field application of after-closure analysis of fracture calibration tests

7/25/2019 Field Application of After-Closure Analysis of Fracture Calibration Tests

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Copyright 1999, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 1999 SPE Mid-Continent OperationsSymposium held in Oklahoma City, Oklahoma, 2831 March 1999.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than 300

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AbstractThis paper describes field examples of fracture optimizationthat are based on the after-closure pressure decline periodfollowing a proppant-free injection. The primary benefit fromthese applications is the determination of reservoirtransmissibility that is central to specifying the fracture lengthand conductivity for optimizing field-development economics.

The transmissibility is obtained from the after-closurepseudo-radial flow period. In the examples thistransmissibility is compared with that calculated from

conventional well testing. In one example, the well-testderived fracture half length is compared to the optimizedlength predicted from a fracturing simulator. Simulated versusactual production results are also compared.

The after-fracture closure period of an unpropped fractureinjection potentially contains the reservoir pseudo-linear flowand pseudo-radial flow periods. Analysis of the linear-flowperiod enhances the standard calibration analysis of the pre-closure period (i.e., mini-frac analysis). One enhancement isthe potential determination of spurt loss that can not beobtained from the pre-closure decline because spurt loss endsas the fracture extension stops. Another enhancement is thereservoir behaviors perspective of closure time and fractures

length that permits validating the values of these parametersfrom the pre-closure analysis. This definition of length isobtained from combining the linear and radial flow analyses.

The field examples are for a moderate permeability,normally pressured, dry-gas Morrow sandstone reservoirlocated in Hemphill County of the Texas panhandle. Theselected testing sequence, and synergy of information fromindependent pre-frac tests, are reviewed as well as operational

and theoretical constraints. A logical application procedure ideveloped for general field use in similar environments.

IntroductionPressure interpretation during and after fracturing has beenused extensively to estimate rock, fluid and fractureparameters1,2,3. The technique is commonly employed onlocation to rapidly estimate fracture design parameters and the

quality of the hydraulic connection between the perforationsand the fracture plane. When coupled with an accurateformation permeability, the fracture geometry can beoptimized for maximum economic benefit4. Unfortunatelyaccurate formation permeability estimates are rarely availablefor reservoirs requiring fracture stimulation. In additionpressure analyses are highly dependent on the selected value oclosure pressure that can vary significantly for differenselection methods. Consequently, because of ill-definedparameters, non-uniqueness pervades the design andinterpretation process. In order to improve the designcapabilities of the stimulation engineer easily appliedtechniques for permeability determination and validation of

formation closure are required. Consideration of the afterclosure period of a standard fracture calibration test canprovide this additional information.

A pressure response chronology for a constant rate fractureinjection and shut-in is shown in Figure 13. Fracture growth isfollowed by a pressure decline that ultimately approachesreservoir pressure. Classic pressure interpretation has dealwith the first two periods represented in this figure. Thepressure response during injection has been used to evaluatethe nature of fracture propagation1. The fracture closingperiod has been used to quantify fluid efficiency, fracturegeometry, plus non-ideal events such as post-injection fracturepropagation, pressure dependent leakoff, height recession

during closure and the existence of a near-wellbore choke2,5

The late time pressure decline becomes pseudo-radial and canbe analyzed in a manner similar to traditional well tes

methods to provide transmissibility (kh/) and initial reservoirpressure6,7.

The period following fracture closure and preceding theonset of pseudo-radial flow can exhibit reservoir pseudo-linearflow. This period can be used8 to determine closure time andsupplemented by other information (discussed later), spurt loss

SPE 52220

Field Application of After-Closure Analysis of Fracture Calibration TestsG. R. Talley, and T. M. Swindell, Barrett Resources, and G. A. Waters and K. G. Nolte, Schlumberger Dowell


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2 G. R. TALLEY, T. M. SWINDELL, G. A. WATERS, K. G. NOLTE SPE 52220

and fracture length. If the decline period is sufficient toinclude radial-flow, the transmissibility can also be attainedfrom the same injection. Otherwise, it must be garneredindependently from as a well test or another injection testdesigned to achieve radial-flow as discussed later.

By coupling the after-closure analysis to standard injectionand conventional decline analysis a more thorough

understanding of the fracturing process can be attained. Theexamples discussed in this paper demonstrate the validity ofthe transmissibility determined from after-closure radial-flowand its use in fracture treatment optimization. A linear-flowanalysis from a calibration treatment was attempted but did notachieve its full potential as discussed later. However, it didconfirm the selection of closure and reservoir pressure.Practical field procedures to improve the success of thetechniques are included.

Technical BackgroundIt is not the objective of this work to provide a review of theafter-closure analysis. The reader is referred to Nolte et al.8

for such a review and the procedures for determining spurtloss, fracture length and closure time. A brief synopsis of thetechniques is included here as background for application inthe following sections.

After-Closure Pseudo-Radial Flow

The late-time pressure decline evolves to pseudo-radialflow allowing transmissibility to be determined using a methodsimilar to a Horner analysis. After-closure radial-flow is afunction of the injected volume, reservoir pressure, formationtransmissibility, and closure time. Their relationship isprovided in the following equations using the radial-flow timefunction, FR,

p t p m F t tr R R c( ) ( , ) = (1)

where tc is the time to closure with time zero set as thebeginning of pumping,pris the initial reservoir pressure, mRisfunctionally equivalent to the Horner slope for conventionaltesting, and

F t tt

t tR cc

c

( , ) ln= +

1

41

,

=

1616

2. (2)

Thus, a Cartesian plot of pressure versus the radial-flow

time function yields reservoir pressure from the y-intercept andthe slope (mR) that permits determination of transmissibility.

kh V

m t

i

R c= 251000, ( ) (3)

with k, h, expressed in oil field units, tcin minutes and Viisinjected volume (bbl). (Note, all other equations are eitherdimensionless or in consistent units.)

After-Closure Pseudo-Linear Flow

The after-closure pseudo-linear flow analysis was adaptedfrom Carslaw and Jaegars heat transfer analysis9. Theyconsidered a semi-infinite body whose surface was held at aconstant temperature relative to its surroundings, followed byinsulation of the surface and then thermal decay ensuing.

For heat transfer and reservoir transient behavior

temperature and pressure are analogous. If one assumes thathe pressure in the fracture is essentially constant duringinjection (as typically is observed), then the pressure declineafter closure behaves as the thermal decay and, in the absenceof spurt loss, can be expressed by the reservoir analog of theheat transfer problem as

p t p m F t tr L L c( ) ( , ) = (4)

The linear flow time function is

F t tt

t

L cc( , ) sin=

2 1

, t tc (5)

and the coefficient or Cartesian-plot slope is

m Ck c

L Tt

=

(6)

where CT is total leakoff coefficient and ct is totacompressibility.

From Equations 5 and 6 the pressure decline during thelinear-flow period can then be written in terms of reservoirdiffusivity, storage, total fluid loss coefficient and closure time

as follows.

p t p Ck c

t

tr T

t

c( ) sin =

2 1, t tc (7)

When spurt loss exists the initial linear-flow behaviorfollows a different time behavior but eventually conforms tothe behavior of FL(t,tc). After this behavior is established thelinear-flow slope analysis can be used, in conjunction withreservoir parameters and the pre-closure decline analysis todetermine the magnitude of spurt loss8.

Fracture half length is determined from the time of

transition from linear to radial-flow

8

. The fracture lengthdetermined from this method can be compared to thatdetermined from the conventional, pre-closure analysis. Ilarge discrepancies exist then an investigation can be initiatedinto which parameters are in error. In this way the afterclosure analysis can be used as a quality check on thefracturing and reservoir parameters used in the pre-closureanalysis.


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SPE 52220 FIELD APPLICATION OF AFTER-CLOSURE ANALYSIS OF FRACTURE CALIBRATION TESTS 3

Field ApplicationIn an effort to optimize fractured-well performance after-closure pressure decline analysis, in conjunction withconventional fracturing pressure interpretation, was performedon two gas wells in the Puryear member of the Upper Morrowsand in the West Allison Field of Hemphill County, Texas.The primary objective was to determine permeability from an

after-closure radial-flow analysis and to estimate stress profilesfor improved fracturing designs. Well tests were performed tovalidate the accuracy of the after-closure permeabilityestimate. A secondary objective was to perform the linear-flow analysis on a gelled fluid injection to determine spurt,closure pressure and fracture length.

In this area, the Puryear member of the Upper Morrowformation was deposited as a non-marine fluvial sequence,with the source being the Amarillo-Wichita Uplift to the south.Mississippian-aged sediments were eroded off the mountains,carried north and northeast and laid down in erosionalchannels.

The location of the study area approaches the northern

extent of Puryear deposition. Because of the distance oftransportation, significant re-working of the sediments has lefta medium grain sandstone comprised of nearly 100% quartz,with few associated minerals. The sub-angular grains arecemented with a slightly calcareous cement, causing parts ofthe zone to be very friable.

Completion Procedure:

The same general completion procedure was followed onboth wells:

1.Perforate with 6.5 gr charges (0.5 in. EHD) at 4 spf and0o, 90o, 0o, and 270o phasing with pressure and temperaturegauges on the bottom of the guns. A 10% density-porosity

cutoff was used for net footage determination.2.Breakdown the wells with small volumes of treated 2%

KCl water that had been spotted across the perforations.Bottomhole temperature and pressure were monitored duringinjection and subsequent decline.

3.Flow the wells for a period to test productivity.4.Fracture stimulate the wells down the casing and liner.5.Clean up the fracture through the casing, kill the well,

run 2 3/8in tubing and kick the well off. Continue clean up andplace on production.

Example 1:

The 3 in liner was perforated in a clean and relatively

homogeneous sand from 13,909 ft to 13,922 ft (Figure 2) with500 psi on the casing. The bottomhole pressure stabilized at6,471 psi and was assumed to be reservoir pressure. Thegauge was raised 700 ft into the 5 in intermediate casing.The well was then broken down with 49.6 bbls of treated 2%KCl water. The bottomhole pressure decline, corrected forhydrostatic offset, was monitored for 45 minutes beforepulling the gauge.

The bottomhole pressure record of the breakdowntreatment was used to estimate the stress profile and formationpermeability. The square root of time versus the pressuredecline plot shown in Figure 3 indicates a closure of 8,830 psiThe bounding stresses determined from injection pressurematching and the rock properties used for the pressure matchare shown in Table 1. The simulated versus measured

bottomhole pressure match is shown in Figure 4.The pressure decline was analyzed and after-closure radial

flow was identified. Flow regime determination was made byplotting the pressure difference, P(t) - Pr, and pressurederivative versus the respective flow regime time function (i.e.FRor FL

2) on a Log-Log plot (Figure 5). This plot results in a slope for linear-flow and a unit slope for radial-flow because

FL2FR shortly after the closure time. A derivative overlying

the data on a unit slope is a confirmation of a radial-flowregime. A -slope derivative displaced from by a factor oone half from the linear-flow slope is a confirmation of linearflow. For ease in identification, unit slope and half slope linesare included on the respective plots. From this analysis the

presence of radial-flow was confirmed.The time function is equivalent to Horner time and

therefore, time increases to the left for plots using thisfunction. From the Cartesian-radial-flow plot the Horneanalysis (Figure 6) gives a slope of 3,504 psi and a reservoirpressure (y-intercept) of 6,209 psi. Employing Eq. 3, with theinjected volume of 49.6 bbls and a closure time of 9.4 minutes(8,830 psi), gives a transmissibility of 377 md-ft/cp. Using alog-indicated net height of 13 ft and a gas viscosity of 0.026cp, the formation permeability is inferred to be 0.75 md.

The last part of the decline data in Figure 5 deviates fromradial behavior (i.e., flattening pressure difference andsteepening derivative). This behavior is often observed and

likely results from wellbore fluid expansion and loss of freecommunication between the wellbore and formation. For thicase the behavior begins at a pressure of about 6,800 psi thatreflects an effective stress of about 2,000 psi (relative toclosure pressure) acting to close the unpropped fracture. Incontrast to conventional testings early-time wellbore effectthis behavior could be termed a late-time wellbore effect.

With stresses, reservoir pressure and permeabilitydetermined, an optimized fracture treatment was designedFigures 7 and 8 show the three year Net Present Value versusfracture half length and production rate versus timerespectively. Tables 1 and 2 list the input parameters. Figure7 indicates a NPV optimum propped half length 800 ft to

1,000 ft.Intermediate Strength Proppant was selected because lowe

quality proppants and bauxite resulted in lower NPVs. Thelower quality proppants did not achieve adequate CfDwhile theISP provided a CfD of approximately 10 making the use obauxite unnecessary. A delayed crosslinked borate fracturingfluid with a guar polymer loading tapered from 35 to 30pounds per 1,000 gallons was used along with an aggressivebreaker schedule for this 265o F reservoir. Immediate forced


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closure was used and complete flowback was started within anhour of job completion.

The treatment execution and simulated bhp match areshown in Figure 9. The pressure match was made using theproperties determined from the breakdown, pressure matchingexercise. The predicted propped length is 902 ft, the grossheight is 238 ft and the fracture conductivity is 1,690 md-ft.

As seen in Figure 8, the actual production is trending to thatpredicted by the NPV job sizing procedure for the first fivemonths. The accelerated decline rate after 150 days ofproduction is related to the establishment of production in anoffset well at 125 days of production.

After three months of production the well was shut in for apressure build-up test. A five day analysis indicated linear-flow so the bombs were rerun. After 9 days the transition toradial-flow began (Figure 10). A homogeneous reservoir,finite conductivity model was used to match the data. Thepermeability was estimated to be 0.47 md versus the 0.75 mdfrom the decline analysis. The conductive half length was 786ft versus 902 ft from pressure matching and the fracture

conductivity was estimated to be 3,200 md-ft versus 1,690 md-ft from pressure matching. Depletion was evident from thereservoir pressure of 4,891 psi determined from the well testversus the 6,209 psi estimated from the radial-flow analysis.

Without an a priori knowledge of permeability, the welltest interpretation is more qualitative than quantitative sincethe start of the transition to radial flow is open tointerpretation. A sensitivity analysis indicated that a variety ofmodels could match the well test reasonably well with resultsvarying as follows: permeabilities ranging from 0.43 md to0.81 md, fracture lengths of 601 ft to 937 ft and fractureconductivities from 206 md-ft to 7,110 md-ft. What isdefinitive is the presence of a fracture length and conductivity

that are consistent with the parameters used for the NPV-baseddesign.

Example 2:

The 3 in liner was perforated from 13,831 ft to 13,853 ftwith 525 psi on the wellhead. Figure 11 indicates that thissand section was thicker and more heterogeneous than for thefirst example. After perforating the bottomhole pressuredeclined to 6,455 psi. This initial estimate of reservoirpressure was thought to be high because pressurecommunication with the first well 1,731 ft away, wasanticipated. The gauges were then raised into the intermediatecasing and the well was broken down with 34.5 bbls of treated

2% KCl water. The bhp decline, corrected for hydrostaticoffset, was monitored for 40 minutes.

After-closure analysis indicated that radial-flow developedduring the decline as evidenced by the unit slope in Figure 12.The slope from the Cartesian-Horner plot (Figure 13) was5,663 psi with a reservoir pressure estimate (y-intercept) of5,671 psi. Given the injected volume of 34.5 bbls and theclosure time of 8.16 minutes (9,365 psi, discussed later), atransmissibility of 187 md-ft/cp was found from Eq. 3. With a

log-indicated net height of 22 ft and a gas viscosity of 0.025cp, the formation permeability was determined to be 0.21 md.

A 5 day pressure buildup was performed after flowing thewell for 24 hours. Infinite-acting homogeneous reservoibehavior was indicated (Figure 14) with a permeability of 0.24md and an initial reservoir pressure of 5,897 psi.

While the permeabilities are in agreement, the reservoir

pressures are not. Depletion from one days production iunlikely as subsequent well performance indicates a largedrainage area. However, in this zone the logs indicate twodistinct layers of varying porosity that could have experienceddifferential depletion from the offset well.

Lower reservoir pressure is likely in the thicker, higherporosity (and presumed higher permeability) layer. During thewell test, the higher reservoir pressure of the bottom lenswould manifest itself. But the upper lens likely received thebulk of the injected fluid during the breakdownConsequently, the transient from the pressure declinefollowing the breakdown would be dominated by the uppersand lens that has likely experienced depletion. Hence, a

lower value for reservoir pressure is not unexpected from theafter-closure analysis.

The well test indicates that the stabilized bottomholepressure taken after perforating (6,455 psi) is not a goodindication of reservoir pressure (5,897 psi from the build-up)This was true for the first example as well, where the postperforating stabilized bottomhole pressure of 6,471 psi is 262psi greater than the reservoir pressure of 6,209 psi determinedfrom the radial-flow analysis. We had hoped to successfullyuse the stabilized bhp following perforating as an accurateestimate of reservoir pressure. But in this environment iappears that this is not feasible without an extended post-perforating monitoring period. The pressure at the end of the

breakdown declines (6,419 psi for Example 1 and 6,106 psi forExample 2) appears to be a better estimate.

A 200 bbl, 35 lbm guar gel, delayed crosslinked boratecalibration treatment was pumped before the fracture treatmenwith the following objectives: 1. Determine fracture geometryand total leakoff coefficient from the injection and pre-closuredecline. 2. Determine spurt and closure time from the afterclosure linear-flow analysis. 3. Estimate the fracture hallength using the after-closure linear-flow analysis andtransmissibility from the breakdown post-closure analysisThen compare the length to the pre-closure analysis results. Ithe lengths are not consistent determine which parameter is inerror. Following the calibration treatment, three step

rate/flow-back tests were performed with linear gel for anindependent definition of closure pressure. Bottomholepressure was recorded throughout the injections.

Difficulty in maintaining the required constant flow ratecaused closure pressure determination from the flow-back testto be inconclusive. The step-rate tests provided moreconsistent results. Pressure versus rate plots of both step-ratesare shown in Figures 15a and 15b. The y-intercept (indicationof closure)10of the line drawn through the data points above


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the fracture extension rates (greater than 8 bpm) are 9,812 psiand 9,669 psi for the first and second step-rates, respectively.An immediate pressure drop of approximately 350 psi wasmeasured at the ISIP of the these tests, as well as all otherinjections, at all rates into this zone. An immediate 300 psipressure rise as rate is established on the step-rate tests(Figures 15a and 15b) was also noted. These rate-independent

pressure changes are possibly associated with a slightmisalignment of the fracture plane with the wellbore. Such aninclination will cause a consistent, near-wellbore pressure dropthat may not be eroded, even during proppant injection.

It is beyond the scope of this paper to determine the sourceof this pressure loss, but it suffices to say that the high netpressures (1,370 psi on the 200 bbl calibration treatment and2,300 psi at the end of the propped treatment) generatedenough width to prevent problems with proppant entry.

Since the near-wellbore pressure drop does not affect thefar-field geometry of the fracture, it can be subtracted from they-intercept of the line drawn through the pressure points abovethe fracture extension rates of the step-rate tests. When

subtracting this excess pressure, closure pressures of 9,439 psiand 9,317 psi are obtained. These generally agree with theclosure pressure estimate of 9,311 psi determined from thesquare root of time plot of the calibration treatment decline(Figure 16).

In order to perform a valid linear-flow analysis, thecrosslinked calibration treatment must be pumped into anundisturbed reservoir. This necessitated that the calibrationtreatment be the first injection. Since the well was notproduced flowed following the build-up, the calibrationtreatment was initiated with the wellbore full of gas.

The unanticipated consequence of the injection of 313 bblsof wellbore gas (more than the gelled fluid) was the corruption

of the after-closure, linear-flow analysis. Because of its highleakoff, the gas created a short, inefficient fracture thatproduced a radial transient near the wellbore. The lineartransient from the crosslinked fluid injection was super-imposed on the pre-existing radial transient. This resulted in acorruption of the linear-flow analysis that precluded adetermination of spurt.

In spite of the corruption of the linear-flow analysis, avalue of closure pressure from the reservoirs perspective wasstill attainable from the after-closure analysis. By fixingreservoir pressure at the value of 5,671 psi determined fromthe radial-flow analysis and varying closure pressure until thebest fit was achieved on the Log-Log flow identification plot, a

closure of 9,365 psi was attained (Figure 17). Finally, a G-Function analysis11 of the pre-closure decline complementedthe closure estimation of 9,365 psi (Figure 18). Consideringthe five independent sources of closure pressure ranging from9,439 psi to 9,311 psi, a value of 9,365 psi was selected.

The G-Function analysis of the calibration treatments pre-closure decline yielded a gross height of 61 ft, a hydraulic halflength of 132 ft and a total leakoff coefficient of 0.015 ft/in 0.5.The rock mechanic parameters from the first example were

used for this analysis. Using these parameters, and the abovevalues of total leakoff coefficient and closure pressure, thecalibration treatment was simulated. Figure 19 indicates that agood bottomhole pressure match was obtained. As with thestep-rate tests, a near-wellbore pressure drop of 370 psi ispresent. Since this pressure drop does not affect the fracturegeometry it was ignored in the bottomhole pressure matching

exercise. Therefore, the simulated bhp is approximately 350psi lower than the measured bhp during injection. The ISIPsdo agree. Finally, the same parameters were used to accuratelymatch the measured bottomhole pressure during the treatedwater breakdown as well.

A fracture optimization exercise was performed using thesame economic parameters as in the first example. Theparameters determined from the after-closure analysis (porepressure, permeability and closure) and the pressure matchingexercise (closure, bounding stresses and leakoff) on thecalibration treatment were used as well. Figures 20 and 2show the three year NPV and predicted well performancerespectively. A fracture length of 800 ft to 1,000 ft was

determined to be optimum.The treatment execution and pressure match (taking into

account the 350 psi of excess pressure) is shown in Figure 22The predicted propped length was 798 ft, the gross height was195 ft and the fracture conductivity was 1,183 md-ft. The firsthree months of post-fracture production agrees well with thapredicted by the NPV analysis. The subsequent, lower rateare likely a sign of depletion from the offset well and otherwells that have since been completed in the reservoir.

Summary of Field Applications:

Formation permeability was attained from after-closurepressure declines following small treated water injections in

both wells. These values were compared to permeabilitiedetermined from conventional pressure build-up tests withgood agreement. For the case with only a post-fracture buildup, the well test permeability is qualitative since radial-flowwas not fully developed. For the case where a pre-frac buildup was performed the permeabilities were within 15%.

Although linear-flow was attained on the crosslinkedcalibration treatment, a complete analysis was impossiblebecause of the gas in the wellbore at the time of injectionAlthough values for spurt and fracture length wereunattainable, an estimate of closure from the reservoirsperspective was still garnered. This estimate agreed well withvalues determined from conventional decline analyses. By

coupling the linear and radial-flow analyses with the preclosure analysis an optimized fracturing treatment wasdesigned.

Real time engineering of the treatments assured successfulfracture placement. Post-fracture production has agreed withthat predicted by the optimization exercises until depletioneffects were encountered. The fracture length from the postfracture well test in the first example agreed with the fracture


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simulators prediction of half length based on pressurematching as well.

Guidelines for Field ApplicationThe attainment of linear and/or radial-flow regimes is requiredfor the successful application of after-closure analysis. Thefollowing are guidelines for improving the likelihood of

achieving these regimes. Although conducive to successfulafter-closure analysis, these guidelines are not strict rules. Asthe technology develops more definitive procedures willevolve.

1. Unless bottomhole shut-off valves are employed, thereservoir pressure should ideally be greater than thehydrostatic pressure of the wellbore fluid. Vacuum-inducedfluid injection violates the no-flow assumption of the analysis.Analyses are possible for reservoirs with pore pressure belowthe hydrostatic pressure of the completion fluid. The secondexample successfully determined transmissibility even thoughthe reservoir pressure of 5,671 psi was less than the 2% KClwater hydrostatic pressure of 6,065 psi (Figure 13). Including

the hydrostatic head on these figures will flag the user not touse pressure data after the well has gone on a vacuum.

2. The wellbore must be free of gas. Otherwise, incorrectvalues for hydrostatic pressure and injected volume would beutilized. As noted in the second example, the pressuretransient from wellbore gas will adversely affect theinterpretation. This necessitates circulating the gas from thewellbore or injecting the gas and shutting down as the fluidreaches the perforations. An extended period would berequired to allow the pressure transient to dissipate beforeliquid injection can resume. If a relatively small gas injectionoccurs ahead of the liquid injection the analysis may not becorrupted. Such an event would occur if gas is circulated from

intermediate casing but remains in a short liner.3. Reservoir pressure should be known a priori for

competent interpretation of both flow regimes. Specifyingreservoir pressure eliminates uniqueness considerations fromthe analysis. For these examples, post-perforation pressurestabilization has proven to over-estimate reservoir pressure.Perhaps this technique can be successful in reservoirs of highermobility or if balanced perforating is employed. Anothersource of reservoir pressure is a stabilized surface pressurewith a known fluid level.

4. In deep, hot reservoirs, bottomhole gauges will berequired because wellbore fluid expansion from decreasingpressure and heating of the fluid will decrease the hydrostatic

pressure. Excessive expansion of the fluid may also violatethe no-flow condition and could require bottomhole shut-off.

5. Large zones of varying lithology will reduce thelikelihood of successful application of the technique. Theanalysis assumes equal fracture penetration andcommunication over the complete interval. Therefore, it isbest suited for relatively thin, or somewhat homogeneouszones.

6. It is unlikely that both flow regimes will be presenduring the same decline. Radial-flow begins at more than 10times the shut-in period that linear-flow ends. This generallyrequires the use of a small, low rate, completion fluid injectionfor radial-flow analysis and a subsequent gelled fluid injectionfor linear-flow analysis.

7.Volume has minimal effect on the time for developmen

of radial-flow (see next guideline). However, a minimumshould be pumped to insure accuracy of the volume injectedthrough the perforations because the calculated transmissibilityis proportional to volume (Eq. #3).

8.To attain radial-flow within a reasonable time frame usea fluid with minimal fluid loss control and adhere to thefollowing rate criterion

q bpm xkh

p pc r( ) ( ) 5 10 6

(10)

If fluid loss is controlled by the reservoir, this guidelineprovides a dimensionless time greater than one, i.e., beginningof radial-flow.

The guideline dictates some a priori estimate of reservoirpermeability for designing an injection test. For lowpermeability reservoirs this necessitates low injection rates. Amobility greater than 5 to 10 md/cp should be considered as aguideline to positively obtain radial-flow with a relativelyshort monitoring period.

Conclusions1. This study confirms the feasibility of the after-closure

method to determine transmissibility in normallypressured, dry-gas reservoirs of moderate permeabilityPressure build-up tests verified the accuracy of thepermeability determined from the after-closure radial-flowanalysis.

2. After-closure analysis coupled with pre-closure pressureinterpretation has been shown to be effective for designingNPV-optimized fracturing treatments.

3. Although the linear-flow analysis did not determine spurtloss or fracture length to complement the calibrationtreatment for the second example, the linear-flow analysisconfirmed the selection of the closure pressureEmploying methods to avoid bullheading significanwellbore gas or completion fluid volumes relative to thegelled fluid are necessary for a comprehensive linear-flowinterpretation.

4. Optimized fractures were designed and placed in thereservoir to achieve the design goals as evidenced by thepre-depletion, post-fracture production matching thapredicted by the optimization technique. The examplewith a post-fracture build-up also confirms the presence ofa fracture similar to that expected from the fracturedesign.


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AcknowledgmentsThe authors wish to express their gratitude to Marc Pearcy forhis analysis of the well tests and Jim Hall for his description ofthe depositional environment. Appreciation is expressed toBarrett Resources and Schlumberger for permission to publishthis work.

References1. Nolte, K.G., and Smith, M. B., Interpretation of

Fracturing Pressures, JPT (Sept. 1981) 1767-75.2. Nolte, K.G., Determination of Fracture Parameters from

Fracturing Pressure Decline. Paper SPE 8341, 1979 SPEAnnual Technical Conference and Exhibition. Las Vegas,NV, Sept. 23-26.

3. Nolte, K.G.: Fracturing Design Considerations Based onPressure Analysis, paper SPE 10911. 1982 [andpublished as two papers in SPEFE (Feb. 1988) 22].

4. Meng, H-Z, and Brown, K.E., Coupling of ProductionForecasting, Fracture Geometry Requirements andTreatment Scheduling in the Optimum Hydraulic Fracture

Design, paper SPE 16435. 1987.5. Cleary, M.P., Doyle, R.S., Teng, E.Y., Cipolla, C.L.,

Meehan, N.D., Massaras, L.V., and Wright, T.B., MajorNew Developments in Hydraulic Fracturing, withDocumented Reductions in Job Costs and Increases inNormalized Production, paper SPE 28565, 1994 SPEAnnual Technical Conference and Exhibition, NewOrleans, LA, Sept 25-28.

6. Gu, H., Elbel, J.L., Nolte, K.G., Cheng, A.H-D. andAbousleiman, Y.: Formation Permeability DeterminationUsing Impulse Fracture Injection, paper SPE 25425,1993 Production Operations Symposium, Oklahoma City,OK, Mar21-23.

7. Abousleiman, Y., Cheng, A.H-D. and Gu, H.: FormationPermeability Determination by Micro or Mini-HydraulicFracturing, J. Ener. Res. Tech. (June 1994) 104.

8. Nolte, K.G., Maniere, J.L. and Owens, K.A.: After-Closure Analysis of Fracture Calibration Tests, paperSPE 38676, 1997 SPE Annual Technical Conference andExhibition, San Antonio, TX, Oct5-8.

9. Carslaw, H.S. and Jaeger, J.C.: Conduction of Heat inSolids, 2ndEd. 1959, Oxford University Press, GreatBrittain.

10. Rutqvist, J. And Setphansson, O., A Cyclic HydraulicJacking Test to Determine the in situ Stress Normal to aFracture, Int. J. Rock Mech. Min. Sci. & Geomechn.

Abstr. Vol. 33(7), 1965, 695.11. Castillo, J.L., Modified Fracture Pressure Decline

Analysis Including Pressure-Dependent Leakoff, paperSPE 16417, 1987.

Table 1

P3D Simulation Stress Data - Example #1

Depth(ft)

Frac. Grad.(psi/ft)

Modulus(psi)

PoissonsRatio

Frac. Tough(psi-in0.5)

13,850 0.835 3.426E6 0.35 100013,907 0.635 5.028E6 0.25 500013,924 0.835 3.426E6 0.35 1000

Table 2

NPV Input Parameters - Example #1

Reservoir Pres. 6,209 psi Pump Rate 25 bpmPorosity 12 % Gas Revenue $2.00 mcfPermeability 0.75 md Interest Rate 8 %Gas Gravity 0.7Fixed Costs $75,000Gas Viscosity 0.026 cp ISP Cost $0.58/lbGas Saturation 75 % Fluid Cost $0.35/galNet Thickness 13 ft Damage Factor 0.4Flowing TBG Pres. 1,500 psi Drainage Area 320 AcTubing Size 3 in


8/12


Figure 2 - Morrow Example #1 Porosity Log

0 1.5 3.0 4.5 6.0 7.56000

7000

8000

9000

10000

-1500

-1200

-900

-600

-300

0

Closure Pressure = 8,830 ps Derivative

Sqrt of Shut-in Time (sqrt(min))

Bo

ttom

Ho

lePr

essure-ps

i

De

rivative

L1-S

L1-EL2-S

L2-E

Figure 3 - Example #1 Closure Pressure Determination

0 3 6 9 12 150

2500

5000

7500

10000

12500

0

2

4

6

8

10

Measured BHP

Treating Pressure

Injection Rate

Simulated BHP

Time min

Pressure

(psi)

Rate(b

bl/min)

Figure 4 - Example #1 Breakdown Simulation

Flow Regime Identification Plot

1295

593

100

1000

10000

0.01 0.1 1Time Function F_R

Pres.

Difference

(psi

)

P-Pr Pres Der

Figure 5 - Example #1 Brkdn Flow Regime Identification

Radial Flow Ho rner Analysis

7504

6209Phyd

6000

6500

7000

7500

8000

8500

9000

0 0.2 0.4 0.6 0.8 1F_R

BHP(ps

i)

Figure 6 - Example #1 Breakdown Horner Time Analysis


9/12


$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

0 200 400 600 800 1000 1200

Propped Half Length (feet)

NPV($)

Figure 7 - Morrow Example #1 3 Year NPV

100

1000

10000

0 200 400 600 800 1000 1200

Time (days)

Gas

Ra

te(mc

f/d)

NPV Rate mcf /dActual Rate mcf/d

Radial Rate mcf/d

Figure 8 - Morrow Example #1 Production Rate

70 80 90 100 110 120 130 140 150 1600

2500

5000

7500

10000

12500

15000

0

5

10

15

20

25

30Treating Pressure

Slurry Rate

Simulated BHP

Calculated BHP

BH Prop Conc

Time min

P

ressure

(ps

i)

Figure 9 - Morrow Example #1 Fracture Treatment

Figure 10 - Example #1 Post-Frac Pressure Build-Up

Figure 11 - Morrow Example #2 Porosity Log


10/12



1428

680

100

1000

10000

0.01 0.1 1Time Function F_R

Pres.

Difference(psi)

P-Pr Pres der

Figure 12 - Example #2 Brkdn Flow Regime Identification

Radial Flow Horner Analysis

7103

5671

Phyd

5600

6100

6600

7100

7600

8100

8600

9100

9600

0 0.2 0.4 0.6 0.8 1F_R

BHP(ps

i)

Figure 13 - Example #2 Breakdown Horner Analysis

Figure 14 - Example #2 Pre-Frac Pressure Build-Up

BHP vs Rate of 1st Step Rate

0 5 10 15 20 256000

7000

8000

9000

10000

11000

Rate - bbl/min

Bo

ttom

Ho

lePressure-ps

i

L1-S

L1-E

L2-S

L2-E

Figure 15a - Closure = 9,439 psi (9,812 psi - 373 psi)

BHP vs Rate of 2nd Step Rate

0 5 10 15 206000

7000

8000

9000

10000

11000

Rate - bbl/min

Bo

ttom

Hole

Pressure-ps

i

L1-S

L1-E

L2-S

L2-E

Figure 15b - Closure = 9,317 psi (9,669 psi - 352 psi)


11/12


0 1.5 3.0 4.5 6.0 7.56000

7000

8000

9000

10000

11000

12000

-1000

-750

-500

-250

0

Closure Pressure = 9,311 psi Derivative

Sqrt of Shut-in Time (sqrt(min))

MeasuredBHP(psi)

Derivative

L1-S L1-E

L2-S

L2-E

Figure 16 - Example #2 Calibration Closure = 9,311 psi


1930

1580

100

1000

10000

0.1 1 10Time Function F_L^2

Pres.

Difference

(ps

i)

P-Pr Pres Der

Figure 17 - Example #2 Calibration Treatment Linear

Flow Regime Identification for Closure Pressure

0 0.5 1.0 1.5 2.06000

7000

8000

9000

10000

11000 -2500

-2000

-1500

-1000

G -Function C losu re = 9,365 psi D eriv ativ e

G Function

MeasuredBHP(psi)

L1-S

L1-E

L2-S

L2-E

Figure 18 - Calibration Treatment G Function Analysis

0 5 10 15 20 25 30 350

4000

8000

12000

0

10

20

30

Treating Pressure

Measured BHP

Injection Rate

Simulated BHP

Time (min)

Pressure

(ps

i)

Rate(bbl/min)

Figure 19 - Simulation of Calibration Treatment


12/12


$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

0 200 400 600 800 1000

Propped Half Length (feet)

NPV(

$)

Figure 20 - Morrow Example #2 3 Year NPV

100

1000

10000

0 200 400 600 800 1000 1200

Time (days)

Gas

Ra

te(mc

f/d)

NPV Rate mcf /d

Actual Rate mcf/d

Radial Rate mcf/d

Figure 21 - Morrow Example #2 Production Rates

0 10 20 30 40 50 60 700

3000

6000

9000

12000

15000

0

5

10

15

20

25

30Treating Pressure

Slurry Rate

Simulated BHP

Calculated BHP

BH Prop Conc

Time (min)

Pressure(psi)

Figure 22 - Morrow Example #2 Fracture Treatment

field application of after-closure analysis of fracture calibration tests

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