fracturing engineering manual-data frac service

SchlumbergerDowell

FRACTURING ENGINEERING MANUALDataFRAC Service

Section 700.1May 1998

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DataFRAC SERVICE

1 Introductory Summary............................................................................................................. 61.1 Closure Test......................................................................................................................... 7

1.1.1 Closure Test in a Permeable Zone............................................................................. 71.1.2 Closure Test in a Nonpermeable Zone....................................................................... 9

1.2 Calibration Test.................................................................................................................... 91.3 Applications........................................................................................................................ 10

2 Design..................................................................................................................................... 112.1 Preparatory Engineering .................................................................................................... 11

2.1.1 Breakdown/Diversion Treatment .............................................................................. 112.1.2 Preliminary Fracture Design ..................................................................................... 112.1.3 Fracture Height......................................................................................................... 112.1.4 Wellbore Logging...................................................................................................... 12

2.1.4.1 Temperature and Gamma-Ray Logs ............................................................. 122.1.4.2 Fracture-Height Logs ..................................................................................... 13

2.1.5 Perforating ................................................................................................................ 132.1.5.1 Wellbore Restrictions ..................................................................................... 132.1.5.2 Perforation Phasing ....................................................................................... 142.1.5.3 Perforation Size ............................................................................................. 14

2.2 Closure Test....................................................................................................................... 152.2.1 Fluid Selection .......................................................................................................... 152.2.2 Injection Rates and Number of Steps ....................................................................... 152.2.3 Step Duration............................................................................................................ 152.2.4 Flow-Back Rate ........................................................................................................ 16

2.3 Calibration Test.................................................................................................................. 172.3.1 Fluid Selection .......................................................................................................... 17

2.3.1.1 Foam.............................................................................................................. 172.3.2 Fluid Volume............................................................................................................. 172.3.3 Fluid Break-Time ...................................................................................................... 18


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2.3.4 Fluid-Loss Additives ..................................................................................................182.3.5 Duration of Pressure Decline ....................................................................................18

2.4 Special Considerations in the DataFRAC Design...............................................................182.4.1 The Influence of Wellbore Fluid ................................................................................182.4.2 Prepad.......................................................................................................................182.4.3 Closure Pressure less than Hydrostatic Pressure.....................................................192.4.4 Post-Job Wireline Surveys ........................................................................................19

2.5 Terminology........................................................................................................................192.5.1 Fracture Extension Pressure.....................................................................................192.5.2 Initial Shut-in Pressure ..............................................................................................192.5.3 Closure Pressure ......................................................................................................192.5.4 Rebound Pressure ....................................................................................................19

2.6 Equipment Requirements ...................................................................................................202.6.1 Monitoring Equipment ...............................................................................................202.6.2 Pumping Equipment..................................................................................................202.6.3 Pressure Measuring Equipment................................................................................20

2.6.3.1 Surface Measurement Methods .....................................................................202.6.3.2 Bottomhole Pressure Gauge Measurement ...................................................22

2.6.4 Treating Equipment...................................................................................................232.6.5 Flowback Equipment.................................................................................................23

2.6.5.1 Magnetic Flowmeters .....................................................................................232.6.5.2 Turbine Flowmeters........................................................................................232.6.5.3 Chokes and Gate Valves................................................................................23

3 Execution ................................................................................................................................243.1 Pre-Performance Guidelines ..............................................................................................243.2 Closure Test .......................................................................................................................27

3.2.1 Step-Rate Phase.......................................................................................................273.2.2 Flowback Phase........................................................................................................32

3.2.2.1 Flow Control ...................................................................................................323.2.2.2 Flowmeters.....................................................................................................34

3.2.3 Closure Test Modifications........................................................................................34

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3.3 Calibration Test.................................................................................................................. 353.3.1 Injection Phase ......................................................................................................... 353.3.2 Pressure-Decline Phase........................................................................................... 363.3.3 Contingency Plans.................................................................................................... 36

4 Evaluation............................................................................................................................... 364.1 Closure Test Analysis ........................................................................................................ 37

4.1.1 Step Rate The BHP-Versus-Rate Plot ................................................................. 374.1.2 Flowback The BHP-Versus-Time Plot.................................................................. 374.1.3 Confirmation of Closure Pressure............................................................................. 384.1.4 Rebound Pressure.................................................................................................... 40

4.2 Calibration Injection for Fracture Geometry ....................................................................... 404.2.1 Elastic Fracture Compliance..................................................................................... 414.2.2 Pressure During Pumping......................................................................................... 43

4.2.2.1 Fluid Flow and Pressure in Fracture.............................................................. 434.2.2.2 Nolte-Smith Plot and Evolution of Pressure During Pumping ........................ 45

4.2.3 Deviations from Ideal Geometry ............................................................................... 464.2.3.1 Height Growth................................................................................................ 464.2.3.2 Fissures ......................................................................................................... 474.2.3.3 T-Shape Fracture........................................................................................... 48

4.2.4 Pressure Capacity .................................................................................................... 494.2.5 Near-Wellbore Restriction......................................................................................... 504.2.6 Fracturing Pressure Interpretation Summary ........................................................... 53

4.2.6.1 Example of Radial Fracture ........................................................................... 544.2.6.2 Simulation of Pressure During Pumping and Decline .................................... 54

4.3 Calibration Decline for Fluid-Loss Behavior ....................................................................... 564.3.1 Review of Decline Analysis....................................................................................... 564.3.2 Volume Function g.................................................................................................... 584.3.3 Fluid Efficiency.......................................................................................................... 594.3.4 Decline Function G ................................................................................................... 614.3.5 Non-Ideal Behavior ................................................................................................... 64

4.3.5.1 Change in Fracture Penetration After Shut-in................................................ 64


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4.3.5.2 Height Growth ................................................................................................654.3.5.3 Pressure-Dependent Leakoff .........................................................................664.3.5.4 Spurt...............................................................................................................694.3.5.5 Closure Pressure Change ..............................................................................694.3.5.6 Compressible Fluids.......................................................................................71

4.3.6 Fluid Efficiency Based on Pressure Analysis ............................................................724.3.7 Decline-Analysis Procedure ......................................................................................734.3.8 Steps to Correct Decline Analysis Using the FracCADE Software............................75

4.3.8.1 The DataFRAC Software................................................................................764.3.8.2 G-plot Interpretation by the DataFRAC Software ...........................................774.3.8.3 Modulus, Height or Fracture Toughness Calibrations ....................................774.3.8.4 The Ratio.....................................................................................................78

4.3.9 Post Proppant Fracture Analysis...............................................................................804.3.10 References..............................................................................................................81

FIGURESFig. 1. The effect of proppant-pack damage and fracture length on fracture NPV. ......................6Fig. 2. Fracture extension pressure (unequal time steps). ...........................................................7Fig. 3. The typical closure test......................................................................................................8Fig. 4. The G-plot (idealized). .....................................................................................................10Fig. 5. Channel restriction at the wellbore. .................................................................................13Fig. 6. The relation of perforation diameter and proppant concentration. ..................................14Fig. 7. The effects of differing flowback rates. ............................................................................16Fig. 8. The change in surface pressure during closure in deep, hot wells..................................21Fig. 9. Hydrostatic head changes during closure. ......................................................................22Fig. 10. The DataFRAC Service rig-up when pumping conductive fluids. ..................................25Fig. 11. The DataFRAC Service rig-up when pumping nonconductive fluids. ............................26Fig. 12. Friction pressure of water in the tubing and casing. ......................................................28Fig. 13. Friction pressure of water in the annulus.......................................................................29Fig. 14. Friction pressure of brine in the tubing and casing........................................................29Fig. 15. Friction pressure of brine in the annulus. ......................................................................30Fig. 16. Friction pressure of diesel in the tubing and casing. .....................................................30Fig. 17. Friction pressure of diesel in the annulus. .....................................................................31Fig. 18. Flow rate versus differential pressure in perforations....................................................31Fig. 19. Flowback test (after Nolte, 1982/1994)..........................................................................38Fig. 20. Effect of closure on BHP versus square root of t and G- plots. .....................................39Fig. 21. Rebound pressure; lower bound of closure pressure....................................................40Fig. 22. Analogy of a pressurized crack to a pre-loaded spring. ................................................42Fig. 23. Evolution of fracture geometry and pressure during pumping.......................................45Fig. 24. Pressure and width for height growth through barriers (after Nolte, 1989)...................46

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Fig. 25. Pressure and width for opening natural fissures (after Nolte, 1989). ........................... 47Fig. 26. Pressure and width for T-shape fracture (after Nolte, 1989)........................................ 48Fig. 27. Definition of pressure capacity from in-situ stresses..................................................... 50Fig. 28. Stress state within the entrance of deviated well or stress. .......................................... 51Fig. 29. Mohr circle of deviated well or stress. ........................................................................... 52Fig. 30. Nolte-Smith plot of fracturing pressure. ........................................................................ 53Fig. 31. Net pressure with radial fracture (after Smith et al. 1987). .......................................... 54Fig. 32. Measured and simulated net pressure: opening natural fissures (after Nolte, 1982). . 55Fig. 33. Example of fracturing-related pressures (after Nolte, 1982). ........................................ 56Fig. 34. Schematic for fracture area and time............................................................................ 57Fig. 35. Dimensionless volume function for fracture closure (after Nolte, 1986)....................... 59Fig. 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). ............................. 60Fig. 37. Conceptual response of pressure decline versus Nolte time-function

(after Castillo, 1987). .................................................................................................... 62Fig. 38. Penetration change during shut-in (after Nolte, 1990). ................................................. 65Fig. 39. Diagnostic for height growth from decline data (after Nolte, 1990). .............................. 66Fig. 40. Diagnostic for stress sensitive fissures from injection and decline (after Nolte, 1990). 67Fig. 41. Decline analysis for filtrate and reservoir control leakoff (after Nolte, 1993)................ 68Fig. 42. Stress change during injection/shut-in for Cc (after Nolte et. al., 1993)......................... 70Fig. 43. Relative volume change of gas (after Nolte et. al., 1993). ........................................... 72Fig. 44. Decline analysis using rule (after Nolte, 1990). ...................................................... 74Fig. 45. Pressure and flow rate in fracture before and after shut-in (after Nolte, 1986)............ 79Fig. 46. Diagnostic for closing on proppant from decline data (after Nolte, 1990). ................... 80

TABLESTable 1. Approximate Choke Settings For Flowback Of Oil-Base Fluids (Sg = 0.7) .................. 33Table 2. Approximate Choke Settings for Flowback of Water-Base Fluids (Sg = 1.0)............... 34Table 3. Interpolated Values of Over the Full Range of n....................................................... 58Table 4. Values of Decline Function "G" .................................................................................... 63Table 5. Correction Factors fc As Function Of tD ...................................................................... 75


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1 Introductory SummaryThe DataFRAC* Service determines the in-situ parameters critical to optimumfracture treatment design. These parameters are specific to each formation andoften to each well. Assumed or inaccurate parameter values can result in thefollowing. 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 acalibration 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 analysisis referenced from it. Closure pressure is also used for proppant selection.The closure test is recommended as one of the initial procedures of any fieldstimulation 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. ANewtonian fluid is injected at an increasing rate until fracture extension occurs. Apressure versus rate plot will show two distinct slopes, the intersection of whichindicates fracture extension pressure (Fig. 2). The change in slope in is a result ofthe different pressure responses for matrix leakoff and fracture extension at thehigher rate. This pressure is normally 50 to 200 psi greater than closure pressurebecause of fluid friction in the fracture and fracture toughness.

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


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Another indication of fracture extension pressure comes from a bottomhole pressureversus time plot and is illustrated in Fig. 3. The pressure steps above fractureextension pressure have squared shoulders compared to the rounded shoulderscharacteristic 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 thenflowed-back at a constant rate. Flowback is started immediately after the final stepand is held constant until pressure has fallen to about 200 psi above the initialwellbore pressure. The pressure response will show a distinct reversal in curvatureonce closure has occurred (Fig. 3), indicating a change of fluid withdrawal from theopen fracture to withdrawal through the matrix. The rebound pressure after shut inserves as a lower bound to closure pressure.Perforation friction pressure is another important parameter that is determined fromthe step-rate/flowback test. At shut-in, the immediate bottomhole pressure drop isthe pressure loss in the perforations during the last stage of the step-rate test. Thepressure loss will give an indication of potential wellbore problems, usually unopenedperforations. Reperforating should be considered if the pressure loss isunacceptable.The closure pressure is determined by quantitative analysis of bottomhole pressureversus 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 analysisof a square-root plot. However, the shut-in/decline method does not provide adefinitive 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 procedurewhere 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 isapproximately equal to the initial shut-in pressure; therefore, net pressure isapproximately 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 thenshut 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 ().The injection test determines the type of fracture being created; Perkins-Kern-Nordgren (PKN), Khristianovic-Geertsma-de Klerk (KGD), or Geertsma-de Klerkradial (RAD). Analysis of the net pressure versus time on a log-log scale (Nolte-Smith plot) determines the type of model (PKN, KGD, or RAD) to use for declineanalysis. 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 PressureAnalysis, Decline Data and DataFRAC modules in the FracCADE software todetermine the parameters listed above.The DataFRAC Service uses the G-plot for complete, consistent analysis. TheG-plot (illustrated in Fig. 4) replaces the curve-matching method and can accentuatenonideal fracture behavior such as unrestrained height growth and extension aftershut-in and closure. Analysis results from the DataFRAC module in the FracCADEsoftware automatically update the fracture geometry simulator. The calculated netpressure is compared and recorded with the net pressure observed at shut-in. Thisdual analysis ensures a consistent set of parameters for the treatment design andindicates potential nonideal fracture behavior when a pressure match cannot bejustified.


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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 generallyavailable design data that is not specific to a particular well is used. However, thisservice can increase the NPV when it results in optimization of a treatment design.The DataFRAC Service can be routinely performed before all fracture treatmentswhen the objective is to optimize the treatment design and resulting production. It isalso an invaluable aid to assure the best possible treatment is performed in caseswhere information is limited. Some opportunities where the DataFRAC Serviceoffers 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 willenhance the DataFRAC analysis.

2.1.1 Breakdown/Diversion Treatment

Perform a breakdown/diversion treatment (for example, acid ballout) prior toperforming a closure or calibration test to ensure that all perforations are open andthat the formation has been broken-down. The initial shut-in pressure recorded on abreakdown/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. Fracturetreatment design is provided in Treatment Design.Before performing the DataFRAC Service, a fracturing treatment should be designedusing the best data available. Use the FracCADE software for the treatment design.The fluid type, expected pad volume and efficiency, fracture geometry, and netpressure will provide a reference for the same parameters that will be determinedfrom the DataFRAC analysis. A preliminary fracture design will also help to identifyunexpected 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 confirmthat and will quantify the fracture capacity based on actual, rather than assumedpumping conditions. The subsequent fracture design can then be prepared witheither more confidence that the fracture capacity will not be exceeded or that specialtechniques 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 onwidth (determined by the fracture compliance). Accurate values for gross fracture-height (formation gross height) and leakoff height (formation net thickness) arecritical to the DataFRAC analysis and to the ultimate success of the fracture designand execution. If these values cannot be selected with a comfortable degree ofcertainty prior to the fracture treatment, the need for the DataFRAC Service andwireline 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.


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Run pre- and post-job temperature logs or radioactive tracers and a gamma-raylog (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 theanalysis. Prior to performing the DataFRAC Service, request that the appropriatewireline services be utilized to estimate fracture height (Gamma-Ray log, Sonic log),leakoff height (SP log, Porosity log), and Young's modulus (Sonic log). Requestradioactive tracers for the calibration test. Request postfracture logs (Temperaturelog 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. Leakoffheight 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 theshale base-line is considered leakoff height. Additional techniques to determinefracture 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 theaverage height of the fracture because of deviated wellbore or zone, height growthinto the barriers at the wellbore or horizontal fractures. The net pressure (duringpumping) and a fracture simulator can give estimation of the average height. In theDataFRAC module, height and Young's modulus are altered to make the FractureGeometry Sensitivity simulator (FGS) and the analysis (actual) net pressure match.When the net pressures are matched, the heights and modulus should match withthose obtained from logs. If no match is obtained, then one of the sources may beincorrect.Shale barriers have very low permeability and porosity and will tend to squeeze outany fluid during fracture closure. A more permeable and porous zone above theshale will retain the fluid. A fracture may grow into this zone and the indication bediscounted because the shale barrier doesn't show radioactivity or temperaturechange. This can also be missed if the wireline service company turns down the toolsensitivity when away from the zone of interest.Without an independent indication of fracture height, analysis is more difficult andmay be less accurate. Analysis will be enhanced with the aid of logs.

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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 netpressure and, therefore, fracture height in the design. This can often demonstratethe sensitivity of vertical fracture growth to pump rate and fluid rheology. Oncesensitivity is established, the need for the DataFRAC service is apparent to pinpointthe critical design parameters and to calibrate the FGS simulator.

2.1.5 Perforating

Perforating technique can have a significant effect on the execution and evaluationof 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. Thevalue for net pressure will be inaccurate because of a shift upward. Fracture modelselection may be affected. During the fracturing treatment the proppant will erodethe restrictions resulting in lower perforation friction pressure. A drop in perforationfriction pressure may be interpreted (falsely) as fracture height-growth.Wellbore restrictions caused by improper or ineffective perforating techniques cancause a screenout. Restrictions can cause the fracture to extend in an area apartfrom the perforation tunnel, resulting in a significant increase in apparent perforationfriction 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 onone side of the casing). For these cases, the orientation of the perforation with theplane 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 fracturewith very limited penetration of the companion wing. Channels are created andcause higher treating pressures because of width restriction (Fig. 5).Fig. 5 also shows a perforation that is approximately 30 out of phase to the fractureplane (minimum stress). The fracturing fluid must partially circumvent the wellbore toreach the fracture. Restrictions may develop, causing an increase in frictionpressure and creating the potential for proppant bridging. Even when a perforationis directly in line with the fracture plane, the fracturing fluid must create a patharound the wellbore. With 90 or 120 phasing, the fracture plane will generally beless than 30 from two perforations and will result in perforation access to bothfracture wings. (Note from Fig. 5 that 180 phasing would not alleviate themisalignment).

2.1.5.3 Perforation Size

Fig. 6 illustrates the relation of perforation diameter and proppant concentration. Aperforation must be large enough to permit the proppant (at the maximumconcentration) 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 are1. 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 aNewtonian fluid such as diesel or water containing 2% (wt:wt) potassium chloride. Inhigher permeability formations (> 10 md) or in formations containing natural fissures,viscosified fracturing fluids may be required to reduce the rate of fluid loss andfracture closure during flowback. The same fluid as the pad fluid of the proposedfracturing treatment would be a good choice in the case of high leakoff.

2.2.2 Injection Rates and Number of StepsWhen injecting a Newtonian fluid, the range of rates is generally one to ten bbl/minfor larger and moderately permeable zones and approximately one-half these valuesfor smaller and very low permeability zones. After a breakdown/diversion treatmenthas been performed, most zones (k > 0.01 md or h > 30 ft) will require a pump rategreater than 3 bbl/min to exceed fracture extension pressure. The actual range for aparticular zone may require trial and error methodology; two or more attempts.Ideally, three values of pressure (end of step) should fall below the extensionpressure 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 portionfor extending the fracture. This allows the pressure versus rate plot to be drawn onCartesian coordinates using the last pressure before a rate change. The intersectionof the two straight lines (fracture extension pressure) provides an upper boundary forclosure pressure.An additional step-rate/flowback test can be performed to verify correct closure. Ifthere were no pre-existing fracture, the plot of injection pressure versus bottomholepressure may show an overshoot of the extension pressure for one or two stepsbecause 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 stepsshould be equal and can be relatively small. The time required for the pumpingequipment 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).


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All steps, except the last step, should be the same duration. The last step should belong enough to establish some fracture volume, thus allowing the flowback, notleakoff, to bring about closure. Five to ten minutes should be sufficient for the laststep.

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 monitoredby a flowmeter. If the flowback rate is within the correct range, the resulting pressuredecline will show a characteristic reversal of curvature at the closure pressure. Theaccelerated pressure decline at the curvature reversal is caused by the flowrestriction introduced when the fracture effectively closes. The correct range offlowback 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 selectionimpossible. The second test need not include a step-rate phase if clear fracture-extension pressure was determined from the first test. Use a different rate thesecond time.Flowback until bottomhole pressure is within 200 psi of initial reservoir pressure. Donot flow reservoir fluids into the wellbore by flowing back more than was injected. Atshut 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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The general steps in a calibration test design are1. 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 offluid 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 beflushed with a linear fluid a fluid containing no nitrogen, carbon dioxide orcrosslinker/activator. Gas in the flush volume will expand due to pressure declineand temperature increase. This will cause fluid displacement into the fracture duringclosure and will invalidate the decline analysis. If bottomhole pressure is calculatedfrom surface measurements, the hydrostatic pressure will change, adverselyaffecting the calculations.

2.3.2 Fluid Volume

The fluid volume may be determined by using the FGS simulator in the FracCADEsoftware. 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 KGDor RAD model is selected (indicated by a lack of barriers). If the PKN model isselected (indicated by significant barriers), calculate a volume sufficient to createa fracture length greater than 1.5 times the fracture height.

3. If undesired height growth or fissure opening is suspected, treatment designshould 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 agood starting place.

2.3.4 Fluid-Loss Additives

FLA 100 has particles large enough to be considered a proppant when used in acalibration test. Therefore, FLA100 can cause a screenout and will affect analysis.FLA100 is not recommended for use in a calibration test. However, in naturally-fractured or high-leakoff formations, FLA100 can be used with caution if a sufficientquantity of clean fluid is pumped ahead of it. Fluid-loss additive J84 or fluid-lossadditive J418 is not a screenout hazard and may be used in the entire fluid volumefor leakoff control.

2.3.5 Duration of Pressure Decline

The minimum time that pressure decline should be monitored is 1.25 times theclosure time or twice the injection time, whichever is longer. The closure time can beestimated by using the Placement module in the FracCADE software. Estimate thefluid and formation parameters and the volume of fluid to be pumped during thecalibration test. A very small proppant stage may be necessary to force thePlacement 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 insubstantial 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 thecalibration test.

2.4.2 Prepad

A prepad is not necessary for the calibration test.

Mark of Schlumberger

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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 isless than hydrostatic pressure. Calculate the quantity of fluid displaced whenclosure pressure occurs. If the displaced fluid is more than 10% of the fracturevolume at shut-in (volume injected times efficiency), a special wellbore isolation toolshould be used in conjunction with a wireline-conveyed bottomhole pressure gauge.Such tools have been used before but may have to be specially constructed. Abottomhole 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 monitoringhas ceased. Cable movement in the wellbore and fluid drag on the cable can affectthe pressure decline data. If postjob logs are to be run, consider using a wirelineconveyed 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 existingfracture. Typically, the fracture extension pressure is 50 to 200 psi greater than theclosure 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 closurepressure.

2.5.3 Closure Pressure

An accurate determination of the closure pressure is essential for an analysis of thefracturing pressure because it is the datum for determining the net pressure. Theclosure pressure is the fluid pressure at which the fracture closes (zero width). Thispressure is equal to, and counteracts, the minimum principal stress in the rock that isperpendicular to the fracture plane. The closure pressure reflects a global averageof the minimum stress, which is a local quantity and is not constant over the zone ofinterest. The closure pressure generally is less than the breakdown pressurerequired 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 thepumping portion of the DataFRAC service. However, a MicroVAX will greatlyenhance data manipulation and examination. A MicroVAX computer is necessary ifonsite 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 (closurepressure) from the flowback pressure plots. Always carry linear graph paper for anyhand plotting needed as well as log-log paper for plotting a Nolte-Smith plot ifnecessary.

2.6.2 Pumping Equipment

Diesel-powered pumpers are recommended for the closure test. Turbine poweredpumpers 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 calibrationtest.

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 canbe calculated from the surface pressure as long as the fluid density is constant andthe bottomhole pressure is greater than the hydrostatic pressure. The main problemwith using the treating pressure for analysis is that the friction pressure makes theNolte-Smith plot less accurate and can indicate erroneous trends. In the overallanalysis, the Nolte-Smith plot is very valuable if accurate bottomhole pressure andclosure pressure are used.A good method for measuring bottomhole pressure is with a live annulus or adead-string tubing and a homogeneous fluid. This eliminates friction pressurecalculations. With a known hydrostatic pressure, bottomhole pressure can beaccurately 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). Thefluid 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 250F (121C) and a depth less than10,000 ft.Significant hydrostatic pressure changes may result from a change in fluid densityduring closure in deep, hot wells. This occurs when the wellbore fluid is warmed bythe formation. After pumping, surface pressures can actually increase while thebottomhole pressure decreases (Fig. 8). In a 16,000 ft, 325F (163C) well,hydrostatic pressure change can be as much as 250 psi for water (Fig. 9). Theeffects on oil will be much greater because of the greater thermal expansion of oil.This compromises any results from surface readings because overly optimistic fluid-loss and efficiency values will be implied. Therefore, the use of surface readings fordeep, 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, thenpressure analysis is not possible from surface measurement and a wireline-conveyed 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 pressuregauge thereby eliminating friction calculations and hydrostatic considerations. Forfluids without proppant, this can safely be done with a wireline-conveyed gauge, inthe fluid stream if necessary. To ensure the wireline tension does not exceed a safelevel, the increased tension due to fluid drag must be calculated using Eq. 1 beforethe job begins.

(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 wirelineservice company prior to rig-up to avoid parting the wire and subsequent job failure.

T d d PID w f= pi

4

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A wireline-conveyed bottomhole pressure gauge interfaces through a Remote DataAcquisition (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 issuggested. The wireline-conveyed pressure gauge should be tested prior to jobexecution.

2.6.4 Treating Equipment

Wellhead rig-up requirements must be considered and communicated to the wirelineservice company. If the injection rate through two-inch treating equipment is greaterthan 8.5 bbl/min, a frac cross may be necessary. At rates less than 8.5 bbl/min, alateral may be sufficient. The Dowell Location Safety Standards manual providesthe maximum pumping rates through treating equipment.

2.6.5 Flowback Equipment

Flowback rate must be monitored accurately for adequate control. Response timeon 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 maybe used. Magnetic flowmeter information is provided in the Sensors VerificationGuide.

2.6.5.2 Turbine Flowmeters

Turbine flowmeters are typically used with oil-base (nonconductive) fluids, but maybe used with any fluid type. Turbine flowmeter information is provided in theSensors 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 ExecutionTreatment 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 approvedon-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 inFig. 10 (conductive fluids) and Fig. 11 (nonconductive fluids). An adjustablechoke 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 ofknown specific gravity with no gas cap. The preferred method is to circulatefrom the tubing to the annulus at high velocity.

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

4. Backup pressure transducers must be rigged-up and calibrated. Do not provideany more than one display for the same pressure. The transducers are accurateto 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 10,000psi transducer for better accuracy. Do not allow anybody to hammer ontransducers during any phase of testing.

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

6. Determine the expected closure pressure. The closure pressure may beapproximated using Eq. 2.

(2)


Approximate closure pressureOverburden pressure essure

=

+ ( PrReservoir 23

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7. If the wellbore is full of fluid, note the initial bottomhole pressure. Otherwise, notethe quantity of fluid required to fill the wellbore (pressure rise). Once the wellboreis full, shut down and record the pisi. Calculate bottomhole pressure using theinitial 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 are1. 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. Gettingthe injection rate (as well as flowback rate) established quickly must be stressed.Exact rates are not important constant rates are. Fluid-end ratings andconstants are provided in the Treating Equipment Manual. Pump performancecurves are provided in the appropriate pumping equipment operators manuals.

2. Take pressure readings after establishing a new pump rate (prior to increasingthe rate again).

3. Determine if fracture extension is occurring during the last injection stage byplotting rate versus pressure. This will indicate fluid loss to the matrix leakoff orfracture extension (Fig. 2). Fracture extension pressure will be 50 to 200 psigreater than the closure pressure. Remember to plot rate versus bottomholepressure (not treating pressure). If treating pressure is plotted, the frictionpressure will distort the values at higher rates and produce erroneous results.

4. Increase the pump rate during the last stage if fracture extension is notoccurring. If fracture extension is occurring, terminate the stage after thedesired length of time. Water hammer effects can be minimized by reducing thepump 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 estimatedperforation friction pressure if all perforations were open. If the true perforationfriction pressure is greater than twice the estimated perforation friction pressure,wellbore restriction is too great and should be reduced by pumping a divertingtreatment or reperforating. Injecting small quantities of proppant near the end ofthe pad of the proposed fracturing treatment may erode the restriction.


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(3)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.

p p p ppf w tf isi=

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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.


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3.2.2 Flowback Phase

Flowback must be initiated at a constant rate as soon as possible. Remember toisolate the pump(s) from the well. Do not allow bottomhole pressure to fall below200 psi above the initial bottomhole pressure. Do not flow-back more fluid than waspumped.Note the indicated change in bottomhole pressure during shutdown and calculate theperforation friction pressure. If the perforation friction pressure is more than twicethe 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 ratewhen 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 raterequired for the last stage.

Flowback rate accuracy is not critical; 20% is acceptable. However, a constantflowback 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 providesapproximate choke settings for flowback of water-base fluids. Verify the setting bypumping through the choke at the anticipated flowback rate and pressure shut-inpressure. 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)Flow Rate (bbl/min)

1 3 15 10 15 201,000 14 24 31 44 53 622,000 12 20 26 37 45 523,000 10 18 23 33 41 474,000 10 17 22 31 38 445,000 9 16 21 29 36 416,000 9 15 20 28 34 397,000 8 15 19 27 33 388,000 8 14 18 26 32 379,000 8 14 18 25 31 36

10,000 8 13 17 25 30 3511,000 8 13 17 24 29 3412,000 7 13 17 23 29 3313,000 7 13 16 23 28 3314,000 7 12 16 23 28 3215,000 7 12 16 22 27 31


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Table 2. Approximate Choke Settings for Flowback of Water-Base Fluids (Sg = 1.0)Pressure

(psi)Flow Rate (bbl/min)

1 3 15 10 15 201,000 15 26 34 48 58 682,000 13 22 28 40 49 573,000 11 20 26 36 44 514,000 11 18 24 34 41 485,000 10 17 23 32 39 456,000 10 17 22 31 37 437,000 9 16 21 29 36 428,000 9 16 20 28 35 409,000 9 15 19 28 34 39

10,000 8 15 19 27 33 3811,000 8 14 19 26 32 3712,000 8 14 18 26 31 3613,000 8 14 18 25 31 3614,000 8 14 17 25 30 3515,000 8 13 17 24 30 34

The downstream 1 x 2 hamer valve (control valve) in the flowline (bleedline) may beused for flow control if the adjustable choke becomes plugged and can not becleared. 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 ratesvia radio is not acceptable.

3.2.2.2 Flowmeters

When using a turbine flowmeter, open the control valve slowly to avoid a fluid surgeand subsequent flowmeter damage. Never allow a low-pressure magnetic flowmeter(for example, Fischer-Porter) to be placed upstream of the choke. Flowmeters musthave 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.

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The general steps in a calibration test are1. 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 PhaseThe type of fluid and injection rate for the calibration test are the same as the type offluid and injection rate of the proposed fracture treatment.Injection phase guidelines are1. 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 notpossible, pump the tubing volume (or annular volume, whichever is applicable)at low rate. Stop pumping and let the pressure fall below closure beforeresuming pumping. Fluid warming will change the fluid characteristics. Do notwait any longer than necessary if the well has a high bottomhole statictemperature.

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

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

4. Calculate fluid friction pressure using bottomhole pressure or obtain the shut-inpressure during the calibration test. Initial shut-in pressure obtained afterpumping the flush fluid yields friction pressure for the flush fluid, not thecalibration fluid.

5. Stop pumping when flush is complete. Reduce water hammer effects byreducing 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 thetreatment 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 are1. 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 finalanalysis 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 atthe design rate. Do not continue pumping at a reduced rate. Do not beconcerned about a fluid leak unless the leak causes safety concerns or istremendous, (gallons/minute). The volume loss compared to the leakoff in thefracture is small and will not affect the pressure decline.

2. If an operational problem occurs with approximately 50% of the fluid volumepumped and the problem can be corrected quickly, stop pumping and note theloss of net pressure. If more than 20% of the net pressure is lost, considera) starting overb) 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 filledin 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 actualvolume of fluid injected into the formation in the analysis.

At least 50% of the total volume should be pumped at the designed rate.

4 EvaluationThe DataFRAC analysis consists of three essential parts.1. closure test for closure pressure2. calibration injection for fracture geometry3. calibration decline for fluid-loss behavior

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For correct analysis, the actual bottomhole pressure (BHP) must be used (SeeRef. 2: Chapter 7.6.2). Combining the analysis of the closure test, pressure duringpumping (as predicted by a fracture simulator) and pressure decline during closureprovide a consistent interpretation and the enhancement of the three parts.Consistent values of the fracturing parameters for all the three analysis provide asound 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 closeswithout proppant. The closure pressure is distinguished from the minimum stress.The stress is a local parameter which can vary over the pay zone, whereas theclosure 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 inthe complete zone as opposed to a micro fracture for the stress test.The methods used for determining the closure pressure include the step rate andflowback test.The step rate is analyzed using a BHP versus rate plot and the flowback is analyzedusing 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 slopesindicating matrix leakoff at low pressures/rates, and fracture response at higherpressures/rates. The extension pressure provides an upper bound for the closurepressure and defines the required range of pump rates for extending a fracture in thezone.

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 throughthe entrance of the fracture. The lowest point of the pressure derivative curve will bethe inflection point. Several publications prior to 1993, indicated closure occurred atthe inflection point. Subsequent analysis, with a comprehensive fracture simulator,indicated closure pressure occurs at a lower pressure and near the intersection ofthe 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 plotor G-plot during the shut-in of the calibration treatment. The closure pressure isinferred as change of the slope on either of these plots (Fig. 20). This methodnormally does not provide a definitive indication of the closure pressure because ofthe existence of multiple slope changes. The fracture closure generally causes oneof the slope changes in the BHP versus: t plot. A change in slope of the G plotalso 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 wellis shut-in and the rebound pressure is monitored. The rebound pressure provides alower bound of the closure pressure and the inflection point provides an upper boundof the closure pressure (Fig. 21).

Fig. 21. Rebound pressure; lower bound of closure pressure.

4.2 Calibration Injection for Fracture GeometryThe Nolte-Smith plot (log-log plot of the net pressure versus pumping time) providesan important diagnostic tool for determining how the fracture is propagating and thefracture geometry during pumping. The analysis enables the simulation andcalibration of the pressure with a numerical fracture simulator and permitsreconciliation of the ideal assumptions and actual field conditions. The magnitude ofthe net pressure from the fracture simulator permits a verification of fractureparameters 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 classicalsolution is applied. From the solution, the average fracture width can be expressedin terms of the closure pressure (pc) fracture compliance (cf) and net wellborepressure (pf) as:

Where:

Fig. 22 indicates that the behavior of a pressurized crack is analogous to a pre-loaded spring. pc = spring pre-loaded

= spring constant

=(see Section 4.3.8.4)

E = rock modulusd = characteristic dimension of frac geometry

w c p c p pf f f f c= = ( ),

cd

Ef=

pi2 '

1c

Edf

'

pP P

fw c

_ _ _


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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,

This relationship is used to model a fracture as follows: PKN:

KGD:

Radial:

The KGD model is more appropriate when the fracture length is smaller than theheight, while the PKN model is more appropriate when the fracture length is muchlarger than the height. The radial model is most appropriate when 2xf

is about equalto 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;

This expression relates the gradient down the fracture length to the fluid velocity orflow rate. Introducing the fracture compliance (w = cf pf), integrating along thefracture length and assuming pf = 0 at the tip, results in;

wd p p

Ef c

=

pi ( )'2

x

h d hff f

=

hx

d xff f

= 2

21 32

3 2x

h d R R and x Rf

f f = =

pi.

dpdx

Kw

qhn

i

f

n

+

'

.

'2 1

1.

p Kc

qh x

w c p c K x qh

ff

n

i

f

n

fn

f f f fi

f

n n

=

+

+'

'

'

' ( ' )

'

2 1

12 2

12


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

KGD:

Radial:

Where:which is the same for all the three models. The relationships also indicate that withincreasing penetration, the net pressure increases for PKN model and decreases forthe KGD and radial models.For constant injection rate, the fracture growth can be expressed in terms of timeand bounded by two extreme cases for fracture efficiency, : Upper bound: No fluid loss (that is, Vf = Vi = qit). V w A tf f= ; 1 Lower bound: Almost total fluid loss (that is, VL Vi = qit and Vf 0).

The fracture penetration increases with time and depends on the fluid loss duringinjection. By combining the bounds for time dependence of penetration, therelationship for net pressure and width, the net pressure yields; PKN:

KGD:

Radial:

p Ah x

ff

nf

n

n

+12

12 2

'

( ' ),

p Ax

hf

f

fn

n

+

+

3 1

12 2

'

( ' ),

p AR

f nn

+13

12 2

'

( ' ).

A E K qn in n

=+ +( ' ) ,' ( ' )2 1

12 2

A t

Aff

=

1 2 0/ ; fracture face area.

p tp t

f nf n

+

+

1 4 11 2 3

01

/ ( ' )/( )

( )( )

p tp t

f n nf n n

+

+

'/2 ( ' )'/( ' )

( )( )

12

01

p tp t

f n nf n n

+

+

3 12

00

'/8 ( ' ))'/( ' )

( )( )

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The previous expressions for pressure assume the fluid viscosity dominates thepressure distribution and ignores the fracture toughness of the formation. Thisassumption is generally valid for fractures with dimension in excess of 50 ft usinghigh-viscosity fluids. For the case of small-scale fractures created with low viscosityfluids, fracture toughness can dominate and result in different exponents for time.The expressions for the net pressure are all exponential expressions. As a result, alog-log plot of net pressure versus time should yield a straight line with slope equalsto the respective exponents: positive for PKN and negative for KGD and radialmodels. The log-log plot of net pressure versus time as introduced by Nolte andSmith, 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 anideal case with bounding formations of higher stress. During the initial phase ofpropagation (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 KGDmodel. 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 occurafter 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 encountersbarriers above and below (stage 2) which results in increasing pressure and the log-log slope is between 1/4 and 1/8. Without proppant, the net pressure is limited to a


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value slightly below the stress difference () of the barrier being penetrated. At thistime, the height begins to increase significantly and the pressure would beapproximately constant (stage 3).Nearly constant pressure indicates the pressure capacity for the formation, which isdetermined by in-situ stress difference. When the net pressure reaches thiscapacity, fracture extension becomes relatively inefficient, as discussed in thefollowing 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. Stagea is the PKN propagation stage. The positive log-log slope will continue until thenet pressure approaches the stress difference of the barrier. At this stage (stageb), 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 zoneresulting in an accelerated rate of growth at decreasing pressure and width in theprimary zone. The width profile indicates that a pinch point occurs in the barrierafter stage b. The pinch point has essentially no width during the transition fromstage b to stage c. The pinch point can cause proppant to bridge as fluid ispermitted to pass through. The resulting excessive dehydration of the slurry coupledwith the decreasing width can result in a rapid screenout even at low proppantconcentration.

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 thefollowing 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 with a diverting agent (INVERTAFRAC or

DIVERTAFRAC).4.2.3.2 Fissures

Another possible cause for a period of constant pressure is the opening and inflatingof natural fissures. Pressure-dependent leakoff due to fluid loss into fissures isthought to contribute to screenouts in low permeability formations where limited fluidloss 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 lossbecomes significant and regulates the pressure to a constant value.

2. Highly stress-sensitive permeability and fluid lossThe permeability and fluid-loss enhancement are significant throughout thetreatment, with the effect accelerating as the pressure increases. If thetreatment continues, the negative effective stress condition can occur withconstant 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 widthprofile. The secondary fracturing occurs in natural fissures or cracks which arecrossed by the primary fracture. These feature normally have relatively higherpermeability than the matrix and the fluid leakoff is high.The fissures will open when the fluid pressure exceeds the formation stress actingacross them.

H = 2 - 1 = horizontal stress difference.This implies that effective fracturing will require a significant stress differencebetween the principal horizontal stress to avoid opening of natural fissures. Whenthis magnitude of pressure is reached, the fissures open and act to regulate theconstant pressure at this critical magnitude. A significant portion of the injected fluidcan be lost because of a large number of fissures that can open at this criticalpressure. The accelerated fluid loss can lead to excessive slurry dehydration and ascreenout (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 screenoutthe 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).

p f H>

2 1

1 2 1 5.

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When the fracturing pressure is greater than overburden stress, a fracture canpropagate in both the horizontal and vertical planes. This geometry is called aT-shape fracture and the pressure response and a vertical cross section of the widthprofile are illustrated in Fig. 26. The figure indicates stage c has a near constantpressure response. The horizontal component growth requires pressures greaterthan the overburden pressure and occurs at;

Where:OB = vertical overburden stresspc

= closure pressure.The width of the horizontal fracture component will be narrow and have twin pinchpoints at the juncture with the vertical component. The limited width of the horizontalcomponent can restrict proppant entry, excessively dehydrate the slurry in thevertical component, and lead to premature screenout.The T-shape fracture is the easiest to diagnose: Bottomhole injection pressureapproximately 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 avertical fracture can occur because The pressure approaches the stress of a barrier and causes significant height

growth;

p f

v

= barrier stress difference. The pressure exceeds the stress acting on natural fissures and the fissures open;

The pressure exceeds the overburden pressure, and the initiation of T-shapefracture begins;

p OB pf c

p OB pf c

p f H1 2 .


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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. Theformation acts as a pressure vessel with a pressure capacity defined by stressdifferences. Exceeding the pressure capacity leads to inefficient extension due toheight 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 hydraulicfracturing treatment should be considered in fracturing pressure analysis, that is,subtracted for determining net pressure. In addition to inadequate perforating, apotential cause of high near-wellbore pressure losses is that the well and the fractureplane are not aligned, that is, on deviated wells or wells close to faults (deviatedprincipal stress). For these cases, the fracture initially aligns with the wellbore, andthen turns to align normal to the far-field minimum stress. The fracture entranceexperiences a normal stress greater than the minimum stress, leading to a fracturewidth restriction and increased pressure losses within the entrance.The stress state within the entrance is illustrated by Fig. 28 and the Mohr circle inFig. 29.AB = fracture plane1 = minimum principal stressy = stress parallel to the wellborex = stress normal to the wellbore.

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Fig. 28. Stress state within the entrance of deviated well or stress.

For the deviated stress case, y and x are equal to overburden and horizontalstress, respectively. The principal (that is, minimum and maximum) stresses are nothorizontal or vertical and the fracture is inclined. For the deviated well case, theprincipal stresses are assumed horizontal and vertical, y

and x are parallel andnormal to the inclined wellbore. x can be estimated as the sum of the minimumstress (that is, closure pressure) and the apparent near-wellbore friction, pwf; that is,

fracturing engineering manual-data frac service

Documents

closure test

fracture height

fractureheight logs

preliminary fracture

fluid selection

nonpermeable zone

preparatory engineering

wellbore logging