO2 HCl H2 H2S FeO Fe2O3 Fe3O4 HNO3 NO NO2 NO3 NaCO3
Phase
g s s s s s s s g g g g g s s s g g g g s 91
− Dht c0
Dht f0 kJ mol –45.9 –62.8 –1207 –795.0 –2607 –986.6 –635.6 0 –110.5 –393.5 –92.31 0 –20.6 –269.0 –822.2 –1117 –134.3 90.29 33.10 71.13 –1131
Btu lb mol –19,700 –27,000 –518,900 –342,000 –1,121,000 –424,200 –273,200 0 –47,510 –169,200 –39,690 0 –8860 –115,700 –353,500 –480,300 –57,740 38,820 14,200 30,580 –486,300
HHV kJ mol 383.0 — — — — — — 393.5 283.0 — — 286.0 546.3 — — — — — — — —
Btu lb mol 164,700 — — — — — — 169,200 121,700 — — 123,000 234,900 — — — — — — — —
Chapter 2: Mass/Energy Balances and Thermodynamics Inorganic Compounds (cont'd) Name
Formula
Sodium carbonate Sodium chloride Sodium hydroxide Sulfur oxide Sulfur dioxide Sulfur trioxide Sulfur trioxide Water Water
Phase
NaCO3 10H2O NaCl NaOH SO SO2 SO3 SO3 H2O H2O
kJ mol –4082 –411.0 –426.7 5.01 –296.8 –395.8 –442.5 –241.83 –285.83
s s s g g g l g l
− Dht c0
Dht f0
HHV
Btu lb mol –1,755,000 –176,700 –183,500 2150 –127,600 –170,200 –190,300 –103,970 –122,890
kJ mol — — — — — — — — —
Btu lb mol — — — — — — — — —
2.3 State Functions and Thermodynamics 2.3.1
Nomenclature
Intensive properties are independent of mass. Extensive properties are proportional to mass.
2.3.2
Properties of State Functions
For a single-phase pure component, specifying any two intensive properties specifies the remaining intensive properties.
State Functions Component
Property
U.S. Units
SI Units
Absolute pressure
P
psia
Pa
Absolute temperature
T
°R
K
Specific volume
V v= m
ft 3 lbm
m3 kg
Specific internal energy
U u= m
Btu lbm Btu lbm Btu lbm-°R
J kg J kg J kg : K
Btu lbm
J kg
Specific enthalpy Specific entropy Specific Gibbs free energy
H h=u+Pv= m S s=m g=h–Ts
Heat Capacity at Constant Pressure 2h c p = c 2T m
P
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Btu kJ lbm -°R or kg : K
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Chapter 2: Mass/Energy Balances and Thermodynamics Heat Capacity at Constant Volume 2u c v = c 2T m
v
Btu kJ lbm -°R or kg : K
The steam tables in Chapter 8 provide T, P, v, u, h, and s data for saturated water and superheated steam. Thermal and physical property tables for selected gases, liquids, and solids are included in Chapter 8.
2.4 First Law of Thermodynamics The First Law of Thermodynamics states that energy is neither created nor destroyed but can change from one form into another. The net energy crossing the system boundary is equal to the change in energy inside the system. Q Heat Q c q = m m is energy transferred due to temperature difference and is considered positive if it is inward (added to the system). Work W b w = m l is considered positive if it is outward (subtracted from the system).
W
Changes in state functions are computed by changes in Q and W, which are path-dependent. The common paths are Isobaric Isochoric
DP = 0 DV = 0
Isothermal
DT = 0
Isenthalpic Adiabatic Adiabatic and reversible (isentropic)
DH = 0 DQ = 0 DS = 0
Efficiencies are used to correct irreversible processes.
2.4.1
Closed Thermodynamic Systems
In a closed thermodynamic system, no mass crosses the system boundary: Q – W = DU + DKE + DPE where DU = change in internal energy DKE = change in kinetic energy DPE = change in potential energy Energy can cross the system boundary only in the form of heat or work. Work can be shaft work (ws) or other work forms, such as electrical. Reversible work is
#
w = P dv The table below displays the work, heat, and internal energy changes in closed systems for each of the four applicable paths for 1 mole of ideal gas. These changes assume constant heat capacities and neglect kinetic and potential energy changes.
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Chapter 2: Mass/Energy Balances and Thermodynamics Closed System Energy Changes for 1 Mole of Ideal Gas Change in Internal Path Work (W) Heat (Q) Energy (DU) 0 ctV DT ctV DT Isochoric (DV = 0) Isobaric (DP = 0)
P(V2 – V1)
ctP DT
P RT ln e P1 o
P RT ln e P1 o
2
Isothermal (DT = 0)
2
V RT ln e V2 o 1
0
V RT ln e V2 o 1
k−1 k
k RT1 P2 k − 1 >1 − e P1 o
Isentropic (Ds = 0)
ctP DT − P (V2 − V1)
H
0
k−1 k
RT − − 1 >1 − e P2 o k 1 P1
H
ct k = ct P V
where
For ideal gas in an isentropic process: k−1
T V e 2o=e 1o T1 V2
2.4.2
k−1 k
P =e 2o P1
Open Thermodynamic Systems
In an open thermodynamic system, mass does cross the system boundary. Flow work (Pv) is defined as the work for mass entering and leaving the system. Reversible flow work = w rev = -
# v d P + DK E + DP E
The First Law applies whether or not processes are reversible. Open System First Law (energy balance): 2
/ mo i =hi + V2i
+ g Z iG -
2
/ mo e =he + V2e
d _ ms us i + g ZeG + Qo in - Wo net = dt
where subscripts i and e refer to inlet and exit states of the system Wo net = rate of net or shaft work mo
= mass flow rate
h
= enthalpy
g
= acceleration of gravity
Z
= elevation
V
= velocity
ms
= mass of fluid within the system
us
= specific internal energy of system
Qin = rate of heat transfer (neglecting kinetic and potential energy of the system) ©2017 NCEES
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Chapter 2: Mass/Energy Balances and Thermodynamics The table below displays the work, heat, and internal enthalpy changes in open systems for each of the five applicable paths for 1 mole of ideal gas. These changes assume constant heat capacities and neglect kinetic and potential energy changes.
Open System Energy Changes for 1 Mole of Ideal Gas Change in Enthalpy Path Work (W) Heat (Q) (DH) ctV DT ctV DT + V _ P2 − P1 i Isochoric (DV = 0) –V(P – P ) 2
1
0
ctP DT
P RT ln e P1 o
P RT ln e P1 o
Isobaric (DP = 0)
2
Isothermal (DT = 0)
2
V RT ln e V2 o 1
V RT ln e V2 o 1
k−1 k
k RT1 P2 k − 1 >1 − e P1 o
Isentropic (DS = 0)
0
Isenthalpic (DH = 0)
ctP DT
H
0
0
0
k−1 k
k RT1 P2 k − 1 >1 − e P1 o 0
The actual work required is w wactual = hrev is where his = isentropic efficiency In the polytropic process, the only condition for process path is reversibility. Pvn = constant where n = empirical constant
= w rev
n _ P2 v 2 - P1 v1 i n R _T2 - T1 i = ^1 - n h ^1 - n h MW ^n − 1 h
− n RT w rev = n - 1 MW1 >1 - e P2 o P 1
n
H
The actual work required is w wactual = h rev poly where hpoly = polytropic efficiency Polytropic efficiencies are always higher than isentropic efficiencies for the same compression stage.
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H
Chapter 2: Mass/Energy Balances and Thermodynamics For multistage compression, the pressure ratio PR is 1
P m PR = e P2 o 1 where m = number of stages The temperature drop on isenthalpic expansion (Joule-Thomson) is DT = n J T DP
2T assuming the Joule-Thomson coefficient nJ T = c 2P m is constant. H
2.4.3
Steady-Flow Systems
The system does not change state with time. This assumption is valid for the steady operation of turbines, pumps, compressors, throttling valves, nozzles, and heat exchangers, including boilers and condensers. The letter V denotes velocity in the following three equations: /mo i d hi +
V2 V i2 + g Z i n - /mo e d he + e + g Ze n + Qo - Ws = 0 2 2
/mo i = /mo e
For a single fluid-flow stream at steady state, the equation reduces to: DV 2 Dh + 2 + g DZ + wo - qo = 0 If the fluid is incompressible with negligible friction losses, the equation reduces to: DP + DV 2 + g DZ + wo s - qo = 0 t 2
2.5 Behavior of Single-Component Systems 2.5.1
Ideal Systems
2.5.1.1 Ideal Gas Law For an ideal gas, P vt T = = P vt RT and P1 vt1 T1 2 2 2 where
1 and 2 indicate separate system states.
Alternatively, m RT = PV n= RT MW
and
P1 V1 n1 T1 = P2 V2 n 2 T2
For ideal gases, ctp − ctv = R . These are independent of both pressure and volume, as are u and h. Assuming constant heat capacities, or average heat capacities over the temperature range T1 to T2, the following apply: c= Dh c P DT v DT P2 v R ln e P o R ln d v2 n T2 T2 1 1 Ds = c P ln e T o − MW Ds = c v ln e T o − MW 1 1 Du
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Chapter 2: Mass/Energy Balances and Thermodynamics
2.5.2
Nonideal Systems
2.5.2.1 Compressibility and the Theorem of Corresponding States The compressibility factor is a dimensionless number defined by the equation: P vt Z = RT Theorem of Corresponding States To first approximation, all fluids have the same compressibility factor when compared at the same reduced temperature and reduced pressure. Reduced temperature (Tr) and reduced pressure (Pr) are defined as
P T = Tr T= and Pr P c c
Compressibility Factor Chart
15
.00
(Ze = 0.27)
Tr
1.0
15.00 5.00 3.00 2.00 1.80
2.00 0.8
0
1.20
0.8 0.90 5
SA TU
RA TE
0.9 5
1.1
1.50 1.30
1.70 1.60
0
1.0
0
1.50
DG
AS
1.40 1.35
0.7 0.75
0.5
1.20 0.80
1.15
0.85
1.10
0.90
0.4
0.95
0.3
1.02 1.00
0.2 0.50
0.1 0.0
1.08 1.06 1.04
0
0.6
1.30 1.25
0.9
COMPRESSIBILITY FACTOR, Z
1.1
0.8
00
GENERALIZED COMPRESSIBILITY FACTORS
1.2
0.9
10.
1.3
3.00 5.00
0.50
1.4
0.70
1.5
0.60 0.90 0.80 1.00 2.00
COMPRESSIBILITY FACTOR CHART
ID D LIQU
ATE
SATUR
0.1
0.2 0.3 0.4 0.5
1.0
2.0 3.0 4.0 5.0
10
20
30
REDUCED PRESSURE, Pr From de Nevers, Noel, Physical and Chemical Engineers, 2nd ed., New York: Wiley, 2012, p. 308. ©2017 NCEES
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Chapter 2: Mass/Energy Balances and Thermodynamics 2.5.2.2 Equations of State Virial Equation of State P vt B C D Z = RT = 1 + vt + 2 + 3 + g vt vt where B, C, D = virial equation coefficients, accounting for two-body, three-body, and four-body interactions, respectively Alternatively, P vt Z = RT = 1 + Bl P + C l P 2 + Dl P 3 g where
Bl , C l , Dl = virial equation coefficients
The two sets of virial coefficients are related by: B Bl = RT C − B2 Cl = (RT) 2 D − 3 B C + 2 B3 Dl = (RT) 3 Generic Cubic Equation of State a (T) RT P = vt − b − (vt + e b) (vt + v b) where a(T) = substance-dependent constant b
= substance-dependent constant
e
= constant for generic cubic equation of state
s
= constant for generic cubic equation of state
For the Van der Waals equation, a(T) = a and e= v= 0.
2.5.3
Phase Equilibrium for a Pure Component
2.5.3.1 Phase Rule For nonreacting systems, the degrees of freedom F (for example, temperature, pressure, and composition) are F=2–p+N where p = number of phases N = number of chemical species
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Chapter 2: Mass/Energy Balances and Thermodynamics 2.5.3.2 Phase Diagrams The pressure-temperature relationship for a pure fluid is often shown in a P-T plot. The intersection of the solidliquid-vapor lines is the triple point where the three phases coexist. The critical point is where vapor and liquid properties become identical. Four kinds of diagrams are often used for calculations involving a pure fluid. Figures below show the qualitative behavior of fluid properties.
Thermodynamic Diagrams for a Pure Fluid CRITICAL POINT
TRIPLE POINT
CON
PRESSURE
PRESSURE
VAPOR PRESSURE CURVE
CONST. T
S T.
S ON
C
TEMPERATURE
ENTHALPY
PRESSURE-TEMPERATURE FOR PURE FLUID
P-h DIAGRAM FOR PURE FLUID
ST. P
CONST. T
NS
ENTHALPY
CO
T. H
CRITICAL POINT
T. P
CON
CONS
QU SA T. L I
UI IQ SA T. L
CONST. H
SA T. V AP
OR
CONST. T
CRITICAL POINT
ID
CONST. QUALITY
D
TEMPERATURE
.V CONST
VAPOR
SUBLIMATION CURVE
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CONST. T
SOLID
LIQUID
SAT. VAPOR
FUSION CURVE
SA T. L IQU ST. Q ID UAL ITY
CRITICAL POINT
CO
NS
SA T. VA PO UA R LIT Y
T. Q
ENTROPY
ENTROPY
T-S DIAGRAM FOR PURE FLUID
MOLLIER DIAGRAM FOR PURE FLUID
99
Chapter 2: Mass/Energy Balances and Thermodynamics 2.5.3.3 Compressibility and Expansivity Volume expansivity:
1 2V b = V c 2T m
P
1 2V Isothermal compressibility: l = − V c 2P m
T
For real liquids, assume that k and b are independent of pressure and temperature: dV = bdT − ldP V V ln e V2 o = b _T2 − T1 i − l _ P2 − P1 i 1
For incompressible liquids: dV = 0 b c dP m = l dT V
2.5.3.4 Vapor Pressure Vapor pressure is the pressure in a closed system containing a pure fluid with both liquid and vapor in equilibrium at a given temperature. The equilibrium phases are saturated. The Antoine equation expresses the temperature dependence of vapor pressure: B ln P sat = A − T + C where Psat
= saturation pressure or vapor pressure
A, B, and C = constants for a given species T
= absolute temperature in K or °R
2.5.3.5 Latent Heat The Clapeyron equation relates enthalpy change to temperature, vapor pressure, and volume in the phase change of a two-phase, single-species system. d P sat = Dh dT T Dv where Dh = specific latent heat for the phase change Dv = specific volume change for the phase change For the phase transition from liquid to vapor as an ideal gas, the Clapeyron equation becomes the ClausiusClapeyron equation: Dh vap d (ln P sat) =− R 1 dc T m Assuming a constant, or average, heat of vaporization between T1 and T2, the integrated form is − Dhvap 1 1 P sat ln f 2sat p = R d T − T n 2 1 P1
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Chapter 2: Mass/Energy Balances and Thermodynamics 2.5.3.6 Properties for Two-Phase (Vapor-Liquid) Systems Quality x (for liquid-vapor systems at saturation) is defined as the mass fraction of the vapor phase: m x = m +vm v l where mv = mass of vapor ml = mass of liquid Specific volume of a two-phase system can be represented as v = xvv + (1 – x) vl
or
v = v1 + xDvvap
where vv
= specific volume of saturated vapor
vl
= specific volume of saturated liquid
Dvvap = specific volume change upon vaporization = vv – vl Similar expressions exist for u, h, and s: u = xuv + (1 – x) ul
or
u = ul + xDuvap
h = xhv + (1 – x) hl
or
h = hl + xDhvap
s = xsv + (1 – x) sl
or
s = sl + xDsvap
The energy difference between two phases in equilibrium at a given temperature (or pressure) is the latent heat. The three types of latent heat are Latent heat of fusion (melting):
Dhfusion = hl – hs
Latent heat of sublimation:
Dhsubl = hv – hs
Latent heat of vaporization:
Dhvap = hv – hl
2.6 Behavior of Multicomponent Systems The properties of a mixture can be estimated using the properties of its pure components, based on either a massfraction average or a mole-fraction average. The one exception is entropy, which must be estimated based only on a mole-fraction average, as shown below. Use volumes when computing the density of a mixture: When i = 1, 2, …, n constituents, the mole fraction is ni = xi n= n /n i /xi = 1 where ni = number of moles of component i n = total moles in the mixture
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Chapter 2: Mass/Energy Balances and Thermodynamics m wi = mi
Mass fraction:
m Molecular weight: MW = n =
m=
/ mi
/ wi = 1
/ xi MWi
To convert mole fractions xi to mass fractions wi: wi =
xi MWi
/ n _ xi MWi i
To convert mass fractions to mole fractions: wi MWi xi = wi n MWi
/
To convert a component from a wet basis to a dry basis: wiWet wiDry = (1– w H 2 O) where w H 2 O = the weight fraction of water in the mixture
2.6.1
Ideal Mixtures
2.6.1.1 Ideal Gas Mixtures Dalton’s Law of Partial Pressures pi V = ni RT
results in
P=
n
/ pi
i=1
or
P = pi + g + p n
and
= yi
pi ni = P n
where pi = partial pressure of component i ni = moles of component i yi = mole fraction of component i in gas phase Amagat’s Law of Partial Volumes PVi = ni RT
results in: V =
n
/Vi
i=1
or
V = Vi + g + Vn
and
Vi ni y=i V= n
where Vi = partial volume of component i
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Chapter 2: Mass/Energy Balances and Thermodynamics Other properties include: u=
/ (yi ui)
/ (yi hi)
h=
s=
/ (yi si) + smix
where ui and hi are evaluated at T si is evaluated at T and Pr To calculate the molar volume of an ideal gas or liquid mixture: vtmix =
/ _ x vt i i i
n
This equation applies to internal energy, enthalpy, and volume but not to density, which is the reciprocal of specific volume. For terms involving entropy, include the entropy of mixing: 1 s mix = R / xi ln d x n n
i
When mixing pure components: 1 stmix = / _ xi sti i + R / xi ln d x n n
i
n
and Gibbs free energy is 1 gt mix = / _ xi gti i − RT / xi ln d x n n
n
i
2.6.1.2 Raoult’s Law Assuming a vapor phase that is an ideal gas and a liquid phase that is an ideal solution: = pi y= xi P isat iP where xi
= mole fraction of component i in liquid phase
P isat = vapor pressure of pure component i
2.6.1.3 Henry’s Law The partial pressure of a component in the gas phase is proportional to the concentration of the component in the liquid phase: pi = yi P = xi Hi where Hi = Henry’s law constant for component i
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Chapter 2: Mass/Energy Balances and Thermodynamics
2.6.2
Nonideal Mixtures
2.6.2.1 Fugacity Coefficients and Activity Coefficients Fugacity The criterion for the vapor-liquid equilibrium of mixtures is ftiV = ftiL where ftiV = fugacity of component i in the vapor phase ftiL = fugacity of component i in the liquid phase Vapor Fugacity of Pure Component f iV = z i P where
z i = fugacity coefficient of pure component i in vapor phase
The fugacity coefficient of a pure component is a function of temperature and pressure and may be determined from any of: The residual Gibbs free energy (GR)
GR ln z = RT
An equation of state
ln z =
A generalized correlation, e.g.,
ln z = (ln z) 0 + ~ (ln z)1
where
#0
P
dP ( Z − 1) P
w = the acentric factor
Liquid Fugacity of Pure Component / = exp =
f iL = z isat P isat /
vt iL (P − P isat) G RT
where z sat i = fugacity coefficient of pure component i at saturation /
= Poynting correction factor
vt iL = molar volume of pure component i in the liquid phase Vapor Fugacity of Mixture = ft V zt= P zt y P i
where
i
i
i
i
zt i = fugacity coefficient of component i in the vapor phase
The fugacity coefficient of a component in a mixture may be determined from an equation of state and a mixing rule. BP ln z i = RT
For a pure component, using the virial equation:
ln z i = a
For a mixture, using the virial equation: ©2017 NCEES
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P / j y j Bij − Bm k RT
Chapter 2: Mass/Energy Balances and Thermodynamics where Bm =
/ / yi y j Bij i
j
Bm = second virial coefficient of the mixture Bij = virial coefficient that characterizes a bimolecular interaction between i and j For i = j, Bij = Bji = Bii = j , Bij must be obtained from measured values or mixing rules. For i Y Liquid Fugacity of Mixture L sat = ftiL c= c i xi z sat i xi f i i Pi / where gi = activity coefficient of component i Activity coefficients are normally based on experimental measurements and fitted to an activity coefficient model, for example the Van Laar model: −2 −2 A x A x ln c1 = A12 e1 + A 12 x1 o and ln c 2 = A 21 e1 + A21 x 2 o 21 2 12 1 where A12 and A21 = Van Laar constants, typically fitted from experimental data Gamma/Phi Approach to Vapor-Liquid Equilibrium (VLE) zt y P = c x z sat P sat / i
i
i
i
i
i
i
Special cases: Ideal vapor phase, ideal liquid solution, and low pressure: Assume= zt i 1= , ci = 1, and / i 1= , then yi P xi P isat Ideal vapor phase, nonideal liquid solution, and low pressure: = Assume zt i 1= and / i 1, then yi P = c i xi P isat Nonideal vapor phase, nonideal liquid solution, and moderate pressure: sat = Assume / i 1= , then zt i yi P c i xi z sat i Pi
2.6.2.2 Heat of Solution Ideal mixing applies to gases at low pressures; liquids and high-pressure gases involve nonideal mixing. In these cases, make calculations on a mole or mass basis instead of on a mole-fraction or mass-fraction basis. For the heat of a solution for a binary mixture on a molar basis: n ht mix, actual = n Dht + n1 ht1 + n 2 ht 2 where n = total moles of solution n1 = moles of component 1 n2 = moles of component 2 This equation also applies to solids or gases dissolving into liquids. The Dht value must be known. ©2017 NCEES
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Chapter 2: Mass/Energy Balances and Thermodynamics Heats of solutions often appear in charts, and enthalpies of mixing are presented as a function of composition. For evolved or absorbed heat: n Dht = n ht mix, final - _n1 ht mix1 + n 2 ht mix2 i
where hmix1 and hmix2 can be either mixtures or pure components. This is calculated on a mass basis if the data are on a mass basis.
2.6.2.3 Boiling Point Elevation and Freezing Point Depression For dilute solutions of nonvolatile solutes in a solvent, the solution has a greater boiling point and lower freezing point than the solvent alone. Boiling point elevation 2 R T bo x DTb = Dhvap where x
= solute mole fraction
Tbo = boiling point of the pure solvent at the system pressure
Δhvap = latent heat of vaporization of the pure solvent at boiling point Tbo and the system pressure
Freezing point depression 2 R T mo x DTm = Dhfusion where x
= solute mole fraction
Tmo
Δhfusion = latent heat of fusion of the pure solvent at the melting point Tmo and the system pressure
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= melting point of the pure solvent at the system pressure
106
Chapter 2: Mass/Energy Balances and Thermodynamics
30
NaNO3 (NH4)2SO4 K2CO3 Ca(NO3)2 KCl
WE
IGH
OL ID 20 S
15 10
60 55 NaCl
5 50
W
KOH
LiCl
110
320
100
300
90
280
4
80
260
2
70
240
60
220
50
200
40
180
30
160
20
140
10
120
0
100
0
EI G 45 HT P
ER C
NaOH
10
6
LiNO3
CaCl2
340
8
TP E 25 RCEN TS
HNO3 H2SO4
120
40
MgCl2
BOILING POINT RISE, °F
35
12
BOILING POINT RISE, °F
SUCROSE 60 55 CITRIC 50 45 ACID KRAFT LIQUID 40 GLYCEROL
EN
T
SO
LID
35
S
30 EXAMPLE: At 270 °F, a 22% CaCl2 solution has a b.p.r. of 9.7 °F
25 20
NOTE: Points shown based mainly on atmospheric boiling point
15
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 6th ed., New York: McGraw-Hill, 1997, p. 12-23.
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SOLUTION TEMPERATURE, °F
For common aqueous solutions, the boiling point elevation can be determined graphically from the solution temperature and the solute mass fraction. Boiling-Point Rise of Aqueous Solutions. °C = 5 (°F – 32) 9
Chapter 2: Mass/Energy Balances and Thermodynamics
2.6.3
Phase Equilibrium for Multicomponent Systems
2.6.3.1 Vapor-Liquid Equilibrium in Binary, Fully Miscible Systems Typical Vapor-Liquid Equilibrium Diagrams for Binary, Fully Miscible Systems V
L
V–L
P
T
y
V–L
L
V x
x-y
x
2.6.3.2 Azeotropes An azeotrope is a mixture that produces a liquid and vapor of equal composition when boiled. No separation of such a mixture is possible by simple distillation. For a positive azeotrope (minimum-boiling azeotrope): • A positive deviation from Raoult’s Law is exhibited on a P-xy diagram, with the P-x curve lying above that for ideal behavior. • The P-x curve and the P-y curve exhibit maxima at a point for which x = y. • A T-xy diagram exhibits a minima at the point for which x = y, which represents a boiling point lower than that of any other composition. • A positive deviation from ideal-solution behavior results when liquid-phase intermolecular forces between like molecules are stronger than between unlike molecules.
Positive Azeotrope Diagrams L P
V–L V–L V x-y
V V–L
T V–L
y
L x-y
x-y
For a negative azeotrope (maximum-boiling azeotrope): • A negative deviation from Raoult’s Law is exhibited on a P-xy diagram, with the P-x curve lying below that for ideal behavior. • The P-x curve and the P-y curve exhibit minima at a point for which x = y. • The T-xy diagram exhibits a maxima at the point for which x = y, which represents a boiling point higher than that of any other composition. • A negative deviation from ideal-solution behavior results when liquid-phase intermolecular forces between unlike molecules are stronger than between like molecules.
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Chapter 2: Mass/Energy Balances and Thermodynamics Negative Azeotrope Diagrams
V
L P
V–L V
V–L
T
V –L V –L
y
L
x-y
x-y
x-y
Lever Rule for a Binary Phase System For a vapor-liquid mixture of A and B, the relative amounts of the liquid and vapor phases in a mixture with an overall composition of xF are given by the following equations: y −x b AL = a + b = y A − x F A A − x x a A V = a + b = y F − xA A A
L P V
a 0
xA
b xF
yA
1
CONCENTRATION OF COMPONENT A
2.6.3.3 Liquid-Liquid Equilibrium for Partially Miscible and Immiscible Systems Many mixtures of chemical species, when mixed in certain ranges of composition, form two liquid phases of different compositions at thermodynamic equilibrium. The criterion for the liquid-liquid equilibrium of mixtures is ftia = ftib where ftia = fugacity of component i in the liquid phase designated a ftib = fugacity of component i in the liquid phase designated b If each species exists as a liquid at the system temperature, then: x ia c ia = x ib c bi
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Chapter 2: Mass/Energy Balances and Thermodynamics A solubility diagram is a T-x diagram at a constant pressure for a binary system. It depicts curves that indicate the compositions of coexisting liquid phases. Such diagrams may show: • A lower critical solution temperature, above which two liquid phases are possible and below which a single liquid phase exists for all compositions. • An upper critical solution temperature, below which two liquid phases are possible and above which a single liquid phase exists for all compositions. • When liquid-liquid equilibrium curves intersect a vapor-liquid equilibrium bubble point curve and where only the lower critical solution temperature exists. • When liquid-liquid equilibrium curves intersect a solid-liquid equilibrium freezing point curve and where only the upper critical solution temperature exists.
Upper and Lower Critical Solution Temperatures UPPER CRITICAL SOLUTION TEMPERATURE
T
T
LOWER CRITICAL SOLUTION TEMPERATURE x
x
Phase Diagrams Most of the ternary or pseudoternary systems used in extraction are of two types: Type I System: One binary pair has limited miscibility. Type II System: Two binary pairs have limited miscibility. The compositions of the two phases are equal at the plait point. Examples of Type I and II systems are shown below.
1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00
COMP
ONENT
C LAYE
R
TIE LINES
WT. FRACTION COMPONENT C
Example: Type I System Components A + B + C
COMPONENT A LAYER 0.05
0.10 0.15 0.20 0.25 WEIGHT FRACTION COMPONENT B
0.30
0.35
Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-26. ©2017 NCEES
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Chapter 2: Mass/Energy Balances and Thermodynamics Type I System
Type II System
PLAIT POINT f z a
c
e
d TWO LIQUID PHASES
b MOL FRACTION
MOL FRACTION
Lever Rule for a Ternary Two-Phase System In the following ternary phase diagram, two phases contain partially miscible components A, B, and C. One phase a is rich in component B and one is lean in component B. The fraction of the B-lean phase is a + b , where a and b represent the length of the tie line on each side of the overall composition, denoted by the heavy black dot.
Ternary Phase Diagram 100% C
100% B
b
a
100% A
2.6.3.4 Vapor-Liquid-Liquid Equilibrium The gamma-phi approach to vapor-liquid equilibrium applies to each liquid phase. Assuming= that z 1= and / 1: a a sat = y i* P * c= and y i* P * c bi x ib P isat i xi Pi
For a binary system, P * = y1* P * + y 2* P * = c1b x1b P1sat + c a2 x 2a P 2sat
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and
y1* =
c1b x1b P1sat P*
Chapter 2: Mass/Energy Balances and Thermodynamics where P* = three-phase equilibrium pressure y1* = three-phase equilibrium concentration of component 1 in the vapor phase x1b = concentration of component 1 in the liquid phase x 2a = concentration of component 2 in the liquid phase c1b = activity coefficient of component 1 c a2 = activity coefficient of component 2 a = liquid phase rich in component 2 b = liquid phase rich in component 1 In an immiscible system, x1b, c1b, x 2a, and c a2 all are equal to 1. As a result: P sat P * = P1sat + P 2sat and y1* = sat 1 sat P1 + P 2 For the range in which the vapor is in equilibrium with pure-liquid component 1: P sat y1 = P1 And similarly, for the range in which the vapor is in equilibrium with pure-liquid component 2: P sat y 2 = P2
Vapor-Liquid-Liquid Equilibrium Diagrams V V–L1
L1 – L 2 P L1
V–L2 V–L1 V
L2
x
T
L1
V–L2 L1 – L 2
L2
x
y
x
2.7 Power Cycles The most efficient means of converting heat into work is the Carnot cycle. Thermal efficiency is defined as W h = Qout in For the Carnot cycle, Q Wout T - TC = = 1 - out = H h Q TH Q in in where TC = temperature of working fluid entering the engine TH = temperature at which heat is emitted from the engine
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Chapter 2: Mass/Energy Balances and Thermodynamics Refrigeration cycles are the reverse of heat-engine cycles. Heat is moved from low to high temperature, requiring work, W. Cycles can be used for refrigeration or in heat pumps. The Coefficient of Performance (COP) is defined as Q COPHP = WH for heat pumps Q COPref = WL for refrigerators and air conditioners The upper limit of COP is based on the reversed Carnot cycle: TH for heat pumps COPC = _TH - TL i COPC =
TL for refrigerators and air conditioners _TH - TL i
Btu 1 ton of refrigeration = 12,000 hr = 3516 W
Combustion Cycles BRAYTON CYCLE (GAS TURBINE)
OTTO CYCLE (GASOLINE ENGINE) P
3
T
3 FUEL GAS q=0
v=c s=c 2
s=c
4
1
2 q=0 1
v
4
1
v=c
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EXHAUST GAS 4 W
AXIAL COMPRESSOR H.P./L.P. TURBINE
s
η = 1 – r1– k v1 r= v 2 k=
AIR
COMBUSTION CHAMBER 3 2
( )
P1 η= 1– P 2
âp ĉv
113
(k– 1) k
=1–
( T4 – T1 ) ( T3 – T2 )
Chapter 2: Mass/Energy Balances and Thermodynamics Common Thermodynamic Cycles CARNOT CYCLE
P 2
T = TH
TH
3
s=c 1
T
TL
η=1—
2
T = TL
TH
1 4
TL
2 q=0 s=c
q=0 s=c 4
4
v
TH
3
3 q=0 s=c
q=0 s=c
s=c
REVERSED CARNOT
T
1
TL
s
s
RANKINE CYCLE
REFRIGERATION
3
q in
3
BOILER
1
CONDENSER
4
q in
2
BOILER
CONDENSER 1
2
T p2 = p 3 h4 = h 3
3 p2 = p 3
1
EVAPORATOR
q out
T
3
TURBINE
CONDENSER EXPANSION VALVE 4
4
EVAPORATOR
COMPRESSOR
1 s
s η=
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wC COMPRESSOR
4
PUMP
2
EXPANSION VALVE
2
PUMP
q out CONDENSER
wT
TURBINE
(h 3 — h 4 ) — (h 2 — h 1 )
h — COP ref = 1 h2 —
h3 — h2
114
h4 h1
COP
h2 — h3 HP = h — h 2 1
3 HEAT TRANSFER 3.1 Symbols and Definitions Symbols Symbol
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Description
Units (U.S.)
Units (SI)
ft2
m2
Btu hr -cF
2 W = kg : m K s3 : K
A
Area
C
Heat-capacity rate
cp
Heat capacity at constant pressure
Btu lbm -cF
J = m2 kg : K s 2 : K
D
Diameter
ft or in.
m
d
Wall thickness, width
ft or in.
m
F
Correction factor for heat-exchanger configuration
dimensionless
Fij
Shape factor (radiation)
dimensionless
f
Moody friction factor
dimensionless
g
Acceleration of gravity
h
Convection heat-transfer coefficient
ft sec 2
m s2
Btu hr -ft 2-cF
W = kg m 2 : K s3 : K
Dhfusion
Latent heat of fusion
Btu lbm
J = m2 kg s 2
Dhsubl
Latent heat of sublimation
Btu lbm
J = m2 kg s 2
Dhvap
Latent heat of vaporization
Btu lbm
J = m2 kg s 2
115
Chapter 3: Heat Transfer Symbols (cont'd) Symbol
DH
Units (U.S.)
Change in enthalpy
Btu
Units (SI)
J=
kg : m 2 s2
jH
Colburn factor for heat transfer
k
Thermal conductivity
Btu hr -ft -cF
W = kg : m m : K s3 : K
L
Length
ft or in.
m
m
Mass
lbm
kg
mo
Mass flow rate
lbm hr
kg s
NTU
dimensionless
Number of thermal transfer units
dimensionless
n
Number of tubes (in shell-and-tube heat exchangers)
dimensionless
P
Pressure
P
Thermal efficiency
Q
Heat
Btu
J=
kg : m 2 s2
Qo
Rate of heat transfer
Btu hr
W=
kg : m 2 s3
qo
Heat flux (rate of heat transfer per area)
Btu hr -ft 2
qo l
Rate of heat transfer per unit length
Btu hr -ft
W = kg m 2 s3 W = kg : m m s3
qo gen
Rate of heat generation per volume
Btu hr - ft3
W = kg m3 m : s3
R
Heat-transfer resistance
hr -cF Btu
K = s3 : K W kg : m 2
R
C C Heat-capacity rate ratio e C tube o or e C min o
Rf
Fouling factor
hr -ft 2- o F Btu
m 2 : K = s3 : K W kg
r
Radius
ft or in.
m
T
Temperature
cF or cR
cC or K
Log-mean temperature difference
cF or cR
K
hr
s
Btu hr -ft 2-cF
W = kg m 2 : K s3 : K
DTlm
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Description
psi =
lbf in 2
= Pa
kg N = m2 m : s2
dimensionless
shell
t
Time
U
Overall heat-transfer coefficient
dimensionless
max
116
Chapter 3: Heat Transfer Symbols (cont'd) Symbol
Description
Velocity
ft sec
m s
V
Volume
ft3
m3
x
Distance
ft or in.
m
a
Adsorptivity (radiation)
a
Thermal diffusivity
ft 2 hr
m2 s
b
Coefficient of thermal expansion
1 R
1 K
g
Surface tension
lbf in.
N kg m = s2
d
Thickness
ft or in.
m
e
Emissivity of a body (radiation)
dimensionless
e
Heat exchanger effectiveness
dimensionless
e
Void fraction (packed bed)
dimensionless
Angle
dimensionless
dimensionless
m
Dynamic viscosity
lbm cP or ft-sec
kg Pa : s = m : s
n
Kinematic viscosity
ft 2 hr
m2 s
r
Density
lbm ft3
kg m3
r
Reflectivity (radiation)
v
Stefan-Boltzmann Constant
t
Time constant
t
Transmissivity (radiation)
dimensionless
Heat Transfer Without Phase Change
3.2.1.1 Heat Capacity/Specific Heat (Cp) dT Qo = m c p dt cp =
Btu ft 2- hr -cR 4
W m2 : K4
hr
s dimensionless
3.2 Heat-Transfer Mechanisms
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Units (SI)
u
q, f
3.2.1
Units (U.S.)
DH m DT
117
Chapter 3: Heat Transfer Heat transferred in or out of a flowing material: Qo = mo c p DT
3.2.1.2 Thermal Conductivity (k), Thermal Diffusivity (a), and Kinematic Viscosity (n) Thermal conductivity is a measure of the rate at which a substance transfers thermal energy: qo k= DT d Thermal diffusivity is a measure of the rate at which a thermal disturbance is transmitted through a substance: k a = tc p Kinematic viscosity (also called momentum diffusivity) is the ratio of the dynamic viscosity m to the density of the fluid r: n v=t
3.2.1.3 Conduction The following equations assume that the thermal conductivity is constant. Fourier’s Law of Conduction
dT Total heat flux (rate of heat transfer): Qo = − k A dx Qo dT Heat flux per area (rate of heat transfer per area): qo = A = − k dx Qo Heat flux per unit length (rate of heat transfer per unit length): qo l = L Conduction Through a Plane Wall T1
kA Qo = (T − T ) d 1 2
k T2
where T1 = temperature of one surface of wall
δ
T2 = temperature of the other surface of wall Conduction Through a Composite Wall A (T1 − T2) Qo = di i ki
/
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Q
Chapter 3: Heat Transfer Conduction Through a Cylindrical Wall
Q
T1
2r k L Qo = (T1 − T2) r ln d r2 n 1
T2 r1
k
where L = cylinder length
r2 Cylinder (Length = L)
Conduction Through a Spherical Wall 4r k r r Qo = r − r1 2 (T1 − T2) 2 1 Conduction Through a Cube With Thick Walls (Approximation) -T T Qo . 0.725 Aouter Ainner e inner outer o d where
Aouter Ainner $ 2
Steady Conduction With Internal Energy Generation For a plane wall: d 2 T + qo gen = 0 k dx 2 qo gen d 2 T −T x T +T x2 T ^ x h = 2 k e1 − 2 o + d 2 1 nc m + d 1 2 n d 2 2 d
T(x) T1 qgen q1
where
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q2 −δ
qo 1 + qo 2 = 2 qo gen d dT dT qo 1 = k c dx m and qo 2 = k c dx m −d +d For a long circular cylinder: 1 d c dT m + qo gen = 0 r dr r dr k qo gen r 02 r2 T (r) = 4 k f1 − 2 p + T0 r0 2 qo l0 = r r 0 qo gen W Btu qo l0 = heat transfer rate per unit length in hr -ft or m
119
T2
k
+δ
0
T0 qgen r0
k
qʹ 0
Chapter 3: Heat Transfer Transient Conduction Using the Lumped Capacitance Model The lumped capacitance model is valid if
Fluid h, T∞
hV Bi = k A << 1 s
Body
where
As
Bi = Biot number V = volume of body As = surface area of body For constant fluid temperature T3 and uniform body temperature T: Heat transfer rate at the body surface is
dT Qo = h As (T − T3) = tV cp dt
Temperature variation of the body with time is
T − T3 = (Ti − T3) exp c − xt m
where
tV c p t = h A = time constant s
Ti = initial temperature of the body Total heat transferred to the body at time t is Q total = tV c p (Ti − T) = tV c p (Ti − T3) d1 − exp c − xt mn
3.2.1.4 Convection Newton’s Law of Cooling Qo = h A (Tw − T3) where Tw = wall surface temperature T∞ = bulk fluid temperature
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ρ, V, c P, T
Chapter 3: Heat Transfer 3.2.1.5 Free/Forced Heat-Transfer Coefficients/Correlations Forced Convection: External Flow
Forced Convection—External Flow Correlation
Conditions
1 1 h= L = Nu 0.664 Re L2 Pr 3 L k
Re L 1 10 5
1 h= L 0.8 3 = Nu 0 . 0366 Re Pr L L k
Re L 2 10 5
Geometry
Flat plate in parallel flow (gas or liquid) tu L ReL = n3
Long cylinder in cross flow (gas or liquid) tu D Re D = n3
Short cylinder (gas only) tu D Re D = n3 Sphere in flow (gas or liquid) tu D Re D = n3 Long, flat plate (width L), perpendicular to flow in gas tu L Re L = n3 Packed bed with gas flow – heat transfer to or from the packing 6Vp Dp = A p t us D p Re D p = n (1 − e) where e = void fraction us = superficial velocity Dp = equivalent packing diameter Vp = particle volume Ap = particle surface area
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1 h= D = Nu C Re Dn Pr 3 D k
hD Nu D = k = D 0.85 0.123 Re 0D.651 + c L m Re 0D.5
1 1 hD Nu D = k = 2.0 + 0.60 Re D2 Pr 3
2 h= D 3 = Nu 0 . 20 Re D D k
NuDp = 1−e e
= Nu Dp
1 d 0.5 Re D2 p
+
h Dp = k
1 2 0.2 Re D3 p n Pr 3
h D p 1.075 0.174 1 3 = e Re D p Pr k
121
ReD
C
n
1–4 4–40 40–4000 4000–40,000 40,000–250,000
0.989 0.911 0.683 0.193 0.0266
0.330 0.385 0.466 0.618 0.805
70,000 < ReD < 110,000 L/D < 4
1 < ReD < 70,000 0.6 < Pr < 400
1 < ReD < 400,000
20 1 ReDp 1 10, 000 0.34 < e < 0.78
0.01 1 ReDp 1 10
Chapter 3: Heat Transfer Forced Convection—External Flow (cont'd) Geometry
Correlation
Packed bed with gas flow – heat transfer to or from the containment wall
Nu D p = 1
Conditions
h Dp = k
40 1 ReDp 1 2000 Packing Shape
1
C1 Re D3 p Pr 3 + C 2 Re 0D.8p Pr 0.4
Cylinder-like Sphere-like
C1 2.58 0.203
C2 0.094 0.220
Config.
Reynolds Range
C
m
n
Inline Staggered
10–100 10–100 1000–200,000 ST S $ 0.7
0.8 0.9
0.4 0.4
0 0
0.27
0.63
0
1000–200,000 ST S <2
0.35
0.60
0.2
1000–200,000 ST S $2
0.40
0.60
0
Inline
>200,000
0.021
0.84
0
Staggered
>200,000 Pr > 1
0.022
0.84
0
Staggered
>200,000 Pr = 0.7
---
---
---
Inline
L
Nu D Pr Tube bundle in cross flow
−0.36
−0.25
Pr d Pr n s
=
Staggered
L
n
S C e S T o Re Dm L
Staggered
L
h= D = Nu 0.019 Re 0D.84 D k where u∞ = free stream velocity of the fluid
us = superficial velocity (velocity through the bed if it were empty) Nu = average Nusselt number h
= average heat-transfer coefficient
Prs = Prandtl number based on properties at tube surface In all cases, evaluate fluid properties at average temperature between that of the body and that of the flowing fluid. For tube bundles in cross flow, the following applies: Inline (square pitch):
FLOW
ST
DO
Staggered (triangular pitch): SL
SL
TRANSVERSE ROW
LONGITUDINAL ROW
FLOW
ST SL
DO
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Chapter 3: Heat Transfer Forced Convection: Internal Flow
Forced Convection—Internal Flow Geometry
Correlation
Conditions
NuD = 4.36 NuD = 3.66 Laminar flow in circular tubes, Re < 2300
Turbulent flow in circular tubes
NuD = 1.86 d
Uniform heat flux, fully developed Constant surface temperature, fully developed 1
0.14
Re D $ Pr 3 n 3 n dn n L/D s
JK N KK 0.0668 L ReD Pr OOO n 0.14 D Od 3 n NuD = 3.66 + KK KK1 + 0.04 L ReD Pr OOO ns D L P 0.14
1 n Nu D = 0.023 Re 0D.8 Pr 3 d n3 n s
Nu D = 6.3 + 0.0167 Re 0D.85 Pr 0.93 Liquid metals
= Re D
Nu D = 7.0 + 0.025 Re 0D.8 Pr 0.8
Constant surface temperature, intermediate tube length with entry effects Constant surface temperature, short tube length with entry effects: D 100 < c Re D Pr L m < 1500; Pr > 0.7 Uniform surface temperature or uniform heat flux: Re > 10,000; Pr > 0.7 Uniform heat flux: 0.003 < Pr < 0.05 Constant surface temperature: 0.003 < Pr < 0.05
t um D hD = and Nu D n k
where um = mean velocity of the fluid n3 = viscosity of the fluid at bulk fluid temperature ms = viscosity of the fluid at tube inside surface temperature 4 # cross-sectional area wetted perimeter = For a circular annulus, use the equivalent hydraulic diameter: DH Douter − Dinner
For noncircular ducts, use the equivalent hydraulic diameter: DH =
Use the Moody friction factor f to predict heat-transfer coefficients for turbulent flow: 2 f c Nu m Pr 3 = Re Pr 8 For flow in coiled tubes with Re > 104, the film coefficient for the coiled pipe is: D hcoil = hstraight e1 + 3.5 Dtube o coil
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−1/3 µ − 0.14 µ µw
cp k
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hi d j H= k
124
1
2
3
6 5 4
8
10
20
30
60 50 40
80
100
200
300
600 500 400
1000 800
10
10
20
20
200
3
4
5 6 7 8 1000
30 40 50 60 80 100 3
4
5 6 7 8 1000 Re =
µ
d.u.ρ
2
2
3
3
4
4
5 6 7 8 10,000
5 6 7 8 10,000
Source: Kern, Donald Q., Process Heat Transfer, 1990, p. 834.
200
24 L/D = 36 48 72 120 180 220 360 600
u = VELOCITY ρ = DENSITY jH = COLBURN FACTOR c p = HEAT CAPACITY OF THE FLUID d = INSIDE DIAMETER OF TUBES h i = FILM COEFFICIENT k = THERMAL CONDUCTIVITY L = LENGTH OF PATH µ = VISCOSITY AT THE BULK TEMPERATURE µw = VISCOSITY AT THE TUBE WALL TEMPERATURE
HEATING AND COOLING
30 40 50 60 80 100
Tube-Side Heat-Transfer Curve (Adapted from Sieder and Tate)
2
2
3
3
4
4
5 6 7 8 100,000
5 6 7 8 100,000
2
2
3
3
Chapter 3: Heat Transfer
Chapter 3: Heat Transfer Natural (Free) Convection
Natural (Free) Convection Geometry
Sketch
Nu L = 1.36 _Gr L Pr i5
GrL Pr < 10 4
Nu L = 0.59 _Gr L Pr i4 1
10 4 < Gr L Pr < 10 9
Nu L = 0.10 _Gr L Pr i3
10 9 < Gr L Pr < 1013
1
∞ g
Vertical plate
Conditions
Correlation
1
L
Long, tilted plate with heated surface facing downward Long, horizontal plate with heated surface facing downward Long, horizontal plate with heated surface facing upward Horizontal circular plate with heated surface facing downward
Single, long horizontal cylinder
∞ θ
g
g
L
Nu L = 0.56 _Gr L Pr cos i i4
10 5 < Gr L Pr cos i < 1011 0 # i # 89c
Nu L = 0.58 _Gr L Pr i5
10 6 < Gr L Pr < 1011
Nu L = 0.16 _Gr L Pr i3
710 6 < Gr L Pr < 210 8
Nu L = 0.13 _Gr L Pr i3
5 # 108 < GrL Pr
1
∞
1
L
1
g L
1
g
Nu D = 0.82 _Gr D Pr i5 Pr 0.034 1
D
Nu D = C _Gr D Pr i
n
D g
Pr > 0.5 C GrD • Pr –3 2 10 – 10 1.02 2 4 10 – 10 0.850 104 – 107 0.480 107 – 1012 0.125
∞
1
Nu D = 0.53 `Gr D Pr 2 j4 Thin horizontal wire
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D g
∞
Nu D = C _Gr D Pr i
n
125
n 0.149 0.188 0.250 0.333
Liquid metals, laminar flow GrD • Pr < 10–5 10–5 – 10–3 10–3 – 1 1 – 104
C 0.49 0.71 1.09 1.09
n 0 0.04 0.10 0.20
Chapter 3: Heat Transfer Natural (Free) Convection (cont'd) Geometry
Sketch
Correlation
∞
Vertical cylinder
D
g
Conditions
Nu D = 0.59 _Gr D Pr i4 1
10 4 < Gr D Pr < 10 9
Nu D = 0.10 _Gr D Pr i3
109 < GrD Pr < 1013
1
Diameter D g
Sphere
Vertical cone
Nu D = 2 + 0.392 _Gr D i4 1
Nu L = 0.63 (1 + 0.73 e) _Gr L i4 2 e= 1 z Gr L4 tan 2 1
φ
g
1 < GrD < 105
L
3c < z < 12c 7.5 < log GrL < 8.7 0.2 < e < 0.8
Vertical enclosed space heated from the side
g
0.28 L Pr Nu d = 0.22 c m c 0.2 + Pr Ra d m d
L
L <2 d −3 10 Pr < 10 5 Ra Pr 10 3 < 0.2 d+ Pr 1<
0.29 Pr Nu d = 0.18 c 0.2 + Pr Ra d m
δ
1708 Nu d = 1 + 1.44 d1 − Ra n d Horizontal enclosed space heated from below
Air 1700 < Rad < 108
1 3
+ >d Rad n − 1H 5830
g
δ
1708 Nu d = 1 + 1.44 d1 − Ra n + d 1 3
>d Ra d n − 1H + 2.0 f 5830
For plates and other linear geometry: Ra L = Gr L Pr = For cylinders and spheres:
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L < 10 d Pr < 10 Rad < 1010
2<
−1 4
Ra D = Gr D Pr =
1
Ra 3 1 1 − ln f d p 140 3 Ra d
140
p
g b (Ts − T3) L3 c p n k v2 g b (Ts − T3) D 3 c p v n k v2
126
Water 1700 < Rad < 3.5 • 109
Chapter 3: Heat Transfer where Ts = surface temperature T3 = bulk fluid temperature For an ideal gas:
1 = 1 `T + T j b 2 s 3
where T = absolute temperature, in K or °R
3.2.1.6 Radiation Stefan-Boltzmann Law of Radiation Qo = f v AT 4 where T = absolute temperature, in K or °R Types of Bodies a = absorptivity (ratio of energy absorbed to incident energy) r = reflectivity (ratio of energy reflected to incident energy) t = transmissivity (ratio of energy transmitted to incident energy) a+r+t=1 Opaque body:
t=0
Gray body:
t = 0 and a = e with
Black body:
t = 0 and a = e = 1
0 < a < 1 and 0 < e < 1
Real bodies are frequently approximated as gray bodies. A black body is one that absorbs all energy incident upon it. It also emits radiation at the maximum rate for a body of its size and temperature. Shape Factor Fij (Also Called View Factor or Configuration Factor) Reciprocity relations: Ai Fij = Aj Fji where Ai = surface area of surface i Fij = fraction of the radiation leaving surface i that is intercepted by surface j; 0 # Fij # 1 Summation rule for N surfaces: N
/ Fij = 1
j=1
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Chapter 3: Heat Transfer Net energy exchange by radiation between two bodies: When the body is small in comparison to its surroundings
Qo 12 = f v A `T14 − T 24 j
where T = absolute temperature in K or °R When both bodies are black bodies
Qo 12 = v A F12 `T14 − T 24 j
Net energy exchange by radiation between two gray bodies v `T14 − T 24 j Qo 12 = 1 − f 1 − f 2 1 + 1 + f1 A1 A1 F12 f 2 A 2
A1, T1, ε1 A2, T2, ε2 Q12
Q12 A1, T1, ε1
A2, T2, ε2
For radiative heat loss at night, neglect any return radiation from the clear night sky, i.e., set T2 to 0 K or 0oR. One-dimensional geometry with a thin, low-emissivity shield inserted between two parallel plates: v `T14 − T 24 j Qo 12 = 1 − f 1 − f31 1 − f32 1 − f2 1 + 1 + + + 1 + f1 A1 A1 F13 f31 A3 f32 A3 A3 F32 f2 A2
RADIATION SHIELD Q12
ε3,1
ε3,2
A1, T1,
A2 , T2 ,
ε1
A3, T3
Energy transfer by radiation from reradiating surfaces: Qo = 1 − f 1 + f1 A1
v `T14 − T 24 j 1 − f2 1 + −1 f 2 A2 1 1 A1 F12 + d A F + A F n 1 1R 2 2R
Reradiating surfaces are considered to be insulated or adiabatic.
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ε2
128
A1 , T1 , ε1
Q12
A2 , T2 , ε2
AR , TR , εR
Chapter 3: Heat Transfer Radiation Heat Transfer—Special Considerations Heat input from solar radiation: Qo = a A p F12 qo solar where a = absorptivity Ap = projected area perpendicular to the source Simplified Equation for the Radiation Heat-Transfer Coefficient This equation is in the same form as the equations for the conduction and convection heat-transfer coefficients and is used when there is a combination of heat-transfer coefficients. The radiation heat-transfer coefficient must be calculated at the system temperatures.
where
Qo rad = h rad A _T1 − T2 i
h rad = v F12 `T12 + T 22 j _T1 + T2 i
3.2.1.7 Combination of Heat-Transfer Mechanisms Overall heat-transfer coefficient Uov: Qo = Uov A DT Thermal Resistance DT Qo = R total total 1 R total = U A ov Plane Wall
Cylindrical Wall
l R= kA
R=
Mean diameter:
r ln d r2 n 1
2r k L
Spherical Wall
Convection
r −r R = 4r2k r 1r 2 1
1 R = hA
Douter − D inner D ln e Douter o inner
Cylindrical wall
D lm =
Spherical wall
D D D mean = D outer− Dinner outer inner
Resistance in series: Resistance
Heat Flux
Temperature
R total = / R
Qo total = constant
DTtotal = /DT
Intermediate Temperatures: Qo =
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TA, 1 − TA, 2 TB, 1 − TB, 2 T −T = = ... = i, 1 i, 2 RA RB Ri
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Chapter 3: Heat Transfer Resistance in parallel: Resistance
Heat Flux
Temperature
1 = 1 R total / R
Qo total = /Qo
DTtotal = constant
o 1 R1 Qo 2 R= ...= Qo i Ri Heat flux relations:= DT Q= 2 Heat Transfer from Fins For a straight fin with uniform cross-section (assuming negligible heat transfer from the tip): A Qo = h P k Ac `Tb − T3 j tanh =d L + Pc n
hP k Ac G
Circular (pin) fin:
r D2 P = p D and Ac = 4
Rectangular fin:
P = 2 (w + l) and Ac = w l
where P = perimeter of the exposed fin cross-section Ac = fin cross-sectional area L = length of the fin D = diameter of a circular fin w = width of a rectangular fin l
= height of a rectangular fin
Tb = temperature at the base of the fin T∞ = bulk fluid temperature Pin Fin: T∞ , h
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Rectangular Fin: T∞ ,hT∞ ,h
P= π D D
Tb
πD 2 Ac = 4
L
Tb Tb
130
L L
2 ( w+L) P =P2 = ( w+L) c= wt Ac=Awt t
t w w
Chapter 3: Heat Transfer
3.2.2
Heat Transfer With Phase Change
3.2.2.1 Latent and Sensible Heat Sensible heat: Qsensible = m c p DT Latent heat:
Q latent = m Dh phase change
Heat-transfer rate during phase change: Rate of phase change:
Qo latent = mo Dh phase change
Qo dm = dt Dh phase change
3.2.2.2 Vaporization and Evaporation Boiling Evaporation is occurring at a solid-liquid interface when Ts > Tsat: qo = h `Ts − Tsat j = h DTe
where Ts
= temperature of solid
Tsat,liquid = saturation temperature of liquid at system pressure DTe = excess temperature Pool boiling: Liquid is quiescent; motion near the solid surface is caused by free convection and mixing induced by bubble growth and detachment. Forced convection boiling: Fluid motion is induced by external means in addition to free convection and bubbleinduced mixing. Sub-cooled boiling: Liquid temperature is below the saturation temperature; bubbles forming at the heating surface may condense in the liquid. Saturated boiling: Liquid temperature slightly exceeds the saturation temperature; bubbles forming at the heated surface are propelled through the liquid by buoyant forces.
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Chapter 3: Heat Transfer Typical Pool Boiling Curve for Water at One Atmosphere Surface Heat Flux as a Function of the Excess Temperature FREE CONVECTION
NUCLEATE
ISOLATED BUBBLES
107
TRANSITION
FILM
JETS AND COLUMNS C - CRITICAL HEAT FLUX, q"MAX
q"MAX
106
q"s (W/m2)
P B
105 q"MIN
104
103
BOILING REGIMES
D A ∆Te,A
1
5
-LEIDENFROST POINT, q"MIN
ONB ∆Te,B 10
∆Te,C
∆Te,D
30 120 ∆Te =Ts –Tsat (°C)
1,000
Free convection boiling: There is insufficient vapor in contact with the liquid phase to cause boiling at the saturation temperature. Nucleate boiling: Isolated bubbles form at nucleation sites and separate from the surface; vapor escapes as jets or columns. Equation for nucleate-boiling heat flux (Rohsenow): g `t liq − t vap jH > c p, liq (Ts − Tsat) H qo nucleate = n liq Dh vap > n Csf Dh vap Pr liq c
3
1/2
where
g
= surface tension of vapor-liquid interface
Ts = surface temperature of heater Tsat = saturation temperature of fluid Csf = experimental constant that depends on surface-fluid combination n
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= 1.0 for water and 1.7 for other liquids
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Chapter 3: Heat Transfer Values of the Coefficient Csf for Various Liquid-Surface Combinations
Heating Surface
Csf
Brass Copper Copper (emory-polished) Copper (emory-polished, paraffin-treated) Copper (scored) Platinum Stainless steel (ground and polished) Stainless steel (Teflon pitted) Stainless steel (chemically etched) Stainless steel (mechanically polished) Chromium Copper Copper Chromium Copper (emory-polished) Nickel (emory-polished) Copper (lapped) Copper (emory-rubbed) Chromium Copper Copper (emory-polished) Copper Copper
0.0060 0.013 0.0128 0.0147 0.0068 0.013 0.0080 0.0058 0.0133 0.0132 0.0027 0.00225 0.00305 0.015 0.0154 0.0127 0.0049 0.0074 0.0100 0.013 0.0070 0.0054 0.00275
Fluid Water Water Water Water Water Water Water Water Water Water Ethyl alcohol Isopropyl alcohol n-Butyl alcohol n-Pentane n-Pentane n-Pentane n-Pentane n-Pentane Benzene Carbon tetrachloride Carbon tetrachloride 35% K2CO3 50% K2CO3
Peak heat flux: The maximum (or critical) heat flux (CHF) in nucleate pool boiling: qo max = Ccr Dh vap 9c g t 2vap `t liq − t vap jC
1/4
where Ccr = constant whose value depends on the heater geometry, but generally about 0.15 The critical heat flux is independent of the fluid-heating surface combination, as well as the viscosity, thermal conductivity, and heat capacity of the liquid. It increases with pressure up to about one-third of the critical pressure, and then starts to decrease and becomes zero at the critical pressure. The critical heat flux is proportional to the latent heat of vaporization; large maximum heat fluxes can be obtained using fluids with a large enthalpy of vaporization, such as water. Values of the coefficient Ccr for maximum heat flux:
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Chapter 3: Heat Transfer g `t liq − t vap j c c K1 = g `t liq − t vap j A heater L* = L
Maximum Heat Flux vs. Heater Geometry Ccr
Characteristic Dimension (L)
Range of L*
0.149 18.9 K1 0.12 0.12 L*-0.25 0.11 0.227 L*-0.5
Width or diameter Width or diameter Radius Radius Radius Radius
L* > 27 9 < L* < 20 L* > 1.2 0.15 < L* <1.2 L* > 4.26 0.15 < L* < 4.26
Heater Geometry
Large horizontal flat heater Small horizontal flat heater Large horizontal cylinder Small horizontal cylinder Large sphere Small sphere
Minimum heat flux: This occurs at the Leidenfrost point and is of practical interest because it represents the lower limit for the heat flux in the film boiling regime. Minimum heat flux for a large horizontal plate: RS V1 SS v g `t liq − t vap jWWW 4 W qo min = 0.09 t vap Dh vap SS SS `t liq + t vap j2 WWW T X Transition boiling: Rapid bubble formation results in vapor film on surface and oscillation between film and nucleate boiling. Film boiling: Surface is completely covered by a vapor blanket; includes significant radiation through the vapor film. Heat flux for film boiling on a horizontal cylinder or sphere of diameter D: 1
4 g k 3 t (t − t vap) 8Dh vap + 0.4 c p, vap (Ts − Tsat)B 4 (Ts − Tsat) qo film = Cfilm * vap vap liq n vap D (Ts − Tsat)
For horizontal cylinders:
Cfilm = 0.62
For spheres:
Cfilm = 0.67
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Chapter 3: Heat Transfer 3.2.2.3 Condensation Heat-Transfer Coefficient for the Condensation of a Pure Vapor Evaluate all liquid properties at the average temperature between the saturated temperature and the surface temperature, where rl
= density of the liquid phase of the fluid
ml
= viscosity of the liquid phase of the fluid
kl
= thermal conductivity of the liquid phase of the fluid
Nu = average Nusselt number h
= average heat-transfer coefficient
Tsat = saturation temperature of the fluid Ts
= temperature of the vertical surface
P
= wetted perimeter (width of a vertical plate, or pd, for a vertical tube)
mo
= condensate generation rate
L
= length of the vertical surface
D
= tube outside diameter
Condensation Film Coefficients Geometry
Correlation
Conditions 3 0.25
Condensation on a vertical or angled surface, laminar flow
t 2 g Dh vap L hL H Nu L = k = 0.943 > l n l kl (Tsat − Ts)
Vertical surface
0.25
t 2 g Dh vap L3 cos i hL H Nu L = k = 0.943 > l n l kl (Tsat − Ts)
0.25
Condensation on the outside of a horizontal tube, laminar flow
Condensation on a tall vertical surface or on the outside of a tall vertical tube, turbulent flow
t 2 g Dh vap D 3 hD H Nu D = k = 0.729 > l n l kl (Tsat − Ts)
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Single tube or horizontal layer of tubes
0.25
t 2 g Dh vap D 3 hD H Nu D = k = 0.729 > l N n l kl (Tsat − Ts)
Tube bank with N layers of horizontal tubes, arranged vertically over one another Condensation Reynolds number:
1
2 t l2 g Dh vap D 3 3 h= D 5 = H Nu D 0.0076 Re h > k n l2
0.25
Condensation on a sphere
Inclined surface, angle q measured from the vertical
t 2 g Dh vap D 3 hD H Nu D = k = 0.815 > l n l kl (Tsat − Ts)
135
4 mo Re h = P n > 1800 l h A `Tsat − Ts j Qo = mo = Dh vap Dh vap
Chapter 3: Heat Transfer
3.3 Heat-Transfer Applications 3.3.1
Heat-Exchange Equipment Design
3.3.1.1 Overall Heat-Transfer Coefficient Energy balance around a heat exchanger: Qo = mo cold c p,cold (Tcold,out − Tcold,in) = mo hot c p,hot (Thot,in − Thot,out) Rate of heat transfer in a heat exchanger: Qo = U ov A F DTlm where F = LMTD correction factor based on exchanger configuration (see F-factor charts at the end of section 3.4) Heat-transfer area in a shell-and-tube heat exchanger: Ao = n r Do L where n = total number of tubes Mass flow rate in a shell-and-tube heat exchanger D2 mo = npass r 4i t u where npass = number of tubes in each pass Overall heat-transfer coefficient for concentric tube and shell-and-tube heat exchangers: D ln e Do o R R i 1 = 1 + fi + + fo + 1 Ao ho Ao Uov A ref hi Ai Ai 2 r k L 1 = 1 e Do o + e Do o + Do e Do o + 1 Rfo + h Rfi D Uov hi D i 2 k ln Di i o where Ai = inside area of the tubes Ao = outside area of the tubes Aref = reference areas for the overall heat-transfer coefficient U (usually the outside area) Di = inside diameter of the tubes Do = outside diameter of the tubes hi = convection heat-transfer coefficient for inside the tubes ho = convection heat-transfer coefficient for outside the tubes Rfi = fouling factor for inside the tubes Rfo = fouling factor for outside the tubes
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Chapter 3: Heat Transfer 3.3.1.2 Fouling Factors Fouling factors are defined as: 1 − 1 Rf = h hclean fouled A table of fouling factors is shown in section 2.4. Fouling factors increase with time. Some common approximations for time dependence are as follows: Linear:
Rf (t) = Rf, initial + a t
Falling-rate:
[Rf (t)] 2 = (Rf, initial) 2 + b t
Asymptotic:
Rf (t) = Rf, 3 a1 − e − x k t
where a, b, and t = empirical constants
3.3.1.3 Log-Mean Temperature Difference Temperature Profiles for Counter- and Co-Current Heat Exchangers Without Phase Change For countercurrent flow in heat exchangers: T ∆Q = U OV ∆ A (THOT – TCOLD)
THOT, IN
HOT
TCOLD, OUT
CO
FLUI
LD
D
FLU
ID
THO
TC
T
∆Q
OL
D
∆A
THOT, OUT
TCOLD, IN A
DTlm =
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`Thot, out − Tcold, in j − `Thot, in − Tcold, out j ln f
Thot, out − Tcold, in p Thot, in − Tcold, out
137
Chapter 3: Heat Transfer For co-current (parallel) flow in heat exchangers: T ∆Q = UOV ∆ A (THOT – TCOLD)
THOT, IN
HOT
FLUI D
THO
T
THOT, OUT ∆Q
TCOLD, IN
COLD
TCOLD, OUT
D
T COLD
FLUI
∆A
A
DTlm =
`Thot, out − Tcold, out j − `Thot, in − Tcold, in j ln f
Thot, out − Tcold, out p Thot, in − Tcold, in
Temperature Profiles for Evaporation and Condensation: During the phase change of a pure substance, the temperature remains constant. Evaporation: T THOT, IN
TCOLD, IN = TCOLD, OUT = TEVAP HOT
∆Q = UOV ∆ A (THOT − TEVAP) FLU
ID
T
HOT
THOT, OUT TEVAP
COLD FLUID
∆Q
∆A A
DTlm =
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`Thot, in − Thot, out j
ln f
Thot, in − Tevap p Thot, out − Tevap
138
Chapter 3: Heat Transfer Condensation:
THOT, IN = THOT, OUT = TCOND T ∆Q = UOV ∆ A (TCOND – TCOLD)
HOT FLUID
TCOND
TCOLD, OUT
∆Q LD D T CO
LUI LD F
CO
TCOLD, IN
∆A
A DTlm =
`Tcold, out − Tcold, in j
ln f
Tcond − Tcold, in p Tcond − Tcold, out
Temperature Approach Minimum temperature difference between a hot and a cold fluid:
Tapproach = (Thot - Tcold)min
Co-current:
Tapproach = Thot, out - Tcold, out
Countercurrent, with Cmin = Chot
Tapproach = Thot, out - Tcold, in
Countercurrent, with Cmin = Ccold
Tapproach = Thot, in - Tcold, out
Evaporation
Tapproach = Thot, out - Tevap
Condensation
Tapproach = Tcond - Tcold, out
where = C m= o c p heat-capacity rate. For
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Tapproach " 0 Constant heat-transfer coefficient Uov
A"3
Constant heat-transfer rate Qo
mo " mo min
Constant flow rate mo
Qo " Qo max
139
Chapter 3: Heat Transfer 3.3.1.4 F-Factor (Log-Mean Temperature Correction Factor or LMTC Factor) DTmean = F DTlog mean Temperature efficiency: Ttube, out − Ttube, in P=T shell, in − Ttube, out Ratio of heat-capacity rates: Tshell, in − Tshell, out Ctube = RTS = T Cshell tube, out − Ttube, in where = C m= o c p heat-capacity rate Charts of the F-factors for various configurations are shown at the end of this chapter.
3.3.1.5 Equipment Selection Types of Evaporators
Evaporators Type and Schematic Forced-Circulation Evaporator V
S G C
P F
Description and Applications
Description:
Advantages and Disadvantages Advantages:
• High heat-transfer coefficients Circulating pump withdraws liquor from the flash chamber and forces it past the heat• Positive circulation ing surfaces. Typically, heating tubes are • Relative freedom from salting, scaling, submerged and hydrostatic heads prevents and fouling boiling; evaporation occurs in the flash chamber. Higher heat-transfer rates can be achieved Disadvantages: if boiling is allowed in the tubes but then scal• High cost ing and salt formation may occur. The forced • Power required for circulating pump circulation keeps solids in suspension. Tube velocities are limited by erosion and typically • High hold-up and residence time are 4–10 ft/s. Difficulties: Applications: • Plugging of tube inlets by detached salt deposits • Crystalline products • Corrosion/erosion • Corrosive solutions • Salting due to boiling in the tubes
• Viscous solutions
• Poor circulation due to high head losses
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Chapter 3: Heat Transfer Evaporators Type and Schematic
Short-Tube Vertical Evaporator V
G S F P
C
Description and Applications
Advantages:
Description: Circulation past the heating surface is generated by boiling in the tubes. The liquid then returns to the chamber through a central well. For crystallizing solutions, a propeller placed in the lower end of the central well will keep solids in suspension. Best heat transfer is achieved when liquid level is halfway up the tubes. Scaling occurs in the tubes where evaporation takes place but can be mechanically cleaned, because the tubes are relatively wide (2–3") and short (4–6'). Applications:
F
S
V G C
P
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• High heat-transfer coefficients • Low head room • Easy mechanical descaling • Relatively inexpensive Disadvantages: • Poor heat transfer at low DT • High floor space and weight • High hold-up • Poor heat transfer for viscous liquids Difficulties:
• Clear liquids
Long-Tube Vertical Evaporator (Falling Film)
Advantages and Disadvantages
• Crystalline products (if using propeller)
• Large body makes use of corrosionresistant higher alloys cost-prohibitive
• Noncorrosive liquids
• Corrosion/erosion
• Mild scaling solutions
• Salting due to boiling in the tubes • Poor circulation due to high head losses Advantages:
Description:
• Low hold-up Liquid is fed to the top of vertical tubes. Tubes are narrow (1–2") and long (20–35'). The • Cheapest per unit of capacity liquid flows down the walls as a film. Pressure • Small floor space drop in the tubes is low and the temperature of • Good heat-transfer coefficients at all the liquid is essentially the same as that of the temperatures vapor head. Vapor-liquid separation typically occurs at the bottom. To ensure proper wetting Disadvantages: of the tubes, external recirculation is usually • High head room required unless feed-to-evaporation rates are high. • Not suitable for scaling or salting liquids Applications: • External recirculation usually required • Heat-sensitive materials Difficulties: • Foaming liquids • Poor feed distribution • Low temperature operation • Plugging of the feed distributor if • Large evaporation loads solids are present in the liquid
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Chapter 3: Heat Transfer Evaporators Type and Schematic
Description and Applications
Long-Tube Vertical Evaporator (Rising Film)
Liquid enters the long, vertical heating tubes from the bottom and rises up, propelled by the vapors generated by the evaporation. Boiling occurs in the tubes. On top of the tubes is a small vapor head with almost no liquid holdup, where the liquid and vapor separate. The product line can be connected to the feed line to create recirculation.
S P
ENT’T
Advantages:
Description:
V
• Simple construction and compactness enables use of corrosion-resistant alloys • Low cost • Low hold-up Disadvantages:
• Black liquid (pulp and paper)
• High head room
• High temperature differences
• Not suitable for scaling or salting liquids
• High evaporation loads
C
• Good heat-transfer coefficients at reasonable temperatures
• Small floor space
Applications:
G
Advantages and Disadvantages
• Poor heat-transfer coefficients at lower temperatures
F
Difficulties:
Horizontal Tube Evaporator G
F
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Description: S
V
• Sensitivity to changes in operating conditions Advantages:
C
• Large vapor-liquid disengaging area The evaporating liquid is on the shell side and the heating medium on the tube side. This • Good heat-transfer coefficients evaporator is mainly used for boiler feedwater. • Semiautomatic descaling (bent-tube It has low entrainment and can be designed for type) high steam and vapor temperatures and pres• Low cost (straight-tube type) sures. Tubes can be designed so that they deform when shocked (sprayed with cold water • Minimal head room required while still heated with steam), which causes Disadvantages: the scale to crack off, making this evaporator suitable for severe scaling applications, such • Not suitable for salting liquids as hard water. • Not suitable for scaling liquids (straight-tube type) Applications: • High cost (bent-tube type) • Boiler feedwater • Typically small capacity • Severely scaling liquids (bent-tube type)
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Chapter 3: Heat Transfer Evaporators Type and Schematic
Wiped Film (Agitated Film) Evaporator
• Very short residence time The liquid is spread on the tube wall by a rotating assembly of blades that maintain close • Ability to handle extremely viscous clearance from the wall or ride on the film. materials The heating surface is one large-diameter tube • High feed-to-product ratios without that may be straight or tapered, horizontal or need for recirculation vertical. The expensive construction limits Disadvantages: application to the most difficult materials.
S
• Low heat-transfer coefficients
Applications: BLADES
• Extremely viscous materials • Heat-sensitive materials in which exposure to high temperature must be minimized
C P
Submerged Combustion Evaporator
P
• High installation costs • High operating costs
Advantages:
Description:
V+G
F
Advantages and Disadvantages
Advantages:
Description:
V
F
Description and Applications
• No surface on which scale can form Heat transfer is provided by bubbling combustion gases through the liquid; thus no • Use of special alloys or nonmetallic heat-transfer surfaces are used. The evaporamaterials is possible tor consists of a tank holding the liquid, a Disadvantages: burner, and a gas distributor. The vapor from the evaporation is mixed with the combustion • High entrainment losses gases, making it impossible to recover the heat • No heat recovery from the vapor, from the vapor. resulting in high fuel costs Applications: • Cannot control crystal size in crystallization applications • Highly corrosive solutions • Severely scaling liquids
Source of first 5 schematics: Perry, Robert H. and Cecil H. Chilton, Chemical Engineer's Handbook, 5th ed., New York: McGraw-Hill, 1973. Source of the sixth schematic: Chemical Engineering Research and Design (www.ichemejournals.com), © Institute of Chemical Engineers, published by Elsevier. Source of the seventh schematic: China Manufacturers and Suppliers of Oil, Gas and Petrochemical Equipment, http://www.china-ogpe.com/buyingguide/, January 2016.
Heat-Transfer Calculations for Evaporators While the general heat-transfer equations apply, evaporators have some special considerations: Heat-transfer coefficient: Depends strongly on the temperature difference. Heat-transfer area: Surface area through which the heat transfer takes place, measured on the liquid side.
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Chapter 3: Heat Transfer Apparent temperature difference: The temperature difference can be difficult to determine because it varies along the length of the evaporator tubes. The apparent temperature difference is calculated as the difference between the heating-medium and boiling-liquid temperatures. Heating-medium temperature is the saturation temperature of the steam at steam pressure. (Superheat or subcooling are not considered.) Boiling-liquid temperature is the saturation temperature of the liquid at vapor head pressure—thus assuming a negligible boiling-point rise. Temperature corrected for boiling-point rise: Boiling-point rise is the difference between the boiling point of the solution and the boiling point of the pure solvent at the same pressure. The temperature corrected for the boilingpoint rise is the apparent temperature difference minus the boiling-point rise. This is typically used as the basis for the calculation of heat-transfer coefficients and also as a basis for comparing efficiencies of different evaporator types. Multi-Effect Evaporators Multi-effect evaporators reduce the energy needed for evaporation by using the steam generated in one stage as the heating medium for another stage. The temperature difference for heat transfer in each effect is: DT = Tcond, steam − Tevap, liquid where the condensation temperature of the steam is determined by the pressure in the effect where the steam was generated: Tcond, steam = Tsat at Pn − 1 The evaporation temperature of the liquid is determined by the pressure in the current effect: Tevap, liquid = Tsat at Pn Different feed arrangements are common: 1. In the forward feed configuration, the product and vapor flow are parallel. This configuration is used when the feed is near the boiling point or when the product is heat-sensitive or prone to scaling and requires low temperature differences. One additional advantage is that flow of the product from one effect can be achieved by pressure difference alone, so that no intermediate liquor pumps are needed.
Forward Feed Configuration VAPOR TO CONDENSER I
II
III
IV
STEAM
CONDENSATE THICK LIQUOR
FEED
Source: McCabe, Warren L, Julian Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993, p. 485.
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Chapter 3: Heat Transfer 2. In the backward feed configuration, the product and vapor flow are countercurrent. It is used when the feed is cold, because most of the feed preheating is done by the vapor generated in the previous effect. It is preferred for highly viscous liquor, because the temperature in the effect will be higher as the liquor becomes more concentrated.
Backward Feed Configuration VAPOR TO CONDENSER I
II
III
IV
STEAM
CONDENSATE THICK LIQUOR
FEED
Source: McCabe, Warren L, Julian Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993, p. 485.
3.3.1.6 Insulation Heat loss from cylindrical, insulated pipe: 2 r kins L (T1 − T3) Qo = k r ln d r2 n + h insr 1
3
2
PIPE r1
T1
r2
T2 T∞
dQo Critical insulation radius (where heat loss is at a minimum): dr = 0 2 k r2, crit = hins 3 2 r kins L (T1 − T3) Qo min = k 1 + ln e h insr o 3 1
T2, crit =
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INSULATION
h∞
Surface temperature of the insulation: h r r T1 + T3 3k 2 ln d r2 n 1 T2 = h r r 1 + 3k 2 ln d r2 n 1
kins
•
Q
k T1 + T3 ln e h insr o 3 1
k 1 + ln e h insr o 3 1
145
Chapter 3: Heat Transfer where T1 = surface temperature of the pipe T2 = surface temperature of the insulation T∞ = temperature of surroundings r1 = outer radius of the pipe r2 = outer radius of the insulation kins = thermal conductivity of the insulation h∞ = convective heat-transfer coefficient for the surroundings
3.3.2
Heat-Exchange Equipment Analysis
3.3.2.1 Pressure Drop and Surface Temperatures Pressure Drop for Single-Phase Heat Transfer Tube-side pressure drop for incompressible, single-phase flow in a shell-and-tube exchanger (including pressure drop in the tubes, in the heads for a multipass exchanger, and at the inlet and outlet nozzles): tu DPtubeside = *1.5 + n >2 f c L m d n n + 2.5H4 2 t D nw m
where
2
ut = velocity in the tubes f = Moody friction factor m = 0.25 for laminar flow (Re < 2,100) m = 0.14 for turbulent flow (Re > 2,100) Pressure Drop in Rising Film Evaporators In rising film evaporators, the pressure drop in the tubes is comprised of frictional pressure drop and acceleration pressure drop from the increased velocity of the flow due to volume change during evaporation. If the inlet flow is liquid, the acceleration pressure drop is calculated from: 2 mo 1 1 1 DPa = y d A n d t − t n g vap liq c cross
where DPa = acceleration pressure drop y
= vapor fraction (by weight)
Across = cross-sectional area of the tube
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Chapter 3: Heat Transfer Surface Temperature for Condensation Surface temperature for the condensation of a superheated vapor: U Tsurface = Tcoolant + Tvapor c1 − h m where h = sensible heat-transfer coefficient for the vapor U = overall heat-transfer coefficient, based on h Condensation occurs only if Tsurface # Tsat .
3.3.2.2 Performance Evaluations (Number of Thermal Transfer Units) Heat-Exchanger Effectiveness (e): Qo actual heat − transfer rate = f= o Q max maximum possible heat − transfer rate C hot (Thot, in − Thot, out) Ccold (Tcold, out − Tcold, in) = f = C (T C min (Thot, in − Tcold, in) min hot, in − Tcold, in) Chot = Cmin
Thot, in − Thot, out f hot = T hot, in − Tcold, in
Ccold = Cmin
Tcold, out − Tcold, in fcold = T hot, in − Tcold, in
Heat-capacity rate is C: C
= mo c p
Cmin = smaller of Chot and Ccold Cmax = larger of Chot and Ccold Ratio of heat-capacity rates is RNTU: C RNTU = Cmin max where 0 # RNTU # 1 RNTU = 0 for exchangers with phase change (condensation or evaporation) Number of Transfer Units (NTU) UA NTU = C min
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Chapter 3: Heat Transfer Heat-Exchanger Effectiveness and NTU Relations Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
Flow Geometry
Double Pipe e
f=
1 − exp 8− NTU (1 + R NTU )B 1 + R NTU
NTU NTU =
Co-Current
− ln 81 − f (1 + R NTU )B 1 + R NTU
1.0
0.00
0.8
0.25 0.50 RNTU
0.6
0.75 1.00
0.4
TUBE FLUID
0.2
SHELL FLUID
0.0 0
1
2
3
4
5
NTU
e
f=
1 − exp 8− NTU (1 − R NTU )B 1 − R NTU exp 8− NTU (1 − R NTU )B
− 1 NTU NTU = d f 1 n R NTU − 1 ln R NTU f − 1
NTU RNTU = 1: f = NTU + 1 f RNTU = 1: NTU = 1 − f
1.0
Countercurrent
0.8 1.00 0.75 0.50 RNTU 0.25 0.00
0.6 0.4 0.2 0.0 0
1
2
3
4
5
NTU
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TUBE FLUID
SHELL FLUID
Chapter 3: Heat Transfer
Heat-Exchanger Effectiveness and NTU Relations (cont'd) Flow Geometry Cross-Flow
Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
e
f = 1 − exp >
exp (− NTU 0.78 R NTU ) − 1 H − NTU 0.22 R NTU
1.0
COLD FLUID
0.8
Both Fluids, Unmixed
1.00 0.75 R 0.50 NTU 0.25
0.6 0.4
0.00
HOT FLUID
0.2 0.0 0
1
2
3
4
5
NTU
e
R NTU 1 = 1 1 f 1 − exp (− NTU) + 1 − exp (− NTU R NTU ) − NTU 1.0
0.00
Both Fluids, Mixed
0.50 RNTU 0.75
0.6
1.00
0.4 0.2 0.0 0
1
2
3
4
NTU
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COLD FLUID
0.25
0.8
149
5
HOT FLUID
Chapter 3: Heat Transfer Heat-Exchanger Effectiveness and NTU Relations (cont'd) Flow Geometry
Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
e
1 % − f= R 1 exp 8− R NTU (1 − exp − NTU )B/ NTU
NTU NTU = − ln <1 + R 1 ln (1 − R NTU f)F NTU 1.0
Cmax Mixed
0.00 0.25
0.8
0.50 0.75 1.00
0.6
Cmin Unmixed
RNTU
UNMIXED FLUID C
min
0.4
MIXED FLUID C max
0.2 0.0 0
1
2
3
4
5
NTU
e
f = 1 − exp ( − R
1 NTU
81 − exp (− NTU R NTU )B2
NTU NTU = − 1 81 + R NTU ln (1 − f)B R NTU
Cmax Unmixed
0.00 0.25 0.50 R NTU
1.0 0.8
0.75
Cmin Mixed
1.00
0.6 0.4
UNMIXED FLUID C max
0.2 0.0 0
1
2
3
4
5
NTU
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150
Chapter 3: Heat Transfer Heat-Exchanger Effectiveness and NTU Relations (cont'd) Flow Geometry Shell-and-Tube
Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
e
1 + exp `− NTU 1 + R NTU 2 j 2= + + + 1 R 1 R NTU NTU f 1 − exp `− NTU 1 + R NTU 2 j 1 1 + R NTU
NTU NTU = −
One shell pass; 2, 4, 6 tube passes
RS VW SS 2 − 1 − R WW − + 1 R NTU NTU WW ln SS f2 SS − 1 − R + + 1 R NTU WWW NTU Sf T X
1.0
0.00
0.8
0.25 R 0.50 NTU
0.6
0.75 1.00
SHELL FLUID
0.4
TUBE FLUID
0.2 0.0 0
1
2
3
4
5
NTU
0.00 0.25 0.50 RNTU 0.75 1.00
1.0 0.8 0.6
Two shell passes; 2, 4, 6 tube passes
0.4 0.2
TUBE FLUID
0.0 0
1
2
3
4
NTU
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151
5
Chapter 3: Heat Transfer Heat-Exchanger Effectiveness and NTU Relations (cont'd) Flow Geometry Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution All Exchangers With Evaporation and Condensation
e
f = 1 − exp (− NTU)
NTU NTU = − ln (1 − f) 1.0
RNTU = ø
0.8
RNTU = 0
0.6 0.4 0.2 0.0 0
1
2
3
4
5
NTU
3.4 Tables and Graphs 3.4.1
Tables of Heat-Transfer Data
3.4.1.1 Heat Capacity Typical Ranges of Heat Capacity at Ambient Temperatures Material
Gases at 1 atm Nonorganic liquids Organic liquids Solid nonmetals Metals
Btu lbm -cF
kJ kg : K
0.15–1 0.50–1.20 0.25–0.75 0.20–0.50 0.03–0.20
0.60–4 2–5 1–3 0.80–2 0.12–0.80
3.4.1.2 Thermal Conductivity Typical Ranges of Thermal Conductivity Material
Gases at 1 atm Insulators Nonmetallic liquids Nonmetallic solids Liquid metals Metallic alloys Pure metals
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Btu hr - ft -cF 0.004–0.10 0.02–0.12 0.05–0.40 0.02–1.50 5–45 8–70 30–240
152
W m:K 0.007–0.17 0.03–0.21 0.09–0.70 0.03–2.60 8.7–78 14–120 52–420
Chapter 3: Heat Transfer
Heat-Transfer Properties of Building and Insulating Materials (U.S. Units) Materials
Asbestos
Density
lbm ft 3
Heat Capacity
Btu lbm-cF
36
0.183
Brick (building) Brick (fireclay)
94 165
0.199 0.229
Calcium silicate
—
—
Cardboard (corrugated)
—
—
Cellular glass
—
—
Clay Concrete Cork Cotton Diatomaceous earth Fiberglass
91 144 8 6 10.6
0.270 0.311 —
—
—
Glass (window) Gypsum
156 30
0.160
Kaolin firebrick
19
—
Leather
62
—
Magnesia (85%)
17
—
Mineral wool
10
—
Plywood Rubber Rubber, foam Sand Sawdust Urethane foam Wood (oak—with the grain) Wood (oak—against the grain)
34 72 4.4 95 12 4.4
— 0.332
48
0.568
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0.420 0.251
153
Temperature
cF –300 –100 32 200 800 — — 100 400 600 68 100 600 100 68 68 68 100 100 300 68 68 400 1400 2100 86 100 400 100 600 68 68 68 68 68 100 68 68
Thermal Conductivity
Btu hr-ft-cF 0.055 0.082 0.088 0.111 0.130 0.416 0.578 0.033 0.046 0.060 0.037 0.030 0.073 0.751 0.739 0.025 0.028 0.026 0.026 0.034 0.430 0.045 0.050 0.110 0.260 0.092 0.034 0.044 0.030 0.057 0.069 0.116 0.017 0.191 0.034 0.016 0.210 0.120
Chapter 3: Heat Transfer Heat-Transfer Properties of Building and Insulating Materials (U.S. Units) (cont'd) Material
Wood (pine—with the grain) Wood (pine—across the grain) Wool
Density
Heat Capacity
33
0.657
lbm ft 3
8.5
Btu lbm-cF
—
Temperature
cF
Thermal Conductivity
Btu hr -ft-cF
68 68 100
0.148 0.062 0.027
Heat-Transfer Properties of Building and Insulating Materials (SI Units) Materials
Asbestos
Density
kg m3
Heat Capacity
W kg : K
577
765
Brick (building) Brick (fireclay)
1500 2640
835 960
Calcium silicate
—
—
Cardboard (corrugated)
—
—
Cellular glass
—
—
1460 2300 128 96 170
— 1130 — 1300 —
—
—
Glass (window) Gypsum
2500 481
670 —
Kaolin firebrick
304
—
1000
—
Magnesia (85%)
272
—
Mineral wool
160
—
Clay Concrete Cork Cotton Diatomaceous earth Fiberglass
Leather
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Temperature
cC
–200 –75 0 100 420 — — 40 200 320 20 40 320 40 20 20 20 40 40 150 20 20 200 750 1150 30 40 200 40 320
Thermal Conductivity
W m:K
0.094 0.142 0.152 0.192 0.225 0.720 1.000 0.057 0.080 0.104 0.064 0.052 0.126 1.300 1.279 0.043 0.048 0.045 0.045 0.059 0.744 0.078 0.087 0.190 0.450 0.159 0.059 0.076 0.052 0.099
Chapter 3: Heat Transfer Heat-Transfer Properties of Building and Insulating Materials (SI Units) (cont'd) Density
Materials
Plywood Rubber Rubber, foam Sand Saw dust Urethane foam Wood (oak—with the grain) Wood (oak—against the grain) Wood (pine—with the grain) Wood (pine—across the grain) Wool
kg m3 540 1150 70 1522 192 70 770
Heat Capacity
Temperature
Thermal Conductivity
— 1392 — 1759 — 1050 2380 — 2750 — —
20 20 20 20 20 40 20 20 20 20 40
0.120 0.200 0.030 0.330 0.059 0.028 0.363 0.207 0.256 0.107 0.047
W kg : K
525 136
cC
3.4.1.3 Heat-Transfer Coefficients (Film Coefficients, h) Typical Values of Heat-Transfer Coefficients Without Phase Change Btu hr -ft 2-cF
System Description
Air and gas (free convection) Air and gas (flowing—low pressure) Air and gas (flowing—high pressure) Liquid (free convection) Oils and heavy organics (flowing) Molten salts and brines Heat-transfer fluids and refrigerants Water (flowing)
0.2–4 2–20 20–60 10–175 35–200 100–200 175–450 150–450
W m2 : K 1–20 10–100 100–360 50–1000 200–1200 500–1000 1000–2700 900–2700
Typical Values of Heat-Transfer Coefficients With Phase Change Btu W System Description hr -ft 2-cF m2 : K Condensation Condensing organic vapors 150–250 850–1500 Condensing ammonia 500–800 2800–4500 Condensing steam 700–900 4000–5000 Boiling Boiling organics 125–250 700–1500 Boiling ammonia 200–350 1100–2000 Boiling water 280–500 1600–2800
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W m:K
Chapter 3: Heat Transfer 3.4.1.4 Overall Heat-Transfer Coefficients (U) Typical Overall Heat-Transfer Coefficients for Building Applications Btu W Building Component hr -ft 2-cF m2 : K Brick wall, uninsulated 0.45 2.55 Frame wall, uninsulated 0.25 1.42 Frame wall, with Rockwool 0.07 0.4 Single-pane glass window 1.1 6.2 Double-pane glass window 0.4 2.3 Typical Overall Heat-Transfer Coefficients for Air Coolers System
Finned air cooler/condensing steam Finned air cooler/water Air cooler (fin-fan)/water Air cooler (fin-fan)/light organics Air cooler (fin-fan)/heavy organics Air cooler (fin-fan)/condensing hydrocarbons Air cooler (fin-fan)/condensing ammonia Air cooler (fin-fan)/condensing Freon Air cooler (fin-fan)/gas <5–10 bar/60–130 psig Air cooler (fin-fan)/gas >10–30 bar/130–420 psig
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Btu hr -ft 2-cF
W m2 : K
5–50 4–10 50–80 50–125 12–25 50–100 110 70 10–20 20–50
30–300 25–60 300–450 300–700 70–150 300–600 650 400 60–120 100–300
Chapter 3: Heat Transfer Typical Overall Heat-Transfer Coefficients in Exchangers Without Phase Change (Shell-and-Tube Exchangers) Btu W System hr -ft 2-cF m2 : K Gas/gas 2–10 10–50 Water or brine/compressed gas 10–30 60–200 Water/hydrogen with natural gas 80–125 450–700 Water/brine 100–200 600–1200 Water/water 150–300 850–1700 Water/alcohol, organic solvents 50–150 280–850 Water/gasoline 60–90 340–510 Water/gas oil, distillate 35–60 200–340 Water/heavy oil 10–50 60–300 Freon or ammonia/water 40–90 220–510 Light organics/light organics 40–75 220–425 Medium organics/medium organics 20–60 110–340 Heavy organics/heavy organics 10–40 57–220 Heavy organics/light organics 10–60 57–340 Crude oil/gas oil 30–55 170–310 Typical Overall Heat-Transfer Coefficients in Water-Cooled Condensers (Shell-and-Tube Exchangers) Btu hr -ft 2-cF
Condensing Fluid
Alcohol vapors Ammonia vapors Freon vapors Aqueous vapors Condensing oil Organic vapors Organic vapors with noncondensables Vacuum condensers
45–125 150–250 45–150 200–1000 40–100 125–175 90–125 35–90
W m2 : K 250–700 850–1400 250–850 1100–5600 220–570 700–1000 500–700 200–500
Typical Overall Heat-Transfer Coefficients in Heaters With Condensing Steam (Shell-and-Tube Exchangers) Btu W Heated Fluid hr -ft 2-cF m2 : K Gas 5–50 30–300 Heavy oil 10–50 60–300 Light oil 35–100 200–600 Kerosene/gasoline 50–200 300–1100 Organic Solvents 90–175 500–1000 Water 250–700 1500–4000 ©2017 NCEES
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Chapter 3: Heat Transfer Typical Overall Heat-Transfer Coefficients for Immersed Heating Coils Btu hr -ft 2-cF
Immersed Coils Pool Liquid
Dilute aq. solution Light oil Heavy oil Molten sulfur Molasses/corn syrup Aqueous solution Light oil
W m2 : K
Heating Medium
Natural convection
Agitated
Natural convection
Agitated
Steam Steam Steam Steam Steam Water Water
100–200 35–50 15–30 20–35 15–30 70–100 20–25
130–275 50–100 50–70 35–45 60–80 110–160 35–50
500–1000 200–300 90–170 100–200 70–170 400–600 100–150
700–1600 300–600 300–400 200–250 350–450 400–650 200–300
Typical Overall Heat-Transfer Coefficients for Plate Exchangers Plate Exchangers Hot Fluid Cold Fluid
Light organic Light organic Viscous organic Light organic Viscous organic Light organic Viscous organic Condensing steam Condensing steam Process water Process water Dilute aqueous solutions Condensing steam
Btu hr -ft 2-cF
Light organic Viscous organic Viscous organic Process water Process water Cooling water Cooling water Light organic Viscous organic Process water Cooling water
450–900 45–90 20–35 450–600 45–90 350–800 45–80 450–600 45–90 900–1300 90–1200
W m2 : K 2500–5000 250–500 100–200 2500–3500 250–500 2000–4500 250–450 2500–3500 250–500 5000–7500 500–7000
Cooling water
900–1200
5000–7000
Process water
600–800
3500–4500
Typical Overall Heat-Transfer Coefficients in Evaporators Btu W System hr -ft 2-cF m2 : K Agitated film Newtonian liquid, m = 1 cP 400 2000 Newtonian liquid, m = 100 cP 300 1500 Newtonian liquid, m = 10,000 cP 120 700 Vertical long tube Natural circulation 200–600 1000–3500 Forced circulation 400–1000 2000–6000
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Chapter 3: Heat Transfer Representative Values for Fouling Factors Values for # 125cF/50cC , unless specified otherwise Material
Water Seawater, brine, salt water Seawater, brine, salt water (> 125°F/50°C) River water (brackish River water (muddy, silty) Hard water City/well water Untreated boiler feedwater (> 125°F/50°C) Treated boiler feedwater Untreated cooling tower water Treated cooling tower water Distilled water Hydrocarbons Fuel oil Asphalt and residue Vegetable oil and heavy gas oil Light hydrocarbons Heavy hydrocarbons Other Quenching liquids Refrigerating liquids, brines Heat-transfer media Polymer forming liquids Vaporizing liquids (organic and inorganic) Condensing organic liquids Organic vapors and liquids (including condensing) Gases and Vapors Steam (clean) Steam (oil-bearing) Alcohol vapors Industrial air or other dirty (oil-bearing) gases Diesel exhaust (> 125°F/50°C)
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hr - ft 2 - cF Btu
m2 : K W
0.0005 0.0010 0.0020 0.0030 0.0033 0.0010
0.00009 0.00018 0.00035 0.00053 0.00059 0.00018
0.0010 0.0010 0.0020 0.0010 0.0005
0.00018 0.00018 0.00035 0.00018 0.00009
0.0050 0.0100 0.0030 0.0010 0.0040
0.00088 0.00176 0.00054 0.00018 0.00072
0.0040 0.0010 0.0010 0.0050 0.0020 0.0010 0.0010
0.00070 0.00018 0.00018 0.00090 0.00035 0.00018 0.00018
0.0005 0.0010 0.0005 0.0020 0.0100
0.00009 0.00018 0.00009 0.00035 0.00176
Chapter 3: Heat Transfer 3.4.1.5 Nucleate Boiling Heat-Transfer Data Relative Magnitude of Nucleate Boiling Heat-Transfer Coefficients at 1 atm, Referenced to Value for Water h Fluid hwater Water 1.0 Water with 20% sugar 0.87 Water with 10% Na2SO4 0.94 Water with 26% glycerin 0.83 Water with 55% glycerin 0.75 Water with 24% NaCl 0.61 Isopropanol 0.70 Methanol 0.53 Toluene 0.36 Carbon-tetrachloride 0.35 0.32 n-Butanol Source: Holman, J.P., Heat Transfer, 5th ed., New York: McGraw-Hill,1981, p. 430.
Maximum Heat Flux in Nucleate Boiling (Burnout Heat Flux) Fluid
Water Benzene Propanol Butanol Ethanol Methanol Liquid H2 Liquid N2 Liquid O2
Surface
Copper Chrome-plated copper Steel Copper Aluminum Nickel-plated copper Nickel-plated copper Aluminum Copper Copper Chrome-plated copper Steel Any metal surface Any metal surface Any metal surface
Heat Flux Btu # -3 10 hr -ft 2
DT °F
200–270 300–400 410 43.5 50.5 67–110 79–105 55 80.5 125 111 125 9.53 31.7 47.5
42–50 54 — — 76–90 60–70 — — — — — 4 20 20
Heat Flux
kW m2 620–850 940–1260 1290 130 160 210–340 250–330 170 250 390 350 390 30 100 150
Source: Holman, J.P., Heat Transfer, 5th ed., New York: McGraw-Hill,1981, p. 431.
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DT
°C
23–28 30 — — 42–50 33–39 — — — — — 2 11 11
Chapter 3: Heat Transfer 3.4.1.6 Solar Radiation Data Maximum Expected Solar Radiation at Various North Latitudes
Month
January February March April May June July August September October November December
30° North 24-hr noon avg.
65 75 90 110 120 130 130 125 115 100 80 65
240 270 305 340 360 365 365 360 350 315 270 240
Btu hr ft 2 40° North 24-hr noon avg. 40 170 55 210 75 255 95 300 120 335 130 345 130 350 125 340 105 315 80 270 60 215 45 175
45° North 24-hr noon avg.
30 45 65 90 115 130 130 120 100 75 50 35
135 175 230 280 320 335 340 325 300 245 185 140
30° North 24-hr noon avg.
205 237 284 347 379 410 410 394 363 315 252 205
757 852 962 1073 1136 1151 1151 1136 1104 994 852 757
W m2 40° North 24-hr noon avg. 126 536 174 662 237 804 300 946 379 1057 410 1088 410 1104 394 1073 331 994 252 852 189 678 142 552
45° North 24-hr noon avg.
95 142 205 284 363 410 410 379 315 237 158 110
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 7th ed., New York: McGraw-Hill, 1997, p. 12-23.
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426 552 726 883 1009 1057 1073 1025 946 773 584 442
Chapter 3: Heat Transfer 3.4.1.7 Emissivity ( f ) Emissivity of Building Materials at Ambient Temperature (Unless Specified Otherwise) Material
Emissivity
Asbestos Brick (building) Brick (fireclay) at 2000°F/1100°C Enamel (white) Glass (smooth) Gypsum Marble Oak Oil Plaster Refractory (good radiator) at 1500°F/800°C Refractory (poor radiator) at 1500°F/800°C Roofing paper Rubber (grey, soft) Rubber (hard) Water
0.96 0.93 0.75 0.90 0.94 0.90 0.93 0.90 0.82 0.91 0.85 0.70 0.91 0.86 0.95 0.96
Emissivity of Metals at Ambient and Elevated Temperatures Material
Aluminum, polished Aluminum, anodized Aluminum, surface roofing Brass, polished Brass, oxidized Chromium, polished Copper, polished Copper, oxidized Gold, polished Iron, polished Iron, cast, oxidized Iron, galvanized Iron, oxide Magnesium Stainless steel, polished Stainless steel, weathered Tungsten Zinc, polished Zinc, galvanized ©2017 NCEES
Emissivity at Ambient Temperatures
Emissivity at ~1000°F/540°C
0.04 0.94 0.22 0.10 0.61 0.08 0.02 0.78 0.02 0.06 0.63 0.25 0.90 0.07 0.15 0.85 0.03 0.05 0.25
0.08 0.60 — — — 0.26 0.18 0.77 0.04 0.13 0.76 0.6 0.85 0.18 0.22 0.85 0.10 0.04 —
162
Chapter 3: Heat Transfer
3.4.2
Charts with Heat-Transfer Data Overall Heat-Transfer Coefficients for Various Applications (U.S. Units):
Btu hr -ft 2-cF
0
u r Bt F h 2 ° ft
CONDENSATION AQUEOUS VAPOURS
0
50
CO EF F
IC IE NT ,
U,
60
0 40
CE SS
FL
UI D
BOILING AQUEOUS
PR O
DILUTE AQUEOUS BOILING ORGANICS
0
30
CONDENSATION ORGANIC VAPORS PARAFFINS HEAVY ORGANICS
0 20
MOLTEN SALTS OILS AIR AND GAS HIGH PRESSURE
Btu hr 2 °F U, ft 350
400
300
O
250
200 150
0 10
RESIDUE
100
50 100 AIR AND GAS LOW PRESSURE
TED
MA
I EST
C
FFI
OE
LC
AL VER
T, IEN
200
300
400
500
600
700
800
900
THERMAL FUID BRINES
CONDENSATE BOILING WATER RIVER, WELL, HOT HEAT SEAWATER TRANSFER OIL REFRIGERANTS
AIR AND GAS
STEAM CONDENSING
SERVICE FLUID COEFFICIENT, Btu ft2 °F hr
COOLING TOWER WATER
Source: Reprinted from Chemical Engineering Design, 2nd ed., Gavin Towler and Ray Sinnott, Chapter 19: “Heat Transfer Equipment,” p. 1052, © 2013, with permission from Elsevier.
Overall Heat-Transfer Coefficients for Various Applications (SI Units):
IE
NT ,U
,W
/m 2 °K
CONDENSATION AQUEOUS VAPOURS
CO EF F
IC
00
25
S
FL UI
D
BOILING AQUEOUS
ES OC PR
DILUTE AQUEOUS
OILS AIR AND GAS HIGH PRESSURE RESIDUE
125
0 00
0 175
0
150
0
1 750
0
50
500 1000
1500
2000
2500
500 AIR AND GAS
0 200
000
1
250 AIR AND GAS LOW PRESSURE
EST
1
PARAFFINS HEAVY ORGANICS
TED IMA
OE LL C ERA V O
0 225
2 °K
W/m
FF
0 50
CONDENSATION ORGANIC VAPORS
U, NT, ICIE
0
0 20
BOILING ORGANICS
MOLTEN SALTS
W m2 : K
BRINES RIVER, WELL, SEAWATER
3000
3500
4000
4500
THERMAL FUID HOT HEAT TRANSFER OIL
BOILING WATER
CONDENSATE
STEAM CONDENSING
REFRIGERANTS
COOLING TOWER WATER
SERVICE FLUID COEFFICIENT, W/m2°K
Source: Reprinted from Chemical Engineering Design, 2nd ed., Gavin Towler and Ray Sinnott, Chapter 19: “Heat Transfer Equipment,” p. 1052, © 2013, with permission from Elsevier. ©2017 NCEES
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Chapter 3: Heat Transfer
3.4.3
Heat-Exchanger Design Information TEMA Heat Exchanger Types FRONT-END STATIONARY HEAD TYPES
REAR-END HEAD TYPES
SHELL TYPES
L
E A
FIXED TUBE SHEET LIKE "A" STATIONARY HEAD
ONE-PASS SHELL
CHANNEL AND REMOVABLE COVER
M
F
FIXED TUBE SHEET LIKE "B" STATIONARY HEAD
PASS SHELL WITH LONGITUDINAL BAFFLE
B
N
G SPLIT FLOW
BONNET (INTEGRAL COVER)
P
H C
REMOVABLE TUBE BUNDLE ONLY
CHANNEL INTEGRAL WITH TUBE SHEET AND REMOVABLE COVER
FIXED TUBE SHEET LIKE ''N" STATIONARY HEAD
OUTSIDE PACKED FLOATING HEAD DOUBLE SPLIT FLOW
S
J
FLOATING HEAD WITH BACKING DEVICE DIVIDED FLOW
T
N
PULL-THROUGH FLOATING HEAD CHANNEL INTEGRAL WITH TUBE SHEET AND REMOVABLE COVER
K KETTLE-TYPE REBOILER
U U-TUBE BUNDLE
D
X SPECIAL HIGH-PRESSURE CLOSURE
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W CROSS FLOW
164
EXTERNALLY SEALED FLOATING TUBE SHEET
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F = MTD CORRECTION FACTOR
165
0
15.0 20.0
T1
R = 10.0
0.1
0.2
4.0
T2
3.0
1.6
2.0
P=
0.7
0.8
0.9
1.0
1.2
1.4
1.5
6.0
8.0
t2 – t1 T1 – t1
0.6
1 SHELL PASS
0.7
0.5
R=
T1 – T2 T2 – t1
0.8
F=
Q/Uov A Δ Tlm
2 OR MORE TUBE PASSES
MTD CORRECTION FACTOR
0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY
0.4
t1
t2
2.5
0.3
0.3
0.5
0.6
0.7
0.8
0.9
1.0
3.4.4
0.9
1.0
Chapter 3: Heat Transfer
F-Factor Charts F-FACTORS CHARTS
0.1
0.2
•
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0
R = 10.0
0.1
T2
2.6
P=
1.2
1.4
1.6
1.8
2.0
6.0
8.0
15.0 20.0
F = MTD CORRECTION FACTOR
166 t2 – t1 T1 – t1
2 SHELL PASS
1.0
0.7
0.9
R=
T1 – T2 T2 – t1
0.8
F=
Q/Uov A Δ Tlm
4 OR MORE TUBE PASSES
MTD CORRECTION FACTOR
0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY
0.8
t1
t2
0.3
0.7
T1
0.2
0.6
0.5
0.6
0.7
0.2
0.9
0.3
0.8
0.9
1.0 0.1
1.0
Chapter 3: Heat Transfer
F-FACTORS CHARTS
0.4 0.5
•
3.0
4.0
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F = MTD CORRECTION FACTOR
167
0
15.0 20.0
T2
R = 10.0
0.1
5.0
4.0
P=
1.4
1.6
1.8
2.0
2.5
t2 – t1 T1 – t1
3 SHELL PASSES
0.7
R=
T1 – T2 T2 – t1
0.8
F=
6 OR MORE TUBE PASSES
MTD CORRECTION FACTOR
0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY
1.0
t1
t2
0.3
1.2
T1
0.2
0.8
0.5
0.6
0.7
0.8
0.9
1.0
•
Q/Uov A Δ Tlm
0.9
0.4
0.2
1.0
Chapter 3: Heat Transfer
0.6
3.0
8.0
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0
15.0 20.0
4 SHELLS
R = 10.0
0.1
6.0
1.8
2.0
2.5
F = MTD CORRECTION FACTOR
168
8.0
t2 – t1 T1 – t1
4 SHELL PASSES
1.4
R=
T1 – T2 T2 – t1
0.8
F=
Q/Uov A Δ Tlm
8 OR MORE TUBE PASSES
MTD CORRECTION FACTOR
0.7
1.2
t1
P=
1.6
0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY
0.8
T2
4.0
t2
0.3
1.0
T1
0.2
0.9
0.6
0.5
0.6
0.7
0.8
0.9
1.0 0.4
0.2
1.0
Chapter 3: Heat Transfer
•
3.0
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15.0 20.0
T2
R = 10.0
0.1
4.0
P=
1.6
1.8
2.0
2.5
F = MTD CORRECTION FACTOR
169 t2 – t1 T1 – t1
5 SHELL PASSES
0.7
R=
T1 – T2 T2 – t1
0.8
F=
10 OR MORE TUBE PASSES
MTD CORRECTION FACTOR
0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY
1.2
t1
t2
0.3
1.4
T1
0.2
1.0
5 SHELLS
0
•
Q/Uov A Δ Tlm
0.9
0.8
0.5
0.6
0.7
0.8
0.9
1.0 0.4
0.2
1.0
Chapter 3: Heat Transfer
0.6
3.0
6.0
8.0
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0
15.0 R = 20.0
6 SHELLS
10.0
0.1
6.0 3.0
P=
1.8
2.0
2.5
F = MTD CORRECTION FACTOR
170
8.0
t2 – t1 T1 – t1
6 SHELL PASSES R=
T1 – T2 T2 – t1
0.8
F=
12 OR MORE TUBE PASSES
MTD CORRECTION FACTOR
0.7
1.4
t1
1.6
0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY
1.0
T2
4.0
t2
0.3
1.2
T1
0.2
•
Q/Uov A Δ Tlm
0.9
0.8
0.5
0.6
0.7
0.8
0.9
1.0 0.4
1.0
0.2
Chapter 3: Heat Transfer
0.6
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0.7
0.8
0.9
1.0
0
15.0 20.0
T1
R = 10.0
0.1
6.0
T2
5.0 3.0
0.7
0.8
0.9
1.0
1.2
1.4
1.6
8.0
F = MTD CORRECTION FACTOR
171 R=
T1 – T2 T2 – t1
1 DIVIDED FLOW SHELL PASS
1.8 2.0
t2 – t1 T1 – t1
0.5
0.8
F=
Q/Uov A Δ Tlm
2 OR MORE TUBE PASSES
MTD CORRECTION FACTOR
0.7
0.4
P=
0.6
0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY
0.2
t1
t2
2.5
0.3
0.3
T1
0.2
0.9
1.0
Chapter 3: Heat Transfer
0.1
•
Chapter 3: Heat Transfer
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4 KINETICS 4.1 Symbols and Definitions Symbols Symbol
CA or [A]
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Description
Concentration of component A
Units (U.S.)
Units (SI)
lb mole ft 3 lb mole sec
mol liter mol s
FA
Molar feed of A
DV gr
Gibbs free energy of reaction (molar)
Btu lb mole
J mol
Dht r
Heat of reaction
Btu lb mole
J mol
varies
varies
K
Equilibrium constant
k
Reaction rate constant
M
Molar ratio of initial reactant concentrations
n
Moles of reactant or product
n
Reaction order
P
Pressure (PA = partial pressure of A)
rA
Rate of reaction – based on component A
SAB
Selectivity to A relative to B
SV T
1 Space velocity = space time Temperature
t
Time
d
^ - nh
lb mole 1 n ft 3 sec
^1 - nh
c mol m liter s
dimensionless lb mole
g mol dimensionless
lbf in 2
Pascal
lb mole ft3-sec
g mol L:s dimensionless
173
1 sec °F or °R
1 s °C or K
sec
s
Chapter 4: Kinetics Symbols (con't) Symbol
4.1.1
Description
Units (U.S.)
Units (SI/metric)
θA
Fraction of surface covered by adsorbed species A
V
Reactor volume
XA
Fractional conversion of component A
dimensionless
YA
Yield of A relative to reactant use
dimensionless
eA
Fractional volume change at full conversion of A
dimensionless
x
1 Space time = space velocity
dimensionless ft3
L
sec
s
Reaction Parameters – Nomenclature
A chemical reaction may be expressed by the general equation: aA + bB * cC + dD The rate of reaction of any component is defined as the number of moles of that component formed per unit time per unit volume: dn − rA = − 1 A (negative because A is consumed) V dt − rA = −
dC A dt if V is constant
The rate of reaction is frequently expressed as − rA = k f _C A, C B, ... i The fractional conversion XA is defined as the moles of A reacted per mole of A fed: C −C C X A = AoC A = 1 − C A if V is constant Ao Ao
4.1.2
Temperature Dependence
The Arrhenius equation gives the dependence of k on temperature: −E a
k = Ae R T where
A = pre-exponential or frequency factor J cal Ea = activation energy c mol or mol m R = universal gas constant For values of rate constant ki at two temperatures Ti: Ea =
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RT1 T2 k ln e k1 o 2 _T1 − T2 i
or
E T −T k ln e k1 o = Ra 1T T 2 1 2 2
174
Chapter 4: Kinetics
4.1.3
Reaction Order
If − rA = k C Ax C By , then the reaction is x order with respect to A and y order with respect to B. The overall order is n = x + y.
4.2 Rate Equations in Differential Form for Irreversible Reactions 4.2.1
Zero-Order (A " R) − rA = −
4.2.2
d XA = k C Ao dt
d CA d XA = C Ao = k CA dt dt
and
d XA k CA = = 1 − XAi C Ao k _ dt
Second-Order ^2A " R h − rA = −
4.2.4
and
First-Order ^A " R h − rA = −
4.2.3
d CA d XA = C Ao =k dt dt
d CA d XA = C Ao = k C A2 dt dt
and
Second-Order _ A + bB " R i − rA = −
and
2 d X A k CA 2 = = k C Ao _1 − X A i C Ao dt
d CA = k C A C B = k bC Ao 2 _1 − X A i _ M − X A i dt
− rA = k bC Ao 2 _1 − X A i
2
C when M = b CBo ! 1 Ao
when M = 1
Integrated forms of these equations for constant- and variable-volume batch, plug flow, and CSTR reactors are included later in this chapter.
4.3 Chemical Equilibrium Constants from Rate Constants for Reversible Reactions 4.3.1
Gaseous Phase Reactions
For general reactions: aA + bB * cC + dD At equilibrium:
rFWD = rREV
where rFWD = k1 PA a PB b rREV = k 2 PC c PD d The equilibrium constant is defined as PC c PD d k1 = KP = PA a PB b k 2 LeChatelier's Principle describes the qualitative effect of pressure on equilibrium: For a gaseous reaction, increasing pressure will shift the equilibrium to the side of the reaction in the reaction equation with fewer moles. Changes in pressure have negligible effect on liquid or solid phase reactions.
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Chapter 4: Kinetics
4.3.2
Liquid Phase Reactions
General reaction: aA + bB * cC + dD At equilibrium:
rFWD = rREV
where rFWD = k1 C A a C B b rREV = k 2 CC c C D d The equilibrium constant is defined as = Kc
CC c C D d k1 = CA a CB b k2
When a + b = c + d, KP = Kc , and both are dimensionless. When they are not equal: KP has units of pressure to the power (c + d – a – b). Kc has units of concentration to the power (c + d – a – b). Thus: KP = Kc (R T)(c+d-a-b)
4.3.3
Effect of Temperature on Chemical Equilibrium Constants
The change of the equilibrium constant with temperature is a function of the heat of reaction: d ^ln K h DV = h 2r dT RT The integrated equation is K 1 ln K2 = R 1
#T
T2
1
V e D h2 r o d T T
Over a range where DV h r is nearly constant, this simplifies to: K DV hr 1 1 ln K2 = − R d T − T n 2 1 1
4.3.4
Relationship Between Gibbs Free Energy and the Equilibrium Constant
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DV g DV g r = − RT ln K or ln K = − RTr
176
Chapter 4: Kinetics
4.3.5
Variation of Reaction Property Changes with Temperature
Gibbs-Helmholtz equation: J Dg N Dg K d nO − Dh2 = K 2 RT O How R T changes with temperature at constant pressure K O RT L 2T PP At equilibrium: dP = 0 0
Dh =− R T2
dd
Dg 0 n RT d ^ln K h = dT dT
4.4 Reactor Equations 4.4.1
Batch Reactor
Constant Volume For a well-mixed, constant-volume batch reactor: − rA = −
d CA d XA = CAo dt dt
and
t = C Ao
#0
XA
d XA − rA
Variable Volume For a well-mixed, variable-volume batch reactor: − rA =
C Ao d XA _1 + f A X A i d t
and
t = C Ao
#0
XA
d XA
_− rA i_1 + f A X A i
where eA = fractional volume change at full conversion of A
4.4.2
Half-Life
The half-life of a reaction, t 1 , is the batch time required to reach 50% conversion. 2 d CA 1 n For − rA = − dt = kC A t 1 occurs when C A = 2 C Ao 2 For n = 1 (first order)
ln 2 t1 = k 2
= 1 For n Y
t1 =
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2
− 2n 1 − 1 − (n − 1) k C Ao(n 1)
177
Chapter 4: Kinetics
4.4.3
Flow Reactors, Steady State (Space Time, Space Velocity)
For flow reactors, space time t is defined as the reactor volume divided by the inlet volumetric feed rate. Space velocity SV is the reciprocal of space time, that is, SV = 1/t.
4.4.3.1 Plug-Flow Reactor For a plug-flow reactor, for all values of f A : x=
C Ao VPFR = C Ao FAo
#0
XA
d XA
_− rA i
where FAo = moles of A fed per unit time For a constant volume plug-flow reactor ( f A = 0 ): x =−
#C
CA Ao
d CA − rA
4.4.3.2 Continuous Stirred Tank Reactor (CSTR) For a well-mixed CSTR for all values of eA: x=
C Ao VCSTR C Ao X A = FAo _− rA i
where - rA is evaluated at exit stream conditions For a constant volume CSTR ( f A = 0 ): x=
C Ao − C A _− rA i
4.4.3.3 Continuous Stirred Tank Reactors in Series With a first-order reaction A " R , with no change in volume: x N− reactors = N x individual 1
N N x N - reactors = k >e C Ao o − 1H CA N
or
N C Ao = d1 + k x N n CA N N
where N
= number of CSTRs (equal volume) in series
C A N = concentration of A leaving the Nth CSTR
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Chapter 4: Kinetics
4.5 Integrated Reactor Equations for Irreversible Reactions 4.5.1
Zero-Order Reactions _A " R, − rA = k i
Constant Volume Batch reactor:
k t = CAq XA = CAq − CA Plug-flow reactor or CSTR: k x = C Aq X A = C Aq − C A Variable Volume
V = Vq _1 + f A X A i ,
DV = Vq f A X A
Batch reactor: C C V k t = fAo ln _1 + f A X A i = fAo ln V A A o Plug-flow reactor or CSTR: k x = C Aq X A
4.5.2
First-Order Reactions _ A " R, − rA = k C A i
Constant Volume Batch reactor:
C 1 k t = ln CAo = ln 1 − X = − ln _1 − X A i A A
Plug-flow reactor: C 1 k x = ln CAo = ln 1 − X = − ln _1 − X A i A A CSTR:
kx =
C Ao − C A X = −A CA 1 XA
Variable Volume V = Vq _1 + f A X A i,
DV = Vq f A X A
Batch reactor: DV 1 k t = ln 1 − X = − ln _1 − X A i = − ln d1 − f V n A
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A o
179
Chapter 4: Kinetics Plug-flow reactor: k x = − _1 + f A i ln _1 − X A i − f A X A CSTR: kx =
4.5.3
X A _1 + f A X A i 1 − XA
Second-Order Reactions `2 A " R, − rA = k C A2 j
Constant Volume Batch reactor: XA 1 1 kt = C − C = A Ao C Ao _1 − X A i
or
CA 1 = C Ao 1 + k t C Ao
or
CA 1 = C Ao 1 + k x C Ao
Plug-flow reactor: XA 1 1 kx = C −C = A Ao C Ao _1 − X A i CSTR: kx =
C Ao − C A XA = 2 2 CA C Ao _1 − X A i
Variable Volume V = Vo (1 + eA XA), DV = Vo eA XA Batch reactor:
1 _1 + f A i X A kt = C > + f A ln _1 − X A iH 1 − XA Ao
Plug-flow reactor: 2 XA 1 G k x = C =2f A _1 + f A i ln _1 − X A i + f A 2 X A + _f A + 1 i 1 − X Ao A
CSTR:
X A _1 + f A X A i
2
kx =
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C Ao _1 − X A i
2
180
Chapter 4: Kinetics
4.5.4
Second-Order Reactions _A + bB " R, − rA = k C A C B i
Constant Volume Batch reactor:
CB M − XA = ln k t b C Ao ^ M − 1 h = ln M C A M _1 − X A i k t C Bo = k t b C Ao =
C when M = b CBo ! 1 Ao
C Ao − C A X = − A when M = 1 CA 1 XA
Plug-flow reactor: C M − XA k t b C Ao ^ M − 1 h = ln MCB = ln A M _1 − X A i k x C Bo = k x b C Ao = CSTR:
C Ao − C A X = −A CA 1 XA
C when M = b CBo ! 1 Ao
when M = 1
kx =
C Ao − C A XA = − + − ^ h 8 B X 1 _ C C M 1 bC Ao bC A Ao Ai _ M − XAi A
C when M = b CBo ! 1 Ao
kx =
C Ao − C A XA = 2 2 bCA b C Ao _1 − X A i
when M = 1
4.6 Complex Reactions 4.6.1
First-Order Reversible Reactions (A − rA = −
k1 k2
R)
d CA = k1 C A − k 2 C R dt
k1 C R eq = K= C k 2 C A eq
and
C M = C Ro Ao
d X A k1 ^ M + 1 h = a X A eq − X A k dt M + X A eq − ln f1 −
C A − C A eq ^ M + 1h XA = = − ln p X A eq C Ao − C A eq a M + X k k1 t A eq
At equilibrium, when XA = XAeq , then -ln(0)"∞ and t"∞.
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Chapter 4: Kinetics
4.6.2
Reactions of Shifting Order
From zero order at high CA to first order at low CA: k C − rA = +1 A 1 k2 CA C ln e CAo o + k 2 `C Ao − C A j = k1 t A
C ln e CAo o A
C Ao − C A
= − k2 +
k1 t C Ao − C A
where k1 k 2 = zero-order rate constant k1 = first-order rate constant This form of the rate equation is used for elementary enzyme-catalyzed reactions and for elementary surfacecatalyzed reactions.
4.6.3
Plug-Flow Reactors With Recycle
First Order (eA = 0) k x = C Ao + RC A R + 1 ln (R + 1) C A Second Order (eA = 0)
k C Ao x C Ao `C Ao − C A j = R+1 C A `C Ao + RC A j
where R = recycle ratio, defined as the fraction of the reactor outlet stream that is recycled Relationship Between Overall Conversion and Single-Pass Conversion XAo XAs = 1 + R `1 − XAo j
4.7 Yield and Selectivity Yield Y is defined as the molar ratio of the desired product formed to the reactant that is consumed. Selectivity S is defined as the molar ratio of the formation of desired product to undesired product.
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Chapter 4: Kinetics
4.7.1
Two Irreversible Reactions in Parallel k
k
A "D D (desired) and A "U U (undesired) − rA = −
d CA = kD CA x + kU CA y dt
= rD
d CD = kD CA x dt
= rU
d CU = kU CA y dt
dC YD = instantaneous fractional yield of D = − d CD A N YD = overall fractional yield of D = N −D N Ao A
N A and N D are the final values measured at the reactor outlet N = = S DU overall selectivity to D over U N D U where
N D and N U are the final values measured at the reactor outlet
where
4.7.2
Two First-Order Irreversible Reactions in Series k
k
A "D D "U U (D = desired, U = undesired) − rA = −
d CA = kD CA dt
dC rD = d tD = k D C A − k U C D = rU
d CU = kU CD dt
The maximum yield of D in a plug-flow reactor is kU kU − kD
CD k =e Do C Ao kU
D 1 = at time x max = k − log mean `kU kDj
The maximum yield of D in a CSTR is C D,max 1 = at time x max = 2 C Ao 1 2 >e K U o + 1H kD
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k ln e k U o
1 kD kU
183
Chapter 4: Kinetics
4.8 Catalytic and Surface Reactions Source for material in Sections 4.8–4.8.3.2: Missen, Ronald W., Charles A. Mims, and Bradley A. Saville, Introduction to Chemical Reaction Engineering and Kinetics, New York: Wiley, 1999, pp. 191–198.
4.8.1
Key Assumptions
•
Catalyst surface contains a fixed number of sites.
•
All the catalytic sites are identical.
•
Reactivities of the sites depend only on temperature. They do not depend on the nature or amounts of other materials present on the surface during the reaction.
4.8.2
Surface Reaction Steps
1. Unimolecular surface reaction:
A:s " B:s
A • S is a surface-bound species involving A and site S. Rate is given by: 2. Bimolecular surface reaction: Rate: 3. Eley-Rideal reaction:
_− rA i = kiA
A:s+B:s " C:s+s
_− rA i = kiA iB
A:s+B " C+s
B is a gas-phase species that reacts directly with an adsorbed intermediate. Rate:
_− rA i = kiACB
CB is the gas-phase concentration of B.
4.8.3 Langmuir Adsorption Isotherm (Adsorption without Reaction) 4.8.3.1 Adsorption of Undissociated Single Species Reversible adsorption of species A:
Rate of adsorption of A:
kaA
A+s ? A:s kdA
raA = kaACA _1 − iA i
Rate is proportional to the rate at which molecules strike the surface, concentration in bulk gas, and fraction of unoccupied sites (1–θA) Rate of desorption of A: At equilibrium, raA = rdA Langmuir adsorption isotherm: k where KA = kaA dA
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rdA = kdA iA
_ kaA/kdA i CA k C K C = +A A iA = k +aAk AC = 1 KACA dA aA A 1 + _ kaA/kdA i CA
184
Chapter 4: Kinetics 4.8.3.2 Adsorption of Dissociated Single Species
kaB2
Adsorption of a dissociating diatomic molecule: B2 + 2s ? 2B : s kdB2
Rate of adsorption of B:
Rate of desorption of B:
raB2 = kaB2CB2 _1 − iB i
2
rdB2 = kdB2CB2 iB2
1*
Langmuir adsorption isotherm:
iB =
` KB2CB2 j2
1*
1 + ` KB2CB2 j2 * If n sites are required for n fragment, the exponent becomes 1/n.
kB where KB2 = ka 2 dB2
4.9 Enzyme Kinetics: Michaelis-Menten Source for material in Sections 4.9–4.9.3: Missen, Ronald W., Charles A. Mims, and Bradley A. Saville, Introduction to Chemical Reaction Engineering and Kinetics, New York: Wiley, 1999, pp. 264–276. k1
S + E E ES k−1
kr
ES " P + E
4.9.1
fast slow
Michaelis-Menten Model
S = substrate E = enzyme ES = enzyme-substrate complex P = product Material balance on total enzyme:
CE + CES = CE0
Concentration of complex:
CES =
Define Michaelis constant:
k− KM = k 1 1
Rate of production of product P: Initial rate: Limiting Cases
k1CsCE kCC CC = 1 s+ E0 = s E0 k−1 k1Cs k−1 k −1 + k1 Cs
kC C rp = krCES = Kr E+0 CS M S krCE0CS0 rP0 = `− rS0 j = K + C M S0
Low CS0
CS0 % KM
rP0 = `− rS0 j =
High CS0
CS0 & KM
rP0, max = krCE0
krCE0CS0 KM maximum rate
1 1 = Intermediate rP0 2 krCE0 = 2 rP0, max CS0 K= M
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Chapter 4: Kinetics Michaelis-Menten Equation rP0, maxCS Standard form: rP = K + C M S rP0, maxCS0 rP0 = K + C M S0
Initial rate:
4.9.2
Estimation of KM and Vmax
Linearized Form
KM 1 1 1 rP0 = rP0, max + rP0, max CS0
Lineweaver-Burk Plot
Intercept = 1/rP0, max
Slope = KM/rP0, max
Linearized Form of Integrated Michaelis-Menten Equation
4.9.3
Constant-volume batch reactor: C ln e C S o
r t = 1 − P0, max KM KM CS0 − CS
S0
CS0 − CS
Single-Substrate Inhibition k1
E + S ? ES k−1
k2
ES + S ? ESS k−2
kr
ES " E + P Rate Law
rP =
krCE0CS
C S2
KM + CS + K 2
=
rP0, max CS C S2 + + KM CS K 2
k− K2 = k 2 2
2
C Inhibition occurs due to the term KS in the denominator. 2 Maximum Rate
Occurs at CS = _ KMK2 i2 rP0, max krCE0 rP0, max, apparent = 1 1 = KM 2 KM 2 1 + 2e K o 1 + 2e K o 2 2 1
The maximum rate from the inhibited reaction is lower than rP0, max for the uninhibited reaction.
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5 FLUIDS 5.1 Symbols and Definitions Symbols Symbol
Units (U.S.)
Units (SI)
ft2
m2
A
Area
Ar
Archimedes diameter
dimensionless
C
Fitting characteristic
dimensionless
CD
Drag coefficient
dimensionless
Cv
Valve flow coefficient
dimensionless
cp
Specific heat (constant pressure)
Btu lbm -cF
J kg : K
cv
Specific heat (constant volume)
Btu lbm -cF
J kg : K
D DH d F f
Diameter Hydraulic diameter Diameter (minor) Force Friction factor (Moody or Darcy) Fanning friction factor
fFanning H h hf hf, fitting hL K KE k ©2017 NCEES
Description
ft or in. ft or in. ft or in. lbf dimensionless
m m m N
dimensionless
Total head Height Head loss Head loss in fitting
ft ft ft ft
m m m m
Head loss (general) Loss coefficient Kinetic energy Ratios of specific heats (cp/cv)
ft
m
187
dimensionless Btu
J dimensionless
Chapter 5: Fluids Symbols (con't) Symbol
Units (U.S.)
Units (SI)
Length or thickness
ft or in.
m
MW
Molecular weight
lb lb mole
kg kmol
Ma m
Mach number Mass
mo
Mass flow rate
Ns
Specific speed Net positive suction head available Net positive suction head required
L
NPSHa NPSHr P
Wetted perimeter Potential energy
Pvap
Vapor pressure
R
Radius
R
Universal gas constant
u
dimensionless
Pressure
P PE
Re r S SG T t
©2017 NCEES
Description
lbm
kg
lbm hr rpm ft
kg s rpm m
ft
m
lbf ft 2
Pa
ft Btu psi
m J Pa
ft or in.
m 3
psi-ft Btu lb mole-cR or lb mole-cR
Reynolds number Radius (minor) Rotational speed Specific gravity Temperature Time
dimensionless ft or in. rpm dimensionless °F or °R hr
Velocity
J mol : K m rpm
ft sec
°C or K s m s
ft3
m3
ft 3 sec
m3 s
V
Volume
Vo
Volumetric flow rate
W
Work
lbf • ft
N•m
Wo X x y Y z a
Power
hp
W
ft or in. ft or in. ft or in. dimensionless ft or in. radian
Distance Length, distance, or position Length Expansion factor Length or elevation difference Angle 188
m m m m radian
Chapter 5: Fluids Symbols (con't) Symbol
Description
Units (U.S.)
β
Ratio of small to large diameter
γ
Surface tension
d e
Thickness of a film Absolute roughness Porosity, void fraction, or volume fraction ^0 1 e 1 1 h
e h q μ n3
dimensionless N kg m = s2 m m
lbf ft
Efficiency Angle
Units (SI)
ft ft dimensionless dimensionless radian
radian
Dynamic viscosity
lbm cP or ft-sec
kg Pa : s or s : m
Infinite, plastic, or high shear viscosity
lbm cP or ft-sec
kg Pa : s or s : m
n
Kinematic viscosity
ft 2 hr
m2 s
r
Density
lbm ft 3
kg m3
τ
Stress
lbf ft 2
Pa
xt
Shear stress
lbf ft 2
Pa
t0
Yield stress of fluid
lbf ft 2
Pa
Φ
Sphericity of particle (0 < Φ ≤ 1, where Φ = 1 is a perfect sphere)
dimensionless
5.2 Mechanical-Energy Balance 5.2.1
General
5.2.1.1 Stress, Pressure, and Viscosity Definitions: Stress is x = lim where
^DA " 0h
DF DA
x = surface stress at a point
Pressure is P = − xn where
xn = stress normal at a point
Newton’s Law of Viscosity relates shear stress (τt = stress tangential to the boundary) to the velocity gradient or shear rate (du/dy), using a constant of proportionality known as the dynamic (absolute) viscosity (μ) of the fluid: du x t = n dy ©2017 NCEES
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Chapter 5: Fluids Kinematic viscosity is n v=t Temperature dependence on viscosity is B
For liquids (Andrade equation): n = De T where
D and B = empirical constants
T
= absolute temperature
3
CT2 For gases (Sutherland equation): n = T + S where C and S = empirical constants = absolute temperature
FLUID TYPES AND CHARACTERISTICS
STIC
LA MP
HA
TIC
BING AS
IAN
ON WT
PL DO EU
SHEAR STRESS (τt ) τ0
5.2.1.2 Fluid Types and Characteristics
PS
T
NE
T
N ATA L I D
SHEAR RATE (du/dy)
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Chapter 5: Fluids Classifications of Fluids Fluid Classification
Fluid Type
Behavior
Examples
Viscosity is constant. Water, light oil, blood plasma
du x t = n dy
Newtonian
The term μ is reserved for Newtonian fluids. Apparent viscosity (m) decreases with increased shear stress. n
Time-Independent Viscosity
du x t = m d dy n
Pseudoplastic (shear thinning) n = power law index, n < 1
Dilatant (shear thickening)
m is also known as the consistency coefficient or consistency index Apparent viscosity (m) increases with increased shear stress. n
du x t = m d dy n
Molasses, latex paint, whole blood
Corn starch suspensions
n = power law index, n > 1 Time-Dependent Viscosity
Viscoplastic
Viscoelastic
Thixotropic
Apparent viscosity (m) decreases with duration of stress.
Yogurt, plastisols
Rheopectic
Apparent viscosity (m) increases with duration of stress.
Gypsum paste, kaolin clay suspensions
Bingham plastic
Kelvin material Maxwell material
Behaves as a rigid body until a minimum stress (yield stress) is applied, then reacts as a Newtonian fluid at shear stresses above the yield stress. du x t = x 0 + h dy h = fluid viscosity x 0 = yield stress The materials exhibit both viscous and elastic characteristics during deformation under stress.
5.2.1.3 Surface Tension and Capillary Rise Surface tension g is the force per unit contact length F c= L where F = surface force at the interface L = length of interface
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Mayonnaise, river mud, slurries
Silicone putty
Chapter 5: Fluids The capillary rise, h, is approximated by 4c gc cos a o h =e tgd where h = height of the liquid in the vertical tube α = angle made by the liquid with the wetted tube wall d = the diameter of the capillary tube
5.2.2
Conservation of Mass
Conservation of mass for flow from point 1 to point 2 is mo 1 = mo 2 The continuity equation is ρ1 A1 u1 = ρ2 A2 u2 For an incompressible fluid, ρ1 = ρ2, therefore: A1 u1 = A2 u2
and Vo1 = Vo2
5.2.2.1 The Bernoulli Equation
2 ft -lbf ft= N m m2 = The Bernoulli equation states, in energy per unit mass , or 2 32.2 lbm s kg s2 P gc u 2 t + 2 + g z = constant
For one-dimensional flows (with uniform velocity profiles) through conduits with flow from point 1 to point 2, expressed in: Energy Per Unit Mass (Energy Basis) P1 gc u12 P2 gc u 22 + + + = g z g w 1 c in t t + 2 + g z 2 + loss 2 where win = net shaft work in = power/mass flow rate Energy Per Unit Volume (Pressure Basis) u2t t g z u2t t g z P1 + 21g + g 1 + t win = P2 + 22g + g 2 + t ^loss h c c c c Height of Fluid (Head Basis) P1 gc u12 P2 gc u 22 + + + = z h t g 2g 1 s t g + 2g + z 2 + h L where hs = shaft work head hL = head loss
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Chapter 5: Fluids 5.2.2.2 The Impulse-Momentum Principle The resultant force in a given direction acting on a fluid equals the rate of change of momentum of the fluid, where
/ F = /Vo2 t 2 u2 - /Vo1 t1 u1 /F = result of all external forces acting on the control volume /Vo1 t1 u1 = rate of momentum of the fluid flow entering the control volume in the same direction as
the force
/ Vo 2 t 2 u 2 = rate of momentum of the fluid flow leaving the control volume in the same direction as the
force
5.2.2.3 Energy Line and Hydraulic Grade Line Energy Line (or Energy Grade Line) The energy line (EL) represents the total head available to a fluid and can be expressed as: For inviscid incompressible flow: Pg u2 EL = t gc + 2g + z = constant along a streamline For incompressible flow with losses: Pg u2 EL = t gc + 2g + z − h L Hydraulic Grade Line (or Hydraulic Gradient Line) The hydraulic grade line (HGL) represents the total head available to a fluid, minus the velocity head, and can be expressed as: For inviscid incompressible flow: Pg HGL = t gc + z For incompressible flow with losses: Pg HGL = t gc + z − h L Note: The energy or hydraulic grade lines do not represent “sources” or “sinks” of energy such as the effects of pumps or turbines.
Energy Line and Hydraulic Grade Line for Incompressible Fluid Between Two Points (With Losses) ENERGY
u 12 2g
HYDRAU
LINE
hL
DE LINE
u 22 2g
LIC GRA
P1 gc g
P2 gc g
FLOW z1
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DATUM
193
2 z2
Chapter 5: Fluids
5.3 Flow Behavior 5.3.1
Velocity
Velocity is defined as the rate of change of position with respect to time dx u = dt where x = position Velocity of a Newtonian fluid in a thin film is y du = u u ^ t h = u dy d d THIN FILM u
δ
y
BOUNDARY
The velocity distribution for laminar flow in circular tubes or between planes is u ^ r h = u max =1 − c r m G R 2
where r
= distance from the centerline
R
= radius of the tube or half the distance between the parallel planes
u
= local velocity at r
umax = velocity at the centerline of the duct u
= average velocity in the duct
Flow Conditions Fully turbulent flow
Circular tubes in laminar flow
Parallel planes in laminar flow
1.18
2
1.5
u max = u The shear stress distribution is x r xw = R
where t and tw = shear stresses at radii r and R, respectively
5.3.2
Reynolds Number
Dimensionless number describing flow behavior with the general definition: inertial forces Re = viscous forces
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Chapter 5: Fluids 5.3.2.1 Hydraulic Diameter DH = hydraulic diameter (also known as the characteristic length)
= # cross sectional area 4PA D H 4= wetted perimeter
Hydraulic Diameters for Various Flow Configurations Flow Configuration
Diagram
Hydraulic Diameter DH =
D
D = inside diameter
Through a circular tube
u a
Through a square duct
a
u
a
a
Through a rectangular duct
2ab a+b
u
Through a circular annulus
u
b
D2-D1
D1
D2
Through a partially filled pipe (tube)
2 8rl - c _r - h iB l
r
c
where
c = 2 h _2r - h i
h l
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Chapter 5: Fluids
Hydraulic Diameters for Various Flow Configurations (cont'd) Flow Configuration
Hydraulic Diameter DH =
Diagram FLUID APPROACH VELOCITY (uo)
Around a sphere (or sphere through a fluid)
Sphere diameter
PROJECTED AREA (Ap)
FLUID STREAMLINES
FLUID APPROACH VELOCITY (uO)
Around any object (or an any object through a fluid)
4Ap P PROJECTED AREA (Ap) P = PERIMETER OF SHAPE PRESENTED NORMAL TO THE APPROACH VELOCITY
FLUID STREAMLINES
5.3.2.2 Newtonian Fluid Re =
DH u t n
where u = approach velocity
Various Forms of Reynolds Numbers and Their Units in Circular Conduits (Pipes) Fluid Velocity
u
Fluid Density ρ
Fluid Viscosity μ
ft
ft sec
lbm ft 3
lbm ft-sec
Dut n
m
m s
kg m3
N:s Pa : s or m2 kg or m : s
Dut 32.2n
ft
ft sec
lbm ft 3
lbf-sec ft 2
Dut 123.9 n
in.
ft sec
lbm ft 3
cP
Vo t 22, 700 D n
in.
lbm ft3
cP
Reynolds Number Form
Diameter
Dut n
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196
Volumetric Flow rate
Vo
ft 3 sec
Mass Flow rate
mo
Kinematic Viscosity
ν
Chapter 5: Fluids Various Forms of Reynolds Numbers and Their Units in Circular Conduits (Pipes) (cont'd) Fluid Velocity
Fluid Density ρ
Fluid Viscosity μ
Volumetric Flow rate
lbm ft 3
cP
gpm
Mass Flow rate
Kinematic Viscosity
Reynolds Number Form
Diameter
Vo t 50.6 D n
in.
mo 6.31 D n
in.
Vo t 35.42 D n
in.
Du v
ft
ft sec
ft 2 sec
Du v
m
m/s
m2 s
Du 12v
in.
ft sec
ft 2 sec
Du 7740 v
in.
ft sec
cS
Vo 1, 419, 000 D v
in.
ft 3 sec
cS
Vo 3160 D v
in.
gpm
cS
D
u
Vo
cP
barrels hr
5.3.2.3 Power Law Fluid Re x =
` D n u (2 − n) t j
f K d _3n + 1 i n 8 (n − 1) p 4n n
where n = power law index K = consistency index
5.3.2.4 Bingham Plastic Bingham plastic flow through a pipe: 4Vo t ReBP = r D3 x0 gc p r D n3 f1 + 24Vo n3 where n3 = infinite viscosity, or plastic viscosity, or high shear limiting viscosity x0 = yield stress of the fluid
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ν
lbm hr
cP lbm ft 3
mo
Chapter 5: Fluids Viscosity as a Function of Temperature for a Variety of Gases and Liquids 100 10 SAE
80
AT RIC LU B
60 40
ING
30
OIL (21°
20
) API
10 8 6 4
35 °A PI
3 LA HY ET OL OH LC
) 0% (10
VISCOSITY, CENTIPOISES (cP)
2
DI ST ILL AT E
1 0.8
CA RB
0.6
BE
NZ
0.4 0.3
N-
0.2
AM
MO
NI
EN
E
ACE
TON
PEN
TAN E
A(
LIQ
ON TE T
E (L
RA CH L
OR IDE
IQU
(LIQ
UID
ID)
GASO
WA TE
LINE
R
)
UI
0.1
D)
0.08 0.06
OXYGEN (1 ATM)
0.04 0.03
OSPHERE
AIR AT ATM
0.02
CHLORINE OR NIA VAP
AMMO
0.01
NE
0.008
PROPA
0.006 0.004
0
100
E
PRESSUR
METHANE
E CARBON DIOXID METHANE
HYDROGEN
R WATER VAPO TANE n - PEN
200
R (1 ATM) WATER VAPO
XIDE CARBON DIO
300
400
500
600
TEMPERATURE, °F
Source: Brown, G. G., et. al., Unit Operations, New York: Wiley, 1951, p. 586.
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700
Chapter 5: Fluids 5.3.2.5 Critical Reynolds Number The critical Reynolds number (Rec ) is the minimum Reynolds number at which flow is expected to become turbulent, as shown in the following table: Rec 2100 10
Flow Regime
Flow through a pipe Flow around a sphere Circular flow (rotating cylinder, Taylor-Couette flow)
5.3.3
1708r1 h where the inner cylinder has a diameter (r1) and height (h)
Friction
5.3.3.1 Absolute Roughness and Relative Roughness f Relative roughness is D . Absolute Roughness or Specific Roughness ( f ) of Various Pipes ε
Material
PVC and plastic pipes Copper, lead, brass, aluminum (new) Stainless steel Steel commercial pipe Asphalted cast iron Galvanized iron Smoothed cement New cast iron Well-planed wood Ordinary concrete Worn cast iron Coarse concrete Ordinary wood
ft 0.0000033 0.000005 0.00005 0.00015 0.0004 0.0005 0.001 0.0016 0.0016 0.0026 0.004 0.0065 0.002
5.3.3.2 Friction Factors for Laminar Flow For laminar flow (Re < 2100) 64 f = Re
5.3.3.3 Friction Factors for Turbulent Flow The Colebrook equation JK f K 1 =− 2 log10 KKK D + 2.51 f K 3.7 Re f L
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NO OO OO O P
199
in. 0.00004 0.00006 0.0006 0.0024 0.0048 0.006 0.012 0.019 0.019 0.031 0.048 0.078 0.024
m 1.0E–06 1.5E–06 1.5E–05 6.0E–05 1.2E–04 1.5E–04 3.0E–04 5.0E–04 5.0E–04 8.0E–04 1.2E–03 2.0E–03 6.1E–04
mm 0.001 0.0015 0.015 0.06 0.12 0.15 0.3 0.5 0.5 0.8 1.2 2.0 0.6
Chapter 5: Fluids The Haaland equation is an empirical approximation of the friction factor that does not require iteration, 10
1 =− 1.8 log10 > 6.9 + c f m 9 H f Re 3.7D for the following conditions
f 4 # 10 4 # Re # 108 and 0 # D # 0.05 For fully turbulent flow 1 = 2f 1.74 − 2 log10 c D m f
Moody Friction MOODY FRICTION FACTOR CHART Factor Chart (Also Darcy or Stanton Diagram) 0.1 0.09
LAMINAR FLOW
0.08
CRITICAL ZONE TRANSITION ZONE
COMPLETELY TURBULENT REGIME 0.05
f = 64 Re
0.07
0.04
0.06
0.03
0.05
0.02
0.006
0.03
0.004
f 0.025
0.002
0.02
0.001 0.0008 0.0006 0.0004
0.015
RELATIVE ROUGHNESS
0.01 0.008
Rcr
e D
0.015 0.04
0.0002 0.0001 SMOOTH PIPES
0.01
0.000,001 0.000,005
0.009 0.008
7 9 103
2
3
4 5 67 9 104
2
3
4 5 67 9 2 3 4 5 67 9 105 106 REYNOLDS NUMBER Re
2
3
4 5 67 9
MOODY DIAGRAM. (FROM L.F. MOODY, TRANS. ASME, VOL. 66, 1944.)
5.3.4
Laminar Flow
5.3.4.1 Pressure Drop for Laminar Flow The Hagen-Poiseuille equation for Vo in terms of the pressure drop DPf is = Vo
r R 4 DP f r D 4 DP = 8n L 128n L
f
This relation is valid only for flow in the laminar region.
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107
2
3
0.000,05
0.000,01 4 5 67 9 108
Chapter 5: Fluids
5.3.5
Turbulent Flow
5.3.5.1 Head Loss in Pipe or Conduit The Darcy-Weisbach equation is L u2 u2 = hL f= K D 2g 2g where f
= the Moody friction factor (also called Darcy or Stanton friction factor)
D
= inside diameter of the pipe or hydraulic diameter (DH) of conduit
L
= length over which the pressure drop occurs
L f D = K = the loss coefficient The total loss coefficient for a system is K = / Ki where Ki = the loss coefficient for individual fittings, valves, and other components Changes in K for different pipe internal diameter are 4
D Ka = Kb e Da o b
An alternative formulation is hL =
2f Fanning Lu 2 Dg
where the Fanning friction factor is f f Fanning = 4
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Chapter 5: Fluids Loss Coefficients and Equivalent Lengths for Fittings and Valves Loss Coefficient Equivalent 1 Length* K = K1 + K d 1 + 3 ID Re
Fitting
90o
Elbows
45o
180o
Used as elbows Tees
inches
L D
K1
K3
r Standard c d = 1 m , threaded
35
800
0.40
r Standard c d = 1 m , flanged or welded
20
800
0.25
r Long radius c d = 1.5 m
16
800
0.20
Mitered
100
1000
1.15
r Standard c d = 1 m , threaded
16
500
0.20
r Long radius c d = 1.5 m
13
500
0.15
Mitered, 1 weld (45°)
20
500
0.25
r Standard c d = 1 m , threaded
60
1000
0.70
r Standard c d = 1 m , flanged or welded
30
1000
0.35
r Long radius c d = 1.5 m
25
1000
0.30
Standard, threaded
60
500
0.70
Long radius, threaded
35
800
0.40
Standard, flanged or welded
65
800
0.80
Stub-in branch
85
1000
1.00
Threaded
10
200
0.10
40
150
0.50
5
100
0.05
Run through Flanged or welded Stub-in branch
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n
Chapter 5: Fluids
Loss Coefficients and Equivalent Lengths for Fittings and Valves (cont'd) Loss Coefficient Equivalent 1 Length* K = K1 + K d 1 + 3 ID Re
Fitting
L D
K1
K3
Dopening = 1.0 p Dpipe
10
300
0.10
Reduced trim f
Dopening = 0.9 p Dpipe
12
500
0.15
Reduced trim f
Dopening = 0.8 p Dpipe
20
1000
0.25
Standard
330
1500
4.00
Angle or Y type
165
1000
2.00
Diaphragm
Fully open
165
1000
2.00
Butterfly
Full open
20
800
0.25
Lift
830
2000
10.00
Swing
125
1500
1.50
Tilting disk
40
1000
0.50
Full line size f Gate, ball, or plug
Valves
inches
Globe
Check
* Approximated from the loss coefficient equation using friction factors for fully turbulent flow for pipe sizes 1" through 24"
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n
Chapter 5: Fluids 5.3.5.2 Loss Coefficients for Contraction and Expansion Notes: 1. Reynolds Number (Re) and friction factor (f) are based on inlet velocity. d 2. b = D CONTRACTION Contraction:
FLOW
When
D
d
θ
θ < 45° and i 160 1 Re < 2500, then K = 1.6 c1.2 + Re m e 4 − 1 o sin c 2 m b Re > 2500, then K = 1.6 `0.6 + 1.92f j f
When
1 − b2 p sin i 2 b4
θ > 45° and
1
i 2 160 1 Re < 2500, then K = 1.6 c1.2 + Re m e 4 − 1 o
1 − b2 i 2 Re > 2500, then K = `0.6 + 0.48f j f 4 p
EXPANSION
FLOW
When
D
θ
θ < 45° and i Re < 4000, then K = 5.2 `1 − b 4 j sin c 2 m i Re >4000, then K = 2.6 `1 + 3.2f j `1 − b 4 j sin c 2 m
When
θ > 45° and Re < 4000, then K = 2 `1 − b 4 j Re > 4000, then K = `1 + 3.2f j `1 − b 4 j
2
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D
Chapter 5: Fluids 5.3.5.3 Loss Coefficients for Pipe Entrance and Exit Loss Coefficients Loss Coefficient Fitting
Entrance
Type
K 1 n K = Re1 + K3 d1 + ID inches
Configuration
K1
K∞
Inward projecting or reentrant
FLOW
160
1.0
Sharp-edged
FLOW
160
0.5
Rounded
d
FLOW
160
r
Exit
All geometries
0.0
r/d 0.02 0.04 0.06 0.10 0.15 & up
K∞ 0.28 0.24 0.15 0.09 0.04
1.0
5.3.5.4 Valve Flow Coefficient (Cv) Valve flow coefficient (Cv ) is a value of the relationship between the pressure drop across a valve and the corresponding flow rate: Cv = Vo
SG DP
Also: Cv =
ad 2 K
where gpm a = constant, 29.9 2 in psi
or
m3 0.0352 2 s m Pa
d = effective diameter of the valve, in inches or meters K = loss coefficient Note: Values of Cv are not interchangeable between unit systems. ©2017 NCEES
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Chapter 5: Fluids The estimated flow rate with a known K value is ad 2 DP Vogpm = K SG where ΔP = pressure drop (psi or Pa)
5.3.6
Particle Flow
The force exerted by a fluid that opposes the weight of an immersed object (buoyant force) can be expressed in terms of differential densities: FG =
`t p − t f j gVp gc
where FG = buoyant force rp = particle density rf = fluid density Vp = volume of particle The force exerted by a fluid flowing past a solid body (drag force) can be expressed in terms of a drag coefficient (CD): C t u2 A FD = D 2f g 3 P c where FD = drag force u3 = approach velocity AP = the projected area of object with axes perpendicular to the flow
5.3.6.1 Stokes Law or Stokes Flow For a sphere moving through a fluid at Re << 1: 24 CD = Re where Re =
Dp u3 t n
Dp = the particle diameter In Stokes flow, viscosity can be determined using: n=
D p2 g `tp − tf j 18ut
where ut = terminal (or settling) velocity of particle
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Chapter 5: Fluids Drag Coefficients For spheres in a flowing fluid with Reynolds numbers (1 < Re < 2×105), the Dallavalle equation applies: 2 4.8 o CD = e 0.632 + Re For cylinders in a flowing fluid with Reynolds numbers (1 < Re < 2×105) and with the axis normal to the flow, this equation applies: 2 1.9 o CD = e1.05 + Re DRAG COEFFICIENTS FOR SPHERES AND FLAT DISKS 10
Drag Coefficients for Spheres and Flat Disks
2 8 6 4
V
2
10
CD
d
8 6 4 2
18 6 4
CIRCULAR DISK
STOKES LAW: CD = 24/Re
V
6 4
SPHERE
EFFECT OF SURFACE ROUGHNESS OR MAINSTREAM TURBULENCE
2 -1
10 8
d
2
10-2 -1 2x10
4 6 8
1
2
46 8
10
2
46 8
10
2 2
46 8
10
3 2
46 8
10
4 2
46 8
10
5 2
46 8
10
6 2
46 8
10
7
REYNOLDS NUMBER (Re)
5.3.6.2 Terminal Velocity (ut) For a sphere of diameter Dp, equation applies for any Reynolds number (Newton's Law of falling particles): 4g Dp `tsphere − tf j 3tf CD
ut =
For a small sphere of diameter Dp, following Stokes Law: ut =
D p2 g _tsphere − tf i 18n
5.3.6.3 Reynolds Numbers for Particles in a Fluid Reynolds number when particle velocity (ut) is unknown and Dp, ρp, ρf, and μ are known: Re = ;_14.42 + 1.827 Ar i2 − 3.798E 1
2
where the Archimedes number (Ar) is: Ar =
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Chapter 5: Fluids Reynolds number when particle diameter (Dp ) is unknown and ut, ρs, ρ, and μ are known: 1
1 =d 0.00433 + 0.203 Re
CD 2 − n 0.0658 Re
4n g `tp − tf j CD = Re 3tf2 u t3
where
Reynolds number when fluid viscosity (μ) is unknown and Dp, ut, ρs, and ρ are known: Re = e
2
4.8 o CD − 0.632
Use known quantities to solve for CD.
5.3.6.4 Settling Operations Free Settling: Particle-to-particle interactions are negligible. Hindered Settling: Particle settling is at a reduced rate relative to the settling velocity of a single particle caused by interactions with neighboring particles.
Approximate Regions of Free and Hindered Settling for Given Solids' Concentration and Density 50
wt. % SOLIDS
40 HINDERED
30
20 FREE
10
0
0.1
0.2
0.3
0.4
PARTICLE
—
0.5
0.6
0.7
0.8
FLUID
PARTICLE
If upwards fluid velocity ( uf ) is less than the settling velocity of the particle (us ), then the particles will settle. For settling operations, the settling velocity (us ) equals the terminal velocity (ut).
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Chapter 5: Fluids 5.3.6.5 Settling Diameter For Stokes flow, the smallest diameter spherical particle (Dp ) that will settle is 18nuf Dp = g `tp − tf j For general flow up to Re < 2×105, the smallest diameter spherical particle that will settle is Re n Dp = u t f f where the Reynolds number can be estimated using 1 =d 0.00433 + 0.203 Re
1
CD 2 − n 0.0658 Re
where
CD 4n g `tp − tf j = Re 3tf2 u t3
5.3.6.6 Flow Through Porous Media and Packed Beds A porous, fixed bed of solid particles can be characterized by: L = length of particle bed ds = average particle diameter (diameter of a sphere with the same volume of the particle) Φ = sphericity of particle (0–1) e = porosity or void fraction of the particle bed (dimensionless) Porosity (e) or void fraction: e =
_Total volume − Volume of solids i
Total volume
=
1 − Asolid Avoids = A A
where Asolid = area of the solid phase in a cross-section of area A Avoids = void area in a cross-section of area A Interstitial velocity (actual velocity of fluid within the pores or voids): Vo u = ui e= A e where u = approach velocity (or superficial velocity) Sphericity of a particle (shape factor): U=
surface area of sphere with same volume as particle surface area of particle
Friction loss through porous media: 3 L u 2 _1 − e i o hf = 4 d f d n g e s e3 Reynolds number for flow through porous media: 1 2 d ut Re = 3 n e _ − i o 1 e
where d = the hydraulic diameter
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Chapter 5: Fluids Use the Ergun equation to estimate the pressure loss through a packed bed (ΔP) under laminar and turbulent conditions: 2 2 DP = _150u n i _1 − e i + `1.75t u j e _1 − e i o 3 L e _U ds i e3 `U 2 ds2 j
Typical Shape Factors
Particle
Φ
Spheres Torus Ideal cylinder (h = d) Octahedron Cube Sand (average) Cylinder (h = 5d) Cylinder (h = 10d) Tetrahedron Berl saddles Raschig rings
1.00 0.89 0.87 0.85 0.81 0.75 0.70 0.58 0.67 0.30–0.37 0.26–0.53
5.3.6.7 Fluidization For a fluid passing vertically through a bed of particles, ΔP increases as fluid velocity u increases. The net upward force FB on the bed is FB = AΔP where A = cross-sectional area of the bed At fluidization, net upward force (fluid drag force) equals the weight of the bed (FB = WB), while the fluid velocity above the bed is less than the terminal velocity of the particles (ut). The Reynolds number for a fluidized bed can be approximated by: Re = C1 + C2 Ar − C1 where Ar = Archimedes number 180 _1 − e i C1 = 3.5 3 e C2 = 1.75 where
ϵ = minimum bed void fraction (porosity) at the point of fluidization
The minimum bed void fraction for bed height H at the first indication of fluidization is mparticles e = 1 − H At particles
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Chapter 5: Fluids The minimum fluidization velocity is `tp − tf j gd 2 particles f3 umf = 150 n 1−f note: 1. usuperficial = umf is the incipient fluidization. 2. For large particles, dparticles ≥ 1 mm, inertial effects are important. Use the Ergun equation. The maximum fluidization velocity is
2 `t p − t f j gd particles (Stokes) 18 n − = c 25 m 1 3f for common operating condition u = 30 umf 3 f
usettling = usettling umf
5.3.7
Two-Phase Flow
5.3.7.1 Flow Patterns Bubble or Froth Flow: Bubbles of gas are dispersed throughout the liquid. Gas bubbles move at roughly the same velocity as the liquid.
BUBBLE FLOW
Plug Flow: Alternate plugs of liquid and gas move along the upper portion of the pipe, with mostly liquid moving along the lower portion.
PLUG FLOW
Stratified Flow: Gas flow moves on top and over the liquid forming a distinct, relatively smooth, liquid-gas interface.
STRATIFIED FLOW
Wave Flow: Similar to stratified flow, the fast-moving gas flow creates waves in the liquid phase.
WAVE FLOW
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Chapter 5: Fluids Slug Flow: High-velocity gas picks up waves to form frothy slugs of liquid. These slugs move at higher velocity than the bulk liquid phase and can create dangerous vibrations that can damage equipment.
SLUG FLOW
Annular Flow:As gas velocity increases, liquid forms around the inside of the pipe wall, with the high-velocity gas flowing through the center.
ANNULAR FLOW
Dispersed Flow (or Spray Flow or Mist Flow): Liquid is entrained as fine droplets in the gas phase.
DISPERSED FLOW
5.3.7.2 Flow Regimes Flow Patterns for Horizontal Two-Phase Flow
100,000
DISPERSED
WAVE
10,000
BUBBLE OR FROTH
ANNULAR
By SLUG
STRATIFIED
1,000
PLUG 100
0
1
10
Bx
100
1,000
Source: Baker, Ovid, Oil and Gas Journal, Nov. 10, 1958, p. 156.
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10,000
Chapter 5: Fluids Baker parameters for the previous chart: RS 1V WW 1 S WL SS_tL tG i2 WW n 3 Bx = 531 e W o SS WW f L p 2 G S c S t L3 WW L T X 1 W 1 p By = 2.16 d G nf A _tL tG i2 where A = internal pipe cross-sectional area, in ft2 lbm WG = gas flow rate, in hr lbm WL = liquid flow rate, in hr lbm ρL = liquid density, in 3 ft lbm ρG = gas density, in 3 ft μL = liquid viscosity, in cP
dyn gL = liquid surface tension, in cm
5.3.8
Jet Propulsion
The force produced by jetting action is
JET PROPULSION
F = mo _u2 − u1 i
m, u1
m, u2
Therefore, according to the conservation of mass: F=
Vo2 t2 u2 − V1o t1 u1 gc
JET FORCES ON PLATES JETon ONaAVertical VERTICALPlate PLATE Jet
Jet Forces on Plates JET HORIZONTALPlate PLATE Jet onONa AHorizontal
JETon ONan ANInclined INCLINEDPlate PLATE Jet
h
Fx =
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− mo ujet gc
Fy =
− mo 3 ujet2 − 2g h gc
213
F=
− mo ujet sin i gc
Chapter 5: Fluids
5.3.9
Open-Channel Flow
5.3.9.1 Specific Energy (or Specific Head) u2 E = 2g + y where E = specific energy (or head) u = fluid velocity y = depth of liquid Critical Depth: The depth of flow for a given discharge where the specific energy is at q minimum. 1
2 3 yc = e q o g
where yc = critical depth
Vo q = unit discharge c B m Vo = total discharge, volumetric flow rate B = channel width
Specific Energy Diagram
CHANNEL DEPTH
y
yc
Emin
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E
SPECIFIC ENERGY
214
Chapter 5: Fluids 5.3.9.2 Froude Number u2 = Fr g= yh
Vo T g A3
where A yh = hydraulic depth = T A = cross-sectional area of flow T = width of fluid surface Supercritical flow: Fr > 1 Subcritical flow:
Fr < 1
Critical flow:
Fr = 1
5.3.9.3 Hydraulic Jump Hydraulic Jump
SUPERCRITICAL FLOW (Fr1 > 1)
HYDRAULIC JUMP
y2
FLOW DIRECTION (1) y1
y2 1 2 y1 = 2 `− 1 + 1 + 8Fr1 j where y1 = flow depth at upstream supercritical flow location y2 = flow depth at downstream subcritical flow location Fr1 = Froude number at upstream supercritical flow location Fr2 = Froude number at downstream subcritical flow location
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SUBCRITICAL FLOW (Fr2 < 1)
215
(2)
Chapter 5: Fluids 5.3.9.4 Manning Equation 2 1 l vo = h A R H3 S 2
where vo = discharge volumetric flow rate k = 1.0 for SI units; 1.49 for U.S. units A = cross-sectional area of flow RH = hydraulic radius S = slope of hydraulic surface h = Manning's roughness coefficient
Manning's Roughness Coefficients Material
h
Cast iron pipe Wrought iron pipe Riveted steel pipe Corrugated storm pipe Glass Vitrified sewer pipe Concrete pipe Excavated canal—earth, uniform Natural channel—uniform cross-section
0.013 0.015 0.016 0.024 0.010 0.014 0.013 0.023 0.050
5.3.10 Compressible Flow 5.3.10.1 Isentropic Flow Relationships In an ideal gas for an isentropic process, the following relationships exist between static properties at any two points in the flow: k
k P2 T ^k − 1 h t =e 2o =d 2n t1 P1 T1
cp where k = ratio of specific heats = c v The stagnation temperature T0 at a point in the flow is related to the static temperature: u2 T0 = T + 2 c
p
Energy relation between two points is u2 u2 h1 + 21 = h2 + 22
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Chapter 5: Fluids The relationship between the static and stagnation properties (T0, P0, and r0) at any point in the flow can be expressed as a function of the Mach number (Ma): T0 − = + k 1 Ma 2 T 1 2 k
k
k
1
P0 ^k − 1 h ^ − 1h = d T0 n = c1 + k − 1 Ma 2 m k P 2 T t0 ^k − 1 h T0 ^k − 1h = c1 + k − 1 Ma 2 m t = dT n 2 Compressible flows are often accelerated or decelerated through a nozzle or diffuser. For subsonic flows, the velocity decreases as the flow cross-sectional area increases and vice versa. For supersonic flows, the velocity increases as the flow cross-sectional area increases and decreases as the flow cross-sectional area decreases, The point at which the Mach number is sonic is called the throat; its area is represented by the variable A*. The following area ratio holds for any Mach number: RS V ^k 1 h SS1 + 1 _ k − 1 i Ma 2 WWW 2^k − 1h A = 1 S 2 WW S 1_ + i WW A* Ma SS S W 2 k 1 T X +
where
A = area A* = area at the sonic point (Ma = 1.0)
5.3.10.2 Simplified Isothermal Equation J N tgc A 2 K O P2−P2 K L mo = P1 Oe 1 P 2 o 1 K f c D m + 2 ln e P o O 2 L P
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Chapter 5: Fluids 5.3.10.3 Net Expansion Factors of Gases for Orifices and Nozzles Expansion Factors for Compressible Flow-Through Orifices and Nozzles k = 1.3 approximately [CO2, SO2, H2O (steam), H2S, NH3, N2O, Cl2, CH4, C2H2, and C2H4]
k = 1.4 approximately [Air, H2, O2, N2, CO, NO, and HCl]
1.0
1.0
SQUARE EDGE ORIFICE
Y — EXPANSION FACTOR
0.90
β = 0.2 = 0.5 = 0.6 = 0.7 = 0.75
0.85
0.80
NOZZLE OR VENTURI METER β = 0.2 = 0.5 = 0.6 = 0.7 = 0.75
0.75
0.70
0.65
0.60
0
0.2
0.90
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β = 0.2 = 0.5 = 0.6 = 0.7 = 0.75
0.85
0.80
NOZZLE OR VENTURI METER β = 0.2 = 0.5 = 0.6 = 0.7 = 0.75
0.75
0.70
0.65
0.4
0.6
0.60
∆P PRESSURE RATIO – — P1
where
SQUARE EDGE ORIFICE
0.95
Y — EXPANSION FACTOR
0.95
0
0.2
0.4
∆P PRESSURE RATIO – — P1
Pl = absolute upstream pressure
218
0.6
Chapter 5: Fluids 5.3.10.4 Net Expansion Factors of Gases for Pipes Expansion Factors for Compressible Flow-Through Pipes k = 1.3 approximately [CO2, SO2, H2O (steam), H2S, NH3, N2O, Cl2, CH4, C2H2, and C2H4]
LIMITING FACTORS FOR SONIC VELOCITY k = 1.3
1.0 0.95 0.90
K
0.85 0.80
Y
3.0
2.0 K= 1.5 K = .2 1
K=
0.60 0.55
0 10 K= 40 K= 20 K = 15 K = 10 K = 8.0 K = 6.0 K= 4.0
K=
K=
0.65
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
∆P PRESSURE RATIO – — P1
0.8
0.9
1.0
k = 1.4 approximately [Air, H2, O2, N2, CO, NO, HCl]
1.0
.612 .631 .635
3 4 6
.642 .678 .722
.658 .670 .685
8 10 15
.750 .773 .807
.698 .705 .718
20 40 100
.831 .877 .920
.718 .718 .718
LIMITING FACTORS FOR SONIC VELOCITY k = 1.4
0.95 0.90
K
0.85 0.80
Y
0.75
K
0.4
0.5
.0
0.3
4.0
0.2
1.5
0.1
2.0
0
=3
K= 1.2
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K=
where
K=
0.55
K=
0.65
0 10 K= 40 K= 0 2 K = 15 K = 10 K = 8.0 K = 6.0 K=
0.70
0.60
0.6
∆P PRESSURE RATIO – — P1
Pl = absolute upstream pressure
219
Y
1.2 .525 1.5 .550 2.0 .593
0.75 0.70
∆P — P1
0.7
0.8
0.9
1.0
∆P — P1
Y
1.2 .552 1.5 .576 2.0 .612
.588 .606 .622
3 4 6
.662 .697 .737
.639 .649 .671
8 10 15
.762 .784 .818
.685 .695 .702
20 40 100
.839 .883 .926
.710 .710 .710
Chapter 5: Fluids 5.3.10.5 Critical Pressure Ratio, rc , for Compressible Flow Critical Pressure Ratio Through Nozzles and Venturi Tubes (Only) 0.64
0.60
β 0.85
P1
rc =
P2
0.62
0.80
0.58
0.75 0.70
0.56
0.65 0.60
0.54
1.25
0.50 0.40 0.20 0 1.30
1.35 k=
where
1.40
1.45
Cp
Cv
P1 and P2 = absolute pressures upstream and downstream of the nozzle or venturi tube, respectively
5.3.10.6 Choked Flow Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed. Choked flow occurs when the Mach number is 1.0 at the minimum cross-section area. Mass velocity of gas at choked flow: k+1
m = Cd A
2 k−1 k t1 P1 gc c k + 1 m
where Cd = discharge r1 = density of gas before restriction P1 = pressure of gas before restriction (absolute)
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Chapter 5: Fluids
5.4 Flow Applications 5.4.1
Pumps Types and Subtypes of Pumps RECIPROCATING
POSITIVE DISPLACEMENT
STEAM POWER CONTROLLED VOLUME PISTON
BLOW CASE ROTARY
VANE SCREW FLEXIBLE MEMBER CIRCUMFERENTIAL PISTON LOBE GEAR
CENTRIFUGAL
CANNED PUMP OVERHUNG IMPELLER IMPELLER BETWEEN BEARINGS TURBINE TYPE REGENERATIVE TURBINE
SPECIAL EFFECT
REVERSE CENTRIFUGAL ROTATING CASING
PUMPS
KINETIC
5.4.1.1 Affinity Laws for Pumps, Fans, and Compressors For small changes in impeller diameter (changes not to exceed 20%): D1 V1o = = D2 Vo2
H1 H2
and
BP1 D13 = BP2 D23
For variations in speed (constant impeller diameter): S1 V1o = = S2 Vo2
H1 H2
and
BP1 S13 = BP2 S23
where BP = brake power D = impeller or wheel diameter H = head (height of fluid) Vo = volumetric capacity S = speed (rpm)
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Chapter 5: Fluids 5.4.1.2 Pump Similitude Predicting Performance of Homologous Pumps
Volume capacity estimate: 3 2 0.5 V1o S1 D1 D1 H1 = = e o e o e o D2 H2 Vo2 S2 D2
Pressure or head estimate: 2
2
H1 S D =e 1o e 1o H2 D2 S2
Brake power estimate: 3
5
2
1.5
t D BP1 t1 S1 D H = = e o e 1 o t1 e 1 o e 1 o BP2 t2 S2 D2 H2 2 D2
Impeller or wheel speed estimate: 0.5 0.5 0.75 Vo2 S1 D2 H1 H1 = = e o e o e o S2 D1 H2 H2 V1o
5.4.1.3 Pump Head Pump head (Hp) is a variation of the head-basis Bernoulli equation: Hp =
` Pd − Ps j gc
tg
+
`ud2 − us2 j + ` zd − zs j − hf 2g
where Ps = suction pressure at suction reference point (absolute) Pd = discharge pressure at discharge reference point (absolute) us = velocity at the pump suction ud = velocity at the pump discharge zs = elevation at the suction reference point zd = elevation at the discharge reference point hf = friction loss in the pipe between the reference points
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Chapter 5: Fluids Centrifugal Pump
PUMP HEAD
SUCTION REFERENCE POINT
Ps
DISCHARGE REFERENCE POINT
Pd
Zs
Ud
Zd
Us
CENTRIFUGAL PUMP
Pump Head in Common Units
Pump Head Calculations U.S. Units
Component
Hp p u z g
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Hp =
2.31 _ pd − ps i `ud2 − us2 j + + _ zd − zs i − hf 2g SG ft psi
Hp =
` pd − ps j
t
+
`ud2 − us2 j + ` zd − zs j − hf 2g
m Pa m s
ft sec ft 32.2
SI Units
m
ft sec 2
9.81
m s2
hf
ft
m
r
lbm ft3
kg m3
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Chapter 5: Fluids 5.4.1.4 Pump Curve A pump curve, head-capacity curve, or H-Q curve is provided by pump manufacturers.
Pump Curve for a Fixed Impeller Diameter and Pump Speed
POWER
CY EN
BEP
EF FIC I
TOTAL HEAD
HEAD
OWER
BRAKE P
NPSH r
VOLUMETRIC CAPACITY
where
BEP = best operating point
5.4.1.5 Net-Positive Suction Head (NPSH) NPSH: Total suction head minus the vapor pressure of the liquid being pumped (units are in height of liquid (absolute) and the referenced datum is the suction nozzle.) NPSHa: Net-positive suction head available to the pump NPSHr: Net-positive suction head required by the pump (provided by the pump manufacturer) For suction lift: NPSHa = ha – hvap – hst – hL For flooded suction: NPSHa = ha – hvap + hst – hL where ha = absolute pressure (in height of liquid) on the surface of the liquid supply level hvap = vapor pressure (in height of liquid) of the liquid at the temperature being pumped hst = static height of liquid supply, either above or below the pump centerline or impeller eye hL = suction line losses in height of liquid
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Chapter 5: Fluids 5.4.1.6 Pump Power Power required to move the fluid, or water power (WP): Flow rate (gpm) # H (ft) # t d
U.S. units
WP (horsepower) =
Metric units
WP (W) = Flow rate c ms m # H ^mh # t e
246, 780
3
lbm n ft3
kg m 3 o # gd 2 n s m
Power required at the pump shaft, or brake power (BP): WP BP = h pump Power required by the pump driver, or supplied power (SP): WP SP = h pump h driver h transmission
5.4.1.7 Temperature Rise in a Centrifugal Pump DT =
BP `1 − hpump j cp Vo t
5.4.1.8 Specific Speed (Ns ) at the BEP S Vo 0.5 H 0.75 head (H) and flow rate ^Vo h are taken at the BEP Ns =
where
5.4.1.9 Suction-Specific Speed (Ns ) at the BEP Ns =
S Vo 0.5 0.75 _ NPSHr i
5.4.1.10 System Curves System curves are developed from different flow rates through a given system, using the Bernoulli equation. u2 Note: The velocity head terms are usually omitted because the changes in 2g are negligible. Hs = pressure head + static head (hs ) + pipe losses* (hf ) *Include friction, entrance, and exit losses: Hs =
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_ PB − PA igc tg
+ hs + hf
225
Chapter 5: Fluids Simple Pumping System
STATIC HEAD ( H S )
PB
PA
PUMP
System Curve Plot
TOTAL HEAD
SYSTEM CURVE
PRESSURE HEAD
STATIC HEAD (hs ) CAPACITY
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Chapter 5: Fluids 5.4.1.11 Pumps in Parallel and Series Operating point: Centrifugal pumps operate at the intersection of the pump curve and the system curve. For pumps in parallel, capacities are added horizontally. For pumps in series, heads are added vertically:
Pumps Operating in Parallel COMBINED (A+B) PUMP CURVE
TOTAL HEAD
PUMP B
OPERATING POINT
PUMP A A
B A+B
E SYSTEM CURV
CAPACITY
Pumps Operating in Series COMBINED (A+B) PUMP CURVE
TOTAL HEAD
OPERATING POINT SYSTEM CURVE
PUMP B
PUMP A
B
A+B
A
CAPACITY
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Chapter 5: Fluids
5.4.2
Fans, Compressors, and Turbines
5.4.2.1 Fans Typical backward curved fans: DPVo Wo = h f
Δp POWER
where Wo = fan power DP = pressure rise
f
hf = fan efficiency
CONSTANT N, D, ρ FLOW RATE
5.4.2.2 Compressors Compressors consume power to add energy to the working fluid. This addition of energy results in an increase in fluid pressure (head). For an adiabatic compressor with DPE = 0 and negligible DKE: Wocomp =− mo `he − hi j
INLET
For an ideal gas with constant specific heats: Wocomp =− mc o p `Te − Ti j
COMPRESSOR
Per unit mass: wcomp =− cp `Te − Ti j
EXIT
Compressor Isentropic Efficiency w T −T hC = ws = Tes − Ti a e i where wa = actual compressor work per unit mass ws = isentropic compressor work per unit mass Tes = isentropic exit temperature For a compressor where DKE is included: u 2 − u i2 n = − d u 2 − u i2 n mo cp `Te − Ti j + e Wocomp = − mo d he − hi + e 2 2
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•
W in
Chapter 5: Fluids Adiabatic compression: Wocomp =
1
1− 1mo Pi k mo RTi k >d Pe n k - 1H >e Pe o k − 1H = _ k − 1 i ti hC Pi MW _ k - 1 i hC ti 1
where Wocomp = fluid or gas power Pi
= inlet or suction pressure
Pe
= exit or discharge pressure
ri
= inlet gas density
hC
= isentropic compressor efficiency
Isothermal compression: Pe mo RTi mo Pi Pe = = Wocomp MW hC ln Pi ti hC ln ti where Wocomp, Pe, Pi, and hC = as defined for adiabatic compression, above R = univeral gas constant Ti = inlet temperature of gas
5.4.2.3 Turbines Turbines produce power by extracting energy from a working fluid. The energy loss shows up as a decrease in fluid pressure (head). For an adiabatic turbine with DPE = 0 and negligible DKE: Woturb = mo ` hi − he j
INLET
For an ideal gas with constant specific heats: Woturb = mc o p `Ti − Te j
TURBINE
Per unit mass: wturb = cp `Ti − Te j
EXIT
Turbine isentropic efficiency: w T−T hT = wa = Ti − Te s i es For a turbine where DKE is included: u 2 − u i2 n = d u 2 − u i2 n mo cp `Te − Ti j + e Woturb = mo d he − hi + e 2 2
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•
Wout
Chapter 5: Fluids
5.4.3
Control Valves
5.4.3.1 Control Valve Flow Characteristics Flow characteristic of a control valve: The relationship between valve capacity and valve stem travel (or valve lift).
Control Valve Flow Versus Stem Travel 100
QUICK OPENING
PERCENT OF MAXIMUM FLOW
80 LINEAR
60
40 MODIFIED PARABOLIC
20
EQUAL PERCENTAGE 0
20
40
60
80
100
PERCENT OF RATED STEM TRAVEL
Linear:
Flow capacity increases linearly with stem travel.
Equal Percentage: Flow capacity increases exponentially with stem travel. Equal increments of stem travel produce equal percentage changes in the existing CV. Modified Parabolic: Valve characteristic is approximately midway between linear and equal-percentage characteristics. It provides fine throttling at low flow capacities and approximately linear characteristics at higher flow capacities. Quick Opening:
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Provides large changes in flow for very small changes in early stem travel.
230
Chapter 5: Fluids 5.4.3.2 Control Valve Sizing (Traditional Method) Control Valve Sizing Equations for Liquids (Incompressible Flow) Use
Equation
Vo = CV
DP SG
CV = Vo
SG DP
Notes
Basic sizing equation; does not consider viscosity effects or valve recovery capabilities
Flow coefficient Corrected flow coefficient for viscosity Maximum allowable differential pressure
CV − Corr = CVFV
CV is the flow coefficient for a control valve. The value of CV is dependent on the type of valve and also varies with stem travel or percentage of valve opening. The units and values for the flow coefficient are provided by the manufacturer. For Newtonian fluids of viscosities similar to water. Use the appropriate FV to predict pressure drop, select valve size, or predict flow rate. where: Km = valve recovery coefficient (provided by manufacturer) P1 = valve body inlet pressure (absolute)
DPmax = K m _ P1 − rC p v i
pv = liquid vapor pressure (absolute) at the valve body inlet temperature rC = critical pressure ratio
rC = 0.96 − 0.28 Re = 17, 250
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pv pc
Vo t n CV
Critical pressure ratio (when manufacturer data is not available) Control valve Reynolds number
231
The critical pressure ratio is provided by the manufacturer or, in the absence of correlation data, the equation below can be used. pc is the critical pressure of the fluid (absolute). For engineering units only, where Vo is in gpm, ΔP is in psi, μ is in cP, and ρ is in lbm . ft 3
Chapter 5: Fluids
5.4.4
Mixing
5.4.4.1 Tank Mixing Tank Mixing LIQUID LEVEL
B
BAFFLE
N
W
IMPELLER
H
BAFFLE
TANK
D
WHERE: T= D= N= V= B= W=
T
Impeller Reynolds number D 2 Nt Re = n Flow Number q ND3 where q = volumetric flow rate through the impeller NQ =
Power Number Pgc N D5 t where P = impeller power NP =
3
Ratio of tangential liquid velocity at blade tips to blade tip velocity (K): N K = r 2 NP Q Froude number for tank agitation: Fr =
N2D g
Power function ( f ) is defined by: N z = Pm Fr where
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m=
a − log10 Re b
232
TANK DIAMETER IMPELLER DIAMETER ROTATIONAL SPEED TANK VOLUME BAFFLE WIDTH IMPELLER WIDTH
Chapter 5: Fluids Examples of Mixing Configurations Configuration (Unbaffled)
Six-blade turbine (vertical blades) Three-blade propeller (pitch 2:1) Three-blade propeller (pitch 1:1)
a 1.0 1.7 2.3
b 40.0 18.0 18.0
Power delivered to the liquid by an impeller: z Fr m N3 D5 t P= gc For tanking mixing where the liquid surface has insignificant wave formation, the Froude number is not a factor: z N3 D5 t P= gc For Re < 10 P=
KL N 2 D3 n gc
where KL = empirical constant (laminar) For Re > 10,000 K N3 D5 t P= T g c where KT = empirical constant (fully turbulent)
Values of Constants KL and KT for Baffled Tanks Having Four Baffles Attached to the Tank Wall With Width Equal to 10% of the Tank Diameter Type of Impeller KL KT Propeller, square pitch, 3 blades 41.0 0.32 Propeller, pitch = 2, 3 blades 43.5 1.00 Turbine, 6 flat blades 71.0 6.30 Turbine, 6 curved blades 70.0 4.80 Fan turbine, 6 blades 70.0 1.65 Flat paddle, 2 blades 36.5 1.70 Shrouded turbine, 6 curved blades 97.5 1.08 Power required to suspend particles to a maximum height (Z) using a turbine impeller is 2
where
1 2
T P = g tm Vmut _1 − em i3 c D m e 4.35b b
− = Z E − 0.1, with E = clearance between impeller and tank floor T
rm , Vm = density and volume, respectively, of solid-liquid suspension, not including the clear liquid in zone above height Z (also known as cloud height)
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= terminal velocity of particles
e m
= volume fraction of liquid in zone occupied by suspension
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Chapter 5: Fluids and 1 1 1 1 tm = tliquid + xsolids d tsolids − tliquids n with
xsolids = mass fraction of the solid particles in the solid-liquid suspension
Suspension of Particles in a Tank
CLEAR LIQUID SOLID-LIQUID SUSPENSION
Z
TANK D
E
T
5.4.4.2 Blending of Miscible Liquids in a Tank CORRELATION OF BLENDING TIMES FOR MISCIBLE
Correlation of Blending Times for Miscible Liquids in aBAFFLED Turbine-Agitated, Baffled Vessel LIQUIDS IN A TURBINE-AGITATED VESSEL 1000
100 fT 10
1
1
10
102
103 ND2p Re = _________ μ
Blending time factor (fT) (for miscible Newtonian fluids only): t _ N D 2 i3 g 6 D 2 2
fT =
1
1
1
3
H2T2
where t = blend time (sec)
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104
105
106
Chapter 5: Fluids
5.4.5
Air Lift Air Lift Operation
LIQUID AND AIR LIQUID
LIQUID
NO AIR
AIR INLET
Common Air Lift Terms DISCHARGE LEVEL LIFT ABOVE GROUND
TOTAL STARTING LIFT TOTAL STATIC PUMPING LEVEL LIFT
GROUND LEVEL
STATIC WATER LEVEL
DRAW-DOWN PUMPING WATER LEVEL
STARTING SUBMERGENCE PUMPING SUBMERGENCE
AIR INLET
Air lifts are used to pump liquids and mixtures of liquids and solids. The air required to pump is Va =
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Chapter 5: Fluids where Va = quantity of free air required per gallon of liquid pumped e
ft3 o gallon pumped
C = constant found for outside airline (VA) and inside airline (VC) in figure below S = pumping submergence (%) in figure below L = total pumping lift (ft)
Constant in Formula for Va
375 350
IDE TS U O
VALUES OF CONSTANT “C”
325 300
DE SI IN
275
E– LIN AIR – INE L AIR
VA
VC
250 225 200 175 150 125 30
SUBMERGENCE – PERCENT
70
35
40
45 50 55 60 65 70 SUBMERGENCE – PERCENT CONSTANT IN FORMULA
75
80
Approximate Percent Submergence for Optimum Efficiency
60 50 40 30 30
100
200
300 400 500 600 TOTAL PUMPING LIFT – FEET
700
800
900
Use for either system with straight or tapered pipe. Graphs only available in U.S. units; SI not available. Source for all figures in this section: Gibbs, C.W., editor, New Compressed Air and Gas Data, 2nd ed., Davidson, N.C.: Ingersoll-Rand Company, 1971, pp. 31–3, 31–5, and 31–8.
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Chapter 5: Fluids
5.4.6
Solids Handling
5.4.6.1 Granular Media Storage Vertical Normal Stress Profile in a Silo
Z
BULK SOLIDS
HYDROSTATIC
PRESSURE Source: Chase, George G., Solids Notes 10, Akron: University of Akron, p.10-10.
Compressive normal stress (Pv) in silos can be calculated by the Janssen equation: tg D −4n K z nG PV = 4 n K g =1 − exp d D c where r = granular bulk density m = solids coefficient of friction D = silo diameter K = lateral pressure ratio, where PW = K PV (Janssen's assumption that vertical normal stress is proportional to the lateral normal stress) z = bed depth at which pressure is being measured Sources: Don McGlinchey, editor, Bulk Solids Handling: Equipment Selection and Operation, and J.M. Rotter, Silo and Hopper Design for Strength, Oxford: Blackwell Publishing Ltd., 2008.
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Chapter 5: Fluids 5.4.6.2 Pneumatic Transport Pneumatic transport (or pneumatic conveying) is using gas to transport particulate solids through a pipeline (such as flour, pulverized coal, powdered clay). Flow Regimes: Dilute Phase—Particles are fully suspended at loadings less than 1%. Dense Phase—Particles are not suspended (or periodically suspended) with loadings greater than 20%.
Pressure Systems FEED HOPPER
FILTER
FILTER
FILTER
DISCHARGE HOPPERS
BLOWER
POSITIVE PRESSURE SYSTEM (PUSH)
FEED HOPPERS
FILTER BLOWER
DISCHARGE HOPPER NEGATIVE PRESSURE SYSTEM (PULL) A “PUSH-PULL” SYSTEM USES BLOWERS TO SIMULTANEOUSLY PUSH (POSITIVE PRESSURE) AND PULL THE SOLIDS (NEGATIVE PRESSURE)
Characteristics of Pneumatic Conveying Flow Regimes Dilute Phase
High velocity Particles subject to attrition Low pressure Low cost/simple operation Low loadings
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Dense Phase
Low velocity Low particle attrition High pressure Complex operation High solids loading
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LOW COST / SIMPLE OPERATION LOW LOADINGS
COMPLEX OPERATION HIGH SOLIDS LOADING
Chapter 5: Fluids Flows in Pneumatic Transport
PRESSURE GRADIENT
DENSE PHASE
DILUTE PHASE
CONTINUOUS DENSE PHASE FLOW PLUG FLOW
DILUTE PHASE FLOW
DISCRETE PLUG FLOW DUNE FLOW DISCONTINUOUS DENSE PHASE FLOW
SALTATING FLOW
GAS VELOCITY
Definitions Saltation—Settling of solid particles in the bottom of the pipe during dilute phase pneumatic transport Superficial gas velocity _ u g i —The gas volumetric flow `Vog j divided by the pipe cross-sectional area (A): Vo ug = g A Superficial solids velocity ^u s h —The solids volumetric flow _Vos i divided by the pipe cross-sectional area:
us =
Vos A
mo where Vos = t s , with mo s and ts as the mass flow rate and density of the solid particles, respectively s Actual gas velocity (ug): Vog ug = Ae where
e = void fraction Actual particle velocity (us): Vos us = A _1 − e i
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Chapter 5: Fluids Relationships In vertical pipes, the minimum gas velocity (umin) to suspend particles is when the net upward force on the bed provided by the gas equals the net weight of the solids bed (see Section 4.3.6.7): FB = WB Practical minimum gas velocity:
u = 2 umin = 2
t 4 g Dt e ts − 1 o g
3CD
24 where CD = Re Mass flow rate of the solid particles: mo s = Aus _1 − e i ts Mass flow rate of the gas: mo g = A ug e tg Solids loading (R): mo R = mo s g Concentration (volume fraction) of solids: us Vo Cs = o +s o = u u Vs Vg s+ g Dilute phase pressure drop: The total pressure drop is the sum of the contributions from the carrier gas pressure drop, acceleration of the solid particles, the friction of the solid particles against the pipe wall and fittings, the lifting of the solid particles through the vertical sections, and miscellaneous factors. DP = DPgf + `DPsa + DPsf + DPsb + DPsv j + DPmisc
Carrier gas pressure drop ( DPgf ): For the purpose of this equation, compressible flow equations are not used. Treat the gas as an incompressible fluid: f L u g2 tg DPgf = 2 g D c Acceleration of solids pressure drop (DPsa): mo u DPsa = Asg s c where A = pipe cross-sectional area
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Chapter 5: Fluids Solids friction in straight pipe pressure drop (DPsf ): ms R tg u g2 Lactual DPsf = 2 D gc where ls
= solids friction factor (if unknown, assume 0.2)
R
= solids loading
Lactual = actual length of pipe (not equivalent length) Solid friction in bends pressure drop (DPsb): DP DPsb = Leq e L s o actual Vertical lift pressure drop (DPsv): R g Z tg ug DPsv = gc us where
Z = total length of vertical pipe where the flow is upwards
Miscellaneous pressure drop (DPmisc): where
DPmisc / additional pressure drop for other components, interferences, and other special conditions
Saltation velocity ( usalt ): b 1 f usalt p = R 10 a g D where
(Rizk correlation)
D = inside diameter of conveying pipe a = 1440 Dp + 1.96 (SI units) = 439 Dp + 1.96 (U.S. units) b = 1100 Dp + 2.5 (SI units) = 325 Dp + 2.5 (U.S. units) Dp = mean particle diameter
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Chapter 5: Fluids
5.4.7
Cyclone Cyclone Separator FINES + AIR
where
De
a = height of tangential inlet
IMMERSION TUBE (OR GAS OUTLET TUBE)
b = width of tangential inlet
FEED (DIRTY AIR)
De = diameter of immersion tube s = immersion length of outlet tube s
D = cyclone diameter
a
h = length of cylindrical section h
D
z = length of conical section
CYCLONE BODY
b
H = cyclone height H
CONICAL SECTION
z
B
TAILS
Particle Removal Efficiency 1 h= 2 Dpc p 1 +f Dp where Dpc = diameter of particle collected with 50% efficiency Dp = diameter of particle of interest h = fractional particle collection efficiency
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B = diameter of tail outlet
Chapter 5: Fluids Effective Number of Turns 1 z Ne = H c h + 2 m where Ne = number of effective turns the gas makes in the cyclone h
= length of body of cyclone
z
= length of cone of cyclone
Cyclone 50% Particle Efficiency for Particle Diameter Dpc = >
9n b H 2 r Ne ui `tp − tg j
0.5
where Dpc = diameter of particle that is collected with 50% efficiency, in meters µ = dynamic viscosity of gas ui = inlet velocity into cyclone ρp = density of particle ρg = density of gas
CYCLONE EFFICIENCY (%)
Cyclone Collection Efficiency CYCLONE COLLECTION EFFICIENCY 100
10
1
0.1
1 PARTICLE SIZE RATIO
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10 Dp Dpc
Chapter 5: Fluids Cyclone Ratio of Dimensions to Body Diameter (D) Capacity Dimension
High Efficiency
Conventional
High Throughput
0.44 0.21 1.40 2.50 0.50 0.40 0.40 3.90
0.50 0.25 1.75 2.00 0.60 0.50 0.40 3.75
0.80 0.35 1.70 2.00 0.85 0.75 0.40 3.70
Inlet height, a Inlet width, b Cylindrical section length, h Cone length, z Immersion length, s Gas exit diameter, D Tails outlet diameter, B Cyclone height, H
Source: Adapted from Cooper, C. David, and F.C. Alley, Air Pollution Control: A Design Approach, 4th ed., Illinois: Waveland Press, 2011.
5.4.8
Special Flow Applications
5.4.8.1 Submerged Orifice Submerged Orifice Operating Under Steady-Flow Conditions
V
h 1 – h2 h1
h2
D
D2
Vo = A2 u2 = C A 2g _h1 − h2 i
where u2 = velocity of fluid exiting the orifice
A = cross-sectional area at diameter D
A2 = vena contracta cross-sectional area at diameter D2
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Chapter 5: Fluids 5.4.8.2 Orifice Discharging Freely into Atmosphere Orifice Discharging Into Atmosphere Atm
h
D Torricelli's equation is u = 2gh Vo = C A 2gh where h
= distance from the liquid surface to the centerline of the orifice opening
A = cross-sectional area at diameter D
5.5 Flow and Pressure Measurement Techniques 5.5.1
Manometers and Barometers
5.5.1.1 Simple Manometer Simple Manometer Patm P2 PA FLUID 1 (ρfluid 1) FLUID 2 (ρfluid 2)
zA P1 z1
g PA − Patm = PA − P2 = g 9tfluid2 _ z2 − z1 i − tfluid1 _ zA − z1 iC c
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z2
Chapter 5: Fluids 5.5.1.2 Manometer With Multiple Fluids Manometer With Multiple Fluids FLUID 3 (ρfluid 3) FLUID 1 (ρfluid 1) z2P2 zAPA
z2P2
A z1P1
B
z1P1 z3P3
zBPB
z3P3
FLUID 2 (ρfluid 2)
FLUID 4 (ρfluid 4)
PA − PB = _ PA − P1 i + _ P1 − P2 i + _ P2 − P3 j + _ P3 − PB j g PA − PB = g 9tfluid1 _ z1 − zA i + tfluid2 _ z2 − z1 i + tfluid3 _ z3 − z2 j + tfluid4 _ zB − z3 jC c
5.5.1.3 Inclined U-Tube Manometer Inclined U-Tube Manometer P1
P2
x
∆h MANOMETER FLUID
θ
g g P1 − P2 = g tm x sini = g tm Dh c c where x = difference in tube fill length rm = density of the manometer fluid (densities of the fluids on each side of the manometer are equal) q = angle of inclination (horizontal = 0°)
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Chapter 5: Fluids 5.5.1.4 Barometers Another device that works on the same principle as the manometer is the simple barometer. tgh tgh Patm = PA = Pv + g = PB + g c c where Pv = vapor pressure of the barometer fluid
Barometer PV
PB
ρ
h
PA
5.5.2
Flow Measurement Devices (Summary) Flow Measurement Devices
Mechanical
Class Meter Type
Rotary piston
Gear
Description
Advantages
Rotary piston spins within a chamber of known volume. For each rotation, an amount of fluid passes through the piston chamber. The rotations are counted and the flow rate is determined from the rate of rotations.
• High permanent pressure drop at high flows
• Suitable for low volume metering • Clear liquids only and laboratory or • High cost bench scale testing
Two rotating gears with synchronized, close-fitting • Accurate; suitable • High permanent teeth. A fixed quantity of liquid passes through the for fuel metering pressure drop at meter for each revolution. Permanent magnets in high flows • Suitable for low the rotating gears transmit a signal to a transducer volume metering • Clear liquids only for flow measurement. and laboratory or • High cost bench scale testing
OPERATION OF AN OVAL GEAR METER Operation of an oval gear meter
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• Accurate; suitable for fuel metering
Drawbacks
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Chapter 5: Fluids Flow Measurement Devices (cont'd) Mechanical (cont'd)
Class Meter Type
Nutating Disk
Description
Also known as a wobbly plate meter. Fluid enters • Accurate and a chamber of known volume. When the chamber is repeatable; used filled, the fluid is released, which causes the disk for water service to perform a nutating action (wobble in a circular metering path without actually spinning on its axis). The • Good for hot motion is detected by either gearing or magnetic liquids transducers. The flow rate is determined from the rate of motions. HOLE SHAFT
Rotameter (variable area)
• Accuracy is adversely affected by viscosities below the meter's designated threshold
OUTLET
Counter-rotation of the gears carries known volumes of liquid axially down the length of the gears. The rotation rate is measured using sensors, which in turn correlates to flow rate.
• Used for heavy and high-viscous liquids
• Can only measure liquids
• Low corrosion al• Highest accuracy lowance of any positive • Cannot handle displacement flow- abrasive fluids meter
Source: Flowserve Corp., Irving, TX Fluid flows upward through a clear tapered tube • Simple operation • Cannot be read by and suspends a bob. The higher the flow rate, the with few moving machine higher the bob suspends in the tube. The bob is the parts and no exter- • Must be mounted indicator and the reading is obtained from the scale nal power source vertically marked on the tube. • Inexpensive and • Changes in fluid FLOW PIPE widely available properties gives • Accurate provided erroneous results the fluid properties • Not suited for TAPERED TUBE remain unchanged large pipes • Resistant to shock and chemical action
BOB
(< 6 inches)
• Readout uncertainty near bottom of the scale • Some fluids may obscure reading.
FLOW
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Drawbacks
NUTATING DISK
INLET
Helical
Advantages
248
Chapter 5: Fluids Flow Measurement Devices (cont'd) Mechanical (cont'd)
Class Meter Type
Description
Advantages
Turbine (or Fluid flows past a turbine wheel positioned in the Woltmann center of the pipe with the shaft in line with the Type) pipe. The rotational speed is proportional to the flow rate. Shaft rotation is detected electronically. ELECTRONIC PICKUP METER HOUSING FLOW ROTOR SUPPORT
Paddle Wheel Type
TURBINE
• Simple and durable structure; can be installed vertically or horizontally
• Cannot tolerate cavitation
• Can be designed to detect flow in either direction
• Sensitive to changes in fluid viscosity
• Operates under a wide range of temperatures and pressures
• Accuracy adversely affected by entrained gas
• Long straight runs of pipe upstream and downstream of the meter are needed
• Low pressure drop • Bearings are prone across the flow to wear (though meter some are provided • Effective in ap“bearingless”) plications with • Not suitable for steady, high-speed steam flows
• Can be used for gasses but not suitable for steam Fluid flows past a paddle wheel positioned off• Simple and du• Requires a full center of the pipe with the shaft perpendicular with rable structure; pipe of liquid the pipe. The rotational speed is proportional to the can be installed • Not suitable for flow rate. Shaft rotation is detected electronically. vertically or horisteam zontally ROTATION • Bearings are prone FLOW • Easy installation to wear into existing systems for insertion PADDLE WHEEL models DETECTOR (MOUNTED EXTERNALLY)
Other meters in this class: Single Jet Multi Jet Pelton Wheel
• Can be designed to detect flow in either direction • Operates under a wide range of temperatures and pressures • Low pressure drop across the flow meter • Effective in applications with steady, high-speed flows
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249
Chapter 5: Fluids Flow Measurement Devices (cont'd) Pressure
Class Meter Type
Venturi
Description
Advantages
The meter constricts the fluid flow and sensors • Highly accurate measure the differential pressure before and within over a wide range the constriction. The differential pressure is then of flows converted to a corresponding flow rate. • No moving parts
• Occupies space L ( D of approximately 50)
FLOW
Flow is restricted using a plate with a hole drilled through it. Sensors measure the differential pressure before and after the meter (two tap configurations are shown). The differential pressure is then converted to a corresponding flow rate. dP MEASUREMENT (FOR FLANGE TAP OPTION)
• Cannot measure fluids in reverse flow • Accurate over a • Flow must be wide range of derived from presflows, but not suitsure drop able for trade use • Accuracy (2–4% of full reduced at low scale) flows • No moving parts • Low cost; price does not dramatically increase with pipe size
dP
FLOW
• Low maintenance (orifice plates can be replaced during maintenance operations)
dP dP MEASUREMENT (FOR VENA CONTRACTA TAP OPTION)
Note: Orifices may be drilled in the middle of the plate (concentric) or off-center (eccentric) to accommodate certain fluid types and flow regimes. Orifices may also be round or segmented.
• Easy to convert to different applications or fluids by replacing the orifice plate • In common use
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• Flow must be derived from pressure drop
• Pipe must be full (mostly used for • Low pressure drop liquid service)
PRESSURE MEASUREMENT
Orifice Plate (also squareedge orifice plate)
Drawbacks
250
• Plate materials prone to wear and corrosion, which adversely effects accuracy • Accuracy effected by high-viscous fluids • Moderate to high permanent pressure drop • Pipe must be full (for liquids)
Chapter 5: Fluids Flow Measurement Devices (cont'd) Pressure (cont'd)
Class Meter Type
Nozzle
Description
Similar to a venturi meter, but the inlet section is in the shape of an ellipse and there is no exit section. dP MEASUREMENT dP
Advantages
Drawbacks
• More accurate than orifice plates
• Flow must be derived from pressure drop
• High flow capacity and high velocity applications
• More expensive than orifice plates
• Takes up slightly • Less susceptible to more room than wear and corroorifice plates sion than orifice • Higher permanent plates pressure drop than • Can operate in venturi meters higher turbulence • Pipe must be full
FLOW
• Tolerant of fluids containing suspended solids
(for liquids)
• Less expensive than the venturi meter • Physically smaller than the venturi meter
Dall Tube
Similar to the venturi meter but more compact at the expense of some loss in accuracy and additional permanent pressure loss.
• Can indicate a reverse-flow condition • Similar performance as the venturi meter • Shorter length than the venturi meter
dP
• Low unrecoverable pressure loss
FLOW
• More expensive than orifice plates or flow nozzle meters • Sensitive to turbulence • More complex to manufacture
• Accurate to within • Accuracy depen1% of full scale dent on actual flow data • Cannot indicate a reverse-flow condition
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Chapter 5: Fluids Flow Measurement Devices (cont'd) Pressure (cont'd)
Class Meter Type
Wedge
Description
Advantages
Similar in principle to the orifice meter, a wedge • Well suited for placed in the flow stream creates the differential sludge, slurry, or pressure element. The fluid is forced downward, high-viscous fluid similar to a segmented orifice plate, but is guided service along a sloping wedge shape rather than a sharp edge. The differential pressure is then converted to a corresponding flow rate. dP
Drawbacks
• Differential pressure to flow rate dependent on empirical data unique to each model and application • High permanent pressure drop
FLOW
WEDGE
Pitot Tube
The pitot tube is primarily used for gas or air • Essentially no • Low accuracy (difservice. The Pitot tube measures the total prespressure drop ferential pressure sure (dynamic and static pressures combined). The • Easy to install and between static and static tube measures the static pressure only. The dynamic is small use difference between the two measurements reveals and therefore • Instrument can be that the dynamic pressure is converted into the prone to error) removed when not flow rate. • Accuracy depenin service dent on placement dP • Can be used to within the flow STATIC TUBE measure gas cross-section velocities and to • Low rangeability establish a veloFLOW city profile • Requires clean fluids (tube easily plugs) PITOT TUBE Note: The pitot tube (impact tube) and the static tube are sometimes provided within a single element.
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Chapter 5: Fluids Flow Measurement Devices (cont'd) Pressure (cont'd)
Class Meter Type
Annubar
Description
Advantages
The annubar or averaging pitot-tube flow meter • Accurate (1% of measures the difference between the total pressure full scale) (upstream) and the static pressure (downstream) to • Compact design derive the flow rate. (sensing lines not required) dP
ANNUBAR (IMPACT TUBE)
Drawbacks
• Not suitable for dirty or viscous fluids • Element must be centered within the pipe
FLOW UPSTREAM SENSING PORTS
FLOW
DOWNSTREAM SENSING PORTS SIMPLIFIED CROSS-SECTION OF SENSING (IMPACT) TUBE
Cone (or V-Cone)
Note: Temperature elements can be made integral with the impact tube to provide temperature compensation and corrections. A cone is inserted in the flow stream to create a differential pressure similar to a venturi meter or Dall tube meter, which is then correlated to the flow rate. dP
FLOW
• Excellent accuracy (0.5% of full scale) • Suitable for fluids with suspended solids
• Requires extensive calibration to achieve rated accuracy
• Compact design (0–2 pipe diameters)
• Must operate within rated β-ratio range
• Suitable for gas flow measurement
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• Moderate permanent pressure drop
Chapter 5: Fluids Flow Measurement Devices (cont'd) Thermal
Class Meter Type
Thermal Mass Meters
Description
Advantages
Drawbacks
A known amount of heat is applied to the heating • Used primarily for • Thermal properties element. Some of this heat is lost to the flowing gas service (stack of the gas must be fluid. As flow increases, more heat is lost. The flow measurement known amount of heat lost is sensed using temperature eland emissions • Moderate accuracy ements (comparing the upstream and downstream monitoring) values). The fluid flow is derived from the known • Low pressure drop • Not for steam service heat input and the temperature measurements. • The temperature and heating eleHEATING ELEMENT DOWNSTREAM T1 = UPSTREAM ments come in a = T2 TEMPERATURE TEMPERATURE single element ELEMENT ELEMENT assembly for a compact design • Detects low flows (laminar flows)
FLOW
Vortex
• Can be used as a velocity meter
Vortex Shedding
• Results are in true mass flow • Can be used for liquids, gases, and steam
Vortices (or eddy currents) created by an obstruc• Not suitable for tion are detected by ultrasonic or optical transduclow flow rates ers. The rate of vortex formation and subsequent • Minimum length shedding caused by the bluff body or obstruction is • Low wear of straight pipe is proportional to the fluid velocity. required upstream • Low cost to install and downstream of RECEIVING and maintain BLUFF BODY the meter TRANSDUCER (STRUT) • Low sensitivity to variations in process conditions FLOW
EDDYS (VORTICES)
• Stable long-term accuracy and repeatability • Applicable to a wide range of process temperatures
TRANSMITTING TRANSDUCER
• Available for a wide variety of pipe sizes
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Chapter 5: Fluids Flow Measurement Devices (cont'd) Magnetic
Class Meter Type
Description
Advantages
Mag Meter The operation of a magnetic flow meter or mag meter is based on Faraday's Law, which states that the voltage induced across any conductor as it moves at right angles through a magnetic field is proportional to the velocity of that conductor. E \ u#B#D where E = voltage generated in a conductor
Ultrasonic
with two-phase flow
• No pressure drop (models are available for full pipe bores) • Accurate
B = magnetic field strength
• Measures true volumetric flow
The flowmeter applies a magnetic field through the entire cross-section of the flow tube. The velocity is then determined by the meter by measuring the magnetic strength. • Sufficiently acFor a simple Doppler system, sound waves are curate for custody used to determine the velocity of a fluid flowing in a pipe. At zero flow, the frequencies of an ultrason- transfer ic wave transmitted into a pipe and its reflections • Clamp-on systems from the fluid are the same. At flow, the frequency suitable for field of the reflected wave is different because of the testing and verifiDoppler effect. As fluid velocity increases, the cation of installed frequency shift increases linearly. A transmitter flow meters evaluates the frequency shift to determine the flow rate. For a Transit time system, ultrasonic waves are sent and received between transducers in both directions in the pipe. At zero flow, it takes the same time to travel upstream and downstream between the transducers. At flow, the upstream wave travels more slowly and takes more time than the downstream wave. As fluid velocity increases, the difference between the upstream and downstream times also increases. A transmitter evaluates the delay times to determine the flow rate. Note: Either method can be deployed as a clampon unit (dry) or be installed integral to the fluid (wet).
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• Ideal for dirty • Does not work water or other con- on nonconductive ductive fluids fluids (e.g., hydrocarbons) • Suitable for fluids
u = velocity of the conductor
D = length of the conductor
255
Drawbacks
• Expensive
• Does not correlate to mass flow until fluid or bulk slurry density is known
• Expensive • Sensitive to stray vibrations • Unwanted attenuation can occur • Fluid must be able to transmit ultrasonic waves
Chapter 5: Fluids Flow Measurement Devices (cont'd) Impulse
Class Meter Type
Coriolis
Description
Drawbacks
A Coriolis flow meter uses the natural phenom• Suitable for highly • Not accurate for enon in which an object begins to “drift” as it viscous fluids gases at low flow travels from or toward the center of a rotation rates • Insensitive to temoccurring in the surrounding environment. Coriolis perature and fluid • High permanent flow meters generate this effect by diverting the properties pressure drop fluid flow through a pair of parallel U-tubes with • Measures mass an induced vibration (by an actuator, not shown) flow rate directly perpendicular to the flow. The vibration simulates a rotation of the pipe and the resulting Coriolis “drift” in the fluid causes the U-tubes to twist and deviate from their parallel alignment. The force producing this deviation is proportional to the mass flow rate through the U-tubes. VIBRATION VIBRATION FLOW
NO DEFLECTION
5.5.3
Advantages
DEFLECTION
Orifice, Nozzle, and Venturi Meters
5.5.3.1 Square-Edge Orifice Meter (Vena Contracta Taps) d2 2
d2
0.66 DISCHARGE COEFFICIENT Corifice FOR SQUARE-EDGE ORIFICE METERS
0.64 d1 Corifice
d2
FLOW
0.62
β =
0.60
SQUARE-EDGE ORIFICE METER 0.58 4 10
105
106 Re
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d1 —— = 0.7 d2 0.6 0.5 0.4 0.2
107
108
Chapter 5: Fluids Flow Coefficient (C) and Orifice Loss Coefficient C=
Corifice 1 − b4
Incompressible Flow 2 gc DP t
Vo = C Aorifice Compressible Flow
2 g c DP t
Vo = Y C Aorifice
where Y = expansion factor
5.5.3.2 Flow Nozzle Meter 1.00
d2 2
d2
0.2 0.6
0.4
d1
d2
Corifice
0.98 d1 β = —— = 0.8 d2
0.96
FLOW
0.94
NOZZLE METER
Cnozzle 1 − b4
Incompressible Flow Vo = C Anozzle
2 gc DP t
Compressible Flow Vo = Y C Anozzle
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106 Re
Flow Coefficient (C) C=
104
DISCHARGE COEFFICIENT Cnozzle FOR NOZZLE METERS
2 gc DP t
257
107
108
Chapter 5: Fluids 5.5.3.3 Venturi Flow Nozzle Meter The venturi discharge coefficient is a function of the specific geometry of the meter. PRESSURE MEASUREMENT
FLOW
Flow Coefficient (C) C=
Cventuri 1 − b4
Incompressible Flow Vo = C Aventuri
2 gc DP t
Compressible Flow Vo = Y C Aventuri
2 gc DP t
5.5.3.4 Pitot Tube Flow Meter STATIC TUBE
P1
P2
FLOW PITOT TUBE (OR IMPACT TUBE)
P1 measures the static pressure. Assuming elevation effects are negligible, P2 is the stagnation pressure: t u2 P1 + 2 g c Therefore: u=
©2017 NCEES
2 gc _ P2 − P1 i t
258
Chapter 5: Fluids 5.5.3.5 Permanent Pressure Loss in Flow Meters FLOW RESTRICTION
VENA CONTRACTA PB
PA
FLOW P VC PERMANENT PRESSURE LOSS PA PB
P vc
Pressure Loss Across Restrictive Flow Meters: The permanent pressure loss (or nonrecoverable pressure drop) across a restrictive flow meter (e.g., orifices and nozzles) is the difference between the upstream pressure, PA, (the static pressure not influenced by the device, or roughly one pipe diameter upstream), and the pressure measured downstream of the device where the static pressure recovery is complete, PB (approximately six pipe diameters downstream). For Reynolds numbers (Re) greater than 10,000, the permanent pressure loss can be estimated by: 2
where
mo dC A n d PA − PB = 2g t `1 − b 2 j c 2 t Vo PA − PB = 2g d C A n `1 − b 2 j d c mo = mass flow rate Vo = volumetric flow rate Cd = coefficient of discharge for the device (e.g., Corifice and Cnozzle) A = device cross-sectional area (e.g., orifice hole area)
For a given measured differential pressure, ΔP (e.g., radius or flange taps for an orifice), the permanent pressure loss can be estimated by: J N 2 K 1 − b 4 `1 − Cd j − Cd b 2 O PA − PB = DP K K 1 − b 4 `1 − C 2 j + C b 2 OO d d L P For orifice plates and nozzles, the flow coefficient, K, can be approximated K=f
©2017 NCEES
1 − b 4 `1 − Cd2 j Cd b 2
2
− 1p
259
Chapter 5: Fluids 5.5.3.6 Weir Meters Rectangular Weir—Suppressed L
V-Notch Weir (90o Notch)
L
H
H 5
3
Vo = C L H 2 Vo = C H 2
where
ft 0.5 C = 3.33 sec
C = 1.84
ft 0.5 where C = 2.5 sec
m 0.5 m 0.5 C = 1.4 s s
Rectangular Weir—Contracted
L
H Vo = C _ L − 0.2H i H 2 3
©2017 NCEES
ft 0.5 where C = 3.33 sec C = 1.84
m 0.5 s
260
Chapter 5: Fluids
5.6 Tables
Pipe Size
OD
inches
inches
1/8 6
0.405 10.3
1/4 8
0.54 13.7
3/8 10
0.675 17.1
1/2 15
0.840 21.3
mm
mm
Iron Pipe
STD XS STD XS STD XS
STD XS XX
3/4 20
1.050 26.7
STD XS XX
1 25
1.315 33.4
STD XS XX
1-1/4 32
1.660 42.2
STD XS XX
1-1/2 40
1.900 48.3
STD XS XX
©2017 NCEES
Pipe Dimensions and Weights Weights are based on carbon steel pipe Identification Wall Thickness Steel Stainless Steel inches mm Schedule Schedule No. 10 10S 0.049 1.24 40 40S 0.068 1.73 80 80S 0.095 2.41 10 10S 0.065 1.65 40 40S 0.088 2.24 80 80S 0.119 3.02 10 10S 0.065 1.65 40 40S 0.091 2.31 80 80S 0.126 3.20 5 5S 0.065 1.65 10 10S 0.083 2.11 40 40S 0.109 2.77 80 80S 0.147 3.73 160 0.188 4.78 0.294 7.47 5 5S 0.065 1.65 10 10S 0.083 2.11 40 40S 0.113 2.87 80 80S 0.154 3.91 160 0.219 5.56 0.308 7.82 5 5S 0.065 1.65 10 10S 0.109 2.77 40 40S 0.133 3.38 80 80S 0.179 4.55 160 0.250 6.35 0.358 9.09 5 10 40 80 160
5S 10S 40S 80S
5 10 40 80 160
5S 10S 40S 80S
0.065 0.109 0.140 0.191 0.250 0.382 0.065 0.109 0.145 0.200 0.281 0.400
261
1.65 2.77 3.56 4.85 6.35 9.70 1.65 2.77 3.68 5.08 7.14 10.15
Weight
lbm ft
Inside Diameter
kg m
inches
mm
0.19 0.24 0.31 0.33 0.43 0.54 0.42 0.57 0.74 0.54 0.67 0.85 1.09 1.31 1.72 0.69 0.86 1.13 1.48 1.95 2.44 0.87 1.41 1.68 2.17 2.85 3.66
0.28 0.37 0.47 0.49 0.63 0.80 0.63 0.84 1.10 0.80 1.00 1.27 1.62 1.95 2.55 1.03 1.28 1.69 2.20 2.90 3.64 1.29 2.09 2.50 3.24 4.24 5.45
0.307 0.269 0.215 0.410 0.364 0.302 0.545 0.493 0.423 0.710 0.674 0.622 0.546 0.464 0.252 0.920 0.884 0.824 0.742 0.612 0.434 1.185 1.097 1.049 0.957 0.815 0.599
7.82 6.84 5.84 10.40 9.22 7.66 13.80 12.48 10.70 18.00 17.08 15.76 13.84 11.74 6.36 23.40 22.48 20.96 18.88 15.58 11.06 30.10 27.86 26.64 24.30 20.70 15.22
1.11 1.81 2.27 3.00 3.77 5.22 1.28 2.09 2.72 3.63 4.86 6.41
1.65 2.69 3.39 4.47 5.61 7.77 1.90 3.11 4.05 5.41 7.25 9.55
1.530 1.442 1.380 1.278 1.160 0.896 1.770 1.682 1.610 1.500 1.338 1.100
38.90 36.66 35.08 32.50 29.50 22.80 45.00 42.76 40.94 38.14 34.02 28.00
Chapter 5: Fluids Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe Pipe Size
OD
inches
inches
mm
2 50
mm
2.375 60.3
Identification Steel Iron Pipe
STD XS XX
2-1/2 65
2.875 73
STD XS XX
3 80
3.5 88.9
STD XS XX
3-1/2 90
4 100
4-1/2 115
5 125
4 101.6
4.5 114.3
5 127
5.563 141.3
STD XS XX
STD XS XX STD XS XX
STD XS XX
©2017 NCEES
Schedule No.
Wall Thickness
Stainless Steel Schedule
5 10 40 80 160
5S 10S 40S 80S
5 10 40 80 160
5S 10S 40S 80S
5 10 40 80 160
5S 10S 40S 80S
5 10 40 80
5S 10S 40S 80S
5 10 40 80 120 160
5S 10S 40S 80S
40 80
40S 80S
5 10 40 80 120 160
5S 10S 40S 80S
Weight
Inside Diameter
inches
mm
lbm ft
kg m
inches
mm
0.065 0.109 0.154 0.218 0.344 0.436 0.083 0.120 0.203 0.276 0.375 0.552 0.083 0.120 0.216 0.300 0.438 0.600 0.083 0.120 0.226 0.318 0.636 0.083 0.120 0.237 0.337 0.438 0.531 0.674 0.247 0.355 0.710 0.109 0.134 0.258 0.375 0.500 0.625 0.750
1.65 2.77 3.91 5.54 8.74 11.07 2.11 3.05 5.16 7.01 9.53 14.02 2.11 3.05 5.49 7.62 11.13 15.24 2.11 3.05 5.74 8.08 16.15 2.11 3.05 6.02 8.56 11.13 13.49 17.12 6.27 9.02 18.03 2.77 3.40 6.55 9.53 12.70 15.88 19.05
1.61 2.64 3.66 5.03 7.47 9.04 2.48 3.53 5.80 7.67 10.02 13.71 3.03 4.34 7.58 10.26 14.34 18.6 3.48 4.98 9.12 12.52 22.87 3.92 5.62 10.8 15.00 19.02 22.53 27.57 12.55 17.63 32.56 6.36 7.78 14.63 20.80 27.06 32.99 38.59
2.39 3.93 5.44 7.48 11.11 13.44 3.69 5.26 8.63 11.41 14.92 20.39 4.52 6.46 11.29 15.27 21.35 27.68 5.18 7.41 13.57 18.64 34.03 5.84 8.37 16.08 22.32 28.32 33.54 41.03 18.67 26.24 48.45 9.46 11.56 21.77 30.97 40.28 49.12 57.43
2.245 2.157 2.067 1.939 1.687 1.503 2.709 2.635 2.469 2.323 2.125 1.771 3.334 3.260 3.068 2.900 2.624 2.300 3.834 3.760 3.548 3.364 2.728 4.334 4.260 4.026 3.826 3.624 3.438 3.152 4.506 4.290 3.580 5.345 5.295 5.047 4.813 4.563 4.313 4.063
57.00 54.76 52.48 49.22 42.82 38.16 68.78 66.90 62.68 58.98 53.94 44.96 84.68 82.80 77.92 73.66 66.64 58.42 97.38 95.50 90.12 85.44 69.30 110.08 108.20 102.26 97.18 92.04 87.32 80.06 114.46 108.96 90.94 135.76 134.50 128.20 122.24 115.90 109.54 103.20
262
Chapter 5: Fluids Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe Pipe Size
OD
inches
inches
mm
6 150
7 175
8 200
mm
6.625 168.3
7.625 193.7
8.625 219.1
Identification Steel
10 250
9.625 244.5
10.75 273
Schedule No.
STD XS
5 10 40 80 120 160
5S 10S 40S 80S
40
40S 80S
5 10 20 30 40 60 80 100 120 140
5S 10S
XX STD XS XX
STD XS
STD XS
©2017 NCEES
11.75 298.5
STD XS XX
40S 80S
160
STD XS XX
XX 11 275
Stainless Steel Schedule
Iron Pipe
XX 9 225
Wall Thickness
40S 80S 5 10 20 30 40 60 80 100 120 140 160
5S 10S 40S 80S
40S 80S
263
Weight
Inside Diameter
inches
mm
lbm ft
kg m
inches
mm
0.109 0.134 0.280 0.432 0.562 0.719 0.864 0.301 0.500 0.875 0.109 0.148 0.250 0.277 0.322 0.406 0.500 0.594 0.719 0.812 0.875 0.906 0.342 0.500 0.875 0.134 0.165 0.250 0.307 0.365 0.500 0.594 0.719 0.844 1.000 1.125 0.375 0.500 0.875
2.77 3.40 7.11 10.97 14.27 18.26 21.95 7.65 12.70 22.23 2.77 3.76 6.35 7.04 8.18 10.31 12.70 15.09 18.26 20.62 22.23 23.01 8.69 12.70 22.23 3.40 4.19 6.35 7.80 9.27 12.70 15.09 18.26 21.44 25.40 28.58 9.53 12.70 22.23
7.59 9.30 18.99 28.60 36.43 45.39 53.21 23.57 38.08 63.14 9.92 13.41 22.38 24.72 28.58 35.67 43.43 51.00 60.77 67.82 72.49 74.76 33.94 48.77 81.85 15.21 18.67 28.06 34.27 40.52 54.79 64.49 77.10 89.38 104.23 115.75 45.60 60.13 101.72
11.31 13.83 28.26 42.56 54.21 67.57 79.22 35.10 56.69 94.00 14.78 19.97 33.32 36.82 42.55 53.09 64.64 75.92 90.44 100.93 107.93 111.27 50.54 72.60 121.85 22.61 27.78 41.76 51.01 60.29 81.53 95.98 114.71 133.01 155.10 172.27 67.91 89.51 151.46
6.407 6.357 6.065 5.761 5.501 5.187 4.897 7.023 6.625 5.875 8.407 8.329 8.125 8.071 7.981 7.813 7.625 7.437 7.187 7.001 6.875 6.813 8.941 8.625 7.875 10.482 10.420 10.250 10.136 10.020 9.750 9.562 9.312 9.062 8.750 8.500 11.000 10.750 10.000
162.76 161.50 154.08 146.36 139.76 131.78 124.40 178.40 168.30 149.24 213.56 211.58 206.40 205.02 202.74 198.48 193.70 188.92 182.58 177.86 174.64 173.08 227.12 219.10 200.04 266.20 264.62 260.30 257.40 254.46 247.60 242.82 236.48 230.12 222.20 215.84 279.44 273.10 254.04
Chapter 5: Fluids Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe Pipe Size
OD
inches
inches
mm
mm
Identification Steel Iron Pipe
STD 12 300
12.75 323.8
XS
XX
STD 14 350
16 400
©2017 NCEES
14 355.6
16 406.4
XS
STD XS
Schedule No.
20 30 40 60 80 100 120 140 160 10 20 30 40 60 80 100 120 140 160 10 20 30 40 60 80 100 120 140 160
Wall Thickness
Stainless Steel Schedule
5S 10S 40S 80S
10S 40S 80S
10S 40S 80S
Weight
Inside Diameter
inches
mm
lbm ft
kg m
inches
mm
0.156 0.180 0.250 0.330 0.375 0.406 0.500 0.562 0.688 0.844 1.000 1.125 1.312 0.188 0.250 0.312 0.375 0.438 0.500 0.594 0.750 0.938 1.094 1.250 1.406 0.188 0.250 0.312 0.375 0.500 0.656 0.844 1.031 1.219 1.438 1.594
3.96 4.57 6.35 8.38 9.53 10.31 12.70 14.27 17.48 21.44 25.40 28.58 33.32 4.78 6.35 7.92 9.53 11.13 12.70 15.09 19.05 23.83 27.79 31.75 35.71 4.78 6.35 7.92 9.53 12.70 16.66 21.44 26.19 30.96 36.53 40.49
21.00 24.19 33.41 43.81 49.61 53.57 65.48 73.22 88.71 107.42 125.61 139.81 160.42 27.76 36.75 45.65 54.62 63.50 72.16 85.13 106.23 130.98 150.93 170.37 189.29 31.78 42.09 52.32 62.64 82.85 107.60 136.74 164.98 192.61 223.85 245.48
31.24 35.98 49.71 65.19 73.86 79.71 97.44 108.93 132.05 159.87 186.92 208.08 238.69 41.36 54.69 67.91 81.33 94.55 107.40 126.72 158.11 194.98 224.66 253.58 281.72 47.34 62.65 77.83 93.27 123.31 160.13 203.54 245.57 286.66 333.21 365.38
12.438 12.390 12.250 12.090 12.000 11.938 11.750 11.626 11.374 11.062 10.750 10.500 10.126 13.624 13.500 13.376 13.250 13.124 13.000 12.812 12.500 12.124 11.812 11.500 11.188 15.624 15.500 15.376 15.250 15.000 14.688 14.312 13.938 13.562 13.124 12.812
315.88 314.66 311.10 307.04 304.74 303.18 298.40 295.26 288.84 280.92 273.00 266.64 257.16 346.04 342.90 339.76 336.54 333.34 330.20 325.42 317.50 307.94 300.02 292.10 284.18 396.84 393.70 390.56 387.34 381.00 373.08 363.52 354.02 344.48 333.34 325.42
264
Chapter 5: Fluids Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe Pipe Size
OD
inches
inches
mm
mm
Identification Steel Iron Pipe
STD 18 450
18 457
XS
STD XS 20 500
22 550
20 508
22 559
STD XS
STD XS 24 600
©2017 NCEES
24 610
Schedule No.
10 20 30 40 60 80 100 120 140 160 10 20 30 40 60 80 100 120 140 160 10 20 30 60 80 100 120 140 160 10 20 30 40 60 80 100 120 140 160
Wall Thickness
Stainless Steel Schedule
10S 40S 80S
10S 40S 80S
10S 40S 80S
10S 40S 80S
265
Weight
Inside Diameter
inches
mm
lbm ft
kg m
inches
mm
0.188 0.250 0.312 0.375 0.438 0.500 0.562 0.750 0.938 1.156 1.375 1.562 1.781 0.218 0.250 0.375 0.500 0.594 0.812 1.031 1.281 1.500 1.750 1.969 0.218 0.250 0.375 0.500 0.875 1.125 1.375 1.625 1.875 2.125 0.250 0.375 0.500 0.562 0.688 0.969 1.219 1.531 1.812 2.062 2.344
4.78 6.35 7.92 9.53 11.13 12.70 14.27 19.05 23.83 29.36 34.93 39.67 45.24 5.54 6.35 9.53 12.70 15.09 20.62 26.19 32.54 38.10 44.45 50.01 5.54 6.35 9.53 12.70 22.23 28.58 34.93 41.28 47.63 53.98 6.35 9.53 12.7 14.27 17.48 24.61 30.96 38.89 46.02 52.37 59.54
35.80 47.44 58.99 70.65 82.23 93.54 104.76 138.30 171.08 208.15 244.37 274.48 308.79 46.10 52.78 78.67 104.23 123.23 166.56 209.06 256.34 296.65 341.41 379.53 50.76 58.13 86.69 114.92 197.60 251.05 303.16 353.94 403.38 451.49 63.47 94.71 125.61 140.81 171.45 238.57 296.86 367.74 429.79 483.57 542.64
53.31 70.57 87.71 105.17 122.38 139.16 155.81 205.75 254.57 309.64 363.58 408.28 459.39 68.61 78.56 117.15 155.13 183.43 247.84 311.19 381.55 441.52 508.15 564.85 75.55 86.55 129.14 171.10 294.27 373.85 451.45 527.05 600.67 672.30 94.53 141.12 187.07 209.65 255.43 355.28 442.11 547.74 640.07 720.19 808.27
17.624 17.500 17.376 17.250 17.124 17.000 16.876 16.500 16.124 15.688 15.250 14.876 14.438 19.564 19.500 19.250 19.000 18.812 18.376 17.938 17.438 17.000 16.500 16.062 21.564 21.500 21.250 21.000 20.250 19.750 19.250 18.750 18.250 17.750 23.500 23.250 23.000 22.876 22.624 22.062 21.562 20.938 20.376 19.876 19.312
447.44 444.30 441.16 437.94 434.74 431.60 428.46 418.90 409.34 398.28 387.14 377.66 366.52 496.92 495.30 488.94 482.60 477.82 466.76 455.62 442.92 431.80 419.10 407.98 547.92 546.30 539.94 533.60 514.54 501.84 489.14 476.44 463.74 451.04 597.30 590.94 584.60 581.46 575.04 560.78 548.08 532.22 517.96 505.26 490.92
Chapter 5: Fluids Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe Pipe Size
OD
inches
inches
26 650
26 660
28 700
28 711
mm
mm
30 750
30 762
32 800
32 813
34 850
34 864
36 900
36 914
42 1050 48 1200
42 1067 48 1219
©2017 NCEES
Identification Steel Iron Pipe
STD XS STD
STD XS
STD XS
STD XS
STD XS
Schedule No.
10 20 10 20 30 10 20 30 10 20 30 40 10 20 30 40 10 20 30 60 30 60
Wall Thickness
Stainless Steel Schedule
40S 80S 40S
10S 40S 80S
40S 80S
40S 80S
40S 80S
inches
mm
0.312 0.375 0.500 0.312 0.375 0.500 0.625 0.312 0.375 0.500 0.625 0.312 0.375 0.500 0.625 0.688 0.312 0.375 0.500 0.625 0.688 0.312 0.375 0.500 0.375 0.500 0.375 0.500
7.92 9.53 12.70 7.92 9.53 12.70 15.88 7.92 9.53 12.70 15.88 7.92 9.53 12.70 15.88 17.48 7.92 9.53 12.70 15.88 17.48 7.92 9.53 12.70 9.53 12.70 9.53 12.70
266
Weight
Inside Diameter
lbm ft
kg m
inches
mm
85.68 102.72 136.30 92.35 110.74 146.99 182.90 99.02 118.76 157.68 196.26 105.69 126.78 168.37 209.62 230.29 112.36 134.79 179.06 222.99 245.00 119.03 142.81 189.75 166.86 221.82 190.92 253.89
127.36 152.88 202.74 137.32 164.86 218.71 272.23 147.29 176.85 234.68 292.2 157.25 188.83 250.65 312.17 342.94 167.21 200.82 266.63 332.14 364.92 176.97 212.57 282.29 248.53 330.21 284.25 377.81
25.376 25.250 25.000 27.376 27.250 27.000 26.750 29.376 29.250 29.000 28.750 31.376 31.250 31.000 30.750 30.624 33.376 33.250 33.000 32.750 32.624 35.376 35.250 35.00 41.250 41.000 47.250 47.000
644.16 640.94 634.60 695.16 691.94 685.60 679.24 746.16 742.94 736.60 730.24 797.16 793.94 787.60 781.24 778.04 848.16 844.94 838.60 832.24 829.04 898.16 894.94 888.60 1047.94 1041.60 1199.94 1193.60
Chapter 5: Fluids Tubing Sizes (U.S.) Size OD (inches) (inches)
1/4 3/8 1/2 5/8 3/4 7/8 1 1.050 1-1/8 1-1/4 1-5/16 1-3/8 1-1/2 1-5/8 1.660 1-3/4 1-7/8 1.900 2 2-1/4 2-3/8 2-1/2 2-7/8 3 3-1/8 3-1/2 3-3/4 4 4-1/2 5 6-1/4
©2017 NCEES
0.2500 0.3750 0.5000 0.6250 0.7500 0.8750 1.0000 1.0500 1.1250 1.2500 1.3125 1.3750 1.5000 1.6250 1.6600 1.7500 1.8750 1.9000 2.0000 2.2500 2.3750 2.5000 2.8750 3.0000 3.1250 3.5000 3.7500 4.0000 4.5000 5.0000 6.2500
24ga
22ga
20ga
18ga
0.022
0.028
0.035
0.049
0.206 0.194 0.331 0.319 0.444 0.430 0.555 0.680 0.805 0.930 0.980 1.055 1.180 1.243 1.305 1.430 1.555 1.590 1.680 1.805 1.830 1.930
Gauge (nominal inches) 16ga 14ga 12ga 11ga Inside Diameter (inches) 0.062 0.083 0.109 0.120
0.402 0.527 0.652 0.777 0.902 0.952 1.027 1.152 1.215 1.277 1.402 1.527 1.562 1.652 1.777 1.802 1.902 2.152 2.277 2.402
0.376 0.501 0.626 0.751 0.876 0.926 1.001 1.126 1.189 1.251 1.376 1.501 1.536 1.626 1.751 1.776 1.876 2.126 2.251 2.376 2.751 2.902 2.876 3.001 3.376
267
0.334 0.459 0.584 0.709 0.834 0.884 0.959 1.084 1.147 1.209 1.334 1.459 1.494 1.584 1.709 1.734 1.834 2.084 2.209 2.334 2.709 2.834 2.959 3.334 3.584 3.834 4.334 4.834
0.532 0.657 0.782 0.832 0.907 1.032 1.095 1.157 1.282 1.407 1.442 1.532 1.657 1.682 1.782 2.032 2.157 2.282 2.657 2.782 2.907 3.282 3.532 3.782 4.282 4.782
0.510 0.635 0.760 0.810 0.885 1.010 1.073 1.135 1.260 1.385 1.420 1.510 1.635 1.660 1.760 2.010 2.135 2.260 2.635 2.760 2.885 3.260 3.510 3.760 4.260 4.760 6.010
9ga
7ga
1/4"
3/8"
0.148
0.180
0.250
0.375
1.364 1.454 1.579 1.604 1.704 1.954 2.079 2.204 2.579 2.704 2.829 3.204 3.454 3.704 4.204 4.704
1.640 2.015 2.140 2.515 2.640 2.765 3.140 3.390 3.640 4.140 4.640 5.890
4.000 4.500 5.750 5.500
Chapter 5: Fluids Tubing Sizes (Metric) Size
1/4" 3/8" 1/2" 5/8" 3/4" 7/8" 1" 1.050" 1-1/8" 1-1/4" 1-5/16" 1-3/8" 1-1/2" 1-5/8" 1.660" 1-3/4" 1-7/8" 1.900" 2" 2-1/4" 2-3/8" 2-1/2" 2-7/8" 3" 3-1/8" 3-1/2" 3-3/4" 4" 4-1/2" 5" 6-1/4"
OD (mm)
6.4 9.5 12.7 15.9 19.1 22.2 25.4 26.7 28.6 31.8 33.4 35.0 38.1 41.3 42.2 44.5 47.7 48.3 50.8 57.2 60.4 63.5 73.1 76.2 79.4 88.9 95.3 101.6 114.3 127.0 158.8
©2017 NCEES
24ga
22ga
20ga
18ga
0.600
0.700
0.900
1.300
5.2 8.3
5.0 8.1 11.3
10.9 14.1 17.3 20.4 23.6 24.9 26.8 30.0 31.6 33.2 36.3 39.5 40.4 42.7 45.9 46.5 49.0
10.1 13.3 16.5 19.6 22.8 24.1 26.0 29.2 30.8 32.4 35.5 38.7 39.6 41.9 45.1 45.7 48.2 54.6 57.8 60.9 73.6
Gauge (nominal mm) 16ga 14ga 12ga 11ga Inside Diameter (mm) 1.600 2.100 2.800 3.100
9.5 12.7 15.9 19.0 22.2 23.5 25.4 28.6 30.2 31.8 34.9 38.1 39.0 41.3 44.5 45.1 47.6 54.0 57.2 60.3 69.9 73.0 76.2 85.7
8.5 11.7 14.9 18.0 21.2 22.5 24.4 27.6 29.2 30.8 33.9 37.1 38.0 40.3 43.5 44.1 46.6 53.0 56.2 59.3 68.9 72.0 75.2 84.7 91.1 97.4 110.1 122.8
268
13.5 16.6 19.8 21.1 23.0 26.2 27.8 29.4 32.5 35.7 36.6 38.9 42.1 42.7 45.2 51.6 54.8 57.9 67.5 70.6 73.8 83.3 89.7 96.0 108.7 121.4
12.9 16.0 19.2 20.5 22.4 25.6 27.2 28.8 31.9 35.1 36.0 38.3 41.5 42.1 44.6 51.0 54.2 57.3 66.9 70.0 73.2 82.7 89.1 95.4 108.1 120.8 152.6
9ga
7ga
1/4"
3/8"
3.800
4.600
6.400
9.600
101.5 114.2 146.0
139.6
34.6 36.9 40.1 40.7 43.2 49.6 52.8 55.9 65.5 68.6 71.8 81.3 87.7 94.0 106.7 119.4
41.6 51.2 54.3 63.9 67.0 70.2 79.7 86.1 92.4 105.1 117.8 149.6
6 MASS TRANSFER 6.1 Symbols and Definitions Symbols Symbol
Description
A
Area
A
Absorption factor
a
Effective interfacial mass-transfer area per unit volume
B
Bottom product flow rate
c
Concentration
cp D
Units (U.S.)
Units (SI)
or
m2
ft2
in2 dimensionless
ft 2 ft 3
m2 m3
lb mole hr lb mole ft 3
mol s mol m3
Heat capacity
Btu lbm -cF
Distillate flow rate
lb mole hr
J = m2 kg : K s 2 : K mol s
DAB
Mass diffusivity (diffusion coefficient)
D, d E
Diameter Efficiency
ft 2 hr ft or in.
m2 s m dimensionless mol s
lb mole hr
F
Molar feed flow
f f
Ratio of vapor phase flow to feed flow (fraction vaporized) Darcy friction factor
f
Fugacity of a pure component
lbf in 2
= Pa
kg N = 2 m m : s2
fti
Fugacity of a component i in a mixture
lbf in 2
= Pa
kg N = m2 m : s2
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dimensionless dimensionless
Chapter 6: Mass Transfer
Symbols (cont'd) Symbol
Description
Units (U.S.)
Units (SI)
lb mole hr lb mole hr ft sec 2 Btu lb mole
mol s
G
Gas flow rate (stripper/absorber)
GS
Gas flow rate, solute-free basis
gc
Gravitational acceleration
gt
Molar Gibbs free energy
H
Henry’s Law constant
lbf in 2
Heat input
Btu hr
2 J kg : m W= s= 3 s
ft or in. ft or in.
m m
Btu lbm
J = m2 kg s 2
DH
mol s m s2 J mol kg N = m2 m : s2
= Pa
h h
Height Head loss, pressure drop
h
Specific enthalpy
ht
Molar specific enthalpy
Btu lb mole
J mol
Dh
Specific enthalpy change
Btu lbm
J = m2 kg s 2
Dhvap
Latent heat of vaporization
Btu lbm
J = m2 kg s 2
HTU
Height of a transfer unit
ft or in.
m
j
Colburn Factor
jA
Molar flux of component A per area
K
Distribution coefficient for phase equilibrium
L
Liquid flow (for a flash, in a column, stripper, or absorber)
LS
Liquid flow rate, solute-free basis
dimensionless lb mole ft 2- hr dimensionless
l
Length, distance
m m m
Mass General phase equilibrium coefficient Slope of the operating line or slope of the equilibrium line
MW
Molecular weight
N n
Number of stages Number of moles
no
Molar flow per area
NTU
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mol m2 : s
lb mole hr lb mole hr ft or in.
mol s
lbm
kg
mol s m dimensionless dimensionless
lbm lb mole dimensionless
Number of transfer units
270
kg mol
lb mole
mol
lb mole ft 2- hr
mol m2 : s
dimensionless
Chapter 6: Mass Transfer
Symbols (cont'd) Symbol
Description
Units (U.S.)
Units (SI)
P
Pressure
lbf in 2
= Pa
kg N = m2 m : s2
Pc
Critical pressure
lbf in 2
= Pa
kg N = 2 m m : s2
Pr
Reduced pressure
P*
Three-phase equilibrium pressure
lbf in 2
Partial pressure
lbf in 2
kg N = m2 m : s2 kg = N = Pa m2 m : s2
psat
Saturation pressure, or vapor pressure
lbf in 2
= Pa
/
Poynting correction factor
dimensionless
q
Ratio of liquid phase flow to feed flow
dimensionless
Qo
Heat duty
q
Ratio of liquid phase flow to feed flow (fraction not vaporized)
dimensionless
R
Reflux ratio
dimensionless
R
Universal gas constant
S
Boil-up ratio
S T Tc Tr
Stripping factor
u
Velocity
V
Volume
V
Vapor flow (for a flash, in a column, stripper, or absorber)
lb mole hr
mol s
vt
Molar volume
ft 3 lb mole
m3 mol
v
Specific volume
ft 3 lbm
m3 kg
ft 3 lb mole
m3 mol
p
dimensionless
Btu hr
= Pa
kg N = 2 m m : s2
2 J kg : m W= s= 3 s
Btu J mol : K lb mole -cR dimensionless dimensionless °R or °F K or °C °R or °F K or °C dimensionless m ft s sec ft3 m3
Temperature Critical temperature Reduced temperature
Dv
Specific volume change during phase change
X x Y y Z z
Mole ratio in liquid phase (solute-free basis) Mole fraction in liquid phase Mole ratio in vapor phase (solute-free basis) Mole fraction in vapor phase Compressibility factor Mole fraction in the feed
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dimensionless dimensionless dimensionless dimensionless dimensionless dimensionless
Chapter 6: Mass Transfer
Symbols (cont'd) Symbol
z
Description
Distance or length
a
Interfacial area per unit volume
aij
Relative volatility for components i and j
d g
Film thickness Activity coefficient
g
Surface tension
e
Void fraction
m
Dynamic viscosity
r
Density
Units (SI)
ft or in.
m
ft ft 3
m2 m3
2
dimensionless ft or in.
m dimensionless
lbf in.
zt i
Fugacity coefficient i of a pure component in the vapor phase Fugacity coefficient i of a component in a mixture in the vapor phase
zd
Volume fraction of the dispersed phase (holdup)
zi
Units (U.S.)
N kg m = s2 dimensionless
lbm cP or ft -sec
kg Pa : s = m : s
lbm ft 3
kg m3 dimensionless dimensionless dimensionless
6.2 Phase Equilibria 6.2.1
Phase Equilibrium Applications
6.2.1.1 Distribution of Components Between Phases in a Vapor/Liquid Equilibrium Assume Dalton’s Law and Raoult’s Law apply. The distribution coefficient is defined as: yi p isat K=i x= P i where Ki = distribution coefficient for component i The relative volatility is defined as: Ki yi x j = = a ij K j y j xi where aij = relative volatility for components i and j For a binary system, the following expressions may be derived: x a K x y1 = 1 + x 1(a 12 − 1) = K + x (1K1 − K ) 1 12 2 1 1 2 y K y x1 = a + y (11 − a ) = K + y (2K 1 − K ) 12 1 12 1 1 2 1
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Chapter 6: Mass Transfer 6.2.1.2 Dew Point The dew point is defined as the point where the vapor reaches saturation and the liquid phase begins to form. It may be determined by iterative calculations from one of the following three relationships, given the vapor composition and either pressure or temperature: n n n n yi yi P 1 = = = xi = 1 or x 1 or P = sat i K p i y n i =i 1=i 1 =i 1=i 1 f i p i = 1 p sat i
/
If If
/
/
/
/
n
/ Kyii > 1, increase temperature or decrease total pressure.
i=1 n
/ Kyii < 1, decrease temperature or increase total pressure.
i=1
6.2.1.3 Bubble Point Similarly, the bubble point is defined as the temperature/pressure combination in which the first bubble of vapor is formed in a liquid. It may be determined by iterative calculations from one of the following three relationships, given the liquid composition and either pressure or temperature: n n n n n xi pi, sat = = = yi = Ki xi 1 or yi = 1 or P xi pi, sat P = = = = =
/
i 1
If If
/
i 1
/
i 1
/
/
i 1
i 1
n
/ Ki xi > 1, decrease temperature or increase total pressure.
i=1 n
/ Ki xi < 1, increase temperature or decrease total pressure.
i=1
6.2.1.4 Single-Stage Flash A single-stage flash determines the distribution of components between the liquid and vapor phase. It may be determined by iterative calculations from one of the following two relationships, given the feed composition, the relative proportions of vapor and liquid resulting from the flash, and either pressure or temperature: n n n n zi zi Ki = = xi = or y 1 i + f (Ki − 1) + f (Ki − 1) = 1 1 1 = = = =
/
where
i 1
/
i 1
/
i 1
/
i 1
zi = mole fraction of component in the feed f = ratio of vapor phase flow to the feed flow The lever rule may be applied to binary single-stage flash calculations as follows: V = = zi − xi F f yi − xi − y z L = − = i i F 1 f yi − xi
F, zi, fi
V, yi T, Ptot L, xi
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Chapter 6: Mass Transfer Operating line equations are: z q 1−f 1 n L F o xi + i =−e − o xi + d − yi =− c V m xi + c V m zi =− e 1 q zi f 1 q f where q = ratio of liquid phase flow to the feed flow
6.2.2
Diffusion
6.2.2.1 Fick’s Law of Diffusion: Molar Flux dc j A = − D AB dzA Mass transport due to diffusion and bulk flow: dx no A = no x A + j A = (no A + no B) x A − c D AB dzA dx no B = no x B + j B = (no A + no B) x B − c D BA dzB where no A = molar flow of species A no = bulk flow
Rules of Thumb for Diffusion Coefficients at 25°C ft 2 m D AB c sec
D AB c ms m
0.43 × 10–4 – 2.4 × 10–4 1.8 × 10–4 – 8.1 × 10–4 0.32 × 10–4 – 1.7 × 10–4
0.4 × 10–5 – 2.2 × 10–5 1.7 × 10–5 – 7.5 × 10–5 0.3 × 10–5 – 1.6 × 10–5
0.75 × 10–8 – 2.2 × 10–8 1.3 × 10–8 – 3.2 × 10–8 0.43 × 10–8 – 1.5 × 10–8 1.6 × 10–8 – 3.2 × 10–8
0.7 × 10–9 – 2.0 × 10–9 1.2 × 10–9 – 3.0 × 10–9 0.4 × 10–9 – 1.5 × 10–9 1.5 × 10–9 – 3.0 × 10–9
2
In Gases
Air Hydrogen Carbon dioxide In Liquids Gases in water Acids in water Organics in water In organic solvents
Diffusion Coefficient (Pressure and Temperature Dependence) For dilute, binary gas systems, changes in the diffusion coefficient can be predicted at any temperature and at any pressure below 25 atm by: P T 2 XD _T1 i DAB _T2, P2 i = DAB _T1, P1 ie P1 oe T2 o 2 1 XD _T2 i 3
where
DAB(T, P) = diffusion coefficient as a function of pressure and temperature ΩD(T) = the "collision integral" for molecular diffusion, which is a dimensionless function of temperature and of the intermolecular potential field for one molecule of A and one molecule of B. ©2017 NCEES
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Chapter 6: Mass Transfer Collision Integral for Diffusion as a Function of Dimensionless Temperature
Collision integral, ΩD
3.0 2.5 2.0 1.5 1.0 0.5 0.0
0.0
2.0
4.0
6.0
8.0
10.0
Dimensionless temperature, κT/εAB Source: Welty, James R., Gregory L. Rorrer, and David G. Foster, Fundamentals of Momentum, Heat, and Mass Transfer, 6th ed., New York: Wiley, 2015, p. 444.
6.2.2.2 Integrated Forms of Fick’s Law of Diffusion Steady-State Equimolar Counterdiffusion of Two Components (No Bulk Flow, DAB = DBA, Ideal Gas): no A =
D AB c D AB (c A − c A, i) = (x A − x A, i) d d
For an ideal gas: D P D no A = AB (p A − p A, i) = AB (y A − y A, i) d RT d RT where i = conditions at the interface d = film thickness Steady-State Diffusion of A Through a Stagnant Film (no B = 0 ) no A =
c D AB 1−x ln f − A p 1 x A, i d
where xA,i = concentration of A at the interface xA = concentration of A at distance z from the interface Concentration profile:
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Chapter 6: Mass Transfer 1−x 1−x z ln f − A p = ln f − A, b p 1 x A, i d 1 x A, i where xA,b = concentration of A in the bulk fluid z
= distance from the interface
For an ideal gas: D P D P y A − y A, i 1−y no A = AB ln f − A p = AB ylm 1 y A, i d RT d RT ylm =
` y A − y A, i j 1−y ln 1 − y A A, i
plm =
` p A − p A, i j P−p ln P − p A A, i
where ylm = logarithmic mean of the mole fractions in the gas phase and at the interface plm = logarithmic mean of the partial pressures in the gas phase and at the interface For diffusion of one component through a multicomponent mixture, the equation above with an effective diffusion coefficient can be used: 1 − yA D A, mix = yj j ! A D Aj
/
Definitions of the Mass-Transfer Coefficient System
Equimolar counter-diffusion, liquid
Equimolar counter-diffusion, ideal gas
Diffusion through a stagnant film, liquid
Diffusion through a stagnant film, ideal gas Diffusion through a stagnant film, ideal gas, mass-basis
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Mole Fraction
Concentration
no A = k x Dx A c D AB kx = d no A = k y Dy A D P k y = AB d RT no A = k xl Dx A c D AB k xl = d clm no A = k yl Dy A D AB P k yl = d RT ylm mo A = k yl Dy A D P MWA k yl = AB d RT ylm
no A = kc Dc A D kc = AB d no A = kc Dc A D kc = AB d no A = kcl Dc A D kcl = AB d clm no A = kc Dc A D kc = AB d clm
276
Pressure
no A = kG Dp A D kG = AB d RT
no A = kGl Dp A D AB kG l = d RT plm
Chapter 6: Mass Transfer where
clm =
c Ao − c A c −c ln cAo − c Ai A Ai
kc = mass-transfer coefficient for liquid (concentration basis) kG = mass-transfer coefficient for gas (pressure basis) kx = mass-transfer coefficient for liquid (mole fraction basis) ky = mass-transfer coefficient for gas (mole fraction basis) kc' = mass-transfer coefficient for liquid (concentration basis), corrected for inert component kG' = mass-transfer coefficient for gas (concentration basis), corrected for inert component kx' = mass-transfer coefficient for liquid (mole fraction basis), corrected for inert component ky' = mass-transfer coefficient for gas (mole fraction basis), corrected for inert component
6.2.2.3 Convective Mass Transfer Reynolds analogy between momentum, heat, and mass transfer with Colburn correction: 2/3 k n j M = GG d t D n AB M 2/3
h c n jH = c G d p n k p
For flow through straight tubes and across plane surfaces: f = j= jM H 8 For turbulent flow around cylinders: f jM = jH # 8 where f
= Darcy friction factor
kg lbm or 2 2 ft - hr m :s GM = molar mass velocity (same as no A ) G = mass velocity in
h jH
Btu W or 2 hr - ft 2 - o F m :K = Colburn heat-transfer factor
= heat-transfer coefficient in
jM = Colburn mass-transfer factor k = thermal conductivity in
W Btu or m : K hr - ft - o F
kG = gas-phase mass-transfer coefficient
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Chapter 6: Mass Transfer Other correlations for the mass-transfer coefficient:
Mass Transfer1 for Simple Situations Fluid Motion
Inside circular pipes
Unconfined flow parallel to flat plates2
Range of Conditions
Equation
Re–0.17
Re = 4000–60,000 Sc = 0.6–3000 Re = 10,000–400,000 Sc > 100 Transfer begins at leading edge Rex < 50,000
jM = 0.023 Sh = 0.023 Re0.83 Sc1/3 jM = 0.0149 Re–0.12 Sh = 0.0149 Re0.88 Sc1/3
Rex = 5 × 105–3 × 107 Pr = 0.7–380
Pr Nu = 0.037 Re x0.8 Pr 00.43 e Pr0 o
jM = 0.664 Rex–0.5 0.25
i
Between above equation and Rex = 2 × 104–5 × 105 Pr = 0.7–380
0.25
Pr Nu = 0.0027 Re x Pr 00.43 e Pr0 o i
Confined gas flow parallel Ree = 2600–22,000 to a flat plate in a duct 4C = 0–1200 n
Liquid film in wetted-wall ripples suppressed tower, transfer between liquid and gas 4C = 1300–8300 n Perpendicular to single cylinders
Re = 400–25,000 Sc = 0.6–2.6 Rel = 0.1–105 Pr = 0.7–1500
jM = 0.11 Ree–0.29 See note 4. 1.506
− Sh = (1.76 # 10 5) c 4nC m
Sc 0.5
kG P 0.56 = 0.281 ^ Relh0.4 G M Sc Nu = 80.35 + 0.34 ^ Relh0.5 + 0.15 ^ Relh0.58B Pr 0.3
Sh = Sh0 + 0.347 _ Rell Sc 0.5 i
0.62
Past single spheres
Through fixed beds of pellets3
0.5
Rell Sc = 1.8–600,000 Sc = 0.6–3200
Sh0 = *
2.0 + 0.569 (GrM Sc) 0.250 2.0 + 0.0254 (GrM Sc) 0.333 Sc 0.244
Rell = 90–4000 Sc = 0.6
−0.575 2.06 j M = j H = f ^ Rellh
Rell = 5000–10,300 Sc = 0.6
−0.815 20.4 j M = 0.95j H = f ^ Rellh
Rell =0.0016–55 Sc = 168–70,600
−2/3 1.09 j M = f ^ Rellh
Rell = 5–1500 Sc = 168–70,600
jM =
GrM Sc < 10 8 4 GrM Sc 2 10 8
0.250 ^ Rellh−0.31 f
1. Average mass-transfer coefficients throughout, for constant solute concentrations at the phase surface. Generally, fluid properties are evaluated at the average conditions between the phase surface and the bulk fluid. The heat-mass-transfer analogy is valid throughout. 2. Mass-transfer data for this case scatter badly but are reasonably well represented by setting jM = jH.
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Chapter 6: Mass Transfer
3. For fixed beds, the relation between e and dp is a = per volume of bed. For mixed sizes:
6 ^1–f h d p , where a is the specific solid surface, surface
n
dp =
/ ni d pi3
i=1 n
/ ni d pi2
i=1
4. For small rates of flow or long contact times:
k L, av d = D AB Shav . 3.41
For large Reynold numbers of short contact times: 1
6D C 2 kl, av = e AB o rtdl
2 3 d Shav = c 2r l Re Sc m
1
Total absorption rate from the average kL: ur y d N A, av = l `crA, l − c A0 j = k L, av `c A, i − crA jM
`c A, i − crA jM =
where
a
= specific surface of a fixed bed of pellets, pellet surface/volume of bed
cA,i
= concentration of A at the interface
cA0
= concentration of A at the approach, or initial, value
cA
= bulk-average concentration of A
c A , l = bulk-average concentration of A across length l
DAB = molecular diffusivity of A in B
dc
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`c A, i − c A0 j − `c A, i − crA, l j RS V SS `c A, i − c A0 j WWW W ln SS SS`c A, i − crA, l jWWW T X
= diameter of a cylinder
de
= equivalent diameter of a noncircular duct = 4 (cross-sectional area)/perimeter
dp
= diameter of a sphere; for a nonspherical particle, diameter of a sphere of the same surface as the particle
G
= mass velocity
GrM = Grashof number for mass transfer
k
kl,av = average mass-transfer coefficient across length l
l
gl 3 Dt t 2 t dn n
= mass-transfer coefficient
= length 279
Chapter 6: Mass Transfer
NA,av = average mass-transfer flux of A at, and relative to, a phase boundary
ni
Nu
Pr
Pr0 = Prandtl number at the approach, or initial, value
Pri
Re
Re'
= a number, dimensionless hd = Nusselt number k cp n = Prandtl number k = Prandtl number at the interface dG lG = Reynolds number n or n
d G = Reynolds number for flow outside a cylinder cn dp G Re'' = Reynolds number for flow past a sphere n d G Ree = Reynolds number for flow in a noncircular duct en xG Rex = Reynolds number with x as the length dimension n n Sc = Schmidt number t D AB kl = Sherwood number D AB
Sh
Sh0 = Sherwood number at the approach, or initial, value
Shi = Sherwood number at the interface
uy
= bulk average velocity in the y direction (parallel to the direction of flow)
C
= mass flow rate per unit width
d
= thickness of a layer
e
= void fraction
Source: Treybal, Robert, Mass Transfer Operations, 3rd ed., New York: McGraw-Hill, 1987, pp. 74–75.
6.2.2.4 Mass Transfer with Reaction Consider a reaction between a dissolving gas A and a liquid phase reactant B, with q moles of B reacting per mole of A, so that: nA + mB " Products m q= n where q = number of moles of B reacting per mole of A CAL and CBL = molar concentrations of A and B, respectively, in the liquid
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Chapter 6: Mass Transfer The rate of reaction of A, JL, is then given by n m J L = k nm C AL C BL m+n−1
3 where knm = reaction velocity constant, in d m n mol JL has units, moles/sec/unit volume of liquid. Alternatively, n m J = k nm C AL C BL fL
mol , n and m are the orders of reaction in A and B, and f L is the liquid s : m3 hold-up fraction. A "reaction time" tR can be defined as JL is the rate of reaction and has units of
tR =
(n + 1 ) ( n − 1) m 2k nm C AL C BL
The mass transfer of A in the liquid is given by * − C AL) J = k L a (C AL
where J
= reaction rate in moles/sec/unit volume of reactor
* = dissolved gas concentration in liquid bulk in C AL
m k L = interphase mass-transfer coefficient in s
mol m3
1 = gas-liquid interphase surface area/unit dispersion volume in m mol J is the rate of reaction and has units of . A mass-transfer "diffusion time," tD, can be defined as s : m3 D t D = AL k L2 where DAL = diffusivity of A in the liquid a
If a fast reaction is occurring near the interface within the "diffusion film," it will enhance the mass-transfer rate and the equation for the mass transfer of A into liquid, above, becomes * − C AL) J = k L* a (C AL
where
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1
* (n 1) m 2 C BL G = = 2D AL k nm (C AL − C AL) n+1 m k L* = enhanced liquid-film mass-transfer coefficient in s
k L*
281
Chapter 6: Mass Transfer Various Gas-Liquid Reaction Regimes and Parameters of Importance Conditions
I Kinetic control
Important Variables
Rate
Slow reaction
eL knm
\ \
* n `C AL j
\ tD t R 1 0.02
II Diffusion control Moderately fast reaction in bulk of liquid, C AL . 0
0.02 1
tD tR 1 2
Design so that D AL eL a 2 100 k L
III Fast reaction Reaction in film, C AL . 0 (pseudo first order in A' )
21
IV Very fast reaction General case of III
21
tD tR
* C BL + C AL
* `C BL j
m
\
FILM
* C AL
\
BULK CBL
* CAL
CAL
CBL
* CAL
Independent of knm Independent of e L (if e L is adequate) Rate \ a
CAL
CBL
k nm
\
n+1 * c 2 m `C AL j
\
* CAL CAL
Independent of kL Independent of e L Rate \ a
CBL * CAL
depends on * k L k nm C AL C BL Independent of e L
V Instantaneous reaction
Rate
Reaction at interface; controlled by transfer of B to interface from bulk, J \ kL a
* Independent of C AL Independent of knm Independent of e L
tD C BL t R 22 qC * AL
LIQUID
Independent of a (if a is adequate) Independent of kL Rate \ a \ kL
tD C BL t R 1 qC * AL
* C BL 22 C AL
Concentration Profiles
GAS
Regime
\ \
CAL
a kL
CBL
* CAL
CAL
Reprinted from Mixing in the Process Industries, 2nd ed., N. Harnby, M.F. Edwards, and A.W. Nienow, "Gas-Liquid Dispersion and Mixing," p. 352, © 1992, with permission from Elsevier.
6.2.2.5 Mass Transfer Between Phases for Dilute Systems no A = k L (x − xi) = kG (yi − y) = k lL (c − ci) = k lG (pi − p)
MASS TRANSFER BETWEEN PHASES: LIQUID PHASE
INTERFACE
VAPOR PHASE T, ptot
= lL tr L and kG k lG P k L k= yi − y k L k lL tr L L M HTUG = = = x − xi kG k lG P G M HTU L
x
xi
yi y
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Chapter 6: Mass Transfer where kL
= liquid-phase mass-transfer coefficient (mole fraction basis)
k lL
= liquid-phase mass-transfer coefficient (concentration basis)
kG
= gas-phase mass-transfer coefficient (mole fraction basis)
k lG
= gas-phase mass-transfer coefficient (partial pressure basis)
LM
= molar-liquid mass velocity, in moles/time/area
GM
= molar-gas mass velocity, in moles/time/area
HTUL = height of a transfer unit based on liquid phase resistance HTUG = height of a transfer unit based on vapor phase resistance pi
= partial pressure
tr L
= average molar density of liquid phase
In most types of separation equipment, the interfacial area for mass transfer cannot be accurately determined and transfer coefficients based on volume of the device are used: 1 = 1 + m KG a kG a kL a
and
1 = 1 + 1 KL a m kG a kL a
where a
= effective interfacial mass-transfer area per unit volume, in
ft 2 m2 or ft3 m3
KG = overall gas-phase mass-transfer coefficient KL = overall liquid-phase mass-transfer coefficient m = slope of equilibrium line Overall Mass-Transfer Coefficients KL and KG for Dilute Systems no A = K L (x − x eq) = KG (y eq − y) where xeq = liquid mole fraction in equilibrium with vapor phase yeq = vapor mole fraction in equilibrium with liquid phase
Overall Mass-Transfer Coefficients for Dilute Systems Equilibrium: y = m • x Use for:
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Gas Phase
Liquid Phase
1 = 1 +m KG kG k L
1 = 1 + 1 K L m kG k L
High solubility, low m; gas-phase resistance is controlling
Low solubility, high m; liquid-phase resistance is controlling
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Chapter 6: Mass Transfer 6.2.2.6 Mass Transfer Between Phases for Concentrated Systems no A =
ktL (x − xi) ktG (yi − y) Kt L (x − x eq) Kt G (y eq − y) = eq eq x BM = y BM = x BM y BM
x BM =
y BM =
(1 − x) − (1 − xi) _1 − x i ln _1 − xi j (1 − y) − (1 − yi) `1 − y j ln `1 − yi j
eq = x BM
eq = y BM
(1 − x) − (1 − x eq) _1 − x i ln _1 − x eq i (1 − y) − (1 − y eq) `1 − y j ln `1 − y eq j
= ktG k= k lG P y BM G y BM = ktL k= k lL PL x BM L x BM yi − y k L ktL y BM L M HTUG y BM = = = x − xi kG ktG x BM G M HTU L x BM where ktG
= gas-phase mass-transfer coefficient for concentrated systems
Kt G
= overall gas-phase mass-transfer coefficient for concentrated systems
ktL
= liquid-phase mass-transfer coefficient for concentrated systems
Kt L
= overall liquid-phase mass-transfer coefficient for concentrated systems
x BM
= logarithmic-mean solvent concentration between bulk and interface
y BM = logarithmic-mean gas concentration between bulk and interface LM
= molar-liquid mass velocity, in moles/time/area
GM
= molar-gas mass velocity, in moles/time/area
HTUL = height of a transfer unit based on liquid-phase resistance HTUG = height of a transfer unit based on vapor-phase resistance Overall Mass-Transfer Coefficients Kt L and Kt G for Concentrated Systems eq 1 = y BM 1 + x BM 1 (y − yi) eq eq Kt G y BM ktG y BM ktL (x − xi) eq 1 = x BM 1 + y BM 1 (xi − x ) eq eq Kt L x BM ktL x BM ktG (yi − y)
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Chapter 6: Mass Transfer 6.2.2.7 Height of a Transfer Unit GM GM = HTUG k= a y G BM ktG a LM LM = HTU L k= L a x BM ktL a
where
HTUOG =
y GM GM mG M x BM = BM eq = t eq HTU G + eq HTU L L M y BM KG a y BM KG a y BM
HTUOL =
LM LM x L M y BM = BM eq = t eq HTU L + eq HTU G mG x K L a x BM M x BM KL a BM
HTUG = height of a transfer unit based on vapor-phase resistance HTUOG = height of an overall vapor-phase mass-transfer unit HTUL = height of a transfer unit based on liquid-phase resistance HTUOL = height of an overall liquid-phase mass-transfer unit Height Equivalent to One Theoretical Plate (HETP) mG If equilibrium line and operating line are parallel e L M = 1 o , then: M HETP = HTU If equilibrium line and operating line are straight, but not parallel, then: mG M −1 HTUOG LM = HETP mG ln e L M o M
6.3 Continuous Vapor-Liquid Contactors 6.3.1
Material and Energy Balances for Trayed and Packed Units
6.3.1.1 Theoretical Stage An ideal theoretical stage has the following characteristics: 1. It operates in steady state and has a liquid product and a vapor product. 2. All vapor and liquid entering the stage are intimately contacted and perfectly mixed. 3. Total vapor leaving the stage is in equilibrium with total liquid leaving the stage.
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Chapter 6: Mass Transfer For a single binary distillation stage, the following balances and equilibrium relationships apply. Overall mass balance:
Ln–1
Vn
Fn + Vn + 1 + L n − 1 = Vn + L n Fn
Component mass balance:
(zn)
z n Fn + y n + 1 Vn + 1 + x n − 1 L n − 1 = y n Vn + x n L n
STAGE n (yn+1) Vn+1
Energy balance:
(xn–1)
(yn)
ΔHn
(xn) Ln
ht f, n Fn + ht V, n + 1 Vn + 1 + ht L, n − 1 L n − 1 + DHo n = ht V, n Vn + ht L, n L n where ht
= molar specific enthalpy
Fn
= feed flow to stage n
Vn
= vapor flow leaving stage n
Ln
= liquid flow leaving stage n
DHo n = heat input to stage n Phase equilibrium: yn = K xn For binary system with relative volatility a12: a12 x n yn = 1 + x n _a12 − 1 i
6.3.1.2 Constant Molal Overflow When the molar heats of vaporization of the components are nearly equal, the molar flow rates of the vapor and liquid are nearly constant in each section of the column. In the rectifying section, the following assumptions then apply: = = L L= L1 L= and V V1 = Vn 0 n And in the stripping section, the following assumptions then apply: = l L= L Lm N
and
l V= V= Vm N
where L = liquid flow in the rectifying section V = vapor flow in the rectifying section Ll = liquid flow in the stripping section V l = vapor flow in the stripping section N = total number of stages m = stage in stripping section n = stage in rectifying section ©2017 NCEES
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Chapter 6: Mass Transfer 6.3.1.3 Column Material Balance Stage Model for Distillation STAGE MODEL FOR DISTILLATION
CONDENSER STAGE 0
•
Qc
V1
RECTIFYING SECTION
L0
F zF
V1
L0
V2
L1
Vn
Ln-1
Vn+1
Ln
Vf
Lf-1
D XD
STAGE 1
STAGE n
STRIPPING SECTION
STAGE f (FEED)
Vf+1
Lf
VM
LM-1
VM+1
LM
VN
LN-1
STAGE M
STAGE N
LN
VN+1
LN
•
QR
REBOILER STAGE N+1
B XB
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Chapter 6: Mass Transfer Overall mass balance: F=D+B Component mass balance: zF F = xD D + xB B Ratios: D = zF − xB F xD − xB B = xD − zF F xD − xB For the rectifying section, the following balances apply: D = V1 − L0 = Vn + 1 − L n x D D = y1 V1 − x0 L0 = y n + 1 Vn + 1 − x n L n For the stripping section, the following balances apply: B = L N − 1 − VN = L m − Vm + 1 x B B = x N − 1 L N − 1 − y N VN = x m L m − y m + 1 Vm + 1 To calculate the composition on each stage (for constants L, Ll , V, and V l ), for the x D x x D R L L L L Rectifying section: y n + 1 = V x n + DV = L + D x n + L D+ D = R + 1 x n + R +D 1 = V x n + c1 − V m x D Ll x x B x B x Ll Ll S+1 Stripping section: ym + 1 = l xm − B l = l − xm − lB− = S xm − SB = lB xm − l B L − L − V V L B L B B 1 B 1 Reflux ratio (also called external reflux ratio): L V−D R= D = D Boil-up ratio: V l Ll S = B = B −1 Slope of the operating line, for the L R Rectifying section: slope = V = R + 1 Ll +1 l L S Stripping section: slope = l = S = lB L − V B 1
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Chapter 6: Mass Transfer 6.3.1.4 Graphical Solution for Binary Distillation (McCabe-Thiele Diagram) McCabe-Thiele Diagram for Binary Distillation With Constant Molal Overflow and Constant Relative Volatility 1
y1
x - INTERCEPT (y = 1) EQUILIBRIUM CURVE
xD E
A
y'
D
y = MOLE FRACTION IN VAPOR
y - INTERCEPT (x = 0)
C x'
q LINE
zF
yN
y=x
B yN+1
0
RECTIFYING OPERATING LINE
STRIPPING OPERATING LINE
xB
xN
0
x = MOLE FRACTION IN LIQUID
1
Equations for the McCabe-Thiele Diagram Name
Equations
ax y = 1 + x (a − 1)
Equilibrium Line Operating Line for the Rectifying Section
A
x D x x D R L L yn + 1 = V xn + DV = L + D xn + L D+ D = R + 1 xn + R +D 1 Slope:
L= R V R+1
Reflux Ratio: x R = y D −1 x=0
Ll x xB B xB B xB +1 l l L L S ym + 1 = l xm − l = l − xm − l − = S xm − S = lB xm − l B L − L − V V L B L B B 1 B 1 − Ll = ` − j + ` + − j x F x B 1 f R 1 f x −x B D F
Operating Line for the Stripping Section
B Slope:
Ll = S + 1 S Vl
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y-Intercept (x = 0): x x D y x = 0 = R +D 1 = L D+ D
x-Intercept (y = 1): Ll xB + B − 1 xy=1 = Ll B
289
Boil-up Ratio: xy = 1 − xB S = 1−x y=1
Chapter 6: Mass Transfer Equations for the McCabe-Thiele Diagram (cont'd) Name
Equations
Feed Line
C
y= Slope:
f−1 q = − f q 1
Intersection of Feed Line/ Operating Lines
E
Intercept:
Feed Quality:
For x F $ 1 − f
For y = 0 intercept: z z f = 1− x F q= x F y=0 y=0
For x F # 1 − f z + f − 1 q − zF = − yx = 1 = F f q 1
For x = 1 intercept z −y = 1−z f =1−y F q = 1F− y x 1 x=1 x=1
z z x y = 0 = 1 −Ff = qF
xI = e
f ^R + 1h zF x − +D o 1 + − R f f R 1
` f − 1j ^R + 1h z z x y I = fF + e F − +D o 1 + R − f f R 1
D Intersection of Feed Line/ Equilibrium Line
f−1 q z z + F = − x − −F f x f q 1 q 1
For constant a: af zF 1 1 H+ xl = − 2 > a − 1 + f − 1 − _a − 1 i ` f − 1 j
2
af zF 1 > 1 + zF − − 4 a − 1 f − 1 _a − 1 i ` f − 1 j H _a − 1 i ` f − 1 j
f − 1 + zF o yl = xl e f f Operating Line for Total Reflux Operating Line for Minimum Reflux
y=x x − yl R min = Dl − l y x
Circled A, B, C, D, and E in table above refer to the previous graph, "Binary Distillation With Constant Molal Overflow."
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Chapter 6: Mass Transfer 6.3.1.5 Feed Conditions The feed condition is defined by q = mole fraction liquid in feed mqlar enthalpy to cqnvert feed to saturated vapqr = molar enthalpy of vaporization f = mole fraction vapor in feed q+f=1 Ll = L + q F = L + `1 − f j F
V = V l + `1 − q j F = V l + f F
Feed Conditions Feed Condition
Values for f and q
Subcooled Liquid
f<0 cpL (Tb − TF) f=− Dhvap
Flows at Feed Location
V
L'
V'
L
V
L'
V'
F
q>1 cpL (Tb − TF) q = 1+ Dhvap Bubble Point (Saturated Liquid)
L
f=0 q=1 F
Partially Vaporized
0
V
0
L F
L'
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V'
Feed Line in McCabe-Thiele
Chapter 6: Mass Transfer Feed Conditions (cont'd) Feed Condition
Dew Point (Saturated Vapor)
Values for f and q
Flows at Feed Location
f=1
V
L
q=0
F L' V' Superheated Vapor
f>1 cpV (TF − Td) f = 1+ Dhvap q<0 cpV (TF − Td) q=− Dhvap
L F
L' V'
where cpL = heat capacity of the liquid cpV = heat capacity of the vapor TF = temperature of the feed Tb = bubble point temperature of the liquid Td = dew point temperature of the vapor
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292
Feed Line in McCabe-Thiele
Chapter 6: Mass Transfer 6.3.1.6 Condensers Types of Condensers Total Condenser
Partial Condenser
A total condenser does not represent a theoretical stage.
A partial condenser represents a theoretical stage.
V1 y1 STAGE 1
STAGE 1
“STAGE” 0 V2 y2
V1 y1 L1 x1
STAGE 2
V2 y2
V1 V1
L0 x0
L1 x1
D x0 NOT A THEORETICAL STAGE
A THEORETICAL STAGE
y
y
b
a
yN
yN
b
D y0 = x0
a
yN+1
c
d
c
e xN
x N–1
x
x N+1
The triangle indicated by abc represents the top stage of the distillation column. Heat Duty: Qo TC = V1 Dhvap = D (R + 1) Dhvap
xN
x N–1
x
The triangle indicated by cde represents the top stage of the distillation column and the triangle indicated by abc represents the partial condenser. = Heat Duty: Qo PC L= D R Dhvap 1 Dhvap
For subcooled reflux: If the reflux is subcooled, a portion of the vapor entering the top stage of the column will condense, providing heat to increase the liquid temperature to the bubble point. The additional amount of liquid that is condensed inside the column is determined by: DL =
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LER cpR _T1 − TR i Dhvap
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Chapter 6: Mass Transfer Effective reflux ratio (also called internal reflux ratio) for the stages in the column: L = LER + DL = D D
LER >1 + cpR
D
_T1 − TR i Dhvap
H
The temperature of the top stage in the column, T1, may be estimated as equal to the bubble point of the external reflux. where T1 = temperature of top stage TR = temperature of the reflux LER = external reflux (LER = RD) DL = rate of liquid condensed on top stage of the column cpR = heat capacity of the reflux
6.3.1.7 Reboilers Types of Reboilers Reboiler Without Mixing
Reboiler With Mixing
If the vapor effluent from the reboiler is in equilibrium with the bottom product, then the reboiler represents a theoretical stage. Other examples: kettle reboiler, internal heating coil.
If liquid effluent from the reboiler mixes with the liquid from the bottom stage of the column, the reboiler does not represent a theoretical stage.
Vap
LIQUID FROM TRAYS Vap
THEORETICAL STAGE
VN+1 LN YN+1 XN
STAGE N+1
Liq
Liq
HOT STREAM LN+1 XN+1
HOT STREAM
LN XN
BOTTOM PRODUCT
BOTTOM PRODUCT
Heat Duty: Qo R = VN + 1 Dhvap = S B Dhvap Heat Duty:
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NOT A THEORETICAL STAGE
= Heat Duty: Qo R V= S B Dhvap R Dhvap
x −x Qo R = B =` R + 1 − f j F − B − f G Dhvap xD xF
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Chapter 6: Mass Transfer 6.3.1.8 Minimum Flow Rates and Reflux Underwood Method With No Distributed Nonkey Components The Underwood method assumes constant relative volatilities and constant molal overflows, and it requires a trialand-error solution. First, by trial-and-error, find a value for φ that is between the relative volatilities of the light key and heavy key components. The relative volatilities are based on a characteristic temperature for the column, such as the bubblepoint temperature of the distillate or the flashed feed temperature at the column pressure. The heavy key is the reference component j for the relative volatilities of each component i. aij zFi = 1−q = aij − { / fi
/
Second, calculate the value of φ from: aij xDi Rmin + 1 = aij − {
/
where zfi = concentration of component i in the feed q = moles of feed to stripping section per mole of feed aij = relative volatility between components i and j φ = adjustable parameter, which has no physical significance fi = fraction of component i in the feed that is vaporized
6.3.1.9 Minimum and Theoretical Stages Minimum Theoretical Stages: Fenske Equation The Fenske equation applies when the relative volatility is constant across the column. If the relative volatility varies across the column, a geometric mean of the range of values for the relative volatility may be used as an approximation. For example: aij = `atop abot j
1/2
or
aij = `atop amid abot j
1/3
For a binary separation, the Fenske equation for the number of stages (including any theoretical stages represented by the condenser and reboiler) at total reflux is x 1 − xB G ln = − D 1 xD xB N min = ln a1, 2 For a multicomponent separation—where 1 and 2 are the two components with the light key indicated by i and the heavy key indicated by j—the Fenske equation is x x ln > xDi xBj H Dj Bi Nmin = aij where Nmin = minimum number of stages, including any theoretical stages represented by the condenser and reboiler ©2017 NCEES
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Chapter 6: Mass Transfer Estimated Number of Theoretical Stages: Gilliland Correlation
Gilliland Correlation 1.0 0.8 0.6 0.4
N – Nmin N+1
0.2 0.1 0.08 0.06 0.04 0.02 0.01 0.01
0.02
0.04
0.10
0.2
0.4 0.6 1.0
R – Rmin R+1 Source: McCabe, Warren L., Julian C. Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993, p. 609.
Estimated Number of Theoretical Stages: Underwood Correlation The Underwood correlation can be used for constant volatility and partial reflux.
Underwood Correlation Rectifying Section (Top)
0 # K1 # 1,
Stripping Section (Bottom)
K2 2 1
K1 1 0,
0 # K2 # 1 V = ` + − j xF − xB − R 1 f x −x f L D F xB b= x −x `R + 1 − f j F − B − f xD xF
V = R+1 L R x b = R +D 1 V 1 − a12 L 1 p! K1, 2 = − 2 f b V − L a12 − 1
2 V V 1 V 1 − a12 L − b L f p 4 b L − a −1 a12 − 1 12
Intersection of feed line with operating lines: xI = e NR = ln
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_ xD − K1 i _ K2 − xI i _ xI − K1 i _ K2 − xD i
f ^R + 1h xF x − +D o 1 + − R f f R 1
NS = ln
296
_ xI − K1 i _ K2 − xB i _ xB − K1 i _ K2 − xI i
Chapter 6: Mass Transfer where K1 , K2 = distribution coefficients of components 1 and 2 b
= intercept of the operating line with the vertical axis
NR
= number of stages in the rectifying section
NS
= number of stages in the stripping section
6.3.1.10 Multicomponent Distillation Key and Nonkey Components Key components are the two components in a mixture that characterize the degree of separation or that may provide the basis for a separation to be achieved. Light key: The more volatile of the two key components. Present in both the distillate and bottoms product, and recovered predominantly in the distillate product. Heavy key: The less volatile of the two key components. Present in both the distillate and bottoms product, and recovered predominantly in the bottoms product. Nonkey: Other components in the mixture to be separated. Light nonkey: Components more volatile than the light key component. Present almost completely in the distillate product. Heavy nonkey: Components less volatile than the heavy key component. Present almost completely in the bottoms product. Distributed key: Components having volatility between that of the light key and heavy key. Present in both the distillate and bottoms product. Also called intermediate key.
6.3.1.11 Absorption and Stripping For dilute solutions (xsolvent . 1) , use solute-free basis for the concentrations (X, Y) and the flow rates (GS, LS): y p x YA = 1 −Ay = P −A p XA = 1 −Ax A tot A A GS = G `1 − yA j =
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G
_1 + YA i
LS = L _1 − xA i =
297
L
_1 + XA i
Chapter 6: Mass Transfer Absorption and Stripping Absorber
Stripper
Feed Yin For fresh solvent: Xin = 0
GS , Yout
LS , Xin
GS, Yin
LS, Xout
Feed Xin For fresh stripping gas: Yin = 0
Material Balance L Yout = Yin − GS ` Xout − Xin j S
and
L Xout = Xin − GS `Yout − Yin j S
Equilibrium Line (EQ): y = m x YEQ =
mX + 1 X _1 − m i
or
XEQ =
Y + m Y _m − 1 i
Operating Line (OL) L L Y = GS X + Yin − GS Xout S S
Operating Line (OL)
Minimum Flow
Minimum Flow
L L Y = GS X + Yout − GS Xin S S
GS `Yin − Yout j LS,min = Yin − Xin m + Yin _ m − 1 i
Diagram Yin Yout
GS,min = Diagram
BOTTOM
Y eq ( Xin )
OL
EQ
Yout
TOP
Absorption Factors:
EQ
Xout
Yin
X eq (Yin )
TOP
Ls
Gs,min
Ls,min Gs Xin
LS ` Xin − Xout j m Xin − Yin m + Xin _ m − 1 i
OL
BOTTOM
Xin
Xout
Equilibrium Equations:
Stripping Factors:
L A = mG
General:
y=mx
mG S= L
L A = KG
Vapor/Liquid: y = K x
KG S= L
P L A = HtotG
H Henry’s Law: y = P x tot
HG S= P L tot
psat L A= HG
psat Raoult’s Law: y = P x tot
S=
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HG psat L
Chapter 6: Mass Transfer Absorption and Stripping (cont'd) Absorber
Efficiency
Stripper
Efficiency
cLm G min yin − yout = E= eq yin − y _ xin i c L m G act
E=
+
A − AN 1 + 1 − AN 1
cG m xin − xout L min = E= eq xin − x _ xin i c G m L act
E=
+
S − SN 1 + 1 − SN 1
Theoretical Stages
Theoretical Stages
NTU (Number of Transfer Units) Y −Y NTUOY = in out DYlm
NTU (Number of Transfer Units) X −X NTUOX = in out DXlm
+ ln c A− E m A AE NA = ln A E NA = 1 + E for A = 1
DYlm =
+ ln d S− E n S SE NS = ln S E NS = 1 + E for S = 1
8Yin − Yeq _ Xout iB − 8Yout − Yeq _ Xin iB
DXlm =
Yin − Yeq _ Xout i H ln > Yout − Yeq _ Xin i
8 Xin − Xeq _Yout iB − 8 Xout − Xeq _Yin iB ln >
Xin − Xeq _Yout i H Xout − Xeq _Yin i
where DYlm
= log mean concentration difference in the vapor phase (solute-free basis)
DXlm
= log mean concentration difference in the liquid phase (solute-free basis)
NTUOY = overall number of transfer units based on the gas phase NTUOX = overall number of transfer units based on the liquid phase
6.3.2
Design Parameters for Trayed Units
6.3.2.1 Primary Tray Unit Design Parameters • Number of passes • Tray spacing • Tray type • Outlet weir type and height • Downcomer type and area • Clearance under downcomer • Hole size, valve size, or bubble cap size and style • Fractional hole area for sieve and valve trays • Tray pressure drop • Tray efficiency • Tray capacity • Tray hydraulics (flooding)
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Chapter 6: Mass Transfer Starting Dimensions for Cross-Flow Sieve Trays Dimension (units)
Vacuum
Atmospheric
Pressure
Tray spacing (in.) Downcomer area (% column) Active area (% column) Hole area (% active) Weir height (in.) Hole diameter (in.) Downcomer clearance (in.)
24 5 90 12 1 0.25 0.5
24 10 80 10 2 0.25 1.0
24 15 70 8 2 0.25 1.5
Source: Copyright ©2008. From Albright's Chemical Engineering Handbook by Lyle F. Albright. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
Tray Selection Criteria for Selecting a Distillation Column Device Criterion
Details
Vapor-Handling Capacity Liquid-Handling Capacity
Entrainment flooding. At incipient flooding, the minimum column diameter is fixed. Fixes the size of downcomers. Downcomer backup can lead to flooding. Sets required height for a given number of theoretical stages. Efficiency can be a function of column diameter. Of concern when the column must be operated under a wide range of feed rates or when future capacity needs must be considered in the initial design. Low pressure drop is critical for vacuum columns, especially when a low bottoms temperature must be maintained. Consider total cost of the system, including auxiliary equipment; a more expensive device may lead to lower operating costs. Device should be proven commercially. Also, the user needs to understand how the device was designed (if by a vendor). Fouling, corrosion, ease of installation or removal, potential foaming problems, adequate residence time for reactions, special heat-transfer needs.
Mass-Transfer Efficiency Flexibility Pressure Drop Cost Design Limitations Special Concerns
Source: Copyright ©2008. From Albright's Chemical Engineering Handbook by Lyle F. Albright. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
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Chapter 6: Mass Transfer 6.3.2.2 Common Types of Distillation Trays Bubble Cap Tray (left) and Various Caps (right)
Source: Adapted from Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 261.
Sieve Tray (left) and Dual-Flow Tray (right)
Source: Adapted from Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 262.
Bubble Cap Trays
Source: Adapted from Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 263.
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Chapter 6: Mass Transfer Sieve Trays
Source: Adapted from Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 263.
Valve Trays
Source: Adapted from Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 263.
6.3.2.3 Comparison of Common Types of Distillation Trays Comparison of the Common Tray Types Feature
Capacity Efficiency
Turndown
Entrainment
Sieve Trays
Bubble-Cap Trays
Dual-Flow Trays
High High About 2:1; not generally suitable for operation under variable loads
High to very high High
Moderately high Moderately high
Very high Lower than other types
About 4–5:1; some special designs achieve (or claim) 10:1 or more
Excellent; better than valve trays; good at extremely low liquid rates
Low; even lower than sieve trays; unsuitable for variable load operation
Moderate
Moderate
High; about 3 times higher than sieve trays
Low to moderate
Pressure Drop
Moderate
Cost
Low
Maintenance
Low
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Valve Trays
Moderate; early designs somewhat higher; High recent designs same as sieve trays High; about 2–3 About 20 percent times the cost of higher than sieve trays sieve trays Low to moderate Relatively high 302
Low to moderate
Low Low
Chapter 6: Mass Transfer Comparison of the Common Tray Types (cont'd) Feature
Sieve Trays
Fouling Tendency
Low
Effects of Corrosion Low Availability of Well-known Design Information
Valve Trays
Low to moderate
Most columns Most columns, services when turnwhere turndown is down is not important critical
Dual-Flow Trays
Extremely low; suitable where High; tends to colfouling is extensive and for lect solids slurry handling High Very low
Low to moderate Proprietary, but inforWell-known mation readily available
Other
Main Applications
Bubble-Cap Trays
Some information available
Instability sometimes occurs in large diameter (> 8 ft) columns Extremely lowCapacity revamps where flow conditions; efficiency and turndown can where leakage be sacrificed; highly fouling must be minimized and corrosive services
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, pp. 266–267.
Tray Efficiency The point efficiency is the ratio of the change of composition at a point to the change that would occur on a theoretical stage: y −y − EOG = f eqn − n 1 p y n yn − 1 po int The Murphree tray efficiency applies to an entire tray instead of to a single point on a tray: yn − yn − 1 p EMV = f eq y n − yn − 1 tray Overall column efficiency: N EOC = Nt a The overall column efficiency is related to the Murphree efficiency by: EOC =
ln 81 + EMV _m − 1 iB ln m
V with m = m L
where EOC = overall column efficiency EOG = point efficiency for a tray EMV = Murphree tray efficiency Nt = number of theoretical stages in a column Na = number of actual stages in a column y neq = vapor mole fraction in equilibrium with the liquid l
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= ratio of slope of equilibrium curve to operating line
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Chapter 6: Mass Transfer 6.3.2.4 Hydraulic Model for Trays The Hydraulic Model for Trays TRAY ABOVE AN ADT
FROTH
hcl ADB
hw
AB LIQUID AND GAS
LIQUID WITH BUBBLES TRAY BELOW
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992. As shown in Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-27.
Tray Area Definitions Tray Area
Symbol
Definition
Total tower crosssectional area
AT
Net area
AN
Bubbling area
AB
Hole area
Ah
Slot area
AS
Open slot area
ASo
Fractional hole area
Af
Downcomer top area Downcomer bottom area
ADT
Total cross-section area minus the area at top of the downcomer; also referred to as free area; represents smallest area available for vapor flow in the intertray spacing Total tower cross-section area minus total downcomer area, downcomer seal area, and any other nonperforated regions; also referred to as the active area (Aa); represents the area available to vapor flow near the tray floor Total area of perforations on the tray; smallest area available for vapor passage Total vertical curtain area for all valves through which vapor passes in a horizontal direction as it leaves the valves, based on the narrowest opening of the valves; smallest area available for vapor flow on a valve tray Slot area when all valves are fully opened Ratio of hole area to bubbling area (in sieve trays) or slot area to bubbling area (in valve trays) Area at top of downcomer
ADB
Area at bottom of downcomer
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Chapter 6: Mass Transfer 6.3.2.5 Definitions of Vapor Load Several different parameters are used for characterization of the vapor load. ft 3 m3 The vapor load (Vload), in s or s , is Vload = CFS
tG tL − tG
where CFS
ft 3 m3 = vapor flow rate at conditions, in sec or s
rL, rG = densities of the liquid and gas phases, respectively The F-factor for gas loading, in F = u tG
ft ft , is or kg 0.5 lb 0.5 sec d 3 n se 3 o ft m
where u = superficial linear gas velocity ft m The C-factor for gas loading, in sec or s , is t C = u t −Gt L G In practice, the F-factor and the C-factor may be based on bubbling area AB, net area AN, or some other area, depending on the source of data and correlations. Care must be taken to use the correct area basis, depending on the source. These terms are related as follows: V F = C = load A tL − tG
6.3.2.6 Definitions of Liquid Load gpm m3 The tray liquid load QL, in in. or hr : m , is gpm QL = L W where gal m3 gpm = liquid volumetric flow rate, in min or s LW
= outlet weir length, in inches or meters gpm ft m The downcomer liquid load QD, in in. or sec or s , is gpm QD = A DT
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Chapter 6: Mass Transfer 6.3.2.7 Flow Regimes on Trays Flow Regimes
Cs, VAPOR LOAD / A, ft / s
FLOODING
SPRAY FROTH EMULSION BUBBLE LIQUID FLOW RATE PER WEIR LENGTH
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992. As shown in Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-29.
VAPOR FLOW RATE
ENTRAINMENT F LOODI NG
AREA OF SATISFACTORY OPERATION
INT
WEEP PO
EXCESSIVE WEEPING
ING FLOOD MER NCO DOW
E EN XCES TR SI AIN VE ME NT
Tray Performance Diagram
DUMP POINT
LIQUID FLOW RATE
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, pp. 266–269.
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Chapter 6: Mass Transfer 6.3.2.8 Flooding Effect of Design Parameters on Flooding Design Parameters That Lower Flooding Point
Spray Entrainment Flooding
Froth Entrainment Flooding
Downcomer Backup Downcomer Choke Flooding Flooding
Low bubbling area Low fractional hole area (< 8%) Low tray spacing High weirs (> 4 in) Small weir length Small clearance under downcomer Small downcomer top area
X
X
X
X
X
X
X
X X X
X X X X X
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 274.
Entrainment Flooding The correlations for entrainment given below are based on C-factors, specifically the Souders and Brown constant ft m CSB at the entrainment flood point, in sec or s . CSB, flood = uS, flood
tG tL − tG
where uS,flood = superficial gas velocity at the entrainment flood point Fair’s Entrainment Flooding Correlation 0.5
0.2 t m e −G o CSB, flood = u N, flood c 20 v tL tG
where uN,flood = superficial gas velocity at the entrainment flood point based on the net area AN. CSB,flood and uN,flood are based on the net area AN. The correlation is applicable to sieve trays, valve trays, and bubble cap trays. These restrictions apply: 1. System is nonfoaming or low-foaming. 2. Weir height is less than 15 percent of tray spacing. 3. Sieve-tray perforations are 13 mm (1/2 in.) or less in diameter. 4. Ratio of slot (bubble cap), perforation (sieve), or full valve opening (valve plate) area Ah to active area Aa is 0.1 or greater. Otherwise the value of uN,flood should be corrected using the table below:
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Ah Aa
uN,flood Correction Factor
0.10 0.08 0.06
1.00 0.90 0.80
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Chapter 6: Mass Transfer
ρg
C sb, flood = Unf
20 0.2 σ
ρ l – ρg
0.5
, ft/s
Fair's Entrainment Flooding Correlation 0.7 0.6 0.5
PLATE SPACING 36"
0.4
24"
0.3
18" 12"
0.2
9" 6"
0.1 0.07 0.06 0.05 0.04 0.03
0.01
0.02
0.03
0.05
0.07
0.1
0.2
L F lv = _ G
ρg ρ
0.5
0.3
0.5
0.7
1.0
2.0
l
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 278. Kister and Haas Entrainment Flooding Correlation CSB = 0.144 e
0.125
d H2 c o tL
0.1
0.5 t S d tG n d h n ct L
where dH = hole diameter hct = clear liquid height at transition from froth to spray regime g
= surface tension
S
= tray spacing
dyne CSB and uflood are based on the net area AN. For surface tensions greater than 25 cm , use the value of dyne 25 cm . The correlation applies to nonfoaming systems.
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Chapter 6: Mass Transfer Recommended Range of Application: The Kister and Haas Entrainment Flood Correlation Criteria
Applicability
Flooding mechanism Tray types Pressure
Entrainment (jet) flood only Sieve or valve trays only 1.5–500 psia
Gas velocity
ft 1.5–13 sec
Liquid load
gpm 0.5–12 in. of outlet weir
Gas density
0.03–10
Liquid density
20–75
Surface tension
dyne 5–80 cm 0.05–2.0 cP 14–36 in. 1/8–1 in. 0.06–0.20 0–3 in.
Liquid viscosity Tray spacing Hole diameter Fractional hole area Weir height
lb ft 3
Notes
1
2, 3, 5 1
lb ft 3
4, 5 5
1. At pressures above 150 psia, downcomer flood is often the capacity limitation. This limitation is not predicted by the correlation. Caution is required. gpm 2. At high liquid loads (above 7–10 in. ), downcomer flood is often the capacity limitation. This limitation is not predicted by the correlation. Caution is required. gpm 3. Equation does not apply for liquid loads lower than 0.5 in. of weir. For this reason, this correlation must not be extended to lower liquid rates. 4. At lower tray spacing, entrainment flooding may be related to lifting of the froth envelope and to froth height rather than to spray height. This correlation must not be extended to lower tray spacing. 5. The correlation does not apply when the following three conditions occur simultaneously: gpm (a) ratio of flow-path length to tray spacing is high, > 3; (b) liquid rate is high, < 6 in. of weir; and (c) fractional hole area is high, > 11%. Under these conditions, entrainment flooding is related to vapor channeling and vapor cross-flow rather than to spray height.
6.3.2.9 Downcomer Backup Flooding The downcomer backup is determined by a pressure balance for the downcomer: hdc = ht + hw + how + hhg + hda
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Chapter 6: Mass Transfer where hdc = height of clear liquid in downcomer, in inch liquid or mm liquid ht = total tray pressure drop hw = height of weir at tray outlet how = height of liquid crest over weir hhg = liquid hydraulic gradient across tray hda = head loss due to liquid flow under downcomer apron The height of aerated liquid in the downcomer is determined by: h hldc = dc z dc where hldc = height of aerated liquid in downcomer z dc = relative froth density (froth density to liquid density) To prevent downcomer backup flooding, the following criterion must be met: hldc 1 S + h W
Criteria for Downcomer Aeration Factors Bolles's Criteria1
Foaming Tendency
Examples
Glitsch's Criteria2
z dc
Examples
Low
Low molecular weight hydrocarbons4 and alcohols
0.6
lb tG < 1.0 3 ft
Moderate
Distillation of medium molecular weight hydrocarbons
0.5
1.0 < t G < 3.0
High
Mineral oil absorbers
0.4
t G > 3.0
Very high Amines, glycols
lb ft 3
Fair et al.'s Criteria3
z dc
Examples
Rapid bubble rise systems, 0.6 such as low gas density, low liquid viscosity systems lb ft 3
0.4
Notes: 1. "Distillation Theory and Practice: an Intensive Course," University of New South Wales/ University of Sydney, August 9–11, 1977. 2. Glitsch, Inc. Ballast Tray Design Manual, 6th ed., Wichita, KS: Koch-Glitsch LP, 1993. 3. Perry, R.H. and D.W. Green (eds). Perry's Chemical Engineers' Handbook, 7th ed., New York: McGraw-Hill, 1997. 4. The author believes that "low molecular weight hydrocarbons" refers to light hydrocarbons at near atmospheric pressure or under vacuum. The foam stability of light hydrocarbon distillation at medium and high pressure is best inferred from the Glitsch criterion. Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992.
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0.5
0.5
Slow bubble rise systems, such as high gas density, high liquid viscosity, foaming systems
0.3
z dc
0.2– 0.3
Chapter 6: Mass Transfer 6.3.2.10 Downcomer Choke Flooding Glitsch Correlation The maximum clear liquid velocity at the downcomer entrance to avoid downcomer choke flooding is the lowest of the three following correlations: `QD, max j1 = 250 SF
`QD, max j2 = 41 tL − tG SF
where
`QD, max j3 = 7.5 S `tL − tG j SF
S
= tray spacing
SF
= system factor
QD,max = maximum downcomer liquid load, in
gpm ft m or s or s ft 2
Koch and Nutter Correlations The maximum downcomer velocity is calculated from: S QD,max = 448.8 d 12 t n SF S # 30 R where tR = apparent residence time, or the ratio of downcomer volume to the clear liquid flow in the downcomer, in seconds KOCH AND NUTTER CORRELATIONS
Koch and Nutter Correlations
14
12
RESIDENCE TIME †R , sec
10
8 †R FOR THE
KOCH CORRELATION (8)
6
5.13 sec SEC
4
SEC 4 sec †R FOR THE
NUTTER CORRELATION (9)
2
0
0
10
20
30
ρL
–
3 ρ G , lb/ft
40
70
80
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 289.
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Chapter 6: Mass Transfer Generalized Criteria for Maximum Downcomer Velocity
Maximum Downcomer Velocities ft
Foaming Tendency
Low Medium High
Clear Liquid Velocity in Downcomer, sec 18-in. 24-in. 30-in. Spacing Spacing Spacing
Example
Low-pressure (< 100 psia) light hydrocarbons, stabilizers, air-water simulators Oil systems, crude oil distillation, absorbers, midpressure (100–300 psia) hydrocarbons Amines, glycerine, glycols, high-pressure (> 300 psia) light hydrocarbons
0.4–0.5
0.5–0.6
0.5–0.6
0.3–0.4
0.4–0.5
0.4–0.5
0.2–0.25
0.2–0.25
0.2–0.3
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992.
Recommended Minimum Residence Time in the Downcomer Foaming Tendency
Low Medium High Very high
Examples
Residence Time, sec
Low molecular weight hydrocarbons, alcohols Medium molecular weight hydrocarbons Mineral oil absorbers Amines and glycols
3 4 5 7
Source: Bolles, W.L., Monsanto Company: private communication, 1977.
System Factors
Capacity Discount Factors for Foaming Systems System Type
Nonfoaming Fluorine systems Moderate foaming Heavy foaming Severe foaming Foam-stable
Examples
Factor
Freon, BF3 Oil absorbers, amine, and glycol regenerators Amine and glycol absorbers MEK units Caustic regenerators
1.00 0.90 0.85 0.73 0.60 0.30
Source: Copyright ©2008. From Albright's Chemical Engineering Handbook by Lyle F. Albright. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.
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Chapter 6: Mass Transfer 6.3.2.11 Tray Hydraulic Parameters Hydraulic Parameters
h ow
h hg h t + h w + h ow + h da + h hg
hw 1
h d + h w + h ow + –2 h hg h da 1 – β ( h w + h ow ) + 2 h hg
SIEVE TRAY h hg P 2
h ow
hw
P1 P1 – P2 = h d
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-39.
where hd = dry tray pressure drop, in inch liquid or mm liquid hda = head loss due to liquid flow under downcomer apron, in inch liquid or mm liquid hhg = liquid hydraulic gradient across tray, in inch liquid or mm liquid how = height of liquid crest over weir, in inch liquid or mm liquid ht = total tray pressure drop, in inch liquid or mm liquid hw = height of weir at tray outlet, in inch liquid or mm liquid b = tray aeration factor in pressure drop equation, dimensionless
6.3.2.12 Tray Pressure Drop The total pressure drop across a tray, ht: ht = hd + hl where hl = pressure drop through the aerated liquid on the tray, in inch liquid or mm liquid Dry tray pressure drop: t hd = K t G u h2 L where K = dry-tray pressure drop coefficient, in
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Chapter 6: Mass Transfer For sieve trays: 0.186 C v2 where Cv = orifice coefficient for dry tray pressure drop correlation ORIFICE COEFFICIENT FOR DRY TRAY PRESSURE DROP Orifice Coefficient for Dry Tray Pressure Drop K=
S KNES THIC METER Y A R T E DIA
DISCHARGE COEFFICIENT C v
0.90
HOTL
1.2
1.0
0.80
0.8 0.6 0.2
0.70
S D LES 0.1 AN
0.60 0.05
0.10
HOLE AREA = ACTIVE AREA
0.15 Ah Aa
0.20
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 311.
K Values (Pressure Drop Coefficients) for Valve Trays Valve Position
Closed Open Open Open
Valve Thickness
Flat Valve
Venturi Orifice Valves
--10 gauge (0.134 in.) 12 gauge (0.104 in.) 14 gauge (0.074 in.)
6.154 0.821 0.931 1.104
3.077 0.448 0.448 0.448
Pressure drop through the aerated liquid is hl = b hc where b = tray aeration factor hc = clear liquid height on tray
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Chapter 6: Mass Transfer Aeration Factor β for Sieve Trays FROTH DENSITY OR AERATION FACTOR
1.0 0.8 AERATION FACTOR β
0.6
0.4
0.2 RELATIVE FROTH DENSITY Φ † 0 0
0.5
1.0
1.5
F ga = U o (ρ g)
2.0
2.5
1/2
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 313.
AERATION FACTORβ β VALVE TRAYS Aeration Factor forFOR Valve Trays
FROTH DENSITY, Φ OR AERATION FACTOR
β
1.0
0.8
AERATION FACTOR, β
0.6
0.4
0.2
0
RELATIVE FROTH DENSITY, Φ 0
0.5
1.0
1.5
Fva = uB
ρv , ft/s
lb / ft
2.0
3
Source: Adapted from Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 314.
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2.5
Chapter 6: Mass Transfer Clear liquid height on the tray is h hg hc = h w + how + 2 Height of the liquid crest over the weir is how = 0.48 Fw _Q L i3
2
where gpm m3 QL = tray liquid load, in in. or h : m hc = clear liquid height on tray, in inch liquid or mm liquid Fw = weir correction factor, dimensionless
Weir Correction Factor FW for Segmental Downcomers in Calculation of Liquid Head Over the Weir
WEIR CORRECTION FACTOR, Fw
1.30
RECOMMENDED LIMIT
1.20
RATIO WEIR LENGTH TO TOWER DIAMETER 0.5 0.6 0.7 0.8
1.10
0.9
1.0
1.00 0.2
0.4
7 10 20 40 0.7 1 2 4 2.5 (LIQUID LOAD, GPM) / (WEIR LENGTH, FT.)
70 100
200
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 315.
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Chapter 6: Mass Transfer The hydraulic gradient is 12 f u L h hg = g Rf f c h where f
= friction factor
ft m uf = velocity of the aerated liquid across the tray, in sec or s Lf = length of flow path across the tray, in feet or meters gc = acceleration due to gravity Rh = hydraulic radius, in feet or meters Rh, the hydraulic radius of the aerated mass, is h D R h = 2 h +f 12f D f f hl hf = { t DT + LW Df = 2 where LW = outlet weir length h1 = pressure drop through the aerated liquid on the tray, in inches or millimeters of liquid hf = froth height on tray, in inches or millimeters Df = average of tower diameter and weir length, in inches or millimeters DT = tower diameter, in inches or millimeters jt = froth density on tray The velocity of the aerated mass across the tray uf is also equal to the velocity of the clear liquid across the tray: 1 Q L uf = 37.4 hL Dw f l The friction factor is correlated with the Reynold number: R u t Re h = h nf L l where ml = viscosity of the liquid
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Chapter 6: Mass Transfer Friction Factor for Froth Cross-Flow on Sieve Trays
FRICTION FACTOR, f
0.5 0.2 0.1
0.05 0.02
0.4 0.7 1.0 1.5 hw , in.
0.01 103
104 REYNOLDS MODULUS =
Rh Uf ρ l
105
μl
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 317.
For a segmental downcomer, the head loss is gpm h da = 0.03 e 100 A o da where Ada = area under the downcomer apron, in ft2 or m2
6.3.2.13 General Considerations for Column Sizing Tray sizing calculations are performed at points where the column loading is expected to be the highest and lowest in each section. Typically, these are • The top tray • Above every feed, product draw-off, and point of heat addition or removal • Below every feed, product drawoff, and point of heat addition or removal • The bottom tray • At any point in the column where the calculated vapor or liquid loading peaks
6.3.3
Nontrayed Continuous Contact Columns (Packed Towers)
6.3.3.1 Primary Packed-Tower Design Parameters • Type of tower separation • Packing height • Packing type and packing factors • Tower pressure drop • Flooding velocity calculation
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Chapter 6: Mass Transfer 6.3.3.2 Gas Absorption With Countercurrent Flow Gas Absorption With Countercurrent Flow Gi , YAi
Li , XAi h=h PACKING
dh G, YA
L, XA h=o Go , YAo Lo , XAo
Operating Line Above Equilibrium Line BOTTOM OF TOWER YAo
PINCH POINT SLOPE = L G MIN
YA
EQUILIBRIUM LINE (SLOPE = m) OPERATING LINE SLOPE = L G
YAi
XAo XA
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(YAo / m) = ( XAo ) MAX
Chapter 6: Mass Transfer where G
= mass velocity of gas phase
L
= mass velocity of liquid phase
XA = mass fraction A in liquid phase YA = mass fraction A in gas phase h
= height of packing
i
= dilute end
o
= rich end
s
= interface
6.3.3.3 Desorption or Stripping With Countercurrent Flow Desorption or Stripping With Countercurrent Flow Go , YAo
Lo , XAo h=h PACKING
dh G, YA
L, XA h=o Gi , YA i L i , XA i
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Chapter 6: Mass Transfer Operating Line Below Equilibrium Line MYAo EQUILIBRIUM LINE YAo (MAX)
YAo
OPERATING LINE FOR MINIMUM GAS FLOW SLOPE = L G MAX
PINCH POINT
YA
TOP OF TOWER
OPERATING LINE
YAi
XAi
XAo XA
6.3.3.4 Gas Absorption With Concurrent Flow Gas Absorption With Concurrent Flow Go, YAo
Lo, XAo h=h
dh G, YA
L, XA h=o Gi , YAi Li , XAi
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Chapter 6: Mass Transfer Absorption Operation With Concurrent Flow TOP OF TOWER YAo
YA
OPERATING LINE SLOPE = L G
YAi L G MIN
(YAi ) MAX
EQUILIBRIUM LINE
XAo
XAi XA
6.3.3.5 Desorption or Stripping With Concurrent Flow Desorption or Stripping With Concurrent Flow Go, YAo
Li , XAi
h=h
dh
h=o Gi , YAi Lo, XAo
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Chapter 6: Mass Transfer Desorption or Stripping Operation With Concurrent Flow
YA
EQUILIBRIUM LINE YAo OPERATING LINE
YAi
L G
MIN
(YAi ) MAX
XAi
XAo
XA
6.3.3.6 Mass Transfer Between Phases Mass-Transfer Coefficients NA = ky (yA – yAs) NA = kx (xAs – xA) NA = Kx (xA* – xA) NA = Ky (yA – yA*) where NA
= molar flux of A
kx, ky
= individual mass-transfer coefficients
Kx, Ky = overall mass-transfer coefficients xAs, yAs = solute mole fraction at interface in liquid and gas phase, respectively xA*
= mole fraction of solute in the liquid phase at equilibrium
yA*
= mole fraction of solute in the gas phase at equilibrium
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Chapter 6: Mass Transfer where a = interfacial area per unit volume, in ft2 A = cross-sectional area, in ft2 h = height of packing, in ft Operating Line The equation for the operating line is Go y Ao − Gy A = Lo x Ao − Lx A
or
1 L y A = G x A + G (Gy Ao − Lo x Ao)
Packing Height of Transfer Unit The height of packing is yAo (1 − y ) dy h = HG #yAi (1 − y )A(ylm − yA ) A A As
and
h = nG HG
where nG = number of gas phase transfer units lm = log mean The number of gas-phase transfer units is yAo (1 − y ) dy nG = #yAi (1 − y )A(ylm − yA ) A A As where
(1 − yA) lm =
(1 − yA) + (1 − yAs) as an approximation 2
For dilute solutions, assume L, G, and slope m are constant. mG mG HOG = HG + L HL = L HOL where HOG and HOL = height of overall transfer units in gas and liquid phases, respectively L = mG A = absorption factor, which ranges from 1.0 to 1.4 1 = A S = stripping factor Hl m= P where P = absolute pressure
H l = Henry's constant
HOL HOG = A nOG =
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yAo − yAi ` yA − y A* jlm
and
nOL =
xAo − xAi ` x A* − xA jlm 324
Chapter 6: Mass Transfer
where
` yA −
y A* jlm
` yA − y A* jo − ` yA − y A* ji = RS V SS` yA − y A* jo WWW W ln SS SS ` yA − y A* ji WWW T X
and similarly for ` x A* − xA jlm For dilute solutions: x −x nOL = Ao * Ai ` x A − x A jlm
6.3.3.7 Packing HETP For gas absorption: h = nOG HOG For gas stripping: h = nOL HOL Also, h = NTP HETP where NTP
= number of theoretical plates
HETP = height of an equivalent theoretical plate RS VW HxAi SSd − HG n d WW n 1 − SS WW pL yAo p HG ln S W + SS H pL WW − y SS WW Ai p NTP = T X pL ln HG H L = = A mG m p
pL A = HG
1= HG = S A pL NTP =
ln >_1 − S i e
yAo − mxAi o + SH yAi − mxAi
1 ln c S m
where A = absorption factor S = stripping factor Note: For absorption and stripping, calculations for tower height are the same, although the operating line slope will differ.
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Chapter 6: Mass Transfer 6.3.3.8 Height of Overall Transfer Unit Gu HOG = K a (1 − y ) y A lm where
(1 − yA) lm =
(1 − y A* ) − (1 − yA) 1 − y* ln f − A p 1 yA
Lu HOL = K a (1 − x ) x A lm where
(1 − xA) lm =
(1 − xA) − (1 − x A* ) 1 − xA p ln f 1 − x A*
6.3.3.9 Number of Gas Phase Transfer Units nOG =
#y y
A0
A1
`1 − yA jlm
* `1 − yA j ` yA − y A j
Using the log mean average: 1−y nOG = 0.5 ln 1 − yAi + Ao
#y y
Ao
Ai
dyA
dyA ` yA − y A* j
In dilute solutions: y −y nOG = Ao *Ai ` yA − y A jlm where
` yA −
y A* jlm
=
` yA − y A* jbottom − ` yA − y A* jtop
ln
` yA − y A* jbottom ` yA − y A* jtop
6.3.3.10 Number of Liquid Phase Transfer Units nOL =
#x x
Ao
Ai
_1 − xA ilm
_1 − xA i ` x A* − xA j
1−x nOL = 0.5 ln 1 − xAo + Ai
#x x
Ao
Ai
dxA
dxA − xA
x A*
6.3.3.11 Absorption With Reaction Dissolved solute reacts with solvent in liquid phase if irreversible reaction: y nOG = ln yAo Ai
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Chapter 6: Mass Transfer 6.3.3.12 Correlations for Mass-Transfer Coefficients For insoluble gases that do not react chemically with the liquid: h
n 1 G H x = a d n x n t Dx x x vx where Hx = individual liquid-phase HTU Gx = mass velocity of liquid mx = viscosity of liquid Dvx = diffusivity of liquid rx = liquid density a and h = constants given in the table below
Values of a and h in Equations1 for Various Packing Materials at 77°F Packing Type
Rings
Saddles
Tile
Packing Size (in.)
a
h
2
80
0.22
1.5
90
0.22
1
100
0.22
0.5
280
0.35
0.375 1.5
550 160
0.46 0.28
1
170
0.28
0.5 3
150 110
0.28 0.28
1. All quantities in equations must be expressed in fps units if these values of a are used. Source: McCabe, W.L., and J.C. Smith, Unit Operations of Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976, p. 735.
The temperature effect of liquids on the HTU can be evaluated as: H x = H xo e
−0.013 (T − To)
where Hx = HTU at T °F Hxo = HTU at To °F T
= final temperature in °F
To = initial temperature in °F
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Chapter 6: Mass Transfer Henry's Law: where
y* = m x y x* = m
m = Henry's Law Constant/Total Pressure
6.3.3.13 Packing Selection Selection of packing is based primarily on packing factors and avoidance of flooding.
Packing Factors PACKING FACTORS** (WET AND DUMP PACKED) NOMINAL PACKING SIZE (INCHES)
TYPE OF PACKING
MAT’L.
SUPER INTALOX
CERAMIC
60
30
SUPER INTALOX
PLASTIC
33
21
16
INTALOX SADDLES
CERAMIC
40
22
18
15
HY-PAK RINGS
¼
725
⅜
330
½
¾
⅝
200
145
METAL
1
1¼
98
1½
52
42
2
3
3½
PALL RINGS
PLASTIC
97
52
40
25
16
PALL RINGS
METAL
70
48
28
20
16
170
110
65
45
125
95
65
37
110
83
57
32
BERL SADDLES
CERAMIC
900
RASCHIG RINGS
CERAMIC
1600
1000
580
380
255
155
RASCHIG RINGS 1/32” WALL
METAL
700
390
300
170
155
115
RASCHIG RINGS 1/16” WALL
METAL
410
290
220
137
EXTRAPOLATED
1/8” WALL
1/32” WALL
3/16” WALL
1/16” WALL
1/4” WALL
3/32” WALL
3/8” WALL
240
F
3
OBTAINED IN 16" AND 30" I.D. TOWER
DATA BY LEVA
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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Chapter 6: Mass Transfer Packing Factors: Stacked Packings & Grids
1000 800 600
SINGLE SINGLESPIRAL SPIRALRINGS RINGS(
PACKING FACTOR– F
400
200
CHECKER BRICK, 55% FREE SPACE
DIAMOND PITCH SQUARE PITCH DIAMOND PITCH SQUARE PITCH
CROSS PARTITION
GRID TILE (CERAMIC)
1/4'' WALL 3/16'' WALL
RASCHIG RINGS (CERAMIC)
CROSS PARTITION RINGS (SQUARE PITCH) 5/16'' WALL
RASCHIG RINGS
100 80
(CERAMIC)
1'' x 1'' x 1/4''
60
1'' x 2'' x 1/4''
40
3/8'' WALL
11/2'' x 11/2'' x 3/16''
RASCHIG RINGS
(METAL 1/8'' WALL)
2'' x 2'' x 3/8''
WOO
METAL GRID
20
D GR
(1'' x 1'' x 1/16'')
10
2''
1''
IDS
4'' x 4'' x 1/2''
3''
4''
NOMINAL PACKING SIZE – INCHES
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
Packing Factors: Screen Packing & Random Dumped Packing
1000 800
STEDMAN
600
PACKING FACTOR– F
400
200 100 80
CANNON
QUARTZ ROCK 2'' SIZE GOODLOE CROSS PARTITION RINGS
60 40
TELLERETTES
20 10
PANAPAK
MAS PAC FN-200
FROM MANUFACTURERS DATA EXCEPT AS NOTED 2'' 3'' 1'' NOMINAL PACKING SIZE - INCHES
MAS PAC FN-90 4''
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001). ©2017 NCEES
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Chapter 6: Mass Transfer 6.3.3.14 Flooding and Pressure Drop Packed Tower Pressure Drop
Generalized Pressure Drop Correlation 0.60
GENERALIZED PRESSURE DROP CORRELATION
0.40
G 2 F µ 0.1 ρG ( ρL ρG ) gC
0.20
FLOODIN
G LINE
0.10
1.50 1.00
.060
0.50
.040 .020
PARAMETER OF CURVES IS PRESSURE PARAMETER OF CURVES IS PRESSURE DROP IN INCHES OF WATER/FOOT OF DROP IN INCHES PACKED HEIGHT OF WATER/FOOT
0.25 0.10
.010 .006 .004
0.05
.002 .001 .01
.02
.04 .06
0.1
0.2 0.4 0.6 L ρG 12 G ρL ρG L = LIQUID RATE, lb/sec, ft2 G = GAS RATE, lb/sec, ft2 ρL = LIQUID DENSITY, lb/ft3
1.0
2.0
4.0 6.0 10.0
ρG = GAS DENSITY, lb/ft3
F = PACKING FACTOR µ = VISCOSITY OF LIQUID, CENTIPOISE Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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Chapter 6: Mass Transfer Pressure Drop Versus Gas Rate
5/8 RASCHIG RINGS (METAL) (1/32" WALL) COLUMN DIA. = 15 in. PACKING HEIGHT = 5.1 ft.
DRY
L=
000 L=
12,
0.4
F = 190 LIQUID RATE lb/ft2, hr AS PARAMETER
L=
0.2
0.1
L L = = 10,0 80,000 00 00 20,00 000 L = 40,000 00 L =
15 ,00 0
L=
0.6
60,000 00
L=
1.0 0.8
30 ,00 0 25 , 00 20 ,00 0 0
2.0
L=
∆P~INCHES WATER / FT. PACKING
4.0
100
2
3 4 500 1000 AIR MASS VELOCITY ~ lb/ft2, hr
2000
5000
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
1/4-in. INTALOX SADDLES (CERAMIC) COLUMN DIA. = 8 in. PACKING HEIGHT = 4.4 ft.
2.0
0.4
F = 725
0.2
0.1
50,00 L = 000 30,00 L = 000 1 L = 0,00000 100 DR Y
10,0
0.6
L=
00
1.0 0.8
L=
∆P~INCHES WATER / FT. PACKING
4.0
2 LIQUID RATE LIQUID RATE lb/ftlbs./ft , hr 2,hr. AS PARAMETER
20
40
60
80 100 200 400 AIR MASS VELOCITY ~ lb/ft2, hr
600
1000
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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Chapter 6: Mass Transfer Pressure Drop Versus Gas Rate (cont'd)
3/8 INTALOX SADDLES (PORCELAIN)
1.0
60,000 00
0.6 0.4
L= 50,00 30,00 000 0 0 0 10,00 DR 000 L = Y L = 5 20,00000 00
L=8
,000000
0.8
8 in. COLUMN DIA. = 8'' 4.4 ft PACKING HEIGHT = 4.4' F =330 330 F= LIQUID RATE lb/ft2, hr AS PARAMETER
L=
L=
L=
∆P~INCHES WATER / FT. PACKING
2.0
0.2
0.1
50
100
200
300
500
1000
2000
AIR MASS VELOCITY ~ lb/ft , hr 2
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
4.
COLUMN DIA. = 30 in. PACKING HEIGHT = 10 ft. NO.2 HY-PAK (METAL)
60 ,00 L= 0 50 ,00 0 L= 40 ,00 0 L= 30, 000 L= 20, 000 L= 10,0 L= 50,000 00 0 DRY 0
1. 0.8 0.6
L=
∆P~INCHES WATER / FT. PACKING
2.
0.4
0.2
FF==18 18
LIQUID RATE lb/ft2, hr AS PARAMETER 0.1
100
2
3
4 500
1000
2000
5000
AIR MASS VELOCITY ~ lb/ft2, hr
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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Chapter 6: Mass Transfer Pressure Drop Versus Gas Rate (cont'd)
4.0
3" X 3" CROSS PARTITION RINGS – DUMPED (CERAMIC)
35 ,0 30 00 L= ,00 L = 25,0 0 0 L = 20,0 0 15, 00 L = 000 12 L = ,000 90,000 L = 00 6,0000 00 L=4 5,50000 L=1 ,550000 DR Y
1.0 0.8 0.6
L=
0.4
L=
∆P~INCHES WATER / FT. PACKING
2.0
F = 78
0.2
LIQUID RATE lb/ft2, hr AS PARAMETER
0.1 100
2
3
4 500
1000
2000
AIR MASS VELOCITY ~ lb/ft , hr 2
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
∆P~INCHES WATER / FT. PACKING
2.0
2 in. RASCHIG RINGS (CARBON STEEL)
COLUMN DIA. = 16 in. PACKING HEIGHT = 6.0 ft. CO-CURRENT FLOW
L= L = 70,0 00 L 60 L = = 50 ,00 40 ,000 0 L = ,000 30 ,00 L= 0 20 L = ,000 1 DR 0,000 YL INE
4.0
1.0 0.6 0.4
F = 57 LIQUID RATE lb/ft2, hr AS PARAMETER
0.2
0.1 100
2
3
4 5
1000
2000
5000
AIR MASS VELOCITY ~ lb/ft2, hr
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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Chapter 6: Mass Transfer Pressure Drop Versus Gas Rate (cont'd) 1-1/2" INTALOX SADDLES (PORCELAIN) COLUMN DIA. = 16 in. PACKING HEIGHT = 6.2 ft. "CO-CURRENT" FLOW
000 80, 000 70, L= 00 0,0 0 6 L = 0,00 5 L= 00 0,0 4 L=
2.0
1.0
30 ,00 0
0.6
20, 000 10, 000 DR Y L=5 0,0000 0
L=
0.4
L=
L=
L=
∆P~INCHES WATER / FT. PACKING
4.0
0.2
0.1
100
LIQUID RATE lb/ft2, hr AS PARAMETER
2
3
4 500 1000 2000 AIR MASS VELOCITY ~ lb/ft2, hr
5000
10,000
Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
4.0
COLUMN DIA. = 16 in. PACKING HEIGHT = 6.0 ftft. CO-CURRENT FLOW
0
,00
40
0.4
L= L = 20,00 DR 10,00 0 YL 0 INE
30 ,00 0
L=
L=
0.6
0
,00 50
L
1.0
0
,00
0 =6
L=
∆P~INCHES WATER / FT. PACKING
2.0
1 in. INTALOX SADDLES (POLYPROPYLENE)
F = 57 LIQUID RATE lb/ft2, hr AS PARAMETER
0.2
0.1 100
2
3 4 5 1000 2000 AIR MASS VELOCITY ~ lb/ft2, hr
5000
Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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Chapter 6: Mass Transfer Pressure Drop Versus Gas Rate (cont'd)
2 in. INTALOX SADDLES (POLYPROPYLENE)
COLUMN DIA. = 16 in. PACKING HEIGHT = 6.0 ft. CO-CURRENT FLOW
2.0
L L =1 L = = 90 00,0 L 80 ,00 00 L = = 70 ,000 0 L = 60 ,00 L = 50, ,000 0 L = 40, 000 L = 30,0 000 L = 20 00 DR 10,0,000 Y L 00 INE
∆P~INCHES WATER / FT. PACKING
4.0
1.0 0.6 0.4
0.2
0.1
F = 21 2 LIQUID RATE lb/ft , hr 2, HR. LBS./FT. AS PARAMETER 100
2
3
4 5
1000
2000
5000
AIR MASS VELOCITY ~ lb/ft2, hr
Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
1-1/2 in. PALL RINGS (CARBON STEEL)
4.0
COLUMN DIA. = 16 in. PACKING HEIGHT ==6.0 6.0ft.ft. "CO-CURRENT" FLOW
00 0,0 0 7 L = 0,00 6 L=
50 ,00 0 40 L= ,00 30 0 ,00 L= 0 20, 0 0 L= 0 10, 000 DRY LIN E
1.0
L=
0.6
L=
∆P~INCHES WATER / FT. PACKING
2.0
0.4
0.2
0.1 100
FF=28 = 28
2 LIQUID LIQUIDRATE RATE LBS./FT. lb/ft2, hr ,- HR. ASAS PARAMETER PARAMETER
2
3 4 5 1000 2000 AIR MASS VELOCITY ~ lb/ft2, hr
5000
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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Chapter 6: Mass Transfer Pressure Drop Versus Gas Rate (cont'd)
2 in. PALL RINGS (POLYPROPYLENE) COLUMN DIA. = 16 in. PACKING HEIGHT = 5.6 ft. "CO-CURRENT" FLOW
0.6 0.4
DRY
1.0
50 ,00 L= 0 40 ,00 L= 0 30 ,00 L= 0 20, L = 000 10, 000
2.0
0 ,00 120 = L 0 0 0 , 110 0 00 L = 0,00 0,0 0 8 1 L = 000 L = , 90 L= 00 0,0 0 7 0 L = 60,0 L=
L=
∆P~INCHES WATER / FT. PACKING
4.0
0.2
0.1 100
2
3
4
500
1000
2 LBS./FT. LIQUID RATE lb/ft , hr 2, AS HR.PARAMETER AS PARAMETER
2000
5000
10,000
AIR MASS VELOCITY ~ lb/ft , hr 2
Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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Chapter 6: Mass Transfer 6.3.3.15 Flooding Velocities Flooding in Gas Absorption Packed Towers 1.0
0.1
G
2
ap 3
µL
G
L
0.2
0.01
gc ρ ρ
.001
.0001
.00001 0.01
0.10
1.0 L G
where ft 2 ft3 = void fraction in packing
ap = packing area, in e
mL = viscosity of liquid in centipoise lb ft3 lb = density of liquid phase, in 3 ft
rG = density of gas phase, in rL
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ρ G ρ
L
10
100
Chapter 6: Mass Transfer
6.4 Miscellaneous Mass Transfer Processes (Continuous, Batch, and Semicontinuous) 6.4.1
Membrane Separation Processes
6.4.1.1 General Background Fluid Stream Schematic TMP
PERMEATE OR FILTRATE RETENTATE
FEED FEED CHANNEL ΔP
Normal flow filtration (NFF) refers to the situation in which retentate flow is zero and all the feed stream flows to the membrane surface are normal. Tangential flow filtration (TFF) refers to the situation in which the feed stream flows are tangential to the membrane surface and exit the module as a retentate stream, creating a velocity gradient at the membrane surface. Permeation flux J in J=
ft 3 mol or 2 indicates the productivity of a membrane: ft day m s 2
volumetric permeate flow rate membrane area
Permeability L indicates the sensitivity of productivity or flux to transmembrane pressure (TMP): flux L = transmembrane pressure TMP may refer to a module average. Pure-component permeability (e.g., water permeability) refers to membrane properties, while the more industrially relevant process permeability includes fouling and polarization effects. The recovery or conversion ratio CR indicates the efficiency of a membrane module: permeate flow rate CR = feed flow rate Solutes entrained by the permeate flow are retained by the membrane. They accumulate on the membrane surface and form a region of high concentration called the polarization boundary layer. A steady state is reached between back transport away from the membrane surface, tangential convective transport along the membrane surface, and normal convective flow towards the membrane. The local transmission or sieving coefficient S indicates the passage of a single component through a membrane. The concentrations may change within a module: c p (local) S = c (local) f The observed passage Sobs indicates the transmission coefficient based on the concentration in the permeate stream exiting a module and in the feed stream entering a module. The observed passage characterizes the module: c p (mod ule) Sobs = c (mod ule) f
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Chapter 6: Mass Transfer The intrinsic passage Sint indicates the transmission coefficient based on the concentration in the permeate stream exiting a module and in the feed stream at the membrane wall. The intrinsic passage characterizes the membrane: cp Sint = c w where cf = concentration in feed cp = concentration in permeate cw = concentration at wall of membrane The retention or rejection R is the complement to the transmission coefficient or passage: R=1–S The multiple-component separation factor aij defines the selectivity for component separation: c f ip p cif S = a ij = S i j c f jp p c jf where cif = concentration of component i in feed cip = concentration of component i in permeate Component transport through membranes can be considered as mass transfer in series: 1. Transport through a polarization layer above the membrane that may include static or dynamic cake layers 2. Partitioning between the upstream polarization layer and membrane phases at the membrane surface 3. Transport through the membrane 4. Partitioning between the membrane and the downstream fluid A simplified model of polarization can be used as the basis for analysis:
Polarization in Tangential Flow Filtration REGIONS: BULK SOLUTIONS POLARIZATION BOUNDARY LAYER PERMEATE
CONCENTRATIONS: Cb
Cw
FLOW VECTORS: TANGENTIAL FLOW PERMEATE NORMAL FLOW
Cp
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 20-38.
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Chapter 6: Mass Transfer 6.4.1.2 Gas Separation The flux for permeation is t Ji = c zi m` pi, feed − pi, permeate j where: Ji = permeation flux of component i, in ri = permeability of component i, in
ft 3 mol or 2 ft 2 hr m s
ft 3 ft mol or 2 ft hr psi m s Pa 2
z = membrane thickness pi = partial pressure of component i Stage cut q is defined by V permeate volume flow rate = i L= feed volume flow rate where mol lb mole hr or s mol lb mole L = molar feed flow rate, in hr or s V = molar permeate flow rate, in
Selectivity is aij = where
y e yi o j
x e xi o j
aij = separation factor xi = mole fraction of component i in the feed or reject yi = mole fraction of component i in the permeate The pressure ratio U is P U = P feed permeate The ratio of permeation flux for two components i and j is RS V SS x − d yi n WWW S i U WW Ji W = a ij SSS Jj SS − e y j oWWW x SS j U WW T X At stage cut U = 0 , the permeate composition as a function of feed composition is U 1 1 yi = c 2 m>c xi + + a − 1 m − U
2 4ax i H c xi + 1 + 1− m − U a 1 _a − 1 i U
For membrane modules, the partial pressure driving force is a point function dependent on the partial pressures at a point on the membrane and is not constant. To take this into account, the equation may be used in iterative calculations for approximating the performance of membrane modules. ©2017 NCEES
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Chapter 6: Mass Transfer The limiting case for a >> F is P yi , xi P feed = xi U permeate The limiting case for a << F is xi a yi , 1 + x i _a − 1 i
Flow Paths in Gas Permeators
PERMEATE
MEMBRANE FEED (a) SPIRAL WOUND MODULES FEED
(HOLLOW-FIBER WALL) MEMBRANE
PERMEATE
FEED
(b) HOLLOW-FIBER MODULES WITH COUNTERCURRENT FLOW FEED
(HOLLOW-FIBER WALL) MEMBRANE
PERMEATE (c) HOLLOW-FIBER MODULES WITH CROSS FLOW
6.4.1.3 Material Balances for Membrane Modules MEMBRANE MODULE FEED L0 x0 PF
MEMBRANE
REJECT LN xN PF PERMEATE VN yN PP
n-1
n
INCREMENT
Overall and component balances for a module are L0 = LN + VN x0 L0 = xN LN + yN VN Overall and component balances for an increment of module area are Ln–1 + Vn–1 = Ln + Vn xn–1 Ln–1 + yn–1 Vn–1 = xn Ln + yn Vn These may be expressed as DVn = Vn − Vn − 1 =
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Chapter 6: Mass Transfer where
1 y n = 2 ` yn − 1 + ynj DV = Vn − Vn − 1 y n DVn / y n Vn − y n − 1 Vn − 1
At any point along the membrane, the permeate composition is yV = /1 y n DVn N
and the permeate composition for the overall module is y N VN = /1 y n D Vn N
Area for Membrane Modules Based on a stepwise incremental solution, the membrane area is = AN where
y DVn
n N N /= A n /1 > J 1 _ ii
avg
H
_ Ji iavg = c t i m c 1 m 9` x n − 1 PF − y n − 1 PP j + ` x n PF − y n PP jC = c t i m c 1 m 9_ x n − 1 + x n i PF − ` y n − 1 + y n j PPC z 2 z 2
The overall module area can be approximated as AN =
where
y n Vn _ Ji iavg
_ Ji iavg = c t i m c 1 m 9` x0 PF − y0 PP j + ` x N PF − y n PP jC = c t i m c 1 m 9_ x0 + x n j PF − ` y0 + y n j PPC z 2 z 2
Procedure for Incremental Calculation Given aij, PF, PP, L0, and x0: 1. Select increment Dx 2. For the initial point 0, calculate y0 and (Ji)0 3. Determine xn 4. Calculate yn and y n 5. Calculate DVn and Vn 6. Calculate y n DVn 7. Calculate Ln 8. Calculate (Ji)n, (Ji)avg, and An 9. After the final increment, calculate (Ji)N and AN
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Chapter 6: Mass Transfer 6.4.1.4 Membrane Separation Processes—Reverse Osmosis Osmotic Pressure The osmotic pressure ps of a solution is ps = Fs is cs R T where ps = osmotic pressure in psi or Pa Fs = osmotic coefficient is = number of ions formed by solute molecules cs = concentration of the solute in
lb mole mol or 3 ft3 m
R = universal gas constant T = absolute temperature in °R or K
Concentration Gradients SKIN
awF awP = c wP
c wF
c wi POROUS SUPPORT PERMEATE P c si
FEED F
c sP c sm c sP
Source: McCabe, Warren L., Julian C. Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993, p. 872.
where aw = activity of water cs = concentration of solute
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Chapter 6: Mass Transfer Flux Across Membrane The flux of solvent JW (water, for example) is c D v − J w = w RTw w c DP z Dr m where J = permeation flux in c = concentration in
ft 3 m3 or 2 2 ft hr m s
lb mole mol or 3 ft 3 m
m2 ft 2 D = effective diffusivity in hr or s ft 3 m3 v = partial specific volume in lbm or kg DP = friction losses in psi or Pa z
= membrane thickness in ft or m
Dp = differential osmotic pressure in psi or Pa The flux of solute is Dc Js = Ds Ss c z s m where: Ss = distribution coefficient of the solute Polarization Factor The polarization factor is the relative concentration difference across the polarization boundary layer and is J f c −c C = sic s = kw s c where f = fraction of solute rejected m ft kc = mass-transfer coefficient based on concentration, in hr or s Pressure Drop The internal flow in a hollow-fiber membrane is laminar, and the internal pressure drop DPf with one closed end is 128 J w n L2 DPf = 2 D3 where L = length D = diameter m = viscosity
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Chapter 6: Mass Transfer
6.4.2
Liquid-Liquid Extraction
6.4.2.1 Partition Ratio The equilibrium partition ratio in mole fraction units is yi c iraffinate o K= i x= i c iextract where yi = mole fraction of solute i in the extract phase xi = mole fraction of solute i in the raffinate phase gi = activity coefficient of solute i in the indicated phase The equilibrium partition ratio in mass ratio units Kil is = Kil
Yil = Xil
e
extract m solute
mextraction solvent
o
raffinate e m solute o mfeed solvent
where Yi l = ratio of mass solute i to mass extract solvent in extract phase Xil = ratio of mass solute i to mass extract solvent in raffinate phase kg lbm m = mass flow rate, in hr or s The advantage of using the solute-free basis is that the feed solvent and extraction solvent flows do not change during the extraction.
6.4.2.2 Extraction Factor On a McCabe-Thiele type of diagram, E is the slope of the equilibrium line divided by the slope of the operating F line S .
S E i = mi F
where E i = extraction factor mi = local slope of the equilibrium line
kg lbm S = mass flow rate of the solvent phase, in hr or s kg lbm F = mass flow rate of the feed phase, in hr or s For dilute systems with straight equilibrium lines, the slope of the equilibrium line is equal to the partition ratio: mi = Kil
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Chapter 6: Mass Transfer 6.4.2.3 Separation Factor The separation factor indicates the relative enrichment of a given component in the extract phase after one theoretical stage of extraction. Yl Yl f il p f ilp Y j extract Xi Kl = = i a ijl = K jl Y jl Xl f il p f p X j raffinate X jl where
a ijl = separation factor for solute i with respect to solute j (mass ratio basis)
Equilibrium Lines Plotting equilibrium data in terms of mass ratios on logarithmic scales often gives a straight line.
Hand-Type Ternary Diagram for Water + Acetic Acid + MIBK at 25oC 8 6 4
R
ER
T WA
PLAIT POINT
1 .8 .6 .4
Y
.2
UM
.1 .08 .06 .04
LIB
RI
X
EQ
UI
R
D
BK
UI
WT. ACETIC ACID WT. MIBK
2
YE LA
-L
IQ
MI
LIQ
UI
D
.02
YE LA
.01 .01
.02
.04 .06 .08 .1
.2
.4 .6 .8 1
2
WT. ACETIC ACID WT. WATER
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-27.
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Chapter 6: Mass Transfer 6.4.2.4 Liquid-Liquid Extraction: Process Calculations Countercurrent Extraction Cascade F 'X f
E 'Ye or Y1 1
FEED STAGE X1
Y2 2
X n–1
Yn n
Xn
Y n+1
r –1
X r–1
Yr r
RAFFINATE STAGE R'X r
S' Ys
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-11.
Theoretical (Equilibrium) Stage Calculations With McCabe-Thiele Method
McCabe-Thiele Graphical Stage Calculation Using Bancroft Coordinates 2
WT. SOLUTE Y ' WT. EXTRACTION-SOLVENT
1
2 E
U
EQ
r 0
0
UM
RI
B ILI
LIN
3
4
G
IN AT R E
NE
X f ' Ye
LI
OP
SLOPE =
F' S'
PARTIAL STAGE X r ' Ys X
WT. SOLUTE ' WT. FEED-SOLVENT
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-45. ©2017 NCEES
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2
Chapter 6: Mass Transfer For immiscible feed and extraction solvents, the operating line for the feed end (stage 1 to stage n) is E l Yel− F l Xf l Fl Y ln + 1 = l X nl+ Sl S where Xfl = mass ratio of solute in feed Yel = mass ratio of solute in extract E l = mass flow rate of extraction solvent only F l = mass flow rate of feed solvent only S l = mass flow rate of extraction solvent only For immiscible feed and extraction solvents, the operating line for the raffinate end (stage n to stage r) is Ynl=
F l l + S l Ysl− Rl X rl X Sl Sl n − 1
where X rl = mass ratio of solute in raffinate Ysl = mass ratio of solute in solvent Rl = mass flow rate of raffinate solvent only The overall material balance is Yel=
F l Xf l+ S l Ysl− Rl X rl El
Kremser-Souders-Brown (KSB) Theoretical Stage Equation For straight equilibrium and operating lines, the number of theoretical stages N is approximated by:
N=
ln f
Xf l− Ysl /ml pc1 − 1 m + 1 E E X rl− Ysl /ml ln E
Sl =1 for E = ml l , E Y F
where N = number of theoretical stages ml = local slope of equilibrium line in mass ratio units lbm S l = mass flow rate of the solvent only (solute-free basis), in hr or F l = mass flow rate of the feed solvent (solute-free basis), in lbm or hr
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kg s kg s
Chapter 6: Mass Transfer An alternate form is Xf l− Ysl /ml E N − 1/E = − 1 1/E X rl− Ysl /ml
=1 for E Y
Xf l− Ysl /ml = N+1 X rl− Ysl /ml
for E = 1
Graphical solutions to the KSB equation are shown below. Note that the term for the abscissa is the inverse of the term used in the KSB equation.
Graphical Solutions to the KSB Equation 1.0 0.8 0.6 0.4
N=1
0.2
2
0.1 .08 .06 .04
3
X r – sY /m X f – sY /m
.02 4
.01 .008 .006 .004 .002
6
.001 .0008 .0006 .0004 .0002
8
.0001 .00008 .00006 .00004
10
.00002
15
.00001 1
2
4
ε, EXTRACTION FACTOR
6
8
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-46.
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10
Chapter 6: Mass Transfer In general, these equations are valid for any concentration range in which equilibrium can be represented by a linear relationship Y = m X + b (written here in general form for any system of units). For applications that involve dilute feeds, the section of the equilibrium line of interest is a straight line that extends through the origin where Yi = 0 at Xi = 0. In this case, b = 0 and the slope of the equilibrium line is equal to the partition ratio where m = K. The KSB equation also may be used to represent a linear segment of the equilibrium curve at higher solute concentrations. In this case, the linear segment is represented by a straight line that does not extend through the origin, and = m is the local slope of the equilibrium line, so b Y 0= and m Y K. Furthermore, a series of KSB equations may be used to model a highly curved equilibrium line by dividing the analysis into linear segments and matching concentrations where the segments meet. For equilibrium lines with moderate curvature, an approximate average slope of the equilibrium line may be obtained from the geometric mean of the slopes at low and high solute concentrations: maverage . m geometric mean = m low m high Stage Efficiency p o (%) = p md
=
p o (%) =
theoretical stages # 100 actual stages cd, n + 1 − cd, n cd, n + 1 − c d* ln [1 + p md (E − 1)] # 100 ln E
where p o = overall stage efficiency p md = Murphree stage efficiency based on the dispersed phase Mass Transfer Between Phases no = k y (yint − y) no = k x (xint − x)
no = k y (y * − y) no = k x (x − x *)
where no = molar flow per area xint = mole fraction of solute i in the raffinate phase at the interface x* = mole fraction of solute i in the raffinate phase in equilibrium with the extract phase yint = mole faction solute i in the extract phase at the interface y* = mole fraction of solute i in the extract phase in equilibrium with the raffinate phase NTUG =
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#y y s
e
(1 − y)1m dy (1 − y) (yint − y)
350
Chapter 6: Mass Transfer For dilute solutions: NTUOL =
x f − xr (x − x *)1m
where xf
= mole fraction of solute i in the feed
xr
= mole fraction of solute i in the raffinate
NTUG = number of transfer units based on gas phase NTUOL = number of transfer units based on liquid phase (
)lm = log mean
Rate-Based Calculations With Mass-Transfer Units In most cases, the dominant mass-transfer resistance resides in the feed (raffinate) phase, because the slope of the equilibrium line usually is greater than one. In that case, the overall mass-transfer coefficient based on the raffinate phase may be written:
where
1 =1 + 1 kor kr mervol ke ke kr kor
m ft = extract phase mass-transfer coefficient, in hr or s m ft = raffinate phase mass-transfer coefficient, in hr or s
m ft = overall mass-transfer coefficient based on the raffinate phase, in hr or s
mervol = local slope of equilibrium line (volumetric concentration basis) The required contacting height of an extraction column is related to the height of a transfer unit and the number of transfer units by: x in V dX = Z t = k ra − eq HTUor NTUor or x out X X
#
where
Zt Vr a Xeq
= total height of extractor ft m = liquid velocity of raffinate phase, in sec or s 2 2 = interfacial area per unit volume, in ft3 or m3 ft m = mass ratio in equilibrium with composition of extract phase
HTUor = height of overall transfer units (based on raffinate phase) NTUor = number of transfer units (based on raffinate phase)
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Chapter 6: Mass Transfer For straight equilibrium and operating lines, the number of transfer units is approximated by the Colburn equation:
where
JK N KK X l− Ysl OOO f K ml OO c1 − 1 m + 1 ln KK E E KK l− Ysl OOO K Xr ml O P NTUor = L 1 1−E
l = lS , EY1 E m= Fl An alternate form is 1 1 Yl Xf l− s l exp
HTUe E
Q HTUr = A kr a col r Q HTUe = A ke a col e where HTUr = height of a transfer unit due to resistance in the raffinate phase, in ft or m HTUe = height of a transfer unit due to resistance in the extract phase, in ft or m Acol = column cross-sectional area, in ft2 or m2 Qr
m3 ft3 = volumetric flow rate of the raffinate phase, in min or s
Qe
3 3 = volumetric flow rate of the extract phase, in ft or ms min
The relation between overall raffinate phase transfer units from the Colburn equation and the number of theoretical stages from the KSB equation is ln E =1 NTUor = N # for E Y 1 1−E Yl Xf l− s l m − 1 for E = 1 NTUor = N = Ysl Xrl− l m
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Chapter 6: Mass Transfer Extraction Factor The solute reduction factor FR, or extraction factor, is an indication of process performance. For a single-stage batch process or for one theoretical stage of a continuous process, the extraction factor is X FR = X in = out
cE − 1 m E 1 c1 − m E
for N = 1
The required solvent-to-feed ratio is approximated by S = FR − 1 F K where
for N = 1
K = distribution coefficient for phase equilibrium
For any extraction configuration, the concentration of solute in the extract is Yout =
Xin 1 d1 − F n R cSm F
for Yin = 0
For cross-flow extraction, in which the raffinate phase for each stage is contacted with fresh solvent, the extraction factor is E poN FR = c1 + N m S = N c p1N F K FRo − 1 m For multistage countercurrent extraction, the extraction factor is
c EpoN − 1 m E FR = c1 − 1 m E For countercurrent extraction without discrete stages, the extraction factor is 1 1 exp
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Chapter 6: Mass Transfer 6.4.2.5 Liquid-Liquid Extraction Equipment: Static Extraction Columns Column Configurations
LIQUID – LIQUID EXTRACTION (2 CONFIGURATIONS) LIGHTER LIQUID
LIGHTER LIQUID
HEAVIER LIQUID
HEAVIER LIQUID
LIGHTER LIQUID
LIGHTER LIQUID
LIGHTER LIQUID
HEAVIER LIQUID
HEAVIER LIQUID
HEAVIER LIQUID
Static extraction columns include spray-type, packed, and trayed columns.
Schematic of Common Static Extractors: (a) Spray Column, (b) Packed Column, and (c) Sieve Tray Column
RAG REMOVAL
LIGHT LIQUID OUT HEAVY LIQUID IN COLUMN INTERFACE LARGE-DIAMETER ELGIN HEAD
LIGHT LIQUID OUT
LIGHT LIQUID OUT
INTERFACE
HEAVY LIQUID IN
OPERATING INTERFACE
HEAVY LIQUID IN
PERFORATED PLATE
REDISTRIBUTOR
DOWNCOMER
PACKING
LIGHT–PHASE DISTRIBUTOR
COALESCED DISPERSED
LIGHT LIQUID IN
LIGHT LIQUID IN HEAVY LIQUID OUT
HEAVY LIQUID OUT HEAVY LIQUID OUT (a)
LIGHT LIQUID IN
(b)
(c)
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-64.
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Chapter 6: Mass Transfer 6.4.2.6 Liquid-Liquid Extraction Equipment: Spray Columns Liquid Dispersion For liquid distributors, the liquid should issue from the hole as a jet that breaks up into drops. As a general guideline, the maximum recommended design velocity corresponds to a Weber number (We) of about 12. The minimum Weber number that ensures jetting in all the holes is about 2. It is common practice to specify a Weber number between 8 and 12 for a new design. We c uo,max . d t o d where uo,max = maximum velocity through an orifice or nozzle We
= Weber number
g
= surface tension
do
= orifice or nozzle diameter
rd
= density of the dispersed phase
Drop Size, Dispersed-Phase Holdup, and Interfacial Area For the general case where the dispersed phase travels through the column as drops, an average liquid-liquid interfacial area can be calculated from the Sauter mean drop diameter and dispersed-phase holdup. The drop diameter is dP = 1.15 h
c Dt gc
where dp = Sauter mean drop diameter Dr = density difference between the raffinate and the extract h = parameter, specifically: h = 1.0 for no mass transfer h = 1.0 for transfer from continuous to dispersed phase h = 1.4 for transfer from dispersed to continuous phase The dispersed-phase holdup is −2
zd =
where
rg ud =cos c 4 mG
uc − 6z H f >uso exp d r d n − f `1 − zd j
,
apdp g= 2
zd = volume fraction of the dispersed phase (holdup) z = tortuosity factor ud = liquid velocity of the dispersed phase ©2017 NCEES
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Chapter 6: Mass Transfer uc = liquid velocity of the continuous phase uso = slip velocity at low dispersed-phase flow rate e = void fraction aP = interfacial area The interfacial area is 6fz ap = d d p Drop Velocity The average velocity of a dispersed drop udrop is u udrop = d fzd Interstitial Velocity of Continuous Phase The interstitial velocity of the continuous phase uic is uc uic = f `1 − zd j Slip Velocity and Characteristic Slip Velocity
The relative velocity between the counterflowing phases is referred to as the slip velocity us: us = udrop + uic The characteristic slip velocity uso obtained at low dispersed-phase flow rate is ReStokes = where
tc Dt gc d P3 18 n c2
Re = Reynolds Number rc = density of the continuous phase Dr = density difference between the two phases mc = viscosity of the continuous phase For ReStokes < 2: uso =
Dt gc d p2 18nc
For ReStokes > 2: Re n uso = d t c p c where
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Re = 0.94H0.757 − 0.857 P0.149
H # 59.3
Re = 3.42H0.441 − 0.857 P0.149
H 2 59.3
356
Chapter 6: Mass Transfer t c2 c3 n c4 gc Dt
P
=
H
2 n = f 4d p gc Dt p d w n nc 3c
0.14
P0.149
P , H = dimensionless groups m w
= reference viscosity equal to 0.9c P or 9 #10-4Pa s
g
lbf = surface tension in in.
The slip velocity at higher holdup is estimated from: us . uso `1 − zd j Flooding Velocity It is generally recommended that flow velocities be limited to 50 percent of the calculated flooding velocities. 0.178uso ucf = u 1 + 0.925 d udf n cf where
ucf = continuous phase flooding velocity udf = dispersed phase flooding velocity Drop Coalescence Rate Problems with coalescence are most likely when the superficial dispersed-phase flooding velocity udf is greater than about 12 percent of the characteristic slip velocity. Mass-Transfer Coefficients and Efficiency vol koc a = m dc kod a = 0.08 #
1/4
g 3 Dt 3 zd `1 − zd j f c 2 p c tc
e
1/2
1/2
nc n o + d m1 n e d o tc Dc td Dd dc
where Dc
= solute diffusion coefficient for the continuous phase
Dd
= solute diffusion coefficient for the dispersed phase
koc
= overall mass-transfer coefficient based on the continuous phase
kod
= overall mass-transfer coefficient based on the dispersed phase
mdc = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase concentration
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Chapter 6: Mass Transfer vol = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase m dc concentration on volumetric concentration basis
γ
= interfacial tension
μc
= viscosity of continuous phase
μ d
= viscosity of dispersed phase
ρc
= density of continuous phase
ρd
= density of dispersed phase
φd
= volume fraction of dispersed phase (holdup)
With the height of one transfer unit (based on the continuous phase): u HTUqc = k ca oc
6.4.2.7 Liquid-Liquid Extraction Equipment: Packed Columns Liquid Redistribution Little benefit is gained from a packed height greater than 10 ft (3 m). Redistributing the dispersed phase about every 5 to 10 ft (1.5 to 3 m) is recommended to generate new droplets and constrain backmixing. Minimum Packing Size For a given application, a minimum packing size or dimension exists below which random packing is too small for good extraction performance. The critical packing dimension dc is dc = 2.4
v Dt gc
Packing Holdup For standard commercial packings of 0.5 in (1.27 cm) and larger, fd varies linearly with the liquid velocity of the dispersed phase (ud) up to values of fd = 0.10 (for low values of ud). As ud increases further, fd increases sharply up to a “lower transition point” resembling loading in gas-liquid contact. At still higher values of ud, an upper transition point occurs, the drops of dispersed phase tend to coalesce, and ud can increase without a corresponding increase in fd. This regime ends in flooding. Below the upper transition point, the dispersed-phase holdup is ud uc + = f uso `1 − zd j zd 1 − zd Packing Flooding: Siebert, Reeves, and Fair Correlation ucf =
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0.178f uso Z] _b 1 ] b udf ]] b 2b `b 1 + 0.925 d u n [] rg mG bb cf ] =cos c ]] 4 b \ a
ap dp g= 2
358
Chapter 6: Mass Transfer Packing Flooding: Modified Crawford-Wilke Correlation
Flooding Velocities
104
LIQUID – LIQUID PACKED TOWERS A MODIFIED CRAWFORD-WILKE CORRELATION
2
Vc l + V D 0.5 ρ C VC
6 4
α
C
0.5
2 103
=
6 4
C
102
α
VD0.5
+
2
VC 0.5 ρ C
2
6 4 2 10
1
2
4
6
10
'c
2
γ
ρ ρc
4
0.2
10
6 F
V = ft./hr. (SUPERFICIAL VELOCITY) C = CONTINUOUS PHASE D = DISPERSE PHASE α = sq. ft. AREA OF PACKING/ c ft. = DIFFERENCE = VOID FRACTION IN PACKING
2
1.5
2
2
4
6
10
3
µ'c = VISCOSITY IN (CENTIPOISE)
ρ = DENSITY (POUNDS PER / CUBIC FOOT)
γ = INTERFACIAL SURFACE TENSION (DYNES / cm) F = PACKING FACTOR (DIMENSIONLESS)
Pressure Drop In general, the pressure drop through a packed extractor is due to the hydrostatic head pressure. The resistance to flow caused by the packing itself normally is negligible; typical packings are large and flooding velocities are much lower than those needed to develop significant DP from resistance to flow between the packing elements. Mass-Transfer Coefficients 1
zd =
2 n e d o td Dd
n d1 + nd n c
For fd < 6: kd =
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Chapter 6: Mass Transfer For fd > 6:
−1 2
nd o kd = 0.023us e t D d d
2
1
kc dp n 5 d ut 2 = 0.698 e c o e p s c o `1 − zd j Dc tc Dc nc vol 1 = 1 + m dc kod kd kc
where kc = continuous-phase mass-transfer coefficient kd = dispersed-phase mass-transfer coefficient Packing Data
Random and Structured Packings Used in Packed Extractors Packing
Surface Area ap1 Metal Random Packing
Koch-Glitsch IMTP® 25 Koch-Glitsch IMTP® 40 Koch-Glitsch IMTP® 50 Koch-Glitsch IMTP® 60 Sulzer I-Ring #25 Sulzer I-Ring #40 Sulzer I-Ring #50 Nutter Ring® NR 0.7 Nutter Ring® NR 1 Nutter Ring® NR 1.5 Nutter Ring® NR 2 Nutter Ring® NR 2.5 HY-PAK® #1 in. HY-PAK® #1-1/2 in. HY-PAK® #2 in. FLEXIRING® 1 in. FLEXIRING® 1-1/2 in. FLEXIRING® 2 in. CMR® 1 CMR® 2 CMR® 3 BETARING® #1 BETARING® #2 FLEXIMAX® 200 FLEXIMAX® 300 FLEXIMAX® 400
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224 151 102 84 224 151 102 226 168 124 96 83 172 118 84 200 128 97 246 157 102 186 136 189 148 92
360
m2 m3
Void Fraction1 (e)
0.964 0.980 0.979 0.983 0.964 0.980 0.979 0.977 0.977 0.976 0.982 0.984 0.965 0.976 0.979 0.959 0.974 0.975 0.973 0.970 0.980 0.963 0.973 0.973 0.979 0.983
Chapter 6: Mass Transfer Random and Structured Packings Used in Packed Extractors (cont'd) Packing
Surface Area ap1 Plastic Random Packing
m2 m3
Super INTALOX® Saddles #1 204 Super INTALOX® Saddles #2 105 BETARING® #1 167 BETARING® #2 114 SNOWFLAKE® 93 FLEXIRING® 1 in. 205 FLEXIRING® 1-1/2 in. 119 FLEXIRING® 2 in. 99 Ceramic Random Packing INTALOX® Saddles 1 in. 256 INTALOX® Saddles 1-1/2 in. 195 INTALOX® Saddles 2 in. 118 Ceramic Structured Packing FLEXERAMIC® 28 282 FLEXERAMIC® 48 157 FLEXERAMIC® 88 102 Metal Structured Packing2 Koch-Glitsch SMV-8 417 Koch-Glitsch SMV-10 292 Koch-Glitsch SMV-16 223 Koch-Glitsch SMV-32 112 Sulzer SMV 2Y 205 Sulzer SMV 250Y 256 Sulzer SMV 350Y 353 INTALOX® 2T 214 INTALOX® 3T 170 INTALOX® 4T 133 Plastic Structured Packing2 Koch-Glitsch SMV-8 330 Koch-Glitsch SMV-16 209 Koch-Glitsch SMV-32 93 Sulzer SMV 250Y 256
Void Fraction1 (e)
0.896 0.934 0.942 0.940 0.949 0.922 0.925 0.932 0.730 0.750 0.760 0.720 0.770 0.850 0.978 0.985 0.989 0.989 0.990 0.988 0.983 0.989 0.989 0.987 0.802 0.875 0.944 0.875
1. Typical value for standard wall thickness. Values will vary depending upon thickness. 2. SMV structured packings also are available with horizontal dual-flow perforated plates installed between elements (typically designated SMVP packing). These plates generally reduce backmixing and improve mass-transfer performance at the expense of a reduction in the open cross-sectional area and somewhat reduced capacity. Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-71.
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Chapter 6: Mass Transfer 6.4.2.8 Liquid-Liquid Extraction Equipment: Sieve Tray Columns Sieve Tray Perforated Area Perforations usually are in the range of 0.125 to 0.25 in (0.32 to 0.64 cm) in diameter, set 0.5 to 0.75 in (1.27 to 1.81 cm) apart, on square or triangular pitch. Hole size appears to have relatively little effect on the mass-transfer rate except that, in systems of high interfacial tension, smaller holes produce somewhat better mass transfer. The entire hole area is normally set at 15 to 25 percent of the column cross-section, although adjustments may be needed. It is common practice to set the velocity of liquid exiting the holes to correspond to a Weber number between 8 and 12. This normally gives velocities in the range of 0.5 to 1.0 ft (15 to 30 cm ). sec s The velocity of the continuous phase in the downcomer (or upcomer) udow, which sets the downcomer crosssectional area, should be set lower than the terminal velocity of some arbitrarily small droplet of dispersed phase, such as a diameter of 1/32 or 1/16 in (0.08 or 0.16 cm). Otherwise, recirculation of entrained dispersed phase around a tray will result in flooding. The terminal velocity ut of these small drops can be calculated using Stokes’ Law: gc d p2 Dt ut = 18n c Downcomer area typically is in the range of 5 to 20 percent of the total cross-sectional area, depending upon the ratio of continuous- to dispersed-phase volumetric flow rates. For large columns, tray spacing between 18 and 24 in. (45 and 60 cm) is generally recommended. The height of the coalesced layer at each tray, h, is DPo + DPdow − zd gc Dt L h= `1 − zd j gc Dt where DPo
= orifice pressure drop
DPdow = pressure drop for flow through a downcomer (or upcomer) L
= downcomer (or upcomer) length
The orifice pressure drop DPo is −2
0.2
2 0.71 v 1 DPo = 2 d1 − log Re n td uo2 + 3.2 d do gc Dt n d v o
where
for Re =
uo do td nd
do = diameter of orifice in ft
The pressure drop through the downcomer is DPdow = where udow
2 4.5udow tc 2
= velocity in downcomer (or upcomer)
For large columns, the design should specify that the height of the coalesced layer is at least 1 in. (2.5 cm) to ensure that all holes are adequately covered.
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Chapter 6: Mass Transfer For segmental downcomers, the area of the downcomer is H A = 6S _3H 2 + 4S 2 i where A
= area of segmental downcomer (or upcomer)
H
= height of segmental downcomer (or upcomer)
S
= chord length of segmental downcomer (or upcomer)
Chord length S is
1
2 D S = =8H d col − H nG 2 2
where Dcol = column diameter Sieve Tray Flooding Velocity Velocity of the continuous phase at the flood point is RS V0.5 SS L − A WWW WW ucf = SSS udf 2 SS B d ucf n + C WWW T X where 1.11td 2.7tc 6c B= C= A= do Dt gc gc Dt f ha2 2gc Dt fda2 where fha = fractional hole area fda = fractional downcomer area The cross-flow velocity of the continuous phase uc flow is Lfp ucflow . z − h uc where Lfp = length of flow path z
= sieve tray spacing
Sieve Tray Efficiency The sieve tray efficiency is approximated by po = 0.21 f
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0.42
u z0.5 pd d n v do0.35 uc
363
Chapter 6: Mass Transfer
6.4.3
Adsorption
6.4.3.1 Adsorption Equilibrium For a single adsorbate in a gas stream, the equilibrium capacity of the adsorbent may be related to the concentration of the adsorbate in the bulk stream by the Freundlich equation: W = a pn where mass qf adsqrbate W = unit mass of adsorbent p
= partial pressure of adsorbate in the bulk gas stream
a, n = empirical coefficients derived from log-log plot of data for W vs. p Both coefficients are a function of temperature. The Freundlich equation can be used for liquid-solid adsorption by entering concentration instead of partial pressure.
Typical Adsorption Isotherms
MASS ADSORBATE/MASS ADSORBANT
TYPICAL ADSORPTION ISOTHERMS INCREASING TEMPERATURE
LOG PARTIAL PRESSURE OF ADSORBATE
6.4.3.2 Adsorption Operation Adsorption in typical commercial operations is conducted by passing the gas or liquid stream through a usually vertical fixed bed of adsorbent particles. Adsorption beds are usually oriented vertically. Adsorption beds have three zones that characterize the operation: 1. Equilibrium zone where adsorbate is in equilibrium with inlet concentration 2. Mass transfer zone where adsorbate is diffusing into adsorbent 3. Active zone where no adsorption has occurred The length of the mass transfer zone (MTZ) is a function of the fluid velocity along with adsorbent porosity and uniformity of pore size.
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Chapter 6: Mass Transfer Adsorption Concentration Profiles Across Bed EQUILIBRIUM ZONE
VAPOR PHASE CONCENTRATION
y IN
ACTIVE ZONE
MASS TRANSFER ZONE
y OUT
O
L
BED LENGTH CONCENTRATION PROFILE AT A GIVEN TIME DURING ADSORPTION OPERATION
Three performance regimes for adsorption beds characterize the operation. Considering a given point in a bed: 1. Dry, when the mass transfer zone is below the point in the bed and the concentration has a low value 2. Break-through, when the mass transfer zone reaches the point in the bed and the concentration increases 3. Saturated, when the concentration at the point in the bed increases to the value of the inlet concentration
Adsorption Outlet Composition Versus Time DRY
BREAK-THROUGH
SATURATED
VAPOR PHASE CONCENTRATION
y IN
y OUT
0
TIME
CONCENTRATION PROFILE AS A FUNCTION OF TIME AT A GIVEN POINT IN THE BED. ADSORPTION STEP. ©2017 NCEES
365
Chapter 6: Mass Transfer 6.4.3.3 Adsorption Regeneration Adsorption processes can be nonregenerative or regenerative. Nonregenerative adsorption is a batch process. For regenerative adsorption, adsorbent beds are cycled between adsorption and desorption (regeneration) modes and multiple beds are required for continuous operation. During regeneration, stripping the adsorbate is accomplished by passing a pure fluid through the bed at a lower pressure for pressure swing adsorption (PSA) or at a higher temperature for temperature swing adsorption (TSA). For TSA, the pressure may be slightly lowered in addition to the temperature increase. Often a split stream from the fluid exiting the adsorbing bed is used as the pure fluid for regenerating adsorption beds. The regeneration of adsorption beds leaves a residual concentration of adsorbate in the adsorbent. This reduces the working capacity of regenerated adsorbent in comparison with the capacity of fresh adsorbent. Working capacity W l = Wsat − Wregen where Wsat = amount adsorbed on the bed at break-through Wregen = amount of adsorbate remaining on the bed after regeneration
6.4.3.4 Characteristics of Typical Adsorption Systems Adsorption System Characteristics TSA
System Type:
Gas Phase
Configuration of system Number of beds Time on adsorption Flow direction on adsorption
2 to 4 4 to 8 hours Down
Flow direction on regeneration
Up
PSA Gas Phase
Liquid Phase
2 to 4 4 to 8 hours Up Down; treated vaporized liquid when feasible
2 to 16 Minutes to hours Up Down
Common adsorbents Hydrophobic
Activated carbons for removing VOCs from gas
Hydrophilic
Silica gel, activated alumina, mol sieve for dehydration and removing slightly polar organics
6.4.4
Activated carbons for water purification
Activated carbon for air separations; heavy hydrocarbons from light hydrocarbons
Leaching
6.4.4.1 Single-Stage Leaching Leaching is the removal of a soluble substance from an insoluble solid via liquid extraction. The desired component diffuses into the solvent by mass transfer. Two common methods of leaching are: • Percolation of liquids through stationary solid beds • Dispersion of solids in each leaching stage by mechanical agitation
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Chapter 6: Mass Transfer 6.4.4.2 Multistage Leaching For multistage leaching processes, the most common setup is continuous countercurrent leaching, where a liquid solvent overflows from stage to stage in a direction opposite to the flow of the solid. The stages are numbered in the direction of flow of the solid. • The flow rates of contained liquid in the solid slurry streams are shown as L-values. • The concentrations of solute in the solid slurries are shown as x-values. • Feed solid slurries enter at stage 1, containing a liquid flow of La with a solute concentration of Xa. • Leached solid slurries exit at stage N, containing a liquid flow of Lb with a solute concentration of Xb. • It is assumed that the solids flow rate is constant from stage to stage. • The flow rates of overflow solvent from each stage are shown as V-values. • The concentrations of solute in the solvent streams are shown as y-values. • Lean solvent enters the process at stage N, at a mass flow rate of Vb and a solute concentration of yb. • The concentrated solvent, or leachate, exits at a mass flow rate of Va and a solute concentration of Ya.
Multistage Leaching Diagram LEACHATE FEED SOLIDS
Va Ya
STAGE
La
ONE
xa
V2
Vn
Y2 L1
Yn Ln-1
x1
xn-1
STAGE n
Vn+1 Yn+1 Ln xn
Vn+2
STAGE Yn+2 Ln+1 n+1 xn+1
VN YN LN-1
STAGE
xN-1
N
Vb Yb Lb xb
LEAN SOLVENT LEACHED SOLIDS
Leaching Calculations Inputs = Outputs: La + Vn+1= Va + Ln Component balance: La (xa) + Vn + 1 (y n + 1) = Va (ya) + L n (x n) Leaching Operating Line V Y −L X L Yn + 1 = V n X n + a aV a a n+1
n+1
Note: If the density of liquid Ln is constant from stage to stage, then the overflow and underflow rates are both constant and the operating line is straight. Calculation of the Number of Required Stages in Leaching With Constant Overflow The equilibrium line for leaching is Xe = Ye
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Chapter 6: Mass Transfer The first stage of the leaching process is calculated initially as a mass balance to set up the flow of slurried solids through the rest of the stages. Therefore, the following calculation determines the total number of stages N, in the format of N–1: y −x ln e b − b o ya xa N−1 = y −y ln e b − a o xb x a
6.4.5
Batch Distillation
6.4.5.1 Rayleigh Equation
#n n
dn = nf = n ln n0
f
0
#x x
f
0
dx y−x
where nf = moles in still at end of run n0 = initial moles in still xf = mole fraction in liquid phase at end of run x0 = initial mole fraction in liquid phase in still
6.4.5.2 Relative Volatility Equation
where
c ym x a ij = 1−y d n 1−x aij = relative volatility y = mole fraction of light component in vapor phase
Rearranging: ax y = 1 + ( a − 1) x Therefore, n n ln n A = a AB ln n B 0A
0B
where nx
= moles of liquid "x" left in the still at any time
0
= time zero
aAB = relative volatility
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Chapter 6: Mass Transfer 6.4.5.3 Operating Line for Batch Distillation With Reflux RD x yn + 1 = R + x n + R D+ 1 1 D D where RD = reflux ratio based on the distillate rate x = liquid composition
6.4.5.4 Batch Distillation Apparatus •
Batch Distillation Apparatus
QC
CONDENSER
N N-1
DISTILLATE ACCUMULATOR
N-2 1 2
COLUMN
3 REBOILER •
QR
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Chapter 6: Mass Transfer
6.4.6
Crystallization
6.4.6.1 Saturation and Supersaturation The Solubility-Supersolubility Diagram C'
CONCENTRATION
LABILE
C" B"
B'
D C A
B
TA
ME
LE
B STA
STABLE
TEMPERATURE
Diagram regions: • Stable (unsaturated) zone, where crystallization is impossible. • Metastable (supersaturated) zone, between the solubility and supersolubility curves, where spontaneous crystallization is improbable. However, if a crystal seed were placed in such a metastable solution, growth would occur on it. • Unstable or Labile (supersaturated) zone, where spontaneous crystallization is probable, but not inevitable.
6.4.6.2 Expressions of Supersaturation Dc = c – c* where c = concentration c* = saturation concentration Dc = driving-force concentration c S = c* where S = supersaturation ratio Dc s = c* = S − 1 where s = relative supersaturation (100s is % supersaturation)
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Chapter 6: Mass Transfer 6.4.6.3 Expression of Supercooling Dq = q* – q where q = temperature of the solution q* = saturation temperature of the solution d c* The supersaturation and supercooling are related by the local slope of the solubility curve by di d c* Dc = c d i m D i
6.4.6.4 Nucleation Diagram of Nucleation NUCLEATION
PRIMARY
HOMOGENEOUS (SPONTANEOUS)
SECONDARY (INDUCED BY CRYSTALS)
HETEROGENEOUS (INDUCED BY FOREIGN PARTICLES)
Gibbs Energy of Nucleation DGcrit =
4r c r c2 3
DGcrit =
4r c r c2 = Gibbs free energy for the critical radius of a stable nucleus 3
where
g = interfacial tension between the developing crystal surface and the supersaturated solution rc = critical radius of a stable nucleus
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Chapter 6: Mass Transfer Homogeneous Nucleation Rate (Arrhenius Form) J = A EXP >−
16r c 3 v 2 H 3k 3 T 3 (ln S) 2
where J = nucleation rate A = rate constant R k = Boltzmann constant (k = Nc , where N is Avogadro's number) v = number of moles of ions produced from one mole of electrolyte (for nonelectrolytes, v = 1) T = absolute temperature S = supersaturation ratio Heterogeneous Nucleation Rate n J = k n Dc max
where J
= nucleation rate
kn
= nucleation rate constant
Dcmax = maximum allowable metastable zone width n
= the observed order of the nucleation (a fitting parameter)
6.4.6.5 Crystal Growth 1 dm 3= a 3a dL 6= a dr 6a g = = RG K= t G = t t t vr G Dc A dt b c b c dt b c dt b c where kg RG = mass deposition rate, in 2 m :s m KG = mass-transfer coefficient with units that are dependent on g (if g = 1), in s g = the order (a fitting parameter) Dcg = concentration driving force for mass transfer, in A = b L2 = particle area, in m2 m = a rc L3 = particle mass, in kg t
= time, in s
a = volume shape factor b = surface shape factor m G = overall linear growth rate, in s kg rc = crystal density, in 3 m
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kg m3
Chapter 6: Mass Transfer L
= some characteristic size of the crystal, in m
r
= radius corresponding to the equivalent sphere, in m
vr
m = mean linear velocity of growth, in s
Some Mean Overall Crystal Growth Rates Expressed as a Linear Velocity1 Crystallizing Substance
cC
S
vr b m sl
(NH 4) 2 SO 4 : Al 2 (SO 4) 3 : 24H 2 O
15 30 30 40 40 30 60 90 20 30 30 40 20 30 30 25 25 25 15 30 30 40 20 40 20 40 20 20 30 50 50 30 30 40 40 50 50 70 70 30 30
1.03 1.03 1.09 1.08 1.05 1.05 1.05 1.01 1.06 1.02 1.05 1.02 1.02 1.01 1.02 1.03 1.09 1.20 1.04 1.04 1.09 1.03 1.02 1.01 1.05 1.05 1.09 1.18 1.07 1.06 1.12 1.07 1.21 1.06 1.18 1.002 1.003 1.002 1.003 1.02 1.08
1.1 × 10–8* 1.3 × 10–8* 1.0 × 10–7* 1.2 × 10–7* 8.5 × 10–7 2.5 × 10–7* 4.0 × 10–7 3.0 × 10–8 6.5 × 10–8 3.0 × 10–8 1.1 × 10–7 7.0 × 10–8 4.5 × 10–8* 8.0 × 10–8* 1.5 × 10–7* 5.2 × 10–9 2.6 × 10–8 4.0 × 10–8 1.4 × 10–8* 2.8 × 10–8* 1.4 × 10–7* 5.6 × 10–8* 2.0 × 10–7 6.0 × 10–7 4.5 × 10–8 1.5 × 10–7 2.8 × 10–8* 1.4 × 10–7* 4.2 × 10–8* 7.0 × 10–8* 3.2 × 10–7* 3.0 × 10–8 2.9 × 10–7 5.0 × 10–8 4.8 × 10–7 2.5 × 10–8 6.5 × 10–8 9.0 × 10–8 1.5 × 10–7 1.1 × 10–7 5.0 × 10–7
NH4NO3 (NH 4) 2 SO 4 NH4H2PO4
MgSO 4 : 7H 2 O NiSO 4 : (NH 4) 2 SO 4 : 6H 2 O K 2 SO 4 : Al 2 (SO 4) 3 : 24H 2 O
KCl KNO3 K2SO4
KH2PO4
NaCl
Na 2 S 2 O 3 : 5H 2 O
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Chapter 6: Mass Transfer Some Mean Overall Crystal Growth Rates Expressed as a Linear Velocity1 (cont'd) Crystallizing Substance Citric acid monohydrate
Sucrose
1
cC
S
vr b m sl
25 30 30 30 30 70 70
1.05 1.01 1.05 1.13 1.27 1.09 1.15
3.0 × 10–8 1.0 × 10–8 4.0 × 10–8 1.1 × 10–8* 2.1 × 10–8* 9.5 × 10–8 1.5 × 10–7
c The supersaturation is expressed by S = l with c and c' as kg of crystallizing substance per kg of free water. The c 1 significance of the mean linear growth velocity, vr c = 2 G m , is explained by equation 6.61 and the values recorded here refer to crystals in the approximate size range 0.5–1 mm growing in the presence of other crystals.
* Denotes that the growth rate is probably size-dependent. Source: Mullin, J.W., Crystallization, 4th ed., Woburn, MA: Reed Educational and Professional Publishing Ltd., 2001, p. 237.
6.4.7
Filtration
Types of filters: 1. Discontinuous pressure filters 2. Continuous filters 3. Centrifugal filters 4. Cartridge filters 5. Bag filters
6.4.7.1 Factors for Selection of Filter Media The filter media in any process filter need to meet the following requirements to be of value in a chemical process: • The septum must obviously be able to retain the solids to be filtered, producing a reasonably clear filtrate • The removed solids must not plug off the media upon initial or subsequent use. • The media must be chemically resistant to the chemicals in the filtrate and the filter cake. • The septum must be strong enough physically to withstand the operating conditions. • The media must allow the cake to be discharged cleanly and completely. • The cost of the media must be reasonable enough not to add significantly to the overall plant or production cost.
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Chapter 6: Mass Transfer 6.4.7.2 Filtration Equations Total pressure drop: Dp = pa − p b = (pa − pl ) + (pl − p b) = Dpc + Dp m where Dp = overall pressure drop pa
= filter inlet pressure
p'
= septum inlet pressure
pb
= filter outlet pressure
Dpc = pressure drop over cake Dpm = pressure drop over medium Filter cake pressure drop: dp 150nu (1 − f) 2 = dL gc (z s D p) 2 f 3 where dp dL = pressure gradient at thickness L µ
= viscosity of filtrate
u
= linear velocity of filtrate, based on filter area
e = porosity of cake Dp = nominal diameter of solid particles 6v p z s = D s for nonspherical particles p p z s = 1 for spherical particles or dp = dL
2
s 4.17n u (1 − f) f v p p p 2
gc f 3
where sp = surface of single particle vp
= volume of single particle
Filter medium resistance: Rm =
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` pl − p b j gc
nu
=
− Dp m g c nu
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Chapter 6: Mass Transfer
6.4.8
Drying of Solids
6.4.8.1 Moisture (Solvent) Percentage Content Typically calculated on a dry solid/dry air basis: m X = % moisture in solid = mw s where X
= moisture (solvent) content in solid, moisture mass/dry solid mass
mw = moisture (solvent) content, mass of water or solvent, in lbm ms = mass of dry solid, in lbm Y
m = % moisture in air = mw a
Y
= moisture (solvent) content in air, moisture mass/dry air mass
where
mw = moisture (solvent) content, mass of water or solvent, in lbm ma = mass of dry air, in lbm
6.4.8.2 Rate of Drying Rate of drying is dictated by the state of the solvent, such as: • "Free" solvent on surface of solids • "Bound" solvent, which must reach the surface through diffusion or capillary action • "Solvated" solvent, which is chemically bound to the solids (sometimes labile to removal, sometimes not) that are not generally considered in drying analyses
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Chapter 6: Mass Transfer Drying Curve
FALLING RATE I
CONSTANT RATE
N, DRYING RATE
FALLING RATE II
X*
X
C
X, MOISTURE (SOLVENT) CONTENT lb/lb DRY SOLID
where X* = equilibrium moisture content: the moisture content of the solid when it reaches equilibrium with the surrounding air; depending upon the specific conditions of the surrounding air Xc = critical moisture content: the moisture content that marks the instant when the liquid content on the surface of the solid is no longer sufficient to maintain a continuous liquid film on the surface Constant Rate: Rate of drying independent of moisture content. During this period the solid is so wet that the entire surface of the solid is covered with a continuous film of liquid. Falling Rate I: Only part of the solid surface is saturated as the entire solid surface can no longer be maintained at saturation conditions by the movement of moisture within the solid. The rate of drying is linear with regard to X. Falling Rate II: The entire solid surface is unsaturated and the drying rate is limited by the rate of internal moisture movement.
6.4.8.3 Specific Drying Applications Drying of slab using gas from one side only:* 1. For drying during the constant rate period Rate of drying can be determined based on the balance between the heat transfer to the material and the rate of vapor removal from the surface. h t A DT = NC = k g A Dp m * Source: McCabe, Warren L., and Julian C. Smith, Unit Operations in Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976. ©2017 NCEES
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Chapter 6: Mass Transfer where DT = gas dry bulb temperature—temperature at surface of solid Dp = vapor pressure of water at surface temperature—partial pressure of water vapor in the gas A = surface area, in ft2 kg = mass-transfer coefficient, in Nc = constant drying rate, in
lbm hr-ft 2-atm
lbm ft 2- hr
Btu l = latent heat of evaporation, in lbm ht = total heat-transfer coefficient, in
Btu hr-ft 2-cF
When the air is flowing parallel to the surface: ht = 0.0128 G0.8 When the air is flowing perpendicular to the surface, the equation is ht = 0.37 G0.37 where G = mass velocity, in t=
lbm ft 2-hr
ms (X1 − X 2) A NC
where t
= drying time
X1 = moisture content in solid at time 1 X2 = moisture content in solid at time 2 2. For linear falling rate period I t=>
N ms (X1 − X 2) H ln 1 N2 A (N1 − N 2)
where N1
= drying rate at time 1, in
lb ft 2-hr
N2
= drying rate at time 2, in
lb ft 2-hr
ms
= mass of dry solids, in lb
3. For falling rate period II, rate curve must be integrated: t =d
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ms n A
#x x 2
1
dX N
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Chapter 6: Mass Transfer 6.4.8.4 Dryer Design and Performance 1. Tray dryers To determine the tray area for a specific production rate: A=
P (t + td) LT
where P
= production rate, in mass of dry solids per hour
t
= drying time
td
= downtime for loading and unloading trays
LT
= tray loading in mass of dry solids per square area of tray, in
m W t s d p2 t = 12k (T − T ) f a s where dp
= drop diameter, in ft
W
lbm = moisture content in the drop, in lbm dry solid
kf
Btu = thermal conductivity of the gas film, in hr-ft-cF
Ta –Ts = temperature difference between drop and gas, in °F l
Btu = latent heat of evaporation, in lbm
rs
= density of dry particle, in
lbm ft 3
2. Continuous through-circulation dryers To determine required conveyor length: Required dryer holding capacity C in pounds is C=Pt where P = production rate, in
lbm dry solid hr
t = drying time, in hr
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lbm ft 2
Chapter 6: Mass Transfer Pt A= L where A = conveyor area, in ft2 lbm dry sqlid L = bed loading, in 2 ft cqnveyqr area A B=W where B = effective dryer length, in ft W = conveyor width, in ft 3. Rotary dryers The residence time can be determined empirically using: for countercurrent flow, sign in the expression below is positive for concurrent flow, sign in the expression below is negative −
t=
5D p0.5 LG 0.23L ! 0 . 6 F SN 0.9 D
where t = retention time, in min D = diameter of shell, in ft Dp = weighted average particle size of material, in micrometers rev N = speed, in min
ft S = slope of shell, in ft G = air mass velocity in F = feed rate in
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lbm hr - ft 2
lbm dry material hr-ft 2 qf dryer crqss-sectional area
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Chapter 6: Mass Transfer 4. Spray dryers An estimate of the drying time can be found using: t= where
mWt s d p2 12Kf `Ta − Ts j
t
= drying time, in min
dp
= drop diameter in ft
W
lbm = moisture content in the drop in lbm dry solid
Kf
Btu = thermal conductivity of the gas film in hr -ft -cF
Ta – Ts = temperature difference between drop and gas in °F rs
= density of the solid
6.4.8.5 Typical Critical Moisture Content of Various Materials Approximate Critical Moisture Contents Obtained on the Air Drying of Various Materials, Expressed as Percentage Water on the Dry Basis1,2 Material
Thickness (in.)
Barium nitrate crystals, on trays Beaverboard Brick clay Carbon pigment Celotex Chrome leather Copper carbonate, on trays English china clay Flint clay refractory brick mix Gelatin, initially 400% water Iron blue pigment, on trays Kaolin Lithol red Lithopone press cake, in trays
1.0 0.17 0.62 1 0.44 0.04 1–1.5 1 2.0 0.1–0.2 (wet) 0.25–0.75 1 0.25 0.50 0.75 1.0
Niter cake fines, on trays Paper, white eggshell Fine book Coated Newsprint Plastic clay brick mix
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Critical Moisture (% Water)
7 Above 120 14 40 160 125 60 16 13 300 110 14 50 6.4 8.0 12.0 16.0 Above 16 41 33 34 60–70 19
Chapter 6: Mass Transfer Approximate Critical Moisture Contents Obtained on the Air Drying of Various Materials, Expressed as Percentage Water on the Dry Basis (cont'd) Material
Thickness (in.)
Poplar wood Prussian blue Rock salt, in trays Sand, 50–150 mesh 200–325 mesh through 325 mesh Sea sand, on trays
0.165 1.0 2.0 2.0 2.0 0.25 0.50 0.75 1.0 2.0 2.0 0.25 1
Silica brick mix Sole leather Stannic tetrachloride sludge Subsoil, clay fraction 55.4% Subsoil, much higher clay content Sulfite pulp Sulfite pulp (pulp lap) White lead Whiting Wool fabric, worsted Wool, undyed serge
0.25–0.75 0.039 0.25–1.5
Critical Moisture (% Water)
120 40 7 5 10 21 3 4.7 5.5 5.9 6.0 8 Above 90 180 21 35 60–80 110 11 6.9 31 8
Source: McCabe, W.L., and J.C. Smith, Unit Operations of Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976.
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Chapter 6: Mass Transfer
6.4.9
Adiabatic Humidification and Cooling Adiabatic Humidification and Cooling FLOW MODEL O
LENGTH OR HEIGHT dZ
Z
G's1 Y'1 TG1
G 's1 Y' TG
G's1 Y '+ dY ' T – dTG
G's1 Y'2 TG2
L'1 Tas
L' Tas
L'+ dL' Tas
L'2 Tas
MATERIAL BALANCE dL' = G'sdY'
L'2 – L'1 = G's (Y '2 – Y '1) INTERFACIAL SERVICE ds = adz
ABS HUMIDITY
MASS TRANSFER Y'as
GAS INTERFACE
BULK
Y'1
Y'
GAS
Y 'as
RATE OF MASS TRANSFER
Y'2
G'sdY '1 = kYa (Y 'as – Y ')dz
dY '
TEMPERATURE
SENSIBLE HEAT TRANSFER BULK
TG1
SENSIBLE RATE OF TRANSFER
GAS
G's Cs1 dT G = hg a (T G – T as) dz
dTG
TG
TG2 Tas
INTERFACE AND BULK LIQUID
Tas
dz
O
z
PSYCHOMETRIC RELATIONS
ABS HUMIDITY
SATURATION HUMIDITY
ADIABATIC SATURATION
Y 'as Y '2 Y '1 Tas TG2
TG1
TEMPERATURE
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Chapter 6: Mass Transfer where Ll = solute-free liquid flow rate Gls = dry-gas mass flow rate Y 1l = initial humidity Y l2 = final humidity Y las = saturation humidity at liquid-gas interface TG = temperature of bulk gas Tas = temperature at liquid-gas interface CS1 = specific heat capacity at the liquid-gas interface hg = gas heat-transfer coefficient Since Y las is constant: ky a z Yl − Yl ln f las − l1 p = Gls Y as Y 2 where ky = overall mass-transfer coefficient a
= interstitial surface per unit volume, in
z
= height, in ft
ft 2 ft 3
Gls _Y l2 − Y 1l i = ky a Z ^DY lhlm where
^DY lhlm = logarithmic mean of humidity difference
or NTUtG = and
Y l2 − Y 1l Y l − Y 1l = ln > as H Y las − Y l2 ^DY lh lm
Gls z = = HTU tG ky a NTUtG where NTUtG = number of gas-phase transfer units HTUtG = height of transfer unit
6.4.9.1 Air-Water Systems 18 YA = 29 yr A where
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Chapter 6: Mass Transfer
YA = where
1 − yrA yrA
yrA = mole fraction of water vapor 18 1 − yr YA = 29 e y A o rA
P Relative humidity = 100 PA A PA = partial pressure of water at a given temperature
where
PA = vapor pressure of water at a given temperature P PA YAS = 1 −AP − 1 PA A where Yas = saturation humidity YA =
PA _1 − PA i Y % saturation = 100 YA = (100) at total pressure of one atmosphere as PA ^1 − PA h Humid heat CPH = 0.24 + 0.46YA CPH = CPy (1 + YA)
where CPy = specific heat of water vapor at constant pressure CPH = humid heat capacity
6.4.9.2 Adiabatic Saturation Temperature m tAS = ty0 − C R `YAS − YA0 j PH
where tAS = adiabatic saturation temperature ty0 = initial inlet temperature lR = latent heat of vaporization at reference temperature YA0 = initial inlet humidity CPH = humid heat capacity YAS = humidity at saturation m tWB = ty − C R `YWB − YA j PH
where YWB = humidity at wet bulb temperature tWB = wet bulb temperature
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Chapter 6: Mass Transfer Humidity Chart for the Air-Water System at One Atmosphere HUMID HEAT, BTU/LB DRY AIR (°F) 0.26
0.28
0.30
0.15 140°
17
20%
130°
30%
40%
12
ADR
135° 100% 90% 80% 70 % 60% 50%
HEA TV
19
HU MID
VOLUME,CU FT/LB DRY AIR
20
PER SATU CENT RATI ON
SH UM IDIT Y
21
125°
0.14
IABA TIC S
ITUA TION
LINE
S
0.12
0.10
16 15 14 13 12
ME OLU
V TED URA
SAT
IFIC
SPEC
ME VOLU
55° 60° 50° 45°
120°
E ATUR PER
EM
VS. T
115°
TURE PERA
M
VS TE
0.08
0.06
110° 105°
100° 95°
65°70°
80° 75°
0.04
90° 85° 0.02
0 25
40
60
80
100
120
140
160
180
200
TEMPERATURE, F°
Source: Brown, G.G., et. al., Unit Operations, New York: Wiley, 1950, p. 545.
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220
240
250
HUMIDITY, LB WATER VAPOR/LB DRY AIR
0.24
10%
22
0.22
Chapter 6: Mass Transfer Cooling Tower Operating Diagram Hy8 vs t4 80 Hy vs tx
H, BTU/LB DRY AIR
60
CpxL GB
40 20 0 50
Hy0 TOP OF TOWER
max
t x0 CpxL SLOPE = GB
HY1 t 1 BOTTOM OF x TOWER 60
70
80 t, °F
C Px L C L o t x + H y0 − e Px o t x0 Hy = e G GB B where Hy = enthalpy of vapor phase CPx = specific of liquid phase L
= liquid phase mass velocity
GB = dry air mass velocity tx = liquid phase temperature Hy0 = initial enthalpy of vapor phase tx0 = liquid phase inlet temperature
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90
100
110
Chapter 6: Mass Transfer
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7 PLANT DESIGN AND OPERATION 7.1 Terms and Definitions Definitions Term
Boiling point
Combustible dust Combustible liquid
Description
The temperature at which the vapor pressure of a liquid equals the atmospheric pressure of 14.7 pounds per square inch (psia), 101 kPa, or 760 mm of mercury. For purposes of this classification, when an accurate boiling point is not available for a material or when a mixture does not have a constant boiling point, use the 20%-evaporated point of a distillation performed in accordance with ASTM D 86. Boiling point is commonly expressed in °F or °C. A finely divided solid material that is 420 microns or less in diameter and that, when dispersed in air in the proper proportions, can be ignited by a flame, spark, or other source of ignition. Will pass through a U.S. No. 40 standard sieve. A liquid having a closed-cup flash point at or above 100°F (38°C). Subdivided into: Class II: Closed-cup flash point at or above 100°F (38°C) and below 140°F (60°C) Class IIIA: Closed-cup flash point at or above 140°F (60°C) and below 200°F (93°C) Class IIIB: Closed-cup flash point at or above 200°F (93°C)
Deflagration
Detonation
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This category does not include compressed gases or cryogenic fluids. An exothermic reaction, such as the extremely rapid oxidation of a flammable dust or vapor in air, in which the reaction progresses through the unburned material at a rate less than the velocity of sound. A deflagration can have an explosive effect. An exothermic reaction characterized by the presence of a shock wave in the material that establishes and maintains the reaction. The reaction zone progresses through the material at a rate greater than the velocity of sound. The principal heating mechanism is one of shock compression. A detonation has an explosive effect.
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Chapter 7: Plant Design and Operation Definitions (cont'd) Term
Explosion
Description
An effect produced by the sudden, violent expansion of gases, which may be accompanied by a shock wave, a disruption of enclosing materials or structures, or both. An explosion could result from: • Chemical changes such as rapid oxidation, deflagration or detonation, decomposition of molecules, or runaway polymerization (usually detonations) • Physical changes such as pressure tank ruptures
Flammable gas
• Atomic changes such as nuclear fission or fusion A material that is a gas at 68°F (20°C) or less at 14.7 psia (101 kPa) of pressure—therefore a material that has a boiling point of 68°F (20°C) or less at 14.7 psia (101 kPa)—and which either: • Ignites at 14.7 psia (101 kPa) when in a mixture of 13% or less by volume with air • Has a flammable range mixed in air at 14.7 psia (101 kPa) and 63°F (20°C)
Flammable liquefied gas Flammable liquid
These levels shall be determined at the specified pressure and temperature in accordance with ASTM E 681. A liquefied compressed gas that, under a charged pressure, is partially liquid at a temperature of 68°F (20°C) and that is flammable. A liquid having a closed-cup flash point below 100°F (38°C). Flammable liquids are further categorized into a group known as Class I liquids and subdivided into: Class IA: Closed-cup flash point below 73°F (23°C) and boiling point below 100°F (38°C) Class IB: Closed-cup flash point below 73°F (23°C) and boiling point at or above 100°F (38°C)
Flammable material Flammable solid
Class IC: Closed-cup flash point at or above 73°F (23°C) and boiling point below 100°F (38°C). The category of flammable liquids does not include compressed gases or cryogenic fluids. A material capable of being readily ignited from a common source of heat or at a temperature of 600°F (316°C). A solid, other than a blasting agent or explosive, that: Is capable of causing fire through friction, absorption or moisture, spontaneous chemical change, or retained heat from manufacturing or processing or Has an ignition temperature below 212°F (100°C) or Burns so vigorously and persistently when ignited as to create a serious hazard
Flammable vapors or fumes Flash point
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A chemical shall be considered a flammable solid in accordance with the test method of CPSC 16 CFR: Part 1500.44 if it ignites and burns with a self-sustained flame at a rate greater than 0.1 inch (2.5 mm) per second along its major axis. The concentration of flammable constituents in air that exceeds 25% of their lower flammable limit (LFL). The minimum temperature in degrees Fahrenheit (or Centigrade) at which a liquid will give off sufficient vapors to form an ignitable mixture with air near the surface or in the container, but will not sustain combustion. The flash point of a liquid shall be determined by appropriate test procedure and apparatus as specified in ASTM D 56, ASTM D 93, or ASTM D 3278. 390
Chapter 7: Plant Design and Operation Definitions (cont'd) Term
Highly toxic
Description
A material that produces a lethal dose or lethal concentration that falls within any of these categories: • A chemical that has a median lethal dose (LD50) of 50 milligrams or less per kilogram of body weight when administered orally to albino rats weighing between 200 and 300 grams each • A chemical that has a median lethal dose (LD50) of 200 milligrams or less per kilogram of body weight when administered by continuous contact for 24 hours (or less if death occurs within 24 hours) with the bare skin of albino rabbits weighing between 2 and 3 kilograms each • A chemical that has a median lethal concentration (LC50) in air of 200 parts per million by volume or less of gas or vapor, or 2 milligrams per liter or less of mist, fume, or dust when administered by continuous inhalation for 1 hour (or less if death occurs within 1 hour) to albino rats weighing between 200 and 300 grams each
Mixtures of these materials with ordinary materials, such as water, may not warrant classification as highly toxic. Immediately The concentration of air-borne contaminants that poses a threat of death, immediate or delayed perdangerous to manent adverse health effects, or effects that could prevent escape from such an environment. This life and health concentration level of contaminants is established by the National Institute for Occupational Safety (IDLH) and Health (NIOSH) based on both toxicity and flammability. Generally it is expressed in parts permillion by volume (ppm/v) or milligrams per cubic meter (mg/m3). Organic peroxide
An organic compound that contains the bivalent -O-O- structure and that may be considered a structural derivative of hydrogen peroxide in which one or both of the hydrogen atoms have been replaced by an organic radical. Organic peroxides can pose an explosion hazard (detonation or deflagration) or can be shock sensitive. They also can decompose into various unstable compounds over an extended period of time. Class I: Formulations that are capable of deflagration but not detonation Class II: Formulations that burn very rapidly and pose a moderate reactivity hazard Class III: Formulations that burn rapidly and pose a moderate reactivity hazard Class IV: Formulations that burn in the same manner as ordinary combustibles and pose a minimal reactivity hazard Class V: Formulations that burn with less intensity than ordinary combustibles or do not sustain combustion and pose no reactivity hazard Unclassified detonable: Organic peroxides that are capable of detonation. These pose an extremely high explosion hazard through rapid explosive decomposition.
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Chapter 7: Plant Design and Operation Definitions (cont'd) Term
Oxidizer
Description
A material that readily yields oxygen or other oxidizing gas or that readily reacts to promote or initiate combustion of combustible materials and, if heated or contaminated, can result in vigorous selfsustained decomposition. Class 4: An oxidizer that can undergo an explosive reaction due to contamination or exposure to thermal or physical shock and that causes a severe increase in the burning rate of combustible materials with which it comes into contact. Additionally, the oxidizer causes a severe increase in the burning rate and can cause spontaneous ignition of combustibles. Class 3: An oxidizer that causes a severe increase in the burning rate of combustible materials with which it comes into contact. Class 2: An oxidizer that causes a moderate increase in the burning rate of combustible materials with which it comes into contact.
Oxidizing gas Physical hazard
Class 1: An oxidizer that does not moderately increase the burning rate of combustible materials. A gas that can support and accelerate combustion of other materials more than air does. A chemical for which there is evidence that it is one of the following: • Combustible liquid • Cryogenic fluid • Explosive or flammable solid, liquid, or gas • Solid or liquid organic peroxide • Solid or liquid oxidizer • Oxidizing gas • Pyrophoric solid, liquid, or gas • Unstable (reactive) solid, liquid, or gas material
Toxic
• Water-reactive solid or liquid material A chemical falling within any of these categories: • Has a median lethal dose (LD50) of more than 50 milligrams per kilogram but not more than 500 milligrams per kilogram of body weight when administered orally to albino rats weighing between 200 and 300 grams each. • A chemical that has a median lethal dose (LD50) of more than 200 milligrams per kilogram but not more than 1000 milligrams per kilogram of body weight when administered by continuous contact for 24 hours (or less if death occurs within 24 hours) with the bare skin of albino rabbits weighing between 2 and 3 kilograms each. • A chemical that has a median lethal concentration (LC50) in air of more than 200 parts per million but not more than 2000 part per million by volume or less of gas or vapor, or more than 2 milligrams per liter but not more than 20 milligrams per liter of mist, fume, or dust, when administered by continuous inhalation for 1 hour (or less if death occurs within 1 hour) to albino rats weighing between 200 and 300 grams each.
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Chapter 7: Plant Design and Operation Definitions (cont'd) Term
Unstable (reactive) material
Description
A material, other than an explosive, that in the pure state or as commercially produced will vigorously polymerize, decompose, condense, or become self-reactive and undergo other violent chemical changes, including explosion, when it is either: • Exposed to heat, friction, or shock • In the absence of an inhibitor • In the presence of contaminants • In contact with incompatible materials Unstable (reactive) materials are subdivided into: Class 4: Materials that in themselves are readily capable of detonation or explosive decomposition or explosive reaction at normal temperatures and pressures. Includes materials that are sensitive to mechanical or localized thermal shock at normal temperatures and pressures Class 3: Materials that in themselves are capable of detonation or of explosive decomposition or explosive reaction but which require a strong initiating source or which must be heated under confinement before initiation. Includes materials that are sensitive to thermal or mechanical shock at elevated temperatures and pressures Class 2: Materials that in themselves are normally unstable and readily undergo violent chemical change but do not detonate; includes materials that can undergo chemical change with rapid release of energy at normal temperatures and pressures and that can undergo violent chemical change at elevated temperatures and pressures
Class 1: Materials that in themselves are normally stable but that can become unstable at elevated temperatures and pressures Water-reactive A material that explodes; violently reacts; produces flammable, toxic, or other hazardous gases; or material evolves enough heat to cause autoignition or ignition of combustibles upon exposure to water or moisture. Water-reactive materials are subdivided into: Class 3: Materials that react explosively with water without requiring heat or confinement Class 2: Materials that react violently with water or have the ability to boil water. Materials that produce flammable, toxic, or other hazardous gases, or evolve enough heat to cause autoignition or ignition of combustibles upon exposure to water or moisture Class 1: Materials that react with water with some release of energy, but not violently Source: 2015 International Building Code, Country Club Hills, Illinois: International Code Council.
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7.2 Economic Considerations Nomenclature Abbreviation
Definition
A BV C Dj
Uniform amount per interest period Book value Cost, present worth Depreciation in year j
F G i m n P r Sn
Future worth, value, or amount Uniform gradient amount per interest period Interest rate per interest period Number of compounding periods per interest period Number of interest periods, or the expected life of an asset Present worth, value, or amount Nominal annual interest rate Expected salvage value in year n Subscripts
7.2.1
e
Effective
j
At time j
n
At time n
Cost Estimation and Project Evaluation Basic Equations Factor Name
Converts
Symbol
Formula
Single payment Compound amount Single payment Present worth Uniform series Sinking fund
to F given P
(F/P, i%, n)
F = P (1 + i)n
to P given F
(P/F, i%, n)
P = F (1 + i)-n
to A given F
(A/F, i%, n)
i A = F d (1 + i) n − 1 n
Capital recovery
to A given P
(A/P, i%, n)
A = Pf
Uniform series Compound amount
to F given A
(F/A, i%, n)
+ n− F = A d (1 i) 1 n i
Uniform series Present worth
to P given A
(P/A, i%, n)
P = Af
Uniform gradient Present worth
to P given G
(P/G, i%, n)
Uniform gradient* Future worth
to F given G
(F/G, i%, n)
F = Gf
Uniform gradient Uniform series
to A given G
(A/G, i%, n)
1 n A = G d i − (1 + i) n − 1 n
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P = Gf
i (1 + i) n p (1 + i) n − 1
( 1 + i) n − 1 p i (1 + i) n
(1 + i) n − 1 n − np i 2 (1 + i) n i (1 + i) (1 + i) n − 1 n − p i i2
Chapter 7: Plant Design and Operation Basic Equations (cont'd) Factor Name
Converts
Symbol
r mm − 1 ie = c1 + m
to ic given r,m
Interest rate
Formula
Book value
BV = initial cost − RD j
F− * F n F A = A = # i G
A
G
Depreciation Methods Method
Description
Formula
Stipulations
where d = annual depreciation, in $ per year V = original value of the property at start the service-life period, completely installed and ready for use, in $ Straight line Vs = salvage value of property at end Book value Va = V − ad of service life, in $ n = service life, in years Va = asset or book value a = number of years in actual use 1 n Fixed percentage V i = annual interest rate expressed as f = 1 −d sn Declining balance factor V a fraction (or fixed percentage) R = uniform annual payments made a Book value Va = V `1 − f j at end of each year (annual depreciation cost), in $ 2_n − a + 1 i Depreciation for V – Vs = total amount of the annuity `V − Vs j da = year a n_n + 1 i accumulated in an estimated Sinking fund a service life of n years (original _1 + i i − 1 − = − ` j value of property minus salvage V V Va V Book value n s _1 + i i − 1 value at end of service life), in $ Annual depreciation cost
V−V d= n s
Source: Peters, Max S., and Klaus D. Timmerhaus, Plant Design and Economics for Chemical Engineers, 4th ed., New York: McGraw-Hill, Inc., 1991, pp. 278, 280, 283, and 284.
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Chapter 7: Plant Design and Operation 7.2.1.1 Cost Indicies Cost indices are used to update historical cost data to the present. If a purchase cost is available for an item of equipment in year M, the equivalent current cost can be found using: Current Index Current $ = (Cost in year M) d Index in year M n
Cost Index Year
Equipment Index
Labor Index
Material Index
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
341 344 352 360 368 383 401 421 432 444 503 552 579 514 554 569
100 107 116 128 139 147 155 164 176 187 197 210 218 223 231 236
100 106 112 113 120 127 139 161 174 188 205 228 241 248 251 255
7.2.1.2 Scaling Equipment Costs The cost of Unit A at one capacity related to the cost of a similar Unit B with X times the capacity of Unit A is approximately X n times the cost of Unit B, or: n Capacity of Unit A o Cost of Unit A = Cost of Unit B e Capacity of Unit B
Typical Scaling Factors (n) for Equipment Cost vs. Capacity Equipment
Size Range
Agitator, propeller Agitator, turbine Boiler, industrial, all sizes Boiler, package Centrifuge, horizontal basket Centrifuge, solid bowl Conveyor, belt Conveyor, bucket Conveyor, screw Conveyor, vibrating
0.50 0.30 0.50 0.72 1.72 1.00 0.65 0.77 0.76 0.87
Compressor, reciprocating, air-cooled, two-stage, 150 psig discharge
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ft3 10 to 400 min
0.69
Chapter 7: Plant Design and Operation Typical Scaling Factors (n) for Equipment Cost vs. Capacity (cont'd) Equipment
Size Range
Compressor, rotary, single-stage, sliding vane, 150 psig discharge Crystallizer, growth Crystallizer, forced circulation Crystallizer, batch Dryer, drum, single vacuum Dryer, drum, single atmospheric Dust collector, cyclone
ft3 100 to 1000 min
10 to 102 ft2 10 to 102 ft2
Exponent
0.79 0.65 0.55 0.70 0.76 0.40 0.80
Dust collector, cloth filter
0.68
Dust collector, precipitator
0.75
Evaporator, forced circulation
0.70
Evaporator, vertical and horizontal tube
0.53
Fan, centrifugal
ft3 103 to 104 min
0.44
Fan, centrifugal
ft3 2 x 104 to 7 x 104 min
1.17
Filter, plate and press Filter, pressure leaf Heat exchanger, shell and tube, floating head, carbon steel Heat exchanger, shell and tube, fixed sheet, carbon steel Mill, ball and roller Mill, hammer Motor, squirrel cage, induction, 440 volts, explosion proof Motor, squirrel cage, induction, 440 volts, explosion proof Pump, centrifugal, carbon steel Pump, centrifugal, stainless steel Pump, reciprocating, cast iron, horizontal, including motor Reactor, stainless steel, 300 psi Tanks and vessels, pressure, carbon steel Tanks and vessels, horizontal, carbon steel Tanks and vessels, stainless steel Tray, bubble cap, carbon steel Tray, sieve, carbon steel
100 to 400 ft2 100 to 400 ft2
5 to 10 hp 20 to 200 hp
2 to 100 gpm 100 to 1000 gal
3- to 10-ft diameter 3- to 10-ft diameter
0.58 0.55 0.60 0.44 0.65 0.85 0.69 0.99 0.67 0.70 0.34 0.56 0.60 0.50 0.68 1.20 0.86
Source: Guthrie, K.M., "Data and Techniques for Preliminary Capital Cost Estimating," Chemical Engineering, New York: Chemical Engineering, 1969.
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7.3 Design 7.3.1
Process Design
The symbology used in this reference is intended to be used for the PE Chemical exam. It does not necessarily correspond to a particular standard.
7.3.1.1 Piping and Instrumentation Diagram (P&ID) Equipment Tag Nomenclature Mechanical Function Codes Code
Equipment or Function
AG AX BL BX CL CM CR CV DR EX FA FI FL FX GN HV HX
Agitator Packaged unit Blower Boiler Column Compressor Crane and winch Conveyor Dryer Expander Fan Filter Flare Fired furnace, heater Generator HVAC Unfired heat transfer equipment, e.g., heat exchanger, condenser, cooler, reboiler Mixer, stirrer, mixing nozzle, inductor, ejector Pump Reactor Turbine Tank Thermal oxidizer, incinerator Vessel, pig receiver/launcher Material handling equipment, lift
MI PM RX TB TK TX VS XX
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Chapter 7: Plant Design and Operation 7.3.1.2 P&ID Equipment Symbols VESSELS
FILTER
CARTRIDGE TYPE FILTER
VERTICAL 1 AND 2 DIAMETERS
DRIVERS
HORIZONTAL
LIQUID EXPANDER HYDRAULIC TURBINE
HORIZONTAL WITH BOOT
GAS EXPANDER/STEAM TURBINE GAS TURBINE G
GEAR BOX
D
DIESEL ENGINE
M
MOTOR
G
GENERATOR
FLAT-TOP VESSEL
VESSEL WITH HEATING OR COOLING JACKET FIRED HEATER
FURNACE VESSEL WITH BODY FLANGE
OTHERS EJECTOR/EDUCTOR NON-PRESSURE VESSEL
MIXER/AGITATOR
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Chapter 7: Plant Design and Operation
HEAT EXCHANGERS
HEAT EXCHANGERS
PLATE-FRAME-TYPE HEAT EXCHANGER
VERTICAL HEAT EXCHANGER FIXED TUBESHEET BRAZED PLATE-FIN HEAT EXCHANGER
VERTICAL HEAT EXCHANGER FLOATING HEAD AIR-COOLED HEAT EXCHANGER
OUTER COIL FOR EQUIPMENT
FLOATING HEAD U-TUBE
HEAT RECOVERY COILS VERTICAL TUBES
FIXED TUBESHEET FLOATING HEAD AND COVER PLATE
HEAT RECOVERY COILS HORIZONTAL TUBES
KETTLE-TYPE U-TUBE KETTLE-TYPE FIXED TUBESHEET KETTLE-TYPE FLOATING HEAD
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Chapter 7: Plant Design and Operation
PUMP AND COMPRESSORS
TANKS
CENTRIFUGAL COMPRESSOR
DOME ROOF TANK
AXIAL COMPRESSOR FLOATING ROOF TANK
RECIPROCATING COMPRESSOR
SCREW COMPRESSOR CONE ROOF TANK BLOWER/FAN
SPHERICAL TANK
ROTARY (GEAR SCREW) PUMP
PROPORTIONING (METERING) PUMP
CONICAL BOTTOM TANK
DIAPHRAGM PUMP
LINE SYMBOLS
VACUUM PUMP M
PRIMARY LINE SECONDARY LINE
SUMP PUMP
UNDERGROUND LINE
M
TRACED LINE
VERTICAL PUMP
JACKETED LINE FLEXIBLE HOSE (FLANGED)
CENTRIFUGAL PUMP
FLEXIBLE HOSE (COUPLING)
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VALVE AND CONTROL SYMBOLS
VALVE AND CONTROL SYMBOLS GATE VALVE
PRESSURE SAFETY RELIEF VALVE
GLOBE VALVE BALL VALVE PLUG VALVE
VACUUM SAFETY RELIEF VALVE
BUTTERFLY VALVE NEEDLE VALVE DIAPHRAGM VALVE
P
PINCH VALVE CHECK VALVE
PILOT-ACTUATED RELIEF OR SAFETY VALVE ACTUATOR SPRING- OR WEIGHT-ACTUATED RELIEF OR SAFETY VALVE ACTUATOR
3-WAY VALVE 4-WAY VALVE
RUPTURE DISC, PRESSURE RELIEF
DAMPER
RUPTURE DISC, VACUUM RELIEF
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GENERAL PIPING SYMBOLS
GENERAL PIPING SYMBOLS
FLANGE
SIGHT GLASS DT
BLIND FLANGE
DRAIN TRAP
WELDED END CAP SCREWED CAP
FLAME ARRESTOR
SPECTACLE BLIND (OPEN)
SPARK ARRESTOR SPECTACLE BLIND (CLOSED)
REDUCER
HOSE CONNECTION QUICK COUPLING
CONSERVATION VENT
COOLING TOWERS VENT (WITH HOOD)
INDUCED-DRAFT COOLING TOWER
OPEN VENT WITH GOOSENECK
FORCED-DRAFT COOLING TOWER
SIPHON DRAIN
Y TYPE STRAINER
HYPERBOLIC COOLING TOWER
BASKET-TYPE STRAINER
IN-LINE STATIC MIXER RO
NATURAL-DRAFT COOLING TOWER
RESTRICTION ORIFICE
RUPTURE DISK
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Chapter 7: Plant Design and Operation 7.3.1.3 Instrumentation Tag Identifiers and Symbols The following identifiers are used in P&ID instrument tags.
Identification Letters First 4 Letters Measured or Initiating Variable
Succeeding 3 Letters Modifier
A Analysis B
Output Function
Modifier
Alarm
Burner, combustion
C D
Control Differential
E
Voltage
F G H I J
Flow rate
K
Time, time schedule
L M O P Q R S T U
Level
Sensor (primary element) Ratio (fraction) Glass, viewing device
Hand Current (electrical) Power
High Indicate Scan Time rate of change
Control station Light
Low Middle, intermediate
Momentary
Pressure, vacuum Quantity Radiation Speed, frequency Temperature Multivariable Vibration, mechanical V analysis W Weight, force X Unclassified Event, state, or Y presence Z
Readout or Passive Function
Position, dimension
Orifice, restriction Point (test) connection Integrate, totalize Record Safety Multifunction
X axis
Well Unclassified
Y axis Z axis
Switch Transmit Multifunction Valve, damper, louver Unclassified Relay, compute, convert Driver, actuator, unclassified final control element
Multifunction
Unclassified
Source: Taken from ANSI/ISA -5.1-2009 - Copyright © 2009, ISA - all rights reserved. Used with permission of ISA.
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Chapter 7: Plant Design and Operation General Instrument or Function Symbols PRIMARY LOCATION **NORMALLY ACCESSIBLE TO OPERATOR DISCRETE INSTRUMENTS
AUXILIARY LOCATION **NORMALLY ACCESSIBLE TO OPERATOR
FIELD MOUNTED
*IP1
SHARED DISPLAY, SHARED CONTROL
COMPUTER FUNCTION
PROGRAMMABLE LOGIC CONTROL
* Abbreviations of the user's choice—such as IP1 (Instrument Panel #1), IC2 (Instrument Console #2), CC3 (Computer Console #3), etc.—may be used when it is necessary to specify instrument or function location. ** Normally inaccessible or behind-the-panel devices or functions may be depicted by using the same symbol but with dashed horizontal lines, as in:
Additional General Instrument or Function Symbols
* PILOT LIGHT
DIAPHRAGM SEAL
INTERLOCK LOGIC
* This diamond is approximately half the size of the larger symbols.
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Chapter 7: Plant Design and Operation Actuator Symbols
M
WITH OR WITHOUT POSITIONER OR OTHER PILOT
PREFERRED FOR DIAGRAM ASSEMBLED WITH PILOT*, ASSEMBLY IS ACTUATED BY ONE INPUT (SHOWN TYPICALLY WITH ELECTRIC INPUT)
DIAPHRAGM PRESSURE–BALANCED
ROTARY MOTOR (SHOWN TYPICALLY WITH ELECTRIC SIGNAL, MAY BE HYDRAULIC OR PNEUMATIC)
DIAPHRAGM SPRING –OPPOSED OR UNSPECIFIED ACTUATOR
SPRING-OPPOSED SINGLE-ACTING
PREFERRED FOR ANY CYLINDER THAT IS ASSEMBLED WITH A PILOT* SO THAT ASSEMBLY IS ACTUATED BY ONE CONTROLLED INPUT
DOUBLE-ACTING
CYLINDER WITHOUT POSITION OR OR OTHER PILOT
S
I
S
SOLENOID
PREFERRED ALTERNATIVE. A BUBBLE WITH INSTRUMENT TAGGING, E.G. TY-I MAY BE USED INSTEAD OF THE I INTERLOCK SYMBOL
SINGLE-ACTING CYLINDER (IMPLIED I/P)
CYLINDER WITH POSITIONER AND OVERRIDING PILOT VALVE
FOR PRESSURE RELIEF OR SAFETY VALVES ONLY. SPRING WEIGHT DENOTES A SPRING WEIGHT OR INTEGRAL PILOT
HAND ACTUATOR OR HANDWHEEL
* Pilot may be positioned solenoid valve signal converter, etc.
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Chapter 7: Plant Design and Operation Symbols for Self-Actuated Regulators, Valves, and Other Devices FCV XX
AUTOMATIC REGULATOR WITH INTEGRAL FLOW INDICATION
AUTOMATIC REGULATOR WITHOUT INDICATION
FLOW
FICV XX
FG XX
RO XX
FLOW SIGHT GLASS, PLAIN OR WITH PADDLE WHEEL FLAPPER, ETC.
RESTRICTION ORIFICE (ORIFICE PLATE, CAPILLARY TUBE OR MULTI-STAGE TYPE. ETC.) IN PROCESS LINE
HAND
HV XX
HAND CONTROL VALVE IN PROCESS LINE
LEVEL
TANK
LEVEL REGULATOR WITH MECHANICAL LINKAGE
PRESSURE
PCV XX
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LCV XX
PRESSURE-REDUCING REGULATOR, SELFCONTAINED, WITH HANDWHEEL ADJUSTABLE SETPOINT
PCV XX
BACKPRESSURE REGULATOR SELF-CONTAINED
407
PSV XX
PRESSURE RELIEF OR SAFETY VALVE, GENERAL SYMBOL
PSV XX
VACUUM RELIEF VALVE, GENERAL SYMBOL
PRESSURE (CONTD.)
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PSE XX
PSE XX
RUPTURE DISC OR SAFETY HEAD FOR PRESSURE RELIEF
RUPTURE DISC OR SAFETY HEAD FOR VACUUM RELIEF
408
P
PILOT-OPERATED RELIEF VALVE
Chapter 7: Plant Design and Operation
7.3.2
Process Equipment Design Installation Practices for Equipment Relief System
Recommendations
For rupture disc in corrosive service, or for highly toxic materials where spring-loaded reliefs may weep.
VESSEL
P
For two rupture discs in extremely corrosive service. The first may need to be replaced periodically.
For rupture disc and spring-loaded relief. Normal relief may go through spring-loaded device and rupture disc is backup for larger reliefs.
For two reliefs in series. The rupture disc protects against toxicity or corrosion. The spring-loaded relief closes and minimizes losses.
P
For two rupture discs with 3-way valve that keeps one valve always directly connected to vessel. This design is good for polymerization reactors that require periodic cleaning.
C
A
B VESSEL
PIPE
A. Pressure drop not more than 3% of set pressure. B. Long radius elbow. C. If distance is greater than 10 feet, support weight and reaction forces below the long radius elbow. For orifice area of a single safety relief in vapor service; should not exceed 2% of the cross-sectional area of the protected line. May require multiple valves with staggered settings.
A. Process lines; should not be connected to safety-valve inlet piping. A
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Chapter 7: Plant Design and Operation Installation Practices for Equipment Relief (cont'd) System
Recommendations
A. Turbulence-causing device. B. Dimension shown below: A
B
Device Causing the Turbulence
Minimum Number of Straight-Pipe Diameters
Regulator or valve 2 ells or bends not in same plane 2 ells or bends in same plane 1 ell or bend Pulsation damper
25 20 15 10 10
Source: Jennet, Eric, "Components of Pressure-Relieving Systems," Equipment Relief Installation Practices: Chemical Engineering Magazine, 1963, pp. 151–158.
7.3.3
Siting Considerations
7.3.3.1 Fixed Facilities Building Siting Evaluation: The procedures used to evaluate the hazards and establish the design criteria for new buildings and the suitability of existing buildings at their specific locations. Facility: The physical location where the management system activity is performed. In early life-cycle stages, a facility may be the company's central research laboratory or the engineering offices of a technology vendor. In later stages, the facility may be a typical chemical plant, storage terminal, distribution center, or corporate office. Site is used synonymously with facility when describing to Risk Management Plan (RMP) audit criteria. Fixed Facility: A portion of or a complete plant, unit, site, complex, or any combination thereof that is generally not moveable. In contrast, mobile facilities, such as ships (e.g., transport vessels, floating platform storage and offloading vessels, drilling platforms), trucks, and trains, are designed to be moveable. Siting: The process of locating a complex, site, plant, or unit.
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Chapter 7: Plant Design and Operation Guiding Principles for Location of Fixed Facility API Recommended Practice 752 is based on the following guiding principles: a. Locate personnel away from process areas consistent with safe and effective operations. b. Minimize the use of buildings intended for occupancy in close proximity to process areas. c. Manage the occupancy of buildings in close proximity to process areas. d. Design, construct, install, modify, and maintain buildings intended for occupancy to protect occupants against explosion, fire, and toxic material releases. e. Manage the use of buildings intended for occupancy as an integral part of the design, construction, mainte nance, and operation of a facility. Source: API Recommended Practice 752: Management of Hazards Associated with Location of Process Plant Buildings, 3rd ed.: American Petroleum Institute, 2009, p. 1. Reproduced courtesy of the American Petroleum Institute.
Overall Building Siting Evaluation Flow Chart START
IS BUILDING WITHIN THE SCOPE OF API752? NO
YES
IS BUILDING INCLUDED IN THE SITING VALUATION? NO
YES
IS BUILDING IMPACTED BY EXPLOSION, FIRE OR TOXICS?
YES
CHOOSE BUILDING SITING EVALUATION APPROACH(ES) AND CRITERIA
NO IS IT A NEW BUILDING OR MODIFICATION TO EXISTING BUILDING?
DESIGN BUILDING (INCLUDING EXTENSIONS AND MODIFICATIONS TO EXISTING BUILDINGS) TO MEET BUILDING SITING EVALUATION
YES
NO
CARRY OUT BUILDING SITING EVALUATION
ARE BUILDING SITING EVALUATION CRITERIA MET?
YES
NO INCLUDE BUILDING IN MITIGATION PLAN. DEVELOP AND IMPLEMENT MITIGATION PLAN.
IMPLEMENT MANAGEMENT OF BUILDING OCCUPANCY AND/OR MANAGEMENT OF CHANGE
STOP
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Chapter 7: Plant Design and Operation Building Siting Evaluation for Explosions START
COULD BUILDING BE IMPACTED BY EXPLOSION?
NO
YES
IS IT A NEW BUILDING OR MODIFICATION TO EXISTING BUILDING?
DETERMINE BLAST LOADS ON BUILDING
YES
DESIGN BUILDING (INCLUDING EXTENSIONS AND MODIFICATIONS TO EXISTING BUILDINGS) TO MEET BUILDING SITING EVALUATION FOR EXPLOSION
NO
DETERMINE BLAST LOADS ON BUILDING
COMPLETE A BUILDING DAMAGE LEVEL ASSESSMENT OR A DETAILED STRUCTURAL ANALYSIS
CARRY OUT MORE DETAILED ANALYSIS?
YES
NO
DOES BUILDING MEET BUILDING SITING CRITERIA FOR EXPLOSION?
YES
NO
INCLUDE BUILDING AND MITIGATION PLAN
BUILDING SITING EVALUATION FOR EXPLOSION NOT REQUIRED.
IMPLEMENT MANAGEMENT OF THE BUILDING OCCUPANCY AND/OR MANAGEMENT OF CHANGE
STOP
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Chapter 7: Plant Design and Operation Building Siting Evaluation for Fire START
COULD BUILDING BE IMPACTED BY FIRE?
YES
IS A SPACING TABLE APPROACH USED?
NO
YES
ARE SEPARATION DISTANCES MET?
YES
NO
NO
DETERMINE FIRE EFFECTS AT BUILDING AND SELECT THE FIRE PROTECTION CONCEPT
IS IT A NEW BUILDING OR MODIFICATIONS TO EXISTING BUILDING?
YES
DESIGN BUILDING TO MEET BUILDING SITING EVALUATION CRITERIA.
NO
DOES BUILDING MEET BUILDING SITING EVALUATION CRITERIA?
YES
NO
BUILDING SITING EVALUATION FOR FIRE NOT REQUIRED.
INCLUDE BUILDING IN MITIGATION PLAN AND IMPLEMENT MITIGATION PLAN
CARRY OUT MORE DETAILED ANALYSIS. IF NEEDED, INCLUDE BUILDING IN MITIGATION PLAN AND IMPLEMENT MITIGATION PLAN
INCLUDE BUILDING AND MITIGATION PLAN AN AND IMPLEMENT MITIGATION PLAN
CARRY OUT MORE DETAILED ANALYSIS IF NEEDED, INCLUDE BUILDING IN MITIGATION PLAN AND IMPLEMENT MITIGATION PLAN
IMPLEMENT MANAGEMENT OF BUILDING OCCUPANCY AND/OR MANAGEMENT OF CHANGE
STOP
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Chapter 7: Plant Design and Operation Building Siting Evaluation for Toxic Material Release START
IS THERE POTENTIAL FOR A TOXIC RELEASE?
NO
YES
IS IT ASSUMED THAT BUILDING IS IMPACTED?
YES
NO
PERFORM TOXIC GAS DISPERSING MODELING.
ARE BUILDING SITING EVALUATION CRITERIA EXCEEDED?
SELECT PROTECTION CONCEPT FOR TOXIC MATERIAL.
YES
NO
IS IT A NEW BUILDING OR MODIFICATION TO EXISTING BUILDING?
YES
DESIGN AND BUILDING TO MEET BUILDING SITING THE EVALUATION CRITERIA.
NO
BUILDING SITING EVALUATION FOR TOXIC NOT REQUIRED
INCLUDE BUILDING A MITIGATION PLAN AND IMPLEMENT MITIGATION PLAN
CARRY OUT MORE DETAILED ANALYSIS . IF NEEDED, INCLUDE BUILDING IN MITIGATION PLAN AND IMPLEMENT MITIGATION PLAN.
IMPLEMENT MANAGEMENT OF BUILDING OCCUPANCY AND MANAGEMENT OF CHANGE.
STOP
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Chapter 7: Plant Design and Operation 7.3.3.2 Portable Buildings Portable Building: Any rigid structure that can be moved easily to another location within the facility, regardless of the length of time it is kept at the site. Examples of portable buildings include wood framed trailers (single- and double-wide), container boxes, semi-trailers, and portable structures designed to be blast resistant. Lightweight fabric enclosures, such as tents, are excluded. Guiding Principles for Siting Portable Buildings API Recommended Practice 753 is based on the following guiding principles: a. Locate personnel away from covered process areas consistent with safe and effective operations. b. Minimize the use of occupied portable buildings in close proximity to covered process areas. c. Manage the occupancy of portable buildings, especially during periods of increased risk including start-up or planned shut-down operations. d. Design, construct, install, and maintain occupied portable buildings to protect occupants against potential hazards. e. Manage the use of portable buildings as an integral part of the design, construction, maintenance, and opera tion of a facility. Source: API Recommended Practice 751: Management of Hazards Associated with Location of Process Plant Portable Buildings: American Petroleum Institute, 2007. Reproduced courtesy of the American Petroleum Institute.
7.3.3.3 Typical Clearances to Railroads Typical Clearances to Railroads
21'-6"
NO CONSTRUCTION ACTIVITIES OR OTHER OBSTRUCTION SHALL BE PLACED IN WITHIN THESE LIMITS
CL TRACK TOP OF RAIL
UPRR* BNSF**
12'-0" 15'-0"
*Union Pacific Railroad **Burlington Northern Santa Fe Railway
MINIMUM CONSTRUCTION CLEARANCE ENVELOPE (NORMAL TO RAILROAD)
Source: Copyright ©2014. California Department of Transportation. All Rights Reserved. Standard Drawing xs11-010 is solely intended for use to inform and guide the officers, employees, and contracted workers of the Department about minimum railroad requirements for overhead structures concerning projects of the California Department of Transportation. It is neither intended as, nor does it establish, a legal standard for these functions. The drawing is not a substitute for engineering knowledge, experience, or judgment. The example given herein is subject to amendment as conditions and experience may warrant.
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Inert gas
Flammable liquid, combination (1A, 1B, 1C) Flammable solid
Flammable liquidc
Flammable gas
Explosives
Consumer fireworks Cryogenics, flammable Cryogenics, inert Cryogenics, oxidizing
Combustible fiber
H-2 or H-3 H-3 N/A N/A
N/A
N/A Gaseous Liquefied
H-2 or H-3
H-2
H-1 H-1 H-1 or H-2 H-3 H-3 H-1 H-1
Division 1.1 Division 1.2 Division 1.3 Division 1.4 Division 1.4G Division 1.5 Division 1.6 Gaseous Liquefied 1A 1B and 1C
N/A
N/A H-3
H-2
N/A
N/A
H-3
H-3
H-2 H-2 or H-3 H-2 or H-3 N/A
1.4G
N/A II IIIA IIIB Loose Baledo
Combustible dust
Combustible liquidc,i
Class
Material
Group When the Maximum Allowable Quantity Is Exceeded
125d,e N/A N/A
N/A
N/A
N/A
1e,g 1e,g 5e,g 50e,g 125d,e,l 1e,g 1d,e,g
N/A
N/A
N/A
125d,e,l
(100) (1000)
N/A
q
Solid Pounds (Cubic Feet)
N/A N/A N/A
120d,e,h
(1)e,g (1)e,g (5)e,g (50)e,g N/A (1)e,g N/A N/A (150)d,e 30d,e 120d,e
45d
N/A
45d
N/A
N/A
N/A 120d,e 330d,e 13,200e,f
Liquid Gallons (Pounds)
Storageb
N/A NL NL
N/A
N/A
N/A N/A N/A N/A N/A N/A N/A 1000d,e N/A
N/A
NL
N/A
N/A
N/A
N/A
N/A
Gas (Cubic Feet at NTP)
125d N/A N/A
N/A
N/A
N/A
0.25g 0.25g 1g 50g N/A 0.25g N/A
N/A
N/A
N/A
N/A
(100) (1000)
N/A
q
N/A N/A N/A
120d,h
(0.25)g (0.25)g (1)g (50)g N/A (0.25)g N/A N/A (150)d,e 30d,e 120d,e
45d
N/A
45d
N/A
N/A
N/A 120d 330d 13,200f
N/A NL NL
N/A
N/A
N/A N/A N/A N/A N/A N/A N/A 1000d,e N/A
N/A
NL
N/A
N/A
N/A
N/A
N/A
Used in Closed Systemsb Solid Gas Liquid Pounds (Cubic Gallons (Cubic Feet at (Pounds) Feet) NTP)
25d N/A N/A
N/A
N/A
N/A
0.25g 0.25g 1g N/A N/A 0.25g N/A
N/A
N/A
N/A
N/A
(20) (200)
N/A
q
N/A N/A N/A
30d,h
10d 30d
N/A
(0.25)g (0.25)g (1)g N/A N/A (0.25)g N/A
10d
N/A
10d
N/A
N/A
N/A 30d 80d 3300f
Used in Open Systemsb Solid Liquid Pounds Gallons (Cubic (Pounds) Feet)
Maximum Allowable Quantity per Control Area of Hazardous Materials Posing a Physical Hazarda,j,m,n,p
7.3.3.4 Building Occupancy
Chapter 7: Plant Design and Operation
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H-1 H-1 or H-2 H-3 N/A H-2 H-3 N/A
4 3 2 1 3 2 1
1e,g 5d,e 50d,e NL 5d.e 50d.e NL
4e,g
1e,g 5d,e 50d,e 125d,e NL NL 1e,g 10d,e 250d,e 4000e.f N/A N/A
Solid Pounds (Cubic Feet)
(1)e,g (5)d,e (50)d,e NL (5)d.e (50)d.e NL
(4)e,g
(1)e,g (5)d,e (50)d,e (125)d,e NL NL (1)e,g (10)d,e (250)d,e (4000)e.f N/A (150)d,e
Liquid Gallons (Pounds)
10g 50d,e 250d,e NL N/A N/A N/A
50e,g
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 1500d,e N/A
Gas (Cubic Feet at NTP)
0.25g 1d 50d NL 5d 50d NL
1g
0.25g 1d 50d 125d NL NL 0.25g 2d 250d 4000f N/A N/A
Solid Pounds (Cubic Feet)
(0.25)g (1)d (50)d NL (5)d (50)d NL
(1)g
(0.25)g (1)d (50)d (125)d NL NL (0.25)g (2)d (250)d (4000)f N/A (150)d,e
Liquid Gallons (Pounds)
2e,g 10d,e 250d,e NL N/A N/A N/A
10g
N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 1500d,e N/A
Gas (Cubic Feet at NTP)
Used in Closed Systemsb
For SI: 1 cubic foot = 0.028 m3, 1 pound = 0.454 kg, 1 gallon = 3.7785 L NL = not limited; N/A = not applicable; UD = unclassified detonable
H-2
H-3
H-1 H-2 H-3 H-3 N/A N/A H-1 H-2 or H-3 H-3 N/A
N/A
UD I II III IV V 4 3k 2 1 Gaseous Liquefied
Class
Storageb
0.25g 1d 10d NL 1d 10d NL
0
0.25g 1d 10d 25d NL NL 0.25g 2d 50d 1000f N/A N/A
Solid Pounds (Cubic Feet)
(0.25)g (1)d (10)d NL (1)d (10)d NL
0
(0.25)g (1)d (10)d (25)d NL NL (0.25)g (2)d (50)d (1000)f N/A N/A
Liquid Gallons (Pounds)
Used in Open Systemsb
Source: 2012 International Building Code, Country Club Hills, Illinois: International Code Council. All footnote references are to the IBC.
Water-reactive material
Unstable (reactive) material
Pyrophoric material
Oxidizing gas
Oxidizer
Organic peroxide
Material
Group When the Maximum Allowable Quantity Is Exceeded
Maximum Allowable Quantity per Control Area of Hazardous Materials Posing a Physical Hazarda,j,m,n,p (cont'd)
Chapter 7: Plant Design and Operation
Chapter 7: Plant Design and Operation a. For use of control areas, see Section 414.2. b. The aggregate quantity in use and storage shall not exceed the quantity listed for storage. c. The quantities of alcoholic beverages in retail and wholesale sales occupancies shall not be limited provided the liquids are packaged in individual containers not exceeding 1.3 gallons. In retail and wholesale sales occupancies, the quantities of medicines, foodstuffs, consumer or industrial products, and cosmetics containing not more than 50 percent by volume of water-miscible liquids, with the remainder of the solutions not being flammable, shall not be limited, provided that such materials are packaged in individual containers not exceeding 1.3 gallons. d. Maximum allowable quantities shall be increased 100% in buildings equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1. Where Note e also applies, the increase for both notes shall be applied accumulatively. e. Maximum allowable quantities shall be increased 100% when stored in approved storage cabinets, day boxes, gas cabinets, or exhausted enclosures or in listed safety cans in accordance with Section 5003.9.10 of the Inter national Fire Code. Where Note d also applies, the increase for both notes shall be applied accumulatively. f. The permitted quantities shall not be limited in a building equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1. g. Permitted only in buildings equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1. h. Containing not more than the maximum allowable quantity per control area of Class IA, IB, or IC flammable liquids. i. The maximum allowable quantity shall not apply to fuel oil storage complying with Section 603.3.2 of the International Fire Code. j. Quantities in parentheses indicate quantity units in parentheses at the head of each column. k. A maximum quantity of 200 pounds of solid or 20 gallons of liquid Class 3 oxidizers is allowed when such materials are necessary for maintenance purposes, operation, or sanitation of equipment. Storage containers and the manner of storage shall be approved. l. Net weight of the pyrotechnic composition of the fireworks. Where the net weight of the pyrotechnic composi tion of the fireworks is not known, 25% of the gross weight of the fireworks, including packaging, shall be used. m. For gallons of liquids, divide the amount in pounds by 10 in accordance with Section 5003.1.2 of the Interna tional Fire Code. n. For storage and display quantities in Group M and storage quantities in Group S occupancies complying with Section 414.2.5, see Tables 414.2.5(1) and 414.2.5(2). o. Densely packed baled cotton that complies with the packing requirements of ISO 8115 shall not be included in this material class. p. The following shall not be included in determining the maximum allowable quantities: 1. Liquid or gaseous fuel in fuel tanks on vehicles 2. Liquid or gaseous fuel in fuel tanks on motorized equipment operated in accordance with this code 3. Gaseous fuels in piping systems and fixed appliances regulated by the International Fuel Gas Code 4. Liquid fuels in piping systems and fixed appliances regulated by the International Mechanical Code q. Where manufactured, generated, or used in such a manner that the concentration and conditions create a fire or explosion hazard based on information prepared in accordance with Section 414.1.3.
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500
Highly toxic
Toxic
Gaseous 810f Liquefied (150)h Gaseous 20g Liquefied (4)g,h Gaseous 810f Liquefied (150)f,h 500
10
5000
(500)i
(10)i
500
Gas Solid Liquid Gallons (Cubic Feet at NTP)e Poundse (Pounds)e
Gaseous 810f Liquefied (150)h Gaseous 20g Liquefied (4)g,h Gaseous 810f Liquefied (150)f,h
Gas (Cubic Feet at NTP)e
For SI: 1 cubic foot = 0.028 m3, 1 pound = 0.454 kg, 1 gallon = 3.785 L
(500)h
(10)h
500
Liquid Gallons (Pounds)e,f
125
3
1000
Solid Poundse
(125)
(3)i
100
Liquid Gallons (Pounds)e
419
Source: 2012 International Building Code, Country Club Hills, Illinois: International Code Council. All footnote references are to the IBC.
a. For use of control areas, see Section 414.2. b. In retail and wholesale occupancies, the quantities of medicines, foodstuffs, consumer or industrial products, and cosmetics containing not more than 50% by volume of water-miscible liquids—with the remainder of the solutions not being flammable—shall not be limited, provided that such materials are packaged in individual containers not exceeding 1.3 gallons. c. For storage and display quantities in Group M and storage quantities in Group S, occupancies complying with Section 414.2.5, see Tables 414.2.5(1) and 414.2.5(2). d. The aggregate quantity in use and storage shall not exceed the quantity listed for storage. e. Maximum allowable quantities shall be increased 100% in buildings equipped throughout with an approved automatic sprinkler system in accordance with Section 903.3.1.1. Where Note f below also applies, the increase for both notes shall be applied accumulatively. f. Maximum allowable quantities shall be increased 100% when stored in approved storage cabinets, gas cabinets, or exhausted enclosures as specified in the International Fire Code. Where Note e above also applies, the increase for both notes shall be applied accumulatively. g. Allowed only when stored in approved exhausted gas cabinets or exhausted enclosures as specified in the International Fire Code. h. Quantities in parentheses indicate quantity units in parentheses at the head of each column. i. For gallons of liquids, divide the amount in pounds by 10 in accordance with Section 5003.1.2 of the International Fire Code.
5000
Solid Pounds (Cubic Feet)
Corrosive
Material
Maximum Allowable Quantity Per Control Area of Hazardous Material Posing a Health Hazarda,b,c,i Used in Closed Systemsd Used in Open Systemsd Liquefied (150)h Storaged
Chapter 7: Plant Design and Operation
Chapter 7: Plant Design and Operation International Building Code Area Classification Descriptions Occupancy Class
A
B
Description
Assembly Group A occupancy includes, among others, the use of a building or structure, or a portion thereof, for the gathering of persons for purposes such as civic, social or religious functions; recreation, food or drink consumption or awaiting transportation. Business Group B occupancy includes, among others, the use of a building or structure, or a portion thereof, for office, professional or service-type transactions, including storage of records and accounts. Business occupancies shall include, but not be limited to, the following: Airport traffic control towers Ambulatory care facilities Animal hospitals, kennels, and pounds Banks Barber and beauty shops Car wash Civic administration Clinic, outpatient Dry cleaning and laundries: pick-up and delivery stations and self-service Educational occupancies for students above the 12th grade Electronic data processing Laboratories: testing and research Motor vehicle showrooms Post offices Print shops Professional services (architects, attorneys, dentists, physicians, engineers, etc.) Radio and television stations Telephone exchanges Training and skill development not within a school or academic program
F
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Factory Industrial Group F occupancy includes, among others, the use of a building or structure, or a portion thereof, for assembling, disassembling, fabricating, finishing, manufacturing, packaging, repair, or processing operations that are not classified as a Group H hazardous or Group S storage occupancy.
420
Chapter 7: Plant Design and Operation International Building Code Area Classification Descriptions (cont'd) Occupancy Class
Description
F-1
Factory Industrial uses which are not classified as Factory Industrial F-2 Low Hazard. Examples include: Aircraft (manufacturing, not to include repair) Appliances Athletic equipment Automobiles and other motor vehicles Bakeries Beverages over 16-percent alcohol content Bicycles Boats Brooms or brushes Business machines Cameras and photo equipment Canvas or similar fabric Carpets and rugs (including cleaning) Clothing Construction and agricultural machinery Disinfectants Dry cleaning and dyeing Electric generation plants Electronics Engines (including rebuilding) Food processing and commercial kitchens not associated with restaurants, cafeterias and similar dining facilities Furniture Hemp products Jute products Laundries Leather products Machinery Metals Millwork (sash and door) Motion pictures and television filming (without spectators) Musical instruments Optical goods Paper mills or products Photographic film Plastic products Printing or publishing Recreational vehicles Refuse incineration Shoes Soaps and detergents Textiles Tobacco Trailers Wood: distillation Woodworking (cabinet) Upholstering
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Chapter 7: Plant Design and Operation International Building Code Area Classification Descriptions (cont'd) Occupancy Class
F-2
H
H-1
H-2
Description
Factory industrial uses that involve the fabrication or manufacturing of noncombustible materials which during finishing, packing or processing do not involve a significant fire hazard. Examples include: Beverages up to and including 16-percent alcohol content Brick and masonry Ceramic products Foundries Glass products Gypsum Ice Metal products (fabrication and assembly) High-Hazard Group H occupancy includes, among others, the use of a building or structure, or a portion thereof, that involves the manufacturing, processing, generation or storage of materials that constitute a physical or health hazard in quantities in excess of those allowed in control areas complying with Section 414, based on the maximum allowable quantity limits for control areas set forth in Tables 307.1(1) and 307.1(2). Hazardous occupancies are classified in Groups H-1, H-2, H-3, H-4 and H-5 and shall be in accordance with this section, with the requirements of Section 415 and the International Fire Code. Hazardous materials stored, or used on top of roofs or canopies shall be classified as outdoor storage or use and shall comply with the International Fire Code. Buildings and structures containing materials that pose a detonation hazard. Examples include: Detonable pyrophoric materials, explosives, organic peroxides (unclassified detonable), Class 4 oxidizers, Class 3 detonable and Class 4 unstable (reactive) materials. Buildings and structures containing materials that pose a deflagration hazard or a hazard from accelerated burning. Examples include: Class I, II, or IIIA flammable or combustible liquids which are used or stored in normally open containers or systems, or in closed containers or systems pressurized at more than 15 psi (103.4 kPa) gage Combustible dusts where manufactured, generated or used in such a manner that the concentration and conditions create a fire or explosion hazard based on information prepared in accordance with Section 414.1.3 Cryogenic fluids, flammable Flammable gases Organic peroxides, Class I Oxidizers, Class 3, that are used or stored in normally open containers or systems or in closed containers or systems pressurized at more than 15 psi (103.4 kPa) gage Pyrophoric liquids, solids, and gases, nondetonable Unstable (reactive) materials, Class 3, nondetonable Water-reactive materials, Class 3
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Chapter 7: Plant Design and Operation International Building Code Area Classification Descriptions (cont'd) Occupancy Class
H-3
H-4
H-5
I
M
R
S
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Description
Buildings and structures containing materials that readily support combustion or that pose a physical hazard. Examples include: Class I, II, or IIIA flammable or combustible liquids that are used or stored in normally closed containers or systems pressurized at 15 pounds psi (103.4 kPa) gauge or less Combustible fibers, other than densely packed baled cotton Consumer fireworks, 1.4G (Class C, Common) Cryogenic fluids, oxidizing Flammable solids Organic peroxides, Class II and III Oxidizers, Class 2 Oxidizers, Class 3, that are used or stored in normally closed containers or systems pressurized at 15 pounds psi (103.4 kPa) gage or less Oxidizing gases Unstable (reactive) materials, Class 2 Water-reactive materials, Class 2 Buildings and structures that contain materials that are health hazards. Examples include: Corrosives Highly toxic materials Toxic materials Semiconductor fabrication facilities and comparable research and development areas in which hazardous production materials (HPM) are used and the aggregate quantity of materials is in excess of those listed in Tables 307.1(1) and 307.1(2). Institutional Group I occupancy includes, among others, the use of a building or structure, or a portion thereof, in which care or supervision is provided to persons who are or are not capable of self-preservation without physical assistance or in which persons are detained for penal or correctional purposes or in which the liberty of the occupants is restricted. Mercantile Group M occupancy includes, among others, the use of a building or structure, or a portion thereof, for the display and sale of merchandise and involves stocks of goods, wares, or merchandise incidental to such purposes and accessible to the public. Mercantile occupancy shall include, but not be limited to, the following: Department stores Drug stores Markets Motor fuel-dispensing facilities Retail or wholesale stores Sales rooms Residential Group R includes among others, the use of a building or structure, or a portion thereof, for sleeping purposes when not classified as an Institution Group I or when not regulated by the International Residential Code. Storage Group S occupancy includes among others, the use of a building or structure, or a portion thereof, for storage that is not classified as a hazardous occupancy.
423
Chapter 7: Plant Design and Operation International Building Code Area Classification Descriptions (cont'd) Occupancy Class
S-1
Description
Moderate hazard Storage Group S-1. Buildings occupied for storage uses that are not classifies as Group S-2, including, but not limited to, storage of the following: Aerosols, levels 2 and 3 Aircraft hangars (storage and repair) Bags: cloth, burlap and paper Bamboos and rattan Baskets Belting: canvas and leather Books and paper in rolls or packs Boots and shoes Buttons, including cloth covered, pearl or bone Cardboard and cardboard boxes Clothing, woolen wearing apparel Cordage Dry boats (indoor) Furniture Furs Glues, mucilage, pastes and size Grains Horns and combs, other than celluloid Leather Linoleum Lumber Motor vehicle repair garages complying with the maximum allowable quantities of hazardous materials listed in Table 307.1(1) (see Section 406.8) Photo engravings Resilient flooring Silks Soaps Sugar Tires, bulk storage of Tobacco, cigars, cigarettes and snuff Upholstery and mattresses Wax candles
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Chapter 7: Plant Design and Operation International Building Code Area Classification Descriptions (cont'd) Occupancy Class
S-2
Description
Low-hazard storage, Group S-2. Includes among others, buildings used for the storage of noncombustible materials such as products on wood pallets or in paper cartons with or without single thickness divisions; or in paper wrappings. Such products are permitted to have a negligible amount of plastic trim such as knobs, handles or film wrapping. Group S-2 storage shall include, but not be limited to, storage of the following: Asbestos Beverages up to and including 16-percent alcohol in metal, glass or ceramic containers Cement in bags Chalk and crayons Dairy products in nonwaxed coated paper containers Dry cell batteries Electrical coils Electrical motors Empty cans Food products Foods in noncombustible containers Fresh fruits and vegetables in nonplastic trays or containers Frozen foods Glass Glass bottles, empty or filled with noncombustible liquids Gypsum board Inert pigments Ivory Meats Metal cabinets Metal desks with plastic tops and trim Metal parts Metals Mirrors Oil-filled and other types of distribution transformers Parking garages, open or enclosed Porcelain and pottery Stoves Talc and soapstones Washers and dryers
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Chapter 7: Plant Design and Operation International Building Code Area Classification Descriptions (cont'd) Occupancy Class
U
Description
General. Buildings and structures of an accessory character and miscellaneous structures not classified in any specific occupancy shall be constructed, equipped and maintained to conform to the requirements of this code commensurate with the fire and life hazard incidental to their occupancy. Group U shall include, but not be limited to, the following: Agricultural buildings Aircraft hangars, accessory to a one- or two-family residence (see Section 412.5) Barns Carports Fences more than 6 feet (1829 mm) in height Grain silos, accessory to a residential occupancy Greenhouses Livestock shelters Private garages Retaining wall Sheds Stables Tanks Towers Source: 2012 International Building Code, Country Club Hills, Illinois: International Code Council.
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Chapter 7: Plant Design and Operation 7.3.3.5 Area Separation Requirements Required Separation of Occupancies (Hours) Occupancy
A, E I-1, I-3, I-4 I-2 R F-2, S-2b, U B, F-1, M, S-1 H-1 H-2 H-3, H-4 H-5
I-1, I-3, A, E I-4 S NS S NS
N — — — —
I-2 S
NS
R S
NS
N 1 2 2 NP 1 2 — N N 2 NP 1 NP — — — N N 2 NP — — — — — N N — — — — — — —
F-2, S-2b, U S NS
B, F-1, M, S-1 S NS
N 1 2 1 N
1 2 NP 2 N
1 1 2 1 1
H-1 S
NS
S
NS
S
NS
2 2 NP 2 2
NP NP NP NP NP
NP NP NP NP NP
3 3 3 3 3
4 NP NP NP 4
2 2 2 2 2
3 NP NP NP 3
2 2 2 2 2
NP NP NP NP NP
2
3
1
2
1
NP
—
—
—
N
N
NP NP
— — — —
— — — —
— — — —
— — — —
— — — —
— — — —
— — — —
N — — —
— — — —
— — — —
— — — —
H-5
NS
— —
— — — —
H-3, H-4
S
— — — — — — — — —
H-2
NP NP NP NP NP NP NP — N NP 1 NP 1 NP — — — 1d NP 1 NP — — — — — N NP
S = Buildings equipped throughout with an automatic sprinkler system installed in accordance with Section 903.3.1.1 NS = Buildings not equipped throughout with an automatic sprinkler system installed in accordance with Section 903.3.1.1 N = No separation requirement NP = Not permitted a. See Section 420. b. The required separation from areas used only for private or pleasure vehicles shall be reduced by 1 hour but to not less than 1 hour. c. See Section 406.3.4. d. Separation is not required between occupancies of the same classification. Source: 2012 International Building Code, Country Club Hills, Illinois: International Code Council. All footnote references are to the IBC.
7.3.3.6 Wind Direction Prevailing winds should be considered in both plant siting and layout: a. For siting, it is undesirable to locate a plant where prevailing winds would carry any fugitive emissions into nearby residential areas. b. In laying out a plant, safety considerations dictate that process units be located such that: 1. Prevailing winds would not carry potentially flammable releases to an area of the plant where there could be a source of ignition. 2. Prevailing winds would not carry potentially hazardous or toxic releases to an area of the plant where workers are in enclosed areas, e.g., offices, control rooms, or enclosed process buildings.
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Chapter 7: Plant Design and Operation
7.3.4
Instrumentation and Process Control
7.3.4.1 First-Order Control System Models The transfer function model for a first-order system is Y (s ) = K R ( s) x s + 1 where K = steady-state gain t = time constant The step response of a first-order system to a step input of magnitude M is y (t) = y0 e
−t/x
+ KM (1 − e −t/x)
In the chemical process industry, y0 is typically taken to be zero, and y(t) is referred to as a deviation variable. For systems with time delay (dead time or transport lag) q, the transfer function is Y (s) Ke − is = R ( s) x s + 1 The step response for t ≥ q to a step of magnitude M is y (t) = 8 y0 e − (t − i)/x + KM (1 − e − (t − i)/x)Bu (t − i) where u(t) = unit step function
7.3.4.2 Second-Order Control System Models One standard second-order control system model is Y (s ) K~ 2n = 2 R (s) s + 2g~ n s + ~ 2n where K = steady-state gain z = the damping ratio wn = the undamped natural (z = 0) frequency ~ d = ~ n 1 − g 2 , the damped natural frequency ~ r = ~ n 1 − 2g 2 , the damped resonant frequency If the damping ratio z is less than unity, the system is said to be underdamped; if z is equal to unity, it is said to be critically damped; and if z is greater than unity, the system is said to be overdamped. For a unit step input to a normalized, underdamped, second-order control system, the time required to reach a peak value tp and the value of that peak Mp are determined by tp =
~n
r 1 − g2
Mp = 1 + e
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− rg/ 1 − g 2
428
Chapter 7: Plant Design and Operation The percent overshoot (%OS) of the response is determined by %OS = 100e
− rg/ 1 − g 2
For an underdamped, second-order system, the logarithmic decrement is x 2rg 1 d = m 1n d x k n = k+m 1 − g2 where xk and xk+m are the amplitudes of oscillation at cycles k and k + m, respectively. The period of oscillation t is related to wd by wdt = 2p The time required for the output of a second-order system to settle to within 2% of its final value (2% settling time) is defined to be Ts =
4 g~ n
An alternative form commonly employed in the chemical process industry is Y (s ) K = R (s) x 2 s 2 + 2gxs + 1 where K = steady-state gain z = the damping ratio t = the inverse natural frequency
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Chapter 7: Plant Design and Operation Feedback Control CONTROLLER TIC
COLD PROCESS FLUID
TEMPERATURE TT TRANSMITTER
STEAM
HOT PROCESS FLUID
Feed Forward Control CONTROLLER FIC COLD PROCESS FLUID
FT
FLOW TRANSMITTER
STEAM
HOT PROCESS FLUID
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Chapter 7: Plant Design and Operation Feed Forward Plus Feedback Control FEED FORWARD CONTROLLER
SUMMING CONTROLLER
FIC
QIC
FEEDBACK CONTROL TIC
FT
COLD PROCESS FLUID
FLOW TRANSMITTER TT
TEMPERATURE TRANSMITTER
STEAM
HOT PROCESS FLUID
Feedback Control TIC PRIMARY CONTROLLER COLD PROCESS FLUID SECONDARY CONTROLLER
TEMPERATURE TT TRANSMITTER
FIC
FT STEAM
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HOT PROCESS FLUID
FLOW TRANSMITTER
431
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Conductivity; ASTM C 177
HTD at 0.46 MPa (66 psi); ASTM D 648 Linear coefficient of expansion; ASTM D 696 10
in. # -5 in. -cC 10
Btu cF ft -hr-in. 0.7
1.1
0.16
7–9.5
167–192
75–89
1.6–4.0
—
—
4.4
135
57
—
—
—
6.0–7.5
— —
1.38
PVC
1.75–1.79
1.76–1.79
—
—
3.9
—
1.18–1.32
0.17–0.19
7.2–14.4
270–300
1.11
0.16
14.0
200–230
—
—
8
194
90
180–260
—
6.6–7.8
Thermal Properties — 132–150 93–110
90–180
—
3.5–6.0
—
5.0–8.0
165–325
—
4.5–7.0
2.9–5.5
—
—
—
—
220–245 460
1.68
PVDF ECTFE HomoCopolymer polymer
— 160–170 141–160 — 320–340 285–320 Physical Properties
1.5
CPVC
Typical Thermoplastic Properties
—
—
6
220
104
7.1
200
—
6.5
270 518
1.70
ETFE
—
—
8–11
158
70
—
80–95
—
2.7–3.1
275 527
2.12–2.17
FEP
—
—
10
250
221
—
190–235
—
2.0–2.7
327 621
2.2–2.3
TFE
Source: Perry, Robert H., and Don W. Green, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 25-42.
2
0.1
225–250
°F
W m -K
107–121
4.5–5.4
°C
kpsi
50–150
165–225
kpsi
4.0–5.3
1135–1550 345–1035
4.5–6.0
150–175 302–347
0.88–0.91
Copolymer
PP
MPa
kpsi
160–175 320–347
°C °F
Melting point (crystalline)
Break strength; ASTM D 638 Modulus flex @ 73oF; ASTM D 790 Yield strength; ASTM D 638
0.91
g cm 3
Unit
Density
Property Homopolymer
Materials of Construction
7.3.5.1 Thermoplastics
7.3.5
—
—
12
166
75
—
120
—
4.0–4.5
310 590
2.12–2.17
PFA
Chapter 7: Plant Design and Operation
Chapter 7: Plant Design and Operation 7.3.5.2 Gasket Materials Important Properties of Gasket Materials* Material
Max Service Temp °F
Important Properties
Rubber (straight): Natural
225
Styrene-butadiene (SBR)
250
Butyl
300
Nitrile
300
Polysulfide
150
Neoprene
250
Silicone
600
Acrylic
450
Chlorosulfonated polyethylene (Hypalon)
250
Floroelastomer (Viton, Fluorel 2141, Kel-F)
450
Asbestos: Compressed asbestosrubber sheet Asbestos-rubber woven sheet Asbestos-rubber (beater addition process) Asbestos composites Asbestos-TFE
Cork compositions
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Good mechanical properties. Impervious to water. Fair to good resistance to acids, alkalies. Poor resistance to oils, gasoline. Poor weathering, aging properties. Better water resistance than natural rubber. Fair to good resistance to acids, alkalies. Unsuitable with gasoline, oils, and solvents. Very good resistance to water, alkalies, many acids. Poor resistance to oils, gasoline, most solvents (except oxygenated). Very good resistance to water. Excellent resistance to oils, gasoline. Fair to good resistance to acids, alkalies. Excellent resistance to oils, gasoline, aliphatic, and aromatic hydrocarbon solvents. Very good resistance to water. Good resistance to alkalies. Fair acid resistance. Poor mechanical properties. Excellent mechanical properties. Good resistance to nonaromatic petroleum, fatty oils, solvents (except aromatic, chlorinated, or ketone types). Good water and alkali resistance. Fair acid resistance. Excellent heat resistance. Fair water resistance. Poor resistance to steam at high pressures. Fair to good acid, alkali resistance. Poor (except fluorosilicone rubber) resistance to oils, solvents. Good heat resistance but poor cold resistance. Good resistance to oils, aliphatic and aromatic hydrocarbons. Poor resistance to water, alkalies, some acids. Excellent resistance to oxidizing chemicals, ozone, weathering. Relatively good resistance to oils, grease. Poor resistance to aromatic or chlorinated hydrocarbons. Good mechanical properties. Can be used at high temperatures with many fuels, lubricants, hydraulic fluids, solvents. Highly resistant to ozone, weathering. Good mechanical properties.
To 700
Large number of combinations available; properties vary widely depending on materials used.
To 250
Same as above.
400
Same as above.
To 1000 To 500
250
Same as above. Combines heat resistance and sealing properties of asbestos with chemical resistance of TFE. Low cost. Truly compressible materials that permit substantial deflections with negligible side flow. Conform well to irregular surfaces. High resistance to oils. Good resistance to water, many chemicals. Should not be used with inorganic acids, alkalies, oxidizing solutions, live steam. 433
Chapter 7: Plant Design and Operation Important Properties of Gasket Materials* (cont'd) Material
Cork rubber
Max Service Temp °F
Important Properties
300
Controlled compressibility properties. Good conformability, fatigue resistance. Chemical resistance depends on kind of rubber used.
Plastics: TFE (solid) (tetrafluoroethylene, Teflon)
150
Excellent resistance to almost all chemicals and solvents. Good heat resistance; exceptionally good low-temperature properties. Relatively low compressibility and resilience. Selectively improved mechanical and physical properties. However, fillers may lower resistance to specific chemicals. Chemical and heat resistance comparable with solid TFE. Inner gasket material provides better resiliency and deformability. Higher cost than TFE. Better chemical resistance than most other gasket materials, although not quite as good as TFE. Good compressibility, resiliency. Resistant to water, oils, gasoline, and many acids and alkalies. Relatively narrow temperature range. Resists most solvents. Poor heat resistance.
175
Nonporous; recommended for glycol, oil, and gasoline to 175°F.
230
Good water resistance.
500
TFE (filled)
To 500
TFE composite
To 500
CFE (chlorotrifluoroethylene, Kel-F)
350
Vinyl
212
Polyethylene Plant fiber: Neoprene-impregnated wood fiber SBR-bonded cotton Nitrile rubber-cellulose fiber Vegetable fiber, glue binder
Resists oil at high temperatures. 212
Vulcanized fiber Inorganic fibers Felt:
To 2200
Pure felt TFE-impregnated Petrolatum- or paraffinimpregnated Rubber-impregnated
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300
Resists oil and water to 212°F. Low cost. Good mechanical properties. Resists gasoline, oils, greases, waxes, many solvents. Excellent heat resistance. Poor mechanical properties. Resilient, compressible, and strong, but not impermeable. Resists medium-strength mineral acids and dilute mineral solutions if not intermittently dried. Resists oils, greases, waxes, most solvents. Damaged by alkalies. Good chemical and heat resistance. High water repellency. Many combinations available; properties vary widely depending on materials used.
434
Chapter 7: Plant Design and Operation Important Properties of Gasket Materials* (cont'd) Material
Metal: Lead Tin
Max Service Temp °F
500
Aluminum
800
Copper, brass Nickel
1400
Monel
1500
Inconel Stainless steel
2000
Metal composites Leather
220
Glass fabric
Rubber (straight)
600
Important Properties
Good chemical resistance. Best conformability of metal gaskets. Good resistance to neutral solutions. Attacked by acids and alkalies. High corrosion resistance. Slightly attacked by strong acids and alkalies. Good corrosion resistance at moderate temperatures. High corrosion resistance. High corrosion resistance. Good against most acids and alkalies, but attacked by strong hydrochloric and strong oxidizing acids. Excellent heat, oxidation resistance. High corrosion resistance. Properties depend on type used. Many combinations available; properties vary widely depending on materials used. Low cost. Limited chemical and heat resistance. Not recommended against pressurized steam, acid, or alkali solutions. High strength and heat resistance. Can be impregnated with TFE for high chemical resistance. Packing and Sealing Materials See Gasket Materials for properties. Mainly used for ring-type seals, although some types are available as spiral packings.
Rubber composites: Cotton-reinforced Asbestos-reinforced Asbestos:
350 450
Plain, braided asbestos
500
Impregnated asbestos
To 750
Asbestos composites Metals:
To 1200
Copper
To 1500
Aluminum
To 1000
Lead
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550
High strength. Chemical resistance depends on type of rubber used; however, most types are noted for high resistance to water, aqueous solutions. High strength combined with good heat resistance. Heat resistance combined with resistance to water, brine, oil, many chemicals. Can be reinforced with wire. Environmental properties vary widely depending on type of asbestos and impregnant used. Neoprene-cemented type resists hot oils, gasoline, and solvents. Oil-and-wax-impregnated type resists caustics. Wax-impregnated blue asbestos type has high acid resistance. TFEimpregnated has good all-around chemical resistance. End properties vary widely depending on secondary material used. Properties depend on other construction materials and form of copper used. Packing made of copper foil over asbestos core resists steam and alkalies to 1000°F. Packing of braided copper tinsel resists water, steam, and gases to 1500°F. Resists hot petroleum derivatives, gases, foodstuffs, many organic acids. Many types are available.
435
Chapter 7: Plant Design and Operation Important Properties of Gasket Materials* (cont'd) Material
Organic fiber: Flax Jute Ramie Cotton Rayon Felt Leather
Max Service Temp °F
300 300 300 300 300 300 To 210
TFE
To 500
Carbon graphite
700
Important Properties
Good water resistance. Good water resistance. Good resistance to water, brine, cold oil. Good resistance to water, alcohol, dilute aqueous solutions. Good resistance to water, dilute aqueous solutions. See Gasket Materials. Good mechanical properties for sealing. Resistant to alcohol, gasoline, many oils and solvents, synthetic hydraulic fluids, water. Available in many forms, all of which have high chemical resistance. Good bearing and self-lubricating properties. Good resistance to chemicals, heat.
* From Materials in Engineering Design, New York: Reinhold, 1959, p. 11-126. Source: Perry, R.H., and D. Green, Perry's Chemical Engineers' Handbook, 6th ed., New York: McGraw-Hill, 1985, pp. 23-61 to 23-62.
7.3.5.3 Corrosion Corrosion is a natural process that converts a refined metal to a more stable form such as its oxide, hydroxide, or sulfide. It is the gradual destruction of a material by chemical reaction with its environment. Corrosion effects must be taken into account during the design of any system, unit, facility, or plant. Use the following corrosion data charts to assist in narrowing the field of choice of materials. Once the choice has been narrowed, the effects of contaminants, aeration, galvanic coupling, erosion, and so on must be taken into account. Field testing is best for final suitability decisions.
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Chapter 7: Plant Design and Operation Source: All corrosion data from Perry, John H., and D. Green, Perry's Chemical Engineers' Handbook, 6th ed., New York: McGraw-Hill, 1963, pp. 23-13 to 23-30.
Detailed Corrosion Data on Construction Materials
100
ACID, HYDROFLUORIC
50
ACID, FORMIC
0
CONCENTRATION, %
ACID, CITRIC
0
ACID, CHROMIC
100
ACID, BORIC
200
ACID, HYDROCHLORIC
300
ACID, ACETIC
TEMPERATURE, °F
KEY TO CHARTS
ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY
AERATED
500 F
NOTE SYMBOLS ON VERTICAL HEAVY LINES REPRESENT 100% CONCENTRATION. SYMBOLS ON HORIZONTAL HEAVY LINES REPRESENT 300 F. TEMPERATURE.
400 F
AIR FREE
450 F
1,500FF 1500
HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR.. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AERATED OR NON-AERATED
HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AERATED OR AIR-FREE 12½ 25 37½
HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
©2017 NCEES
AIR FREE
CARBON-FILLED CEMENT
FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AIR FREE
12½ 25 37½
437
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AIR FREE
AERATED
ACID, HYDROFLUORIC
50
ACID, FORMIC
0
CONCENTRATION, %
ACID, CITRIC
0
ACID, CHROMIC
100
ACID, BORIC
200
ACID, HYDROCHLORIC
300
ACID, ACETIC
TEMPERATURE, °F
KEY TO CHARTS
AIR FREE
AIR FREE
AIR FREE
AIR FREE
AIR FREE
AIR FREE
NEOPRENE = SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AIR FREE
AERATED
PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR-S)
HARD RUBBER
HARD RUBBER
= SATISFACTORY = SATISFACTORY FOR LIMITED USE = GENERALLY UNSATISFACTORY
HARD RUBBER
RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED USE = GENERALLY UNSATISFACTORY
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SOFT GR-S CANNOT BE USED
438
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
STRESS CORROSION
STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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ACID, HYDROFLUORIC
50
ACID, FORMIC
0
CONCENTRATION, %
ACID, CITRIC
0
ACID, CHROMIC
100
ACID, BORIC
200
ACID, HYDROCHLORIC
300
ACID, ACETIC
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
IN ETHANOL
ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = UNSATISFACTORY
AIR FREE
COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = NOT RECOMMENDED
AERATED
HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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DRY
IN ETHANOL
GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AIR FREE
AERATED, NO VELOCITY
IN ETHANOL
FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY
HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AMMONIA, AQUEOUS
50
ALUMINUM POTASSIUM SULFATE (ALUM)
0
CONCENTRATION, %
ALUMINUM CHLORIDE
0
ACID, SULFURIC
100
ACID, OXALIC
200
ACID, PHOSPHORIC
300
ACID, NITRIC
TEMPERATURE, °F
KEY TO CHARTS
300
400 F
200 TECH NOT RECOMMENDED 600 F
TECH
440
SLUDGEHCI AND 250 PSI
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
CONCENTRATION, % IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AIR FREE, NO VELOCITY
AIR FREE
AERATED, NO VELOCITY
AIR FREE
AERATED
NEOPRENE = SATISFACTORY = FOR LIMITED USE = UNSATISFACTORY AERATED
NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
IN ETHANOL
PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR-S) = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY
©2017 NCEES
AERATED, NO VELOCITY
441
AMMONIA, AQUEOUS
50
ALUMINUM POTASSIUM SULFATE (ALUM)
0
ALUMINUM CHLORIDE
0
ACID, SULFURIC
100
ACID, OXALIC
200
ACID, PHOSPHORIC
300
ACID, NITRIC
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
STRESS AIR FREE, NO VELOCITY CRACKS
IN ETHANOL
STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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442
AMMONIA, AQUEOUS
50
ALUMINUM POTASSIUM SULFATE (ALUM)
0
CONCENTRATION, %
ALUMINUM CHLORIDE
0
ACID, SULFURIC
100
ACID, OXALIC
200
ACID, PHOSPHORIC
300
ACID, NITRIC
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
0
0
50
100
CONCENTRATION, % ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = NOT RECOMMENDED FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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CALCIUM HYPOCHLORITE
100
CALCIUM CHLORIDE
200
AMMONIUM CHLORIDE
300
AMMONIUM CARBONATE
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
0
0
50
100
CONCENTRATION, % IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. NEOPRENE = SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY
AVOID HCI AND Fe, NI IONS
NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR–S) = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY
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CALCIUM HYPOCHLORITE
100
CALCIUM CHLORIDE
200
AMMONIUM CHLORIDE
300
AMMONIUM CARBONATE
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
0
0
50
100
CONCENTRATION, % STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
pH > 7
STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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pH > 7
CALCIUM HYPOCHLORITE
100
CALCIUM CHLORIDE
200
AMMONIUM CHLORIDE
300
AMMONIUM CARBONATE
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
FERROUS SULFATE
50
FERROUS CHLORIDE
0
CONCENTRATION, %
FERRIC CHLORIDE
0
ETHYLENE GLYCOL
100
ETHANOL
200
ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY AIR FREE
COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = NOT RECOMMENDED FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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446
GLYCERINE
300
COPPER SULFATE
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. NEOPRENE = SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY PITS
NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR–S) = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY
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FERRIC CHLORIDE
50
FERROUS SULFATE
0
CONCENTRATION, %
FERROUS CHLORIDE
0
ETHYLENE GLYCOL
100
ETHANOL
200
GLYCERINE
300
COPPER SULFATE
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY
DRY
ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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FERROUS SULFATE
50
FERROUS CHLORIDE
0
CONCENTRATION, %
FERRIC CHLORIDE
0
ETHYLENE GLYCOL
100
ETHANOL
200
GLYCERINE
300
COPPER SULFATE
TEMPERATURE, °F
KEY TO CHARTS
DISCOLORS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS
AIR FREE
AIR FREE
= SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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AIR FREE
POTASSIUM HYDROXIDE
100
PHENOL
50
NICKEL SULFATE
0
CONCENTRATION, %
NICKEL CHLORIDE
0
METHANOL
100
MAGNESIUM SULFATE
200
MAGNESIUM CHLORIDE
300
HYDROGEN PEROXIDE
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. NEOPRENE
ALKALINE
DISCOLORS
DRY AIR FREE
= SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY DRY
NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR-S) = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY
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AIR FREE, SULFER FREE PITS
POTASSIUM HYDROXIDE
100
PHENOL
50
NICKEL SULFATE
0
CONCENTRATION, %
NICKEL NITRATE
0
METHANOL
100
MAGNESIUM SULFATE
200
MAGNESIUM CHLORIDE
300
HYDROGEN PEROXIDE
TEMPERATURE, °F
KEY TO CHARTS
AIR FREE
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY
800 F.
800 F.
ALKALINE
pH > 7
pH > 7
STRESS CRACKS
PITS
DISCOLORS, SULFUR FREE
AIR FREE
STRESS CRACKS
ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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POTASSIUM HYDROXIDE
100
PHENOL
50
NICKEL SULFATE
0
CONCENTRATION, %
NICKEL NITRATE
0
METHANOL
100
MAGNESIUM SULFATE
200
MAGNESIUM CHLORIDE
300
HYDROGEN PEROXIDE
TEMPERATURE, °F
KEY TO CHARTS
451
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
ZINC SULFATE
50
ZINC CHLORIDE
0
CONCENTRATION, %
SODIUM NITRATE
0
SODIUM HYDROXIDE
100
SODIUM CHLORIDE
200
SODIUM CARBONATE
300
POTASSIUM SULFATE
TEMPERATURE, °F
KEY TO CHARTS
ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY PITS
COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
10 20 30
HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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AIR FREE
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
ZINC SULFATE
50
ZINC CHLORIDE
0
CONCENTRATION, %
SODIUM NITRATE
0
SODIUM HYDROXIDE
100
SODIUM CHLORIDE
200
SODIUM CARBONATE
300
POTASSIUM SULFATE
TEMPERATURE, °F
KEY TO CHARTS
DRY
= < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
AIR FREE
= < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
1300 F.
400 F.
= SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY 600 F.
= < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
1300 F.
= SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY
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STRESS CRACKS
950 F.
DRY
AIR FREE
Chapter 7: Plant Design and Operation Detailed Corrosion Data on Construction Materials (cont'd)
100
STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
DRY
pH > 7 STRESS CRACKS STRESS CRACKS AT HIGHER TEMPS.
STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.
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ZINC SULFATE
50
ZINC CHLORIDE
0
CONCENTRATION, %
SODIUM NITRATE
0
SODIUM HYDROXIDE
100
SODIUM CHLORIDE
200
SODIUM CARBONATE
300
POTASSIUM SULFATE
TEMPERATURE, °F
KEY TO CHARTS
Chapter 7: Plant Design and Operation 7.3.5.4 Galvanic Corrosion Galvanic Corrosion 0.2
0
–0.2
–0.4
–0.6
–0.8
–1.0
–0.2
–1.4
–1.6
MAGNESIUM ZINC BERYLLIUM ALUMINUM ALLOYS CADMIUM MILD STEEL & CAST IRON LOW ALLOY STEEL AUSTIENITIC CAST IRON ALUMINUM BRONZE NAVAL BRASS, YELLOW BRASS & RED BRASS TIN COPPER 50/50 LEAD TIN SOLDER ADMIRALTY BRASS, ALUMINUM BRASS MANGANESE BRONZE SILICON BRONZE STAINLESS STEEL – GRADES 410, 416 NICKEL SILVER 90/10 COPPER NICKEL 80/20 COPPER NICKEL STAINLESS STEEL – GRADE 430 LEAD 70/30 COPPER NICKEL NICKEL ALUMINUM BRONZE NICKEL CHROMIUM ALLOY 600 NICKEL 200 SILVER STAINLESS STEEL – GRADES 302, 304, 321 & 347 NICKEL COPPER ALLOYS – 400, K500 STAINLESS STEEL – GRADES 316 & 317 ALLOY 20 STAINLESS STEEL NICKEL IRON CHROMIUM ALLOY 825 TITANIUM GOLD, PLATINUM GRAPHITE
MOST NOBLE – CATHODIC
LEAST NOBLE – ANODIC
Note: Unshaded symbols show ranges exhibited by stainless steels in acidic water such as may exist in crevices or in stagnant, low-velocity, or poorly aerated water. Source: Davis, J.R., ASM Specialty Handbook on Stainless Steel, 2nd ed.: American Society for Metals, 1996, p. 139. Reprinted with permission of ASM International. All rights reserved. www.asminternational.org.
7.3.5.5 Electrochemistry Electrochemical Terms
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Term Cathode
Definition The electrode at which reduction occurs
Anode Oxidation Reduction Cation Anion
The electrode at which oxidation occurs The loss of electrons The gaining of electrons Positive ion Negative ion
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Chapter 7: Plant Design and Operation 7.3.5.6 Standard Oxidation Potentials Standard Oxidation Potentials for Corrosion Reactions* Potential (Eo) Volts vs. Corrosion Reaction Normal Hydrogen Electrode + − -1.498 Au " Au3 + 3e + − 2H2O " O2 + 4H + 4e
-1.229
+ − Pt " Pt 2 + 2e
-1.200
+ − Pd " Pd 2 + 2e
-0.987
+ − Ag " Ag + e
-0.799
+ − 2Hg " Hg 22 + 2e
-0.788
+ + − Fe 2 " Fe3 + e
-0.771
4 ^OH h " O2 + 2H2O + 4e −
-0.401
−
+ − Cu " Cu 2 + 2e
-0.337
+ + − Sn 2 " Sn 4 + 2e
-0.150
+ − H2 " 2H + 2e
+0.000
+ − Pb " Pb 2 + 2e
+0.126
+ − Sn " Sn 2 + 2e
+0.136
+ − Ni " Ni 2 + 2e
+0.250
+ − Co " Co 2 + 2e
+0.277
+ − Cd " Cd 2 + 2e
+0.403
+ − Fe " Fe 2 + 2e
+0.440
+ − Cr " Cr3 + 3e
+0.744
+ − Zn " Zn 2 + 2e
+0.763
+ − Al " Al3 + 3e
+1.662
+ − Mg " Mg 2 + 2e
+2.363
+ − Na " Na + e
+2.714
+ − K " K +e
+2.925
*Measured at 25°C. Reactions are written as anode half-cells. Arrows are reversed for cathode half-cells. Note: In some chemistry texts, the reactions and the signs of the values (in this table) are reversed; for example, the half-cell + − potential of zinc is given as –0.763 volt for the reaction Zn 2 + 2e " Zn . When the potential Eo is positive, the reaction proceeds spontaneously as written. Source: Republished with permission of Houghton Mifflin Harcourt, from Flinn, Richard A., and Paul K. Trojan, Engineering Materials and Their Applications, 3rd ed., 1986. Permission conveyed through Copyright Clearance Center, Inc.
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Chapter 7: Plant Design and Operation
7.4 Operation 7.4.1
Process and Equipment Reliability
7.4.1.1 Operating Procedures The main types of process operating procedures are 1. Standard Operating Procedures (SOP)—Written instructions documenting step-by-step instructions for safely performing a task within operating limits. The SOP covers all modes of operation. The purpose of the standard operating procedure is to ensure operations are always carried out correctly and in the same manner. An SOP should be available at the place where the work is done. 2. Startup/Shutdown Procedures—Written procedures for startup and shut-down phased so that interlinked plant operations can resume or stop in a safe and controlled manner. 3. Emergency or Abnormal Operating Procedures—Written instructions documenting step-by-step instructions for reaching a safe state following a process in an upset condition. The emergency procedures should cover the PPE, the level of intervention which is safe, and when to evacuate. The procedures will also need to tie in with site emergency plans. 4. Temporary Operating Procedures—Written instructions for a finite period of time. At the conclusion of this time, the facility returns to using the Standard Operating Procedures. Temporary operating procedures should include an expiration date. 5. Maintenance Procedures—Written instructions that address material control and maintenance practices needed to ensure system operability and integrity. These procedures specify the required maintenance, testing, and inspection frequencies. Source: Guidelines for Engineering Design for Process Safety, 2nd ed., New York: Wiley, 2012, pp. 135–137.
The zones for safe operation of process equipment are defined as 1. Normal Operating Zone: The minimum or maximum values of an operating parameter that define the boundaries of normal operations. Some examples of operating parameters to be defined include •
High and low pressure
•
High and low temperature
•
High and low level
•
High and low pH
•
High and low flow
2. Troubleshooting Zone: An area that provides time for troubleshooting, so that operations personnel can make adjustments in time to return the operating parameters to the Normal Operating Zone. Human factors and process response time generally indicate zone size. Immediate actions, and in some cases predetermined actions, to avoid Safe Operating Limit (SOL) deviation are taken in this zone. 3. Buffer Zone: The upper and lower area of the known safe zone provides a buffer to ensure no operating parameter can reach the Unknown/Unacceptable Operation Zone. Factors that influence Buffer Zone size may include engineering judgment, reliability of instrumentation, operating experience, probability and consequence of human error, and so on. A process will not be operated intentionally in this zone.
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Chapter 7: Plant Design and Operation 4. Safe Operating Limit (SOL): A value for an operating parameter that defines the equipment or process unit's safe-operating envelope, beyond which a process will not intentionally be operated due to the risk of imminent, catastrophic equipment failure or loss of containment. Operational or mechanical corrective action ceases and immediate predetermined actions are taken at these operating parameter values in order to bring equipment and process units to a safe state. Each SOL should be documented in the plant's Process Safety Information. 5. Unacceptable or Unknown Operating Zone: An area beyond the Safe Operating Limit. A process will not be intentionally operated in this zone.
Operation Zones for Process Equipment EQUIPMENT LIMIT UNACCEPTABLE/UNKNOWN OPERATING ZONE SAFE OPERATING LIMIT NEVER EXCEED LIMIT
INSTRUMENT RANGE
BUFFER ZONE TROUBLESHOOTING ZONE
MAXIMUM NORMAL OPERATING LIMIT NORMAL OPERATING ZONE MINIMUM NORMAL OPERATING LIMIT TROUBLESHOOTING ZONE NEVER EXCEED LIMIT SAFE OPERATING LIMIT
BUFFER ZONE UNACCEPTABLE/UNKNOWN OPERATING ZONE
INSTRUMENT RANGE EQUIPMENT LIMIT
Source: Smith, David J., Reliability, Maintainability and Risk—Practical Methods for Engineers, 5th ed., Appendix A1: "Terms Related to Failure," Amsterdam: Elsevier, 1997.
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Chapter 7: Plant Design and Operation 7.4.1.2 Maintenance and Reliability Maintenance and Reliability Term
Definition
Up Time Availability (%) = Total Time Availability
The proportion of time that an item is capable of operating to specification within a large time interval.
Diversity
The same performance of a function by two or more independent and dissimilar means.
Failure Modes and Effects Analysis (FMEA)
A qualitative tool for analysis identifying all the ways a particular component can fail and the effects of the failure on the system.
Mean Time Between Failures (MTBF)
The total cumulative functioning time of a population divided by the number of failures, MTBF is used for items that involve repair and excludes downtime. Total Up Time MTBF = Number of Failures
Predictive Maintenance
The aim of predictive maintenance is, first, to predict when equipment failure may occur and, second, to prevent occurrence of that failure by performing maintenance.
Preventive Maintenance
Redundancy
Reliability
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Example or Application
The availability of a gas turbine generator was increased to 95% by minimizing the scheduled maintenance duration. In-line check valves of two different technologies or separate manufacturers are installed to decrease the likelihood of reverse flow from waste-water treatment back to the process. An FMEA identifies internal spring failure from excessive wear on a solenoid valve. The local and system consequences are documented. A recommendation is made for regular inspection to prevent this point of failure.
For 10,000 total hours of recorded uptime, the MTBF for 4 power supplies is 2500 hours.
A plant predictive maintenance program could use regular vibration analyses and motor current signature analyses to determine equipment conditions and predict failure. A preventive maintenance program for a Actions carried out for the purpose of centrifugal pump at a plant could include keeping equipment or instrumentation in monthly inspection of the gland packing, a specified condition. bearing lubrication, and pump mountings. The provision of more than one means of achieving a function. An active pump runs continuously for long periods of time without having to go Active/Duty: All items remain operating through the start-up process. The standby prior to failure. pump remains dormant and is tested reguStandby: Replicated items do not oper- larly to ensure reliability. ate until needed. The probability that the system will not leave the operational state. The availSafety-instrumented function; probability of ability for a given system is always failure on demand. greater than or equal to the reliability.
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Chapter 7: Plant Design and Operation 7.4.1.3 Decision-Tree Approach to Determine the Optimum Maintenance Period Decision Tree for Optimum Maintenance IS IMPACT AND FREQUENCY OF FAILURE ON AVAILABILITY AND COST ACCEPTABLE?
NO
YES
NO
IS FAILURE PREDICTABLE
YES
UNSCHEDULED MAINTENANCE
YES
PREVENTIVE MAINTENANCE
CALENDAR TIME BASIS
IS IMPENDING FAILURE DETECTABLE?
PREDICTIVE MAINTENANCE
USAGE BASIS
CONTINUOUS MONITORING
NO
UNSCHEDULED MAINTENANCE
PERIODIC MANUAL MONITORING
Source: Koshal, D., Manufacturing Engineer's Reference Book, 18.6.3 "Establishing Preventive-Maintenance Routines," Amsterdam: Elsevier, 1993, pp. 18 and 20, used with permission .
7.4.1.4 Typical Equipment Failure Diagram TYPICAL EQUIPMENT FAILURE DIAGRAM
Equipment Failure
FAILURE RATE (λ)
DURING EXTREME EVENTS
DURING NORMAL OPERATION INFANT MORALITY
USEFUL LIFE PERIOD
TIME
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WEAROUT PERIOD
Chapter 7: Plant Design and Operation
7.4.2
Process Improvement and Troubleshooting
The variety and complexity of modern processing industries requires that engineers be able to find ways to improve the processes of their facilities for the benefit of their employers or clients. Process improvement allows for the optimization of utilities, raw materials, and other resources to maximize production and minimize the cost per unit produced. Engineers who are tasked with process improvement and troubleshooting focus their knowledge and training to make a facility or process work more efficiently and economically. Work in this area will focus on one of the following types of activities: • Optimum balance of process variables • Increased capacity—Debottleneck and/or add equipment • Improved product quality—Control contamination and deterioration • Improved mechanical performance—Reduce corrosion and fouling • Decreased utility and raw material consumption—Steam, power, water, chemicals, and so on • More efficient maintenance • Improved safety practices The use of data is paramount to any of the activities listed above. The modern process-industries plant typically has an abundance of data that is part of the control systems. This data is collected from all aspects and areas of the facility. One of the most common methods of using data to improve a process is the DMAIC method. The five phases in the DMAIC method are 1. Define the problem and system by setting goals and understanding the requirements of the customer and the system. 2. Measure the key aspects of the process and gather the data that is available and relevant to the issue, project, or problem to be solved. This data can be used to determine the "as is" state of the process. 3. Analyze the data to investigate the process and determine the cause-and-effect relationships in the process. Seek out the root cause(s) of the problem being evaluated. 4. Improve or optimize the current process based on data analysis techniques to create a new, future-state process and run pilot trials to establish the process capability. 5. Control the new process to ensure that any deviations are corrected quickly before they result in defects or issues. Data analysis can be a complex activity and techniques in this area include 5 Whys Regression analysis Cause-and-effect diagraming Design of experiments Taguchi loss function General linear modeling Cost-benefit analysis Failure modes, effects, and diagnostic analysis (FMEDA)
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Analysis of variance Correlation Control/run charts Pareto analysis Value stream mapping Axiomatic design Root-cause analysis
Chapter 7: Plant Design and Operation One of the most useful techniques for troubleshooting is root-cause analysis (RCA). RCA is a method of problemsolving used to identify the root cause(s) of faults or problems. A factor is considered a root cause if removal from the problem-fault sequence prevents the final undesirable event from recurring. A causal factor is one that affects an event's outcome and, if removed, might benefit the process but does not prevent the recurrence of the problem being addressed. RCA is applied to methodically identify and correct the root causes of events, rather than to simply address the symptomatic result. Focusing correction on root causes has the goal of entirely preventing problem recurrence. RCA is typically used as a reactive method for identifying event causes, revealing problems, and solving them. Analysis is most typically done after an event has occurred; however, it can also be used as a predictive tool. The basic steps in root-cause analysis are: 1. Define the problem or describe the event to prevent in the future. 2. Gather data and evidence, classifying it along a time line. 3. Data-mine for clusters of similar problems that are close to the problem or event. 4. Ask why this happens and identify the causes, giving each sequential step toward the problem or event. 5. Classify all causes into either "causal" or "root." 6. Identify any other items that affect the problem or event. 7. Identify the corrective action(s) that will, with certainty, prevent recurrence of each harmful effect. 8. Identify solutions that prevent recurrence and that are within the control of the institution. 9. Implement the recommended root-cause corrections. 10. Ensure effectiveness by observing the implemented solutions in operation. Observation is one of the best ways to identify issues that need to be addressed when working and troubleshooting in any type of plant.
7.5 Safety, Health, and Environment 7.5.1
General
7.5.1.1 Definition of Safety Safety is the condition of protecting people from threats or failure that could harm their physical, emotional, occupational, psychological, or financial well-being. Safety is also the control of known threats to attain an acceptable level of risk. The United States relies on public codes and standards, engineering designs, and corporate policies to ensure that a structure or place does what it should do to maintain a steady state of safety—that is, long-term stability and reliability. Some safety/regulatory agencies that develop codes and standards commonly used in the United States are shown below.
Insurance, Safety, and Regulatory Agencies Acronym
ANSI CGA CSA FAA FMG IEC ITSNA
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Name
Jurisdiction
American National Standards Institute Compressed Gas Association Canadian Standards Association Federal Aviation Administration FM Global International Electrotechnical Commission Intertek Testing Services NA (formerly Edison Testing Labs) 462
Nonprofit standards organization Nonprofit trade association Nonprofit standards organization U.S. federal regulatory agency Insurance Nonprofit standards organization Nationally recognized testing laboratory
Chapter 7: Plant Design and Operation Insurance, Safety, and Regulatory Agencies (cont'd) Acronym
MSHA NFPA OSHA UL USCG USDOT USEPA
Name
Jurisdiction
Mine Safety and Health Administration National Fire Protection Association Occupational Health and Safety Administration Underwriters Laboratories United States Coast Guard United States Department of Transportation United States Environmental Protection Agency
Federal regulatory agency Nonprofit trade organization Federal regulatory agency Nationally recognized testing laboratory Federal regulatory agency Federal regulatory agency Federal regulatory agency
7.5.1.2 Elements of Process Safety Management (PSM) The U.S. Occupational Safety and Health Administration (OSHA) 1910.119 defines all 14 elements of a process safety management plan: 1. Employee Participation—Consult with employees and their representatives on the development and conduct of hazard assessments and the development of chemical accident prevention plans, and provide access to these and other records required under the standard. 2. Process Safety Information—Develop and maintain written safety information identifying workplace chemical and process hazards, equipment used in the processes, and technology used in the processes. 3. Process Hazard Analysis—Perform a workplace hazard assessment including, as appropriate, identification of potential sources of accidental releases, identification of any previous release within the facility that had a potential for catastrophic consequences in the workplace, estimation of workplace effects of a range of releases, and estimation of the health and safety effects of such a range on employees. Establish a system to respond to the workplace hazard assessment findings, which shall address prevention, mitigation, and emergency responses. 4. Operating Procedures—Develop and implement written operating procedures for the chemical processes, including procedures for each operating phase, operating limitations, and safety and health considerations. 5. Training—Provide written safety and operating information for employees and employee training in operating procedures, by emphasizing hazards and safe practices that must be developed and made available. 6. Contractors—Ensure contractors and contract employees are provided with appropriate information and training. 7. Pre-startup Safety Review—Conduct pre-startup safety reviews of all newly installed or modified equipment. 8. Mechanical Integrity—Establish maintenance systems for critical process-related equipment, including written procedures, employee training, appropriate inspections, and testing of such equipment to ensure ongoing mechanical integrity. Establish a quality-assurance program to ensure that initial process-related equipment, maintenance materials, and spare parts are fabricated and installed consistent with design specifications. 9. Hot-Work Permit—A permit must be issued for hot-work operations conducted on or near a covered process. The permit must document that the fire prevention and protection requirements have been implemented prior to beginning the hot-work operations; it must indicate the date(s) authorized for hot work and identify the object on which hot work is to be performed. The permit must be kept on file until completion of the hot work. 10. Management of Change—Establish and implement written procedures managing change to process chemicals, technology, equipment, and facilities. 11. Incident Investigation—Investigate every incident that results in or could have resulted in a major accident in the workplace, with any findings to be reviewed by operating personnel and modifications made if appropriate. ©2017 NCEES
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Chapter 7: Plant Design and Operation 12. Emergency Planning and Response—Develop and implement an emergency action plan for the entire plant in accordance with the provisions of other OSHA rules. Include in the emergency action plan procedures for handling small releases of hazardous chemicals. 13. Compliance Audits—Employers must certify that they have evaluated compliance with the provisions of PSM at least every three years. This will verify that the procedures and practices developed under the standards are adequate and are being followed. 14. Trade Secrets—Employers must make available all information necessary to comply with PSM to those persons responsible for compiling the process safety information, those developing the process hazard analysis, those responsible for developing the operating procedures, and those performing incident investigations, emergency planning and response, and compliance audits, without regard to the possible tradesecret status of such information.
7.5.1.3 Safety, Health, and Prevention A traditional preventive approach to both accidents and occupational illness involves recognizing, evaluating, and controlling hazards and work conditions that may cause physical injuries or adverse health effects. Hazard is the capacity to cause harm. It is an inherent quality of a material or a condition. For example, a rotating saw blade or an uncontrolled high-pressure jet of water has the capability (hazard) to slice through flesh. A toxic chemical or a pathogen has the capability (hazard) to cause illness. Risk is the chance or the probability that a person will experience harm and is not the same as a hazard. Risk always involves both probability and severity elements. The hazard associated with a rotating saw blade or the water jet continues to exist, but the probability of causing harm, and thus the risk, can be reduced by installing a guard or by controlling the jet's path. Risk is expressed by the equation: Risk = Hazard # Probability When people discuss the hazards of disease-causing agents, the term exposure is typically used more than probability. If a certain type of chemical has a toxicity hazard, the risk of illness rises with the degree to which that chemical contacts your body or enters your lungs. In that case, the equation becomes: Risk = Hazard # Exposure Organizations evaluate hazards using multiple techniques and data sources.
7.5.1.4 Job Safety Analysis Job safety analysis (JSA) is known by many names, including activity hazard analysis (AHA), or job hazard analysis (JHA). Hazard analysis helps integrate accepted safety and health principles and a specific task. In a JSA, each basic step of the job is reviewed, potential hazards identified, and recommendations documented as to the safest way to do the job. JSA techniques work well when used on a task that the analysts understand well. JSA analysts look for specific types of potential accidents and ask basic questions about each step, such as these: Can the employee strike against or otherwise make injurious contact with the object? Can the employee be caught in, on, or between objects? Can the employee strain muscles by pushing, pulling, or lifting? Is exposure to toxic gases, vapors, dust, heat, electrical currents, or radiation possible?
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Chapter 7: Plant Design and Operation
7.5.2
Protection Systems
7.5.2.1 Major Types of Relief Devices Relief Devices CAP CAP
Conventional pressure relief valve (PRV)/ Pressure Safety Valve (PSV) with a single adjusting ring for blowdown control
STEM STEM SPINDLE SPINDLE ADJUSTING SCREW SCREW ADJUSTING BONNET BONNET SPRING SPRING
VENT (PLUGGED) (PLUGGED) VENT
Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, 8th ed., December 2008, Figure 1. Courtesy of the American Petroleum Institute.
DISK DISK SEATING SURFACE SEATING SURFACE ADJUSTING RING RING ADJUSTING BODY BODY NOZZLE NOZZLE
CAP CAP
Balance-Bellows PRV/PSV
STEM STEM SPINDLE SPINDLE ADJUSTING SCREW SCREW ADJUSTING BONNET BONNET SPRING SPRING
VENT VENT (UNPLUGGED) (UNPLUGGED)
BELLOWS BELLOWS DISK DISK
SEATING SEATING SURFACE SURFACE
ADJUSTING ADJUSTING RING RING BODY BODY NOZZLE NOZZLE
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Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, 8th ed., December 2008, Figure 2. Courtesy of the American Petroleum Institute.
Chapter 7: Plant Design and Operation
SET PRESSURE ADJUSTMENT SCREW SEAT
SPINDLE
PILOT VALVE
EXTERNAL BLOWDOWN ADJUSTMENT
PILOT EXHAUST
PILOT SUPPLY LINE
OPTIONAL PILOT FILTER
Pop-Action Pilot-Operated Valve (Flowing Type)
Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, 8th ed., December 2008, Figure 10. Courtesy of the American Petroleum Institute.
OUTLET PISTON SEAT
INTERNAL PRESSURE PICKUP MAIN VALVE
INLET
Rupture Disc Assembly DISC
Source: Crowl, Daniel A., and Louvar, Joseph F., Chemical Process Safety: Fundamentals with Applications, 2nd ed., New York: Pearson Education 2002. With permission.
CARRIER ASSEMBLY
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Chapter 7: Plant Design and Operation 7.5.2.2 Pressure-Level Relationships for Pressure Relief Valves Pressure-Level Relationships for PRVs PRESSURE VESSEL REQUIREMENTS
VESSEL PRESSURE
MAXIMUM ALLOWABLE ACCUMULATED PRESSURE (FIRE EXPOSURE ONLY)
121
MULTIPLE VALVES AND MAXIMUM RELIEVING PRESSURE FOR PROCESS SIZING
116 115
SINGLE–VALVE MAXIMUM RELIEVING PRESSURE FOR PROCESS SIZING PERCENT OF MAXIMUM ALLOWABLE WORKING PRESSURE (GAUGE)
MAXIMUM ALLOWABLE WORKING PRESSURE OR DESIGN PRESSURE (SEE NOTE 4)
MAXIMUM RELIEVING PRESSURE FOR FIRE SIZING
120
MAXIMUM ALLOWABLE ACCUMULATIVE PRESSURE FOR MULTI-VALVE INSTALLATION (OTHER THAN FIRE EXPOSURE)
MAXIMUM ALLOWABLE ACCUMULATED PRESSURE FOR SINGLE–VALVE INSTALLATION(OTHER THAN FIRE EXPOSURE))
TYPICAL CHARACTERISTICS OF PRESSURE RELIEF VALVES
THE MAXIMUM ALLOWABLE SET PRESSURE FOR SUPPLEMENTAL VALVES (FIRE EXPOSURE)
110
OVERPRESSURE (MAXIMUM)
105
100
MAXIMUM ALLOWABLE SET PRESSURE FOR ADDITIONAL VALVES (PROCESS)
SIMMER (TYPICAL)
MAXIMUM ALLOWABLE SET PRESSURE FOR SINGLE VALVE
BLOWDOWN (TYPICAL) (SEE NOTE 6) 95
CLOSING PRESSURE FOR A SINGLE VALVE MAXIMUM EXPECTED OPERATING PRESSURE (SEE NOTES 5 AND 6)
90
LEAK TEST PRESSURE (TYPICAL)
85 NOTES: 1. THIS FIGURE CONFORMS WITH THE REQUIREMENTS OF SECTION VIII OF THE ASME BOILER AND PRESSURE VESSEL CODE FOR MAWPS GREATER THAN 30 PSIG. 2. THE PRESSURE CONDITIONS SHOWN ARE FOR PRESSURE RELIEF VALVE INSTALLED A PRESSURE VESSEL. 3. ALLOWABLE SET-PRESSURE TOLERANCES WILL BE IN ACCORDANCE WITH THE APPLICABLE CODES. 4. THE MAXIMUM ALLOWABLE WORKING PRESSURE IS EQUAL TO OR GREATER THAN THE DESIGN PRESSURE FOR COINCIDENT DESIGN TEMPERATURE. 5. THE OPERATING PRESSURE MAYBE HIGHER OR LOWER THAN 90%. 6. SECTION VIII, DIVISION 1, APPENDIX M OF THE ASME CODE SHOULD BE REFERRED TO FOR GUIDANCE ON BLOWDOWN AND PRESSURE DIFFERENTIALS.
Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, 8th ed., December 2008. Courtesy of the American Petroleum Institute.
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Chapter 7: Plant Design and Operation 7.5.2.3 Relief Vent Sizing Relief-Venting Flammable Liquids
HEAT ABSORPTION, Q (BTU/HR)
.82
Q
14,090,000
0 (A) 0 0 1,0 =2
8
0.33
9,950,000
566
.
Q=
4,000,000
Q
0 (A) 0 0 ,3 199
Q
0 (A) 3,40 6 9 =
Q = 14,090,000
0A ,00 0 =2
400,000 20
200 1000 2800 2 EXPOSED WITH A SURFACE AREA, A (FT )
Source: Reproduced with permission from NFPA 30, Flammable and Combustible Liquid Code, © 2015, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.
Estimation of Emergency Relief Venting for Specific Liquids CFH =
70.5Q L M
where CFH = cubic feet of free air per hour 70.5 = factor for converting pounds of gas to ft3 of air
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Q
= total heat input per hour (Btu)
L
Btu = latent heat of vaporization c lb m
M
= molecular weight
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Chapter 7: Plant Design and Operation 7.5.2.4 Pressure Relief Variables and Constants Pressure Relief Variables and Constants Symbol
Description
Units (U.S.)
Units (metric)
in2
mm2
lbm-lb mole-cR lbf -hr
A
Required effective discharge area of the device
C
Cp o of the A function of the ratio of the ideal gas-specific heats e k = Cv gas or vapor at inlet-relieving temperature
Cp
Specific heat at constant pressure
Btu lb cF
kg : kg mol : K mm 2 : hr : K Pa KJ kg K
Cv
Specific heat at constant volume
Btu lb cF
KJ kg K
F2
Coefficient of subcritical flow
Gl
Specific gravity of a liquid at flowing temperature referred to water at standard conditions
k
Ratio of the specific heats e
Kb
Kc
Kd for liquid
Kd for gas, vapor, steam
Cp o for an ideal gas at relieving temperaCv
ture. The ideal-gas to specific-heat ratio is independent of pressure. Capacity correction factor due to back pressure; can be obtained from manufacturer's literature or estimated for preliminary sizing. The back-pressure correction factor applies to balanced-bellows valves only. For conventional and pilot-operated valves, use a value for Kb equal to 1.0. Combination correction factor for installations with a rupture disc upstream of the pressure relief valve. Equals 1.0 when a rupture disc is not installed; equals 0.9 when a rupture disc is installed in combination with a PRV and the combination does not have a certified value. Rated coefficient of discharge that should be obtained from the valve manufacturer. For preliminary sizing, an effective discharge coefficient can be used as follows: • 0.65 when a PRV is installed with or without a rupture disc in combination
dimensionless
dimensionless
dimensionless
dimensionless
• 0.62 when a PRV is not installed and sizing is for a rupture disc with minimum net flow area Effective coefficient of discharge. For preliminary sizing, use the following values: • 0.975 when a PRV is installed with or without a rupture disc in combination
dimensionless
• 0.62 when a PRV is not installed and sizing is for a rupture disc with minimum net flow area
KN
Correction factor for the Napier equation (KN = 1.0)
dimensionless
KSH
Superheat correction factor; can be obtained from the "Superheat Correction Factors" table in this section. For saturated steam at any pressure, KSH = 1.0. For temperatures above 1200°F, use the critical vapor sizing equations.
dimensionless
Kv
Correction factor due to viscosity
dimensionless
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Chapter 7: Plant Design and Operation Pressure Relief Variables and Constants (cont'd) Symbol
KW
M
Description
Units (U.S.)
Correction factor due to back pressure. If the back pressure is atmospheric, use a value for KW of 1.0. Balanced-bellows valves in backpressure service require the correction determined from the figure "Capacity Correction Factor, KW, Due to Back Pressure on BalancedBellows PRVs in Liquid Service." Conventional and pilot-operated valves require no special correction. Molecular weight of the gas or vapor at inlet-relieving conditions. Various handbooks carry tables of molecular weights of materials; however, the composition of the flowing gas or vapor is seldom the same as that listed in such tables. This composition should be obtained from the process data.
Units (metric)
dimensionless
P1
Upstream relieving pressure; set pressure plus allowable overpressure plus atmospheric pressure
psia
kPa
P2
Back pressure
psia
kPa
Q
Flow rate
U.S. gal min
L min
r Re T m U V
P Ratio of back pressure to upstream relieving pressure, P2 1 Reynolds number Relieving temperature of the inlet gas or vapor Absolute viscosity at the flowing temperature Viscosity at the flowing temperature Required flow through the device
W
Required flow through the device.
Z
Compressibility factor for the deviation of the actual gas from a perfect gas, evaluated at inlet-relieving conditions.
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dimensionless dimensionless °R (°F + 460) K (°C + 273) cP Saybolt universal seconds scfm at 14.7 psia and 60°F
normal m3 at 0°C min
lb h
kg h
and 101.325 kPa
dimensionless
Chapter 7: Plant Design and Operation Pressure Relief Equations Description
Coefficient C
Units (U.S.) (units per previous table)
C = 520
^k + 1 h
2 ^k − 1 h kc k + 1 m
Units (metric) (units per previous table)
C = 0.03948
KN = 1.0
KN = 1.0
where P1 # 1, 500 psia Correction Factor KN
^k + 1 h
2 ^k − 1 h kc k + 1 m
where P1 # 10, 339 kPa
0.1906 P − 1, 000 KN = 0.2292 P1 − 1, 061 1
0.02764 P − 1, 000 KN = 0.03324 P1 − 1, 061 1
where P1 > 1,500 psia and # 3, 200 psia
where P1 > 10,339 kPa and # 22, 057 kPa
F2 =
Coefficient F2
2 ck 1m c −k m rc k m >1 − r k H k 1 1−r −
W A=CK PK K d 1 b c
Sizing for Gas or Vapor Service at Critical Flow Conditions
TZ M
Sizing for Subcritical Flow: Gas or Vapor, Conventional and Pilot-Operated PRVs When the ratio of back pressure to inlet pressure exceeds the critical pressure ratio Pcf /P1, the flow through the pressure-relief device is subcritical. These equations may be used to calculate the required effective discharge area for a conventional PRV whose spring setting is adjusted to compensate for superimposed back pressure. Equations may also be used for sizing a pilot-operated PRV. Sizing for Steam-Relief Operating at Critical Flow Conditions
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W A = 735 F K K 2 d c
TZ M P1 (P1 − P2)
W A = 51.5 P K K K K K 1 d b c N SH
471
17.9W A= F K K 2 d c
TZ M P1 (P1 − P2)
190.5W A= PK K K K K 1 d b c N SH
Chapter 7: Plant Design and Operation Pressure Relief Equations (cont'd) Description
Units (U.S.)
Units (metric)
Sizing for Liquid Relief: PRVs Requiring Capacity Certification The ASME Code requires that capacity certification be obtained for PRVs designed for liquid service. The procedure for obtaining capacity certification includes testing to determine the rated coefficient of discharge for the liquid PRVs at 10% overpressure. The sizing equations for pressure-relief devices in liquid service provided here assume that the liquid is incompressible (i.e., the density of the liquid does not change as the pressure decreases from the relieving pressure to the total back pressure).
Q A = 38 K K K K d w c v
G1 P1 − P2
11.78 Q A= K K K K d w c v
Kv = d 0.9935 +
2.878 + 342.75 1 0 n Re0.5 Re1.5
G1 P1 − P2
Valves in liquid service that are designed in accordance with the ASME Code may be initially sized using these area equations. Kv: Correction Factor Due to Viscosity
− .
Re = Reynolds Number When a PRV is sized for viscous liquid service, it should first be sized as if it were for a nonviscous application (i.e., Kv = 1.0), so that a preliminary required discharge area A can be obtained from the liquid relief area equations above. From API 526 standard orifice sizes, use the next orifice size larger than A to determine the Reynolds Number, Re, from either of the following relationships: Second equation is not recommended for viscosities less than 100 Saybolt universal seconds (SSU)
Re =
Q (2, 800 Gl) n A
Re =
12, 700 Q U A
After determining the Reynolds Number, Re, obtain the factor KV. Apply KV in the liquid relief area equations above to correct the preliminary required discharge area. If the corrected area exceeds the chosen standard orifice area, repeat the above calculations using the next larger standard orifice size. Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008. Courtesy of the American Petroleum Institute. ©2017 NCEES
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Chapter 7: Plant Design and Operation Superheat Correction Factors, KSH
Superheat Correction Factors Set Pressure psig (kPag)
15 (103) 20 (138) 40 (276) 60 (414) 80 (551) 100 (689) 120 (827) 140 (965) 160 (1103) 180 (1241) 200 (1379) 220 (1516) 240 (1654) 260 (1792) 280 (1930) 300 (2068) 350 (2413) 400 (2757) 500 (3446) 600 (4136) 800 (5514) 1000 (6893) 1250 (8616) 1500 (10,339) 1750 (12,063) 2000 (13,786) 2500 (17,232) 3000 (20,679)
300 (149)
400 (204)
500 (260)
Temperature °F (°C) 600 700 800 (316) (371) (427)
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 -----------------
0.98 0.98 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 ---------
0.93 0.93 0.93 0.93 0.93 0.94 0.94 0.94 0.94 0.94 0.95 0.95 0.95 0.95 0.96 0.96 0.96 0.96 0.96 0.97 1.00 1.00 1.00 ------
0.88 0.88 0.88 0.88 0.88 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.90 0.90 0.90 0.90 0.90 0.91 0.92 0.92 0.95 0.96 0.97 1.00 1.00 1.00 1.00 --
0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.86 0.86 0.86 0.87 0.88 0.89 0.91 0.93 0.94 0.95 0.95 1.00
0.80 0.80 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.82 0.82 0.82 0.82 0.83 0.84 0.85 0.86 0.86 0.86 0.85 0.82
900 (482)
1000 (538)
1100 (593)
1200 (649)
0.77 0.77 0.77 0.77 0.77 0.77 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.79 0.79 0.78 0.80 0.81 0.81 0.80 0.78 0.74
0.74 0.74 0.74 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.76 0.76 0.77 0.77 0.77 0.76 0.73 0.69
0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.73 0.73 0.73 0.73 0.74 0.74 0.73 0.72 0.69 0.65
0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.71 0.71 0.71 0.70 0.69 0.66 0.62
Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008. Courtesy of the American Petroleum Institute.
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Chapter 7: Plant Design and Operation Capacity Correction Factor, KW, Due to Back Pressure on Balanced-Bellows PRVs in Liquid Service 1.00 0.95 0.90 0.85
Kw
0.80 0.75 0.70 0.65 0.60 0.55 0.50
0
10 20 30 40 PERCENT OF GAUGE BACKPRESSURE = (PB /PS) x 100
50
Kw = CORRECTION FACTOR DUE TO BACK PRESSURE. PB = BACK PRESSURE, IN PSIG. PS = SET PRESSURE, IN PSIG. NOTE: THE CURVE ABOUT REPRESENTS VALUES RECOMMENDED BY VARIOUS MANUFACTURERS. THIS CURVE MAY BE USED WHEN THE MANUFACTURER IS NOT KNOWN. OTHERWISE, THE MANUFACTURER SHOULD BE CONSULTED FOR THE APPLICABLE CORRECTION FACTOR.
Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008. Courtesy of the American Petroleum Institute.
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Chapter 7: Plant Design and Operation 7.5.2.5 Designs for Preventing Fires and Explosions Designs for Fire- and Explosion-Prevention Feature
Maintenance programs
Fireproofing Control rooms Water supplies Control valves for deluge Manual fire protection Separate units Utilities Personnel areas Group units Isolation valves Railroads and flares Compressors Dikes Block valves Online analyzers Fail-safe designs Safety-instrumented systems (SIS)
Explanation
The best way to prevent fires and explosions is to stop the release of flammable materials. Preventive maintenance programs are designed to upgrade systems before failures occur. Insulate vessels, pipes, and structures to minimize damage resulting from fires. Add deluge systems and design to withstand some damage from fires and explosions, e.g., use multiple deluge systems with separate shutoffs. Design control rooms to withstand explosions. Provide supply for maximum demand. Consider many deluge systems running simultaneously. Diesel-engine pumps are recommended. Place shutoffs well away from process areas. Install hydrants, monitors, and deluge systems. Add good drainage. Separate (space) plants on a site, and separate units within plants. Provide access from two sides. Design steam, water, electricity, and air supplies to be available during emergencies. Place substations away from process areas. Locate personnel areas away from hazardous process and storage areas. Group units in rows. Design for safe operation and maintenance. Create islands of risk by concentrating hazardous process units in one area. Space units so hot work can be performed on one group while another is operating. Install isolation valves for safe shutdowns. Install in safe and accessible locations at edge of unit or group. Process equipment should be separated from flares and railroads. Place gas compressors downwind and separated from fired heaters. Locate flammable storage vessels at edge of unit. Dike vessels to contain and carry away spills. Place automated block valves to stop and/or control flows during emergencies. Consider the ability to transfer hazardous materials from one area to another. Add appropriate online analyzers to (1) monitor the status of the process, (2) detect problems at their incipient stage, and (3) take appropriate action to minimize effects of problems while still in initial phase of development. Design all controls to fail safely. Add safeguards for automated and safe shutdowns during emergencies. Use SIS to automatically bring process to a safe state upon detection of potentially hazardous conditions.
Source: Davenport, John A., "Prevent Vapor Cloud Explosions," Hydrocarbon Processing: 1977, pp. 205–214.
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Chapter 7: Plant Design and Operation
7.5.3
Industrial Hygiene
Personal protective equipment (PPE) is designed to protect employees from serious injuries or illnesses resulting from contact with chemical, radiological, physical, electrical, mechanical, or other workplace hazards. Besides face shields, safety glasses, hard hats, and safety shoes, PPE includes a variety of devices and garments, such as goggles, coveralls, gloves, vests, earplugs, and respirators.
7.5.3.1 Respirators Assigned protection factors (APFs)—Per 29 CFR 1910.134, employers must use the assigned protection factors (listed in the table that follows) to select a respirator that meets or exceeds the required level of employee protection. When using a combination respirator (e.g., airline respirators with an air-purifying filter), employers must ensure that the assigned protection factor is appropriate to the mode of operation in which the respirator is being used. Immediately dangerous to life or health (IDLH)—An atmosphere that poses an immediate threat to life, would cause irreversible adverse health effects, or would impair an individual's ability to escape from a dangerous atmosphere. Powered air-purifying respirator (PAPR)—An air-purifying respirator that uses a blower to force the ambient air through air-purifying elements to the inlet covering. Supplied-air respirator (SAR) or airline respirator—An atmosphere-supplying respirator for which the source of breathing air is not designed to be carried by the user. Workplace protection factor (WPF) study—A study, conducted under actual conditions of use in the workplace, that measures the protection provided by a properly selected, fit-tested, and functioning respirator, when the respirator is worn correctly and used as part of a comprehensive respirator program that is in compliance with OSHA's Respiratory Protection Standard at 29 CFR 1910.134. Measurements of Co and Ci are obtained only while the respirator is being worn during performance of normal work tasks (that is, samples are not collected when the respirator is not being worn). As the degree of protection afforded by the respirator increases, the WPF increases. Simulated workplace protection factor (SWPF) study—A study, conducted in a controlled laboratory setting, in which Co and Ci sampling is performed while the respirator user performs a series of set exercises. The laboratory setting is used to control many of the variables found in workplace studies, while the exercises simulate the work activities of respirator users. This type of study is designed to determine the optimum performance of respirators by reducing the impact of sources of variability through maintenance of tightly controlled study conditions.
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Chapter 7: Plant Design and Operation Assigned Protection Factors5 Type of Respirator1,2
1. Air-purifying respirator 2. Powered air-purifying respirator (PAPR) 3. Supplied-air respirator (SAR) or airline respirator • Demand mode • Continuous flow mode • Pressure-demand or other positive-pressure mode 4. Self-contained breathing apparatus (SCBA) • Demand mode • Pressure-demand or other positive-pressure mode (e.g., open or closed)
Quarter Mask
Half Mask
Full Face Piece
Helmet/ Hood
LooseFitting Face Piece
5 —
103 50
50 1000
— 25/10004
— 25
— —
10 50
50 1000
— 25/10004
— 25
—
50
1000
—
—
—
10
50
50
—
—
—
10,000
10,000
—
Notes: 1. Employers may select respirators assigned for use in higher workplaces concentration of a hazardous substance for use at lower concentrations of that substance, or when required respirator use is independent of concentration. 2. The assigned protection factors in this table are only effective when the employer implements a continuing, effective respirator program as required by this section (29 CFR 1910.134), including training, fittesting, maintenance, and use requirements. 3. This APF category includes filtering face pieces, and half masks with elastomeric face pieces. 4. The employer must have evidence provided by the respirator manufacturer that testing of these respirators demonstrates performance at a level of protection of 1000 or greater to receive an APF of 1000. This level of performance can best be demonstrated by performing a WPF or SWPF study or equivalent testing. Absent such testing, all other PAPRs and SARs with helmets/hoods are to be treated as loose-fitting face piece respirators, and receive an APF of 25. 5. These APFs do not apply to respirators used solely for escape. Tor escape respirators used in association with specific substances covered by 29 CFR 1910 subpart Z, employers must refer to the appropriate substance-specific standards in that subpart. Escape respirators for other IDLH atmospheres are specified by 29 CFR 1910.134(d)(2)(ii). Source: Assigned Protection Factors for the Revised Respiratory Protection Standard, Washington, D.C.: Occupational Safety and Health Administration, 2009, p. 14.
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Chapter 7: Plant Design and Operation 7.5.3.2 Hazard Assessment The fire/hazard diamond below summarizes common hazard data available on the Safety Data Sheet (SDS) and is frequently shown on chemical labels.
A
B D
C
Position A – Health Hazard (Blue) 0 = Normal material 1 = Slightly hazardous 2 = Hazardous 3 = Extreme danger 4 = Deadly Position B – Flammability (Red) 0 = Will not burn 1 = Will ignite if preheated 2 = Will ignite if moderately heated 3 = Will ignite at most ambient temperature 4 = Burns readily at ambient conditions Position C – Reactivity (Yellow) 0 = Stable and not reactive with water 1 = Unstable if heated 2 = Violent chemical change 3 = Shock short may detonate 4 = May detonate Position D – (White) ALKALI = Alkali OXY = Oxidizer ACID = Acid Cor = Corrosive = Use no water W = Radiation
7.5.3.3 Globally Harmonized System (GHS) The Globally Harmonized System of Classification and Labeling of Chemicals, or GHS, is a system for standardizing and harmonizing the classification and labeling of chemicals. GHS is a comprehensive approach to:
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Defining health, physical, and environmental hazards of chemicals
•
Creating classification processes that use available data on chemicals for comparison with the defined hazard criteria
•
Communicating hazard information, as well as protective measures, on labels and Safety Data Sheets (SDSs), formerly called Material Safety Data Sheets (MSDSs). 478
Chapter 7: Plant Design and Operation GHS label elements include: •
Precautionary statements and pictograms: Measures to minimize or prevent adverse effects
•
Product identifier (ingredient disclosure): Name or number used for a hazardous product on a label or in the SDS
•
Supplier identification: The name, address, and telephone number of the supplier
•
Supplemental information: nonharmonized information
Other label elements include symbols, signal words, and hazard statements.
GHS Label Elements
GHS LABEL ELEMENTS Product Name Or Identifier (Identify Hazardous Ingredients, Where Appropriate)
Signal Word Physical, Health, Environmental, Hazard Statements Supplemental Information Precautionary Measures And Pictograms
First Eight Statements Name and Address of Company Telephone Number
Note: Pictograms for hazard statements must have red borders. Source: A Guide to the Globally Harmonized System of Classification and Labeling of Chemicals (GHS), Washington, D.C.: Occupational Safety and Health Administration, 2009, p. 38.
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Chapter 7: Plant Design and Operation HCS Quick Card SAMPLE LABEL
CODE _______________________________ Product Name________________________
}
Product Identifier
Company Name_______________________ Street Address________________________ City_______________________ State_____ Postal Code______________Country_____ Emergency Phone Number_____________
}
Supplier Identification
E L
P M A S
Keep container tightly closed. Store in a cool, well-ventilated place that is locked. Keep away from heat/sparks/open flame. No smoking. Only use non-sparking tools. Use explosion-proof electrical equipment. Take precautionary measures against static discharge. Ground and bond container and receiving equipment. Do not breathe vapors. Wear protective gloves. Do not eat, drink or smoke when using this product. Wash hands thoroughly after handling. Dispose of in accordance with local, regional, natio national, onal, international regulations as specified.
In Case of Fire: use dry chemical (BC) C) oorr Ca C Carbon arbo b n Dioxi Dioxide xide de ((C (CO CO2) fire extinguisher to extinguish. First Aid If exposed call Poison Center. If on skin (or hair): Take off immediately tely ly aany ny ccontaminated onta clothing. Rinse skin with water.
S Signal Word Danger
}
Highly H gh flammable liquid and vapor. Hi May M cause liver and kidney damage.
Hazard Statements
Precautionary P reca e ut Statements Sta St ate
Supplemental Information
Directions for Use __________________________________ __________________________________ __________________________________ Fill weight:____________ Lot Number:___________ Gross weight:__________ Fill Date:______________ Expiration Date:________
Note: Pictograms for hazard statements must have red borders. Source: A Guide to the Globally Harmonized System of Classification and Labeling of Chemicals (GHS), Washington, D.C.: Occupational Safety and Health Administration, 2009, p. 40.
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OSHA 3492-01R 2016
}
Hazard P Pictograms
Chapter 7: Plant Design and Operation HCS Pictograms and Hazards Card
Note: Pictograms for hazard statements must be printed with red borders. Source: A Guide to the Globally Harmonized System of Classification and Labeling of Chemicals (GHS), Washington, D.C., Occupational Safety and Health Administration.
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Chapter 7: Plant Design and Operation Acute Oral Toxicity CATEGORY 1
CATEGORY 2
≤ 5 mg/kg
> 5 < 50 mg/kg
LD50
CATEGORY 3
CATEGORY 4
50 < 300 mg/kg
CATEGORY 5
300 < 2000 mg/kg
PICTOGRAM
2000 > 5000 mg/kg
NO SYMBOL
SIGNAL WORD
DANGER
HAZARD STATEMENT FATAL IF SWALLOWED
DANGER
DANGER
WARNING
WARNING
FATAL IF SWALLOWED
TOXIC IF SWALLOWED
HARMFUL IF SWALLOWED
MAY BE HARMFUL IF SWALLOWED
Source: A Guide to the Globally Harmonized System of Classification and Labeling of Chemicals (GHS), Washington, D.C.: Occupational Safety and Health Administration, 2009, p. 41.
7.5.3.4 Safety Data Sheets (SDS) Source: Appendix D to OSHA CFR 1910.1200 - Safety Data Sheets (Mandatory).
A safety data sheet (SDS) must include the information in the table below under the section number and heading indicated for Sections 1–11 and 16. If no relevant information is found for any given subheading within a section, the SDS must clearly indicate that no applicable information is available. Sections 12–15 may be included in the SDS, but are not mandatory.
Minimum Information for a Safety Data Sheet Heading
1.
2.
Identification
Hazard(s) Identification
Subheading
a. b. c. d. e. a. b.
c. d.
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Product identifier used on the label Other means of identification Recommended use of the chemical and restrictions on use Name, address, and telephone number of the chemical manufacturer, importer, or other responsible party Emergency phone number Classification on the chemical in accordance with paragraph (d) of §1910.1200 Signal word, hazard statement(s), symbol(s), and precautionary statement(s) in accordance with paragraph (f) of §1910.1200. (Hazard symbols may be provided as graphical reproductions in black and white or the name of the symbol, e.g., flame, skull and crossbones) Describe any hazards not otherwise classified that have been identified during the classification process Where an ingredient with unknown acute toxicity is used in a mixture at a concentration = 1% and the mixture is not classified based on testing of the mixture as a whole, a statement that X % of the mixture consists of ingredient(s) of unknown acute toxicity is required
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Chapter 7: Plant Design and Operation Minimum Information for a Safety Data Sheet (cont'd) 3.
Heading
Subheading
Composition and Information on Ingredients
Except as provided for in paragraph (i) of §1910.1200 on trade secrets: For Substances a. b. c. d.
Chemical name Common name and synonyms CAS number and other unique identifiers Impurities and stabilizing additives that are themselves classified and that contribute to the classification of the substance
For Mixtures In addition to the information required for substances: a. The chemical name and concentration (exact percentage) or concentration ranges of all ingredients that are classified as health hazards in accordance with paragraph (d) of §1910.1200 and either (1) Are present above their cut-off/concentration limits (2) Present a health risk below the cut-off/concentration limits b. The concentration (exact percentage) shall be specified unless a trade secret claim is made in accordance with paragraph (i) of §1910.1200, when there is batch-to-batch variability in the production of a mixture, or for a group of substantially similar mixtures (See A.0.5.1.2) with similar chemical composition. In these cases, concentration ranges may be used. For All Chemicals for Which a Trade Secret Is Claimed
4.
First-aid Measures
5.
Fire-fighting Measures
6.
Accidental Release Measures
7.
Handling and Storage
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When a trade secret is claimed in accordance with paragraph (i) of §1910.1200, a statement that the specific chemical identity and/or exact percentage (concentration) of composition has been withheld as a trade secret is required. a. Description of necessary measures, subdivided according to the differ ent routes of exposure, i.e., inhalation, skin and eye contact, and ingestion b. Most important symptoms/ effects, acute and delayed c. Indication of immediate medical attention and special treatment needed, if necessary a. Suitable (and unsuitable) extinguishing media b. Specific hazards arising from the chemical (e.g., nature of any hazard ous combustion products) c. Special protective equipment and precautions for fire-fighters a. Personal precautions, protective equipment, and emergency procedures b. Methods and materials for containment and cleaning up a. Precautions for safe handling b. Conditions for safe storage, including any incompatibilities
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Chapter 7: Plant Design and Operation Minimum Information for a Safety Data Sheet (cont'd) Heading
Subheading
8.
Exposure Controls and Personal Protection
9.
Physical and Chemical Properties
10.
Stability and Reactivity
11.
Toxicological Information
a. OSHA permissible exposure limit (PEL), American Conference of Governmental Industrial Hygienists' (ACGIH) threshold limit value (TLV), and any other exposure limit used or recommended by the chemical manufacturer, importer, or employer preparing the safety data sheet, where available b. Appropriate engineering controls c. Individual protection measures, such as personal protective equipment a. Appearance (physical state, color, etc.) b. Odor c. Odor threshold d. pH e. Melting point/freezing point f. Initial boiling point and boiling range g. Flash point h. Evaporation rate i. Flammability (solid, gas) j. Upper/lower flammability or explosive limits k. Vapor pressure l. Vapor density m. Relative density n. Solubility(ies) o. Partition coefficient: n-octanol/water p. Auto-ignition temperature q. Decomposition temperature r. Viscosity a. Reactivity b. Chemical stability c. Possibility of hazards reactions d. Conditions to avoid (e.g., static discharge, shock, or vibration) e. Incompatible materials f. Hazardous decomposition products Description of the various toxicological (health) effects and the available data used to identify those effects, including:
12.
Ecological Information (Nonmandatory)
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a. Information on the likely routes of exposure (inhalation, ingestion, skin and eye contact b. Symptoms related to the physical, chemical, and toxicological characteristics c. Delayed and immediate effects and also chronic effects from short- and long-term exposure d. Numerical measures of toxicity (such as acute toxicity estimates) e. Whether the hazardous chemical is listed in the National Toxicology Program (NTP) Report on Carcinogens (latest edition) or has been found to be a potential carcinogen in the International Agency for Research on Cancer (IARC) Monographs (latest editions), or by OSHA a. Ecotoxicity (aquatic and terrestrial, where available) b. Persistence and degradability c. Bioaccumulative potential d. Mobility in soil e. Other adverse effects (such as hazardous to the ozone layer)
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Chapter 7: Plant Design and Operation Minimum Information for a Safety Data Sheet (cont'd) Heading
13. 14.
15. 16.
Subheading
Disposal Considerations (Nonmandatory) Transport Information (Nonmandatory)
Description of waste residues and information on their safe handling and method of disposal, including disposal of any contaminated packaging. a. UN number b. UN proper shipping name c. Transport hazard class(es) d. Packing group, if applicable e. Environmental hazards (e.g., Marine pollutant [Yes/No]) f. Transport in bulk (according to Annex II of MARPOL 73/78 and IBC Code) g. Special precautions which a user needs to be aware of, or needs to comply with, in connection with transport or conveyance either within or outside their premises Regulatory Information (NonSafety, health, and environmental regulations specific for the product in mandatory) question Other Information, Including Date The date of preparation of the SDS or the last change to it of Preparation or Last Revision
Source: Hazard Communication, "Safety Data Sheets," Washington, D.C.: Occupational Safety and Health Administration.
7.5.3.5 Pesticides This section establishes four toxicity categories for acute hazards of pesticide products. Category I is the highest category. Most human hazard, precautionary statements, and human personal protective equipment statements are based on the toxicity category of the pesticide product as sold or distributed. In addition, toxicity categories may be used for regulatory purposes other than labeling, such as classification for restricted use and requirements for child-resistant packaging. In certain cases, statements based on the toxicity category of the product as diluted for use are also permitted. A toxicity category is assigned for each of five types of acute exposure, as specified in the table below.
Acute Toxicity Categories for Pesticide Products Hazard Indicators
Oral LD50 Dermal LD50 Inhalation LC50 Eye irritation
Skin irritation
I
Up to and including 50 mg/kg Up to and including 200 mg/kg Up to and including 0.2 mg/liter Corrosive: corneal opacity not reversible within 7 days Corrosive
II
III
>50 through 500 mg/kg
>500 through 5000 mg/kg
> 5000 mg/kg
>200 through 2000 mg/kg
>2000 through 20,000 mg/kg
>20,000 mg/kg
>0.2 through 2 mg/liter
>2 through 20 mg/liter
>20 mg/liter
Corneal opacity reversible within 7 days; irritation persisting for 7 days
No corneal opacity; irritation reversible within 7 days
No irritation
Severe irritation at 72 hours
Moderate irritation at 72 hours
Mild or slight irritation at 72 hours
Source: From Regulating Pesticides, U.S. Environmental Protection Agency.
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Chapter 7: Plant Design and Operation Pesticide Toxicity Categories Toxicity Category
Signal Word
I II III IV
Poison Warning Caution Caution
Source: 40 CFR 156: Labeling Requirements for Pesticides and Devices: U.S. Environmental Protection Agency, p. 68.
7.5.3.6 Fundamentals of Ventilation Ventilation Definitions Aerosol: An assemblage of small particles, solid or liquid, suspended in air. The diameter of the particles may vary from 100 microns down to 0.01 micron or less, e.g., dust, fog, smoke. Air cleaner: A device designed for the purpose of removing atmospheric airborne impurities such as dusts, gases, mists, vapors, fumes, and smoke. (Air cleaners include air washers, air filters, electrostatic precipitators, and charcoal filters.) Air filters: An air-cleaning device that removes light particulate loadings from normal atmospheric air before introducing into the building. Usual range: loadings up to 3 grains per thousand cubic feet (0.003 grains per cubic foot). Note: Atmospheric air in heavy industrial areas and in-plant air in many industries have higher loadings than this, and dust collectors are then indicated for proper air cleaning. W Aspect ratio: The ratio of the width (W) to the length (L); AR = L . Aspect ratio of an elbow: The width (W) along the axis of the bend divided by the depth (D) in the plane of the W bend; AR = D . Blast gate: Sliding damper. Capture velocity: The air velocity at any point in front of the hood or at the hood opening necessary to overcome opposing air currents and capture the contaminated air at that point by causing it to flow into the hood. Density factor: The ratio of actual air density to density of standard air. The product of the density factor and the lb lb ) gives the actual air density in pounds per cubic foot; Density = df # 0.075 3 . ft 3 ft Dust: Small solid particles created by breakup of larger particles by processes, such as crushing, grinding, drilling, and explosions. Dust particles already in existence in a mixture of materials may escape into the air through such operations as shoveling, conveying, screening, or sweeping. density of standard air (0.075
Dust collector: An air-cleaning device to remove heavy particulate loadings from exhaust systems. Usual range of particulate loading: 0.003 grains per cubic foot or higher. Entry loss: Loss in pressure caused by air flowing into a duct or hood (inches H2O). Fumes: Small solid particles formed by the condensation of vapors of solid materials. Gases: Formless fluids that tend to occupy an entire space uniformly at ordinary temperatures and pressures.
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Chapter 7: Plant Design and Operation Hood: A shaped inlet designed to capture contaminated air and conduct it into the exhaust duct system. Hood flow coefficient: The ratio of flow caused by a given hood static pressure compared to the theoretical flow that would result if the static pressure could be converted to velocity pressure with 100 percent efficiency. Inch of water: A unit of pressure equal to the pressure exerted by a column of liquid water one inch high at a standard temperature. Minimum design duct velocity: Minimum air velocity required to move the particles in the air stream (fpm). Mists: Small droplets of materials that are ordinarily liquid at normal temperature and pressure. Pressure, static: The potential pressure exerted in all directions by a fluid at rest. For a fluid in motion, it is measured in a direction normal to the direction of flow. Usually expressed in inches of water gauge when dealing with air. (The tendency to either burst or collapse the pipe.) Pressure, total: The algebraic sum of the velocity pressure and the static pressure (with due regard to sign). Pressure, velocity: The kinetic pressure in the direction of flow necessary to cause a fluid at rest to flow at a given velocity. Usually expressed in inches of water gauge. Replacement air: A ventilation term used to indicate the volume of controlled outdoor air supplied to a building to replace air being exhausted. Slot velocity: Linear flow rate of contaminated air through a slot, fpm. Smoke: An air suspension (aerosol) of particles, usually but not necessarily solid, often originating in a solid nucleus, formed from combustion or sublimation. Standard air: Dry air at 70°F and 29.92 (in Hg) barometer. This is substantially equivalent to 0.075
lb . Specific ft 3
heat of dry air = 0.24 Btu/lb/°F. Turn-down ratio: The degree to which the operating performance of a system can be reduced to satisfy part-load conditions. Usually expressed as a ratio; for example, 30:1 means the minimum operation point is 1/30th of full load. Source: From ACGIH®, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., © 2013. Reprinted with permission.
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Chapter 7: Plant Design and Operation Ventilation Abbreviations Abbreviation
Definition
AR As
Aspect ratio Slot area
B Cc
Barometric pressure Hood flow coefficient
CLR df dfe dfm dfp dft F ld Fel Fen Fh Fs gr H hd he hel hen hh hs HEPA
Abbreviation
HVAC "wg L mo
Definition
Heating, ventilation, and air conditioning Inches water gauge Length Mass flow rate
Centerline radius Overall density factor Elevation density factor Moisture density factor Pressure density factor Temperature density factor Loss per unit length (duct)
ME mm wg MRT Q sfpm SP SPgov
Elbow loss coefficient Entry loss coefficient Hood entry-loss coefficient Slot loss coefficient Grains Height Loss in straight duct run Overall hood entry loss Elbow loss Entry loss Hood entry loss
SPh SPs TP V Vd VP VPd VPr VPs Vs Vt
Hood static pressure SP, system handling standard air Total pressure Velocity, in fpm Duct velocity Velocity pressure Duct velocity pressure Resultant velocity pressure Slot velocity pressure Slot velocity Duct transport velocity
Slot or opening entry loss
~
lbm H O Moisture content, in lbm dry2 air
High-efficiency particulate air filter
z
Elevation, in feet above sea level
Mechanical efficiency Millimeters water gauge Mean radiant temperature Flow rate, in cfm Surface feet per minute Static pressure Higher static pressure at junction of 2 ducts
ft 3 mix Humid volume, in lb dry air
HV
Source: From ACGIH®, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., © 2013. Reprinted with permission.
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Chapter 7: Plant Design and Operation Ventilation Equations Description
Equation
Velocity pressure (VP)
2 tV 2 = c V m df 2g c 4005
= VP
Units
V in fpm VP in "wg "wg
TP = SP +VP
Total pressure (TP)
"wg hh = Fh(VPd)
Hood entry loss (hh)
Values of Fh can be found in the Hood Loss Coefficients table later in this chapter.
SPh = – (VPd + hh)
Hood static pressure (SPh)
"wg
0 50 % OF DIAMETER
100
0
7. 5% 7.5%
15%
30%
100% 60%
7.5% 7. 5%
15%
30%
60%
100%
Velocity Contours Plain Circular Opening—% of Opening Velocity Flanged Circular Opening—% of Opening Velocity
50 100 % OF DIAMETER
Source: From ACGIH®, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., © 2013. Reprinted with permission.
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Chapter 7: Plant Design and Operation Summary of Hood Airflow Equations Aspect Ratio, W/L
Hood Type
Description
L X
Airflow
Slot
0.2 or less
Q = 3.7 LVXX
Flanged Slot
0.2 or less
Q = 2.6 LVXX
Plain opening
0.2 or greater and round
Q = VX(10X 2 + A)
Flanged opening
0.2 or greater and round
Q = 0.75VX(10X 2 + A)
Booth
To suit work
Q = VA = VWH
W
X
L
W X
A = WL
X
H W
Q = 1.4 PVD D
L
W X
L
W X
Canopy
To suit work
Plain multiple-slot opening, 2 or more slots
0.2 or greater
Q = VX(10X 2 + A)
Flanged multiple-slot opening, 2 or more slots
0.2 or greater
Q = 0.75VX(10X 2 + A)
P = Perimeter D = Height above work
Source: From ACGIH®, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., © 2013. Reprinted with permission. ©2017 NCEES
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7.5.3.7 Flow-Capture Velocity of Suspended Hoods (Small Side-Draft Hoods) Freely Suspended Hood L
H
X
Q
SOURCE Q = VX(10X 2 + A) Large Hood
SOURCE
X 2X
For a large hood with small X, measure X perpendicular to the hood face and not less than 2X from the edge of the opening. Hood on Bench or Floor SOURCE
X
Q
Q = VX(5X 2 + A) Hood with Wide Flange
SOURCE X
Q FLANGE WIDTH ≥ A
Q = 0.75VX(10X 2 + A)
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Chapter 7: Plant Design and Operation where
m3 Q = required exhaust airflow, in acfm or s X = distance from hood face to farthest point of contamination, in ft or m A = hood face area, in ft2 or m2 m VX = capture velocity at distance X, in fpm or s , at distance X
Note: Airflow rate must increase as the square of distance of the source from the hood. Baffling by flanging or by placing on bench, floor, etc. has a beneficial effect. Source: Hood illustrations in this section are from ACGIH®, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., © 2013. Reprinted with permission.
7.5.3.8 Flow-Capture Velocity of Canopy Hood 45° MINIMUM 0.4D
D
Q = 1.4 PDV where P = Perimeter of tank, in ft or m m Not recommended if workers must bend over source. V ranges from 50 to 500 fpm or 0.25 to 2.50 s , depending on crossdrafts. Side curtains on two or three sides to create a semi-booth or booth are desirable.
Recommended Capture Velocities Energy of Dispersion
VX
Examples
Little motion
Evaporation from tanks, degreasing Intermittent container filling, low-speed Average motion conveyor transfers, welding, plating, pickling High Barrel filling, conveyor loading, crushers Very high Grinding, abrasive blasting, tumbling Factors affecting choices within ranges:
ft min 75–100
m s 0.38–0.51
100–200
0.51–1.02
200–500 500–2000
1.02–2.54 2.54–10.2
• Strength of cross-drafts due to makeup air, traffic, etc. • Need for effectiveness in collection: - Toxicity of contaminants produced by the source - Exposures from other sources, which reduce acceptable exposure from this source - Quantity of air contaminants generated: production rate, volatility, time generated Source: From ACGIH®, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., © 2013. Reprinted with permission. ©2017 NCEES
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Chapter 7: Plant Design and Operation Hood Type Efficiency
Hood Loss Coefficients Hood Type
Description
Hood Entry Loss (Fh) Coefficient
Plain opening
0.93
Flanged opening
0.49
Taper or cone hood
0.15–0.4
Bell mouth inlet
0.04
Orifice
0.55 when duct velocity = slot velocity
Straight takeoff: 0.65 Typical grinding hood Tapered takeoff: 0.40 Source: From ACGIH®, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., © 2013. Reprinted with permission.
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Chapter 7: Plant Design and Operation 7.5.3.9 Electrical Safety Probable Effects of Various Levels of Current on the Human Body Level of Current (milliamperes)
1 mA 5 mA 6 mA-16 mA 17 mA-99 mA 100 mA-2000 mA >2000 mA
Probable Effect
Perception level. Slight tingling sensation. Still dangerous under certain conditions. Slight shock felt; not painful but disturbing. Average individual can let go. However, strong involuntary reactions to shocks in this range may lead to injuries. Painful shock; begin to lose muscular control. Commonly referred to as the freezing current or "let-go" range. Extreme pain, respiratory arrest, severe muscular contractions. Individual cannot let go. Death is possible. Ventricular fibrillation (uneven, uncoordinated pumping of the heart). Muscular contraction and nerve damage begins to occur. Death is likely. Cardiac arrest, internal organ damage, and severe burns. Death is probable.
Sources: NIOSH, Worker Deaths by Electrocution; A Summary of NIOSH Surveillance and Investigative Findings, Ohio: U.S. Health and Human Services, 1998. And Greenwald, E.K., Electrical Hazards and Accidents—Their Cause and Prevention, New York: Van Nostrand Reinhold, 1991.
7.5.3.10 Risk Assessment/Toxicology The Dose-Response Curve The dose-response curve relates toxic response (i.e., percentage of test population exhibiting a specified symptom mg or dying) to the logarithm of the dosage (i.e., kg : day ingested). A typical dose-response curve is shown below.
TOXIC RESPONSE %
Typical Dose-Response Curve 100
TOXICANT
50
10 LD10 LD50 LOGARITHM OF LD50 DOSE
where LC50 = Median lethal concentration in air that, based on laboratory tests, is expected to kill 50% of a group of test animals when administered as a single exposure over one or four hours. LD50 = Median lethal single dose, based on laboratory tests, expected to kill 50% of a group of test animals, usually by oral or skin exposure. Similar definitions exist for LC10 and LD10, where the corresponding percentages are 10%.
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Chapter 7: Plant Design and Operation The following table lists the LD50 values for several chemicals:
Comparative Acutely Lethal Doses Actual Ranking Number
1 2 3 4 5 6 7 8 9 10 11 12 13
LD50 e
mg o kg
Toxic Chemical
15,000 10,000 4000 1500 1375 900 150 142 2 1 0.5 0.001 0.00001
PCBs Alcohol (ethanol) Table salt—sodium chloride Ferrous sulfate—an iron supplement Malathion—a pesticide Morphine Phenobarbital—a sedative Tylenol (acetaminophen) Strychnine Nicotine Curare—an arrow poison 2,3,7,8-TCDD (dioxin) Botulinum toxin (food poison)
Adapted from Loomis, T.A., and A.W. Hayes. Loomis's Essentials of Toxicology, 4th ed., San Diego: Academic Press, 1996.
Selected Chemical Interaction Effects Effect
Relative toxicity (hypothetical)
Additive Synergistic
2+3=5 2 + 3 = 20
Antagonistic
6+6=8
Example
Organophosphate pesticides Cigarette smoking + asbestos Toluene + benzene or caffeine + alcohol
Adapted from Williams, P.L., R.C. James, and S.M. Roberts. Principles of Toxicology: Environmental and Industrial Applications, 2nd ed., New York: Wiley, 2000.
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Chapter 7: Plant Design and Operation Exposure Limits for Selected Compounds(a) Regulatory Limits Substance
CAS
No.(c)
OSHA PEL(b) ppm (d)
mg m3
(e)
Recommended Limits NIOSH REL(g) ACGIH® 2015 (as of 4/26/13) TLV® (h) Up to 10-hour TWA, 8-hour TWA, (ST) STEL, (ST) STEL, (C) Ceiling (f) (C) Ceiling
Acetic acid
64-19-7
10
25
10 ppm (ST) 15 ppm
Acetone
67-64-1
1000
2400
250 ppm
Benzoyl peroxide
94-36-0
5
5
mg m3
0.1 ppm (ST) 0.3 ppm (C) 0.5 ppm [15-min] 5000 ppm (ST) 30,000 ppm 35 ppm (C) 200 ppm (C) 0.5 ppm [15-min] (ST) 2 ppm [60-min]
Bromine
7726-95-6
0.1
0.7
Butyl mercaptan
109-79-5
10
35
Carbon dioxide
124-38-9
5000
9000
Carbon monoxide
630-08-0
50
55
Chlorine
7782-50-5
(C) 1
(C) 3
Chloroform (trichloromethane)
67-66-3
(C) 50
(C) 240
Cresol, all isomers
1319-77-3
5
22
2.3 ppm
Cumene Ethyl alcohol (ethanol)
98-82-8 64-17-5
50 1000
245 1900
50 ppm 1000 ppm
Ethyl ether
60-29-7
400
1200
N/A
Iodine
7553-56-2
(C) 0.1
(C) 1
(C) 0.1 ppm
Isopropyl ether
108-20-3
500
2100
500 ppm
68476-85-7
1000
1800
1000 ppm
Methyl mercaptan
74-93-1
(C) 10
(C) 20
Naphthalene
91-20-3
10
50
10028-15-6
0.1
0.2
L.P.G. (liquefied petroleum gas)
Ozone
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(C) 0.5 ppm [15-min] 10 ppm (ST) 15 ppm (C) 0.1 ppm
10 ppm (ST) 15 ppm 250 ppm (ST) 500 ppm mg 5 3 m 0.1 ppm (ST) 0.2 ppm 0.5 ppm 5000 ppm (ST) 30,000 ppm 25 ppm 0.5 ppm (ST) 1 ppm 10 ppm 20
mg (IFV) m3
50 ppm (ST) 1000 ppm 400 ppm (ST) 500 ppm 0.01 ppm (IFV) (ST) 0.1 ppm (V) 250 ppm (ST) 310 ppm N/A 0.5 ppm 10 ppm (ST) 15 ppm 0.05–0.20 ppm depending on workload and time
Chapter 7: Plant Design and Operation Exposure Limits for Selected Compounds(a) (cont'd) Regulatory Limits Substance
CAS No.(c)
OSHA PEL(b) ppm (d)
Phosphoric acid
mg m3
(e)
7664-38-2
N/A
1
Propane
74-98-6
1000
1800
n-Propyl alcohol
71-23-8
200
500
Sulfuric acid
1,1,1-Trichloroethane (methyl chloroform)
7664-93-9
71-55-6
1
350
1900
Recommended Limits NIOSH REL(g) ACGIH® 2015 (as of 4/26/13) TLV® (h) Up to 10-hour TWA, 8-hour TWA, (ST) STEL, (ST) STEL, (C) Ceiling (f) (C) Ceiling
mg m3 mg (ST) 3 3 m 1000 ppm 200 ppm (ST) 250 ppm 1
1
mg m3
350 ppm (ST) 450 ppm (C) 800 ppm
mg m3 mg (ST) 3 3 m N/A 1
100 ppm 0.2
mg m3
(Thoracic-size fraction) 350 ppm (ST) 450 ppm
a. Columns 3 and 4 list PELs from OSHA Table Z-1 in 29 CFR 1910.1000. Columns 5 and 6 list other occupational exposure limits (OELs) from NIOSH and ACGIH®. b. Occupational Safety and Health Administration (OSHA) Permissible Exposure Limits (PELs) from 29 CFR 1910.1000 Z-1 Table [58 FR 35340, June 30, 1993; 58 FR 40191, July 27, 1993, as amended at 61 FR 56831, Nov. 4, 1996; 62 FR 1600, Jan 10,1997; 62 FR 42018, Aug. 4, 1997; 71 FR 10373, Feb. 28, 2006; 71 FR 16673, Apr. 3, 2006; 71 FR 36008, June 23, 2006.]. PELs are 8-hour time-weighted averages (TWAs), unless otherwise indicated. OSHA enforces these limits under section 5(a)(2) of the OSH Act. In addition to the values listed in this table, the Z tables in 29 CFR 1910.1000 list skin absorption designations. c. The CAS number is for information only. Enforcement is based on the substance name. For an entry covering more than one metal compound measured as the metal, the CAS number for the metal is given—not CAS numbers for the individual compounds. d. Parts of vapor or gas per million parts of contaminated air by volume at 25 oC and 760 torr. e. Milligrams of substance per cubic meter of air. When entry is in this column only, the value is exact; when listed with a ppm entry, it is approximate. f. TWA indicates a time-weighted average concentration. A short-term exposure limit (STEL) is designated by ST preceding the value; unless noted otherwise, the STEL is a 15-minute TWA exposure that should not be exceeded at any time during a work day. A ceiling REL is designated by C preceding the value; unless noted otherwise, the ceiling value should not be exceeded at any time. g. National Institute for Occupational Safety and Health (NIOSH) Recommended Exposure Limits (RELs) from the NIOSH Pocket Guide to Chemical Hazards (http://www.cdc.gov/niosh/npg) (NIOSH 2007). RELs are for up to 10-hour time weighted averages (TWAs) during a 40-hour work week, unless otherwise indicated. NIOSH has established occupational exposure limits for compounds not included in the OSHA Z Tables. Please see the NIOSH Pocket Guide for additional limits, skin absorption and other designations, and explanations.
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Chapter 7: Plant Design and Operation h. ACGIH® Threshold Limit Values (TLVs®) (ACGIH® 2015). TLVs® are listed in the order of 8-hour timeweighted averages (TWAs), STELs (ST), and Ceilings (C), if available. ACGIH® has established TLVs® for compounds not included in the OSHA Z Tables. Please see ACGIH® Documentation for additional limits, skin absorption and other designations, and explanations. The 2015 TLV® and BEI® Book and Documentation of the Threshold Limit Values on Chemical Substances, 7th Edition, are available through the ACGIH® website at http://www.acgih.org. The TLVs® and BEIs® are copyrighted by ACGIH® and are not publicly available. Permission must be requested from ACGIH® to reproduce the TLVs® and BEIs®. Carcinogens For carcinogens, the EPA considers an acceptable risk to an individual to be a lifetime excess cancer risk within the range of 10-4 to 10-6. The added risk of cancer is calculated as follows: Risk = dose # toxicity = CDI # CSF where CDI = Chronic daily intake CSF = Cancer slope factor, the slope of the dose-response curve for carcinogenic materials X X
RESPONSE
X X
X NO THRESHOLD LINEAR AT LOW DOSE
DOSE CARCINOGENIC DOSE RESPONSE CURVE
Noncarcinogens For noncarcinogens, a hazard index (HI) characterizes the risk from all pathways and exposure routes. The EPA considers that an HI > 1.0 represents an unacceptable risk of an adverse effect occurring. CDI noncarcinogen HI = RfD where CDInoncarcinogen = chronic daily intake of noncarcinogenic compound RfD
= reference dose X
RESPONSE
X
X X
X
NOAEL RfD
X
THRESHOLD
DOSE
NONCARCINOGENIC DOSE RESPONSE CURVE
mass of chemical Dose is expressed as d body weight # exposure time n NOAEL = No observable adverse effect level (the dose below which no harmful effects are apparent)
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Chapter 7: Plant Design and Operation Reference Dose Reference dose (RfD) is determined from the noncarcinogenic dose-response curve using the NOAEL: RfD = lifetime (i.e., chronic) dose that a healthy person could be exposed to daily without adverse effects RfD = and
NOAEL UF
SHD = RfD # W =
NOAEL # W UF
where SHD
= safe human dose (mg/day)
mg NOAEL = threshold dose per kg of test animal kg day from the dose-response curve UF
= the total uncertainty factor, depending on nature and reliability of the animal test data
W
= the weight of the adult male (typically 70 kg)
Exposure
Residential Exposure Equations for Various Pathways Pathway
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Exposure Equation
Ingestion in drinking water
CDI =
Ingestion while swimming
CDI =
Dermal contact with water
AD =
Ingestion of chemicals in soil
CDI =
Dermal contact with soil
AD =
Inhalation of airborne (vapor phase) chemicals
CDI =
Ingestion of contaminated fruits, vegetables, fish, and shellfish
CDI =
499
^CW h^ IRh^ EF h^ ED h ^ BW h^ AT h
^CW h^CRh^ ET h^ EF h^ EDh ^ BW h^ AT h
^CW h^SA h^ PC h^ ET h^ EF h^ ED h^CF h ^ BW h^ AT h ^CS h^ IRh^CF h^ FI h^ EF h^ ED h ^ BW h^ AT h
^CW h^CF h^SAh^ AF h^ ABS h^ EF h^ ED h ^ BW h^ AT h ^CAh^ IRh^ ET h^ EF h^ ED h ^ BW h^ AT h
^CF h^ IRh^ FI h^ EF h^ EDh ^ BW h^ AT h
Chapter 7: Plant Design and Operation where ABS = absorption factor for soil contaminant is unitless mg AD = absorbed dose in kg : day mg cm 2
AF = soil-to-skin adherence factor in AT = averaging time in days BW = body weight in kg
CA = contaminant concentration in air in mg CDI = chronic daily intake in kg : day
mg m3
CF = volumetric conversion factor for water is -
10 6 kg = conversion factor for soil in mg L CR = contact rate in hr mg CS = chemical concentration in soil in kg mg CW = chemical concentration in water in L
1L 1000 cm3
ED = exposure duration in years days events EF = exposure frequency in year or year hr hr ET = exposure time in day or event FI = fraction ingested is unitless mg soil kg L IR = ingestion rate in day or day or meal
m3 = inhalation rate in hr
cm PC = Chemical-specific dermal permeability constant in hr SA = skin surface area available for contact in cm2 Source: Risk Assessment Guidance for Superfund: Volume 1, Human Health Evaluation Manual (Part A), 1st ed., Washington, D.C.: U.S. Environmental Protection Agency, 1989, pp. 6-40–6-48.
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Chapter 7: Plant Design and Operation 7.5.3.11 Intake Rates EPA-Recommended Values for Estimating Intake Parameter Average body weight, female adult Average body weight, male adult Average body weight, childa 6-11 months 1-5 years 6-12 years Amount of water ingested, adult Amount of water ingested, child Amount of air breathed, female adult Amount of air breathed, male adult Amount of air breathed, child (3-5 years) Amount of fish consumed, adult Water swallowing rate, while swimming Inhalation rates adult (6-hr day) adult (2-hr day) child Skin surface available, adult male Skin surface available, adult female Skin surface available, child 3-6 years (average for male and female) 6-9 years (average for male and female) 9-12 years (average for male and female) 12-15 years (average for male and female) 15-18 years (female) 15-18 years (male) Soil ingestion rate, child 1-6 years Soil ingestion rate, persons > 6 years Skin adherence factor, gardener's hands Skin adherence factor, wet soil Exposure duration Lifetime (carcinogens; for noncarcinogens use, actual exposure duration) At one residence, 90th percentile National median Averaging time
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Standard Value 65.4 kg 78 kg 9 kg 16 kg 33 kg 2.3 L/day 1.5 L/day 11.3 m3/day 15.2 m3/day 8.3 m3/day 6 g/day 50 mL/hr 0.98 m3/hr 1.47 m3/hr 0.46 m3/hr 1.94 m2 1.69 m2 0.720 m2 0.925 m2 1.16 m2 1.49 m2 1.60 m2 1.75 m2 >100 mg/day 50 mg/day 0.07 mg/cm2 0.2 mg/cm2 75 years 30 years 5 years (ED) (365 days/year)
Chapter 7: Plant Design and Operation EPA-Recommended Values for Estimating Intake (cont'd) Parameter Standard Value Exposure Frequency (EF) Swimming 7 days/year Eating fish and shellfish 48 days/year Oral ingestion 350 days/year Exposure time (ET) Shower, 90th percentile 12 min Shower, 50th percentile 7 min aData
in this category taken from Copeland, T., A. M. Holbrow, J. M. Otan, et al. "Use of probabilistic methods to understand the conservatism in California's approach to assessing health risks posed by contaminants." Journal of the Air and Waste Management Association, Vol. 44, pp. 1399–1413, 1994. Source: U.S. Environmental Protection Agency, Risk Assessment Guidance for Superfund: Volume 1, Human Health Evaluation Manual (part A), EPA/540/1-89/002,1989.
7.5.3.12 Concentrations of Vaporized Liquids Vaporization rate (Qm, mass/time) from a liquid surface: Qm = =
MKA s P sat G Rg TL
where M = molecular weight of volatile substance K = mass transfer coefficient As = area of liquid surface Psat = saturation vapor pressure of the pure liquid at TL Rg = ideal gas constant TL = absolute temperature of the liquid Mass flow rate of liquid from a hole in the wall of a process unit: Qm = AHC0 (2tgcPg) ½ where AH = area of hole C0 = discharge coefficient ρ = density of the liquid Pg = gage pressure within the process unit
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Chapter 7: Plant Design and Operation Concentration (Cppm) of vaporized liquid in ventilated space: Cppm = >
QmRgT×106 H (kQVPM)
where T = absolute ambient temperature k
= nonideal mixing factor
QV = ventilation rate P = absolute ambient pressure Sweep-through concentration change in a vessel: C –C QVt = V ln =C1 –C0 G 2 0 where QV = volumetric flow rate t
= time
V = vessel volume C0 = inlet concentration C1 = initial concentration C2 = final concentration
7.5.3.13 Noise Pollution SPL (dB) = 10 log10 f SPLtotal
P2 p P02
= 10 log10 R10 SPL
10
r Point Source Attenuation: DSPL ^dBh = 10 log10 d r1 n 2
r Line Source Attenuation: DSPL ^dBh = 10 log10 d r1 n 2
where SPL (dB)
= sound pressure level, measured in decibels
P
= sound pressure (Pa)
P0
= reference sound pressure (2 × 10–5 Pa)
SPLtotal
= sum of multiple sources
∆ SPL (dB) = change in sound pressure level with distance, measured in decibels
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= distance from source to receptor at point 1
r2
= distance from source to receptor at point 2 503
Chapter 7: Plant Design and Operation 7.5.3.14 Permissible Noise Exposure (per OSHA Regulations) Noise dose D should not exceed 100%. C D = 100% # ! i Ti where Ci = time spent at specified sound pressure level (SPL) in hours Ti = time permitted at SPL in hours ! Ci = 8 (hours)
Permissible Noise Level vs. Permissible Time of Exposure Noise Level (dBA)
Permissible Time (hr)
80 85 90 95 100 105 110 115 120 125 130
32 16 8 4 2 1 0.5 0.25 0.125 0.063 0.031
If D > 100%, noise abatement is required. If 50% ≤ D ≤ 100%, hearing conservation program is required. Note: D = 100% is equivalent to 90 dBA time-weighted average (TWA). D = 50% is equivalent to TWA of 85 dBA. Hearing conservation program requires: (1) testing employee hearing, (2) providing hearing protection at employee's request, and (3) monitoring noise exposure. Exposure to impulsive or impact noise should not exceed 140 dB sound pressure level (SPL).
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Chapter 7: Plant Design and Operation
7.5.4
Hazard Identification and Management Terms and Definitions for Hazards Identification and Management Term
Alarm As Low as Reasonably Practicable (ALARP)
Consequences
Frequency
Failure Mode and Effect Analysis (FMEA)
Hazards and Operability Analysis (HAZOP)
Independent Protection Layer (IPL)
Initiating Event
Layer of Protection Analysis (LOPA)
Lock-OutTag-Out (LOTO)
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Definition
An audible and/or visible means of indication to the operator an equipment malfunction, process deviation, or abnormal condition requiring a timely response. The concept that efforts to reduce risk should be continued until the incremental sacrifice (in terms of cost, time, effort, or other expenditure of resources) is grossly disproportionate to the incremental risk reduction achieved. The term as low as reasonably achievable (ALARA) is often used synonymously. The direct, undesirable result of an accident sequence usually involving a fire, explosion, or release of toxic material. Consequence descriptions may be qualitative or quantitative estimates of the effects of an accident. Number of occurrences of an event per unit time d e.g., 1 event in 1000 yr. = 1 # 10 −3 events n . yr
A hazard identification technique in which all known failure modes of components or features of a system are considered in turn and undesired outcomes are noted. It is usually used in combination with fault tree analysis. It is a complicated procedure, usually carried out by experienced risk analysts. A systematic qualitative technique to identify process hazards and potential operating problems using a series of guide words to study process deviations. A HAZOP is used to question every part of a process to discover what deviations from the intention of the design can occur and what their causes and consequences may be. This is done systematically by applying suitable guide words. This is a systematic detailed review technique, for both batch and continuous plants, which can be applied to new or existing processes to identify hazards. A device, system, or action that is capable of preventing a postulated accident sequence from proceeding to a defined, undesirable endpoint. An IPL is independent of the event that initiated the accident sequence and independent of any other IPLs. IPLs are normally identified during layer of protection analysis. The minimum combination of failures or errors necessary to start the propagation of an incident sequence. It can be comprised of a single initiating cause, multiple causes, or initiating causes in the presence of enabling conditions. (The term initiating event is the usual term employed in Layer of Protection Analysis to denote an initiating cause or where appropriate, an aggregation of initiating causes with the same immediate effect, such as "BPCS failure resulting in high reactant flow.") An approach that analyzes one incident scenario (cause-consequence pair) at a time, using predefined values for the initiating event frequency, independent protection layer failure probabilities, and consequence severity, in order to compare a scenario risk estimate to risk criteria for determining where additional risk reduction or more detailed analysis is needed. Scenarios are identified elsewhere, typically using a scenario-based hazard evaluation procedure such as the HAZOP study. Specific practices and procedures to safeguard employees from the unexpected energization or startup of machinery and equipment, or the release of hazardous energy during service or maintenance activities.
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Chapter 7: Plant Design and Operation Terms and Definitions for Hazards Identification and Management (cont'd) Term
Definition
An organized effort to identify and evaluate hazards associated with processes and operations to enable their control. This review normally involves the use of qualitaProcess Hazard Analysis (PHA) tive techniques to identify and assess the significance of hazards. Conclusions and appropriate recommendations are developed. Occasionally, quantitative methods are used to help prioritized risk reduction. A management system that is focused on prevention of, preparedness for, mitigaProcess Safety Management tion of, response to, and restoration from catastrophic releases of chemicals or (PSM) energy from a process associated with a facility. QRA is a technique that provides advanced quantitative means to supplement other hazard identification, analysis, assessment, control, and management methods to identify the potential for such incidents and to evaluate risk reduction and control strategies. QRA identifies those areas where operation, engineering, or manageQuantitative Risk Analysis ment systems may be modified to reduce risk and may identify the most economi(QRA) cal way to do it. The primary goal of QRA is that appropriate management actions, based on results from a QRA study, help to make facilities handling hazardous chemicals safer. QRA is one component of an organization's total process risk management. It allows the quantitative assessment of risk alternatives that can be balanced against other considerations. The systematic development of numerical estimates of the expected frequency and/ or consequenceof potential accidents associated with a facility or operation. Using Qualitative Risk Analysis consequence and probability analyses and other factors such as population density (QRA) and expected weather conditions, QRA predicts the fatality rate for a given event. This methodology is useful for evaluation of alternatives, but its value as an absolute measure of risk should be considered carefully. A measure of human injury, environmental damage, or economic loss in terms of both the incident likelihood and the magnitude of the loss or injury. A simplified Risk version of this relationship expresses risk as the product of the likelihood and the consequences (i.e., Risk = Consequence x Likelihood) of an incident.
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Chapter 7: Plant Design and Operation 7.5.4.1 Layers of Protection Typical Risk Reduction Methods Found in Process Plants COMMUNITY EMERGENCY RESPONSE EMERGENCY BROADCASTING
PLANT EMERGENCY RESPONSE EVACUATION PROCEDURES
MITIGATION
MECHANICAL MITIGATION SYSTEMS SAFETY INSTRUMENTED CONTROL SYSTEMS SAFETY INSTRUMENTED MITIGATION SYSTEMS OPERATOR SUPERVISION
PREVENTION
MECHANICAL PROTECTION SYSTEM PROCESS ALARMS WITH OPERATOR CORRECTIVE ACTION SAFETY INSTRUMENTED CONTROL SYSTEMS SAFETY INSTRUMENTED PREVENTION SYSTEMS
CONTROL AND MONITORING
BASIC PROCESS CONTROL SYSTEMS MONITORING SYSTEMS ( PROCESS ALARMS) OPERATOR SUPERVISION
PROCESS
Source: With thanks to the International Electrotechnical Commission (IEC) for permission to reproduce information from its International Standards. All such extracts are copyright of IEC, Geneva, Switzerland. All rights reserved. Further information on the IEC is available from www.iec.ch. IEC has no responsibility for the placement and context in which the extracts and contents are reproduced by the author, nor is IEC in any way responsible for the other content or accuracy therein. IEC 61511-1 ed.2.0. Copyright (c) 2016 IEC Geneva, Switzerland. www.iec.ch.
Hierarchy of Controls
Source: Controls for Noise Exposure, Atlanta: The National Institute for Occupational Safety and Health (NIOSH), 2016. ©2017 NCEES
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Chapter 7: Plant Design and Operation 7.5.4.2 Elements of Risk-Based Process Safety Commitment to process safety
Understanding hazards and risk Managing risk
Learning from experience
Process safety culture Compliance with standards Workforce involvement Stakeholder outreach Process knowledge management Hazards identification and risk analysis Operating procedures Safe work practices Asset integrity and reliability Contractors management Training and performance assurance Management of change Operational readiness Conduct of operations Emergency management Incident investigation Measurements and metrics Auditing Management review and continuous improvement
7.5.4.3 Safety Instrumented Systems Definitions of Safety Integrity Terms Term
Definition
Arrangement of hardware and/or software elements in a system; for example: Architecture
Average Probability of Failure on Demand (PFDavg) Basic Process Control System (BPCS) Common Cause Failure MooN Mean Time to Fail (MTTF)
(1) Arrangement of safety instrumented system (SIS) subsystems (2) Internal structure of an SIS subsystem (3) Arrangement of software programs Average probability that a safety-instrumented function will fail in such a way that it cannot respond to a potentially dangerous condition. PFD or PFDavg is applied to repairable systems. System that responds to input signals from the process, its associated equipment, other programmable systems, and/or an operator and generates output signals causing the process and its associated equipment to operate in the desired manner but that does not perform any safety-instrumented functions with a claimed SIL $ 1. Failure that is the result of one or more events and that causes failure of two or more separate channels in a multiple-channel system, leading to system failure. Safety instrumented system, or part thereof, made up of N independent channels that are so connected that M channels are sufficient to perform the safety-instrumented function. Mean time to random failure for a component population. MTTF is applied to items that are not repaired, such as bearings and transistors.
Mean Time to Trip Spurious (MTTFS)
Mean time for a safety function to fail in a mode that causes a spurious trip.
Safe Failure Fraction (SFF)
Fraction of the overall random hardware failure rate of a device that results in either a safe failure or a detected dangerous failure.
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Chapter 7: Plant Design and Operation Definitions of Safety Integrity Terms (cont'd) Term
Definition
Safety Instrumented System (SIS) Safety Integrity Level (SIL) Safety Instrumented Function (SIF) Systematic Failure Tolerable Risk Validation
Verification
Instrumented system used to implement one or more safety-instrumented functions.An SIS is composed of any combination of sensor(s), logic solver(s), and final element(s). Discrete level (one out of four) for specifying the safety integrity requirements of the safety-instrumented functions to be allocated to the safety instrumented systems. SIL 4 has the highest level of safety integrity; SIL 1, the lowest. Safety function with a specified safety integrity level that is necessary to achieve functional safety and that can be either a safety instrumented protection function or a safety instrumented control function. Failure related in a deterministic way to a certain cause, which can only be eliminated by a modification of the design or of the manufacturing process, operational procedures, documentation, or other relevant factors. Risk that is accepted in a given context based on the current values of society. Activity of demonstrating that the safety-instrumented function(s) and safety instrumented system(s) under consideration after installation meet in all respects the safety requirements specification. Activity of demonstrating for each phase of the relevant safety life-cycle, by analysis and/or tests, that for specific inputs the outputs meet in all respects the objectives and requirements for the specific phase.
Source: With thanks to the International Electrotechnical Commission (IEC) for permission to reproduce information from its International Standards. All such extracts are copyright of IEC, Geneva, Switzerland. All rights reserved. Further information on the IEC is available from www.iec.ch. IEC has no responsibility for the placement and context in which the extracts and contents are reproduced by the author, nor is IEC in any way responsible for the other content or accuracy therein. IEC 61511-1 ed.2.0. Copyright (c) 2016 IEC Geneva, Switzerland. www.iec.ch.
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Chapter 7: Plant Design and Operation 7.5.4.4 Functional Safety Life Cycle SIS Safety Life-Cycle Phases and Functional Safety Assessment Stages MANAGEMENT OF FUNCTIONAL SAFETY IN FUNCTIONAL SAFETY ASSESSMENT AND AUDITING
SAFETY LIFE-CYCLE STRUCTURE AND PLANNING
1
HAZARD AND RISK ASSESSMENT CLAUSE 8
VERIFICATION
ALLOCATION OF SAFETY FUNCTIONS TO PROTECTION LAYERS CLAUSE 9 2 SAFETY REQUIREMENTS SPECIFICATION FOR SAFETY INSTRUMENTED SYSTEM 3 CLAUSES 10 AND 11 STAGE 1 DESIGN AND ENGINEERING OF SAFETY INSTRUMENTED SYSTEM CLAUSES 11 AND 12
4
DESIGN AND DEVELOPMENT OF OTHER MEANS OF RISK REDUCTION CLAUSE 9
STAGE 2 INSTALLATION, COMMISSIONING AND VALIDATION 5 CLAUSES 14 AND 15 STAGE 3
OPERATION AND MAINTENANCE CLAUSE 16 6
STAGE 4
CLAUSE 5
10
CLAUSE 6.2
7
MODIFICATION CLAUSE 17
8
DECOMMISSIONING CLAUSE 18
STAGE 5
11
9
CLAUSES 7, 12.4, AND 12.7
KEY: TYPICAL DIRECTION OF INFORMATION FLOW. NO DETAILED REQUIREMENTS GIVEN IN THIS STANDARD. REQUIREMENTS GIVEN IN THIS STANDARD. NOTE 1 STAGES 1 THROUGH 5 INCLUSIVE ARE DEFINED IN 5.2.6.1.3. NOTE 2 ALL REFERENCES ARE TO PART 1 UNLESS OTHERWISE NOTED.
Source: With thanks to the International Electrotechnical Commission (IEC) for permission to reproduce information from its International Standards. All such extracts are copyright of IEC, Geneva, Switzerland. All rights reserved. Further information on the IEC is available from www.iec.ch. IEC has no responsibility for the placement and context in which the extracts and contents are reproduced by the author, nor is IEC in any way responsible for the other content or accuracy therein. IEC 61511-1 ed.2.0. Copyright (c) 2016 IEC Geneva, Switzerland. www.iec.ch.
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Chapter 7: Plant Design and Operation 7.5.4.5 SIS Safety Life-Cycle Overview The Safety Instrumented System (SIS) Safety Life-Cycle Safety Life-Cycle Phase or Activity Box # in Previous Title Image
1
Hazard and Risk Assessment
2
Allocation of Safety Functions to Protection Layers
3
SIS Safety Requirements Specification
4
SIS Design and Engineering
5
SIS Installation Commissioning and Validation
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Requirements Clause or Subclause
Objectives
Inputs
Outputs
To determine the hazards and hazardous events of the process and associated equipment, the sequence of events leading to the hazardous event, the process risks associated with the hazardous event, the requirements for risk reduction, and the safety functions required to achieve the necessary risk reduction Allocation of safety functions to protection layers and the associated safety integrity level for each safety-instrumented function
8
Process design, layout, work force arrangements, safety targets
Description of hazards of the required safety function(s) and their associated risk reduction(s)
9
Description of allocation of safety requirements (see Clause 9)
To specify the requirements for each SIS, in terms of the required safety-instrumented functions and their associated safety integrity, in order to achieve the required functional safety To design the SIS to meet the requirements for safetyinstrumented functions and safety integrity
10
Description of required safetyinstrumented function(s) and associated safety integrity requirements Description of allocation of safety requirements (see Clause 9)
SIS safety requirements; software safety requirements
Design of the SIS in conformance with the SIS safety requirements; planning for the SIS integration test Fully functioning SIS in conformance with the SIS design results of SIS integration tests
To integrate and test the SIS To validate that the SIS meets in all respects the requirements for safety in terms of the required safety-instrumented functions and the required safety integrity
511
11, 12.4
12.3, 14, 15
SIS design SIS integration test plan SIS safety requirements Plan for the safety validation of the SIS
SIS safety requirements; software safety requirements
Results of the installation, commissioning, and validation activities
Chapter 7: Plant Design and Operation SIS Safety Life-Cycle Overview (cont'd) Safety Life-Cycle Phase or Activity Box # in Previous Title Image
Requirements Clause or Subclause
Objectives
6
SIS Operation To ensure that the functional and Maintenance safety of the SIS is maintained during operation and maintenance
16
7
SIS Modification To make corrections, enhancements, or adaptations to the SIS, ensuring that the required safety integrity level is achieved and maintained Decommission- To ensure proper review and ing sector organization, and to ensure SIF remains appropriate SIS Verification To test and evaluate the outputs of a given phase to ensure correctness and consistency with respect to the products and standards provided as inputs to that phase SIS Functional To investigate and arrive at Safety a judgment on the functional Assessment safety achieved by the SIS
17
8
9
10
7, 12.7
As-built safety requirements and process information Plan for the verification of the SIS for each phase
SIF placed out of service
Planning for SIS functional safety assessment
Results of SIS functional safety assessment
SIS safety requirement
7.5.4.6 Safety Integrity Levels: Probability of Failure on Demand Safety Integrity Level (SIL)
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Demand Mode of Operation Target Average Probability Target Risk Reduction of Failure on Demand
4
$ 10
-5
to 1 10
-4
2 10, 000 to # 100, 000
3
$ 10
-4
to 1 10
-3
2 1000 to # 10, 000
2
$ 10
-3
to 1 10
-2
2 100 to # 1000
1
$ 10
-2
to 1 10
-1
2 10 to # 100
512
Outputs
SIS requirements Results of the operation and SIS design maintenance activities Plan for SIS operation and maintenance Revised SIS Results of SIS safety requiremodification ments
18
5
Inputs
Results of the verification of the SIS for each phase
Chapter 7: Plant Design and Operation 7.5.4.7 Functional Safety Equations Average Probability of Failure on Demand (PFDavg) 1 PFavg = T
T
#
PF (t) dt
(Rigorous version)
0
mt PFavg = 2
(Approximation)
Safe Failure Fraction (SFF) SFF =
mSD + mSU + mDD mSD + mSU + mDD + mDU
where l = failure rate (failures/year) and subscripts indicate failure mode: SD = safe detected SU = safe undetected DD = dangerous detected DU = dangerous undetected
7.5.4.8 Management of Change Management of Change (MOC)—A management system to identify, review, and approve all modifications to equipment, procedures, raw materials, and processing conditions, other than replacement in kind, prior to implementation, to help ensure that changes to processes are properly analyzed (for example, for potential adverse impacts), documented, and communicated to affected employees. Key Principles: • Maintain a dependable practice • Identify potential change situations • Evaluate possible impacts • Decide whether to allow the change • Complete follow-up activities
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Chapter 7: Plant Design and Operation 7.5.4.9 Hazardous Waste Compatibility Hazardous Waste Compatibility Chart REACTIVITYGROUP NO. 1
NAME ACID, MINERALS NON-OXIDIZING
1
ACIDS, MINERALS
2 OXIDIZING
2
3 ACIDS,ORGANIC
G H
3
KEY REACTIVITY CODE
4 ALCOHOLS & GLYCOLS
H
H F
H F
5 ALDEHYDES
H F
H F
H F
5
6 AMIDES
H
H GT
H
H GT
H
S
AZO COMPOUNDS, H DIAZO COMP, HYDRAZINES S
H GT
H S
H G
H GT
AMINES ALIPHATIC &
7 AROMATIC 8
9 CARBAMATES
H
H
H
11 CYAMIDES
GT GF
GT GF
12 DITHIOCARBAMATES
H GF F
H GF F
H GF GT
13 ESTERS
S
H F
14 ETHERS
S
H F
15 FLUORIDES, INORGANIC
GT
GT
H 17 HALOGENATED ORGANICS GT
H F GT H F GT
18 ISOCYANATES 19 KEYTONES
H G H
20
METAPHORS & OTHER ORGANIC SULFIDES
GT GF
21
METAL, ALKALI & ALKALINE EARTH, ELEMENTAL
GF H F
H F H F GT GF H F
104 OXIDIZING AGENTS,
H F
105 REDUCING AGENTS,
H G
H F GT
H
H
STRONG STRONG
106 WATER & MIXTURES
CONTAINING WATER
7 8
H
H G
GT GF
16 CARBONS, AROMATIC
H S
9 H G
H
G
11
H G
EXAMPLE H F GT
12
H G
13
H
15
GT
16
H G
H F
H GT
H G
H G
H
H F
H G
H F G
H G
H G
H
H
GF H
GF H
GF GT H
GF H
H F GT
H F GT
H F
H GT
H F
17 18
U
19
H G GF H F
GF H F
GF H F
GF H
GF H
GF H
GF H
H F
H F
H F
H F GT
H G
GF H F
F GT H
H E
H GF F
H F GT GF H
H G
H G
H F
SUBSTANCES
3
4
5
6
7
8
H F
H
H
H
20
H E
GF H
GF H
GF H
21
H GT
H F GF
H F
H F GF
H F GF
H T
GF H
GF H
GF H
104 105
GF H
H G
G EXTREMELY REACTIVE!
2
HEAT GENERATION FIRE, AND TOXIC GAS GENERATION
14
107 WATER REACTIVE
1
HEAT GENERATION FIRE INNOCUOUS & NON-FLAMMABLE GAS TOXIC GAS GENERATION FLAMMABLE GAS GENERATION EXPLOSION POLYMERIZATION SOLUBILIZATION OF TOXIC MATERIAL MAY BE HAZARDOUS BUT UNKNOWN
10
G GF GT
CONSEQUENCES
H F G GT GF E P S U
6
10 CAUSTICS
H F
4
DO NOT MIX WITH ANY CHEMICAL OR WASTE MATERIAL
107
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 101 102 103 104 105 106 107
Source: Hatayama, H.K., et. al., A Method for Determining the Compatibility of Hazardous Wastes, Cincinnati: U.S. Environmental Protection Agency, 1980, p. 20.
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Chapter 7: Plant Design and Operation 7.5.4.10 OSHA Highly Hazardous Chemicals The following is from 29 CFR 1910.119, Appendix A. It contains a list of toxic and reactive highly hazardous chemicals that present a potential for a catastrophic event at or above the threshold quantity.
Highly Hazardous Chemicals Chemical Name
Acetaldehyde Acrolein (2-Propenal) Acrylyl Chloride Allyl Chloride Allylamine Alkylaluminum Ammonia, Anhydrous Ammonia solutions (greater than 44% ammonia by weight) Ammonium Perchlorate Ammonium Permanganate Arsine (also called Arsenic Hydride) Bis (Chloromethyl) Ether Boron Trichloride Boron Trifluoride Bromine Bromine Chloride Bromine Pentafluoride Bromine Trifluoride 3-Bromopropyne (also called Propargyl Bromide) Butyl Hydroperoxide (Tertiary) Butyl Perbenzoate (Tertiary) Carbonyl Chloride (see Phosgene) Carbonyl Fluoride Cellulose Nitrate (concentration greater than 12.6% nitrogen) Chlorine Chlorine Dioxide Chlorine Pentrafluoride Chlorine Trifluoride Chlorodiethylaluminum (also called Diethylaluminum Chloride) 1-Chloro-2,4-Dinitrobenzene Chloromethyl Methyl Ether Chloropicrin Chloropicrin and Methyl Bromide mixture Chloropicrin and Methyl Chloride mixture Cumene Hydroperoxide Cyanogen Cyanogen Chloride
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CAS*
TQ**
75-07-0 107-02-8 814-68-6 107-05-1 107-11-9 Varies 7664-41-7 7664-41-7 7790-98-9 7787-36-2 7784-42-1 542-88-1 10294-34-5 7637-07-2 7726-95-6 13863-41-7 7789-30-2 7787-71-5 106-96-7 75-91-2 614-45-9 75-44-5 353-50-4 9004-70-0 7782-50-5 10049-04-4 13637-63-3 7790-91-2 96-10-6 97-00-7 107-30-2 76-06-2 None None 80-15-9 460-19-5 506-77-4
2500 150 250 1000 1000 5000 10,000 15,000 7500 7500 100 100 2500 250 1500 1500 2500 15,000 100 5000 7500 100 2500 2500 1500 1000 1000 1000 5000 5000 500 500 1500 1500 5000 2500 500
Chapter 7: Plant Design and Operation Highly Hazardous Chemicals (cont'd) Chemical Name
Cyanuric Fluoride Diacetyl Peroxide (concentration greater than 70%) Diazomethane Dibenzoyl Peroxide Diborane Dibutyl Peroxide (tertiary) Dichloro Acetylene Dichlorosilane Diethylzinc Diisopropyl Peroxydicarbonate Dilauroyl Peroxide Dimethyldichlorosilane 1,1-Dimethylhydrazine Dimethylamine, Anhydrous 2,4-Dinitroaniline Ethyl Methyl Ketone Peroxide (also Methyl Ethyl Ketone Peroxide; concentration greater than 60%) Ethyl Nitrite Ethylamine Ethylene Fluorohydrin Ethylene Oxide Ethyleneimine Fluorine Formaldehyde (Formalin) Furan Hexafluoroacetone Hydrochloric Acid, Anhydrous Hydrofluoric Acid, Anhydrous Hydrogen Bromide Hydrogen Chloride Hydrogen Cyanide, Anhydrous Hydrogen Fluoride Hydrogen Peroxide (52% by weight or greater) Hydrogen Selenide Hydrogen Sulfide Hydroxylamine Iron, Pentacarbonyl Isopropylamine Ketene Methacrylaldehyde Methacryloyl Chloride Methacryloyloxyethyl Isocyanate ©2017 NCEES
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CAS*
TQ**
675-14-9 110-22-5 334-88-3 94-36-0 19287-45-7 110-05-4 7572-29-4 4109-96-0 557-20-0 105-64-6 105-74-8 75-78-5 57-14-7 124-40-3 97-02-9
100 5000 500 7500 100 5000 250 2500 10,000 7500 7500 1000 1000 2500 5000
1338-23-4
5000
109-95-5 75-04-7 371-62-0 75-21-8 151-56-4 7782-41-4 50-00-0 110-00-9 684-16-2 7647-01-0 7664-39-3 10035-10-6 7647-01-0 74-90-8 7664-39-3 7722-84-1 7783-07-5 7783-06-4 7803-49-8 13463-40-6 75-31-0 463-51-4 78-85-3 920-46-7 30674-80-7
5000 7500 100 5000 1000 1000 1000 500 5000 5000 1000 5000 5000 1000 1000 7500 150 1500 2500 250 5000 100 1000 150 100
Chapter 7: Plant Design and Operation Highly Hazardous Chemicals (cont'd) Chemical Name
CAS*
TQ**
Methyl Acrylonitrile Methylamine, Anhydrous Methyl Bromide Methyl Chloride Methyl Chloroformate Methyl Ethyl Ketone Peroxide (concentration greater than 60%) Methyl Fluoroacetate Methyl Fluorosulfate Methyl Hydrazine Methyl Iodide Methyl Isocyanate Methyl Mercaptan Methyl Vinyl Ketone Methyltrichlorosilane Nickel Carbonyl (Nickel Tetracarbonyl) Nitric Acid (94.5% by weight or greater) Nitric Oxide Nitroaniline (para Nitroaniline) Nitromethane Nitrogen Dioxide Nitrogen Oxides (NO; NO(2); N2O4; N2O3) Nitrogen Tetroxide (also called Nitrogen Peroxide) Nitrogen Trifluoride Nitrogen Trioxide Oleum (65% to 80% by weight; also called Fuming Sulfuric Acid) Osmium Tetroxide Oxygen Difluoride (Fluorine Monoxide) Ozone Pentaborane Peracetic Acid (concentration greater 60% Acetic Acid; also called Peroxyacetic Acid) Perchloric Acid (concentration greater than 60% by weight) Perchloromethyl Mercaptan Perchloryl Fluoride Peroxyacetic Acid (concentration greater than 60% Acetic Acid; also called Peracetic Acid) Phosgene (also called Carbonyl Chloride) Phosphine (Hydrogen Phosphide) Phosphorus Oxychloride (also called Phosphoryl Chloride) Phosphorus Trichloride Phosphoryl Chloride (also called Phosphorus Oxychloride)
126-98-7 74-89-5 74-83-9 74-87-3 79-22-1 1338-23-4 453-18-9 421-20-5 60-34-4 74-88-4 624-83-9 74-93-1 79-84-4 75-79-6 13463-39-3 7697-37-2 10102-43-9 100-01-6 75-52-5 10102-44-0 10102-44-0 10544-72-6 7783-54-2 10544-73-7 8014-95-7 20816-12-0 7783-41-7 10028-15-6 19624-22-7
250 1000 2500 15,000 500 5000 100 100 100 7500 250 5000 100 500 150 500 250 5000 2500 250 250 250 5000 250 1000 100 100 100 100
79-21-0
1000
7601-90-3 594-42-3 7616-94-6
5000 150 5000
79-21-0
1000
75-44-5 7803-51-2 10025-87-3 7719-12-2 10025-87-3
100 100 1000 1000 1000
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Chapter 7: Plant Design and Operation Highly Hazardous Chemicals (cont'd) Chemical Name
Propargyl Bromide Propyl Nitrate Sarin Selenium Hexafluoride Stibine (Antimony Hydride) Sulfur Dioxide (liquid) Sulfur Pentafluoride Sulfur Tetrafluoride Sulfur Trioxide (also called Sulfuric Anhydride) Sulfuric Anhydride (also called Sulfur Trioxide) Tellurium Hexafluoride Tetrafluoroethylene Tetrafluorohydrazine Tetramethyl Lead Thionyl Chloride Trichloro (chloromethyl) Silane Trichloro (dichlorophenyl) Silane Trichlorosilane Trifluorochloroethylene Trimethyoxysilane
CAS*
TQ**
106-96-7 627-3-4 107-44-8 7783-79-1 7803-52-3 7446-09-5 5714-22-7 7783-60-0 7446-11-9 7446-11-9 7783-80-4 116-14-3 10036-47-2 75-74-1 7719-09-7 1558-25-4 27137-85-5 10025-78-2 79-38-9 2487-90-3
100 2500 100 1000 500 1000 250 250 1000 1000 250 5000 5000 1000 250 100 2500 5000 10,000 1500
* Chemical abstract service number ** Threshold quantity in pounds (amount necessary to be covered by OSHA CFR 1910.119 standard)
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Chapter 7: Plant Design and Operation 7.5.4.11 Hazardous Classification Based on NFPA 70 NFPA Hazardous Classification CLASS I GASES OR VAPOR
DIVISION 1 HAZARDOUS VAPORS PRESENT ZONE 0, 1, OR 2
CLASS II COMBUSTIBLE DUST
DIVISION 2 HAZARDOUS VAPORS CONTAINED BUT MAY BE PRESENT
CLASS III FIBERS
DIVISION 1 HANDLED, MANUFACTURED OR USED
DIVISION 1 AIR SUSPENDED
DIVISION 2 STORED OR HANDLED OTHER THAN MANUFACTURE
DIVISION 2 SURFACE ACCUMULATED – NON AIR SUSPENDED
GROUP A ACETYLENE GROUP E COMBUSTIBLE METAL DUSTS
GROUP B FLAMMABLE GAS, FLAMMABLE OR COMBUSTIBLE VAPOR MESG ≤ 0.45 MM MIC RATIO ≤ 0.40
GROUP F COMBUSTIBLE CARBONACEOUS DUSTS CONTAINING >8% AND TRAPPED VOLATILES
GROUP C FLAMMABLE GAS, FLAMMABLE OR COMBUSTIBLE VAPOR 0.45 MM ≤MESG ≤ 0.75 MM 0.45 MM ≤ MIC RATIO ≤ 0.80
GROUP G COMBUSTIBLE DUSTS NOT INCLUDED ELSEWHERE
GROUP D FLAMMABLE GAS, FLAMMABLE OR COMBUSTIBLE VAPOR 0.75MM ≤ MESG 0.80MM ≤ MIC RATIO
CLASS 1, ZONE 0: IGNITABLE CONCENTRATIONS PRESENT CONTINUOUSLY OR FOR LONG PERIODS OF TIME
MSEG: MAXIMUM EXPERIMENTAL SAFE GAP MIC: MINIMUM IGNITING CURRENT RATIO
CLASS 1, ZONE 1: IGNITABLE CONCENTRATIONS LIKELY TO EXIST UNDER NORMAL OPERATION CLASS 1, ZONE 2: IGNITABLE CONCENTRATIONS NOT LIKELY TO EXIST UNDER NORMAL OPERATION
Source: Reproduced with permission from NFPA 70®, National Electric Code®, © 2011, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety. National Electrical Code and NEC are registered trademarks of the National Fire Protection Association, Quincy, MA.
Maximum Experimental Safe Gap (MESG): The maximum clearance between two parallel metal surfaces that has been found, under specified test conditions, to prevent an explosion in a test chamber from being propagated to a secondary chamber containing the same gas or vapor at the same concentration. Minimum Igniting Current (MIC) Ratio: The ratio of the minimum current required from an inductive spark discharge to ignite the most easily ignitable mixture of a gas or vapor, divided by the minimum current required from an inductive spark discharge to ignite methane under the same test conditions. ©2017 NCEES
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Chapter 7: Plant Design and Operation 7.5.4.12 Flammability Flammable describes any solid, liquid, vapor, or gas that will ignite easily and burn rapidly. A flammable liquid is defined by NFPA and USDOT as a liquid with a flash point below 100°F (38°C). Flammability is further defined with lower and upper limits: LFL = lower flammability limit (volume % in air) UFL = upper flammability limit (volume % in air) A vapor-air mixture will only ignite and burn over the range of concentrations between LFL and UFL. Flammability data is shown at the end of this chapter. Predicting Lower Flammable Limits of Mixtures of Flammable Gases (Le Chatelier's Rule) Based on an empirical rule developed by Le Chatelier, the lower flammable limit of mixtures of multiple flammable gases in air can be determined. A generalization of Le Chatelier's rule is
C k / a LFL $1 n
i
i
i=1
where
Ci
= the volume percent of fuel gas i in the fuel/air mixture
LFLi = the volume percent of fuel gas i at its lower flammable limit in air alone If the indicated sum is greater than unity, the mixture is above the lower flammable limit. This can be restated in terms of the lower flammable limit concentration of the fuel mixture (LFLm):
LFL m = where
100 Cfi k / a LFL i i=1 n
Cfi = the volume percent of fuel gas i in the fuel gas mixture.
Predicting Lower Flammable Limits
COMBUSTABLE CONCENTRATION
SATURATED VAPORAIR MIXTURES
UPPER LIMIT
FLAMMABLE MIXTURES
MIST
B A
TL
AUTOIGNITION
LOWER LIMIT AIT
TU TEMPERATURE
* THE SFPE HANDBOOK OF FIRE PROTECTION ENGINEERING, NATIONAL FIRE PROTECTION ASSOCIATION. 1988.
WITH PERMISSION FROM THE SOCIETY OF FIRE PREVENTION ENGINEERS. Source: DiNenno, Philip J., The SFPE Handbook of Fire Protection Engineering, 1st ed., Gaithersburg: Society of Fire Protection Engineers, 1988, p. 1-288.
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Chapter 7: Plant Design and Operation 7.5.4.13 Fundamental Burning Velocities Fundamental Burning Velocities of Selected Gases and Vapors Gas
Acetone Acetylene Acrolein Acrylonitrile Allene (propadiene) Benzene n-butyltert-butyl1,2-dimethyl1,2,4-trimethyl1,2-Butadiene (methylallene) 1,3-Butadiene 2,3-dimethyl2-methyln-Butane 2-cyclopropyl2,2-dimethyl2,3-dimethyl2-methyl2,2,3-trimethylButanone 1-Butene 2-cyclopropyl2,3-dimethyl 2-ethyl2-methyl3-methyl2,3-dimethyl-2-butene 2-Buten 1-yne (vinylacetylene) 1-Butyne 3,3-dimethyl2-Butyne Carbon disulfide Carbon monoxide
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Fundamental Burning Velocity
a cm s k 54 166* 66 50 87 48 37
Gas
Cyclobutane ethylisopropylmethylCyclohexane methylCyclopentadiene
Fundamental Burning Velocity
a cm s k 67 53 46 52 46 44 46
39 37 39
Cyclopentane methylCyclopropane
44 42 56
68 64 52 55 45 47 42 43 43 42 42 51 50 46 46 46 49 44 89 68 56 61 58 46
cis-1,2-dimethyltrans-1,2-dimethylethylmethyl1,1,2-trimethyltrans-Decalin (decahydronaphthalene) n-Decane 1-Decene Diethyl ether Dimethyl ether Ethane Ethene (ethylene) Ethyl acetate Ethylene oxide Ethylenimine Gasoline (100-octane) n-Heptane Hexadecane 1,5-Hexadiene n-Hexane 1-Hexene 1-Hexyne 3-Hexyne HFC-23 (Difluoromethane)
55 55 56 58 52 36 43 44 47 54 47 80* 38 108 46 40 46 44 52 46 50 57 53 6.7
521
Chapter 7: Plant Design and Operation Fundamental Burning Velocities of Selected Gases and Vapors (cont'd) Gas
Fundamental Burning Velocity
HFC-143 (1,1,2-Trifluoroethane) HFC-143a (1,1,1-Trifluoroethane) HFC-152a (1,1-Difluoroethane) Hydrogen Isopropyl alcohol Isopropylamine Jet fuel, grade JP-1 (average) Methane diphenyl-
13.1 7.1 23.6 312* 41 31 40 40* 35
Methyl alcohol Methylene 1,2-Pentadiene (ethylallene) cis-1,3-Pentadiene trans-1,3-Pentadiene (piperylene) 2-methyl-(cis or trans) 1,4-Pentadiene 2,3-Pentadiene n-Pentane 2,2-dimethyl2,3-dimethyl2,4-dimethyl2-methyl3-methyl2,2-trimethyl-
a cm s k
Gas
1-Pentene 2-methyl4-methyl1-Pentene 4-methylcis-2-Pentene 2-Pentyne 4-methylPropane
Fundamental Burning Velocity
a cm s k 50 47 48 63 53 51 61 54 46*
56 61 61 55 54 46 55 60 46 41 43
2-cyclopropyl1-deutero1-deutero-2-methyl2-deutero-2-methyl2,2-dimethyl2-methyl2-cyclopropyl2-methylPropionaldehyde Propylene oxide (1,2-epoxypropane) 1-Propyne
50 40 40 40 39 41 53 44 58 82 82
42 43 43 41
Spiropentane Tetrahydopyran Tetralin (tetrahydronaphthalene) Toluene (methylbenzene)
71 48 39 41
* Gases that were critically examined as to their fundamental burning velocities, in studies by Andrews and Bradley (Andrews, G.E., and D. Bradley, "Determination of Burning Velocities: a Critical Review," Combustion and Flame, Vol. 18, New York: Elsevier Scientific Publishing Co., 1972, pp. 133–153) or by France and Pritchard (France, D.H., and R. Pritchard, "Burning Velocity Measurements of Multicomponent Fuel Gas Mixtures," Gas Warnie International, Vol. 26, No. 12, 1977). Source: Reproduced with permission from NFPA 68, Standard on Explosion Protection by Deflagration Venting, © 2013, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.
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Chapter 7: Plant Design and Operation The table below compares values from the Andrews/Bradley and France/Pritchard studies to those in the preceding table.
Comparison of Fundamental Burning Velocities for Selected Gases Fundamental Burning Velocity a s k Andrews and Bradley From Table Above In Air In Oxygen
cm
Gas
Acetylene Ethylene Hydrogen Methane Propane
166 80 312 40 46
158 79 310 45
1140
-
1400 450 -
-
Flammability Properties of Gases 5L (0.005 m3) Sphere; E = 10J, normal conditions Flammable Material Pmax (bar) a Acetophenone 7.6 Acetylene 10.6 b Ammonia 5.4 c b-Naphthol 4.4 Butane 8.0 Carbon disulfide 6.4 Diethyl ether 8.1 a Dimethyl formamide 8.4 a Dimethyl sulfoxide 7.3 Ethanea 7.8 Ethyl alcohol 7.0 a Ethyl benzene 7.4 Hydrogen 6.8 Hydrogen sulfide 7.4 a Isopropanol 7.8 Methane 7.1 a Methanol 7.5 Methylene chloride 5.0 Methyl nitrite 11.4 Neopentane 7.8 Octanola 6.7 Octyl chloridea 8.0
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France and Pritchard (in Air)
0 347 43 46
Chapter 7: Plant Design and Operation Flammability Properties of Gases 5L (0.005 m3) Sphere; E = 10J, normal conditions (cont'd) Flammable Material Pmax (bar) a Pentane 7.8 Propane 7.9 South African crude oil 6.8–7.6 a Toluene 7.8 a. Measured at elevated temperatures and extrapolated to 25°C (77°F) at normal conditions b. E = 100J - 200J c. 200°C (392°F) Source: Reproduced with permission from NFPA 68, Standard on Explosion Protection by Deflagration Venting, © 2013, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.
7.5.4.14 Combustible Dust Combustible dust is a solid material composed of distinct particles or pieces, regardless of size, shape, or chemical composition, that presents a fire or deflagration hazard when suspended in air or some other oxidizing medium over a range of concentrations. Combustible dusts are often either organic or metal dusts that are finely ground into very small particles, fibers, fines, chips, chunks, flakes, or a small mixture of these. According to OSHA's Safety and Health Information Bulletin (SHIB) "Combustible Dust in Industry: Preventing and Mitigating the Effects of Fire and Explosions," dust particles with an effective diameter of less than 420 microns (those passing through a U.S. No. 40 standard sieve) should be deemed to meet the criterion of the definition. However, larger particles can still pose a deflagration hazard (for instance, as larger particles are moved, they can abrade each other, creating smaller particles). In addition, particles can stick together (agglomerate) due to electrostatic charges accumulated through handling, causing them to become explosible when dispersed. Types of dusts include, but are not limited to: •
Metal dust, such as aluminum and magnesium
•
Wood dust
•
Plastic or rubber dust
•
Biosolids
•
Coal dust
•
Organic dust, such as flour, sugar, paper, soap, and dried blood
•
Dusts from certain textiles
Kst is the dust deflagration index, which measures relative explosion severity compared to other dusts. The larger the value for Kst, the more severe the explosion. Kst provides the best "single number" estimate of the anticipated behavior of a dust deflagration. MIE, the minimum ignition energy, predicts the ease and likelihood of ignition of a dispersed dust cloud. MEC, the minimum explosible concentration, measures the minimum amount of dust dispersed in air required to spread an explosion. The MEC is analogous to the Lower Flammable Limit (LFL) or Lower Explosive Limit (LEL) for gases and vapors in air.
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Chapter 7: Plant Design and Operation Examples of Kst Values for Different Types of Dusts Dust Explosion Class*
m Kst c bar : s m *
Characteristic
St 0 St 1 St 2 St 3
0 > 0 and < 200 > 200 and < 300 > 300
No explosion Weak explosion Strong explosion Very strong explosion
Typical materials**
Silica Powered milk, charcoal, sulfur, sugar, zinc Cellulose, wood flour, poly methyl acrylate Anthraquinone, aluminum, magnesium
* OSHA CPL 03-00-008 - Combustible Dust National Emphasis Program ** NFPA 68, Standard on Explosion Prevention by Deflagration Venting Source: OSHA 3371-08: Hazard Communication Guidance for Combustible Dust: Occupational Safety and Health Administration, 2009, p. 8-9.
The actual class is sample-specific and will depend on varying characteristics of the material, such as particle size or moisture. Source for next five tables: Reproduced with permission from NFPA 68, Standard on Explosion Protection by Deflagration Venting, © 2013, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.
Agricultural Products Material
Mass Median Diameter (mm)
Cellulose Cellulose pulp Cork Corn Egg white Milk, powdered Milk, nonfat, dry Soy flour Starch, corn Starch, rice Starch, wheat Sugar Sugar, milk Sugar, beet Tapioca Whey Wood Flour
33 42 42 28 17 83 60 20 7 18 22 30 27 29 22 41 29
©2017 NCEES
Minimum Flammable Concentration
g l m3 60 30 30 60 125 60 200 60 30 200 60 60 125 125 -
b
525
Pmax _ bar i
Kst c bar : m sm
Dust Hazard Class
9.7 9.9 9.6 9.4 8.3 5.8 8.8 9.2 10.3 9.2 9.9 8.5 8.3 8.2 9.4 9.8 10.5
229 62 202 75 38 28 125 110 202 101 115 138 82 59 62 140 205
2 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2
Chapter 7: Plant Design and Operation Carbonaceous Dusts
Material
Mass Median Diameter (mm)
Minimum Flammable Concentration
Charcoal, activated Charcoal, wood Coal, bituminous Coke, petroleum Lampblack Lignite Peat, 22% H2O
28 14 24 15 <10 32 -
g l m3 60 60 60 125 60 60 125
Soot, pine
<10
-
b
Kst c bar : m sm
Dust Hazard Class
7.7 9.0 9.2 7.6 8.4 10.0 84.0
14 10 129 47 121 151 67
1 1 1 1 1 1 1
7.9
26
1
Pmax _ bar i
Kst c bar : m sm
Dust Hazard Class
8.0 10.6 9.0 5.2 6.5 9.1
97 364 111 9 21 132
1 3 1 1 1 1
Pmax _ bar i
Chemical Dusts
Material
Adipic acid Anthraquinone Absorbic acid Calcium acetate Calcium acetate Calcium stearate Carbonyl- methylcellulose Dextrin Lactose Lead stearate Methyl cellulose Paraformaldehyde Sodium ascorbate Sodium stearate Sulfur
©2017 NCEES
Mass Median Diameter (mm)
Minimum Flammable Concentration
<10 <10 39 92 85 12
g l m3 60 60 500 250 30
24
125
9.2
136
1
41 23 12 75 23 23 22 20
60 60 30 60 60 60 30 30
8.8 7.7 9.2 9.5 9.9 8.4 8.8 6.8
106 81 152 134 178 119 123 151
1 1 1 1 1 1 1 1
b
526
Chapter 7: Plant Design and Operation
Metal Dusts Material
Aluminum Bronze Iron, carbonyl Magnesium Phenolic resin Zinc Zinc
Minimum Flammable Concentration
Mass Median Diameter (mm)
g l m3 30 750 125 30 250 125
b
29 18 <10 28 55 10 <10
Pmax _ bar i
Kst c bar : m sm
Dust Hazard Class
12.4 4.1 6.1 17.5 7.9 6.7 7.3
415 31 111 508 269 125 176
3 1 1 3 2 1 1
Plastic Dusts Material
(poly) Acrylamide (poly) Acrylonitrile (poly) Ethylene (low-pressure process) Epoxy resin Melamine resin Melamine, molded (wood flour and mineral filled phenol-formaldehyde) Melamine, molded (phenolcellulose) (poly) Methyl acrylate (poly) Methyl acrylate, emulsion polymer Phenolic resin (poly) Propylene Terpene-phenol resin Urea-formaldehyde/cellulose, molded (poly) Vinyl acetate/ethylene copolymer (poly) Vinyl alcohol (poly) Vinyl butyral (poly) Vinyl chloride
©2017 NCEES
Mass Median Diameter (mm)
Minimum Flammable Concentration
b
g l m3
Dust m Hazard Pmax _ bar i Kst c bar : s m Class
10 25
250 -
5.9 8.5
12 121
1 1
<10
30
8.0
156
1
26 18
30 125
7.9 10.2
129 110
1 1
15
60
7.5
41
1
12
60
10.0
127
1
21
30
9.4
269
2
18
30
10.1
202
2
<10 25 10
15 30 15
9.3 8.4 8.7
129 101 143
1 1 1
13
60
10.2
136
1
32
30
8.6
119
1
26 65 107
60 30 200
8.9 8.9 7.6
128 147 46
1 1 1
527
Chapter 7: Plant Design and Operation Plastic Dusts (cont'd) Mass Median Diameter (mm)
Material
(poly) Vinyl chloride/vinyl acetylene emulsion copolymer (poly) Vinyl chloride/ethylene/vinyl acetylene suspension copolymer
Minimum Flammable Concentration
35
g l m3 60
60
60
b
Dust m Pmax _ bar i Kst c bar : s m Hazard Class
8.2
95
1
8.3
98
1
Ignition and Reaction Temperatures of Metal-Powder Layers in an Air, Carbon Dioxide, or Nitrogen Atmosphere Line No.
Sample No.
35 21 80 102 110 120 136 151 154 156 157 159 164 165 168 176 190 191 193 195 198 199 201 204 211 212 217 225 ©2017 NCEES
Material
701 Aluminum, atomized 897 Aluminum, atomized 702 Aluminum, flake 705 706 712 716 725 727 729 730 1020 734 733 736 737 1652 1653 739 1555 740 1556 864 1649 1625 1626 744 745
Chromium Copper Iron, hydrogen-reduced Lead Magnesium Magnesium Magnesium Magnesium Magnesium Magnesium Magnesium Magnesium Silicon Thorium Thorium hydride Tin Titanium Titanium Titanium, copper-coated Titanium Titanium hydride Uranium Uranium hydride Zinc Zirconium
Ignition Temperature, °C Reaction Temperature, °C Carbon Carbon Air Nitrogen Nitrogen Dioxide Dioxide
900 490 590
-540 660
----
900 ---
750 800 700
670 270 290 210 490 510 520 490 490 480 480 420 950 280 20 430 480 460 430 470 500 100 20 460 210
----630 ---600 ----450 340 -900 680 900 470 710 350 360 480 560
----530 510 520 500 550 490 500 --500 330 900 900 -900 500 750 410 210 -530
(1)
700 700 200 400 -------900 1000 ----900 -----600 --
528
-(1)
870 -------700 1000 --720 ----------
Chapter 7: Plant Design and Operation Ignition and Reaction Temperatures of Metal-Powder Layers in an Air, Carbon Dioxide, or Nitrogen Atmosphere (cont'd) Line No.
228 229 233 247
Ignition Temperature, °C Reaction Temperature, °C Carbon Carbon Air Nitrogen Nitrogen Dioxide Dioxide
Sample No.
Material
1632 1633 1627 1021
Zirconium Zirconium Zirconium hydride Aluminum-magnesium
190 300 340 460
620 710 650 660
790 --550
-----
-----
746 Aluminum-magnesium 748 Aluminum-magnesium
470 480
700 670
550 630
---
---
248 249 1
No reaction at 850°C
Source: Jacobson, M., A.R. Cooper, and J. Nagy, Explosibility of Metal Powders, Bureau of Mines Report of Investigations 6516, Washington, D.C.: United States Department of the Interior, Bureau of Mines, 1964, p.10.
7.5.5
Environmental Considerations
7.5.5.1 Air Pollution Concentrations in air can be converted from ppb to P _ MW i ng 3 = ppb RT m
ng as follows: m3
where ppb = parts per billion P = pressure, in atm liter : atm R = ideal gas law constant = 0.0821 mol : K T = absolute temperature, K = 273.15 + °C g MW = molecular weight, in mol
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Chapter 7: Plant Design and Operation 7.5.5.2 Atmospheric Dispersion Modeling (Gaussian) σy and σz are functions of downwind distance and stability class: 2 Q ^z − H h ^z + H h 1 y + exp f − 1 p pH C = 2ruv v exp f − 2 2 p>exp f − 1 2 2 vz 2 v 2z y z vy 2
where
2
ng C = steady-state concentration at a point (x, y, z) in 3 m ng Q = emissions rate in s σy = horizontal dispersion parameter, in meters σz = vertical dispersion parameter, in meters
m u = average wind speed at stack height in s x
= downwind distance along plume center line, in meters
y
= horizontal distance from plume center line, in meters
z
= vertical distance from ground level, in meters
H = effective stack height (m) = h + ∆h where
h
∆h = plume rise
= physical stack height
Maximum concentration at ground level and directly downwind from an elevated source: 2 Q 1 _H i Cmax = ruv v exp f − 2 2 p y z vz
where variables are as above except for Cmax = maximum ground-level concentration H vz = for neutral atmospheric conditions 2
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Chapter 7: Plant Design and Operation 7.5.5.3 Characteristic Hazardous Waste A waste is a characteristic waste if it meets any of the characteristics identified in 40 CFR 261 Subpart C (D code waste).
Hazardous Waste Characteristics Characteristic (D Code) [Subpart #]
Definition
(1) A liquid (other than an aqueous solution containing <24% alcohol by volume) that has flash point <140oF [Method Pensky-Martens or Setaflash]. Ignitability (D001) [40 CFR 261.21]
(2) A nonliquid that is capable (under STP) of causing fire through friction, absorption of moisture, or spontaneous chemical changes and, when ignited, burns so vigorously and persistently that it creates a hazard. (3) An ignitable compressed gas.
Corrosivity (D002) [40 CFR 261.22]
(1) An aqueous solution with a pH # 2 or $ 12.5 [Method 9040C in SW-846]. (2) A liquid that corrodes steel (SAE 1020) at a rate of > 1/4 inch per year at a test temperature of 130oF [Method 1110A in SW-846]. (1) Normally unstable and readily undergoes violent change without detonating. (2) Reacts violently with water. (3) Forms potentially explosive mixtures with water. (4) When mixed with water, generates toxic gases, vapors, or fumes in a quantity sufficient to present a danger to human health or the environment.
Reactivity (D003) [40 CFR 261.23]
(5) A cyanide- or sulfide-bearing waste that, when exposed to pH conditions between 2 and 12.5, can generate toxic gases, vapors, or fumes in a quantity sufficient to present a danger to human health or the environment. (6) Capable of detonation or explosive reaction if subjected to a strong initiating source or if heated under confinement. (7) Readily capable of detonation or explosive decomposition or reaction at standard temperature and pressure. (8) A forbidden explosive as defined in 49 CFR 173.54, or a Division 1.1, 1.2, or 1.3 explosive as defined in 49 CFR 173.50 and 173.53. A waste that contains constituents above the regulatory threshold listed in Table 1 of 40 CFR 261.24 using the Toxicity Characteristic Leaching Procedure (TCLP) test [Method 1311 in SW846].
Toxicity (D004 to D043) [40 CFR 261.24]
©2017 NCEES
Constituents: arsenic, barium, benzene, cadmium, carbon tetrachloride, chlordane, chlorobenzene, chloroform, chromium, ocresol, m-cresol, p-cresol, total cresols, 2,4D, 1,4-dichlorobenzene, 1,2-dichloroethane, 1,1-dichloroethylene, 2,4-dinitrotoluene, endrin, heptachlor (and its epoxide), hexachlorobenzene, hexachlorobutadiene, hexachloroethane, lead, lindane, mercury, methoxychlor, methyl ethyl ketone, nitrobenzene, pentachlorophenol, pyridine, selenium, silver, tetrachloroethylene, toxaphene, trichloroethylene, 2,4,5-trichlorophenol, 2,4,6-trichlorophenol, 2,4,5-TP (silvex), and vinyl chloride.
531
Chapter 7: Plant Design and Operation Atmospheric Stability Under Various Conditions Surface Wind m Speeda in s
<2 2-3 3-5 5-6 >6
Strongb
Day: Solar Insulation Moderatec
Slightd
A A-B B C C
A-Bf B B-C C-D D
B C C D D
Night: Cloudinesse Cloudy (<4/8) Clear (<3/8)
E E D D D
F F E D D
Source: Turner, D.B., Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed., Florida: Lewis Publishing/CRC Press, 1994.
a. b. c. d. e. f.
Surface wind speed is measured at 10 m above the ground. Corresponds to a clear summer day with sun higher than 60° above the horizon. Corresponds to a summer day with a few broken clouds, or clear day with sun 35–60° above the horizon. Corresponds to a fall afternoon or a cloudy summer day with the sun 15–35°. Cloudiness is defined as the fraction of sky covered by the clouds. For A - B, B - C, or C - D conditions, average the values obtained for each.
A = Very unstable B = Moderately unstable C = Slightly unstable D = Neutral E = Slightly stable F = Stable Regardless of wind speed, Class D should be assumed for overcast conditions, day or night.
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Chapter 7: Plant Design and Operation
103 5 4 3 2
A
102
B
C
D E
5 4 3 2
σy STANDARD DEVIATION, METERS
σz STANDARD DEVIATION, METERS
Standard Deviations of a Plume
F
10 5 4 3 2
2
103 5 4 3 2
102 5 4 3 2
10 1
102
103 2 3 4 5 104 2 3 4 5 105 DISTANCE DOWNWIND, x, METERS 3 4 5
ABCDEF-
MODERATELY UNSTABLE EXTREMELY UNSTABLE SLIGHTLY UNSTABLE NEUTRAL SLIGHTLY STABLE MODERATELY STABLE
2
103 2 3 4 5 104 2 3 4 5 105 DISTANCE DOWNWIND, x, METERS 3 4 5
HORIZONTAL STANDARD DEVIATION OF A PLUME
VERTICAL STANDARD DEVIATION OF A PLUME
©2017 NCEES
5 4 3 2
5
1
102
A B C D E F
104
Source: D.B. Turner, Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed. Florida: Lewis Publishing/CRC Press, 1994.
533
Chapter 7: Plant Design and Operation
100
F E
200 300
180 250
1
0.1 10
A - EXTREMELY UNSTABLE B - MODERATELY UNSTABLE C - SLIGHTLY UNSTABLE D - NEUTRAL E - SLIGHTLY STABLE F - MODERATELY STABLE
150
30 200 D 0 2 50
10
xmax km
Effective Stack Height
-7
10
150 100 200 70 EFF EC 150 100 TIV E 300 50 STA 250 C CK 100 70 HE 40 200 IGH 300 150 7 5 0 30 T, H 0 B 250 40 200 60 150 100 50 20 40 30 300 70 100 200 15 A 30 50 150 20 7 250 100 0 40 20 15 70 50 30 50 40 1 30 20 5 40 15 30 20 20 15
-6
10
-5
10
-4
10 10 10
10
8
7 8 7 8
-3
5
4
10
-2
(Cu/Q)max m-2 ’
Source: Turner, D.B., Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed., CRC Press (Lewis Publishing), 1994.
Effective stack height is shown on curves numerically. xmax
= distance along plume center line to the point of maximum concentration
(Cu/Q)max = e[a H
+ b (ln H) + c (ln H) 2 + d (ln H) 3]
= effective stack height, stack height + plume rise, in meters
Values of Curve-Fit Constants for Estimating (Cu/Q)max from H as a Function of Atmospheric Stability Stability
A B C D E F
Constants
a –1.0563 –1.8060 –1.9748 –2.5302 –1.4496 –1.0488
b –2.7153 –2.1912 –1.9980 –1.5610 –2.5910 –3.2252
c 0.1261 0.0389 0 –0.0934 0.2181 0.4977
d 0 0 0 0 –0.0343 –0.0765
Source: Table 1, Ranchoux, R.J.P., "Determination of Maximum Ground Level Concentration," Journal of the Air Pollution Control Association, vol. 26, no. 11, Lexington: Taylor & Francis Ltd, 1976, p. 1089, reprinted by permission of the Air & Waste Management Association, www.awma.org, and Taylor & Francis Ltd, http://www.tandfonline.com. Journal's website can be found at htpp://informaworld.com.
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Chapter 7: Plant Design and Operation 7.5.5.4 Incineration DRE =
Win - Wout # 100% Win
DRE
= destruction and removal efficiency (%)
where
Win Wout
kg lb = mass feed rate of a particular POHC*, in hr or hr kg lb = mass emission rate of the same POHC*, in hr or hr
*POHC = principal organic hazardous contaminant CO2 CE = # 100% CO2 + CO where CO2 = volume concentration (dry) of CO2 , in parts per million (volume: ppmv) CO = volume concentration (dry) of CO, in ppmv CE = combustion efficiency
7.5.5.5 Kiln Formula L 2.28 D t= SN where t
= mean residence time, in minutes
L/D = internal length-to-diameter ratio S N
in. = kiln rake slope, in ft of length rev = rotational speed, in min
Energy Content of Waste Typical Waste Values
Food waste Paper Cardboard Plastics Wood Glass Bimetallic cans
©2017 NCEES
Moisture (%)
Energy c Btu m
70 6 5 2 20 2 3
2000 7200 7000 14,000 8000 60 300
535
lb
©2017 NCEES
536
Dd Dd Cd Dd B(C)d,e Dd Dd D D
74-84-0 64-17-5 74-85-1 107-06-2 75-21-8 141-78-6 64-17-5 100-41-4 75-00-3
D Dd Cd D Dd,f D Dd Dd,g B(D)d,e Dd D Cd D D Dd
Ad
GAS I GAS I I I I I GAS
I
II I GAS II I I I GAS IIIA I GAS GAS I I GAS I I I
Dd
Dd
Cd
64-19-7 67-64-1 74-86-2 79-10-7 107-13-1 107-18-6 107-05-1 7664-41-7 62-53-3 71-43-2 3583-47-9 106-99-0 71-36-3 25167-67-3 630-08-0 98-82-8 110-82-7 75-19-4
Acetic Acid Acetone Acetylene Acrylic Acid Acrylonitrile Allyl Alcohol Allyl Chloride Ammonia Aniline Benzene n-Butane 1,3-Butadiene 1-Butanol Butylene Carbon Monoxide Cumene Cyclohexane Cyclopropane Diethyl Ether (Ethyl Ether) Ethane Ethanol (Ethyl Alcohol) Ethylene Ethylene Dichloride Ethylene Oxide Ethyl Acetate Ethyl Alcohol Ethyl Benzene Ethyl Chloride
I
Cd
Class I Division Typea Group
60-29-7
75-07-0
CAS No.
Acetaldehyde
Chemical
7.6 Flammability Data
13 −20 −4 13 15 −50
−29 13
−45
36 −17
36
70 –11
54 0 22 −32
39 –20
−38
Flash Point (°C)
472 363 490 413 429 427 363 432 519
160
426 465 305 488 481 378 485 651 615 498 288 420 343 385 609 424 245 503
175
AIT (°C)
3 3.3 2.7 6.2 3 2 3.3 0.8 3.8
1.9
2.5 2.5 2.4 3 2.5 2.9 15 1.2 1.2 1.9 2 1.4 1.6 12.5 0.9 1.3 2.4
4
% LFL
12.5 19 36 16 100 11.5 19 6.7 15.4
36
19.9 12.8 100 8 17 18 11.1 28 8.3 7.8 8.5 11.5 11.2 10 74 6.5 8 10.4
60
1 1.6 1 3.4 1.5 3 1.6 3.7 2.2
2.6
2.1 2 0.9 2.5 1.8 2 2.6 0.6 3.2 2.8 2 1.9 2.6 1.9 0.97 4.1 2.9 1.5
1.5
79.7 1314 93.2 59.5 9.6
59.5
538
4.6 98.8 5430
7 2214.6
15.6 230.7 36,600 4.3 108.5 25.4 366 7498 0.7 94.8
874.9
IIB IIA IIA
IIA IIA IIB
IIB
IIA IIA IIC IIB IIB IIB IIA IIA IIA IIA IIA IIB IIA IIA IIB IIA IIA IIA
IIA
Vapor Vapor Class % Density Pressureb 1 Zone UFL (Air=1) (mm Hg) Groupc
680
0.065 0.46
0.07
0.24
0.19
0.22 0.17
0.88
0.47
0.82 0.88 0.53
0.88
1 0.84
1 0.94 0.76
1.33 6.85 0.2 0.25 0.13
0.78
2.67 1 0.28
0.98
0.59 0.99 0.89
0.91 0.89 0.65
0.83
0.99 1.07 0.79 0.91 0.94 0.54 1.05 0.94 0.91
1.76 1.02 0.25 0.86 0.87 0.84 1.17 3.17
0.92
MIC MESG Ratio (mm)
0.16
1.15 0.017
0.37
MIE (mJ)
Chapter 7: Plant Design and Operation
©2017 NCEES
8008-20-6
Fuel Oil 1 (Jet Fuel)
Dg Dd Dd D D Dd D Cd Dd Dd,h Dd,g Dd,g Bi Dd Dd Dd Dd
8006-61-9 142-82-5 110-54-3 1333-74-0 7783-06-4 75-28-5 78-79-5 108-20-3 8008-20-6 68476-85-7 67-56-1 74-87-3 115-10-6 78-93-3 8030-30-6 111-65-9 109-66-0 1333-74-0 74-98-6 71-23-8 115-07-1 100-42-5
Isobutane Isoprene Isopropyl Ether Kerosene Liquefied Petroleum Gas Methanol (Methyl Alcohol) Methyl Chloride Methyl Ether Methyl Ethyl Ketone Naptha (Petroleum) n-Octane n-Pentane Process Gas > 30% H2 Propane 1-Propanol Propylene Styrene
Dd Dd Dd,g Bd Cd
D
Cd B D
537
GAS GAS I I I I GAS GAS I GAS I
I
I
GAS I I II
I GAS II II or IIIAk II or IIIAk I I I GAS GAS
Class I Division Typea Group
Gasoline n-Heptane n-Hexane Hydrogen Hydrogen Sulfide
Fuel Oil 2 (Diesel)
75-08-1 50-00-0 64-18-6
CAS No.
Ethyl Mercaptan Formaldehyde (Gas) Formic Acid
Chemical
31
15
−46 −41 −6 42 13 −40
12
−54 −28 72
−46 −4 −23
52–96k
38–72k
50
−18
Flash Point (°C)
632 350 404 288 206 243 520 450 413 460 490
385
405
460 220 443 210
280 204 225 500 260
257
210
300 430 434
AIT (°C)
8.1 3.4 1.4 1.1 1 1.5 4 2.1 2.2 2.4 0.9
6
1.8 1.5 1.4 0.7
1.4 1 1.1 4 4
0.7
2.8 7 18
% LFL
17.4 27 11.4 5.9 6.5 7.8 75 9.5 13.7 10.3 6.8
36
8.4 8.9 7.9 5
7.6 6.7 7.5 75 44
5
18 73 57
1.7 1.6 2.5 2.5 3.9 2.5 0.1 1.6 2.1 1.5 3.6
1.1
2 2.4 3.5
3 3.5 3 0.1 1.2
2.1 1 1.6
6.1
20.7
14 513
92.4
126.3
550.6 148.7
45.5 152
42.7
527.4
IIA IIA IIA IIA
IIA IIB IIB IIA IIA IIA
IIA
IIA IIA
IIA
IIA IIA IIC IIB
IIB IIB IIA
Vapor Vapor Class 1 % Density Pressureb Zone UFL (Air=1) (mm Hg) Groupc
0.28
0.28 0.019 0.25
0.53
0.14
1.14
0.24 0.24 0.019 0.68
MIE (mJ)
1.21
0.97 0.45 0.82
0.85 0.92
0.82
0.88 0.88 0.25
0.9
0.97 0.89 0.91
0.94 0.93
1 0.84 0.84
0.92
0.94
0.95
0.91 0.93 0.28 0.9
0.9 0.57 1.86
MIC MESG Ratio (mm)
Chapter 7: Plant Design and Operation
©2017 NCEES
121-44-8 108-05-4 75-01-4 1330-20-7
Triethylamine Vinyl Acetate Vinyl Chloride Xylene
Cd Dd Dd Dd
Cd Dd I I GAS I
I I
Class I Division Typea Group
–9 −6 −78 25
−14 4
Flash Point (°C)
249 402 472 464
321 480
AIT (°C)
1.2 2.6 3.6 0.9
2 1.1
% LFL
8 13.4 33 7
11.8 7.1 3.5 3 2.2 3.7
2.5 3.1 68.5 113.4
161.6 28.53 IIA IIA IIA IIA
IIB IIA
Vapor Vapor Class 1 % Density Pressureb Zone UFL (Air=1) (mm Hg) Groupc
0.2
0.75 0.7
0.54 0.24
MIE (mJ)
1.05 0.94 0.96 1.09
0.87
MIC MESG Ratio (mm)
538
Source: Reproduced with permission from NFPA 497, Recommended Practice for the Classification of Flammable Liquids, Gases, or Vapors and of Hazardous (Classified) Locations for Electrical Installations in Chemical Process Area, © 2012, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.
a. Type designates whether the material is a gas, flammable liquid, or combustible liquid. b. Vapor Pressure is reflected in units of mm Hg at 25°C (77°F), unless stated otherwise. c. Class I Zone Groups are based on 1996 IEC TR3 60079-20, Electrical apparatus for explosive gas atmospheres—Part 20: Data for flammable gases and vapors, relating to the use of electrical apparatus, which contains additional data on MESG and group classifications. d. Material has been classified by test. e. When all conduits run into explosion-proof equipment are provided with explosion-proof seals installed within 450 mm (18 in.) of the enclosure, equipment for the group classification shown in parentheses is permitted. f. For classification of areas involving ammonia, see ASHRAE 15, Safety Code for Mechanical Refrigeration, and ANSI/CGA G2.1, Safety Requirements for the Storage and Handling of Anhydrous Ammonia. g. Commercial grades of aliphatic hydrocarbon solvents are mixtures of several isomers of the same chemical formula (or molecular weight). The autoignition temperatures of the individual isomers are significantly different. The electrical equipment should be suitable for the AIT of the solvent mixture. h. [deleted] i. Petroleum naphtha is a saturated hydrocarbon mixture whose boiling range is 20°C to 135°C (68°F to 275°F). It is also known as benzine, ligroin, petroleum ether, and naphtha. j. Fuel and process gas mixtures found by test not to present hazards similar to those of hydrogen may be grouped based on the test results. k. [deleted]
109-99-9 108-88-3
CAS No.
Tetrahydrofuran Toluene
Chemical
Chapter 7: Plant Design and Operation
8 PHYSICAL PROPERTIES 8.1 Symbols and Definitions Symbols Symbol
Units (U.S.)
Units (SI)
cp
Heat capacity (at constant pressure)
Btu lbm -cF
J = m2 kg : K s 2 : K
cv
Heat capacity (at constant volume)
Btu lbm -cF
h
Specific enthalpy
Btu lbm
J = m2 kg : K s 2 : K J kg
Dhfusion
Enthalpy of fusion
Btu lbm
J kg
Enthalpy of vaporization
Btu lbm
J kg
Btu hr -ft -cF lbm lb mole
W m:K g mol
Dhvap k MW
©2017 NCEES
Description
Thermal conductivity Molar mass (molecular weight)
lbf or psi in 2
kg m : s2
P
Pressure
r
cp Ratio of heat capacities = c v
s
Specific entropy
Btu lbm -cF
J kg : K
T
Temperature
cF or cR
cC or K
v
Specific volume
ft 3 lbm
m3 kg
a
Thermal diffusivity
ft 2 sec
m2 s
Pa =
dimensionless
539
Chapter 8: Physical Properties Symbols (cont'd) Description
Symbol
Units (U.S.)
Units (SI)
dyne cm lbm ft -sec
N m kg Pa : s = m : s
g
Surface tension
m
Dynamic viscosity
u
Kinematic viscosity
ft 2 sec
m2 s
r
Density
lbm ft 3
kg m3
r
Electrical resistivity
X - ft
X:m
8.2 Physical Properties of Metals 8.2.1
U.S. Customary Units
Thermal Conductivity
Thermal Diffusivity
lbm ft 3
Btu lbm-cF
Btu hr -ft -cF
ft 2 hr
26.98
168 532.0 540.0 95.5 449.1 557.0 557.7 1203.7 491.5 455.0 708.1 33.3 108.5 466.5 845.7 638.2 556.1 530.0 748.8 1339.1 53.8
0.214 0.091 0.082 0.152 0.097 0.098 0.093 0.031 0.109 0.100 0.031 1.093 0.250 0.120 0.034 0.065 0.105 0.106 0.055 0.032 0.180
136.35 61.80 15.00
3.55 1.27
Aluminum Brass 70%Cu, 30%Zn Bronze 75%Cu, 25%Sn Calcium Chromium Constantan Copper Gold Iron Iron, cast Lead Lithium Magnesium Manganese Mercury (liquid) Molybdenum Nickel Nichrome V Palladium Platinum Potassium ©2017 NCEES
40.08 52.00 63.54 196.97 55.85 207.20 6.94 24.31 54.94 200.59 95.94 58.69 106.40 195.08 39.09
55.75 13.10 232.84 184.31 48.24 29.60 20.80 49.69 90.71 4.62 4.51 80.31 54.31 7.06 41.60 41.60 60.09 540
X -ft : 10 8.20
3.68
0.87 0.12 0.09
cF
Btu lbm
5.09 6.73 29.20
1220 1700 1200 1544 2939 2336 1983 1947 2804
62.99 28.05 12.93 452.75 308.72 16.40 20.34
621 356 1202 2282 –38 4748 2651
32.81 32.18 20.01
2829 3222 145
10.50 41.67 0.24 3.98 4.52 0.83 0.65 0.80
−8
Heat of Fusion
Heat Capacity
lbm lb mole
Melting Point
Density
U.S. Unit:
Electrical Resistivity (0°C)
Property:
Molar Mass
Physical Properties of Metals at 68°F (U.S. Units)
138.2 72.2 83.58 215.4 89 28.8 114.7 41.4 10.62 147.4 114.6 5.08 186.3 132.8
43.3 25.0
Chapter 8: Physical Properties
8.2.2
Btu hr -ft -cF
ft 2 hr
X -ft : 10
6.42
87.24 247.28 82.04
118.69 47.88 183.85 238.03 65.38
488.0 488.0 454.8 281.4 1202.0 1189.3 445.4
0.113 0.110 0.055 0.126 0.034 0.028 0.094
24.80 9.40 39.29 12.71 102.26 15.60 67.60
0.45 0.17 1.57 2.44 0.53 1.55
Heat of Fusion
0.058 0.056 0.295
Melting Point
Btu lbm-cF
102.91 107.87 22.99
lbm ft 3 775.4 655.5 60.3
Electrical Resistivity (0°C)
Thermal Diffusivity
Rhodium Silver Sodium Steel, carbon Steel, mild (1%C) Steel, stainless Tin Titanium Tungsten Uranium Zinc
Thermal Conductivity
lbm lb mole
Heat Capacity
U.S. Unit:
Density
Property:
Molar Mass
Physical Properties of Metals at 68°F (U.S. Units) (cont'd)
cF
Btu lbm
14.11 4.82 13.78
3565 1762 208
45.0 37.8
37.73 127.95 16.08 91.86 18.04
450 3038 6129 2075 786
25.2 122.6 109.7
−8
43.9
SI Units
©2017 NCEES
63.54 196.97 55.85 207.20 6.94 24.31 54.94 200.59
m2 s
896 381 343 636 407 410 389 130 456 419 130 4576 1047 502 142
236.0 107.0 26.0
91.61 32.77
541
96.5 22.7 403.0 319.0 83.5 51.2 36.0 86.0 157.0 8.0 7.8
Electrical Resistivity (0°C)
W m:K
Heat of Fusion
40.08 52.00
J kg : K
Melting Point
26.98
Thermal Diffusivity
Aluminum Brass 70%Cu, 30%Zn Bronze 75%Cu, 25%Sn Calcium Chromium Constantan Copper Gold Iron Iron, cast Lead Lithium Magnesium Manganese Mercury (liquid)
kg m3 2698 8522 8650 1530 7194 8922 8933 19,281 7873 7288 11,343 533 1738 7473 13,547
Thermal Conductivity
g mol
Heat Capacity
SI Unit:
Density
Property:
Molar Mass
Physical Properties of Metals at 20°C (SI Units)
cC
kJ kg 321.5 167.9
1.55 2.05 8.90
660 927 649 840 1615 1280 1084 1064 1540
19.20 8.55 3.94 138.00 94.10
327 180 650 1250 –39
X -ft : 10 2.50
3.20 12.70 6.19 102.71 116.64 21.42 16.77 20.64 94.97
−8
194.4 501.1 207.0 67.0 266.7 96.3 24.7 342.9 266.6 11.8
Chapter 8: Physical Properties
m2 s
Molybdenum Nickel Nichrome V Palladium Platinum Potassium Rhodium Silver Sodium Steel, carbon Steel, mild (1%C) Steel, stainless Tin Titanium Tungsten Uranium Zinc
106.40 195.08 39.09 102.91 107.87 22.99
10,222 8907 8490 11,995 21,450 862 12,420 10,500 966
272 440 444 230 134 754 243 235 1235
139.0 94.0 12.2 72.0 72.0 104.0 151.0 428.0 142.0
118.69 47.88 183.85 238.03 65.38
7817 7817 7285 4508 19,254 19,050 7135
473 461 230 528 143 117 394
42.9 16.3 68.0 22.0 177.0 27.0 117.0
95.94 58.69
Heat of Fusion
Thermal Diffusivity
W m:K
g mol
Melting Point
Thermal Conductivity
J kg : K
SI Unit:
Electrical Resistivity (0°C)
Heat Capacity
kg m3
Property:
Molar Mass
Density
Physical Properties of Metals at 20°C (SI Units) (cont'd)
cC
kJ kg
5.00 6.20
2620 1455
433.3 308.9
10.00 9.81 6.10 4.30 1.47 4.20
1554 1772 63 1963 961 98
11.50 39.00 4.90 28.00 5.50
232 1670 3387 1135 419
X -ft : 10
22.45 3.10 2.32
165.67
11.61 4.39 40.52 62.97 13.68 40.00
−8
8.3 Physical Properties of Plastics 8.3.1
U.S. Customary Units Physical Properties of Plastics (U.S. Units) Property:
Density
Heat Capacity
Thermal Conductivity
U.S. Unit:
lbm ft 3 64–75 64–71 57–78 57–60 69–125 77–97 1.0–2.0 109–117 134 130–140 134 106
Btu lbm-cF 0.361–0.370 0.330–0.399 0.279–0.301 0.499–0.549 0.320–0.499 0.251
Btu hr -ft -cF 0.092–0.156 0.098–0.196 0.110–0.127 0.243–0.283 0.191–0.526 0.081–0.110 0.017–0.023 0.083–0.110 0.113 0.142–0.375 0.113 0.138
ABS Nylon Polycarbonate Polyethylene Polyester PVC Polystyrene foam PVDF PFA PTFE FEP ETFE ©2017 NCEES
0.28–0.36 0.28 0.28 0.28 542
100.8 58.1 104.7 87.9
58.6 285.1 255.1 102.1
Chapter 8: Physical Properties
8.3.2
SI Units Physical Properties of Plastics (SI Units) Property: SI Unit:
ABS Nylon Polycarbonate Polyethylene Polyester PVC Polystyrene foam PVDF PFA PTFE FEP ETFE
©2017 NCEES
Density
Heat Capacity
Thermal Conductivity
kg m3 1020–1200 1030–1140 910–1250 913–968 1100–2010 1240–1550 16–32 1746–1874 2150 2082–2243 2150 1700
J kg : K
W m:K
1510–1550 1380–1670 1170–1260 2090–2300 1340–2090 1050
0.16–0.27 0.17–0.34 0.19–0.22 0.42–0.49 0.33–0.91 0.14–0.19 0.03–0.04 0.14–0.19 0.20 0.25–0.65 0.20 0.24
543
1172–1507 1172 1172 1172
Chapter 8: Physical Properties
8.3.3
Chemical Resistance of Plastics Acrylonitrile Butadiene Styrene Polymer (ABS)
Polyvinyl Chloride, Type I (PVC)
Saran
Polyester Glass
Epoxy Glass
Phenolic Asbestos
Fluorocarbons
Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Poor Excel. Poor Poor Poor Poor Poor
Good Poor Excel. Poor Good Fair Poor Poor Excel. Excel. Excel. Excel. Excel. Poor Poor Excel. Poor Poor Poor Poor
Excel. Excel. Excel. Good Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Poor Poor Poor Excel.
Excel. Excel. Excel. Excel. Excel. Good Excel. Excel. Excel. Excel. Excel. Excel. Excel. Good Excel. Excel. Poor Fair Poor Excel.
Excel. Excel. Excel. Excel. Excel. Fair Fair Poor Excel. Excel. Excel. Excel. Excel. Poor Good Excel. Fair Fair Fair Excel.
Excel. Good Excel. Good Excel. Fair Poor Fair Excel. Excel. Excel. Excel. Excel. Poor Excel. Excel. Good Excel. Poor Excel.
Excel. Good Excel. Good Excel. Excel. Good Excel. Excel. Excel. Excel. Excel. Excel. Poor Excel. Excel. Excel. Good Good Excel.
Excel. Excel. Excel. Fair Excel. Poor Poor Poor Excel. Excel. Excel. Good Excel. Excel. Excel. Excel. Excel. Excel. Poor Excel.
Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.
Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Fair Fair Good Excel.
Polycarbonate
Cellulose Acetate Butyrate (CAB)
10% H2SO4 50% H2SO4 10% HCl 10% HNO3 10% Acetic 10% NaOH 50% NaOH NH4OH NaCl FeCl2 CuSO4 NH4NO3 Wet H2S Wet Cl2 Wet SO2 Gasoline Benzene CCl4 Acetone Alcohol
Chlorinated Polyether (Penton)
Plastic:
Polypropylene, Polyethylene
Chemical Resistance of Plastics
Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.
Excel. Fair Poor Good Excel.
Source: Perry, R.H., and D. Green, Perry’s Chemical Engineers’ Handbook, 6th ed., New York: McGraw-Hill, 1985, p. 23-52.
©2017 NCEES
544
Chapter 8: Physical Properties
8.4 Physical Properties of Liquids and Gases—Temperature-Independent Properties 8.4.1
U.S. Customary Units
Triple Point
Heat of Vaporization at NBP
Critical Temperature
Critical Pressure
cF
Btu lbm
cF
psia
69.8 244.2 455.1 –114.7 –317.6 –28.0 –302.5 176.1 31.1 10.9 20.6 245.8 23.8 51.7 –109.2 –312.7 –58.3 170.0 –29.2
–190.1 62.0 –138.5 564.4 –352.1 –107.8 –301.7 41.9 –216.9 –255.0 –301.6 –128.7 –164.0 –213.2 –69.8 –337.0 –217.9 –9.1 –149.7
253.2 167.4 219.3 270.5 588.8 69.3 169.3 165.7 157.0 167.5 249.6 178.1 190.4 246.5 92.3 132.8 83.0 121.5
379.1 605.8 455.1 95.4 –221.1 270.1 –188.4 552.0 305.5 274.4 295.4 553.9 305.5 362.0 87.8 –220.5 222.1 541.8 290.7
807.8 839.2 681.7 900.1 549.1 1643.7 724.1 711.7 550.6 526.3 583.1 640.2 619.4 702.9 1070.0 506.8 923.7 661.4 1157.1
lbm ft 3 17.85 21.17 17.34 13.82 21.39 14.05 33.44 19.02 14.23 14.08 14.54 16.95 15.16 15.45 29.19 18.97 27.78 34.79 34.01
C9H12
120.192
306.2
–140.8
131.9
676.4
462.2
17.78
C6H12 C10H22 C4H10O C2H6 C2H6O C4H8O2 C8H10 C2H4
84.160 142.282 74.122 30.069 46.068 88.105 106.165 28.053
177.3 345.4 94.0 –127.4 172.9 170.7 277.1 –154.8
44.1 –21.4 –177.3 –297.0 172.9 –118.4 –138.9 –272.5
153.2 118.8 154.2 210.4 365.7 156.9 144.2 207.4
536.8 652.2 380.4 89.9 465.5 482.3 651.2 48.6
591.8 305.0 527.9 706.7 890.1 562.7 525.4 731.3
16.94 14.57 16.52 12.87 17.11 19.23 18.17 13.37
545
Critical Density
Normal Boiling Point (NBP)
Acetaldehyde Acetic Acid Acetone Acetylene Air Ammonia Argon Benzene n-Butane iso-Butane 1-Butene 1-Butanol 1,3-Butadiene 1,2-Butadiene Carbon dioxide Carbon monoxide Carbonyl sulfide Carbon tetrachloride Chlorine Cumene (isopropylbenzene) Cyclohexane n-Decane Diethyl ether Ethane Ethanol Ethyl acetate Ethylbenzene Ethylene
©2017 NCEES
cF
C2H4O C2H4O2 C3H6O C2H2 NH3 Ar C6H6 C4H10 C4H10 C4H8 C4H10O C4H6 C4H6 CO2 CO COS CCl4 Cl2
lbm lb mole 44.053 60.052 58.079 26.037 28.965 17.031 39.948 78.112 58.122 58.122 56.106 74.1216 54.090 54.090 44.010 28.010 60.075 153.823 70.906
$
Chemical
Formula
Property:
Molar Mass
Temperature-Independent Properties of Liquids and Gases (U.S. Units)
Chapter 8: Physical Properties
62.000 37.997 30.026 4.003 100.202 86.175 2.016 36.461 34.081 16.043 32.042 74.07854 31.057 72.106 20.180 123.109 28.013 128.255 114.229
387.0 –306.6 –2.7 –781.7 209.1 155.7 –423.0 –121.0 –76.5 –258.7 148.5 134.5 20.6 175.4 –410.9 411.5 –320.4 303.4 258.1
7.9 –363.4 –180.4 –788.4 –131.1 –139.6 –434.6 –173.5 –121.8 –296.4 –143.8 –144.4 –136.2 –124.0 –415.5 42.4 –346.0 –64.2 –70.2
C8H18
114.229
210.6
O2 C5H12 C5H12 C3H8 C3H8O C3H6 SO2 C8H8 C7H8 H2O C8H10 C8H10 C8H10
31.999 72.149 72.149 44.096 60.095 42.080 64.064 104.149 92.138 18.015 106.165 106.165 106.165
–297.3 82.1 96.9 –43.8 207.0 –53.7 14.0 293.5 231.1 212.0 281.0 282.3 291.9
546
Critical Density
C2H6O2 F2 CH2O He C7H16 C6H14 H2 HCl H2S CH4 CH4O C3H6O2 CH5N C4H8O Ne C6H5NO2 N2 C9H20 C8H18
Critical Pressure
cF
Critical Temperature
Triple Point
cF
Heat of Vaporization at NBP
Normal Boiling Point (NBP)
Ethylene glycol Fluorine Formaldehyde Helium n-Heptane n-Hexane Hydrogen Hydrogen chloride Hydrogen sulfide Methane Methanol Methyl acetate Methyl amine Methyl ethyl ketone Neon Nitrobenzene Nitrogen n-Nonane n-Octane iso-Octane (2,2,4trimethylpentane) Oxygen iso-Pentane n-Pentane Propane 1-Propanol Propylene Sulfur dioxide Styrene Toluene Water p-Xylene m-Xylene o-Xylene
©2017 NCEES
lbm lb mole
$
Chemical
Formula
Property:
Molar Mass
Temperature-Independent Properties of Liquids and Gases (U.S. Units) (cont'd)
Btu lbm
cF
psia
lbm ft 3
75.0 329.7 8.8 136.2 144.0 192.9 190.7 234.9 219.6 473.1 176.7 361.0 188.5 36.9 190.0 85.6 124.1 129.9
–199.7 296.3 –450.3 512.6 453.8 –400.0 124.5 211.9 –116.7 462.8 452.1 314.4 504.2 –379.6
770.2 955.8 33.1 396.8 436.9 188.0 1202.1 1305.3 667.1 1172.5 688.9 1082.0 601.9 398.9
37.01 22.02 4.34 14.48 14.56 1.95 26.86 21.68 10.15 17.09 20.28 12.59 16.85 30.09
–232.5 610.5 564.2
492.5 330.8 360.7
19.56 14.49 14.66
–161.3
115.3
519.5
373.0
15.12
–361.8 –256.9 –201.4 –305.7 –195.2 –301.4 –103.8 –23.2 –139.3 32.0 55.9 –54.1 –13.3
91.6 147.6 153.7 183.0 297.5 188.7 167.3 151.2 155.1 970.1 144.6 146.2 147.3
–181.4 369.0 385.8 206.1 506.6 195.9 315.5 683.7 605.5 705.1 649.4 650.7 674.8
731.4 489.9 488.8 616.6 749.7 660.6 1143.5 563.2 598.5 3200.1 512.2 512.7 542.1
27.23 14.73 14.48 13.76 17.13 14.33 32.77 18.24 18.23 20.10 17.85 17.66 17.79
Chapter 8: Physical Properties
8.4.2
SI Units
Triple Point
Heat of Vaporization at NBP
Critical Temperature
Critical Pressure
cC
cC
kJ kg
cC
MPa
C2H4O C2H4O2 C3H6O C2H2 NH3 Ar C6H6 C4H10 C4H10 C4H8 C4H10O C4H6 C4H6 CO2 CO COS CCl4 Cl2
44.053 60.052 58.079 26.037 28.965 17.031 39.948 78.112 58.122 58.122 56.106 74.1216 54.090 54.090 44.010 28.010 60.075 153.823 70.906
21.0 117.9 235.1 –81.5 –194.2 –33.3 –185.8 80.1 –0.5 –11.7 –6.35 118.75 –4.6 11.0 –78.5 –191.5 –50.2 76.6 –34.0
C9H12
120.192
152.3
–96.0
306.8
C6H12 C10H22 C4H10O C2H6 C2H6O C4H8O2 C8H10 C2H4 C2H6O2 F2 CH2O He C7H16 C6H14
84.160 142.282 74.122 30.069 46.068 88.105 106.165 28.053 62.000 37.997 30.026 4.003 100.202 86.175
80.7 174.1 34.4 –88.6 78.3 77.1 136.2 –103.8 197.2 –188.1 –19.3 –452.1 98.4 68.7
6.7 –29.7 –116.3 –182.8 78.3 –83.6 –95.0 –169.2 –13.4 –219.7 –118.0 –455.8 –90.6 –95.3
356.3 276.3 358.6 489.4 850.6 365.0 335.4 482.4 174.4 767.0 20.6 316.8 334.9
547
Critical Density
Normal Boiling Point (NBP)
Acetaldehyde Acetic Acid Acetone Acetylene Air Ammonia Argon Benzene n-Butane Isobutane 1-Butene 1-Butanol 1,3-Butadiene 1,2-Butadiene Carbon dioxide Carbon monoxide Carbonyl sulfide Carbon tetrachloride Chlorine Cumene (isopropylbenzene) Cyclohexane n-Decane Diethyl ether Ethane Ethanol Ethyl acetate Ethylbenzene Ethylene Ethylene glycol Fluorine Formaldehyde Helium n-Heptane n-Hexane ©2017 NCEES
g mol
$
Chemical
Formula
Property:
Molar Mass
Temperature-Independent Properties of Liquids and Gases (SI Units)
5.57 5.79 4.70 6.21 3.79 11.33 4.99 4.91 3.80 3.63 4.02 4.414 4.27 4.85 7.38 3.49 6.37 4.56 7.98
kg m3 286 339 278 221 343 225 536 305 228 226 233 272 243 247 468 304 445 557 545
358.0
3.19
285
280.5 344.6 193.6 32.2 240.9 250.2 344.0 9.2 –128.7 146.9 –268.0 267.0 234.3
4.08 2.10 3.64 4.87 6.14 3.88 3.62 5.04 5.31 6.59 0.23 2.74 3.01
271 233 265 206 274 308 291 214
–123.4 588.8 192.9 16.7 389.3 318.8 –94.7 510.0 235.1 295.8 629.3 35.2 –213.4 –140.6 –77.7 1,369.5 132.3 –185.4 161.2 –122.5 5.5 393.8 288.9 –138.3 385.5 152.0 –159.4 365.2 134.7 –185.35 389.7 146.35 –89.3 580.573 289.95 –108.9 414.3 151.9 –136.2 442.9 183.4 –56.6 573.4 31.0 –205.0 214.7 –140.3 –138.8 308.9 105.6 –22.82 193.1 283.2 –100.9 282.6 143.7
593 353 70 232 233
Chapter 8: Physical Properties
cC
2.016 36.461 34.081 16.043 32.042 74.07854 31.057 72.106
–252.8 –85.0 –60.3 –161.5 64.7 56.9 –6.3 79.6
–259.2 –114.1 –85.5 –182.5 –97.7 –98.0 –93.5 –86.7
–246.0 210.9 –195.8 150.8 125.6
Hydrogen Hydrogen chloride Hydrogen sulfide Methane Methanol Methyl acetate Methyl amine Methyl ethyl ketone
H2 HCl H2S CH4 CH4O C3H6O2 CH5N C4H8O
Neon Nitrobenzene Nitrogen n-Nonane n-Octane iso-Octane (2,2,4-trimethylpentane) Oxygen iso-Pentane n-Pentane Propane 1-Propanol Propylene Sulfur dioxide Styrene Toluene Water p-Xylene m-Xylene o-Xylene
Ne 20.180 C6H5NO2 123.109 N2 28.013 C9H20 128.255 C8H18 114.229
kJ kg
cC
MPa
448.7 443.6 546.4 510.8 1100.5 411.1 839.8 438.3
–240.0 51.4 100.0 –82.6 239.4 233.4 156.9 262.4
1.30 8.29 9.00 4.60 8.08 4.75 7.46 4.15
kg m3 31 430 347 163 274 325 202 270
–248.6 5.8 –210.0 –53.5 –56.8
85.8 442.7 199.2 288.7 302.1
–228.7
2.75
482
–147.0 321.4 295.7
3.40 2.28 2.49
313 232 235
Critical Density
Critical Pressure
cC
Critical Temperature
Triple Point
g mol
Heat of Vaporization at NBP
Normal Boiling Point (NBP)
$
Chemical
Molar Mass
Property:
Formula
Temperature-Independent Properties of Liquids and Gases (SI Units) (cont'd)
C8H18
114.229
99.2
–107.4
268.2
270.9
2.57
242
O2 C5H12 C5H12 C3H8 C3H8O C3H6 SO2 C8H8 C7H8 H2O C8H10 C8H10 C8H10
31.999 72.149 72.149 44.096 60.095 42.080 64.064 104.149 92.138 18.015 106.165 106.165 106.165
–183.0 27.8 36.1 –42.1 97.2 –47.6 –10.0 145.3 110.6 100.0 138.3 139.1 144.4
–218.8 –160.5 –129.7 –187.6 –126.2 –185.2 –75.5 –30.7 –95.2 0.0 13.3 –47.9 –25.2
213.1 343.3 357.5 425.7 692.0 438.9 389.1 351.7 360.8 2256.5 336.3 340.1 342.6
–118.6 187.2 196.6 96.7 263.7 91.1 157.5 362.1 318.6 705.1 343.0 343.7 357.1
5.04 3.38 3.37 4.25 5.17 4.55 7.88 3.88 4.13 22.06 3.53 3.53 3.74
436 236 232 220 274 230 525 292 292 322 286 283 285
Source for tables in Section 8.4: "Table of Physical Properties for Hydrocarbons and Other Compounds of Interest to the Natural Gas and Natural Gas Liquids Industries," GPS Standard 2145-16, Tulsa, OK: GPA Midstream Association, 2016, pp. 4–9, and NIST Chemistry Web Book, NIST Standard Reference Database Number 69, P.J. Linstrom and W.G. Mallard, eds.
©2017 NCEES
548
Chapter 8: Physical Properties
8.5 Physical Properties of Liquids and Gases—Temperature-Dependent Properties 8.5.1
U.S. Customary Units Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) Gas
Temperature
cF
Nitrogen
Oxygen
Carbon Monoxide
Carbon Dioxide
Sulfur Dioxide
Air
©2017 NCEES
0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000
Density
lbm ft 3 0.0835 0.0582 0.0446 0.0362 0.0304 0.0263 0.0955 0.0664 0.0510 0.0414 0.0348 0.0300 0.0835 0.0581 0.0446 0.0362 0.0304 0.0263 0.131 0.0914 0.0701 0.0569 0.0479 0.0413 0.195* 0.134 0.102 0.0829 0.0697 0.0601 0.0864 0.0601 0.0461 0.0374 0.0315 0.0272
Heat Thermal Capacity (Cp) Conductivity
Btu lbm - cF 0.248 0.249 0.251 0.256 0.262 0.269 0.218 0.222 0.230 0.239 0.246 0.252 0.248 0.249 0.253 0.259 0.266 0.273 0.190 0.219 0.239 0.255 0.268 0.279 0.143 0.158 0.171 0.182 0.190 0.196 0.239 0.240 0.244 0.249 0.256 0.262 549
Btu ft - hr -cF 0.0129 0.0175 0.0217 0.0256 0.0294 0.0331 0.0133 0.0184 0.0231 0.0276 0.0318 0.0359 0.0126 0.0172 0.0213 0.0251 0.0286 0.0320 0.00763 0.0127 0.0179 0.0230 0.0279 0.0325 0.00443 0.00738 0.0107 0.0142 0.0177 0.0208 0.0132 0.0178 0.0220 0.0259 0.0297 0.0333
Thermal Diffusivity 2
ft hr 0.624 1.21 1.93 2.76 3.69 4.68 0.637 1.24 1.97 2.79 3.71 4.74 0.608 1.18 1.88 2.68 3.54 4.47 0.307 0.632 1.07 1.59 2.18 2.82 0.159 0.349 0.612 0.945 1.34 1.76 0.639 1.23 1.95 2.78 3.69 4.68
Viscosity
lbm ft - sec 10.6E–6 13.9E–6 16.8E–6 19.5E–6 22.0E–6 24.3E–6 12.2E–6 16.3E–6 19.9E–6 23.1E–6 26.1E–6 28.8E–6 10.5E–6 13.9E–6 16.8E–6 19.4E–6 21.7E–6 23.9E–6 8.65E–6 12.2E–6 15.3E–6 18.2E–6 20.8E–6 23.2E–6 7.38E–6 10.7E–6 13.8E–6 16.6E–6 19.3E–6 21.8E–6 11.06E–6 14.5E–6 17.5E–6 20.1E–6 22.5E–6 24.7E–6
Prandtl Number
0.730 0.713 0.704 0.701 0.704 0.709 0.722 0.710 0.714 0.721 0.727 0.730 0.745 0.727 0.719 0.721 0.726 0.733 0.774 0.760 0.739 0.723 0.716 0.715 0.856 0.823 0.791 0.764 0.746 0.741 0.716 0.705 0.698 0.697 0.698 0.698
Chapter 8: Physical Properties Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) (cont'd) Temperature Gas
cF
Hydrogen
Ammonia
Helium
Neon
Argon
Fluorine
©2017 NCEES
0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000
Density
lbm ft 3 0.00600 0.00420 0.00320 0.00260 0.00220 0.00190 0.0514 0.0355 0.0272 0.0220 0.0185 0.0160 0.0119 0.00830 0.00640 0.00520 0.00440 0.00380 0.0601 0.0419 0.0321 0.0261 0.0219 0.0189 0.119 0.0830 0.0636 0.0516 0.0434 0.0375 0.113 0.0789 0.0605 0.0491 0.0413 0.0356
Heat Thermal Capacity (Cp) Conductivity
Btu lbm - cF
Btu ft - hr -cF
3.37 3.45 3.47 3.47 3.48 3.51 0.484 0.529 0.581 0.630 0.677 0.722 1.24 1.24 1.24 1.24 1.24 1.24 0.246 0.246 0.246 0.246 0.246 0.246 0.124 0.124 0.124 0.124 0.124 0.124 0.192 0.204 0.214 0.220 0.225 0.229
0.0911 0.121 0.148 0.174 0.199 0.222 0.0117 0.0193 0.0278 0.0371 0.0471 0.0577 0.0802 0.102 0.123 0.142 0.160 0.178 0.0253 0.0325 0.0390 0.0449 0.0505 0.0558 0.00903 0.0121 0.0148 0.0173 0.0196 0.0217 0.0127 0.0179 0.0229 0.0279 0.0328 0.0376**
550
Thermal Diffusivity 2
ft hr 4.50 8.34 13.3 19.3 25.9 33.4 0.471 1.03 1.76 2.67 3.76 4.99 5.43 9.94 15.5 22.0 29.4 37.8 1.71 3.15 4.93 7.00 9.38 12.0 0.609 1.17 1.87 2.69 3.63 4.66 0.585 1.11 1.77 2.58 3.53 4.62
Viscosity
lbm ft - sec 5.38E–6 6.89E–6 8.27E–6 9.54E–6 10.7E–6 11.9E–6 5.76E–6 8.48E–6 11.2E–6 13.9E–6 16.6E–6 19.3E–6 12.0E–6 15.4E–6 18.5E–6 21.4E–6 24.2E–6 26.8E–6 19.0E–6 24.3E–6 29.1E–6 33.5E–6 37.6E–6 41.5E–6 13.4E–6 18.0E–6 22.1E–6 25.8E–6 29.2E–6 32.4E–6 13.6E–6 18.4E–6 22.7E–6 26.7E–6 30.4E–6 33.9E–6
Prandtl Number
0.718 0.708 0.697 0.685 0.678 0.675 0.857 0.837 0.843 0.851 0.860 0.869 0.669 0.671 0.672 0.672 0.672 0.672 0.664 0.662 0.660 0.660 0.659 0.659 0.663 0.666 0.667 0.667 0.667 0.667 0.740 0.758 0.763 0.759 0.751 0.741
Chapter 8: Physical Properties Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) (cont'd) Temperature Gas
cF
Chlorine
Methane
Ethane
Propane
Acetylene
©2017 NCEES
0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000
Density
lbm ft 3 0.215 0.148 0.113 0.0918 0.0772 0.0666 0.0480 0.0333 0.0256 0.0207 0.0174 0.0150 0.0907 0.0627 0.0480 0.0389 0.0327 0.0282 0.135 0.0923 0.0705 0.0571 0.0480 0.0414 0.0784 0.0542 0.0415 0.0337 0.0283 0.0244
Heat Thermal Capacity (Cp) Conductivity
Btu lbm - cF
Btu ft - hr -cF
0.112 0.118 0.121 0.123 0.124 0.125 0.512 0.578 0.673 0.772 0.866 0.953 0.377 0.485 0.599 0.700 0.787 0.863 0.353 0.470 0.589 0.690 0.773 0.844 1.60 0.442 0.494 0.531 0.558 0.581
0.00429 0.00649 0.00861 0.0106 0.0126 0.0144 0.0164 0.0256 0.0360 0.0475 0.0599** 0.0731** 0.00939 0.0179 0.0282 0.0399 0.0526 0.0663 0.00777 0.0151 0.0242 0.0348 0.0467 0.0597 0.0193 0.0171 0.0241 0.0309 0.0375 0.0441
551
Thermal Diffusivity 2
ft hr 0.178 0.372 0.629 0.943 1.31 1.73 0.667 1.33 2.09 2.97 3.97 5.11 0.275 0.590 0.981 1.46 2.04 2.72 0.163 0.348 0.583 0.884 1.26 1.71 0.0377 0.715 1.18 1.73 2.37 3.11
Viscosity
lbm ft - sec 7.72E–6 11.0E–6 14.1E–6 17.0E–6 19.8E–6 22.5E–6 6.57E–6 8.93E–6 11.0E–6 12.9E–6 14.6E–6 16.3E–6 5.43E–6 7.59E–6 9.56E–6 11.4E–6 13.1E–6 14.7E–6 4.87E–6 6.74E–6 8.56E–6 10.3E–6 12.1E–6 13.8E–6 9.36E–6 8.38E–6 10.6E–6 12.7E–6 14.6E–6** 16.4E–6**
Prandtl Number
0.724 0.720 0.713 0.708 0.705 0.704 0.739 0.727 0.741 0.755 0.762 0.763 0.786 0.739 0.731 0.720 0.706 0.691 0.797 0.757 0.750 0.738 0.720 0.702 0.774 0.778 0.786 0.787 0.783 0.777
Chapter 8: Physical Properties Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) (cont'd) Temperature Gas
cF
Ethylene
Propylene
Hydrogen Sulfide
0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000
Density
lbm ft 3 0.0844 0.0584 0.0447 0.0363 0.0305 0.0263 0.128 0.0880 0.0673 0.0545 0.0458 0.0395 0.1027 0.0711 0.0544 0.0441 0.0371 0.0320
Heat Thermal Capacity (Cp) Conductivity
Btu lbm - cF
Btu ft - hr -cF
0.332 0.424 0.515 0.595 0.665 0.725 0.329 0.428 0.518 0.600 0.674 0.738 0.237 0.246 0.258 0.272 0.286 0.300
0.00930 0.0170 0.0266 0.0380 0.0508** 0.0651** 0.00765 0.0146 0.0229 0.0323 0.0425 0.0535 0.0065 0.0108 0.0144 0.0184 0.0229** 0.0279**
Thermal Diffusivity 2
ft hr 0.332 0.685 1.16 1.76 2.51 3.41 0.182 0.386 0.656 0.986 1.38 1.84 0.267 0.616 1.03 1.53 2.16 2.90
Viscosity
lbm ft - sec 5.90E–6 8.31E–6 10.5E–6 12.4E–6 14.2E–6 15.8E–6 4.94E–6 7.10E–6 9.08E–6 10.9E–6 12.6E–6 14.2E–6 7.27E–6 10.5E–6 13.7E–6 16.9E–6** 20.2E–6** 23.4E–6**
Prandtl Number
0.758 0.749 0.730 0.702 0.669 0.635 0.763 0.751 0.741 0.730 0.718 0.703 0.956 0.862 0.884 0.901 0.908 0.908
* The vapor pressure of sulfur dioxide at 0˚F is 10.2 psia. Hypothetical vapor density at 0˚F and 14.7 psia is reported in the table. ** Extrapolated values Sources: These data are provide courtesy of the American Institute of Chemical Engineering (AIChE) and its thermophysical property research consortium, the Design Institute for Physical Properties (DIPPR®) using DIPPR® 2016 version. Vapor densities were obtained using SRK equation of state with DIPPR 801 values for critical temperature, critical pressure, and acentric factor. These data are provided for the sole purpose of the preparation for and taking of NCEES engineering exams with no warrantee expressed or implied.
©2017 NCEES
552
Chapter 8: Physical Properties
8.5.2
SI Units Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) Temperature Gas
cC
Nitrogen
Oxygen
Carbon Monoxide
Carbon Dioxide
Sulfur Dioxide
Air
©2017 NCEES
0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500
Density
kg m3 1.23 0.903 0.712 0.588 0.500 0.436 1.41 1.03 0.813 0.671 0.572 0.498 1.23 0.903 0.712 0.588 0.500 0.436 1.94 1.42 1.12 0.924 0.786 0.685 2.87 2.08 1.63 1.35 1.15 0.997 1.28 0.933 0.736 0.608 0.517 0.450
Heat Thermal Capacity (Cp) Conductivity
Thermal Diffusivity
Viscosity
kJ kg : K
W m:K
m hr
nPa : s
1.04 1.04 1.05 1.07 1.09 1.12 0.914 0.933 0.963 0.995 1.02 1.05 1.04 1.04 1.06 1.08 1.11 1.13 0.816 0.924 1.00 1.06 1.11 1.15 0.609 0.664 0.714 0.756 0.788 0.813 1.00 1.01 1.02 1.04 1.06 1.09
0.0237 0.0307 0.0372 0.0434 0.0494 0.0551 0.0244 0.0323 0.0397 0.0466 0.0533 0.0597 0.0231 0.0301 0.0365 0.0425 0.0481 0.0535 0.0145 0.0224 0.0306 0.0386 0.0464 0.0536 0.00843 0.0131 0.0183 0.0238 0.0292 0.0343 0.0242 0.0312 0.0377 0.0439 0.0498 0.0556
0.0665 0.117 0.179 0.249 0.326 0.408 0.0682 0.121 0.182 0.251 0.328 0.412 0.0650 0.115 0.175 0.241 0.313 0.390 0.0331 0.0617 0.0985 0.142 0.192 0.245 0.0174 0.0342 0.0565 0.0842 0.117 0.152 0.0681 0.120 0.181 0.250 0.326 0.408
16.6 21.0 24.9 28.5 31.8 35.0 19.2 24.6 29.4 33.8 37.8 41.5 16.5 20.9 24.8 28.3 31.5 34.5 13.8 18.4 22.6 26.5 30.0 33.3 11.8 16.2 20.3 24.2 27.8 31.2 17.2 21.8 25.8 29.4 32.7 35.7
553
2
Prandtl Number
0.727 0.712 0.704 0.701 0.703 0.707 0.718 0.710 0.713 0.720 0.725 0.729 0.741 0.726 0.719 0.720 0.725 0.731 0.772 0.758 0.740 0.725 0.717 0.715 0.851 0.821 0.792 0.767 0.749 0.741 0.714 0.704 0.698 0.697 0.697 0.698
Chapter 8: Physical Properties Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) (cont'd) Temperature Gas
cC
Hydrogen
Ammonia
Helium
Neon
Argon
Fluorine
©2017 NCEES
0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500
Density
kg m3 0.0887 0.0649 0.0512 0.0423 0.0360 0.0314 0.758 0.551 0.434 0.358 0.304 0.265 0.176 0.129 0.102 0.0840 0.0715 0.0623 0.888 0.650 0.513 0.423 0.361 0.314 1.76 1.29 1.02 0.838 0.714 0.621 1.67 1.22 0.966 0.797 0.679 0.591
Heat Thermal Capacity (Cp) Conductivity
kJ kg : K
W m:K
14.2 14.5 14.5 14.5 14.6 14.6 2.05 2.23 2.42 2.61 2.79 2.96 5.19 5.19 5.19 5.19 5.19 5.19 1.030 1.030 1.030 1.030 1.030 1.030 0.520 0.520 0.520 0.520 0.520 0.520 0.812 0.858 0.893 0.919 0.938 0.953
0.166 0.212 0.255 0.295 0.334 0.371 0.0222 0.0342 0.0475 0.0618 0.0772 0.0934 0.145 0.179 0.211 0.241 0.270 0.298 0.0459 0.0570 0.0670 0.0764 0.0852 0.0935 0.0165 0.0212 0.0254 0.0293 0.0329 0.0364 0.0235 0.0314 0.0393 0.0470 0.0547 0.0623*
554
Thermal Diffusivity 2
m hr 0.475 0.814 1.23 1.73 2.29 2.91 0.0516 0.100 0.163 0.238 0.327 0.429 0.571 0.964 1.44 1.99 2.62 3.32 0.181 0.306 0.457 0.630 0.826 1.04 0.0649 0.114 0.173 0.242 0.319 0.405 0.0622 0.108 0.164 0.231 0.309 0.398
Viscosity
nPa : s 8.39 10.4 12.2 13.9 15.6 17.1 9.21 12.9 16.5 20.1 23.7 27.4 18.7 23.2 27.3 31.3 35.0 38.6 29.6 36.6 43.0 48.9 54.5 59.8 21.1 27.1 32.6 37.6 42.2 46.6 21.5 27.8 33.6 38.9 43.9 48.7
Prandtl Number
0.716 0.708 0.697 0.687 0.679 0.675 0.849 0.837 0.843 0.850 0.858 0.866 0.669 0.671 0.672 0.672 0.672 0.672 0.663 0.661 0.660 0.660 0.659 0.659 0.663 0.666 0.667 0.667 0.667 0.667 0.744 0.759 0.763 0.760 0.753 0.745
Chapter 8: Physical Properties Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) (cont'd) Temperature Gas
cC
Chlorine
Methane
Ethane
Propane
Acetylene
Ethylene
©2017 NCEES
0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500
Density
kg m3 3.17 2.30 1.81 1.49 1.27 1.10 0.708 0.517 0.408 0.337 0.287 0.250 1.34 0.973 0.765 0.631 0.537 0.468 1.98 1.43 1.125 0.927 0.788 0.686 1.16 0.842 0.663 0.547 0.465 0.405 1.24 0.907 0.714 0.589 0.501 0.436
Heat Thermal Capacity (Cp) Conductivity
kJ kg : K
W m:K
0.473 0.494 0.506 0.514 0.519 0.523 2.17 2.44 2.80 3.17 3.53 3.87 1.64 2.06 2.49 2.88 3.21 3.51 1.55 2.00 2.45 2.83 3.16 3.44 1.60 1.87 2.06 2.20 2.31 2.40 1.45 1.80 2.14 2.45 2.72 2.95
0.00803 0.0115 0.0148 0.0179 0.0210 0.0239 0.0307 0.0453 0.0615 0.0793 0.0983 0.119* 0.0184 0.0320 0.0481 0.0661 0.0857 0.107 0.0152 0.0270 0.0412 0.0575 0.0757 0.0955 0.0193 0.0304 0.0412 0.0518 0.0622 0.0724 0.0180 0.0303 0.0453 0.0628 0.0824* 0.104*
555
Thermal Diffusivity 2
m hr 0.0193 0.0363 0.0581 0.0844 0.115 0.149 0.0720 0.129 0.194 0.267 0.350 0.442 0.0301 0.0575 0.0908 0.131 0.179 0.234 0.0178 0.0339 0.0539 0.0788 0.109 0.146 0.0377 0.0696 0.109 0.155 0.208 0.268 0.0359 0.0668 0.107 0.157 0.218 0.290
Viscosity
nPa : s 12.3 16.7 20.8 24.8 28.5 32.1 10.4 13.5 16.3 18.8 21.2 23.4 8.62 11.5 14.1 16.6 18.9 21.1 7.70 10.2 12.6 15.0 17.4 19.7 9.36 12.7 15.7 18.5 21.1 23.5* 9.38 12.6 15.5 18.1 20.5 22.8
Prandtl Number
0.724 0.720 0.714 0.709 0.706 0.704 0.733 0.727 0.741 0.754 0.761 0.764 0.772 0.738 0.731 0.722 0.709 0.696 0.785 0.756 0.750 0.740 0.724 0.708 0.774 0.778 0.786 0.788 0.785 0.779 0.755 0.748 0.731 0.706 0.677 0.646
Chapter 8: Physical Properties Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) (cont'd) Temperature Gas
cC
Propylene
Hydrogen Sulfide
0 100 200 300 400 500 0 100 200 300 400 500
Density
Heat Thermal Capacity (Cp) Conductivity
kg m3 1.89 1.37 1.07 0.884 0.752 0.655 1.51 1.10 0.868 0.716 0.609 0.530
kJ kg : K
W m:K
1.44 1.82 2.15 2.47 2.75 3.00 1.00 1.03 1.08 1.13 1.18 1.24
0.0150 0.0260 0.0390 0.0535 0.0692 0.0860 0.0126 0.0190 0.0247 0.0308 0.0376* 0.0452*
Thermal Diffusivity 2
m hr 0.0198 0.0376 0.0608 0.0882 0.120 0.158 0.0302 0.0601 0.0949 0.137 0.188 0.248
Viscosity
nPa : s 7.88 10.7 13.4 15.9 18.1 20.3 11.6 15.9 20.2 24.5* 28.9* 33.2*
Prandtl Number
0.760 0.751 0.741 0.732 0.722 0.709 0.911 0.862 0.883 0.899 0.907 0.909
* Extrapolated values Sources: These data are provide courtesy of the American Institute of Chemical Engineering (AIChE) and its thermophysical property research consortium, the Design Institute for Physical Properties (DIPPR®) using DIPPR® 2016 version. Vapor densities were obtained using SRK equation of state with DIPPR 801 values for critical temperature, critical pressure, and acentric factor. These data are provided for the sole purpose of the preparation for and taking of NCEES engineering exams with no warrantee expressed or implied.
8.6 Physical Properties of Air 8.6.1
Dry Atmospheric Air Composition Composition of Dry Atmospheric Air
©2017 NCEES
Component
Mole Fraction
Nitrogen Oxygen Argon Carbon dioxide Neon Helium Methane Krypton Hydrogen Nitrous oxide Carbon monoxide
0.780848 0.209390 0.009332 0.000400 18.2 × 10–6 5.2 × 10–6 1.5 × 10–6 1.1 × 10–6 0.5 × 10–6 0.3 × 10–6 0.2 × 10–6
556
d
Molar Mass
g lb n lb mole or mol 28.0134 31.9988 39.948 44.0095 20.1797 4.0026 16.0325 83.798 2.01588 44.0128 28.0101
Chapter 8: Physical Properties Composition of Dry Atmospheric Air Component
Xenon Total
8.6.2
Mole Fraction
0.1 × 10–6 1.0
d
Molar Mass
g lb n lb mole or mol 131.294 28.96546
Dry Atmospheric Air Properties Properties of Dry Atmospheric Air Property
Molar mass NBP temperature Triple point temperature Critical temperature Critical pressure Critical density
Density of liquid at NBP
U.S. Units*
SI Units**
lb 28.965 lb mole –317.64 °F –352.12 °F –221.12 °F 549.11 psia
g 28.965 mol 78.903 K 59.75 K 132.53 K 3.7860 MPa
lbm ft 3
342.68
kg m3
lbm ft 3 lbm 7.3039 gal
875.21
kg m3
21.393 54.637
Volume of liquid at NBP
gal 0.13691 lbm
Density of ideal gas
0.07633
Volume of ideal gas
ft 3 13.101 lbm
m3 0.81631 kg
ft 1090 sec
m 330 s
ft 1130 sec
m 343 s
Speed of sound in air p = 14.696 psia, T = 32°F p = 0.1 MPa, T = 0°C Speed of sound in air p = 14.696 psia , T = 68°F p = 0.1 MPa, T = 20°C
lbm ft 3
m3 0.0011426 kg 1.2250
kg m3
* U.S. unit values are given at 60°F and 14.696 psia, except where noted otherwise. ** SI unit values are given at 15°C and 0.101325 MPa, except where noted otherwise.
©2017 NCEES
557
Chapter 8: Physical Properties
8.6.3
Temperature-Dependent Properties of Air (U.S. Customary Units)
©2017 NCEES
lbm ft -sec
Btu hr - ft -cF
9.98E–06 1.09E–05 1.15E–05 1.28E–05 1.44E–05 1.60E–05 1.74E–05 1.89E–05 2.01E–05 2.14E–05 2.25E–05
558
0.0120 0.0132 0.0140 0.0156 0.0179 0.0202 0.0225 0.0247 0.0268 0.0288 0.0307
Thermal Diffusivity
1.40 1.40 1.40 1.40 1.40 1.39 1.39 1.38 1.38 1.37 1.37
Thermal Conductivity
Heat Capacity Ratio
(cp)
Heat Capacity
Btu lbm-cF 0.2400 0.2400 0.2400 0.2400 0.2401 0.2424 0.2452 0.2476 0.2507 0.2533 0.2567
Prandtl Number
–50 0 32 100 200 300 400 500 600 700 800
lbm ft 3 0.094 0.086 0.081 0.071 0.060 0.052 0.046 0.041 0.0374 0.034 0.0286
Viscosity
°F
Density
Temperature
Temperature-Dependent Properties of Air at 14.7 psia (U.S. Units)
0.719 0.714 0.710 0.708 0.701 0.692 0.685 0.681 0.678 0.677 0.679
ft 2 hr 0.530 0.642 0.726 0.917 1.233 1.599 1.989 2.415 2.857 3.323 4.173
Chapter 8: Physical Properties
8.6.4
Temperature-Dependent Properties of Air (SI Units)
–50 0 20 40 60 80 100 120 140 160 180 200 250 300 350 400
©2017 NCEES
1.005 1.005 1.005 1.005 1.009 1.009 1.009 1.013 1.013 1.017 1.022 1.026 1.034 1.047 1.055 1.068
1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.39 1.39 1.39 1.38 1.38 1.37 1.37
W m:K
14.6 17.2 18.2 19.1 20.2 20.9 21.8 22.7 23.5 24.3 25.2 25.8 27.8 29.5 31.2 32.8
559
0.0204 0.0243 0.0257 0.0271 0.0285 0.0299 0.0314 0.0328 0.0343 0.0358 0.0372 0.0386 0.0421 0.0454 0.0485 0.0515
Thermal Diffusivity
nPa : s
Prandtl Number
Heat Capacity Ratio
(cp)
Heat Capacity
kJ kg : K
Thermal Conductivity
kg m3 1.534 1.293 1.205 1.127 1.067 1.000 0.946 0.898 0.854 0.815 0.779 0.746 0.675 0.616 0.566 0.524
Viscosity
°C
Density
Temperature
Temperature-Dependent Properties of Air at 0.1 MPa (SI Units)
m2 s 0.722 0.711 0.712 0.709 0.714 0.707 0.701 0.700 0.695 0.691 0.691 0.687 0.683 0.680 0.678 0.679
1.32E–05 1.87E–05 2.12E–05 2.39E–05 2.65E–05 2.96E–05 3.29E–05 3.61E–05 3.96E–05 4.32E–05 4.67E–05 5.04E–05 6.03E–05 7.04E–05 8.12E–05 9.20E–05
8.6.5
©2017 NCEES
∞
Source: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, 1992.
∆ ∆
∞
∞
Psychrometric Chart (U.S. Customary Units)
Chapter 8: Physical Properties
560
8.6.6
©2017 NCEES
∞
∆ ∆
∞
∞
Source: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, 1992.
Psychrometric Chart (SI Units)
Chapter 8: Physical Properties
561
Chapter 8: Physical Properties
8.7 Physical Properties of Water 8.7.1
U.S. Customary Units
0.08872 0.12173 0.17814 0.2564 0.36336 0.50747 0.69904 0.95051 1.2767 1.695 2.2259 2.893 3.7232 4.7472 5.9998 7.5195 9.3496 11.538 14.136 17.201 20.795 24.986 29.844 35.447 41.878 49.222 57.574 67.029 89.667 118.02
Btu lbm-cF 1.0086 1.0055 1.0028 1.0010 0.9999 0.9993 0.9990 0.9989 0.9991 0.9993 0.9998 1.0003 1.0009 1.0016 1.0025 1.0035 1.0046 1.0059 1.0073 1.0088 1.0106 1.0125 1.0147 1.0170 1.0196 1.0224 1.0254 1.0287 1.0362 1.0449
©2017 NCEES
lbm ft -sec 1.204E–03 1.038E–03 8.776E–04 7.533E–04 6.552E–04 5.761E–04 5.114E–04 4.577E–04 4.127E–04 3.744E–04 3.417E–04 3.134E–04 2.888E–04 2.673E–04 2.484E–04 2.316E–04 2.168E–04 2.035E–04 1.916E–04 1.808E–04 1.712E–04 1.624E–04 1.544E–04 1.471E–04 1.405E–04 1.344E–04 1.288E–04 1.236E–04 1.144E–04 1.065E–04
562
Btu hr-ft -cF 0.3244 0.3293 0.3353 0.3413 0.3471 0.3527 0.3579 0.3628 0.3672 0.3713 0.3750 0.3783 0.3813 0.3839 0.3862 0.3881 0.3898 0.3912 0.3924 0.3934 0.3941 0.3947 0.3951 0.3953 0.3953 0.3952 0.3949 0.3944 0.3931 0.3912
Surface Tension
Heat Capacity
32.02 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 320 340
lbm ft 3 62.415 62.423 62.406 62.364 62.299 62.213 62.110 61.991 61.857 61.710 61.549 61.377 61.193 60.998 60.793 60.578 60.354 60.120 59.877 59.626 59.366 59.097 58.820 58.535 58.241 57.940 57.630 57.312 56.650 55.955
Prandtl Number
Density
psia
Thermal Conductivity
Vapor Pressure
°F
Viscosity
Temperature
Physical Properties of Liquid Water (U.S. Units)
13.47 11.42 9.45 7.95 6.79 5.88 5.14 4.54 4.04 3.63 3.28 2.98 2.73 2.51 2.32 2.16 2.01 1.88 1.77 1.67 1.58 1.50 1.43 1.36 1.30 1.25 1.20 1.16 1.09 1.02
dyne cm 75.65 75.02 74.22 73.40 72.57 71.71 70.84 69.96 69.05 68.13 67.19 66.24 65.27 64.28 63.28 62.26 61.23 60.19 59.13 58.05 56.96 55.86 54.74 53.62 52.47 51.32 50.16 48.98 46.59 44.16
Chapter 8: Physical Properties
Btu lbm-cF 1.0550 1.0666 1.0802 1.0959 1.1143 1.1358 1.1612 1.1916 1.2285 1.2740 1.3317 1.4072 1.5100 1.6588 1.8958 2.3480 3.5861 15.5790 28.2960 97.4060
360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 702 704 705.1
©2017 NCEES
153.03 195.74 247.26 308.76 381.48 466.75 565.95 680.55 812.10 962.24 1132.7 1325.5 1542.5 1786.2 2059.2 2364.9 2707.3 3093.0 3134.5 3176.6 3200.1
563
lbm ft -sec 9.958E–05 9.354E–05 8.820E–05 8.343E–05 7.913E–05 7.523E–05 7.165E–05 6.833E–05 6.521E–05 6.225E–05 5.940E–05 5.661E–05 5.382E–05 5.097E–05 4.796E–05 4.463E–05 4.054E–05 3.399E–05 3.268E–05 3.180E–05 3.333E–05
Btu hr-ft-cF 0.3888 0.3857 0.3819 0.3776 0.3725 0.3666 0.3599 0.3522 0.3436 0.3340 0.3233 0.3118 0.2995 0.2867 0.2735 0.2600 0.2461 0.2547 0.2765 0.3584
Surface Tension
Heat Capacity
lbm ft 3 55.225 54.458 53.652 52.804 51.912 50.971 49.976 48.920 47.795 46.590 45.290 43.876 42.318 40.572 38.566 36.152 32.936 27.283 26.085 24.196 20.102
Prandtl Number
Density
psia
Thermal Conductivity
Vapor Pressure
°F
Viscosity
Temperature
Physical Properties of Liquid Water (U.S. Units) (cont'd)
0.97 0.93 0.90 0.87 0.85 0.84 0.83 0.83 0.84 0.85 0.88 0.92 0.98 1.06 1.20 1.45 2.13 7.48 12.04 31.11
dyne cm 41.69 39.19 36.66 34.10 31.52 28.92 26.30 23.69 21.08 18.47 15.89 13.35 10.846 8.415 6.078 3.876 1.877 0.2565 0.1375 0.0375
Chapter 8: Physical Properties
8.7.2
SI Units
©2017 NCEES
kJ kg : K
Pa : s
W m:K
4.2199 4.2055 4.1955 4.1888 4.1844 4.1816 4.1801 4.1795 4.1796 4.1804 4.1815 4.1831 4.1851 4.1875 4.1902 4.1933 4.1969 4.2008 4.2053 4.2102 4.2157 4.2283 4.2435 4.2615 4.2826 4.3071 4.3354 4.3678 4.4050 4.4474
1.791E–03 1.518E–03 1.306E–03 1.138E–03 1.002E–03 8.901E–04 7.974E–04 7.193E–04 6.530E–04 5.961E–04 5.468E–04 5.040E–04 4.664E–04 4.332E–04 4.039E–04 3.777E–04 3.543E–04 3.333E–04 3.144E–04 2.973E–04 2.817E–04 2.547E–04 2.321E–04 2.129E–04 1.965E–04 1.825E–04 1.702E–04 1.596E–04 1.501E–04 1.418E–04
0.5610 0.5705 0.5800 0.5893 0.5984 0.6072 0.6155 0.6233 0.6306 0.6373 0.6436 0.6492 0.6544 0.6590 0.6631 0.6668 0.6700 0.6728 0.6753 0.6773 0.6791 0.6817 0.6832 0.6837 0.6833 0.6820 0.6800 0.6771 0.6733 0.6688
564
Surface Tension
kg m3 999.79 999.92 999.65 999.06 998.16 997.00 995.61 993.99 992.18 990.17 988.00 985.66 983.16 980.52 977.73 974.81 971.77 968.59 965.30 961.88 958.35 950.95 943.11 934.83 926.13 917.01 907.45 897.45 887.00 876.08
Prandtl Number
0.000612 0.000873 0.001228 0.001706 0.002339 0.00317 0.004247 0.005629 0.007385 0.009595 0.012352 0.015762 0.019946 0.025042 0.031201 0.038595 0.047414 0.057867 0.070182 0.084608 0.10142 0.14338 0.19867 0.27028 0.36154 0.47616 0.61823 0.79219 1.0028 1.2552
Thermal Conductivity
0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190
Viscosity
MPa
Heat Capacity
Vapor Pressure
°C
Density
Temperature
Physical Properties of Liquid Water (SI Units)
N −3 m : 10 13.47 11.19 9.45 8.09 8.09 6.13 5.42 4.82 4.33 3.91 3.55 3.25 2.98 2.75 2.55 2.38 2.22 2.08 1.96 1.85 1.75 1.58 1.44 1.33 1.23 1.15 1.09 1.03 0.98 0.94
75.65 74.94 74.22 73.49 72.74 71.97 71.19 70.40 69.60 68.78 67.94 67.10 66.24 65.37 64.48 63.58 62.67 61.75 60.82 59.87 58.91 56.96 54.97 52.93 50.86 48.74 46.59 44.41 42.19 39.95
Chapter 8: Physical Properties
©2017 NCEES
1.5549 1.9077 2.3196 2.7971 3.3469 3.9762 4.6923 5.503 6.4166 7.4418 8.5879 9.8651 11.284 12.858 14.601 16.529 18.666 21.044 21.297 21.554 21.814 22.064
kJ kg : K
Pa : s
W m:K
4.4958 4.5512 4.6146 4.6876 4.7719 4.8701 4.9856 5.1230 5.2889 5.4931 5.7504 6.0848 6.5373 7.1863 8.2080 10.1160 15.0040 45.1550 62.3510 102.1500 243.7800
565
1.343E–04 1.276E–04 1.215E–04 1.160E–04 1.109E–04 1.061E–04 1.017E–04 9.750E–05 9.351E–05 8.966E–05 8.590E–05 8.217E–05 7.841E–05 7.454E–05 7.043E–05 6.588E–05 6.033E–05 5.207E–05 5.075E–05 4.908E–05 4.781E–05 4.854E–05
0.6633 0.6570 0.6497 0.6413 0.6319 0.6212 0.6092 0.5959 0.5812 0.5650 0.5474 0.5288 0.5092 0.4891 0.4685 0.4474 0.4257 0.4250 0.4384 0.4674 0.5479
Surface Tension
kg m3 864.66 852.72 840.22 827.12 813.37 798.89 783.63 767.46 750.28 731.91 712.14 690.67 667.09 640.77 610.67 574.71 527.59 451.43 438.64 422.26 398.68 322.00
Prandtl Number
Thermal Conductivity
200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 371 372 373 373.94
Viscosity
MPa
Heat Capacity
Vapor Pressure
°C
Density
Temperature
Physical Properties of Liquid Water (SI Units) (cont'd)
N −3 m : 10 0.91 0.88 0.86 0.85 0.84 0.83 0.83 0.84 0.85 0.87 0.90 0.95 1.01 1.10 1.23 1.49 2.13 5.53 7.22 10.72 21.27
37.68 35.38 33.07 30.74 28.39 26.04 23.69 21.34 18.99 16.66 14.36 12.09 9.864 7.703 5.626 3.665 1.877 0.388 0.269 0.160 0.065
Chapter 8: Physical Properties
8.7.3
Properties of Water Properties of Water Property
Molar mass Boiling temperature Triple point temperature Triple point pressure Critical temperature Critical pressure
U.S. Units
SI Units
lb 18.01528 lb mole 212°F 32°F 0.0887 psia 705.1°F 3200.1 psia
g 18.01528 mol 373.15 K 273.15 K 611.657 Pa 647.09 K 22.06 MPa
Critical density
20.102
lbm ft 3
322.00
kg m3
lbm ft 3 lbm 8.3455 gal
1000
Minimum volume of liquid (4°C = 39°F)
gal 0.11983 lbm
m3 0.001 kg
Heat of vaporization (100°C = 212°F)
Btu 970.17 lbm
kJ 2257 kg
Density of ice (0°C = 32°F)
57.227
Latent heat of fusion (0°C = 32°F) Dielectric constant of liquid (0°C = 32°F) Dielectric constant of liquid (100°C = 212°F) Refractive index of liquid (20°C = 68°F)*
Btu 143.38 lbm
kJ 333.55 kg
87.90
87.90
55.53
55.53
1.3333
1.3333
Maximum density of liquid (4°C = 39°F)
62.426
lbm ft 3
916.7
kg m3
kg m3
*Refractive index at Sodium D line Source: Harvey, Allan H., and Eric W. Lemmon, NIST/ASME Steam Properties, Version 3.0, Gaithersburg: National Institute of Standards and Technology, 2013.
©2017 NCEES
566
Chapter 8: Physical Properties
8.8 Steam Tables Source for all tables in Section 8.8: GPSA Engineering Data Book, 13th ed., Vol. 2, Tulsa, OK: GPSA, 2012, Figures 24-30 and 24-31 on pp. 24-35 through 24-38.
8.8.1
Properties of Saturated Steam (U.S. Customary Units) Saturated Steam (U.S. Units)—Temperature Table Specific Volume, v
Temperature
Pressure
cF 32.018 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 212 220 230 240
psia
Liquid
0.08865 0.09991 0.12163 0.14744 0.17796 0.21392 0.25611 0.30545 0.36292 0.42964 0.50683 0.59583 0.69813 0.81534 0.94294 1.2750 1.6927 2.2230 2.8892 3.7184 4.7414 5.9926 7.5110 9.3400 11.5260 14.1230 14.6960 17.1860 20.7790 24.9680
0.016022 0.016020 0.016019 0.016020 0.016023 0.016027 0.016033 0.016041 0.016050 0.016060 0.016072 0.016085 0.016099 0.016114 0.016130 0.016165 0.016204 0.016247 0.016293 0.016343 0.016395 0.016451 0.016510 0.016572 0.016637 0.016705 0.016719 0.016775 0.016849 0.016926
©2017 NCEES
Specific Enthalpy, h
Specific Entropy, s
Btu lbm
Btu lbm - cF
3
ft lbm Vapor
3302.4 2948.1 2445.8 2037.8 1704.8 1432.0 1207.6 1022.1 868.4 740.3 633.3 543.6 468.1 404.4 350.4 265.39 203.26 157.33 122.98 97.07 77.27 62.08 50.225 40.957 33.639 27.816 26.799 23.148 19.381 16.321
567
Liquid
Vapor
Liquid
Vapor
0.000 3.002 8.027 13.044 18.054 23.059 28.060 33.057 38.052 43.045 48.037 53.027 58.018 63.008 67.999 77.98 87.97 97.96 123.00 117.95 127.96 137.97 148.00 158.04 168.09 178.15 180.17 188.23 198.33 208.45
1075.5 1076.8 1079.0 1081.2 1083.4 1085.6 1087.7 1089.9 1092.1 1094.3 1096.4 1098.6 1100.8 1102.9 1105.1 1109.3 1113.6 1117.8 1122.0 1126.1 1130.2 1134.2 1138.2 1142.1 1146.0 1149.7 1150.5 1153.4 1157.1 1160.6
0.0000 0.0061 0.0162 0.0262 0.0361 0.0458 0.0555 0.0651 0.0745 0.0839 0.0932 0.1024 0.1115 0.1206 0.1295 0.1472 0.1646 0.1817 0.1985 0.2150 0.2313 0.2473 0.2631 0.2787 0.2940 0.3091 0.3121 0.3241 0.3388 0.3533
2.1872 2.1767 2.1594 2.1426 2.1262 2.1102 2.0946 2.0794 2.0645 2.0500 2.0359 2.0221 2.0086 1.9954 1.9825 1.9577 1.9339 1.9112 1.8895 1.8686 1.8487 1.8295 1.8111 1.7934 1.7764 1.7600 1.7568 1.7442 1.7290 1.7142
Chapter 8: Physical Properties Saturated Steam (U.S. Units)—Temperature Table (cont'd) Temperature
cF 250 260 270 280 290 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 702 704 705.47
©2017 NCEES
Pressure psia
29.8250 35.4270 41.8560 49.2000 57.5500 67.0050 89.6430 117.9920 153.01 195.73 247.26 308.78 381.54 466.87 566.15 680.86 812.53 962.79 1133.38 1326.17 1543.2 1786.9 2059.9 2065.7 2708.6 3094.3 3135.5 3177.2 3208.2
Specific Volume, v
Specific Enthalpy, h
Specific Entropy, s
ft 3 lbm
Btu lbm
Btu lbm - cF
Liquid
0.017066 0.017089 0.017175 0.017264 0.01736 0.01745 0.01766 0.01787 0.01811 0.01836 0.01864 0.01894 0.01926 0.01961 0.02000 0.02043 0.02091 0.02146 0.02207 0.02279 0.02364 0.02466 0.02595 0.02768 0.03037 0.03662 0.03824 0.04108 0.05078
Vapor
Liquid
Vapor
Liquid
Vapor
13.819 11.762 10.060 8.644 7.4603 6.4658 4.9138 3.7878 2.9573 2.3353 1.8630 1.4997 1.2169 0.99424 0.81717 0.67492 0.55956 0.46513 0.38714 0.32216 0.26747 0.22081 0.18021 0.14431 0.11117 0.07519 0.06997 0.06300 0.05078
218.59 228.76 238.95 249.17 259.4 269.7 290.4 311.3 332.3 353.6 375.1 396.9 419.0 441.5 464.5 487.9 512.0 536.8 562.4 589.1 617.1 646.9 679.1 714.9 758.5 825.2 835.0 854.2 906.0
1164.0 1167.4 1170.6 1173.8 1167.8 1179.7 1185.2 1190.1 1194.4 1198.0 1201.0 1203.1 1204.4 1204.8 1204.1 1202.2 1199.0 1194.3 1187.7 1179.0 1167.7 1153.2 1133.7 1107.0 1068.5 991.7 979.7 956.2 906.0
0.3677 0.3819 0.3960 0.4098 0.4236 0.4372 0.4640 0.4902 0.5161 0.5416 0.5667 0.5915 0.6161 0.6405 0.6648 0.6890 0.7133 0.7378 0.7625 0.7876 0.8134 0.8403 0.8686 0.8995 0.9365 0.9924 1.0006 1.0169 1.0612
1.7000 1.6862 1.6729 1.6599 1.6473 1.6351 1.6116 1.5892 1.5678 1.5473 1.5274 1.5080 1.4890 1.4704 1.4518 1.4333 1.4146 1.3954 1.3757 1.3550 1.3330 1.3092 1.2821 1.2498 1.2086 1.1359 1.1210 1.1046 1.0612
568
Chapter 8: Physical Properties Saturated Steam (U.S. Units)—Pressure Table Pressure Temperature psia
0.1 0.2 0.3 0.4 0.6 0.8 1 2 3 4 6 8 10 20 30 40 50 60 70 80 90 100 150 200 250 300 350 400 450 500 600 700 800 900 1000 1200 1400 1600 ©2017 NCEES
cF 35.02 53.16 64.48 72.87 85.22 94.38 101.74 126.07 141.47 152.96 170.05 182.80 193.21 227.96 250.34 267.25 281.02 292.71 302.93 312.04 320.28 327.82 358.43 381.80 400.97 417.35 431.73 444.60 456.28 467.01 486.20 503.08 518.21 531.95 544.58 567.19 587.07 604.87
Specific Volume, v
Specific Enthalpy, h
Specific Entropy, s
Btu lbm
3
Liquid
Vapor
Liquid
Vapor
Btu lbm - cF Liquid Vapor
0.016020 0.016025 0.016040 0.016056 0.016085 0.016112 0.016136 0.016230 0.016300 0.016358 0.016451 0.016527 0.016592 0.016834 0.017009 0.017151 0.017274 0.017383 0.017482 0.017573 0.017659 0.01774 0.01809 0.01839 0.01865 0.01889 0.01912 0.01934 0.01954 0.01975 0.02013 0.02050 0.02087 0.02123 0.02159 0.02232 0.02307 0.02387
2,945.5 1,526.3 1,039.7 792.1 540.1 411.69 333.60 173.76 118.73 90.64 61.98 47.35 38.42 20.087 13.744 10.4965 8.5140 7.1736 6.2050 5.4711 4.8953 4.4310 3.0139 2.2873 1.84317 1.54274 1.32554 1.16095 1.03179 0.92762 0.76975 0.65556 0.56896 0.50091 0.44596 0.36245 0.30178 0.25545
3.03 21.22 32.54 40.92 53.25 62.39 69.73 94.03 109.42 120.92 138.03 150.87 161.26 196.27 218.9 236.1 250.2 262.2 272.7 282.1 290.7 298.5 330.6 355.5 376.1 394.0 409.8 424.2 437.3 449.5 471.7 491.6 509.8 526.7 542.6 571.9 598.8 624.2
1076.8 1084.7 1089.7 1093.3 1098.7 1102.6 1105.8 1116.2 1122.6 1127.3 1134.2 1139.3 1143.3 1156.3 1164.1 1169.8 1174.1 1177.6 1180.6 1183.1 1185.3 1187.2 1194.1 1198.3 1201.1 1202.9 1204.0 1204.6 1204.8 1204.7 1203.7 1201.8 1199.4 1196.4 1192.9 1184.8 1175.8 1164.5
0.0061 0.0422 0.0641 0.0799 0.1028 0.1195 0.1326 0.1750 0.2009 0.2199 0.2174 0.2676 0.2836 0.3358 0.3682 0.3921 0.4112 0.4273 0.4411 0.4534 0.4643 0.4743 0.5141 0.5438 0.5679 0.5882 0.6059 0.6217 0.6360 0.6490 0.6723 0.6928 0.7111 0.7279 0.7434 0.7714 0.7966 0.8199
ft lbm
569
2.1766 2.1060 2.0809 2.0562 2.0215 1.9970 1.9781 1.9200 1.8864 1.5626 1.8294 1.8060 1.7879 1.7320 1.6995 1.6765 1.6586 1.6440 1.6316 1.6208 1.6113 1.6027 1.5695 1.5454 1.5264 1.5105 1.4968 1.4847 1.4738 1.4639 1.4461 1.4304 1.4163 1.4032 1.3910 1.3683 1.3474 1.3274
Chapter 8: Physical Properties Saturated Steam (U.S. Units )—Pressure Table (cont'd) Specific Volume, v
Pressure Temperature psia
1800 2000 2200 2400 2600 2800 3000 3100 3200 3208.2
8.8.2
Specific Enthalpy, h
Specific Entropy, s
Btu lbm
Btu lbm - cF
3
ft lbm Liquid
cF 621.02 635.80 649.45 662.11 673.91 684.96 695.33 700.28 705.08 705.47
0.02472 0.02565 0.02669 0.02790 0.02938 0.03134 0.03428 0.03681 0.04472 0.05078
Vapor
Liquid
Vapor
Liquid
Vapor
0.21861 0.18831 0.16272 0.14076 0.1211 0.10305 0.08500 0.07452 0.05663 0.05078
648.5 672.1 695.5 719.0 744.5 770.7 801.8 824.0 875.5 906.0
1152.3 1138.3 1122.2 1103.7 1082.0 1055.5 1020.3 993.3 931.6 906.0
0.8417 0.8625 0.8828 0.9031 0.9247 0.9468 0.9728 0.9914 1.0351 1.0612
1.3079 1.2881 1.2676 1.2460 1.2225 1.1958 1.1619 1.1373 1.0832 1.0612
Saturated Steam (SI Units) Saturated Steam (SI Units)—Temperature Table Temperature
cC 0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 ©2017 NCEES
Pressure kPa
0.6113 0.8721 1.2276 1.7051 2.339 3.169 4.246 5.628 7.384 9.593 12.349 15.758 19.94 25.03 31.19 38.58 47.39 57.83 70.14 84.55
Specific Volume, v
Specific Enthalpy, h
Specific Entropy, s
J kg
J kg : K
3
m kg Liquid
0.001000 0.001000 0.001000 0.001001 0.001002 0.001003 0.001004 0.001006 0.001008 0.001010 0.001012 0.001015 0.001017 0.001020 0.001023 0.001026 0.001029 0.001033 0.001036 0.001040
Vapor
206.14 147.12 106.38 77.93 57.79 43.36 32.89 25.22 19.52 15.26 12.03 9.568 7.671 6.197 5.042 4.131 3.407 2.828 2.361 1.982 570
Liquid
Vapor
Liquid
Vapor
0.01 20.98 42.01 62.99 83.96 104.89 125.79 146.68 167.37 188.45 209.33 230.23 251.13 272.06 292.98 313.93 334.91 355.90 376.92 397.96
2501.4 2510.6 2519.8 2528.9 2538.1 2547.2 2556.3 2565.3 2574.3 2583.2 2592.1 2600.9 2609.6 2618.3 2626.8 2635.3 2643.7 2651.9 2660.1 2668.1
0 0.0761 0.151 0.2245 0.2966 0.3674 0.4369 0.5053 0.5725 0.6387 0.7038 0.7679 0.8312 0.8935 0.9549 1.0155 1.0753 1.1343 1.1925 1.2500
9.1562 9.0257 8.9008 8.7814 8.6672 8.5580 8.4533 8.3531 8.2570 8.1648 8.0763 7.9913 7.9096 7.8310 7.7553 7.6824 7.6122 7.5445 7.4791 7.4159
Chapter 8: Physical Properties Saturated Steam (SI Units)—Temperature Table (cont'd) Temperature
Pressure
cC 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285
kPa
©2017 NCEES
101.35 120.82 143.27 169.06 198.53 232.1 270.1 313.0 361.3 415.4 475.8 543.1 617.8 700.5 791.7 892.0 1002.1 1122.7 1254.4 1397.8 1553.8 1723.0 1906.2 2104 2318 2518 2795 3060 3344 3618 3973 4319 4688 5081 5499 5942 6412 6909
Specific Volume, v
Specific Enthalpy, h
Specific Entropy, s
J kg
J kg : K
3
m kg Liquid
0.001044 0.001048 0.001052 0.001056 0.001060 0.001065 0.001070 0.001075 0.001080 0.001085 0.001091 0.001096 0.001102 0.001108 0.001114 0.001121 0.001127 0.001134 0.001141 0.001149 0.001157 0.001164 0.001173 0.001181 0.001190 0.001199 0.001209 0.001219 0.001229 0.001240 0.001251 0.001263 0.001276 0.001289 0.001302 0.001317 0.001332 0.001348
Vapor
Liquid
Vapor
Liquid
Vapor
1.6729 1.4194 1.2102 1.0366 0.8919 0.7706 0.6685 0.5822 0.5089 0.4463 0.3928 0.3468 0.3071 0.2727 0.2428 0.2168 0.194005 0.174009 0.156054 0.141005 0.127036 0.115021 0.104041 0.094079 0.086019 0.078049 0.071058 0.065037 0.059076 0.054071 0.050130 0.045098 0.042021 0.038077 0.035064 0.032079 0.030017 0.027077
419.04 440.15 461.30 482.48 503.71 524.99 546.31 567.69 589.13 610.63 632.20 653.84 675.55 697.34 719.21 741.17 763.22 785.37 807.62 829.98 852.45 875.04 897.76 920.62 943.62 966.78 990.12 1013.62 1037.32 1061.23 1085.36 1109.73 1134.37 1159.28 1184.51 1210.07 1235.99 1262.31
2676.1 2683.8 2691.5 2699.0 2706.3 2713.5 2720.5 2727.3 2733.9 2740.3 2746.5 2752.4 2758.1 2763.5 2768.7 2773.6 2778.2 2782.4 2786.4 2790.0 2793.2 2796.0 2798.5 2800.5 2802.1 2803.3 2804.0 2804.2 2803.8 2803.0 2801.5 2799.5 2796.9 2793.6 2789.7 2785.0 2779.6 2773.3
1.3069 1.3630 1.4185 1.4734 1.5276 1.5813 1.6344 1.6870 1.7391 1.7907 1.8418 1.8925 1.9427 1.9925 2.0419 2.0909 2.1396 2.1879 2.2359 2.2835 2.3309 2.3780 2.4248 2.4714 2.5178 2.5639 2.6099 2.6558 2.7015 2.7472 2.7927 2.8383 2.8838 2.9294 2.9751 3.0208 3.0668 3.1130
7.3549 7.2958 7.2387 7.1833 7.1296 7.0775 7.0269 6.9777 6.9299 6.8833 6.8379 6.7935 6.7502 6.7078 6.6663 6.6256 6.5857 6.5465 6.5079 6.4698 6.4323 6.3952 6.3585 6.3221 6.2861 6.2503 6.2146 6.1791 6.1437 6.1083 6.0730 6.0375 6.0019 5.9662 5.9301 5.8938 5.8571 5.8199
571
Chapter 8: Physical Properties Saturated Steam (SI Units)—Temperature Table (cont'd) Temperature
cC 290 295 300 305 310 315 320 330 340 350 360 370 374.14
Pressure kPa
7436 7993 8581 9202 9856 10,547 11,274 12,845 14,586 16,513 18,651 21,030 22,090
Specific Volume, v
Specific Enthalpy, h
Specific Entropy, s
J kg
J kg : K
3
m kg Liquid
0.001366 0.001384 0.001404 0.001425 0.001447 0.001472 0.001499 0.001561 0.001638 0.001740 0.001893 0.002213 0.003155
Vapor
Liquid
Vapor
Liquid
Vapor
0.025057 0.023054 0.021067 0.019948 0.018350 0.016867 0.015488 0.012996 0.010797 0.008813 0.006945 0.004925 0.003155
1289.07 1316.3 1344.0 1372.4 1401.3 1431.0 1461.5 1525.3 1594.2 1670.6 1760.5 1890.5 2099.3
2766.2 2758.1 2749.0 2738.7 2727.3 2714.5 2700.1 2665.9 2622.0 2563.9 2481.0 2332.1 2099.3
3.1594 3.2062 3.2534 3.3010 3.3493 3.3982 3.4480 3.5507 3.6594 3.7777 3.9147 4.1106 4.4298
5.7821 5.7437 5.7045 5.6643 5.6230 5.5804 5.5362 5.4417 5.3357 5.2112 5.0526 4.7971 4.4298
Saturated Steam (SI Units)—Pressure Table Pressure
Temperature
kPa
cC 0.01 6.98 13.03 17.50 21.08 24.08 28.96 32.88 40.29 45.81 53.97 60.05 64.97 69.10 75.87 81.33 91.78 99.63
0.6113 1 1.5 2 2.5 3 4 5 7.5 10 15 20 25 30 40 50 75 100 ©2017 NCEES
Specific Volume, v
Specific Enthalpy, h
Specific Entropy, s
J kg
J kg : K
3
m kg Liquid
0.001000 0.001000 0.001001 0.001001 0.001002 0.001003 0.001004 0.001005 0.001008 0.001010 0.001014 0.001017 0.001020 0.001022 0.001027 0.001030 0.001037 0.001043
Vapor
Liquid
206.14 129.21 87.98 67 54.25 45.67 34.8 28.19 19.24 14.67 10.02 7.649 6.204 5.229 3.993 3.24 2.217 1.694
1 29.3 54.71 73.48 88.49 101.05 121.46 137.82 168.79 191.83 225.94 251.4 271.93 289.23 317.58 340.49 384.39 417.46 572
Vapor
Liquid
Vapor
2501.4 2514.2 2525.3 2533.5 2540.0 2545.5 2554.4 2561.5 2574.8 2584.7 2599.1 2609.7 2618.2 2625.3 2636.8 2645.9 2663.0 2675.5
0 0.1059 0.1957 0.2607 0.3120 0.3545 0.4226 0.4764 0.5764 0.6493 0.7549 0.8320 0.8931 0.9439 1.0259 1.0910 1.2130 1.3026
9.1562 8.9756 8.8279 8.7237 8.6432 8.5776 8.4746 8.3951 8.2515 8.1502 8.0085 7.9085 7.8314 7.7686 7.6700 7.5939 7.4564 7.3594
Chapter 8: Physical Properties Saturated Steam (SI Units)—Pressure Table (cont'd) Pressure
Temperature
kPa
cC 105.99 111.37 116.06 120.23 124.00 127.44 130.60 133.55 136.30 138.88 141.32 143.63 147.93 151.86 155.48 164.97 167.78 170.43 172.96 175.38 177.69 179.91 184.09 187.99 191.64 195.07 198.32 205.76 212.42 218.45 223.99 233.90 242.60 250.40 263.99 275.64 285.88 295.06
125 150 175 200 225 250 275 300 325 350 375 400 450 500 550 700 750 800 850 900 950 1000 1100 1200 1300 1400 1500 1750 2000 2250 2500 3000 3500 4000 5000 6000 7000 8000 ©2017 NCEES
Specific Volume, v
Specific Enthalpy, h
Specific Entropy, s
J kg
J kg : K
3
m kg Liquid
0.001048 0.001053 0.001057 0.001061 0.001064 0.001067 0.001070 0.001073 0.001076 0.001079 0.001081 0.001084 0.001088 0.001093 0.001097 0.001108 0.001112 0.001115 0.001118 0.001121 0.001124 0.001127 0.001133 0.001139 0.001144 0.001149 0.001154 0.001166 0.001177 0.001187 0.001197 0.001217 0.001235 0.001252 0.001286 0.001319 0.001351 0.001384
Vapor
1.3749 1.1593 1.0036 0.8857 0.7933 0.7187 0.6573 0.6058 0.5620 0.5243 0.4914 0.4625 0.4140 0.3749 0.3427 0.2729 0.2556 0.2404 0.2270 0.2150 0.2042 0.194044 0.177053 0.163033 0.151025 0.140084 0.131077 0.113049 0.099063 0.088075 0.079098 0.066068 0.057007 0.049078 0.039044 0.032044 0.027037 0.023052 573
Liquid
Vapor
Liquid
Vapor
444.32 467.11 486.99 504.7 520.72 535.37 548.89 561.47 573.25 584.33 594.81 604.74 623.25 640.23 655.93 697.22 709.47 721.11 732.22 742.83 753.02 762.81 781.34 798.65 814.93 830.30 844.89 878.50 908.79 936.49 962.11 1008.42 1049.75 1087.31 1154.23 1213.35 1267.00 1316.64
2685.4 2693.6 2700.6 2706.7 2712.1 2716.9 2721.3 2725.3 2729.0 2732.4 2735.6 2738.6 2743.9 2748.7 2753.0 2763.5 2766.4 2769.1 2771.6 2773.9 2776.1 2778.1 2781.7 2784.8 2787.6 2790.0 2792.2 2796.4 2799.5 2801.7 2803.1 2804.2 2804.2 2801.4 2794.3 2784.3 2772.1 2758.0
1.3740 1.4336 1.4849 1.5301 1.5706 1.6072 1.6408 1.6718 1.7006 1.7275 1.7528 1.7766 1.8207 1.8607 1.8973 1.9922 2.0200 2.0462 2.0710 2.0946 2.1172 2.1387 2.1792 2.2166 2.2515 2.2842 2.3150 2.3851 2.4474 2.5035 2.5547 2.6457 2.7253 2.7964 3.9202 3.0267 3.1211 3.2068
7.2844 7.2233 7.1717 7.1271 7.0878 7.0527 7.0209 6.9919 6.9652 6.9405 6.9175 6.8959 6.8565 6.8213 6.7893 6.7080 6.6847 6.6628 6.6421 6.6226 6.6041 6.5865 6.5536 6.5233 6.4953 6.4693 6.4448 6.3896 6.3409 6.2972 6.2575 6.1869 6.1253 6.0701 5.9734 5.8892 5.8133 5.7432
Chapter 8: Physical Properties Saturated Steam (SI Units)—Pressure Table (cont'd) Pressure
Temperature
kPa
cC 303.40 311.06 318.15 324.75 330.93 336.75 342.24 347.44 352.37 357.06 361.54 365.81 369.89 373.80 374.14
9000 10,000 11,000 12,000 13,000 14,000 15,000 16,000 17,000 18,000 19,000 20,000 21,000 22,000 22,090
©2017 NCEES
Specific Volume, v
Specific Enthalpy, h
Specific Entropy, s
J kg
J kg : K
3
m kg Liquid
0.001418 0.001452 0.001489 0.001527 0.001567 0.001611 0.001658 0.001711 0.001770 0.001840 0.001924 0.002036 0.002207 0.002742 0.003155
Vapor
0.020048 0.018026 0.015987 0.014263 0.01278 0.011485 0.010337 0.009306 0.008364 0.007489 0.006657 0.005834 0.004952 0.003568 0.003155
574
Liquid
Vapor
Liquid
Vapor
1363.26 1407.56 1450.1 1491.3 1531.5 1571.1 1610.5 1650.1 1690.3 1732.0 1776.5 1826.3 1888.4 2022.2 2099.3
2742.1 2724.7 2705.6 2684.9 2662.2 2637.6 2610.5 2580.6 2547.2 2509.1 2464.5 2409.7 2334.6 2165.6 2099.3
3.2858 3.3596 3.4295 3.4962 3.5606 3.6232 3.6848 3.7461 3.8079 3.8715 3.9388 4.0139 4.1075 4.3110 4.4298
5.6772 5.6141 5.5527 5.4924 5.4323 5.3717 5.3098 5.2455 5.1777 5.1044 5.0228 4.9269 4.8013 5.5327 4.4298
©2017 NCEES
575
100 (327.81)
80 (312.03)
60 (292.71)
40 (267.25)
20 (227.96)
14.696 (212)
10 (193.21)
5 (162.24)
1 (101.74)
v h s v h s v h s v h s v h s v h s v h s v h s v h s
392.6 1150.4 2.0512 78.16 1148.8 1.8718 38.85 1146.6 1.7927
200
452.3 1195.8 2.1153 90.25 1195.0 1.9370 45.00 1193.9 1.8595 30.53 1192.8 1.8160 22.36 1191.6 1.7808 11.04 1186.8 1.6994 7.259 1181.6 1.6492
300
512.0 1241.7 2.1720 102.26 1241.2 1.9942 51.04 1240.6 1.9172 34.68 1239.9 1.8743 25.43 1239.2 1.8396 12.628 1236.5 1.7608 8.357 1233.6 1.7135 6.220 1230.7 1.6791 4.937 1227.6 1.6518
400
571.6 1288.3 2.2233 114.22 1288.0 2.0456 57.05 1287.5 1.9689 38.78 1287.1 1.9261 28.46 1286.6 1.8918 14.168 1284.8 1.8140 9.403 1283.0 1.7678 7.020 1281.1 1.7346 5.589 1279.1 1.7085
500
631.2 1335.7 2.2702 126.16 1335.4 2.0927 63.03 1335.1 2.0160 42.86 1334.8 1.9734 31.47 1334.4 1.9392 15.688 1333.1 1.8619 10.427 1331.8 1.8162 7.797 1330.5 1.7836 6.218 1329.1 1.7581
600
690.8 1383.8 2.3137 138.10 1383.6 2.1361 69.01 1383.4 2.0596 46.94 1383.2 2.0170 34.47 1382.9 1.9829 17.198 1381.9 1.9058 11.441 1380.9 1.8605 8.562 1379.9 1.8281 6.835 1378.9 1.8029
750.4 1432.8 2.3542 150.03 1432.7 2.1767 74.98 1432.5 2.1002 51.00 1432.3 2.0576 37.46 1432.1 2.0235 18.702 1431.3 1.9467 12.449 1430.5 1.9015 9.322 1429.7 1.8694 7.446 1428.9 1.8443
Temperature (°F) 700 800
809.9 1482.7 2.3923 161.95 1482.6 2.2148 80.95 1482.4 2.1383 55.07 1482.3 2.0958 40.45 1482.1 2.0618 20.20 1481.4 1.9850 13.452 1480.8 1.9400 10.077 1480.1 1.9079 8.052 1479.5 1.8829
900
869.5 1533.5 2.4283 173.87 1533.4 2.2509 86.92 1533.2 2.1744 59.13 1533.1 2.1319 43.44 1533.0 2.0978 21.70 1532.4 2.0212 14.454 1531.9 1.9762 10.830 1531.3 1.9442 8.656 1530.8 1.9193
1000
3 Btu Btu Superheated Steam (U.S. Units) v = d ft n h = c lbm m s = c lbm - cF m lbm
Superheated Steam (U.S. Customary Units)
Pressure (psia) Saturated Temp. (°F)
8.8.3
988.7 1637.7 2.4952 197.71 1637.7 2.3178 98.84 1637.6 2.2413 67.25 1637.5 2.1989 49.41 1637.4 2.1648 24.69 1637.0 2.0883 16.451 1636.6 2.0434 12.332 1636.2 2.0115 9.860 1635.7 1.9867
1200
1107.8 1745.7 2.5566 221.60 1745.7 2.3792 110.77 1745.6 2.3028 75.37 1745.5 2.2603 55.37 1745.4 2.2263 27.68 1745.1 2.1498 18.446 1744.8 2.1049 13.830 1744.5 2.0731 11.060 1744.2 2.0484
1400
1227.0 1857.5 2.6137 245.40 1857.4 2.4363 122.69 1857.3 2.3598 83.48 1857.3 2.3174 61.34 1857.2 2.2834 30.66 1857.0 2.2069 20.440 1856.7 2.1621 15.325 1856.5 2.1303 12.258 1856.2 2.1056
1600
Chapter 8: Physical Properties
©2017 NCEES
576
280 (411.05)
260 (404.42)
240 (397.37)
220 (389.86)
200 (381.79)
180 (373.06)
160 (363.53)
140 (353.02)
120 (341.25)
v h s v h s v h s v h s v h s v h s v h s v h s v h s
Pressure (psia) Saturated Temp. (°F)
200
300
400 4.081 1224.4 1.6287 3.468 1221.1 1.6087 3.008 1217.6 1.5908 2.649 1214.0 1.5745 2.361 1210.3 1.5594 2.125 1206.5 1.5453 1.9276 1202.5 1.5319
500 4.636 1277.2 1.6869 3.954 1275.2 1.6683 3.443 1273.1 1.6519 3.044 1271.0 1.6373 2.726 1268.9 1.6240 2.465 1266.7 1.6117 2.247 1264.5 1.6003 2.063 1262.3 1.5897 1.9047 1260.0 1.5796
600 5.165 1327.7 1.7370 4.413 1326.4 1.7190 3.849 1325.0 1.7033 3.411 1323.5 1.6894 3.060 1322.1 1.6767 2.772 1320.7 1.6652 2.533 1319.2 1.6546 2.330 1317.7 1.6447 2.156 1316.2 1.6354
5.683 1377.8 1.7822 4.861 1376.8 1.7645 4.244 1375.7 1.7491 3.764 1374.7 1.7355 3.380 1373.6 1.7232 3.066 1372.6 1.7120 2.804 1371.5 1.7017 2.582 1370.4 1.6922 2.392 1369.4 1.6834
6.195 1428.1 1.8237 5.301 1427.3 1.8063 4.631 1426.4 1.7911 4.110 1425.6 1.7776 3.693 1424.8 1.7655 3.352 1424.0 1.7545 3.068 1423.2 1.7444 2.827 1422.3 1.7352 2.621 1421.5 1.7265
Temperature (°F) 700 800 900 6.702 1478.8 1.8625 5.738 1478.2 1.8451 5.015 1477.5 1.8301 4.452 1476.8 1.8167 4.002 1476.2 1.8048 3.634 1475.5 1.7939 3.327 1474.8 1.7839 3.067 1474.2 1.7748 2.845 1473.5 1.7662
1000 7.207 1530.2 1.8990 6.172 1529.7 1.8817 5.396 1529.1 1.8667 4.792 1528.6 1.8534 4.309 1528.0 1.8415 3.913 1527.5 1.8308 3.584 1526.9 1.8209 3.305 1526.3 1.8118 3.066 1525.8 1.8033
3 Btu Btu Superheated Steam (U.S. Units) (cont'd) v = d ft n h = c lbm m s = c lbm - cF m lbm
1200 8.212 1635.3 1.9664 7.035 1634.9 1.9493 6.152 1634.5 1.9344 5.466 1634.1 1.9212 4.917 1633.7 1.9094 4.467 1633.3 1.8987 4.093 1632.9 1.8889 3.776 1632.5 1.8799 3.504 1632.1 1.8716
1400 9.214 1743.9 2.0281 7.895 1743.5 2.0110 6.906 1743.2 1.9962 6.136 1742.9 1.9831 5.521 1742.6 1.9713 5.017 1742.3 1.9607 4.597 1742.0 1.9510 4.242 1741.7 1.9420 3.938 1741.4 1.9337
1600 10.213 1856.0 2.0854 8.752 1855.7 2.0683 7.656 1855.5 2.0535 6.804 1855.2 2.0404 6.123 1855.0 2.0287 5.565 1854.7 2.0181 5.100 1854.5 2.0084 4.707 1854.2 1.9995 4.37 1854.0 1.9912
Chapter 8: Physical Properties
©2017 NCEES
577
800 (518.23)
700 (503.1)
600 (486.21)
550 (476.94)
500 (467.01)
450 (456.28)
400 (444.59)
350 (431.72)
300 (417.33)
v h s v h s v h s v h s v h s v h s v h s v h s v h s
Pressure (psia) Saturated Temp. (°F)
200
300
400
500 1.7675 1257.6 1.5701 1.4923 1251.5 1.5481 1.2851 1245.1 1.5281 1.1231 1238.4 1.5095 0.9927 1231.3 1.4919 0.8852 1223.7 1.4751 0.7947 1215.7 1.4586
600 2.005 1314.7 1.6268 1.7036 1310.9 1.6070 1.477 1306.9 1.5894 1.3005 1302.8 1.5735 1.1591 1298.6 1.5588 1.0431 1294.3 1.5451 0.9463 1289.9 1.5323 0.7934 1280.6 1.5084 0.6779 1270.7 1.4863
2.227 1368.3 1.6751 1.898 1365.5 1.6563 1.6508 1362.7 1.6398 1.4584 1359.9 1.6250 1.3044 1357.0 1.6115 1.1783 1354.0 1.5991 1.0732 1351.1 1.5875 0.9077 1345.0 1.5665 0.7833 1338.6 1.5476
2.442 1420.6 1.7184 2.084 1418.5 1.7002 1.8161 1416.4 1.6842 1.6074 1414.3 1.6699 1.4405 1412.1 1.6571 1.3038 1409.9 1.6452 1.1899 1407.7 1.6343 1.0108 1403.2 1.6147 0.8763 1398.6 1.5972
Temperature (°F) 700 800 900 2.652 1472.8 1.7582 2.266 1471.1 1.7403 1.9767 1469.4 1.7247 1.7516 1467.7 1.7108 1.5715 1466.0 1.6982 1.4241 1464.3 1.6868 1.3013 1462.5 1.6762 1.1082 1459.0 1.6573 0.9633 1455.4 1.6407
1000 2.859 1525.2 1.7954 2.445 1523.8 1.7777 2.134 1522.4 1.7623 1.8928 1521.0 1.7486 1.6996 1519.6 1.7363 1.5414 1518.2 1.7250 1.4096 1516.7 1.7147 1.2024 1513.9 1.6963 1.0470 1511.0 1.6801
3 Btu Btu Superheated Steam (U.S. Units) (cont'd) v = d ft n h = c lbm m s = c lbm - cF m lbm
1200 3.269 1631.7 1.8638 2.798 1630.7 1.8463 2.445 1629.6 1.8311 2.1700 1628.6 1.8177 1.9504 1627.6 1.8056 1.7706 1626.6 1.7946 1.6208 1625.5 1.7846 1.3853 1623.5 1.7666 1.2088 1621.4 1.7510
1400 3.674 1741.0 1.9260 3.147 1740.3 1.9086 2.751 1739.5 1.8936 2.4430 1738.7 1.8803 2.1970 1737.9 1.8683 1.9957 1737.1 1.8575 1.8279 1736.3 1.8476 1.5641 1734.8 1.8299 1.3662 1733.2 1.8146
1600 4.078 1853.7 1.9835 3.493 1853.1 1.9663 3.055 1852.5 1.9513 2.7140 1851.9 1.9381 2.4420 1851.3 1.9262 2.2190 1850.6 1.9155 2.0330 1850.0 1.9056 1.7405 1848.8 1.8881 1.5214 1847.5 1.8729
Chapter 8: Physical Properties
©2017 NCEES
578
2500 (668.13)
2000 (635.82)
1800 (621.03)
1600 (604.9)
1400 (587.1)
1200 (567.22)
1100 (556.31)
1000 (544.61)
900 (531.98)
v h s v h s v h s v h s v h s v h s v h s
200
v h s v h s
Pressure (psia) Saturated Temp. (°F)
300
400
500
0.4532 1236.7 1.4251 0.4016 1223.5 1.4052 0.3174 1193.0 1.3639
0.5873 1260.1 1.4653 0.5140 1248.8 1.4450
600
0.5445 1318.3 1.4989 0.4909 1311.0 1.4843 0.4062 1295.5 1.4567 0.3417 1278.7 1.4303 0.2907 1260.3 1.4044 0.2489 1240.0 1.3783 0.1686 1176.8 1.3073
0.6863 1332.1 1.5303 0.6084 1325.3 1.5141 0.6191 1384.3 1.5535 0.5617 1379.3 1.5409 0.4714 1369.1 1.5177 0.4034 1358.4 1.4964 0.3502 1347.2 1.4765 0.3074 1335.5 1.4576 0.2294 1303.6 1.4127
0.7716 1393.9 1.5814 0.6878 1389.2 1.5670
Temperature (°F) 700 800
0.6866 1444.5 1.5995 0.6250 1440.7 1.5879 0.5281 1433.1 1.5666 0.4553 1425.3 1.5476 0.3986 1417.4 1.5301 0.3532 1409.2 1.5139 0.2710 1387.8 1.4772
0.8506 1451.8 1.6257 0.7604 1448.2 1.6121
900
0.7503 1502.2 1.6405 0.6843 1499.2 1.6293 0.5805 1493.2 1.6093 0.5027 1487.0 1.5914 0.4421 1480.8 1.5752 0.3935 1474.5 1.5603 0.3061 1458.4 1.5273
0.9262 1508.1 1.6656 0.8294 1505.1 1.6525
1000
3 Btu Btu Superheated Steam (U.S. Units) (cont'd) v = d ft n h = c lbm m s = c lbm - cF m lbm
0.8716 1615.2 1.7130 0.7967 1613.1 1.7025 0.6789 1608.9 1.6836 0.5906 1604.6 1.6669 0.5218 1600.4 1.6520 0.4668 1596.1 1.6384 0.3678 1585.3 1.6088
1.0714 1619.3 1.7371 0.9615 1617.3 1.7245
1200
0.9885 1728.4 1.7775 0.9046 1726.9 1.7672 0.7727 1723.7 1.7489 0.6738 1720.5 1.7328 0.5968 1717.3 1.7185 0.5352 1714.1 1.7055 0.4244 1706.1 1.6775
1.2124 1731.6 1.8009 1.0893 1730.0 1.7886
1400
1.1031 1843.8 1.8363 1.0101 1842.5 1.8263 0.8640 1840.0 1.8083 0.7545 1837.5 1.7926 0.6693 1835.0 1.7786 0.6011 1832.5 1.7660 0.4784 1826.2 1.7389
1.3509 1846.3 1.8595 1.2146 1845.0 1.8474
1600
Chapter 8: Physical Properties
©2017 NCEES
579
5500
5000
4500
4000
3500
3206.2 (705.4)
3000 (695.36)
v h s v h s v h s v h s v h s v h s v h s
Pressure (psia) Saturated Temp. (°F)
200
300
400
500
600
0.0984 1060.7 1.1966 0.0306 780.5 0.9515 0.0287 763.8 0.9347 0.0276 753.5 0.9235 0.0268 746.4 0.9152 0.0262 741.3 0.9090
0.1760 1267.2 1.3690 0.1583 1250.5 1.3508 0.1364 1224.9 1.3241 0.1052 1174.8 1.2757 0.0798 1113.9 1.2204 0.0593 1047.1 1.1622 0.0463 985.0 1.1093
Temperature (°F) 700 800 900 0.2159 1365.0 1.4439 0.1981 1355.2 1.4309 0.1762 1340.7 1.4127 0.1462 1314.4 1.3827 0.1226 1286.5 1.3529 0.1036 1256.5 1.3231 0.0880 1224.1 1.2930
1000 0.2476 1441.8 1.4984 0.2288 1434.7 1.4874 0.2058 1424.5 1.4723 0.1743 1406.8 1.4482 0.1500 1388.4 1.4253 0.1303 1369.5 1.4034 0.1143 1349.3 1.3821
3 Btu Btu Superheated Steam (U.S. Units) (cont'd) v = d ft n h = c lbm m s = c lbm - cF m lbm
1200 0.3018 1574.3 1.5837 0.2806 1569.8 1.5742 0.2546 1563.3 1.5615 0.2192 1552.1 1.5417 0.1917 1540.8 1.5235 0.1696 1529.5 1.5066 0.1516 1518.2 1.4908
1400 0.3505 1698.0 1.6540 0.3267 1694.6 1.6452 0.2977 1689.8 1.6336 0.2581 1681.7 1.6154 0.2273 1673.5 1.5990 0.2027 1665.3 1.5839 0.1825 1657.0 1.5699
1600 0.3966 1819.9 1.7163 0.3703 1817.2 1.7080 0.3381 1813.6 1.6968 0.2943 1807.2 1.6795 0.2602 1800.9 1.6640 0.2329 1794.5 1.6499 0.2106 1788.1 1.6369
Chapter 8: Physical Properties
©2017 NCEES
580
0.8 (170.43)
0.6 (158.85)
0.5 (151.86)
0.4 (143.63)
0.3 (133.55)
0.2 (120.23)
0.1 (99.63)
0.05 (81.33)
0.01 (45.81)
v h s v h s v h s v h s v h s v h s v h s v h s v h s
100
150
21.8250 2879.5 8.9038 4.35600 2877.7 8.1580 2.17200 2875.3 7.8343 1.08030 2870.5 7.5066 0.71630 2865.6 7.3115 0.53420 2860.5 7.1706 0.42490 2855.4 7.0592 0.35200 2850.1 6.9665 0.26080 2839.3 6.8158
200
24.1360 2977.3 9.1002 4.82000 2976.0 8.3556 2.40600 2974.3 8.0333 1.19880 2971.0 7.7086 0.79640 2967.6 7.5166 0.59510 2964.2 7.3789 0.47440 2960.7 7.2709 0.39380 2957.2 7.1816 0.29310 2950.0 7.0384
250
26.4450 3076.5 9.2813 5.28400 3075.5 8.5373 2.63900 3074.3 8.2158 1.31620 3071.8 7.8926 0.87530 3069.3 7.7022 0.65480 3066.8 7.5662 0.52260 3064.2 7.4599 0.43440 3061.6 7.3724 0.32410 3056.5 7.2328
31.0630 3279.6 9.6077 6.20900 3278.9 8.8642 3.10300 3278.2 8.5435 1.54930 3276.6 8.2218 1.03150 3275.0 8.0330 0.77260 3273.4 7.8985 0.61730 3271.9 7.7938 0.51370 3270.3 7.7079 0.38430 3267.1 7.5716
Temperature (°C) 300 400
35.6790 3489.1 9.8978 7.13400 3488.7 9.1546 3.56500 3488.1 8.8342 1.78140 3487.1 8.5133 1.18670 3486.0 8.3251 0.88930 3484.9 8.1913 0.71090 3483.9 8.0873 0.59200 3482.8 8.0021 0.44330 3480.6 7.8673
500
600
40.2950 3705.4 10.1608 8.05700 3705.1 9.4178 4.02800 3704.7 9.0976 2.01300 3704.0 8.7770 1.34140 3703.2 8.5892 1.00550 3702.4 8.4558 0.80410 3701.7 7.3522 0.66970 3700.9 8.2674 0.50180 3699.4 8.1333
J kJ kJ Superheated Steam (SI Units) v = d kg n h = d kg n s = d kg : K n
14.8690 17.1960 19.5120 2592.6 2687.5 2783.0 8.1749 8.4479 8.6882 3.41800 3.88900 2682.5 2780.1 7.6958 7.9401 1.69580 1.93640 2676.2 2776.4 7.3614 7.6134 0.95960 2768.8 7.2795 0.63390 2761.0 7.0778 0.47080 2752.8 6.9299
50
Superheated Steam (SI Units)
Pressure (MPa) Saturated Temp. (°C)
8.8.4
44.9110 3928.7 10.4028 8.98100 3928.5 9.6599 4.49000 3928.2 9.3398 2.24400 3927.6 9.0194 1.49570 3927.1 8.8319 1.12150 3926.5 8.6987 0.89690 3925.9 8.5952 0.74720 3925.3 8.5107 0.56010 3924.2 8.3770
700
49.5260 4159.0 10.6281 9.90400 4158.9 9.8852 4.95200 4158.6 9.5652 2.47500 4158.2 9.2449 1.64990 4157.8 9.0576 1.23720 4157.3 8.9244 0.98960 4156.9 8.8211 0.82450 4156.5 8.7367 0.61810 4155.6 8.6033
800
54.1410 4396.4 10.8396 10.8280 4396.3 10.0967 5.41400 4396.1 9.7767 2.70600 4395.8 9.4566 1.80410 4395.4 9.2692 1.35290 4395.1 9.1362 1.08220 4394.7 9.0329 0.90170 4394.4 8.9486 0.67610 4393.7 8.8153
900
Chapter 8: Physical Properties
©2017 NCEES
v h s v h s v h s v h s v h s v h s v h s v h s v h s
581
3.5 (242.60)
3.0 (233.90)
2.5 (223.99°C)
2.0 (212.42)
1.8 (207.15)
1.6 (201.41)
1.4 (195.07)
1.2 (187.99)
1.0 (179.91)
50
Pressure (MPa) Saturated Temp. (°C)
100
150
0.20600 2827.9 6.6940 0.16930 2815.9 6.5898 0.14302 2803.3 6.4975
200
0.23270 2942.6 6.9247 0.19234 2935.0 6.8294 0.16350 2927.2 6.7467 0.14184 2919.2 6.6732 0.12497 2911.0 6.6066 0.11144 2902.5 6.5453 0.08700 2880.1 6.4085 0.07058 2855.8 6.2872 0.05872 2829.2 6.1749
250
0.25790 3051.2 7.1229 0.21380 3045.8 7.0317 0.18228 3040.4 6.9534 0.15862 3034.8 6.8844 0.14021 3029.2 6.8226 0.12547 3023.5 6.7664 0.09890 3008.8 6.6438 0.08114 2993.5 6.5390 0.06842 2977.5 6.4461
300
0.30660 3263.9 7.4651 0.25480 3260.7 7.3774 0.21780 3257.5 7.3026 0.19005 3254.2 7.2374 0.16847 3250.9 7.1794 0.15120 3247.6 7.1271 0.12010 3239.3 7.0148 0.09936 3230.9 6.9212 0.08453 3222.3 6.8405
400
Temperature (°C)
0.35410 3478.5 7.7622 0.29460 3476.3 7.6959 0.25210 3474.1 7.6027 0.22030 3472.0 7.5390 0.19550 3469.8 7.4825 0.17568 3467.6 7.4317 0.13998 3462.1 7.3234 0.11619 3456.5 7.2338 0.09918 3450.9 7.1572
500
0.40110 3697.9 8.0290 0.33390 3696.3 7.9435 0.28600 3694.8 7.8710 0.25000 3693.2 7.8080 0.22200 3691.7 7.7523 0.19960 3690.1 7.7024 0.15930 3686.3 7.5960 0.13243 3682.3 7.5085 0.11324 3678.4 7.4339
600
J kJ kJ Superheated Steam (SI Units) (cont'd) v = d kg n h = d kg n s = d kg : K n
0.44780 3923.1 8.2731 0.37290 3922.0 8.1881 0.31950 3920.8 8.1160 0.27940 3919.7 8.0535 0.24820 3918.5 7.9983 0.22320 3917.4 7.9487 0.17832 3914.5 7.8435 0.14838 3911.7 7.7511 0.12699 3908.8 7.6837
700
0.49430 4154.7 8.4996 0.41180 4153.8 8.4148 0.35280 4153.0 8.3431 0.30860 4152.1 8.2808 0.27420 4151.2 8.2258 0.24670 4150.3 8.1765 0.19716 4148.2 8.0720 0.16414 4145.9 7.9862 0.14056 4143.7 7.9134
800
0.54070 4392.9 8.7118 0.45050 4392.2 8.6272 0.38610 4391.5 8.5556 0.33770 4390.8 8.4935 0.30010 4390.1 8.4386 0.27000 4389.4 8.3895 0.21590 4387.6 8.2853 0.17980 4385.9 8.1999 0.15402 4384.1 8.1276
900
Chapter 8: Physical Properties
©2017 NCEES
v h s v h s v h s v h s v h s v h s v h s v h s v h s
582
12.5 (327.89)
10.0 (311.06)
9.0 (303.40)
8.0 (295.06)
7.0 (285.88)
6.0 (275.64)
5.0 (263.99
4.5 (257.49)
4.0 (250.40)
50
Pressure (MPa) Saturated Temp. (°C)
100
150
200
250
0.05884 2960.7 6.3615 0.05135 2943.1 6.2828 0.04532 2924.5 6.2084 0.03616 2884.2 6.0674 0.02947 2838.4 5.9305 0.02426 2785.0 5.7906
300
0.07341 3213.6 6.7690 0.06475 3204.7 6.7047 0.05781 3195.7 6.6459 0.04739 3177.2 6.5408 0.03993 3158.1 6.4478 0.03432 3138.3 6.3634 0.02993 3117.8 6.2854 0.02641 3096.5 6.2120 0.02000 3039.3 6.0417
400
Temperature (°C)
0.08643 3445.3 7.0901 0.07651 3439.6 7.0301 0.06857 3433.8 6.9759 0.05665 3422.2 6.8803 0.04814 3410.3 6.7975 0.04175 3398.3 6.7240 0.03677 3386.1 6.6576 0.03279 3373.7 6.5966 0.02560 3341.8 6.4618
500
0.09885 3674.4 7.3688 0.08765 3670.5 7.3110 0.07869 3665.5 7.2589 0.06525 3658.4 7.1677 0.05565 3650.3 7.0894 0.04845 3642.0 7.0206 0.04285 3633.7 6.9589 0.03837 3625.3 6.9029 0.03029 3604.0 6.7810
600
J kJ kJ Superheated Steam (SI Units) (cont'd) v = d kg n h = d kg n s = d kg : K n
0.11095 3905.9 7.6198 0.09847 3903.0 7.5631 0.08849 3900.1 7.5122 0.07352 3894.2 7.4234 0.06283 3888.3 7.3476 0.05481 3882.4 7.2812 0.04857 3876.5 7.2221 0.04358 3870.5 7.1687 0.03460 3855.3 7.0536
700
0.12287 4141.5 7.8502 0.10911 4139.3 7.7942 0.09811 4137.1 7.7440 0.08160 4132.7 7.6566 0.06981 4128.2 7.5822 0.06097 4123.8 7.5173 0.05409 4119.3 7.4596 0.04859 4114.8 7.4077 0.03869 4103.6 7.2965
800
0.13469 4382.3 8.0647 0.11965 4380.6 8.0091 0.10762 4378.8 7.9593 0.08958 4375.3 7.8727 0.07669 4371.8 7.7991 0.06702 4368.3 7.7351 0.05950 4364.8 7.6783 0.05349 4361.2 7.6272 0.04267 4352.5 7.5182
900
Chapter 8: Physical Properties
©2017 NCEES
v h s v h s v h s v h s v h s v h s v h s
583
40.0
35.0
30.0
25.0
20.0 (365.81)
17.5 (354.75)
15.0 (342.24)
50
Pressure (MPa) Saturated Temp. (°C)
100
150
200
250
300
0.01565 2975.5 5.8811 0.01245 2902.9 5.7213 0.00994 2818.1 5.5540 0.00604 2580.2 5.1418 0.00279 2151.1 4.4728 0.00210 1987.6 4.2126 0.00191 1930.9 4.1135
400
Temperature (°C)
0.02080 3308.6 6.3443 0.01736 3274.1 6.2383 0.01477 3238.2 6.1401 0.01112 3162.4 5.9592 0.00868 3081.1 5.7905 0.00693 2994.4 5.6282 0.00562 2903.3 5.4700
500
0.02491 3582.3 6.6776 0.02106 3560.1 6.5866 0.01818 3537.6 6.5048 0.01414 3491.4 6.3602 0.01145 3443.9 6.2331 0.00953 3395.5 6.1179 0.00894 3346.4 6.0114
600
J kJ kJ Superheated Steam (SI Units) (cont'd) v = d kg n h = d kg n s = d kg : K n
0.02861 3840.1 6.9572 0.02434 3824.6 6.8736 0.02113 3809.0 6.7993 0.01665 3777.5 6.6707 0.01366 3745.6 6.5605 0.01153 3713.5 6.4631 0.00994 3681.2 6.3750
700
0.03210 4092.4 7.2040 0.02738 4081.1 7.1244 0.02385 4069.7 7.0544 0.01891 4047.1 6.9345 0.01562 4024.2 6.8332 0.01328 4001.5 6.7450 0.01152 3978.7 6.6662
800
0.03546 4343.8 7.4279 0.03031 4335.1 7.3507 0.02645 4326.4 7.2830 0.02145 4309.1 7.1680 0.01745 4291.9 7.0718 0.01488 4274.9 6.9886 0.01296 4257.9 6.9150
900
Chapter 8: Physical Properties
Chapter 8: Physical Properties
8.9 Diagrams for Water and Steam Pressure-Enthalpy (p-H) Diagram (U.S. Customary Units)
Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.
©2017 NCEES
584
Chapter 8: Physical Properties Temperature-Entropy (T-S) Diagram (U.S. Customary Units)
Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.
©2017 NCEES
585
Chapter 8: Physical Properties Pressure-Enthalpy (p-H) Diagram (SI Units) ,
,
,
,
,
,
,
,
,
,
Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.
©2017 NCEES
586
Chapter 8: Physical Properties Temperature-Entropy (T-S) Diagram (SI Units)
Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.
©2017 NCEES
587
