Fracturing Engineering Manual-Data FRAC Service

FRACTURING ENGINEERING MANUAL Schlumberger

Dowell

DataFRAC Service

Section 700.1 May 1998 Page 1 of 81

DataFRAC SERVICE 1 Introductory Summary............................................................................................................. 6 1.1 Closure Test......................................................................................................................... 7 1.1.1 Closure Test in a Permeable Zone ............................................................................. 7 1.1.2 Closure Test in a Nonpermeable Zone....................................................................... 9 1.2 Calibration Test.................................................................................................................... 9 1.3 Applications........................................................................................................................ 10 2 Design ..................................................................................................................................... 11 2.1 Preparatory Engineering .................................................................................................... 11 2.1.1 Breakdown/Diversion Treatment .............................................................................. 11 2.1.2 Preliminary Fracture Design ..................................................................................... 11 2.1.3 Fracture Height......................................................................................................... 11 2.1.4 Wellbore Logging...................................................................................................... 12 2.1.4.1 Temperature and Gamma-Ray Logs ............................................................. 12 2.1.4.2 Fracture-Height Logs ..................................................................................... 13 2.1.5 Perforating ................................................................................................................ 13 2.1.5.1 Wellbore Restrictions ..................................................................................... 13 2.1.5.2 Perforation Phasing ....................................................................................... 14 2.1.5.3 Perforation Size ............................................................................................. 14 2.2 Closure Test....................................................................................................................... 15 2.2.1 Fluid Selection .......................................................................................................... 15 2.2.2 Injection Rates and Number of Steps ....................................................................... 15 2.2.3 Step Duration............................................................................................................ 15 2.2.4 Flow-Back Rate ........................................................................................................ 16 2.3 Calibration Test.................................................................................................................. 17 2.3.1 Fluid Selection .......................................................................................................... 17 2.3.1.1 Foam.............................................................................................................. 17 2.3.2 Fluid Volume............................................................................................................. 17 2.3.3 Fluid Break-Time ...................................................................................................... 18 DOWELL CONFIDENTIAL


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2.3.4 Fluid-Loss Additives ..................................................................................................18 2.3.5 Duration of Pressure Decline ....................................................................................18 2.4 Special Considerations in the DataFRAC Design...............................................................18 2.4.1 The Influence of Wellbore Fluid ................................................................................18 2.4.2 Prepad.......................................................................................................................18 2.4.3 Closure Pressure less than Hydrostatic Pressure.....................................................19 2.4.4 Post-Job Wireline Surveys ........................................................................................19 2.5 Terminology........................................................................................................................19 2.5.1 Fracture Extension Pressure.....................................................................................19 2.5.2 Initial Shut-in Pressure ..............................................................................................19 2.5.3 Closure Pressure ......................................................................................................19 2.5.4 Rebound Pressure ....................................................................................................19 2.6 Equipment Requirements ...................................................................................................20 2.6.1 Monitoring Equipment ...............................................................................................20 2.6.2 Pumping Equipment..................................................................................................20 2.6.3 Pressure Measuring Equipment................................................................................20 2.6.3.1 Surface Measurement Methods .....................................................................20 2.6.3.2 Bottomhole Pressure Gauge Measurement ...................................................22 2.6.4 Treating Equipment...................................................................................................23 2.6.5 Flowback Equipment.................................................................................................23 2.6.5.1 Magnetic Flowmeters .....................................................................................23 2.6.5.2 Turbine Flowmeters........................................................................................23 2.6.5.3 Chokes and Gate Valves................................................................................23 3 Execution ................................................................................................................................24 3.1 Pre-Performance Guidelines ..............................................................................................24 3.2 Closure Test .......................................................................................................................27 3.2.1 Step-Rate Phase.......................................................................................................27 3.2.2 Flowback Phase........................................................................................................32 3.2.2.1 Flow Control ...................................................................................................32 3.2.2.2 Flowmeters.....................................................................................................34 3.2.3 Closure Test Modifications........................................................................................34 DOWELL CONFIDENTIAL


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3.3 Calibration Test.................................................................................................................. 35 3.3.1 Injection Phase ......................................................................................................... 35 3.3.2 Pressure-Decline Phase ........................................................................................... 36 3.3.3 Contingency Plans.................................................................................................... 36 4 Evaluation............................................................................................................................... 36 4.1 Closure Test Analysis ........................................................................................................ 37 4.1.1 Step Rate  The BHP-Versus-Rate Plot ................................................................. 37 4.1.2 Flowback  The BHP-Versus-Time Plot.................................................................. 37 4.1.3 Confirmation of Closure Pressure............................................................................. 38 4.1.4 Rebound Pressure.................................................................................................... 40 4.2 Calibration Injection for Fracture Geometry ....................................................................... 40 4.2.1 Elastic Fracture Compliance..................................................................................... 41 4.2.2 Pressure During Pumping......................................................................................... 43 4.2.2.1 Fluid Flow and Pressure in Fracture .............................................................. 43 4.2.2.2 Nolte-Smith Plot and Evolution of Pressure During Pumping ........................ 45 4.2.3 Deviations from Ideal Geometry ............................................................................... 46 4.2.3.1 Height Growth ................................................................................................ 46 4.2.3.2 Fissures ......................................................................................................... 47 4.2.3.3 T-Shape Fracture........................................................................................... 48 4.2.4 Pressure Capacity .................................................................................................... 49 4.2.5 Near-Wellbore Restriction......................................................................................... 50 4.2.6 Fracturing Pressure Interpretation Summary ........................................................... 53 4.2.6.1 Example of Radial Fracture ........................................................................... 54 4.2.6.2 Simulation of Pressure During Pumping and Decline .................................... 54 4.3 Calibration Decline for Fluid-Loss Behavior ....................................................................... 56 4.3.1 Review of Decline Analysis....................................................................................... 56 4.3.2 Volume Function g.................................................................................................... 58 4.3.3 Fluid Efficiency.......................................................................................................... 59 4.3.4 Decline Function G ................................................................................................... 61 4.3.5 Non-Ideal Behavior ................................................................................................... 64 4.3.5.1 Change in Fracture Penetration After Shut-in................................................ 64 DOWELL CONFIDENTIAL



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4.3.5.2 Height Growth ................................................................................................65 4.3.5.3 Pressure-Dependent Leakoff .........................................................................66 4.3.5.4 Spurt...............................................................................................................69 4.3.5.5 Closure Pressure Change ..............................................................................69 4.3.5.6 Compressible Fluids.......................................................................................71 4.3.6 Fluid Efficiency Based on Pressure Analysis ............................................................72 4.3.7 Decline-Analysis Procedure ......................................................................................73 4.3.8 Steps to Correct Decline Analysis Using the FracCADE Software............................75 4.3.8.1 The DataFRAC Software................................................................................76 4.3.8.2 G-plot Interpretation by the DataFRAC Software ...........................................77 4.3.8.3 Modulus, Height or Fracture Toughness Calibrations ....................................77 4.3.8.4 The β Ratio.....................................................................................................78 4.3.9 Post Proppant Fracture Analysis...............................................................................80 4.3.10 References..............................................................................................................81 FIGURES Fig. 1. The effect of proppant-pack damage and fracture length on fracture NPV. ......................6 Fig. 2. Fracture extension pressure (unequal time steps). ...........................................................7 Fig. 3. The typical closure test......................................................................................................8 Fig. 4. The G-plot (idealized). .....................................................................................................10 Fig. 5. Channel restriction at the wellbore. .................................................................................13 Fig. 6. The relation of perforation diameter and proppant concentration. ..................................14 Fig. 7. The effects of differing flowback rates. ............................................................................16 Fig. 8. The change in surface pressure during closure in deep, hot wells..................................21 Fig. 9. Hydrostatic head changes during closure. ......................................................................22 Fig. 10. The DataFRAC Service rig-up when pumping conductive fluids. ..................................25 Fig. 11. The DataFRAC Service rig-up when pumping nonconductive fluids. ............................26 Fig. 12. Friction pressure of water in the tubing and casing. ......................................................28 Fig. 13. Friction pressure of water in the annulus.......................................................................29 Fig. 14. Friction pressure of brine in the tubing and casing........................................................29 Fig. 15. Friction pressure of brine in the annulus. ......................................................................30 Fig. 16. Friction pressure of diesel in the tubing and casing. .....................................................30 Fig. 17. Friction pressure of diesel in the annulus. .....................................................................31 Fig. 18. Flow rate versus differential pressure in perforations....................................................31 Fig. 19. Flowback test (after Nolte, 1982/1994)..........................................................................38 Fig. 20. Effect of closure on BHP versus square root of t and G- plots. .....................................39 Fig. 21. Rebound pressure; lower bound of closure pressure....................................................40 Fig. 22. Analogy of a pressurized crack to a pre-loaded spring. ................................................42 Fig. 23. Evolution of fracture geometry and pressure during pumping.......................................45 Fig. 24. Pressure and width for height growth through barriers (after Nolte, 1989)...................46 DOWELL CONFIDENTIAL


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Fig. 25. Fig. 26. Fig. 27. Fig. 28. Fig. 29. Fig. 30. Fig. 31. Fig. 32. Fig. 33. Fig. 34. Fig. 35. Fig. 36. Fig. 37. Fig. 38. Fig. 39. Fig. 40. Fig. 41. Fig. 42. Fig. 43. Fig. 44. Fig. 45. Fig. 46.

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Pressure and width for opening natural fissures (after Nolte, 1989)............................ 47 Pressure and width for T-shape fracture (after Nolte, 1989)........................................ 48 Definition of pressure capacity from in-situ stresses..................................................... 50 Stress state within the entrance of deviated well or stress. .......................................... 51 Mohr circle of deviated well or stress. ........................................................................... 52 Nolte-Smith plot of fracturing pressure. ........................................................................ 53 Net pressure with radial fracture (after Smith et al. 1987). .......................................... 54 Measured and simulated net pressure: opening natural fissures (after Nolte, 1982). . 55 Example of fracturing-related pressures (after Nolte, 1982). ........................................ 56 Schematic for fracture area and time............................................................................ 57 Dimensionless volume function for fracture closure (after Nolte, 1986)....................... 59 Efficiency from closure time for no proppant, no spurt loss during pumping and other ideal assumptions given in Section 4.3.1 (after Nolte, 1986). ............................. 60 Conceptual response of pressure decline versus Nolte time-function (after Castillo, 1987). .................................................................................................... 62 Penetration change during shut-in (after Nolte, 1990). ................................................. 65 Diagnostic for height growth from decline data (after Nolte, 1990)............................... 66 Diagnostic for stress sensitive fissures from injection and decline (after Nolte, 1990). 67 Decline analysis for filtrate and reservoir control leakoff (after Nolte, 1993)................ 68 Stress change during injection/shut-in for Cc (after Nolte et. al., 1993)......................... 70 Relative volume change of gas (after Nolte et. al., 1993). ........................................... 72 Decline analysis using “¾” rule (after Nolte, 1990). ...................................................... 74 Pressure and flow rate in fracture before and after shut-in (after Nolte, 1986)............ 79 Diagnostic for closing on proppant from decline data (after Nolte, 1990). ................... 80 TABLES

Table 1. Table 2. Table 3. Table 4. Table 5.

Approximate Choke Settings For Flowback Of Oil-Base Fluids (Sg = 0.7) .................. 33 Approximate Choke Settings for Flowback of Water-Base Fluids (Sg = 1.0)............... 34 Interpolated Values of α Over the Full Range of n....................................................... 58 Values of Decline Function "G" .................................................................................... 63 Correction Factors f c As Function Of ∆tD ...................................................................... 75

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Section 700.1 May 1998


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1 Introductory Summary The DataFRAC* Service determines the in-situ parameters critical to optimum fracture treatment design. These parameters are specific to each formation and often to each well. Assumed or inaccurate parameter values can result in the following. • Premature screenout and reduced fracture penetration caused by pad fluid depletion. •

Unpropped fracture, increased damage to proppant-pack conductivity and increased treatment cost because of excessive pad volume.

Both outcomes result in reduced net present value (NPV), illustrated in Fig. 1.

Fig. 1. The effect of proppant-pack damage and fracture length on fracture NPV. (THIS FIGURE IS FOR ILLUSTRATIVE PURPOSES ONLY.) The DataFRAC Service typically consists of two tests  a closure test and a calibration test.

*

Mark of Schlumberger

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1.1 Closure Test The closure test determines closure pressure  the minimum in-situ rock stress. Accurate determination of closure pressure is important because all fracture analysis is referenced from it. Closure pressure is also used for proppant selection. The closure test is recommended as one of the initial procedures of any field stimulation operation. Performance of a valid closure test • ensures the zone has been fractured (a necessary condition for valid performance of other tests) •

provides upper and lower bounds for determination of the closure pressure

•

defines the required range of pump rates for extending a fracture in the zone.

1.1.1 Closure Test in a Permeable Zone The closure test in a permeable zone is a step-rate/flowback procedure. A Newtonian fluid is injected at an increasing rate until fracture extension occurs. A pressure versus rate plot will show two distinct slopes, the intersection of which indicates fracture extension pressure (Fig. 2). The change in slope in is a result of the different pressure responses for matrix leakoff and fracture extension at the higher rate. This pressure is normally 50 to 200 psi greater than closure pressure because of fluid friction in the fracture and fracture toughness.

Fig. 2. Fracture extension pressure (unequal time steps). (THIS FIGURE IS FOR ILLUSTRATIVE PURPOSES ONLY.) DOWELL CONFIDENTIAL



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Another indication of fracture extension pressure comes from a bottomhole pressure versus time plot and is illustrated in Fig. 3. The pressure steps above fracture extension pressure have squared shoulders compared to the rounded shoulders characteristic of matrix leakoff.

Fig. 3. The typical closure test. (THIS FIGURE IS FOR ILLUSTRATIVE PURPOSES ONLY.) Pumping continues for five to ten minutes after fracture extension. The well is then flowed-back at a constant rate. Flowback is started immediately after the final step and is held constant until pressure has fallen to about 200 psi above the initial wellbore pressure. The pressure response will show a distinct reversal in curvature once closure has occurred (Fig. 3), indicating a change of fluid withdrawal from the open fracture to withdrawal through the matrix. The rebound pressure after shut in serves as a lower bound to closure pressure. Perforation friction pressure is another important parameter that is determined from the step-rate/flowback test. At shut-in, the immediate bottomhole pressure drop is the pressure loss in the perforations during the last stage of the step-rate test. The pressure loss will give an indication of potential wellbore problems, usually unopened perforations. Reperforating should be considered if the pressure loss is unacceptable. The closure pressure is determined by quantitative analysis of bottomhole pressure versus time using the Pressure Analysis and DataFRAC modules in the FracCADE* software.

*


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The closure pressure may also be determined from a shut-in/decline test by analysis of a square-root plot. However, the shut-in/decline method does not provide a definitive indication of the closure pressure and is not the preferred method. 1.1.2 Closure Test in a Nonpermeable Zone The closure test in a nonpermeable zone (shale) is an injection/shut-in procedure where a small quantity (tens of gallons) of a Newtonian fluid is injected at low rate. Pumping stops and an initial shut-in pressure is observed. Local stress is approximately equal to the initial shut-in pressure; therefore, net pressure is approximately equal to zero and the initial shut-in pressure is used to infer the stress. 1.2 Calibration Test The calibration test is an injection/shut-in/decline procedure. A viscosified fluid (without proppant) is pumped at proposed fracturing treatment rate. The well is then shut in and a pressure decline analysis is performed. The following critical design parameters are determined from the calibration test. • fracture half-length (xf) •

fracture width (w)

•

fracture height (hf)

•

fluid-loss coefficient (C)

•

Young's modulus (E)

•

fluid efficiency (η).

The injection test determines the type of fracture being created; Perkins-KernNordgren (PKN), Khristianovic-Geertsma-de Klerk (KGD), or Geertsma-de Klerk radial (RAD). Analysis of the net pressure versus time on a log-log scale (NolteSmith plot) determines the type of model (PKN, KGD, or RAD) to use for decline analysis. The injection test also serves as the pumping portion of the decline test. Pressure decline after shut-in is monitored and is analyzed using the Pressure Analysis, Decline Data and DataFRAC modules in the FracCADE software to determine the parameters listed above. The DataFRAC Service uses the G-plot for complete, consistent analysis. The G-plot (illustrated in Fig. 4) replaces the curve-matching method and can accentuate nonideal fracture behavior such as unrestrained height growth and extension after shut-in and closure. Analysis results from the DataFRAC module in the FracCADE software automatically update the fracture geometry simulator. The calculated net pressure is compared and recorded with the net pressure observed at shut-in. This dual analysis ensures a consistent set of parameters for the treatment design and indicates potential nonideal fracture behavior when a pressure match cannot be justified. DOWELL CONFIDENTIAL



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Fig. 4. The G-plot (idealized). (THIS FIGURE IS FOR ILLUSTRATIVE PURPOSES ONLY) 1.3 Applications The DataFRAC Service is an expense to the client that is not incurred if generally available design data that is not specific to a particular well is used. However, this service can increase the NPV when it results in optimization of a treatment design. The DataFRAC Service can be routinely performed before all fracture treatments when the objective is to optimize the treatment design and resulting production. It is also an invaluable aid to assure the best possible treatment is performed in cases where information is limited. Some opportunities where the DataFRAC Service offers particular benefits are • pilot projects or test wells that are critical to future development plans •

wells that are considered typical to a field where designs are being tested to settle on an optimum

•

exploration wells that have no history on which to design a treatment with a high level of confidence

•

areas where fracture response is not as anticipated and the cause requires identification.

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2 Design 2.1 Preparatory Engineering The DataFRAC Service is mainly analytical in nature. Other sources of data will enhance the DataFRAC analysis. 2.1.1 Breakdown/Diversion Treatment Perform a breakdown/diversion treatment (for example, acid ballout) prior to performing a closure or calibration test to ensure that all perforations are open and that the formation has been broken-down. The initial shut-in pressure recorded on a breakdown/diversion treatment will be a very rough estimate of the closure pressure. 2.1.2 Preliminary Fracture Design The parameters important to the DataFRAC Service are discussed below. Fracture treatment design is provided in Treatment Design. Before performing the DataFRAC Service, a fracturing treatment should be designed using the best data available. Use the FracCADE software for the treatment design. The fluid type, expected pad volume and efficiency, fracture geometry, and net pressure will provide a reference for the same parameters that will be determined from the DataFRAC analysis. A preliminary fracture design will also help to identify unexpected or nonideal behavior during the closure and calibration tests. If the preliminary fracture design indicates that the fracture capacity will be exceeded (undesired height growth or opening of fissures), the DataFRAC Service will confirm that and will quantify the fracture capacity based on actual, rather than assumed pumping conditions. The subsequent fracture design can then be prepared with either more confidence that the fracture capacity will not be exceeded or that special techniques can be used to alleviate the problem. 2.1.3 Fracture Height Fracture height affects fracture volume in two ways: directly, and through its effect on width (determined by the fracture compliance). Accurate values for gross fractureheight (formation gross height) and leakoff height (formation net thickness) are critical to the DataFRAC analysis and to the ultimate success of the fracture design and execution. If these values cannot be selected with a comfortable degree of certainty prior to the fracture treatment, the need for the DataFRAC Service and wireline surveys (logs) becomes even more critical for stimulation success. The following methodology may be used to determine fracture height. • Select “apparent” barriers from logs. •

Perform the DataFRAC Service to verify that height and Young's modulus match with log-derived values. DOWELL CONFIDENTIAL

Section 700.1 May 1998 Page 12 of 81 •


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Run pre- and post-job temperature logs or radioactive tracers and a gamma-ray log (or all) to identify the actual fracture height.

2.1.4 Wellbore Logging Pre- and postjob logs can give a starting point for height determination in the analysis. Prior to performing the DataFRAC Service, request that the appropriate wireline services be utilized to estimate fracture height (Gamma-Ray log, Sonic log), leakoff height (SP log, Porosity log), and Young's modulus (Sonic log). Request radioactive tracers for the calibration test. Request postfracture logs (Temperature log and Gamma-Ray log) for fracture height verification. 2.1.4.1 Temperature and Gamma-Ray Logs Temperature and gamma-ray logs are commonly used to determine fracture height. Gross fracture-height is commonly determined from lithology information. Leakoff height can be based on a porosity cut-off or gamma-ray/spontaneous potential (SP) deflection. Normally, the height of any zone with greater than 1/3 deflection from the shale base-line is considered leakoff height. Additional techniques to determine fracture height are provided in Reservoir Stimulation. During analysis, the following should be considered. 1.

Logs only detect radioactive material and temperature differences a few inches away from the wellbore.

2.

The fracture tends to be away from the wellbore outside the perforated interval.

3.

The formation must have both permeability and porosity to hold enough radioactive fluid for detection.

In the first consideration, wellbore fracture height may not be the same as the average height of the fracture because of deviated wellbore or zone, height growth into the barriers at the wellbore or horizontal fractures. The net pressure (during pumping) and a fracture simulator can give estimation of the average height. In the DataFRAC module, height and Young's modulus are altered to make the Fracture Geometry Sensitivity simulator (FGS) and the analysis (actual) net pressure match. When the net pressures are matched, the heights and modulus should match with those obtained from logs. If no match is obtained, then one of the sources may be incorrect. Shale barriers have very low permeability and porosity and will tend to “squeeze out” any fluid during fracture closure. A more permeable and porous zone above the shale will retain the fluid. A fracture may grow into this zone and the indication be discounted because the shale barrier doesn't show radioactivity or temperature change. This can also be missed if the wireline service company turns down the tool sensitivity when away from the zone of interest. Without an independent indication of fracture height, analysis is more difficult and may be less accurate. Analysis will be enhanced with the aid of logs. DOWELL CONFIDENTIAL


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2.1.4.2 Fracture-Height Logs If a fracture-height log is available, use stress information from the log to limit net pressure and, therefore, fracture height in the design. This can often demonstrate the sensitivity of vertical fracture growth to pump rate and fluid rheology. Once sensitivity is established, the need for the DataFRAC service is apparent to pinpoint the critical design parameters and to calibrate the FGS simulator. 2.1.5 Perforating Perforating technique can have a significant effect on the execution and evaluation of the DataFRAC Service by affecting the breakdown and treating pressure. 2.1.5.1 Wellbore Restrictions Wellbore restrictions will mask the formation pressure response while pumping. The value for net pressure will be inaccurate because of a shift upward. Fracture model selection may be affected. During the fracturing treatment the proppant will erode the restrictions resulting in lower perforation friction pressure. A drop in perforation friction pressure may be interpreted (falsely) as fracture height-growth. Wellbore restrictions caused by improper or ineffective perforating techniques can cause a screenout. Restrictions can cause the fracture to extend in an area apart from the perforation tunnel, resulting in a significant increase in apparent perforation friction pressure (Fig. 5).

Fig. 5. Channel restriction at the wellbore. (THIS FIGURE IS FOR ILLUSTRATIVE PURPOSES ONLY)

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2.1.5.2 Perforation Phasing Wells are commonly perforated with 0° phasing (perforations vertically aligned on one side of the casing). For these cases, the orientation of the perforation with the plane of the hydraulic fracture may be as large as 90°. With 0° phase perforations, near perfect alignment will cause preferential propagation of one wing of the fracture with very limited penetration of the companion wing. Channels are created and cause higher treating pressures because of width restriction (Fig. 5). Fig. 5 also shows a perforation that is approximately 30° out of phase to the fracture plane (minimum stress). The fracturing fluid must partially circumvent the wellbore to reach the fracture. Restrictions may develop, causing an increase in friction pressure and creating the potential for proppant bridging. Even when a perforation is directly in line with the fracture plane, the fracturing fluid must create a path around the wellbore. With 90 or 120° phasing, the fracture plane will generally be less than 30° from two perforations and will result in perforation access to both fracture wings. (Note from Fig. 5 that 180° phasing would not alleviate the misalignment). 2.1.5.3 Perforation Size Fig. 6 illustrates the relation of perforation diameter and proppant concentration. A perforation must be large enough to permit the proppant (at the maximum concentration) to pass through and not bridge in the perforation.

Fig. 6. The relation of perforation diameter and proppant concentration.

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2.2 Closure Test The general steps in a closure-test design are 1.

Determine the fluid type.

2.

Determine the injection rates and number of steps.

3.

Determine the duration of steps.

4.

Determine the flowback rate.

5.

Determine equipment requirements.

2.2.1 Fluid Selection In low-permeability formations, the closure test is usually performed with a Newtonian fluid such as diesel or water containing 2% (wt:wt) potassium chloride. In higher permeability formations (> 10 md) or in formations containing natural fissures, viscosified fracturing fluids may be required to reduce the rate of fluid loss and fracture closure during flowback. The same fluid as the pad fluid of the proposed fracturing treatment would be a good choice in the case of high leakoff. 2.2.2 Injection Rates and Number of Steps When injecting a Newtonian fluid, the range of rates is generally one to ten bbl/min for larger and moderately permeable zones and approximately one-half these values for smaller and very low permeability zones. After a breakdown/diversion treatment has been performed, most zones (k > 0.01 md or h > 30 ft) will require a pump rate greater than 3 bbl/min to exceed fracture extension pressure. The actual range for a particular zone may require trial and error methodology; two or more attempts. Ideally, three values of pressure (end of step) should fall below the extension pressure to define the initial portion for flow into the matrix or a pre-existing fracture, and a similar number of values above the extension pressure to define the portion for extending the fracture. This allows the pressure versus rate plot to be drawn on Cartesian coordinates using the last pressure before a rate change. The intersection of the two straight lines (fracture extension pressure) provides an upper boundary for closure pressure. An additional step-rate/flowback test can be performed to verify correct closure. If there were no pre-existing fracture, the plot of injection pressure versus bottomhole pressure may show an overshoot of the extension pressure for one or two steps because of the larger pressure required for breakdown and initiation of a fracture. 2.2.3 Step Duration For the purpose of defining closure pressure, the duration of the individual rate steps should be equal and can be relatively small. The time required for the pumping equipment to change and maintain a constant rate (one or two minutes) is sufficient. The last step is maintained for a longer time (five to ten minutes). DOWELL CONFIDENTIAL

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May 1998

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All steps, except the last step, should be the same duration. The last step should be long enough to establish some fracture volume, thus allowing the flowback, not leakoff, to bring about closure. Five to ten minutes should be sufficient for the last step. 2.2.4 Flow-Back Rate The step-rate phase is followed by an immediate flowback at a constant rate. Flowback should start immediately after shutdown. The rate must be held constant. Flowback rate is controlled by an adjustable choke or a gate valve and is monitored by a flowmeter. If the flowback rate is within the correct range, the resulting pressure decline will show a characteristic reversal of curvature at the closure pressure. The accelerated pressure decline at the curvature reversal is caused by the flow restriction introduced when the fracture effectively closes. The correct range of flowback rates must be determined by trial and error for any specific field; however, the range is on the order of one-sixth to one-quarter of the fracture extension rate. The effect of flow rates outside the correct range is shown in Fig. 7. A second test may be required if the flowback rate made closure selection impossible. The second test need not include a step-rate phase if clear fractureextension pressure was determined from the first test. Use a different rate the second time. Flowback until bottomhole pressure is within 200 psi of initial reservoir pressure. Do not flow reservoir fluids into the wellbore by flowing back more than was injected. At shut in, the pressure will rebound and stabilize.

Fig. 7. The effects of differing flowback rates. THIS FIGURE IS FOR ILLUSTRATIVE PURPOSES ONLY

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2.3 Calibration Test The general steps in a calibration test design are 1.

Determine the fluid type and injection rate.

2.

Determine the fluid volume.

3.

Determine the fluid break time.

4.

Determine if fluid-loss additives are required.

5.

Determine the pressure decline duration.

2.3.1 Fluid Selection The type of fluid and injection rate for the calibration test are the same as the type of fluid and injection rate of the proposed fracture treatment. 2.3.1.1 Foam A foamed fluid may be used for the calibration test. However, the well must be flushed with a linear fluid  a fluid containing no nitrogen, carbon dioxide or crosslinker/activator. Gas in the flush volume will expand due to pressure decline and temperature increase. This will cause fluid displacement into the fracture during closure and will invalidate the decline analysis. If bottomhole pressure is calculated from surface measurements, the hydrostatic pressure will change, adversely affecting the calculations. 2.3.2 Fluid Volume The fluid volume may be determined by using the FGS simulator in the FracCADE software. Use the following methodology.

*

1.

Determine the gross fracture-height and leakoff height.

2.

Using a leakoff coefficient twice the value provided in the Fracturing Materials Manual, calculate a minimum volume to ensure coverage of the zone if the KGD or RAD model is selected (indicated by a lack of barriers). If the PKN model is selected (indicated by significant barriers), calculate a volume sufficient to create a fracture length greater than 1.5 times the fracture height.

3.

If undesired height growth or fissure opening is suspected, treatment design should incorporate methods to avoid them (DIVERTAFRAC* Service, INVERTAFRAC* Service, or fluid-loss additives).


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2.3.3 Fluid Break-Time Fluid break-time is designed for bottomhole static temperature and a long time (compared with expected closure time). Five times the expected pumping time is a good starting place. 2.3.4 Fluid-Loss Additives FLA∗ 100 has particles large enough to be considered a proppant when used in a calibration test. Therefore, FLA100 can cause a screenout and will affect analysis. FLA100 is not recommended for use in a calibration test. However, in naturallyfractured or high-leakoff formations, FLA100 can be used with caution if a sufficient quantity of clean fluid is pumped ahead of it. Fluid-loss additive J84 or fluid-loss additive J418 is not a screenout hazard and may be used in the entire fluid volume for leakoff control. 2.3.5 Duration of Pressure Decline The minimum time that pressure decline should be monitored is 1.25 times the closure time or twice the injection time, whichever is longer. The closure time can be estimated by using the Placement module in the FracCADE software. Estimate the fluid and formation parameters and the volume of fluid to be pumped during the calibration test. A very small proppant stage may be necessary to force the Placement module simulator to run. 2.4 Special Considerations in the DataFRAC Design 2.4.1 The Influence of Wellbore Fluid A large quantity of wellbore fluid injected prior to fracturing fluid entry can result in substantial effects on analysis. If the static wellbore fluid volume is more than 10% of the calibration test fluid volume, one of the following actions should be performed. • Circulate the wellbore fluid out of the tubing with fracturing fluid. •

Bullhead the fracturing fluid to the top perforation at a low rate if circulation is not possible. Allow the pressure to fall below closure pressure before starting the calibration test.

2.4.2 Prepad A prepad is not necessary for the calibration test.

∗


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2.4.3 Closure Pressure less than Hydrostatic Pressure Fluid will flow from the wellbore into the fracture during closure if closure pressure is less than hydrostatic pressure. Calculate the quantity of fluid displaced when closure pressure occurs. If the displaced fluid is more than 10% of the fracture volume at shut-in (volume injected times efficiency), a special wellbore isolation tool should be used in conjunction with a wireline-conveyed bottomhole pressure gauge. Such tools have been used before but may have to be specially constructed. A bottomhole pressure gauge must always be used in these cases. 2.4.4 Post-Job Wireline Surveys Postjob logs should not be run until closure has occurred and pressure monitoring has ceased. Cable movement in the wellbore and fluid drag on the cable can affect the pressure decline data. If postjob logs are to be run, consider using a wireline conveyed bottomhole pressure gauge set below the perforations. 2.5 Terminology 2.5.1 Fracture Extension Pressure The fracture extension pressure is the pressure required to extend an existing fracture. Typically, the fracture extension pressure is 50 to 200 psi greater than the closure pressure because of fluid friction in the fracture and fracture toughness. 2.5.2 Initial Shut-in Pressure The initial shut-in pressure provides an upper bound for the determination of closure pressure. 2.5.3 Closure Pressure An accurate determination of the closure pressure is essential for an analysis of the fracturing pressure because it is the datum for determining the net pressure. The closure pressure is the fluid pressure at which the fracture closes (zero width). This pressure is equal to, and counteracts, the minimum principal stress in the rock that is perpendicular to the fracture plane. The closure pressure reflects a global average of the minimum stress, which is a local quantity and is not constant over the zone of interest. The closure pressure generally is less than the breakdown pressure required to initiate a fracture and always less than the fracture extension pressure. 2.5.4 Rebound Pressure The rebound pressure after shut-in is a lower bound of the closure pressure.

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2.6 Equipment Requirements 2.6.1 Monitoring Equipment An on-site MicroVAX1 computer is not absolutely necessary for performance of the pumping portion of the DataFRAC service. However, a MicroVAX will greatly enhance data manipulation and examination. A MicroVAX computer is necessary if onsite data analysis and treatment design using the FracCADE software is desired. There are two alternatives if a MicroVAX computer is not available. 1.

Perform a hand analysis.

2.

Perform the analysis in the office. This option may force a redesigned treatment to be pumped at some later date.

Two French curves are helpful for determining the reversal in curvature (closure pressure) from the flowback pressure plots. Always carry linear graph paper for any hand plotting needed as well as log-log paper for plotting a Nolte-Smith plot if necessary. 2.6.2 Pumping Equipment Diesel-powered pumpers are recommended for the closure test. Turbine powered pumpers are not recommended for the closure test because rate control is poor, especially at low pressures. Any type of pumpers may be used for the calibration test. 2.6.3 Pressure Measuring Equipment Accurate pressure measurement is critical to the success of the DataFRAC Service. 2.6.3.1 Surface Measurement Methods For the pressure-decline phase of the calibration test, the bottomhole pressure can be calculated from the surface pressure as long as the fluid density is constant and the bottomhole pressure is greater than the hydrostatic pressure. The main problem with using the treating pressure for analysis is that the friction pressure makes the Nolte-Smith plot less accurate and can indicate erroneous trends. In the overall analysis, the Nolte-Smith plot is very valuable if accurate bottomhole pressure and closure pressure are used. A good method for measuring bottomhole pressure is with a “live” annulus or a “dead-string tubing” and a homogeneous fluid. This eliminates friction pressure calculations. With a known hydrostatic pressure, bottomhole pressure can be accurately calculated. The density of the static column of fluid must be known (circulate the well and check the specific gravity of the fluid prior to injection). The fluid must not contain any trapped gas. This method is generally adequate for wells 1

Trademark of Digital Equipment Corporation

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with a bottomhole static temperature less than 250°F (121°C) and a depth less than 10,000 ft. Significant hydrostatic pressure changes may result from a change in fluid density during closure in deep, hot wells. This occurs when the wellbore fluid is warmed by the formation. After pumping, surface pressures can actually increase while the bottomhole pressure decreases (Fig. 8). In a 16,000 ft, 325°F (163°C) well, hydrostatic pressure change can be as much as 250 psi for water (Fig. 9). The effects on oil will be much greater because of the greater thermal expansion of oil. This compromises any results from surface readings because overly optimistic fluidloss and efficiency values will be implied. Therefore, the use of surface readings for deep, hot wells is not acceptable.

Fig. 8. The change in surface pressure during closure in deep, hot wells. THIS FIGURE IS FOR ILLUSTRATIVE PURPOSES ONLY

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Fig. 9. Hydrostatic head changes during closure. If closure pressure is less than the hydrostatic pressure of the injected fluid, then pressure analysis is not possible from surface measurement and a wirelineconveyed bottomhole pressure gauge must be used. 2.6.3.2 Bottomhole Pressure Gauge Measurement The best choice for measuring bottomhole pressure is with a bottomhole pressure gauge thereby eliminating friction calculations and hydrostatic considerations. For fluids without proppant, this can safely be done with a wireline-conveyed gauge, in the fluid stream if necessary. To ensure the wireline tension does not exceed a safe level, the increased tension due to fluid drag must be calculated using Eq. 1 before the job begins. T=

π × d ID × d w × Pf 4

(1)

Where: T = tension due to fluid drag (lbf) dID = inside diameter of pipe (in.) dw = diameter of wire (in.) pf = estimated total friction pressure in pipe (psi). Wireline tension must be calculated and confirmed to be safe with the wireline service company prior to rig-up to avoid parting the wire and subsequent job failure. DOWELL CONFIDENTIAL


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A wireline-conveyed bottomhole pressure gauge interfaces through a Remote Data Acquisition (RDA) box. Voltage and frequency inputs for the RDA box are: • 0-20 mA •

4-20 mA

•

0-4000 Hz (12 volts)

Additional information is provided in the PPR System Operator's Manual. Use of the PPR* pumping parameter recorder or other monitoring device is suggested. The wireline-conveyed pressure gauge should be tested prior to job execution. 2.6.4 Treating Equipment Wellhead rig-up requirements must be considered and communicated to the wireline service company. If the injection rate through two-inch treating equipment is greater than 8.5 bbl/min, a frac cross may be necessary. At rates less than 8.5 bbl/min, a lateral may be sufficient. The Dowell Location Safety Standards manual provides the maximum pumping rates through treating equipment. 2.6.5 Flowback Equipment Flowback rate must be monitored accurately for adequate control. Response time on the flowmeter should be 3 sec or less. 2.6.5.1 Magnetic Flowmeters Magnetic flowmeters are used in conjunction with water-base (conductive) fluids. The Dowell Flumag flowmeter is commonly used. Other magnetic flowmeters may be used. Magnetic flowmeter information is provided in the Sensors Verification Guide. 2.6.5.2 Turbine Flowmeters Turbine flowmeters are typically used with oil-base (nonconductive) fluids, but may be used with any fluid type. Turbine flowmeter information is provided in the Sensors Verification Guide. 2.6.5.3 Chokes and Gate Valves An adjustable choke or a gate valve is commonly used to regulate flowback rate.

*


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3 Execution Treatment design for the closure test and the calibration test is provided in Section 2. Location Safety Standard Number 5, 5A, and 5B provides procedures for approved on-location practices. 3.1 Pre-Performance Guidelines Certain guidelines are common for both the closure test and the calibration test. 1.

Equipment is rigged-up in accordance with Location Safety Standard Number 5, 5A, and 5B. Additional details for equipment rig-up and flowback are provided in Fig. 10 (conductive fluids) and Fig. 11 (nonconductive fluids). An adjustable choke or a gate valve is used in place of the choke nipple in the flowline (bleedline).

2.

If a static string is used, ensure the static fluid column is filled with a fluid of known specific gravity with no gas cap. The preferred method is to circulate from the tubing to the annulus at high velocity.

3.

Ensure that suction hoses, discharge hoses, manifolds, pumps, blenders, and discharge piping do not contain proppant.

4.

Backup pressure transducers must be rigged-up and calibrated. Do not provide any more than one display for the same pressure. The transducers are accurate to 1% of full scale. This means a 15,000 psi transducer is accurate to ±150 psi. If the maximum pressure will be low, suggest using a 0 to 5,000 or 0 to 10,000 psi transducer for better accuracy. Do not allow anybody to hammer on transducers during any phase of testing.

5.

The recording period for data acquisition should be 5 to 15 sec. High permeability formations and/or low-volume (short closure time) pump tests require a shorter time interval (5 sec or less). Do not set a PPR to record data from the POD* blender or the storage capacity of the tapes will be exceeded. During the pressure decline, do not allow pausing or constant changing of calculated data.

6.

Determine the expected closure pressure. approximated using Eq. 2.

The closure pressure may be

Approximate closure pressure = Overburden pressure + ( Reservoir Pr essure × 2 3

*


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7. If the wellbore is full of fluid, note the initial bottomhole pressure. Otherwise, note the quantity of fluid required to fill the wellbore (pressure rise). Once the wellbore is full, shut down and record the pisi. Calculate bottomhole pressure using the initial fluid level.

Fig. 10. The DataFRAC Service rig-up when pumping conductive fluids.

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Fig. 11. The DataFRAC Service rig-up when pumping nonconductive fluids.

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3.2 Closure Test The general steps in a closure test are 1.

Rig-up, mix fluid, and perform quality control activities.

2.

Perform the step-rate phase of the closure test.

3.

Perform the flowback phase of the closure test.

4.

Perform a modified step-rate phase if necessary.

5.

Perform a modified flowback phase if necessary.

3.2.1 Step-Rate Phase Step-rate phase guidelines are: 1.

The pump operator should know the pump gear and speed for each of the steps prior to pumping operations. This will facilitate rapid step-rate changes. Getting the injection rate (as well as flowback rate) established quickly must be stressed. Exact rates are not important  constant rates are. Fluid-end ratings and constants are provided in the Treating Equipment Manual. Pump performance curves are provided in the appropriate pumping equipment operators manuals.

2.

Take pressure readings after establishing a new pump rate (prior to increasing the rate again).

3.

Determine if fracture extension is occurring during the last injection stage by plotting rate versus pressure. This will indicate fluid loss to the matrix leakoff or fracture extension (Fig. 2). Fracture extension pressure will be 50 to 200 psi greater than the closure pressure. Remember to plot rate versus bottomhole pressure (not treating pressure). If treating pressure is plotted, the friction pressure will distort the values at higher rates and produce erroneous results.

4.

Increase the pump rate during the last stage if fracture extension is not occurring. If fracture extension is occurring, terminate the stage after the desired length of time. Water hammer effects can be minimized by reducing the pump rate to 10% of the final rate for 10 to 15 sec before shutdown.

5.

Determine the true perforation friction pressure using Eq. 3 and Fig. 12, Fig. 13, Fig. 14, Fig. 15, Fig. 16, or Fig. 17. Using Fig. 18, determine the estimated perforation friction pressure if all perforations were open. If the true perforation friction pressure is greater than twice the estimated perforation friction pressure, wellbore restriction is too great and should be reduced by pumping a diverting treatment or reperforating. Injecting small quantities of proppant near the end of the pad of the proposed fracturing treatment may erode the restriction.

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p pf = pw − ptf − pisi Where: ppf = perforation friction pressure (psi) pw = surface fracturing pressure (psi) ptf = tubular friction pressure (psi) pisi = initial shut-in pressure (psi).

Fig. 12. Friction pressure of water in the tubing and casing.

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Fig. 13. Friction pressure of water in the annulus.

Fig. 14. Friction pressure of brine in the tubing and casing.

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Fig. 15. Friction pressure of brine in the annulus.

Fig. 16. Friction pressure of diesel in the tubing and casing.

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Fig. 17. Friction pressure of diesel in the annulus.

Fig. 18. Flow rate versus differential pressure in perforations. DOWELL CONFIDENTIAL



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3.2.2 Flowback Phase Flowback must be initiated at a constant rate as soon as possible. Remember to isolate the pump(s) from the well. Do not allow bottomhole pressure to fall below 200 psi above the initial bottomhole pressure. Do not flow-back more fluid than was pumped. Note the indicated change in bottomhole pressure during shutdown and calculate the perforation friction pressure. If the perforation friction pressure is more than twice the expected amount, discuss the discrepancy with the client. 3.2.2.1 Flow Control Adjustment of the choke or valve may be accomplished using one of two methods. 1. Pump through the choke or valve prior to performing the step-rate/flowback test to preset the choke or valve. The choke or valve is adjusted to the desired rate when flowback is initiated. 2. Adjust the choke or valve during the last pumping stage of the step-rate test. The pump rate through the choke or valve will be in addition to the pump rate required for the last stage. Flowback rate accuracy is not critical; ± 20% is acceptable. However, a constant flowback rate is critical. Table 1 provides approximate choke settings (using a 15,000 lbf adjustable choke, part number 515077000) for flowback of oil-base fluids. Table 2 provides approximate choke settings for flowback of water-base fluids. Verify the setting by pumping through the choke at the anticipated flowback rate and pressure shut-in pressure. This is a good time to functionally check the flowmeter.

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Table 1. Approximate Choke Settings For Flowback Of Oil-Base Fluids (Sg = 0.7) Pressure (psi) 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000

Flow Rate (bbl/min) 1 14 12 10 10 9 9 8 8 8 8 8 7 7 7 7

3 24 20 18 17 16 15 15 14 14 13 13 13 13 12 12

15 31 26 23 22 21 20 19 18 18 17 17 17 16 16 16

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10 44 37 33 31 29 28 27 26 25 25 24 23 23 23 22

15 53 45 41 38 36 34 33 32 31 30 29 29 28 28 27

20 62 52 47 44 41 39 38 37 36 35 34 33 33 32 31

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Table 2. Approximate Choke Settings for Flowback of Water-Base Fluids (Sg = 1.0) Pressure (psi) 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000

Flow Rate (bbl/min) 1 15 13 11 11 10 10 9 9 9 8 8 8 8 8 8

3 26 22 20 18 17 17 16 16 15 15 14 14 14 14 13

15 34 28 26 24 23 22 21 20 19 19 19 18 18 17 17

10 48 40 36 34 32 31 29 28 28 27 26 26 25 25 24

15 58 49 44 41 39 37 36 35 34 33 32 31 31 30 30

20 68 57 51 48 45 43 42 40 39 38 37 36 36 35 34

The downstream 1 x 2 hamer valve (control valve) in the flowline (bleedline) may be used for flow control if the adjustable choke becomes plugged and can not be cleared. Use the hamer valve for flow control only as a last resort. The choke (or valve) operator must have a rate display for reference. Relaying rates via radio is not acceptable. 3.2.2.2 Flowmeters When using a turbine flowmeter, open the control valve slowly to avoid a fluid surge and subsequent flowmeter damage. Never allow a low-pressure magnetic flowmeter (for example, Fischer-Porter) to be placed upstream of the choke. Flowmeters must have a full pipe of flow to maintain accuracy. A backup flowmeter is recommended. 3.2.3 Closure Test Modifications Modifications to the closure test may be required for the following reasons. • Extension pressure was not attained. •

An overshoot of fracture extension pressure took place.

•

Flowback rate was inaccurate.

Section 2.2 provides design modifications for the closure test. DOWELL CONFIDENTIAL


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3.3 Calibration Test The general steps in a calibration test are 1.

Rig-up, mix fluid, and perform quality control activities.

2.

Perform the injection phase of the calibration test.

3.

Perform the pressure-decline phase of the calibration test.

3.3.1 Injection Phase The type of fluid and injection rate for the calibration test are the same as the type of fluid and injection rate of the proposed fracture treatment. Injection phase guidelines are 1.

If the flush fluid volume is more than 10% of the calibration fluid volume, the treatment fluid should be circulated to the top perforation. If circulation is not possible, pump the tubing volume (or annular volume, whichever is applicable) at low rate. Stop pumping and let the pressure fall below closure before resuming pumping. Fluid warming will change the fluid characteristics. Do not wait any longer than necessary if the well has a high bottomhole static temperature.

2.

When using crosslinked fluids, accurate crosslinker/activator additive rate is especially critical for correct DataFRAC analysis. A linear fluid, as opposed to a crosslinked fluid, will cause a different pressure response and have different fluid-loss characteristics. A back-up additive pump is recommended.

3.

Use the closure pressure determined from the closure test in calculation of net pressure for the Nolte-Smith plot. Reset pump time to zero when fluid enters the perforations and start the plot.

4.

Calculate fluid friction pressure using bottomhole pressure or obtain the shut-in pressure during the calibration test. Initial shut-in pressure obtained after pumping the flush fluid yields friction pressure for the flush fluid, not the calibration fluid.

5.

Stop pumping when flush is complete. Reduce water hammer effects by reducing the pump rate to 10% of the final rate for 10 to 15 sec before shutdown.

6.

Record the shut-in pressure when the pump rate falls to less than 2% of the treatment pump rate.

7.

Isolate the pumping equipment when all pumping has stopped.

8.

Calibration tests using foamed fluids must be flushed with a linear fluid not containing carbon dioxide, nitrogen, or crosslinker/activator.

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3.3.2 Pressure-Decline Phase Pressure-decline phase guidelines are 1.

Monitor pressure decline for 1.25 times the closure time or for twice the injection time, whichever is longer. Recording closure is very important.

2.

Do not allow anybody to hammer on the line or disturb the transducers during monitoring activities.

3.

Do not run postcalibration-test wireline surveys during monitoring activities.

4.

If the annulus is isolated, do not reduce or increase pressure during monitoring activities. Expansion or contraction will affect the tubing pressure and the final analysis if surface pressure is used.

3.3.3 Contingency Plans 1.

If an operational problem occurs with less than 30% of the fluid volume pumped, stop pumping and correct the problem. Resume pumping the remaining fluid at the design rate. Do not continue pumping at a reduced rate. Do not be concerned about a fluid leak unless the leak causes safety concerns or is tremendous, (gallons/minute). The volume loss compared to the leakoff in the fracture is small and will not affect the pressure decline.

2.

If an operational problem occurs with approximately 50% of the fluid volume pumped and the problem can be corrected quickly, stop pumping and note the loss of net pressure. If more than 20% of the net pressure is lost, consider a) starting over b) monitoring the pressure decline and pumping a second calibration test with the remaining fluid. If less than 20% of the net pressure is lost, resume pumping and analyze using the total volume pumped and the final injection rate. The pump time will be filled in on the DataFRAC form.

3. If an operational problem occurs with more than 70% of the fluid volume pumped, stop pumping and monitor the pressure decline. Be sure to use the actual volume of fluid injected into the formation in the analysis. At least 50% of the total volume should be pumped at the designed rate.

4 Evaluation The DataFRAC analysis consists of three essential parts. 1.

closure test for closure pressure

2.

calibration injection for fracture geometry

3.

calibration decline for fluid-loss behavior

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For correct analysis, the actual bottomhole pressure (BHP) must be used (See Ref. 2: Chapter 7.6.2). Combining the analysis of the closure test, pressure during pumping (as predicted by a fracture simulator) and pressure decline during closure provide a consistent interpretation and the enhancement of the three parts. Consistent values of the fracturing parameters for all the three analysis provide a sound basis for proper DataFRAC evaluation and subsequent treatment design. 4.1 Closure Test Analysis The closure pressure is the fluid pressure for which the fracture effectively closes without proppant. The closure pressure is distinguished from the minimum stress. The stress is a local parameter which can vary over the pay zone, whereas the closure pressure is a global parameter reflecting the gross behavior of the pay zone. The field procedures for the closure pressure test require the creation of a fracture in the complete zone as opposed to a “micro” fracture for the stress test. The methods used for determining the closure pressure include the step rate and flowback test. The step rate is analyzed using a BHP versus rate plot and the flowback is analyzed using a BHP versus time plot. 4.1.1 Step Rate  The BHP-Versus-Rate Plot The BHP-versus-rate plot (Fig. 2 and Fig. 3) should show two different slopes indicating matrix leakoff at low pressures/rates, and fracture response at higher pressures/rates. The extension pressure provides an upper bound for the closure pressure and defines the required range of pump rates for extending a fracture in the zone. 4.1.2 Flowback  The BHP-Versus-Time Plot The inflection point from concave up to concave down on the BHP-versus-time plot (Fig. 19) of the flowback response, is the point of increased pressure drop through the entrance of the fracture. The lowest point of the pressure derivative curve will be the inflection point. Several publications prior to 1993, indicated closure occurred at the inflection point. Subsequent analysis, with a comprehensive fracture simulator, indicated closure pressure occurs at a lower pressure and near the intersection of the tangents shown in Fig. 19.

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Fig. 19. Flowback test (after Nolte, 1982/1994). 4.1.3 Confirmation of Closure Pressure The confirmation of closure pressure can be done using the square-root of time plot or G-plot during the shut-in of the calibration treatment. The closure pressure is inferred as change of the slope on either of these plots (Fig. 20). This method normally does not provide a definitive indication of the closure pressure because of the existence of multiple slope changes. The fracture closure generally causes one of the slope changes in the BHP versus: t plot. A change in slope of the “G” plot also is a typical indication of closure pressure.

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Fig. 20. Effect of closure on BHP versus square root of t and G- plots.

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4.1.4 Rebound Pressure After the pressure drops below the estimated closure point during flowback, the well is shut-in and the rebound pressure is monitored. The rebound pressure provides a lower bound of the closure pressure and the inflection point provides an upper bound of the closure pressure (Fig. 21).

Fig. 21. Rebound pressure; lower bound of closure pressure. 4.2 Calibration Injection for Fracture Geometry The Nolte-Smith plot (log-log plot of the net pressure versus pumping time) provides an important diagnostic tool for determining how the fracture is propagating and the fracture geometry during pumping. The analysis enables the simulation and calibration of the pressure with a numerical fracture simulator and permits reconciliation of the ideal assumptions and actual field conditions. The magnitude of the net pressure from the fracture simulator permits a verification of fracture parameters such as modulus, height, toughness or barrier stress difference.

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4.2.1 Elastic Fracture Compliance For fracturing applications, the linear elastic assumption of Sneddon's classical solution is applied. From the solution, the average fracture width can be expressed in terms of the closure pressure (pc) fracture compliance (cf) and net wellbore pressure (∆pf) as: w = c f ∆p f = c f ( p f − pc ), Where: cf =

πβd 2 E'

Fig. 22 indicates that the behavior of a pressurized crack is analogous to a preloaded spring. pc 1 E' ∝ cf d

= “spring pre-loaded” = “spring constant” ___

E

∆p f Pw − Pc = rock modulus

d

= “characteristic” dimension of frac geometry

β

=

(see Section 4.3.8.4)

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Fig. 22. Analogy of a pressurized crack to a pre-loaded spring.

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The average crack width can be expressed by Sneddon's relationship in terms of “d”, πβd ( p f − pc ) 2 E' This relationship is used to model a fracture as follows: xf • PKN: → ∞ d = hf hf w=

•

KGD:

•

Radial:

hf → ∞ d = 2x f xf 2x f 32 →1 d= R ≈ R and x f = R. hf 3π 2

The KGD model is more appropriate when the fracture length is smaller than the height, while the PKN model is more appropriate when the fracture length is much larger than the height. The radial model is most appropriate when 2xf is about equal to the height. 4.2.2 Pressure During Pumping 4.2.2.1 Fluid Flow and Pressure in Fracture The pressure gradient in the fracture can be expressed as; n′

dp K'  q  ∝ 2n' +1  i  . dx w  hf  This expression relates the gradient down the fracture length to the fluid velocity or flow rate. Introducing the fracture compliance (w = cf∆ pf), integrating along the fracture length and assuming ∆pf = 0 at the tip, results in; 1

1.

 K '  q  n'  ( 2n' + 2) ∆p f ∝  2n' + 1  i  x f  c f   hf   

1 n'  2n

  qi  w = c f ∆p f ∝  c f K ' x f     hf    

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These proportionalities indicate the effect on pressure and width from variations of fluid rheology, injection rate, fracture geometry and models (in terms of fracture compliance). Substituting the appropriate compliance relationship for the three basic models gives; •

1

PKN:

 x f  ( 2n' + 2) ∆p f ∝ A 3n' +1  ,  h f  1

•

  ( 2n' + 2) 1 ∆p f ∝ A n 2n'  ,  h f x f 

KGD:

1

•

 1  ( 2n' +2) ∆p f ∝ A 3n'  . R 

Radial:

A = (E

Where:

2n' +1

1 n ′ ( 2n' + 2) K ' qi ) ,

which is the same for all the three models. The relationships also indicate that with increasing penetration, the net pressure increases for PKN model and decreases for the KGD and radial models. For constant injection rate, the fracture growth can be expressed in terms of time and bounded by two extreme cases for fracture efficiency, η: • Upper bound: No fluid loss (that is, Vf = Vi = qit). V f = w A f ∝ t ; η → 1 •

Lower bound: Almost total fluid loss (that is, VL → Vi = qit and Vf → 0). A f ∝ t 1/ 2 ;

η→0

A f = fracture face area. The fracture penetration increases with time and depends on the fluid loss during injection. By combining the bounds for time dependence of penetration, the relationship for net pressure and width, the net pressure yields; ∆p f ∝ t 1/ 4( n' +1) ( η → 0) • PKN: ∆p f ∝ t 1/( 2n+ 3) ( η → 1)

•

•

KGD:

Radial:

∆p f ∝ t − n'/2 ∆p f ∝ t − n'/(

( n' +1) n' +2)

∆p f ∝ t −3n'/8 ( n' +1)) ∆p f ∝ t − n'/( n' +2)

( η → 0) ( η → 1) ( η → 0) (η → 0)

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The previous expressions for pressure assume the fluid viscosity dominates the pressure distribution and ignores the fracture toughness of the formation. This assumption is generally valid for fractures with dimension in excess of 50 ft using high-viscosity fluids. For the case of small-scale fractures created with low viscosity fluids, fracture toughness can dominate and result in different exponents for time. The expressions for the net pressure are all exponential expressions. As a result, a log-log plot of net pressure versus time should yield a straight line with slope equals to the respective exponents: positive for PKN and negative for KGD and radial models. The log-log plot of net pressure versus time as introduced by Nolte and Smith, forms a basis for the interpretation of pressure data during fracturing. 4.2.2.2 Nolte-Smith Plot and Evolution of Pressure During Pumping Fig. 23 shows the evolution of the fracture geometry and the Nolte-Smith plot for an ideal case with bounding formations of higher stress. During the initial phase of propagation (stage 1), the fracture area increases in the radial mode (point source) or as expanding ellipses (line source). The line source can be approximated by KGD model. For this initial phase, the log-log slope is negative and between -1/8 and 1/4. This phase continues until the fracture is affected by barriers, which may occur after a very short time.

Fig. 23. Evolution of fracture geometry and pressure during pumping. The fracture will then propagate in PKN mode after the radial model encounters barriers above and below (stage 2) which results in increasing pressure and the loglog slope is between 1/4 and 1/8. Without proppant, the net pressure is limited to a DOWELL CONFIDENTIAL



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value slightly below the stress difference (∆σ) of the barrier being penetrated. At this time, the height begins to increase significantly and the pressure would be approximately constant (stage 3). Nearly constant pressure indicates the pressure capacity for the formation, which is determined by in-situ stress difference. When the net pressure reaches this capacity, fracture extension becomes relatively inefficient, as discussed in the following sections. 4.2.3 Deviations from Ideal Geometry 4.2.3.1 Height Growth Height growth into stress barriers is a common deviation from the ideal PKN model. Fig. 24 illustrates the pressure and vertical cross section of the width profile. Stage “a” is the PKN propagation stage. The positive log-log slope will continue until the net pressure approaches the stress difference of the barrier. At this stage (stage “b”), the height will increase and the pressure would be approximately constant. During stage “c”, the barrier is crossed and the fracture enters a lower stress zone resulting in an accelerated rate of growth at decreasing pressure and width in the primary zone. The width profile indicates that a “pinch point” occurs in the barrier after stage “b”. The pinch point has essentially no width during the transition from stage “b” to stage “c”. The pinch point can cause proppant to bridge as fluid is permitted to pass through. The resulting excessive dehydration of the slurry coupled with the decreasing width can result in a rapid screenout even at low proppant concentration.

Fig. 24. Pressure and width for height growth through barriers (after Nolte, 1989).

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The slurry dehydration, decreasing width, and height growth can be reduced by the following methods: 1.

Place an impermeable mixture of proppant between the pad and the proppant stages to form an impermeable bridge at the pinch point.

2.

Pumping a pre-treatment DIVERTAFRAC).

with

a

diverting

agent

(INVERTAFRAC

or

4.2.3.2 Fissures Another possible cause for a period of constant pressure is the opening and inflating of natural fissures. Pressure-dependent leakoff due to fluid loss into fissures is thought to contribute to screenouts in low permeability formations where limited fluid loss would otherwise be anticipated. Two fissure models have been reported.

1.

Slight permeability enhancement The permeability enhancement is not significant until the effective stress becomes negative and the fissure aperture opens. At this time, fluid loss becomes significant and regulates the pressure to a constant value.

2.

Highly stress-sensitive permeability and fluid loss The permeability and fluid-loss enhancement are significant throughout the treatment, with the effect accelerating as the pressure increases. If the treatment continues, the negative effective stress condition can occur with constant pressure.

Fig. 25. Pressure and width for opening natural fissures (after Nolte, 1989).

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Fig. 25 illustrates the pressure response and the horizontal cross section of the width profile. The secondary fracturing occurs in natural fissures or cracks which are crossed by the primary fracture. These feature normally have relatively higher permeability than the matrix and the fluid leakoff is high. The fissures will open when the fluid pressure exceeds the formation stress acting across them. σ − σ1 ∆p f > 2 ≈ 1.5 ∆σ H 1 − 2ν ∆σH = σ2 - σ1 = horizontal stress difference. This implies that effective fracturing will require a significant stress difference between the principal horizontal stress to avoid opening of natural fissures. When this magnitude of pressure is reached, the fissures open and act to regulate the constant pressure at this critical magnitude. A significant portion of the injected fluid can be lost because of a large number of fissures that can open at this critical pressure. The accelerated fluid loss can lead to excessive slurry dehydration and a screenout (stage “c” of Fig. 25). The accelerated fluid loss can be reduced using the following methods. 1.

Before the fissure aperture opens, use very fine particles (for example, 300-mesh particles) in the pad.

2.

After the fissures open, and maintain constant pressure, use 100-mesh particles between the pad and proppant stages (Note: 100-mesh particles can screenout the treatment when they reach the tip).

4.2.3.3 T-Shape Fracture

Fig. 26. Pressure and width for T-shape fracture (after Nolte, 1989). DOWELL CONFIDENTIAL


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When the fracturing pressure is greater than overburden stress, a fracture can propagate in both the horizontal and vertical planes. This geometry is called a T-shape fracture and the pressure response and a vertical cross section of the width profile are illustrated in Fig. 26. The figure indicates stage “c” has a near constant pressure response. The horizontal component growth requires pressures greater than the overburden pressure and occurs at; ∆p f ≥ OB − pc Where: OB = vertical overburden stress pc = closure pressure. The width of the horizontal fracture component will be narrow and have twin pinch points at the juncture with the vertical component. The limited width of the horizontal component can restrict proppant entry, excessively dehydrate the slurry in the vertical component, and lead to premature screenout. The T-shape fracture is the easiest to diagnose: Bottomhole injection pressure approximately constant at a value slightly above the overburden pressure (that is, about one psi/ft of true vertical depth). 4.2.4 Pressure Capacity Summarizing the prior sections (using Fig. 27) a period of constant pressure for a vertical fracture can occur because  • The pressure approaches the stress of a barrier and causes significant height growth; ∆p f ≤ ∆σ ν •

•

∆σv = barrier stress difference. The pressure exceeds the stress acting on natural fissures and the fissures open; ∆σ H ∆p f ≈ . 1 − 2ν The pressure exceeds the overburden pressure, and the initiation of T-shape fracture begins;

∆p f ≥ OB − pc

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Fig. 27. Definition of pressure capacity from in-situ stresses. For these cases, the limiting pressure is called the formation pressure capacity. The formation acts as a pressure vessel with a pressure capacity defined by stress differences. Exceeding the pressure capacity leads to inefficient extension due to height growth, the formation of T-shape fracture or fissures opening. 4.2.5 Near-Wellbore Restriction High near-wellbore pressure losses sometimes experienced during the hydraulic fracturing treatment should be considered in fracturing pressure analysis, that is, subtracted for determining net pressure. In addition to inadequate perforating, a potential cause of high near-wellbore pressure losses is that the well and the fracture plane are not aligned, that is, on deviated wells or wells close to faults (deviated principal stress). For these cases, the fracture initially aligns with the wellbore, and then turns to align normal to the far-field minimum stress. The fracture entrance experiences a normal stress greater than the minimum stress, leading to a fracture width restriction and increased pressure losses within the entrance. The stress state within the entrance is illustrated by Fig. 28 and the Mohr circle in Fig. 29. AB = fracture plane σ1 = minimum principal stress σy = stress parallel to the wellbore σx = stress normal to the wellbore. DOWELL CONFIDENTIAL


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Fig. 28. Stress state within the entrance of deviated well or stress. For the deviated stress case, σy and σx are equal to overburden and horizontal stress, respectively. The principal (that is, minimum and maximum) stresses are not horizontal or vertical and the fracture is inclined. For the deviated well case, the principal stresses are assumed horizontal and vertical, σy and σx are parallel and normal to the inclined wellbore. σx can be estimated as the sum of the minimum stress (that is, closure pressure) and the apparent near-wellbore friction, pwf; that is, DOWELL CONFIDENTIAL

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σx = σ1 + pwf with σ1 estimated from a closure pressure test and pwf from the BHP change during a shut-in.

Fig. 29. Mohr circle of deviated well or stress. Using the Mohr's circle in Fig. 29, information about the state of stress and relative fracture orientation can be obtained from known information (for example, θ for deviated well, or σy = OB for vertical well). Radius of Mohr circle,

R=

σx + σy − σ1 2

Therefore; cos 2θ =

R − pwf , R

Where: θ = angle between wellbore axis and fracture plane pwf = near-wellbore friction pressure. Significant entrance friction can be diagnosed by a large difference in the bottomhole injection pressure during fracturing and the initial shut-in pressure (ISIP). The entrance friction responds the same as perforation friction and tends to decrease when proppant is added. For pre-fracture tests, a significant entrance restriction can be indicated by a large difference (for example, greater than 200 psi) between the extension pressure (Fig. 2 and Fig. 3) and closure pressure (Fig. 20 and Fig. 21).

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4.2.6 Fracturing Pressure Interpretation Summary

Fig. 30. Nolte-Smith plot of fracturing pressure. Small Positive Slope The fracture is propagating under contained height and free lateral extension in a manner similar to PKN model. The approximate log-log slope is 1/8 to 1/4.

Zero Slope Reduced penetration rate potentially caused by: height growth, fissures opening or the formation of T- shape fracture. The constant pressure during this period is called formation pressure capacity which is determined by the in-situ stresses; and hence likely to be the same for offset wells.

Positive Slope Flow restriction causing fracture width to be increased with limited extension, potential proppant bridging and screenout. 1− η ∆t D • Tip screenout condition, the log-log slope ≈ 1 + 0.64 η where η is the efficiency at screenout and ∆tD is the time after screenout divided by the screenout time. •

Log-log slope > 1 indicates restriction in the fracture.

•

Log-log slope >>1 (very high slope) indicates restriction near or at the wellbore resulting from a near-wellbore restriction (Section 4.2.5) or exceeding the pressure capacity (Section 4.2.4). DOWELL CONFIDENTIAL



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Negative Slope Unrestricted height growth through a lower stress formation. It also indicates growth of a radial fracture with the fracture propagating in a manner similar to the KGD or radial model. 4.2.6.1 Example of Radial Fracture Fig. 31 shows the interpretive log-log plot of a radially propagating fracture from a calibration treatment of a massive chalk section in the North Sea. The plot shows the expected behavior of a radial fracture with a log-log slope equal to about – 1/8. The period of lower pressure at about 10 min resulted from a shut-in. The small pressure change of about 50 psi indicates there was no significant entrance restrictions.

Fig. 31. Net pressure with radial fracture (after Smith et al. 1987). 4.2.6.2 Simulation of Pressure During Pumping and Decline The numerical simulation of the pressure response is an important tool in the calibration injection for fracture geometry and calibration decline, for cases in which the idealized 2D geometry models are inadequate. These nonideal cases may include height growth, stress sensitive fissures, and fracture penetration and recession during the decline. The log-log plot of the fracturing pressure is generally a qualitative and diagnostic tool. Quantitative interpretation can be obtained by comparing the predictions from a DOWELL CONFIDENTIAL


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numerical fracture simulator and the actual treatment. The net pressure is primarily governed by the rock mechanical properties and is relatively insensitive to rate and viscosity. Numerical simulation is used to calibrate or confirm values for the parameters that govern the pressure response, that is, fracture compliance, rock stress difference and fluid-loss coefficient. The calibrated parameters can then be used to make design changes in subsequent treatments. Even though there is not a unique set of fracturing parameters that match a pressure response, a calibrated set provides a rational basis for more effective treatment design.

Fig. 32. Measured and simulated net pressure: opening natural fissures (after Nolte, 1982). Fig. 32 shows an example of the reported application of fracturing pressure simulation during injection and decline. The pressure plot shows a near-constant pressure period indicating that the formation capacity has been reached. The pressure capacity value of 1700 psi, because of the opening of natural fissures, lasted for about 100 minutes prior to shut-in. The pressure capacity is governed by the rock stress and should be expected to be similar throughout the field, provided there are no significant lithological or tectonic changes. Consequently, once the pressure capacity is determined and the pressure calibrated by the simulator, rational design changes can be made for more effective treatment for the remainder of the wells in the field, that is, design using a pressure calibrated simulator to stay below the pressure capacity for more efficient penetration. In addition, the pressure simulation during decline may provide consistent interpretation and result in enhancement of both injection and closure analysis; however, an appropriate numerical fracture simulator is required to correctly apply these concepts. Ideally the simulator should include the effects of spurt loss, pressure-dependent fluid loss (with and without sensitive fissures), fluid temperature and compressibility, poroelastic stress changes, height growth, and fracture penetration and recession during closure. The Placement II fracture simulator in the FracCADE software addresses most of these effects.

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4.3 Calibration Decline for Fluid-Loss Behavior An analysis and use of a specialized plot for the pressure decline during shut-in, pioneered by Nolte, provides relationships for width, penetration, fluid efficiency and fluid-loss coefficient in terms of rate of pressure decline and closure time after injection. The leakoff coefficient can be quantified from the rate of pressure decline, an important parameter in fracture treatment design. Fig. 33 shows the pressure decline period between the end of pumping and closure.

Fig. 33. Example of fracturing-related pressures (after Nolte, 1982). 4.3.1 Review of Decline Analysis The bases for the information within the following sections comes from SPE 25845, “A Systematic Method for Applying Fracturing Pressure Decline” by Nolte et al and should be consulted if required for more detail. The assumptions of the basic decline analysis are • constant fluid density •

constant fracture area

•

constant β (dimensionless fluid pressure distribution)

•

constant cf (fracture compliance)

•

constant closure pressure

•

constant fluid-loss area and coefficient

•

Spurt loss is negligible after shut-in

•

The fluid loss follows the Carter assumptions of:

•

Fracture area during injection evolves with the relation A ∝ t α ( 0. 5 < α < 1).

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The last condition is met if injection conditions are approximately constant and excessive height growth does not occur. The fracture area evolves in time as (see Fig. 34) The area exponent (α) can be found using two bounding cases: a

A t =  . Af  ti  •

Lower bound η → 0, α0 = 0.5

•

Upper bound η → 1, α1 = (2n + 2)/(2n + 3) PKN α1 = (n + 1)/(n + 2) KGD α1 = (4n + 4)/(3n + 6) Radial

with n = the power-law fluid exponent.

Fig. 34. Schematic for fracture area and time. The appropriate value of α for use in an application can be found by interpolating using the actual value of efficiency; α = 0.5 + η (α1 - 0.5). The interpolated values of α over the full range of n are provided in Table 3, from which a typical value is α ≈ 0.6 for 0.4 < n < 0.6 and 0.2 < η < 0.6.

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Table 3. Interpolated Values of α Over the Full Range of n n′

0.4

0.6

0.8

Efficiency PKN KGN Radial PKN KGD Radial PKN

1.0

KGD Radial PKN

KGD

Radial

0

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.2

0.55

0.52

0.55

0.55

0.52

0.56

0.56

0.53

0.57

0.56

0.53

0.58

0.4

0.60

0.53

0.61

0.61

0.55

0.63

0.61

0.56

0.64

0.62

0.57

0.66

0.6

0.64

0.55

0.67

0.66

0.57

0.69

0.67

0.59

0.71

0.68

0.60

0.73

0.8

0.69

0.57

0.72

0.71

0.59

0.76

0.73

0.61

0.79

0.74

0.63

0.81

1.0

0.74

0.58

0.78

0.76

0.62

0.82

0.78

0.64

0.86

0.80

0.67

0.89

4.3.2 Volume Function g For the decline assumptions, the volume lost during pumping and shut-in can be derived analytically and expressed in terms of volume function g(∆tD). The volume lost during pumping; VLP = 2κgo C L rp A f t p . The volume lost during shut-in;

[

]

VLS = 2C L rp A f t p g( ∆t D ) − go , Where: g( ∆t D ) = 4 / 3[(1 + ∆t D ) 3 / 2 − ∆t D3 / 2 ] with go = g(o ) =

4 3

for α = 1,

1/ 2 g( ∆t D ) = (1 + ∆t D )sin − 1 (1 + ∆t D ) − 1/ 2 + ∆t D π 1 with go = for α = , 2 2 Sp κ = spurt correction = 1 + . go C L t p

g(∆tD) as function of ∆tD is shown in Fig. 35. It is important to note that the difference between the upper and the lower bound decreases significantly during the shut-in period (that is, the precise value of α is not critical).

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Fig. 35. Dimensionless volume function for fracture closure (after Nolte, 1986). 4.3.3 Fluid Efficiency The fluid efficiency is the ratio of fracture volume to the total volume injected. For ideal conditions and no proppant, the efficiency can be expressed in terms of the dimensionless closure time (refer to Section 4.3.4 for efficiency in terms of G function); V f ( ∆t = 0) VLS ( ∆t = tc ) = Vi VLP + VLS g( ∆tcD ) − go η= . g( ∆tcD ) + (κ − 1)go η=

For the case of no spurt, κ = 1 and the efficiency; η=

g( ∆tcD) − go g( ∆tcD)

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Fig. 36. Efficiency from closure time for no proppant, no spurt loss during pumping and other ideal assumptions given in Section 4.3.1 (after Nolte, 1986). Fig. 36 shows the relationship of η and the dimensionless closure time for the nonpropped case. The relationship is constructed in terms of upper and lower bound (α = 1 and α = 0.5). For determining the effect of proppant on efficiency, the proppant volume will be expressed as the bulk proppant volume fraction; v prop =

v prop Vi

Where: Vprop = proppant bulk volume Vi = total slurry volume injected. The expression for efficiency can be shown as follows (See Ref. 2); η=

(V f − Vprop )(1 − v prop ) (1 − v prop ) Vf = = η' Vi v prop  v prop    (Vi − Vprop ) 1 −  1 −  η  η   

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Vf is the fracture volume at the end of pumping. Denoting the apparent efficiency η’ based on closure time assuming no proppant (that is, Fig. 36) and rearrange the previous equation, the efficiency of a propped fracture can be determined from η’; η = v prop (1 − η' ) + η' 4.3.4 Decline Function G The pressure decline analysis utilizes a plot of net pressure versus the dimensionless decline function G; G ( ∆t D ) =

4 [ g( ∆t D ) − go ]. π

A combination of fracture compliance, material balance and the relationship between the generated fracture area and time permit the development of the pressure decline analysis. If the ideal assumptions of the basic decline analysis hold, the basic pressure decline relation gives; cf

π dpw dG( ∆t D ) =− t p C L rp . dt dt 2

At shut-in, the pressure is pws with ∆tD = 0 giving a relationship between pw versus G(∆tD); πC L rp t p Pw = pws − G( ∆t D ) . 2c f This provides a straight-line interpretation with negative slope, mG = p*, of the plot of pw versus G(∆tD) as shown in Fig. 37. Where p* is defined as; p* = =

πC L rp t p

2c f This relationship is used to infer a leakoff coefficient (CL). It should be noted that if the ideal assumptions are not valid, the straight line can not be identified and mG ≠p*. Fig. 37 shows the conceptual response of the ideal pressure decline.

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Fig. 37. Conceptual response of pressure decline versus Nolte time-function (after Castillo, 1987). The G-plot is analogous to the use of a Horner plot for pressure buildup or falloff to characterize reservoir flow parameters. In addition to the leakoff parameters, it provides the diagnostic for the deviations from ideal behavior, as discussed in Section 4.3.5. From the efficiency expression in Section 4.3.3, definition of G and go ≈π;/2, the fluid efficiency for ideal behavior can be expressed in terms of “G” function; η' =

Gc 2κ + Gc

where Gc = G(∆tcD) = G at closure and κ = 1 for no spurt. The values of decline function “G” are provided in Table 4 in terms of α and ∆tD. This table is used to calculate G(∆tD) if the DataFRAC software is not available. α is typically between 0.5 and 0.7. For most applications, α ≈ 0.6 can be assumed with sufficient accuracy for fracture closure analysis.

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Table 4. Values of Decline Function "G" α

0.5

0.6

0.7

1.0

∆tp

g

η

G

g

η

G

g

η

G

g

η

G

0.00 0.02 0.04 0.06 0.08 0.10 0.12

1.57 1.60 1.63 1.66 1.68 1.71 1.73

.000 .018 .035 .051 .066 .080 .093

0.000 0.038 0.073 0.108 0.141 0.174 0.206

.000 .020 .038 .055 .070 .085 .099

0.000 0.039 0.076 0.112 0.147 0.180 0.213

1.48 1.51 1.54 1.57 1.60 1.62 1.65

.000 .021 .041 .058 .075 .091 .105

0.000 0.041 0.080 0.117 0.152 0.187 0.221

1.33 1.37 1.40 1.44 1.47 1.50 1.52

.000 .027 .050 .071 .091 .109 .126

0.000 0.046 0.089 0.130 0.169 0.207 0.244

0.14 0.16 0.18 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50

1.76 1.78 1.80 1.83 1.88 1.94 1.99 2.04 2.09 2.14 2.19 2.23 2.32 2.41 2.49 2.57 2.65 2.72 2.80 2.87 2.94 3.00 3.14 3.26 3.38 3.50 3.61 3.72 3.83 4.08 4.32 4.54 4.76 4.97 5.16 5.35 5.54 5.71

.106 .118 .129 .140 .166 .190 .211 .231 .249 .266 .282 .297 .324 .348 .369 .389 .407 .423 .438 .452 .465 .477 .499 .518 .535 .551 .565 .578 .589 .615 .636 .654 .670 .684 .696 .707 .716 .725

0.237 0.267 0.297 0.327 0.399 0.468 0.535 0.600 0.663 0.725 0.785 0.844 0.957 1.066 1.172 1.273 1.372 1.467 1.560 1.651 1.739 1.825 1.992 2.152 2.305 2.454 2.598 2.737 2.872 3.195 3.498 3.786 4.060 4.322 4.573 4.816 5.050 5.276

1.52 1.55 1.58 1.61 1.64 1.66 14.6 9 1.72 1.74 1.76 1.79 1.85 1.90 1.96 2.01 2.06 2.11 2.16 2.20 2.29 2.38 2.46 2.54 2.62 2.70 2.77 2.84 2.91 2.98 3.11 3.24 3.36 3.48 3.59 3.70 3.81 4.06 4.30 4.53 4.75 4.95 5.15 5.34 5.52 5.70

.112 .125 .137 .148 .175 .199 .221 .241 .260 .277 .293 .308 .336 .360 .382 .401 .419 .435 .450 .464 .477 .489 .511 .530 .547 .562 .576 .589 .600 .625 .646 .664 .679 .692 .704 .715 .724 .733

0.245 0.277 0.308 0.338 0.411 0.482 0.551 0.617 0.681 0.744 0.805 0.865 0.980 1.091 1.197 1.300 1.399 1.496 1.590 1.681 1.770 1.857 2.025 2.186 2.340 2.490 2.634 2.774 2.910 3.234 3.539 3.827 4.102 4.635 4.617 4.860 5.095 5.322

1.68 1.70 1.73 1.75 1.81 1.87 1.92 1.97 2.03 2.08 2.12 2.17 2.26 2.35 2.44 2.52 2.60 2.67 2.75 2.82 2.89 2.96 3.09 3.22 3.34 3.46 3.57 3.68 3.79 4.05 4.29 4.51 4.73 4.94 5.14 5.33 5.51 5.69

.119 .132 .145 .157 .184 .209 .232 .252 .271 .289 .305 .320 .348 .372 .394 .414 .432 .448 .463 .477 .489 .501 .523 .542 .558 .573 .587 .599 .611 .635 .656 .673 .688 .701 .713 .723 .732 .741

0.254 0.286 0.318 0.349 0.424 0.497 0.566 0.634 0.700 0.763 0.825 0.886 1.003 1.115 1.223 1.326 1.427 1.525 1.619 1.711 1.801 1.889 2.058 2.220 2.376 2.526 2.671 2.812 2.948 3.274 3.579 5.869 4.145 4.408 4.661 4.905 5.140 5.367

1.55 1.58 1.61 1.63 1.70 1.76 1.82 1.87 1.93 1.98 2.03 2.08 2.17 2.27 2.35 2.44 2.52 2.60 2.67 2.75 2.82 2.89 3.03 3.16 3.28 3.40 3.52 3.63 3.74 4.00 4.24 4.47 4.69 4.90 5.10 5.29 5.48 5.66

.141 .156 .170 .184 .214 .241 .266 .288 .308 .326 .343 .359 .387 .412 .433 .453 .471 .487 .501 .515 .527 .539 .560 .578 .594 .608 .621 .633 .643 .666 .686 .702 .716 .728 .738 .748 .757 .764

0.280 0.315 0.349 0.382 0.463 0.540 0.614 0.685 0.754 0.821 0.886 0.949 1.071 1.187 1.299 1.406 1.510 1.610 1.708 1.802 1.894 1.984 2.157 2.322 2.481 2.633 2.781 2.924 3.062 3.392 3.701 3.994 4.272 4.538 4.793 5.038 5.275 5.504

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4.3.5 Non-Ideal Behavior The assumptions of the basic decline analysis are seldom met in practice. Several deviations from these ideal assumptions that have to be considered are • change in fracture penetration after shut-in •

height growth

•

pressure-dependent fluid loss

•

spurt

•

closure pressure change

•

compressible fluids.

4.3.5.1 Change in Fracture Penetration After Shut-in A varying fracture length after shut-in will affect the basic pressure decline analysis. The effect of length change is illustrated in Fig. 38, which shows an initial slope greater than the slope at closure. The early rapid decline results from fluid flow past the fracture tip at shut-in, that is, fracture extension after shut-in. The fracture length will then recede toward the wellbore during closing. The slope will decrease as high leakoff area is lost. Fig. 38 shows the G-plot for this case, which clearly indicates a significant reduction in slope with time. The correct value of leakoff can be obtained by applying a correction to the standard “G” plot. Corrected slope m′G = fcmG, Where: fc = correction factor mG = slope of the G-plot near closure. fc =

β' βs

1 + ∆t D f ( ∆t D )

1/ 2 f ( ∆t D ) = 2[(1 + ∆t D )1/ 2 − ∆t D ] for α = 1

f ( ∆t D ) = sin − 1 (1 + ∆t D ) − 1/ 2

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Values of fc are provided in Table 5. The features of the G-plot also indicates that the correct value of p* can be obtained dA f at the transition between extension and recession, that is, when: = 0 at the end dt ∆pw ≈ 3 / 4 (with of extension. The transition from extension to recession occurs at ∆ps ∆ps = net pressure immediately after shut-in) and resulted in suggestion of a “3/4 rule” to eliminate the effect of penetration changes during shut-in; that is, select p* as the value of mG at ∆pw = 3/4 ∆ps as shown in Fig. 38.

Fig. 38. Penetration change during shut-in (after Nolte, 1990). 4.3.5.2 Height Growth Height growth will reduce the rate of pressure decline during initial shut-in. During this period, the decreasing height dispels fluid into the primary fracture and creates an equivalent flow rate source. This flow rate source delays the closure time. This period will last until the net pressure decreases to about 0.4∆σ for the barrier and provides a height growth diagnostic (Fig. 39). The transition to a greater decline after the height growth closes provides the period of the decline analysis similar to the case of no growth. Applying the correction to the slope near closure provides correct estimate of p* (the similar correction for the case of length recession). Fig. 39 also suggests the governing stress barrier difference can be defined from the Gplot;

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∆pknee with ∆pknee the net pressure at the “knee” of the dog-leg. 0.4

Fig. 39. Diagnostic for height growth from decline data (after Nolte, 1990). 4.3.5.3 Pressure-Dependent Leakoff There are two mechanism for the pressure-dependent fluid loss. 1.

stress-sensitive fissure

2.

filtrate - and reservoir-control mechanism

Stress-Sensitive Fissures For the stress-sensitive fissures, the governing pressure is the difference between principal horizontal stresses (∆σH, see Section 4.2.2.2). During a fracture treatment, the pressure within the fissure increases as fluid leaks off into it. The effective normal stress on the fissure decreases and its permeability increases. The permeability and fluid loss are enhanced throughout the treatment, with the effect accelerating as the pressure increases. If the pressure continues to increase, the pressure in the fissure can become greater than the normal stress, the fissure will open and the leakoff is further accelerated. At this time, the pressure capacity is reached and regulates the pressure at a constant value. The diagnostic for the stress-sensitive fissure as shown in Fig. 40 is a progressively decreasing log-log slope on the Nolte-Smith plot during pumping until the pressure capacity is reached (that is, showing constant pressure condition) and a progressively decreasing slope on the G-plot (positive curvature) during decline DOWELL CONFIDENTIAL


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period. Height growth can also produce a constant pressure condition similar to fissures; however, height growth (Fig. 39) provides negative curvature (increasing slope) on the G-plot; the distinguishing diagnostic for fissures relative to height growth.

Fig. 40. Diagnostic for stress sensitive fissures from injection and decline (after Nolte, 1990).

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The pressure behavior of stress-sensitive fissures is more complex than filtrate- or reservoir-controlled fluid loss. Numerical simulations are required to properly asses this effect. The value of the leakoff coefficient is best determined by pumping pressure history match, using an appropriate fracture simulator. To approximate CL ∆pw ≈ 3 / 4 that is, when the from the G-plot, the slope of the G-plot is selected at ∆ps area is constant and with a high value of net pressure so the effect of fissures dominates the fluid loss.

Filtrate- and Reservoir-Controlled Mechanism If leakoff is controlled by the filtrate viscosity (Cv) or by reservoir permeability and compressibility (Cc), the leakoff is pressure dependent. No significant pressure dependence is expected for a wall-building fluid. For the filtrate- and reservoircontrol fluid loss, the governing pressure is the difference between fracturing pressure (pf) and reservoir pressure (pr). This mechanism is significantly affected by pressure change during decline as shown in Fig. 41. The figure shows the G-plot found by numerical simulation and indicates a significant reduction in slope with time, that is, mG < p* at later stage of closure. Using the fracture simulator, the leakoff coefficient was found to be approximated by the slope of the net pressure at ∆pw ≈ 3 / 4 as shown in Fig. 41. ∆ps

Fig. 41. Decline analysis for filtrate and reservoir control leakoff (after Nolte, 1993).

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4.3.5.4 Spurt Spurt (Sp) is the fluid volume lost during the formation of a filter cake. It is negligible for low-permeability formations (less than one md). The rate of spurt is controlled by the filtrate (Cv) and reservoir fluid (Cc) during the spurt period (tsp). Generally, spurt is negligible after shut-in since the new area exposed is small; therefore, spurt loss has a negligible effect on the pressure decline and cannot be defined from the pressuredecline analysis. For large values of spurt (which can occur at high ∆p or in high-permeability formations without using effective fluid-loss control additives), the large spurt time and volume can affect the decline analysis. Spurt will affect the pressure-decline analysis based on the “3/4” rule if the spurt time is greater than the time at ∆pw ≈ 3 / 4 . It can be shown from the volume balance relation at shut-in that the ∆ps spurt will not affect the decline analysis if; tsp κη < . ti 4(1 − η) Although the spurt generally does not influence the decline analysis using the “3/4” rule, the magnitude of spurt during injection may be important and must be characterized. The effect of spurt can be eliminated for the treatment by performing a calibration treatment of a size comparable to the treatment and using effective fluid-loss control additives. The spurt can be estimated from the laboratorySp determined ratio of for representative formation and fluid samples. Assuming CL the ratio is the same in the laboratory and field, Sp can be defined by using CL from Sp calibration treatment and keeping the ratio of constant; CL Spurt correction κ = 1 +

Sp go C L ti

The spurt correction κ is used to account for additional fluid loss due to spurt. The effective fluid-loss coefficient during pumping = κCL. 4.3.5.5 Closure Pressure Change The closure pressure is assumed constant in the basic pressure-decline analysis. Leakoff of the fracturing fluid under high pressure will cause an increase of the closure pressure because of poroelastic effect. Although not common, evidence of increased closure pressure with injection time has been reported in the field. The poroelastic stress changes have little effect on fracture geometry, but the pressure is increased by an amount approximately equal to the stress change during injection or decline.

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The most significant stress changes occurs for the PKN model. The upper bound of the stress change for this case; ∆σ ≈

2.64 MC L t φct h

    kt   M ≈ 1 − 0.6 2   φµct  h    2   

1/ 4

The equation indicates that the stress change is proportional to the fluid-loss coefficient, and hence depends on the controlling fluid-loss mechanism, that is, wall cake (Cw), filtrate viscosity (Cv) or reservoir control (Cc). The analysis by Nolte has shown that this closure stress change is bounded by a maximum for constant CL (Cw controlled or small ∆pf) and a minimum for Cc. Fig. 42 shows the wellbore stress change for Cc = 0.001 ft / min and 0.002 ft / min.

Fig. 42. Stress change during injection/shut-in for Cc (after Nolte et. al., 1993).

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The rate of change of ∆σ; d∆σ 1.32 M 2C L ≈ . dt φct h t The rate of stress change decreases with time. When stress changes are significant, the closure pressure test should be conducted immediately after the decline of the calibration treatment instead of before the treatment. Fig. 42 indicates that the stress change is generally positive; the stress continues to increase during pumping and after shut-in. This would result in an underestimate of CL. A conservative estimate of CL can be obtained from the inferred CL as follows; 0.43   C' L = C L 1 + φ ct E'   4.3.5.6 Compressible Fluids Most fracturing fluids can be assumed to have constant density since they are relatively incompressible compared to the elastic response of the fracture. The basic pressure-decline analysis assumes that the fluid density is constant (incompressible). Foams, however, are much more compressible than liquids. The foam density change can have an effect on the pressure-decline analysis and must therefore be considered. When the fracturing fluid is compressible and significant warming of the fracturing fluid occurs after shut-in, the thermal expansion of a compressible fracturing fluid will affect the pressure behavior during decline. The analysis indicates that the pressure of a compressible fluid will decline at a slower rate compared with an incompressible fluid (decrease the slope of the G-plot). The fluid-loss coefficient will therefore be underestimated. The effect of foam fluids on the decline analysis is expressed in terms of the ratio of ∆Vg ∆Vg the change in gas volume to fracture volume, denoted as . The value of ∆V f ∆V f is governed by the effect of temperature and pressure of the compressible fluid. Fig. 43 shows a simulation for an extreme case (foam fracturing of hot, shallow formations) using a fracture simulator; a case of high temperature, high efficiency and low closure pressure to illustrate the large effect on the gas volume increase. For this case the error is about 13% for the fluid-loss coefficient obtained by the “3/4” rule.

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Although the effect for the increase in gas volume of the compressible fluid during shut-in is small, a correction factor can be applied to the inferred CL. The correction term is provided in SPE 25845 (Nolte et al, 1993) and is a relatively complex relation.

Fig. 43. Relative volume change of gas (after Nolte et. al., 1993). 4.3.6 Fluid Efficiency Based on Pressure Analysis The expressions for fluid efficiency in Section 4.3.3 and Section 4.3.4 define this parameter in terms of dimensionless closure time for ideal behavior with or without spurt. These expressions can be generalized for non-ideal behavior by defining the efficiency in terms of shut-in net pressure (∆ps) and match pressure (p*). The fluid efficiency can be expressed as follows; Vf Vf Af w η= = = . Vi VLP + V f 2κgo C L rp A f t p + A f w From the relationship of width and pressure directly after shut-in (w = cf ∆ps), and 2c f p * CL = , πrp t p

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η=

with go ≈

A f c f ∆ps 4 κA c p * go + A f c f ∆ps π f f


,

π , 2 η≈

∆ ps , 2κp * + ∆ps

η≈

G* , 2κ + G *

∆ps . For ideal conditions, G* = Gc and the expression for efficiency p* becomes as in Section 4.3.4. For non-ideal behavior, p* ≠ mGC and G* ≠ Gc. Because the ideal assumptions are not generally valid, the closure point is not a reliable predictor for efficiency. where G* =

4.3.7 Decline-Analysis Procedure As discussed in the previous section, the corrections can be provided for violating the basic assumptions. The non-ideal behavior is related to penetration changes, height growth, pressure-dependent fluid loss, spurt, closure pressure change, and density effects. The decline-analysis procedure is (see Fig.44): 1.

Find the slope of the “G” plot (mG) at

∆pw ≈ 3 / 4 (that is, m3/4, referred to as the ∆ps

“3/4 rule”). 2.

For the KGD and radial models, p* = m3/4

3.

For the PKN model, p* = max of { m3/4 , m′G } m’G = fc mGc where fc is the correction factor (see Table 5) and mGc is the slope near closure.

4.

Calculate CL. CL =

5.

Calculate η. η=

2c f p * πrp t p

∆p G* where G* = s 2κ + G * p*

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The correction factor (fc) is the product of

Dowell

β′ 1 + ∆t D f ( ∆t D ) and is provided in βs

Table 5. From numerical simulations, β′≈1. The decline-analysis procedure provides the following results. • For height growth without pressure-dependent fluid loss, p* ≈ m′G, In this case, m′G > m3/4. •

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For no significant height growth but pressure-dependent loss, p* ≈ m′3/4, In this case, m′G > m3/4.

Fig. 44. Decline analysis using “¾” rule (after Nolte, 1990).

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Table 5. Correction Factors fc As Function Of ∆tD ∆ tD

fc

G(∆ ∆tD)

∆ tD

fc

G(∆ ∆tD)

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

2.09 1.77 1.68 1.63 1.59 1.56 1.54 1.52 1.50 1.49 1.48 1.47 1.46 1.46 1.45 1.44 1.44 1.43 1.43 1.43 1.42

0.00 0.17 0.33 0.47 0.60 0.72 0.84 0.96 1.07 1.17 1.27 1.37 1.47 1.56 1.65 1.74 1.83 1.91 1.99 2.07 2.15

2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00

1.42 1.41 1.41 1.41 1.41 1.40 1.40 1.40 1.40 1.40 1.39 1.39 1.39 1.39 1.39 1.39 1.39 1.38 1.38 1.38

2.23 2.31 2.38 2.45 2.53 2.60 2.67 2.74 2.80 2.87 2.94 3.00 3.07 3.13 3.19 3.26 3.32 3.38 3.44 3.50

4.3.8 Steps to Correct Decline Analysis Using the FracCADE Software The following steps are required to correctly analyze the pressure decline from a calibration test: 1.

Ensure the decline data is good. After the data has been imported into the DataFRAC software, examine the G-plot using 'Graphics' mode to see if the data are smooth and continuous. Remove any bad initial data which included the pressures when the pumps were still rolling over. This initial data gives high net pressure and steep initial decline. Another type of bad data is not enough data points (resembling a dot-to-dot puzzle).

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Determine the analysis type to be performed on the “G” plot. For the basic decline analysis portion of the “G” plot can be condition of non-ideal behavior, the previous section can be DataFRAC software.

3.

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when the ideal assumptions hold, the linear determined using 'Manual' analysis. For the the procedure of the “3/4” rule as discussed in performed using “recession” analysis in the

Match net pressures. The last step is to match the net pressure at shut-in with the predicted net pressure from the fracture simulator using the parameters derived from the analysis of the “G” plot. The match is performed by adjusting Young's modulus (E) or gross fracture height (H) for the PKN model and adjusting E or rock toughness (K) for the KGD or radial model. This pressure match assumes ideal behavior and application of the ideal models. For non-ideal behavior, the net pressure match should be done using the Placement module in the DataFRAC software.

4.3.8.1 The DataFRAC Software The well, reservoir, rock mechanics, and fluids screens should be completed before performing the DataFRAC analysis. The Job Record Data Entry form is used to read the pressure datafile into the FracCADE software (refer to the FracCADE User's Manual for complete information). The fluid Sp and Cw values can be obtained from laboratory data or the Fracturing Materials Manual  Fluids. The ratio of Sp and Cw will be used and kept constant in calculating the new spurt based on the leakoff coefficient (CL) obtained from the analysis. The new values of Sp and Cw are used to determine efficiency. The DataFRAC analysis information should be completed to define how the analysis of the G-plot is controlled and performed. The types of analysis available in the DataFRAC program are 1.

Graphic Analysis The 'Graphic' option allows the user to look at the G-plot. It is normally used first to determine if the data set is good. This option does not perform any calculation.

2.

Automatic Analysis The 'Automatic' option requires the least amount of interaction from the user. It is used for the ideal conditions of the basic pressure decline by automatically selecting the best straight line of the G-plot. The program uses the derivative of the G-plot to look for the minimum curvature within the analysis range. The straight line selected likely will not correspond to p* and may or may not correspond to the fracture closure period.

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3.


Manual Analysis The 'Manual' option is also used for the ideal conditions. The user supplies the maximum and minimum pressure constraints to be used for determining the straight line of the G-plot.

4.

Recession Analysis The recession analysis with “closure pressure” as the closure variable is the preferred option and uses the “¾” rule or correction to slope on the G-plot as outlined in the previous sections to account for the non-ideal behavior.

Closure Variable Closure input variables control the determination of the closure point, which indicates if closure pressure or closure time is to be specified. Using “closure pressure”, the corresponding “closure time” will be extrapolated and vice versa. The closure pressure should be determined from an independent closure test analysis (see Section 4.1). If the closure variable is not specified, the program will automatically take the last point on the straight line of the G-plot as the closure point. 4.3.8.2 G-plot Interpretation by the DataFRAC Software ∆pw ≈ 3 / 4 or at ∆ps closure) compared to the actual Initial shut-in pressure (ISIP) gives some indications of the fracture evolution. The difference should generally not be greater than 200 psi.

The value of Yint (Y intercept from the tangent line to the G-plot at

A condition in which Yint is less than the ISIP is equivalent to a positive curvature of the G-plot due to the non-ideal behavior described in the previous sections, that is, penetration change and pressure-dependent fluid loss. When Yint is greater than the ISIP, it indicates a negative curvature of the G-plot because of height growth into stress barriers. It can also be concluded that the equivalent 2D model is PKN since height growth into stress barriers is inconsistent with the basic requirements of the radial or KGD model. The inequality of Yint and the ISIP is corrected by shifting the tangent line upward or downward to intercept the ISIP. This will also allow the user to use a proper value of net pressure based on the ISIP instead of Yint for determining the efficiency and making a net pressure match with the fracture simulator. Answer “Yes” to the “Adjustment for Initial Deviation” field to perform this function. 4.3.8.3 Modulus, Height, or Fracture Toughness Calibrations The most important and uncertain parameters for a proper evaluation of the leakoff coefficient are Young's modulus, total fracture height, and fracture toughness. The values of Young's modulus obtained from the log can be crossed-checked and

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calibrated using the DataFRAC software. The fracture height for the PKN model and the fracture toughness for the KGD or radial model can also be calibrated. The procedure is to make the simulator net pressure match up with the analysis by adjusting the Young's modulus and holding other parameters constant. The gross fracture height for the PKN model and the fracture toughness for the KGD or radial model can also be adjusted until the net pressure from the fracture simulator matches that from the analysis. For the case with barriers, the preferred method is to select the height as the gross pay (or sand) section and calibrate the modulus from the DataFRAC analysis. The calibrated modulus can be much greater (that is, twice) than actual modulus to account for interbedded shales (that is, high stress zone). Compliance for each model gives an understanding as to which parameter is controlling the pressure response. The compliance for each model is cf ∝

•

PKN:

•

KGD:

cf ∝

2βx f E'

•

Radial:

cf ∝

βR E'

βh f E′

E′ = plain strain modulus

E′ = E/1 - v2

The average width is expressed in terms of fracture compliance (cf) and net wellbore pressure (∆pf), that is, w = cf ∆pf. This indicates that both total fracture height and Young's Modulus have a large impact on net pressure for the PKN model. For the KGD and radial models, Young's Modulus has an impact on pressure. The fracture width and length (xf or R) are also affected by fracture toughness for the KGD and radial model. The fracture toughness will therefore have an important effect on net pressure for these models. In a 1991 publication, Nolte incorporated toughness in the PKN model. The β factor, and therefore, the pressure is affected by the toughness. The pressure matching using toughness for the PKN model has not been implemented in the DataFRAC software because the PKN pressure is not very dependent on the tip behavior. 4.3.8.4 The β Ratio The β ratio is the ratio of the average net pressure in the fracture and the wellbore net pressure; ∆p f p f − pc β= = ∆p f pw − pc

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This parameter is necessary for volumetric calculations of the fracture in terms of the pressure value at the wellbore. The analysis of fluid flow in the fracture indicates there is a gradient of pressure from the maximum value at the well, pw, to the minimum value at the fracture tip, approximately pc. Fig.45 shows an example of the pressure and flow profiles during pumping and after shut-in using the PKN model.

Fig. 45. Pressure and flow rate in fracture before and after shut-in (after Nolte, 1986). The value of β during pumping (βp) differs from the value of β after shut-in (βs). During pumping,

βp ≈

n' +2 n' +3

β p ≈ 0.9

PKN KGD and Radial

During shut-in, βs ≈

2n' +2 2n' +3

β s ≈ 0.95

PKN KGD and Radial

βs and βp are used to convert the net pressure at shut-in (∆ps) to the net pressure at the end of pumping (∆pp); β ∆p p = s ∆ps . βp

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The net pressure at the end of pumping is used by the DataFRAC program in the net pressure matching to calibrate Young's modulus, total fracture height, or fracture toughness. 4.3.9 Post Proppant Fracture Analysis The “G” plot analysis after the propped fracture treatment can provide information on the effectiveness of the fracture treatment. The effectiveness is indicated by the ratio of net pressure at closure on proppant to net pressure at shut-in; w prop ∆p prop = ∆ps whyd If fracture closure did not occur until most of the net pressure was lost (that is, ∆pf = 0), very little of the fracture width was propped and hence, the job was not effective.

Fig. 46. Diagnostic for closing on proppant from decline data (after Nolte, 1990). The closure on proppant will change the rate of pressure decline, that is, with significant slope change. Fig.46 illustrates the effect of fracture closing on proppant. Two cases affect the pressure decline behavior after closure. 1.

Decrease in rate of pressure decline. A decrease in the rate of pressure decline is indicative of a relatively impermeable proppant-pack caused by unbroken fluid and the filter cake impairing communication between the fracture and the wellbore. DOWELL CONFIDENTIAL


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2.


Increase in rate of pressure decline. An increase in the rate of pressure decline indicates the fracture system stiffening during closure on a permeable pack communicating freely with the well after closure.

Although the initial closure period may be relatively free of the effects of proppant, the G-plot may be different from the representative condition and any analysis could be subject to a high degree of uncertainty. Therefore, an unpropped calibration treatment is always preferred over a propped fracture pressure decline; but for obtaining some insight into a failed treatment, the decline from the treatment can be used to infer the fluid-loss coefficient. The effect of proppant or the inference of efficiency is discussed in Section 4.3.3. 4.3.10 References Comprehensive discussion of fracturing pressure analysis are provided in the following publications: 1.

Nolte, K.G.: Fracturing Pressure Analysis, Recent Advances in Hydraulic Fracturing, J. Gidley et al. (eds.), Monograph Series, SPE, Richardson, TX (1989) 12, Chap. 14.

2.

Nolte, K.G. and Economides, M.J.: Fracturing Diagnosis Using Pressure Analysis, Reservoir Stimulation, second edition, Prentice Hall, Englewood Cliffs, NJ (1989) Chap. 7.

3.

Nolte, K.G.: “Fracturing Pressure Analysis for Nonideal Behavior,” JPT (Feb., 1991) 210-18.

4.

Nolte, K.G.: “A General Analysis of Fracturing Pressure Decline With Application To Three Models,” SPEFE (Dec. 1986) 571-83.

5.

Nolte, K.G., Mack, M.G. and Lie, W.L.: “A Systematic Method For Applying Fracturing Pressure Decline, Part 1,” SPE 25845, Denver (April 1993).

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