13.A-1 The gas driven off when low-grade coal is burned with insufficient air for complete combustion is known as producer gas. A particular producer gas has been analyzed and has the volumetric (molar) composition summarized in Table 13.A-1. Table 13.A-1: Molar analysis of a producer gas Constituent Mole fraction Methane, CH4 0.038 Ethane, C2H6 0.001 Carbon dioxide, CO 2 0.048 Hydrogen, H2 0.117 Oxygen, O2 0.006 Carbon monoxide, CO 0.232 Nitrogen, N2 balance
a.) Determine the apparent molecular weight of the gas mixture b.) Determine the mass fractions of each gas. c.) Determine the air-fuel ratio ratio if this gas mixture mixture is combusted with with 150% of stoichiometric dry air. d.) What is the dew point of the products of the reaction from (c) at 1 atm?
13.A-2 A small air-cooled gasoline engine is tested and the output is found to be 1.34 hp. The fuel is liquid octane (C8H18) and it is is provided to the engine at a rate of 0.15 g/s. The fuel and air both enter the engine at 25 C. The relative humidity is 42%. The products are analyzed with the results in Table 13.A-2, reported on a dry volumetric basis:
Table 13.C-4(a): Combustion gas analysis
CO2 O2 CO N2
11.4 % 1.47 % 2.90 % 84.23 %
a.) Determine the air-fuel ratio. b.) Determine the percent of theoretical air used in this combustion process. c.) The combustion products cool as they pass through the exhaust system. At what temperature will condensation initiate? c.) If the exhaust products exit the exhaust pipe at 32°C, at what rate will liquid water need to be removed?
13.A-2 A small air-cooled gasoline engine is tested and the output is found to be 1.34 hp. The fuel is liquid octane (C8H18) and it is is provided to the engine at a rate of 0.15 g/s. The fuel and air both enter the engine at 25 C. The relative humidity is 42%. The products are analyzed with the results in Table 13.A-2, reported on a dry volumetric basis:
Table 13.C-4(a): Combustion gas analysis
CO2 O2 CO N2
11.4 % 1.47 % 2.90 % 84.23 %
a.) Determine the air-fuel ratio. b.) Determine the percent of theoretical air used in this combustion process. c.) The combustion products cool as they pass through the exhaust system. At what temperature will condensation initiate? c.) If the exhaust products exit the exhaust pipe at 32°C, at what rate will liquid water need to be removed?
13.A-3 An analysis of a hydrocarbon fuel indicates that it consists of 83% carbon and 17% hydrogen on a mass basis. This fuel is completely combusted with 50% excess dry air at 25°C, 1 atm pressure. The combustion products are cooled to 35°C at 1 atm. a.) What is the dew point temperature of the combustion products? b.) What is the mass of condensate resulting from the combustion of 1 kg of the fuel? c.) How are your answers to a.) and b.) affected if the air used for combustion has a relative humidity of 100%?
13.A-4 A gas mixture obtained from a coal gasification process has the composition listed in column 2 of the table below. This gas mixture at 25 C and 5 atm is completely combusted air at 1 atm, 25 C, 40% relative humidity. The air to fuel ratio is 2.4 on a mass basis.
Table 13.A-4 Composition of a Coal Gasification Gas
Substance CH4 H2 N2 O2 CO CO2
Composition [volume %] 3.0 14.0 50.9 0.6 27.0 4.5
a.) What is the equivalent molar mass of the gas mixture? b.) What is the percent of excess air used in the combustion process? c.) Determine the dew point temperature of the combustion products at 1 atm pressure.
13.A-5 An experimental automotive fuel consists of 50% (by mole) liquid ethanol (C2H5OH) and 50% (by mole) liquid octane (C8H18). This mixture is steadily combusted with 120% theoretical dry air at 1 atm (101.3 kPa). a.) Determine the balanced chemical reaction equation for complete combustion of 1 mole of fuel mixture with 120% theoretical air. b.) Determine the air-fuel ratio for these conditions. c.) What is the dew point of the combustion products at 1 atm (101.3 kPa) pressure? d.) How does the dew point calculated in part c.) compare to the dew point that would result if the fuel were pure liquid octane?
13.A-6 C8H18 (butane) is combusted with air that is a 18°C, 1 atm, and 44% relative humidity. The combustion products are eventually cooled to 18°C. Calculate and plot the dew point temperature and the mass of condensate per kg of n-butane as a function of the percent excess air for values ranging from 0% to 500%. How would the plot changed if perfectly dry air were used in the combustion process?
13.A-7 The life of an automobile’s exhaust system can be related to the amount of liquid water that is condensed from the combustion products. A company interested in manufacturing replacement exhaust systems would like you to develop estimates for exhaust system life expectancy. The model engine operates with octane (C8H18) as the fuel with an average air/fuel ratio of 20:1. The products are cooled to 30°C prior to exiting the exhaust system. Empirical data suggest that the life expectancy (in months) of the exhaust is Life 48 8mw
where mw is the mass of water condensed in units kg of water per kg of fuel a.) Determine the percent excess air being used for this engine model. b.) What is the dew point of the exhaust products? c.) Assuming the empirical relation is correct, what is life expectancy of the exhaust system?
13.A-8 A fuel gas mixture used in steel production is delivered at 700 K, 250 kPa. This gas mixture is combusted with 200% theoretical dry air in a boiler. The composition of the gas mixture is provided in Table 13.A-8 on a volumetric basis. Complete combustion occurs and combustion products exit the boiler at 500 K, 100 kPa. Table 13.A-8: Volume percentages of fuel gas mixture
Gas H2 CH4 CO CO2 N2
Volume % 2.4 5.1 23.3 9.4 59.8
a.) What is the apparent molar mass of the fuel gas mixture? b.) What is the air-fuel ratio for the combustion process? c.) What is the dew point of the combustion products resulting from the combustion process?
13.A-9 The volumetric analysis of a gas mixture indicates that it is 11% CO2, 3% O2, and 86% N2. Water vapor is added to the mixture until it is saturated at 30°C, 101.3 kPa. The total 3 volume of the saturated gas mixture is 14 m . a.) Determine the volume percentage of CO2, O2, N2 and H2O after the mixture is saturated. b.) What is the apparent molar mass of this mixture after it has been saturated? c.) The mixture is now cooled to 10°C. What is the mass of water that condenses?
13.A-10 Liquid methyl alcohol (CH3OH) is combusted with air. The air and methanol enter a combustion chamber separately at 25°C and 100 kPa. The combustion products are cooled to 44°C and exhausted to the surroundings at 100 kPa. A volumetric analysis of the dried combustion products resulted in the following volumetric percentages: 1.2% CO, 10.7% CO2, 4.8% O2, with the remainder being nitrogen. a.) What is the air-fuel ratio assuming the air is complete dry? b.) Calculate the ratio of the kg of water that condenses to the kg of liquid methanol. c.) Repeat part b assuming that the air used for combustion is saturated with water.
13.B-1 Propylene (C3H6) is burned with 10% excess air in a combustor. The enthalpy of formation of propylene at 25°C is 20,410 kJ/kmol. The flow rate of air entering the 3 combustor is V air = 2.4 cfm (0.00113 m /s). The air and fuel are drawn into the combustor at T i = 25ºC and P = 1 atm. The products leave at T e = 450ºC and 1 atm. Model the gases as ideal gases with constant specific heat capacity: cP ,N2 = 29.18 kJ/kmol-K,
cP ,O2
= 29.63 kJ/kmol-K,
cP ,CO2
= 39.31 kJ/kmol-K, and
kJ/kmol-K. a.) What is the air-fuel ratio for the reaction? b.) Determine the rate of heat transfer from the combustor.
cP ,H2O
= 33.87
13.B-2 Figure 13.B-2 illustrates a simple, un-recuperated gas turbine engine. T f,i = 25°C
T a,i = 120°C
T t,in
turbine compressor
air in
combustion products out
Figure 13.B-2: Un-recuperated gas turbine engine.
The air leaves the compressor at T a,i = 120°C and enters the combustor where it is mixed with jet fuel (assume that jet fuel has composition C8H18) that enters at T f,i = 25°C. The air flow rate is such that there is 50% excess air. The combustor is adiabatic. Model the mixture components as ideal gas but do not assume constant specific heat capacities. a.) Determine the temperature of the combustion products leaving the combustor and entering the turbine. b.) Plot the temperature of the gas entering the turbine as a function of the percent excess air. c.) Plot the temperature of the gas entering the turbine as a function of the air fuel ratio.
13.B-3 a.) Write the chemical reaction associated with burning pentane (C5H12) with 50% excess air. b.) What is the air-fuel ratio (on a mass basis) for the reaction in (a)? The molecular weight of pentane is 72.151 kg/kmol. c.) What is the dew-point of the products of the reaction in (a) at 1 atm? d.) Determine the higher heating value (in kJ/kg) of pentane. The enthalpy of formation of pentane is -146,440 kJ/kmol.
13.B-4 Ethane (C2H6) is burned with a stoichiometric amount of air in a combustor, as shown in Figure 13.B-4. air air 10 m3 /s V T in 25C combustor ethane (C2H6)
combustion products T out = 350°C
T in = 25°C
Q Figure 13.B-4: Ethane burned in a combustor.
The fuel and air enter the combustor at T in = 25°C and combustion products leave at T out = 350°C. The inlet and exit pressure is P = 1 atm. The volumetric flow rate of air 3 entering the combustor is V air = 1 m /s. Assume that the specific heat capacities of carbon dioxide, water vapor, nitrogen, and oxygen are constant and equal to cP ,CO2 = 37.0 kJ/kmol-K, cP ,H 2O = 33.7 kJ/kmol-K, cP,N 2 = 29.2 kJ/kmol-K, and cP,O 2 = 29.5 kJ/kmolK, respectively. a.) Determine the rate of heat transfer from the combustor, Q .
13.B-5 Fuel oil is used in a modern condensing furnace. The fuel oil consists of a mixture of hydrocarbons. An elemental analysis shows that the fuel oil consists of 84.28% carbon (by weight), 15.22% hydrogen, and 0.5% sulfur. The lower heating value of this fuel oil is 42.5 MJ/kg. The furnace, which provides residential space heat, uses 50% excess air at 25°C, 60% relative humidity. Fuel oil enters the furnace at 25°C. Combustion gases and condensate exit at 43°C, 1 atm. a.) Determine the dew point temperature of the combustion products b.) Calculate the ratio of condensate to fuel oil on a mass basis c.) Determine the higher heating value of the fuel oil d.) Determine the efficiency of the furnace based on the lower and higher heating values
13.B-6 A sample of dried manure at 25°C is being tested for use as a fuel. The mass analysis of the sample is 42.7% carbon (C), 5.5% elemental hydrogen (H), 21.3% elemental oxygen (O), 12.4% elemental nitrogen (N), 0.3% elemental sulfur (S), 17.1% noncombustible material (cnc=1.0 kJ/kg-K), and 0.6% water (H2O). Air at 25°C, and 60% relative humidity is supplied to the combustor. The lower heating value of the sample is 12,500 kJ/kg. Prepare a plot of the combustion gas product temperature (assuming complete combustion) as a function of air-fuel ratio for a range of air-fuel ratios between stoichiometric conditions and 300% theoretical air. Also plot the dew point temperature of the combustion product gas as a function of air-fuel ratio.
13.B-7 The combustion gas mixture in Table 13.A-4 is reacted with air at 25°C, 1 atm, and 40% relative humidity to heat water. The air-fuel ratio is 2.4. The products exit the water heater at 68°F. Determine: a.) the lower and higher heating values of the gas mixture per kg of combustion gas mixture b.) the efficiencies of the water heating appliance relative to both the lower and the higher heating values.
13.B-8 A solid oxide fuel cell operates on an equimolar mixture of carbon monoxide (CO) and hydrogen (H2) produced from a reformation process. The fuel gas mixture enters at 25°C and reacts with dry air at 25°C within the fuel cell stack. The fuel cell produces 8 kJ of electrical energy for each gram of fuel mixture that enters. The fuel cell operation is nearly adiabatic and products exit at 800°C. The high temperatures and catalytic processes within the fuel cell ensure complete combustion. Determine: a.) the % of excess air that must be provided. b.) the efficiency of the fuel cell at these conditions. (Indicate how you are defining efficiency.)
13.B-9 Hydrogen has been proposed as a alternative to natural gas as a fuel for residential use. Hydrogen can be produced by electrolysis of water. In a particular process, water at 50 F, 1 atm is supplied to an electrolysis cell. The electrical current supplied to the cell decomposes the water to produce steady streams of hydrogen and oxygen at 100 F. For each pound of hydrogen produced, 45,000 Btu of heat are transferred from the cell to the surroundings in a steady operating condition. a.) Determine the efficiency of the electrolysis process.
b.) The collected hydrogen is then pumped through a pipeline where it is cooled to the environmental temperature (77°F) and later used to heat water from 50 F to 140 F in a water heater by combusting it with 80% excess air at 75°F. The combustion products exit the water heater at 150°F. Determine the efficiency of the water heating process
c.) A figure of merit for the overall process can be obtained by calculating the volume (gallons) of water heated per kW-hr of electricity expended in the electrolysis process. Calculate this figure of merit and compare it with the corresponding value that would be expected from a common electrical water heater. Would you recommend hydrogen as a substitute for natural gas if it were produced and used as described? Why or why not?
13.B-10 Since hydrogen does not naturally occur, it is necessary to make it from other fuels. Hydrogen can be produced by reacting methane and liquid vapor (both at 25°C). heat in from combustion
3 H 2 CO CH 4 H 2O
enter at 25 C
exit at 300 C
The above reaction is endothermic and it requires an environment at 800°C or higher to proceed. The hydrogen and carbon monoxide exit at 300°C as a result of heat exchange with the reactants. The thermal energy input to this reaction is provided by combusting methane with air in a separate process that has an efficiency of 90% based on the lower heating value of methane. Determine the moles of hydrogen produced per mole of methane including both the methane reacted and the methane used to provide the energy needed for the reaction. Also determine the ratio of lower heating value of the hydrogen produced to the lower heating value of the methane required to produce it.
13.B-11 A boiler for a power plant combusts methane with 125% excess air to heat water at 62 bar from 125°C to saturated vapor as shown in Figure 13.B-11. The mass flow rate of the steam is 2.4 kg/s. The air used in the combustion process enters at 25°C, 1 atm and it is preheated with the combustion products in a regenerator having an effectiveness of 0.78. Combustion products enter the regenerator at 375°C. Methane enters the boiler at 25°C. Losses from the jacket of the boiler are negligible. Methane Regenerator
Air 25°C, 1 atm
2
1
Boiler
4
3
Water 62 bar, 125°C
62 bar sat’d vapor
Figure 13.B-11: Boiler with regenerator
a.) Determine the required flow rates of air and methane b.) Determine the temperature of the combustion products that exit the regenerator.
13.B-12 The part-load operation of a gas turbine engine is controlled by adjusting the air-fuel ratio in the combustion chamber, thereby controlling the temperature of the combustion products at state 3 in the schematic shown in Figure 13.B-12. Air enters the compressor at 60°F, 1 atm at state 1. The compressor pressure ratio is 7.5 and the isentropic efficiency of the compressor is 0.72. Fuel enters the combustion chamber at 77°F, 1 atm. The fuel is a mixture of hydrocarbons consisting of 86% carbon and 14% hydrogen on a mass basis. The lower heating value of this fuel has been measured to be 18,500 Btu/lbm. combustor fuel, m f 2 compressor
1
3
c W
W
turbine
t
4
ambient air amb ,Pamb m,T Figure 13.B-12: Gas turbine system
a.) Determine the temperature of the air entering the combustion chamber at state 2 in °F. b.) Determine the specific enthalpy of the fuel in Btu/lbm c.) You have been asked to help develop an algorithm to control the power output of this engine. To help with this task, prepare a plot of the temperature of the combustion products at state 3 as a function of air-fuel ratio for air-fuel ratios between 20 and 120 (mass basis).
13.B-13 Combustion fuels are seldom pure chemicals, but rather a mixture of many chemicals. In a particular case, the lower heating value of a fuel mixture is determined to be 21,300 kJ/kg and a chemical analysis indicates that it contains 12.5% H, 37.5% C, and 50% O on a mass basis. Using this information, construct a plot of the adiabatic combustion temperature versus the % theoretical air for values between 100% and 400%. Assume complete combustion.
13.B-14 The purpose of this problem is to compare methane (CH4), propane (C3H8) and hydrogen (H2) as possible fuels for a residential furnace. 100% excess air is is used for all fuels. For each fuel, calculate and plot the following quantities for flue gas temperatures between 30°C and 80°C. Assume that the fuel and air enter the furnace at 25°C. a.) the furnace efficiencies based on the lower lower and higher heating values of the fuel b.) the mass flow rate of fuel required to supply 10 kW of thermal energy c.) the mass flow rate of condensate
13.B-15 A mixture of octane (C8H18) and 20% excess air at 25°C, 1 atm occupying 0.575 liters is adiabatically compressed with a compression ratio of 8 in one cylinder of an engine. Combustion then initiates at constant volume and proceeds to complete combustion in an adiabatic process. a.) What is the temperature and pressure of the mixture of octane and air after the adiabatic compression process has concluded and before combustion is initiated? b.) What is the work required to compress the mixture? c.) The reaction of octane and air is is initiated and occurs adiabatically adiabatically at constant volume. What is the temperature and pressure of the combustion products? d.) The combustion products expand isentropically until the volume is again 0.575 liters. Determine the work produced in this process. e.) The engine operates at 3000 rpm with a 4-stroke process (i.e., one combustion process for every eve ry 2 revolutions revo lutions of the crank shaft. What is the power generated from the one cylinder? f.) The efficiency of the engine is the net work divided by the lower heating value of the the octane. What is the efficiency for this engine?
13.B-16 Hydrogen has been proposed as an alternative to natural gas because it could be distributed through existing pipelines. Consider using hydrogen in place of natural gas in a residential furnace. Hydrogen at 40°F, 1 atm is completely combusted with with 120% excess dry air at 20°F, 1 atm. Combustion products exit the furnace furnace through a chimney at 300°F, 1 atm. a.) Determine the air-fuel ratio for the combustion reaction of hydrogen with 120% excess air. b.) Determine the dew point and relative humidity of the combustion products that e xit at 300°F, 1 atm. c.) What is the First Law efficiency efficiency of the furnace, based on the higher heating value of the fuel? d.) The furnace must supply 80,000 Btu/hr to maintain the indoor temperature at 70°F when it is 20°F outdoors. What is the necessary mass flow rate of hydrogen? e.) The exergy of the hydrogen is approximately equal to its lower heating value. Using this value, determine the Second-Law efficiency of the furnace.
13.B-17 A furnace combusts propane with air. The air enters at the outdoor temperature of 10°F and may be considered to be dry. The propane is taken from an outdoor tank that also is at 10°F. A volumetric analysis of the combustion products on a dry basis (i.e., after removing the water) resulted in the composition shown in Table 13.B-17. The 3 volumetric flow rate of the propane is 10 scfm (i.e., ft /min at 77°F, 1 atm). Combustion products exit the furnace at 95°F. Table 13.B-17: Volumetric analysis of combustion products
CO2 CO O2 N2 a.) b.) c.) d.)
5.5 1.1 11.0 remainder
Determine the percent excess air used in this furnace. At what rate must condensate be removed in gallons/hr? Determine the rate at which heat is provided to the building. What is the furnace efficiency, based on the higher heating value of propane?
3
13.B-18 n-octane (C8H18) is reacted with dry air in a 1.5 m constant volume cylinder. The air and fuel are initially at 25°C, 1 atm. An analysis of the combustion products indicates the volume percentages shown in Table 13.B-18, which are reported on a dry basis: Table 13.B-18: Combustion gas analysis
CO2 O2 CO N2
11.4% 1.6% 2.9% remainder
a.) Determine the percent of theoretical air used in this combustion process. b.) Determine the mass of n-octane initially present in the cylinder. c.) Determine the temperature and pressure of the combustion products if the reaction occurs adiabatically. d.) The combustion eventually cool to 25°C. What is the pressure at this point?
13.B-19 A proton exchange membrane (PEM) fuel cell involves electrochemical reactions between hydrogen and oxygen that is in air. In a particular case, air and hydrogen are provided at 25°C, 1 atm in separate streams, as shown in Figure 13.B-9. Two exit streams exhaust from the PEM at 92°C and atmospheric pressure. The fuel cell generates 3.2 kW. The hydrogen and air flow rates are carefully measured to be 0.0564 g/s and 2.9 g/s, respectively. It is known that 5% of the hydrogen exits the fuel cell unreacted with the water vapor. 3.2 kW -
+ H2O vapor and unreacted H2
Hydrogen
N2 and
Air
unreacted O2 Heat
Figure 13.B-19: Schematic of a hydrogen fuel cell
a.) What is the percent excess air that is provided relative to that needed for complete combustion? b.) What is the heat transfer rate from the fuel? c.) What is the efficiency of the fuel cell at this operating condition?
13.B-20 Propane (C3H8) is burned with a stoichiometric amount of air in a combustor. The propane and air enter the combustor at T in = 25°C and Pin = 1 atm. The products of combustion leave the combustor at T out = 25°C and Pout = 1 atm. a.) Write the balanced chemical reaction that described the combustion reaction. b.) What is the dew point of the combustion products? c.) Determine the number of kmols of water vapor that are produced per kmol of propane that is burned. Determine the number of kmols of liquid water that are produced per kmol of propane. d.) Assume that your calculation from (c) showed that 2 kmol of liquid water and 2 kmol of water vapor are produced per kmol of propane that is burned (this may or may not be the correct answer). Determine the heat transfer from the combustor per kmol of propane.
13.B-21 Liquid hydrogen peroxide (H2O2) is used as the oxidizer with methane fuel in a rocket engine. The methane and hydrogen peroxide steadily enter the engine in separate streams at 25°C, 1 atm at low velocity. To ensure complete combustion 25% excess oxidizer is supplied. Combustion products (which are all gaseous) exit the engine at 1200 K, 1 atm through a nozzle at high velocity. Note: The enthalpy of vaporization of liquid H2O2 at 25°C is 1535 kJ/kg. Properties for gaseous H2O2 are available in EES. a.) Estimate the velocity of the products b.) Estimate the Mach number (defined as the ratio of the velocity of the products) to the sound speed of the products.
13.B-22 A space heating application uses liquid ethanol (C2H5OH) as a fuel and it employs a combustion air preheater, as shown in Figure 13.B-22. Liquid methanol enters the combustion chamber at 15°C, 1 atm. At the design condition, air enters the preheater at –10°C and it is heated to 34°C before entering the furnace. Building air at atmospheric pressure and 15°C is circulated through a heat exchanger within the furnace at a rate of 0.88 kg/s; the air exits the furnace at 38°C. Combustion products exit the furnace at 185°C. Thermal losses from the jackets of the boiler and preheater are negligible. An exhaust gas analysis of the combustion gases resulted in the following volumetric percentages, expressed on a dry basis: 1.2% CO; 10.7% CO2; 4.8% O2; 83.3% N2. The specific enthalpy of liquid methanol at 25°C is -277.69 MJ/kmol.
Figure 13.B-22: Furnace with preheater that uses ethanol as the fuel
a.) b.) c.) d.) e.)
What is the % stoichiometric air? Determine the rate at which ethanol must be provided. Will condensation occur in the preheater? Why or why not? What is the effectiveness of the preheater? nd What is the 2 Law efficiency of this process assuming the exergy of the ethanol is equal to its lower heating value?
13.B-23 A gas-fired absorption cooling system utilizes the exergy of a combustible fuel to provide chilled water. A schematic of a two-stage gas-fired absorption chiller is shown in Figure 13.B-23. The purpose of this problem is to analyze the overall performance of this system from a First and Second-Law view point. It is not necessary to understand the internal operation of the absorption process to do this analysis. Chilled water enters the evaporator of the system (state 1) at 12 C, 60 kg/s and exits at 6 C (state 2). The absorption processes require cooling water which enters at 25 C, 115 kg/s (state 3) and exits at 30 C (state 4). The cooling water is discarded. Methane (CH4, Mol Wt.=16) is provided at 0.034 kg/s with dry air, both at 25 C, 1 atm. The two pumps require a total of 2 kW of electrical power. Combustion gases exit the stack at 230 C. A combustion analysis of the stack gases produced the volume percentages shown in the figure, reported on a dry basis:
Stack gas 230°C 6.6% CO2, 8.9% O2, 0.20% CO
Air 25°C, 1 bar CH4 25°C, 0.034 kg/s 4
Cooling water out 30°C, 115 kg/s
3
Cooling water in 25°C, 115 kg/s
2
Chilled water out 6°C, 60 kg/s 1
Chilled water in 12°C, 60 kg/s
2 kW electric
Figure 13.B-23: Schematic of a 2-stage gas-fired absorption cooling system
a.) What is the % excess air used to combust the methane? b.) Determine the COP of this absorption cooling system based on the higher heating value of the fuel. nd c.) Estimate the 2 Law efficiency of this absorption cooling system. (Approximate the exergy of the methane to be equal to its lower heating value.)
13.B-24 A new type of residential furnace is fueled with a liquid fuel consisting of 90% ethanol and 10% (liquid) water on a molar basis. The liquid fuel enters at 25°C and is combusted with (dry) air at 25°C from the building. The gaseous combustion products and condensate exit the furnace at 45°C, 1 atm. Analysis of the gaseous combustion products on a dry basis produces the following volumetric percentages: 8.4% CO2 5.0% O2 0.6% CO 86.0% N2. The energy released in the combustion reaction is used to heat air from 25°C to 40°C in order to maintain the building space at 25°C on a day in which it is –5°C outdoors. a.) Determine the percentage of excess air used in the combustion process. b.) Determine the lower heating value per unit mass of the liquid fuel c.) Determine the ratio of the mass of liquid water in the products (i.e., the condensate) to the mass of liquid fuel that is combusted. d.) What is the First law efficiency of the overall house heating process based on the lower heating value of the liquid fuel?
13.B-25. You are probably aware of the global warming concerns. Carbon dioxide is one (of many) ‘greenhouse’ gases that is mostly transparent to visible radiation but absorbent in certain bands within the infra-red region. The current U.S. administration has stated a goal of capping and later reducing carbon dioxide production. A logical question is how best to do this, since all hydrocarbon fuels produce carbon dioxide as an end product. Shown in the table below are the enthalpy of formation, absolute entropy, and molar specific heat capacity at 25°C, 1 atm for four common fuels. Rank these fuels with respect to their contribution to global warming. Use 1 for the best fuel and 4 for the worst from a global warming perspective. Explain the methodology behind your ranking. Rank
Fuel
___
Ethanol (liq)
___ ___
Coal (solid) Natl. Gas
___
Octane (liq)
Chemical Formula C2H5OH C CH4 C8H18 CO2 H2O(g) O2
h f, 25°C
so25°C
c p, 25°C
kJ/kmol -277,402
kJ/kmol-K
kJ/kmol-K
38.0
115.4
0 -32,211
1.369 186.3
8.53 36.06
-250.302
360.8
254.3
–393,500
213.7
37.0
-241,810
188.7
33.6
0
205.0
29.2
o
13.C-1 The purpose of this problem is to provide a thermodynamic analysis of the solid oxide fuel cell (SOFC) system shown in Figure 13.C-1.
Figure 13.C-1: Schematic of solid oxide fuel cell system
Inside of the fuel cell, methane reacts with water that is recycled from the anode of the fuel cell. Four moles of hydrogen are produced per mole of methane reacted according to the reaction, CH 4
2 H 2O 4 H 2 CO2
All of the methane is reacted. The hydrogen that is produced is subsequently reacted with oxygen in the fuel cell according to 4 H 2 a O2
3.76 N2 4U
H 2 O 4(1 U ) H 2
a3.76 N2
bO2
According to Faraday’s Law, each mole of hydrogen that is reacted produces two moles of hydrogen protons, which results in a charge transfer of 2 F where F is 9.64867E7 coulomb/kmol. Thus, the current is directly proportional to the rate at which hydrogen is converted into water. Note that not all of the hydrogen is reacted. The fraction of the available hydrogen (from reformed methane) that is reacted is U , the fuel utilization. Having some unreacted hydrogen exit the stack is needed to maintain the voltage in the fuel cell. Consequently, the current through each cell is i
8 F U nCH 4 / N s
where nCH 4 is the molar flow rate of methane and
N s is
the number of cells in series
(48). Air and methane enter at 25°C, 101.3 kPa at points 1 and 6, respectively. The methane flow rate is 0.06 g/sec. Water vapor, carbon dioxide and some unreacted hydrogen at 800°C emerge from the stack at point 8. Some of this gas is recycled back to the stack so that additional water is not required. Unreacted oxygen and nitrogen at 800°C exit the stack at point 4 and are used to preheat the incoming air. The temperature at state 5 is measured found to be 108°C. A second heat exchanger uses the preheated air to preheat the methane to 250°C. The air enters the fuel cell (state 3) at 700°C. The fuel cell stack produces 1.6 kW of electrical power at 28.2 V. Since there 48 cells in series, each cell operates at 0.5875 V. Heat losses from the jackets of the heat exchanger are negligible, but there is heat loss from the SOFC stack. Calculate: a.) the efficiency of the fuel cell system at these conditions (not considering parasitic losses). Please be sure to indicate how you are defining efficiency. b.) the fuel utilization, U
c.) the % stoichiometric air supplied d.) the rate of heat loss from the SOFC stack
13.C-2 A Second-Law analysis of this fuel cell system described in problem 13.C-1 is requested. Base your exergy calculations on the reference environment provided in Table 13.C-2. Table 13.C-2 Reference Environment :
T=25C P=101.3 kPa Substance Mole fraction N2 0.75670 O2 0.20350 H2O(g) 0.03035 CO2 0.00035 Other 0.00910 a.) b.) c.) d.)
Determine the exergy flow rate at each of the states in the system Determine the heat exchanger effectiveness of heat exchangers 1 and 2 Determine the Second-Law efficiency of heat exchangers 1 and 2 Determine the Second-Law efficiency of the fuel cell system assuming that both streams 5 and 8 are discarded e.) Determine the Second-Law efficiency of the fuel cell system assuming that stream 5 is discarded but the exergy in stream 8 is recovered.
13.C-3 Incineration is one method used for the reduction of waste material that is normally sent to landfills. Some types of waste may require supplemental energy to achieve complete combustion at the required temperature of 1200 K. In a particular case, it is necessary to incinerate a food waste. Prior analyses indicate that the food waste has the composition (by mass on a wet basis) shown in Table 13.C-3 and a higher heating value of 5,510 kJ/kg of wet waste at 25°C. Table 13.C-3: Elemental analysis of the food waste
Element Carbon Hydrogen Oxygen Nitrogen
Mass % 45% 6.5% 29% 3%
Sulfur Non-combustibles
0.5% 16%
The specific heat of the non-combustible material is 2.5 kJ/kg-K. The food waste enters the incinerator at the ambient temperature (25C) and it is combusted with 25% excess air at a rate of 0.32 kg/s. Heat transfer through the incinerator walls can be represented as: Q UA Tinc
Tamb
where (UA) is the heat transfer conductance of the incinerator, estimated to be 400 W/K. T inc and T amb are the incineration and ambient temperatures, respectively.
a.) What is the temperature of the products resulting from incineration of the wet food waste with stoichiometric ambient air, assuming that no supplemental energy is provided? b.) Natural gas at ambient temperature can be injected into the incinerator with the food waste to at a rate that provides a combustion temperature of 1200 K with 25% excess air. Assuming natural gas costs about $1.50/therm, estimate the cost per hour to incinerate the food waste. c.) What is the dew point temperature of the combustion products for case b? d.) An engineer suggested that it may be less costly to inject oxygen into the food waste rather than to purchase natural gas in order to maintain a 1200 K incineration temperature. Can the injection of oxygen help to maintain the incineration temperature at 1200 K? If so, calculate and compare the cost per hour of this option, assuming that no free oxygen exists in the products. Oxygen at 95% purity is available for $15 per 1000 standard cubic feet.
13.C-4 A small air-cooled gasoline engine is tested and the output is found to be 1.34 hp. The temperature of the combustion products is measured and found to be 493 C. The products are analyzed with the results in Table 13.C-4(a), reported on a dry volumetric basis:
Table 13.C-4(a): Combustion gas analysis
Table 13.C-4(b): Reference Environment 25°C, 101.3 kPa
Substance CO2 O2 CO N2
11.4 % 1.47 % 2.90 % 84.23 %
N2 O2 H2O(g) CO2 Other
Mole fraction 0.7567 0.2035 0.01314 0.00040 0.02628
The fuel supplied to the engine is pure n-octane (C8H18) liquid. The fuel and air enter the engine at 25 C. The relative humidity is 42%. The fuel flow rate is 0.15 g/s.
a.) What is the First-Law efficiency of this engine? (Clearly indicate on how you define efficiency.) b.) What fraction of the energy in the fuel shows up in the exhaust? c.) What is heat transfer rate from the engine to the air d.) What is the Second-Law efficiency of this engine assuming that the combustion products will be discarded to the atmosphere (defined in the Table 13.C-4(b)) e.) What is the rate at which exergy is discarded with the combustion products? Is this rate of exergy discarded in this manner significant?
13.C-5 The purpose of this problem is to evaluate the feasibility of injecting liquid water into an engine in order to increase power output. Consider a specific case for an Otto cycle in which n-octane (C8H18 -vapor state) is combusted with 5% excess air at 25°C, 1 bar. The temperature and pressure after the compression stroke is completed is 335°C and 17.2 bar. At this point, liquid water at 25°C is quickly injected to produce a saturated mixture with no liquid droplets. The spark ignites the mixture and the combustion process proceeds adiabatically at constant volume. The combustion products adiabatically expand to 1 bar thereby producing mechanical power. You may assume complete combustion and neglect friction and other irreversible processes in your analysis. a.) What is the compression ratio for these conditions? b.) What is the temperature and pressure of the fuel-air mixture directly after the water is adiabatically injected and the corresponding mole fraction of water vapor assuming complete mixing and no change in volume during the injection process. c.) Calculate the work required to compress the fuel air mixture per mole of n-octane assuming an adiabatic compression process. d.) The combustion process occurs adiabatically at constant volume. Determine the maximum temperature and pressure of the combustion products and compare the results with those that would result if there were no water injection. e.) A concern has been raised regarding the effect of the water on the exhaust system. Compare the dew point temperatures of the exiting exhaust products with and without water injection.
13.C-6 This problem is a continuation of problem 13.C.5, which analyzes an Otto cycle with water injection. Please prepare an analysis to answer the following questions. a. Determine the exhaust temperature with and without the water injection assuming that the expansion process is adiabatic and internally reversible. b. Calculate and compare the net work per mole of fuel with and without the water injection. c. Calculate the First Law efficiency of the engine with and without the water injection. d. Calculate the mass of water required per mass of n-octane consumed. Is this water injection process feasible in passenger vehicles? Indicate the advantages and disadvantages of water injection and whether you think it is a useful idea.
13.C-7 The Rankine power plant shown in Figure 13.C-7 is required to produce a net mechanical power output of 20 MW by combusting natural gas (methane) with excess air, both at 25°C, 1 atm. The turbine efficiency is 0.84 (for both stages) and pump efficiencies are 0.56. The condenser pressure is maintained at 8 kPa. The air used for combustion is preheated with the exiting combustion gas in a heat recovery wheel. Heat exchange with water in the boiler/superheater produces steam at 520°C, 75 bar. After leaving the boiler, the combustion gas is used to preheat the pressurized water in the economizer, which is a gas to water heat recuperator. The boiler, economizer and heat recovery wheels can each be modeled as heat exchangers with an effectiveness relation. Pressure losses can be neglected. The effectivenesses of the economizer and heat recovery wheel are both 0.50. The effectiveness of the boiler is 0.90 when defined as follows.
Tmax T 3 Tmax T sat
where
T max is
the adiabatic combustion temperature T sat is the saturation temperature of water at the boiler pressure (75 bar) Turbine
Methane
Heat Recovery Wheel
7
Boiler
2
8
9
Stage 2
520°C
Air at 2 5°C, 1 bar 1
Stage 1
(75 bar) 6
3
Economiser
r e t a e H
11 10
r e ) s a n P e k d 8 n ( o C
Pump 1
Combustion gases at 1 bar, Th,out
12
4
5
13 Pump 2
Figure 13.C-7: Rankine cycle with heat recovery wheel
a.) Assume the pressure at state 8 is 20 bar. Prepare a plot of the required methane flow rate as a function of the percentage of excess air for percentages between 0 and 200%. What is the optimum percent excess air? b.) Using the excess air determined in part a, investigate the effect of the pressure at state 8. Is there an optimum pressure? If so what is it? c.) Determine the dew point temperature for the exiting combustion gases (state 5). Is condensation a concern in this system?
13.C-8 A small stationary gas turbine plant is used for provide 50 kW of electrical power during times of peak demand with a generator that has an efficiency of 0.95. A schematic of the plant is shown in Figure 13.C-8. combustor fuel, m f 2 compressor
3
c W
W gt
4
1 ambient air m ,Ta mb , Pa mb
gasifier turbine
pt W generator
power turbine 5 to ambient
Figure 13.C-8: Stationary gas turbine system
Dry air enters at state 1 at 25°C and 1 atm. The maximum turbine inlet temperature at state 3 is 1450 K. The turbine isentropic efficiencies are 0.84 and the compressor isentropic efficiency is 0.82. Assume complete combustion and neglect the pressure loss in the combustor and between components. Prepare plots of following quantities as a function of the pressure ratio P2/P1 for a range between 1.5 and 15. a.) the air fuel ratio b.) the required flow rate of methane in kmole/s c.) the efficiency of the cycle d.) the temperature at state 5
13.C-9 Although fuel cells are receiving a great deal of developmental attention, a major impediment to their widespread adoption is that they use hydrogen as a fuel and the low density of hydrogen makes it difficult to store and transport. Consequently alternative ways of providing storing or providing a hydrogen source are being investigated. One alternative is to use liquid ammonia. Liquid anhydrous ammonia has a relatively high fuel value, and products of consumption, in at least hydrogen transferring fuel cells, are only water and elemental nitrogen. Ammonia of course has several major drawbacks, but it is worth investigating. Data for ammonia at 25ºC, 1.013 bar in an ideal gas state are provided below: o o Molar Mass 17.03 h f ,298 K 45,937 kJ/kmol s298K 192.8 kJ/K-kmol
a) What are the lower and higher heating values of liquid ammonia in units of kJ/kg? b) What pressure would the ammonia need to be maintained at in the fuel tank? Provide a short description of how you arrive at this answer. c) What is the volume ratio of the ammonia tank to a gasoline tank necessary to provide the same theoretical driving distance?
13.C-10 A stationary gas-turbine plant used for generating electricity by combusting methane during times of peak demand is configured as shown in Figure 13.C-10. At design conditions, the turbine-generator produces 92 MW with air and fuel (CH4) entering at 25°C, 1 atm entering the compressor. (The generator efficiency is 0.94.) The compressor pressure ratio at design conditions is 14.1 and the air-fuel ratio is 42.0. Independent measurements have indicated that the compressor and turbine isentropic efficiencies are 0.78 and 0.81, respectively. The pressure loss across the burner is small.
Figure 13.C-10: Gas turbine system operating at part load
When the electrical demand is less than 92 MW, the fuel flow rate is reduced. Because the compressor and turbine must spin at constant speed, the volumetric flow rate at both the compressor and turbine inlets is constant. As the fuel flow rate is reduced, the temperature of the combustion gases entering the turbine decreases and the pressure at the turbine inlet must adjust to maintain the fixed volumetric flow rate. a.) Calculate the methane consumption and the overall plant efficiency at the full-load operating point where the system produces 92 MW. b.) Calculate and plot the relative efficiency versus the part-load factor. (The relative efficiency is defined as the efficiency divided by the efficiency at full load; the part-load factor is the ratio of the electrical power to the full-power electrical power (92 MW).
13.C-11 One method to improve the performance of a stationary gas turbine system is to inject steam into the combustion products before they enter the turbine, as shown in Figure 13.C-11. The steam is produced by a heat exchange process using the exhaust of the gas turbine as the heat source.
Figure 13.C-11: Gas turbine system with steam injection
In a particular case, ambient air at 20 C, 1 bar (state 1) enters the compressor and is compressed to 12 bar (state 2). The isentropic efficiency of the compressor is 0.62. The air then enters the combustor which is fueled with methane which enters at 20 C. To ensure complete combustion, the fuel flow rate is adjusted to achieve 75% excess air. The combustion products exit at state 3. Metallurgical considerations dictate that the gas entering the turbine at state 4 must be no higher than 1200 C. The turbine isentropic efficiency is 0.74. Steam at 365 C, 12 bar (state 9) is injected into the combustion products at a rate sufficient to maintain this temperature. The steam is generated from entering water at 20°, 1 bar (state 7) by heat exchange with the combustion products exiting at state 5.
a.) What is the necessary mass ratio of steam to air entering the compressor to keep the turbine inlet stream at state 4 from exceeding 1200 C? b.) What is the temperature and dew point of the exhaust stream at state 6? c.) What is the First Law efficiency of the system with the steam injection and the corresponding back-work ratio? d.) If steam injection were not used, what would the % excess air have to be in order to maintain a combustor outlet temperature of 1200 C? e.) What is the First Law efficiency of the system without steam injection and the corresponding back-work ratio? f.) Provide a short explanation for the results you found in parts e and f.
13.C-12 One means of gasifying coal (assumed here to be pure carbon) is based upon the carbon– steam reaction. C + H2O
CO + H2
→
The energy input for this endothermic reaction and for producing the steam is provided by heat exchange with combustion gas obtained by combusting coal (carbon) with 75% excess air. The schematic of the process, along with state point information is provided in Figure 13.C-12. (Neglect any losses from the equipment.) 3
Combustion products at 50°C exhausted to enviroment
Steam 320°C, 1 atm Steam Generator
Water 25°C, 1 atm
2
Coal Gasifier
Carbon 25°C
Coal gas 930°C, 1 atm 40% CO, 40% H2, 20% H2O
1
Carbon 25°C
Furnace
T=298 K, P=101.3 kPa 75.67% N2 20.35% O2 3.12% H2O
75% excess Air 25°C, atm
Environment:
0.038% CO2
0.822 % inert
a.) Determine the temperature of the gas at state 1. b.) Determine the temperature of the gas at state 2 and the ratio of the mass of carbon that goes to the furnace relative to the carbon that is fed to the gasifier. c.) Determine the exergy per mole of carbon d.) Determine the exergy per mole of the product gas e.) Calculate the Second-Law efficiency of this process and comment on the advantages and disadvantages of coal gasification. Assume the 50°C combustion products are discarded. Refer your calculations to the environment described in the table.
13.C-13 Hydrogen has been proposed as an alternative to natural gas as a fuel for residential use. Hydrogen can be produced by electrolysis of water. In a particular process, water at 10°C, 1 atm is supplied to an electrolysis cell. The electrical current supplied to the cell decomposes the water to produce steady streams of hydrogen and oxygen at 35°C, 1 atm. For each kmol of hydrogen produced, 110 MJ of heat are transferred from the cell to the surroundings in order to maintain steady operating conditions. Environment: T=298 K, P=101.3 kPa 75.67% N220.35% O2 3.12% H2O 0.038% CO2 0.822 % inert a.) Determine the required electrical energy per kmol of water in the electrolysis process. b.) Determine the exergy per mole of the hydrogen that is produced in this process relative to the environment defined in the table. c.) Determine the exergy per mole of oxygen that is produced in this process relative to the environment defined in the table. c.) Determine the Second-Law efficiency of the electrolysis process. d.) The collected hydrogen is then pumped through a pipeline, combusted with air, and used in a residence to heat water from 10°C to 50°C in a water heater that has an 80% efficiency based on the higher heating value of the fuel. What is the Second-Law efficiency of the water heating process? e.) What is the Second-Law efficiency of the combined electrolysis and water heating processes? f.) Would you recommend hydrogen as a substitute for natural gas if it were produced and used as described? Explain your answer.
13.C-14 Gas-fired heat pumps utilize the high availability of a combustible fuel to supply space heat at a thermal efficiency greater than 1.0. One proposed type of heat pump is the Stirling/Rankine System, shown in a space heating configuration in Figure 13.C-14. The purpose of this problem is to analyze the test results of this system. Test results are given in Table 13.C-14 for methane consumption of 3 lbm/hr. The following assumptions may be applied. i) The methane is completely combusted with 100% excess air. ii) Heat losses occur only from the combustion chamber and the Stirling engine. These losses occur outdoors and do not contribute to heating the house. The heat loss from the engine is 2750 Btu/hr. iii) The constant pressure specific heat for the water-glycol solution is 0.78 Btu/lbm-F. iv) The compressor has an adiabatic efficiency of 0.80. Table 13.C-14: Test results for a gas-fired heat pump
Fluid 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17.
Methane Air Gas Gas Gas Helium Helium R134a R134a R134a R134a Glycol Glycol Glycol Air Air Air
Temp. °F 45 0 2060 1160 260 1150 1300 -Sat'd Liq. -Sat'd vap 90 117 197 60 120 0
Pressure psia 14.7 14.7 14.7 14.7 14.7 1600 1520 250 250 12 12 20 20 20 14.7 14.7 14.7
5
Combustion Products (260°F)
Heat Exchanger #2 13 4
14 2750 Btu/hr
6 Heat Exchanger #1
Stirling Engine
Heated Air to House 16
7
12
3 R134a Compressor =0.8
•
Q cs Combustion Chamber 1
Heat Exchanger #3
11 2
8
Outside Air 17
Condenser 9 15 Cool House Air
Throttle Valve
Evaporator Methane 45°F (3.0 lbm/hr)
100% Excess Air - 0°F
10
Figure 13.C-14: Schematic of a gas-fired heat pump
a.) b.) c.) d.) e.) f.) g.)
Calculate the heat loss from the combustion chamber in Btu/hr. How many horsepower does the Stirling cycle engine develop? Determine the total rate of heat addition to the house. 3 Determine the volumetric flow rate of air at state 16 in ft /min. What is the efficiency of this system for house heating? What is the dew point of the combustion products at point 5? What are the advantages and disadvantages of this system?
13.C-15 A simplified analysis of the processes occurring in a spark-ignition internal combustion engine is provided by the air-standard Otto cycle as presented in Chapter 8. The purpose of this problem is to develop a more realistic model which considers combustion and heat transfer processes. a.) Calculate and plot the thermal efficiency and mean effective pressure for an air standard Otto cycle for compression ratios between 6 and 12 with a maximum cycle temperature of 3,000 K. Assume that the state of the air before compression is 25°C, 1 atm. b.) The working fluid entering the engine is not air, but rather a mixture of propane (C3H8) and stoichiometric air. The maximum cycle temperature is the temperature that results during the adiabatic constant volume combustion process. Compute the maximum cycle temperature and plot the engine thermal efficiency (based on the lower heating value of the fuel) and the mean effective pressure versus compression ratio for compression ratios between 6 and 12 using the same assumptions as used in the air-standard Otto cycle, i.e., isentropic compression and expansion, and combustion occurring at constant volume. c) Some of the energy released in the combustion process is transferred to the ‘cold’ engine walls which are maintained at 105°C. Assume that the rate of heat transfer to the engine walls is: qwall
K T
Twall
where K =628 kJ/K-kmol propane and T is the average temperature occurring during the combustion process, e.g, (T 2+T 3)/2. Calculate and plot the thermal efficiency and mean effective pressure versus the compression ratio including this heat transfer consideration.
13.C-16 Steady-state operating data for a turbojet engine shown in Figure 13.C-16 are provided in Table 13.C-16. This engine runs on methane gas. The fuel is completely combusted with air. The composition of air is 21.0% oxygen, 0.965% water, and 0.035% carbon dioxide, with the remainder being nitrogen. 0
1
2
Diffuser
Methane
3
Combustor
4
5
Nozzle
Compressor
Turbine Figure 13.C-16: Schematic of a turbojet engine
Table 13.C-16: Operating data for the engine shown in Figure 13.C-16
a.) b.) c.) d.) e.) f.) g.)
Position
Fluid
0 1 2 3 4 5
Air air Air Mixture Mixture Mixture Methane
Temperature [°C] 25 42 276 1450 1288 1060 45
Pressure [kPa] 100 118 655 647 374 100 1000
Velocity [m/s] 250 ~0 ~0 ~0 ~0 750 ~0
What is the compressor isentropic efficiency? What is the percentage of excess air at this operating condition? Determine the rate of heat loss from the combustor Compare the powers of the turbine and compressor Estimate the isentropic efficiency of the turbine Estimate the rate of heat loss in the nozzle Estimate the nozzle efficiency
Flow Rate [kg/s] 0.450 0.450 0.450 0.464 0.464 0.464 0.014
13.C-17 Steady-state operating data for a turbojet engine fueled by methane are provided in problem 13.C-16. The fuel is completely combusted with air. The composition of air is 21.0% oxygen, 0.965% water, and 0.035% carbon dioxide, with the remainder being nitrogen. a.) Determine the rate of exergy destruction in the combustor of this engine. b.) A Second-Law efficiency for this engine can be defined as the increase in kinetic energy of the fluids divided by the exergy supplied to the engine. Determine the value of the Second-Law efficiency defined in this manner.
13.C-18 The physical plant of a large building complex produces both electricity and steam at 250 psia. A sketch of the plant appears in Figure 13.C-8 and a table with property information is provided in Table 13.C-18. The boiler is fueled with methane (CH4) which enters separately from the air. Both the methane and air enter at 77°F, 1 atm. A combustion analysis of the stack gases produced the following volumetric percentages, reported on a dry basis: 3.6% CO2
14.5% O2
0.04% CO
81.86% N2
Figure 13.C-18: Schematic of physical plant that produces electricity and steam Table 13.C-18: Property Information for the physical plant at selected states
State
1 2 3 4 5 6 7 8 Dead
m
T
P
v
h
s
[F]
[psia]
[ft3/lbm]
[Btu/lbm]
[Btu/R-lbm]
[lbm/hr]
900 550 102 102 102 320 388 390 70
1200 250 1 1 200 200 1250 220 14.7
0.6250 2.2909 303.6 0.0161 0.0161 0.0184 0.0185 0.0185 0.0160
1440.9 1291.8 1012.6 69.7 70.0 290.4 362.2 364.2 38.0
1.5883 1.6239 1.8120 0.1326 0.1331 0.5438 0.5516 0.5540 0.0745
100,000 30,000 70,000 70,000 70,000 100,000 100,000 30,000 --------
a.) Assuming energy losses from the boiler jacket to be negligible, what is the rate at which methane is combusted? b.) The generator has en efficiency of 0.92. What is the electrical power produced by the generator in kW? nd c.) What is the 2 Law efficiency of this plant relative to a dead state at 77°F, 1 atm and 50% relative humidity? (Assume that atmospheric air is at at 77°F, 1 atm with the partial pressures of nitrogen, oxygen, carbon dioxide and water being 0.769 atm, 0.206 atm, 0.0004 atm and 0.016 atm, respectively.) d.) If the electricity is valued at 13 cents/kW-hr, what is the value of the process steam supplied by this plant in cents/1000 lbm?
13.C-19 A commercial laundry facility requires 4500 kg/hr of water at 60°C. Supply water is available at 10°C. The simple steam turbine system shown in Figure 13.C-19 has been proposed to supply the energy needed to heat the water and a portion of the electrical needs as well. The boiler produces saturated steam at 700 kPa by combusting methane that is provided at 25°C, 1 atm with 125% excess air at 25°C, 1 atm. Combustion gases exit the boiler at 180°C, 1 atm. The combined efficiency of the turbine and generator is 0.72. The pump efficiency is 0.40. The condenser pressure is 50 kPa.
Figure 13.C-19: System to provide hot water and electricity
a.) What is the required rate of methane consumption assuming that the hot water needs are supplied? b.) How much power is produced by the system in kW? c.) Determine the heat exchanger effectiveness of the condenser. nd
d.) Calculate the 2 Law efficiency of this system assuming that the specific exergy of methane is equal to its lower heating value. e.) The pump, turbine, and generator efficiencies can not be changed. What other nd suggestions can you provide that would increase the 2 Law efficiency of this system.
3
13.C-20 0.025 lbm of liquid methyl alcohol (CH3OH) are placed in a 1.5 ft constant volume container with a stoichiometric amount of air. The container is well-insulated and equipped with a spark plug to initiate the reaction. The methanol and air are initially at 77°F. The enthalpy of formation of liquid methanol at 77°F is –102,605 Btu/lbmol. a.) What is the pressure in the container before ignition? b.) Assuming complete combustion has occurred, estimate the temperature and pressure of the combustion products directly after the reaction occurs. (Assume ideal gas behavior.) c.) As the combustion gas is cooled, at what temperature will condensation begin?
13.C-21 The exergy of sulfur and compounds containing sulfur presents a question concerning the dead state to which the availability of these compounds should be referenced. One proposal is to take CaSO4•2H2O as the dead state molecule involving sulfur. CaSO4•2H2O is formed from chemical reactions of sulfur and sulfur dioxide with CaCO3, O2, and H2O, which are found in the reference environment. S + CaCO3 + 1.5 O2 + 2H2O
CaSO4•2H2O + CO2
→
SO2 + CaCO3 + 0.5 O2 + 2H2O
CaSO4•2H2O + CO2
→
Property data at 25°C, 1 atm for the species involved in these reactions are presented in Table 13.C-21. Also in last column of the table are the partial pressures of the gaseous species as they exist in the reference environment. Using these data, what is your estimate for the specific exergy of sulfur dioxide (SO2) at 25°C, 1 atm? Table 13.C-21: Property data and partial pressures for selected chemicals Species hf,25°C so Pi,o
[kJ/kmol]
[kJ/kmol-K]
[atm]
S SO2
0 -296,792
32.068 248.098
solid 0
O2
0
205.028
0.204
H2O(v) CaCO3
-241,811 -1,206,526
188.709 91.704
0.0088 solid
CaSO4•2H2O CO2
-2,021,123 -393,486
193.970 213.665
solid 0.000394
N2
0
191.489
0.76746
13.C-22 Diesel engines are used in many communities for generating electricity. A particular case is shown schematically in Figure 13.C-22. The engine produces 385 kW of electrical power. Cooling water enters at 25° C and exits as saturated steam at 100°C at a rate of 0.60 kg/sec. Fuel at a rate of 0.055 kg/sec with 10% excess air enters the engine at 25°C. Exhaust products exit at 425°C. (Assume complete combustion.) Depending on the cost of fuel relative to the cost of capital equipment, opportunities exist for recovering availability from the cooling water, from the exhaust products, or from both. The Diesel fuel has a composition of 85% carbon and 15% hydrogen on a mass basis. The lower heating value of the fuel is 42,600 kJ/kg. The reference environment consists of a mixture of the following gases (volumetric basis) at 25°C and a total pressure of 1.0 atm: 20.4% oxygen, 0.04% carbon dioxide, 78.68% nitrogen, and 0.88% water vapor.
Figure 13.C-22: Schematic of the Diesel generator system
a.) What is the efficiency of the engine (assuming that the cooling water and exhaust products are discarded)? b.) Estimate the enthalpy of formation of the Diesel fuel at 25°C in J per kg. c.) What is the rate at which cooling water must be provided? d). What is the rate of flow of the exergy with the exhaust products exiting the engine? e.) What is the rate of flow of the exergy with the exiting cooling water stream? f.) Estimate the rate of exergy destruction in the engine, assuming that the specific exergy of the fuel is equal to its lower heating value.
3.C-23
A modern pulse-combustion residential furnace is fueled with natural gas. Analysis of the natural gas shows it to be 94% methane (CH4) and 6% nitrogen (N2) on a volumetric basis. The gas enters the furnace at 10°C from a pipeline and is combusted with air at 25°C from the building. The gaseous combustion products and condensate exit the furnace at 40°C, 1 atm. Analysis of the gaseous combustion products on a dry basis produces the following volumetric percentages: 8.4% CO2 5.0% O2 0.6% CO 86.0% N2. The energy released in the combustion reaction is used to heat air from 25°C to 40°C in order to maintain the building space at 25°C on a day in which it is –5°C outdoors. a) The percentage of excess air used in the combustion is ________%. b) The lower heating value per unit mass of natural gas is ________ kJ/kg c) The first law efficiency of the overall house heating process based on the lower heating value of the natural gas is __________. nd d) The 2 Law efficiency of the overall house heating process is __________. (Approximate the exergy of the natural gas with its lower heating value.) f) Carbon monoxide is released to the environment, along with the other combustion gases. The specific exergy of this carbon monoxide is _________ kJ/kmol. Base your calculations on the following composition of outdoor air. 78.3% N2, 20.35% O2 , 0.4% H2O, 0.04% CO2, 0.93% other.
13.C-24 A large meat packing company uses electricity (to operate machinery and lights) and 5 bar steam generated in a natural gas-fueled boiler to provide the thermal energy needed for cooking and water heating. The company currently buys all of the electricity and gas from a utility. Engineers working for this company are considering the installation of the gas turbine system shown in figure 13.C-24, which can supply 27 MW of electricity and some of the steam needs of the plant as well. The generator has an efficiency of 0.90. The gas turbine is fueled with natural gas (CH 4). A combustion analysis of the exhaust products yields the following volume percentages reported on a dry basis: 3.9% CO2, 14.0% O2, 87.1% N2. The exhaust from the turbine is heat exchanged to generate 5.0 bar saturated steam, which is used to supplement the steam needs in the plant. Estimated operating data for this gas turbine system are provided in Table 13.C-24.
Figure 13.C-24: Gas turbine cogeneration system
State 1 2 3 4 5 6 7 8
Table 13.C-24: State point information fluid T P Flowrate °C kPa kg/s air 25 101 146.3 air 396 1013 146.3 gas 1212 1010 gas 750 110 gas 402 101 gas 25.0 101 water 25.1 510 23.0 water 155.5 500 23.0
a.) What is the air/fuel ratio and the rate at which methane is combusted? b.) What is the 2nd Law efficiency of this physical plant? (Approximate the exergy of the fuel with its lower heating value.) c.) If the methane cost is $0.20 per kg, what should the production costs of the electricity and process steam each be in $/kW and $/kg, respectively, in order to recover the cost of the methane?
13.C-25 Figure 13.C-25 shows a schematic of a residential heating system that uses an enginedriven heat pump. The fuel to the engine is propane (C3H8). During normal operation, the engine drives the compressor of the heat pump, which uses R134a as the refrigerant. The condenser of the heat pump is located in one of two coils in the furnace ductwork and provides heat to the building. In addition, a glycol coolant is circulated through the engine and then through a heat exchanger that recovers some of the energy in the engine exhaust gas. The heated glycol solution then proceeds through a second coil in the furnace providing additional heat to the building.
Figure 13.C-25: Schematic of a gas-fired heat pump system
Test data for the engine driven heat pump are as follows. The engine provided 3.59 kW of power to the compressor. The isentropic efficiency of the compressor is known to be 0.72 under these operating conditions. The saturation temperatures in the evaporator and condenser were -12°C and 36°C, respectively. (Assume states 2 and 4 to be saturated vapor and liquid, respectively and neglect pressure losses in the piping and heat exchangers.) The glycol solution, which has a specific heat capacity of 3.43 kJ/kg-K, was circulated at a rate of 0.062 kg/s. The measured temperatures of the glycol solution at states 5, 6, and 7 were 76°C, 91°C, and 58°C. The exhaust gas exited at state 9 at 124°C. A combustion gas analysis of the indicated the following volume percentages of the exhaust gases, expressed on a dry basis: 8.3% CO2, 1.5% O2, 0.6% CO, remainder N2. a.) What is the mass flow rate of the R134a? b.) What is the percent theoretical air and the corresponding air-fuel ratio for the engine? c.) What is the efficiency of the engine based on the lower heating value of the fuel? d.) The exhaust gas recovery heat exchanger uses a cross-flow design with both fluids unmixed. Estimate the heat transfer rate and the effectiveness of this heat exchanger. e.) Determine the total rate heat transfer of heat transfer to the building. Also, indicate the fractional contributions of this heat transfer for the heat pump, the recovery of energy from the engine coolant, and the recovery of energy from the exhaust gas. f.) Determine the efficiency of this heating system based on the lower heating value of the fuel defined in the same manner as for a conventional furnace.
13.C-26 Problem 13.C-25 requires an analysis of a gas-fired heat pump heating system fueled with propane. In this problem, you are to complete a Second Law analysis of the same system. Base your exergy calculations on the reference environment provided below. Reference Environment: T=0°C P=101.3 kPa Substance Mole fraction N2 & inerts 0.7820 O2 0.2035 H2O(g) 0.0050 CO2 0.0004 Other 0.0091 a.) Determine the exergy flow rate of the propane that is supplied to the engine. b.) Determine the exergy flow rate of the exhaust gas at state 9 before it enters the environment. c.) Determine the COP of the heat pump for the maintaining the building at 21°C. d.) Determine the Second Law efficiency of the heat pump by itself. e.) Determine the Second-Law efficiency of the engine, not including the space heating contributions. f.) Determine the Second-Law efficiency of the overall heating process.
13.C-27 Most fuel cells cannot directly operate using natural gas (methane) as a fuel so it is necessary to convert the methane into hydrogen using a process called reforming. One step in this process is shown in Figure 13.C-27. Methane at 25 C, 1 atm enters an adiabatic reformer at a rate of 0.00025 kmol/s along with water vapor at 800 C, 1.5 atm. The reaction between methane and water is endothermic. In this case, energy is provided from an electrical source. Products exit the reformer at 800 C, 1 atm with the mole fractions indicated in the figure. The surroundings are at 25°C, 1 atm, with the following composition of a volumetric basis: 20.4% O2, 0.04% CO2, 0.88% H2O, remainder is N2 and inert gases.
Figure 13.C-27: Schematic of a methane-steam reformer
a.) What is the molar flow rate of H 2O at the reformer inlet? b.) Calculate the required electrical power. c.) Determine the rate at which exergy is supplied to the reformer with the methane. d.) Determine the rate at which exergy is supplied to the reformer with the entering steam. e.) What is the exergy flow rate of the products leaving the reformer? f.). Determine the Second Law efficiency for this reformation process.
13.C-28 The advent of fuel cell technology has increased interest in hydrogen. One way that hydrogen can be produced is by electrolysis of water. In a particular process, water at 25 C, 1 atm and electrical energy are supplied to an electrolysis cell. The final products from this process are hydrogen and oxygen in separate tanks, each at 100 C, 5 atm. The necessary electrical energy is 500,000 kJ per kmol of hydrogen. Atmospheric conditions: 25 C, 1 atm, 40% relative humidity, 21 volume % oxygen
a.) What is the specific molar exergy of the hydrogen produced in this process? b.) What is the specific molar exergy of the oxygen produced in this process? c.) Determine the required heat transfer per kmol of hydrogen. nd d.) What is the 2 Law efficiency of the overall process?
