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Copyright 2004, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the SPE Annual Technical Conference andExhibition held in Houston, Texas, U.S.A., 2629 September 2004.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in a proposal 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 at

SPE 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 a proposal of not more than 300

words; illustrations may not be copied. The proposal must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abst ractThe primary objective of hydraulic fracturing is to create apropped fracture with sufficient conductivity and length tomaximize or at least optimize well performance. In permeablereservoirs where transient flow is short lived, a fracture with aDimensionless Fracture Capacity, FCD, of 2 is required to meetthe design objective. In low permeability formations wheretransient flow can be extensive and where fracture fluidcleanup requires additional conductivity, an FCD in excess of10 is desired. As a result, reservoir permeability becomes/is akey fracture design and analysis parameter. In higherpermeability applications, permeability is determined simply,inexpensively, and routinely through conventional well testingtechniques. Conventional well testing in tight formation gasreservoirs has not been proven as effective, can be expensive(cost of lengthy tests and production deferment), and is quitesimply not routinely utilized. These reservoirs are often nonproductive without fracture stimulation and post fracturestimulation testing requires extensive shut-in time as the timeto pseudo radial flow is proportional to the square of thefracture half-length. As a result, the development and routine

use of any technique to determine permeability in these tightformation gas reservoirs has great value.

In addition, without adequate well testing techniques andcapabilities in tight gas reservoirs, the engineer is left with theuse of log derived values of permeability which can oftenoverstate in-situ permeability by factors of five to ten.Determination of in-situ permeability not only aids the wellcompletion and stimulation but can be used to calibrate the logand core derived estimates of permeability improvingperformance predictions and field development. Prior papershave developed the use of After Closure Analysis techniquesin permeable reservoirs, this paper will show the application

of this technique to several tight gas formations in NorthAmerica.

This paper will demonstrate the following:1) The effective application of this technique in

tight gas formations in the U.S. and Canada,2) Develop a cost effective and operationally

simple means of collecting and analyzing thedata,

3) Compare and contrast the technique to othermethods of determining permeability in tighformation gas reservoirs, such as impulsePerforation Inflow Diagnostic (PID), ClosedChamber Drill-Stem Tests (CCDST), post-fracbuild-up, production decline analysis, ModularDynamic Formation Tester (MDT).

4) Show the application and value of calibrating logand core-derived permeability with in-situmeasurements for improved well performancepredictions.

IntroductionKnowledge of reservoir permeability and pressure is importanto field development. Such knowledge prior to welcompletion and hydraulic fracture stimulation is especiallycritical to optimum well performance and is thereforedesireable. In higher permeability applications, permeability isdetermined simply, inexpensively, and routinely throughconventional well testing techniques. Conventional weltesting in tight formation gas reservoirs has not been provennearly as effective, can be expensive, and perhaps mostimportant is, not timely enough for completion and fractureoptimization, and as a result is not routinely utilized.

Tight gas reservoirs are often non productive withoufracture stimulation and post fracture stimulation testingrequires extensive shut-in times. As a result, the developmentand routine use of any technique to determine permeabilitypre-frac in these tight formation gas reservoirs has great value

Conventional pressure transient analysis methods have along history in the ground water and petroleum industries andanalysis techniques with application to hydraulically fracturedwells has a shorter but equally illustrious theoretical andapplication history with just some of the noted papersidentified here1-8. These works and others established afoundation for subsequent advances in many areas of the

SPE 90865

Application of After-Closure Analysis Techniques to Determine Permeability in TightFormation Gas ReservoirsLarry K. Britt, NSI Technologies, Inc., Jack R. Jones and J. Harmon Heidt, BP America, Inc., Imtiaz Adil, Patrick Kelly,Dan Sparkes, and Bruce Collin, BP-Canada Energy Company

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2 Larry K. Britt, Jack Jones, Harmon Heidt, Imtiaz Adil, Patrick Kelly, Dan Sparkes, and Bruce Collin SPE 90865

petroleum industry including hydraulic fracturing of tightformation gas wells for which this paper is focused.

Ramey et al9 provided a complete discussion of DSTapplications of the Slug Test in 1975. The work included thedevelopment of additional typecurves and was included in theEarlougher Monograph10 in 1977. Fenske11 showed that the

pressure behavior for a well that was flowed for a short periodof time would match the slug test type curves. In addition,numerous authors12-15 have shown that the fluid withdrawalcan be considered to be an instantaneous source if the well isproduced for a short period of time as compared to the shut-intime, This assumption has led to the development of impulseand slug testing for determination of permeability.

Within the last decade, several methods have beendeveloped to determine permeability from pre-frac diagnosticinjections. These methods fall into two main categories; pre-closure and after-closure methods. The pre-closure methodswere initially published by Mayerhofer et al16-18and advancedby Valko and Economides19-21, Ispas et al22, and Craig et al23-25. Though these techniques could be used to determinepermeability for specific applications their broad applicationhas been hindered by the complex interactions between thefracture and reservoir during fracture closure and the methodssensitivity to fracture dimensions, rock properties, andreservoir pressure considerations. The sensitivity to thesereservoir and geomechanical properties was well documentedby Ispas et al22.

An alternate approach is the use of an Impulse-FractureIinjection Test and analysis of the post-closure pseudo-radialflow period. Evaluation of this flow regime, allows for thedetermination of reservoir transmissibility, flow capacity, andreservoir permeability. The Impulse-Fracture Iinjection Test issimilar to more conventional well test methods, such as the

slug test, closed chamber DST, and impulse test26-35. In thesetests, a small volume of fluid is injected or produced from thereservoir to create a pressure perturbation that is evaluated todetermine the reservoir flow properties.

Like the slug test or the more conventional impulse test thetheory and analysis of the Impulse-Fracture Iinjection Test arebased on an instantaneous source solution to the diffusivityequation. When the injection period is short as compared tothe shut-in time, the injection can be considered as aninstantaneous source, the pressure response approaches 1/t andthe reservoir parameters can de determined. The Impulse-Fracture Iinjection Test and After-Closure Analysis techniqueto evaluate radial flow was developed and advanced by Gu et

al36

and Abousleiman et al37

. This latter paper also developedapproximations for the early time pseudo-linear flowregime. Nolte et al38-39, and Guirajani et al40 extended theanalysis of the pseudo-linear flow regime further. These worksshowed how the after-closure analysis of impulse-fractureinjection tests when used with the standard fracture pressureanalysis techniques of Nolte41-42 and Nolte and Smith43comprehensively addresses all aspects of fracture evaluation.The combined evaluation estimates the reservoir parameters(transmissibility and reservoir pressure) as well as thoseaffecting fracture behavior (fluid loss, stresses, and formationcompliance). Thus, all of the parameters required for

optimization of fracture treatments can be determined prior tothe fracture stimulation.

Talley et al44, Chipperfield et al45, and Gulrajani et al4

addressed field applications of the Impulse-Fracture IinjectionTest and techniques and procedures for successful/economicapplication. All of these papers deal with impulse-fracture

injection testing in permeable reservoirs. Application of thistechnique to wells in tight formation gas reservoirs has beenlimited.

Conventional well testing is also very limited in tighformation gas wells, since these wells often produce little orno gas prior to fracture stimulation. In contrast, since pre-fracfluid injections are routinely utilized by the industry tobreakdown formations and gather pre-fracture data, theincremental cost of performing an Impulse-Fracture IinjectionTest and subsequent After-Closure Analysis is often less thanconventional well test methods since there is no requiremenfor additional equipment and flow to sales is not furtherpostponed. In addition, because the Impulse-Fracture InjectionTest and After-Closure Analysis technique is an injection testprocedure, it does not require the well to flow prior to thefracture stimulation for analysis. Thus, this technique hassignificant potential for application in tight formation gasreservoirs.

Finally, any successful permeability test for applicationto tight gas reservoirs must provide reliable and timely resultscost effectively with some level of operational simplicity forroutine application. Each of these objectives is achievable withthe Impulse-Fracture Injection Test in tight formation gasreservoirs as shown by the following series of case histories.

DiscussionThe subsequent sections detail three field applications of

impulse-fracture injection testing and after closure analysis forthe determination of reservoir pressure and permeability intight formation gas reservoirs in North America.

Case History 1: TFG Formations, Canadian RockiesGeologic Setting:

The first two case histories encompass a series of tightformations in the Western Canadian Sedimentary Basin. Oneof the formations in this evaluation is a widespread sandyconglomerate. The gross zone is twenty-to-thirty meters thickand persistent throughout the study area; net-to-gross paythickness is typically greater than 0.7. Within the zone, thedepositional environment is expected to result in large latera

variability in reservoir character on the scale of tens ofmeters.

Core and log analysis data show characteristics consistenwith a tight gas reservoir. Porosities range from two to sixpercent. These unusually low values of porosity result fromthe solid pebbles combined with the more porous sand matrixInsitu, klinkenberg permeabilities from core range from five-to one-hundred microdarcies. Average water saturation fromlogs is calculated at around thirty percent.

In addition to this horizon a package of tidally-influenceddeltaic, stacked and isolated fluvial channel sands were alsoincluded in this analysis. Well logs show interbedded

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SPE 90865 Application of After Closure Analysis Techniques to Determine Permeability in Tight Formation Gas Reservoirs 3

sandstones and shales with thin coal beds, lacking regionallycorrelative surfaces or clearly-defined depositional trends.

These sandstones are poorly- to moderately-sorted, fine tocoarse-grained litharenites. They have been highly compacted,and extensively cemented by silica. Reservoir quality rangesfrom poor to very poor. Net clean sand thicknesses range up to

40 meters in the east, but thicken westward into the fore deep.Insitu, klinkenberg permeabilities from core range from one-to fifty microdarcies and average water saturation from logs iscalculated at around twenty five percent.

Neither of these formations in the area produce as aconventional reservoir, except in isolated locations.Occasionally, an anomalous development of secondaryporosity in these sands yields a high-quality gas well, whichdrains a very small area. Tests elsewhere indicate very poorreservoir quality.

Formation Permeability Testing Chronology:This first case history shows the chronological development ofa viable testing methodology for determining formation

permeability in tight formation gas reservoirs. Though thechronology encompassed several wells and numerousformation intervals all were extremely low permeability drygas completions. Further, the chronological development of atesting procedure started first with the more conventionalpressure transient techniques to develop an understanding ofreservoir permeability. Theses tests consisted of aconventional post frac build-up test, production declineanalysis, Perforation Inflow Diagnostic (PID), an impulseinjection test with nitrogen, and a PID/Closed Chamber Drill-Stem Test (CCDST).

Each of these conventional testing techniques failed topass the criteria for a successful tight gas permeability test

as they failed to provide timely, cost effective, reliable resultswith some degree of operational simplicity. For example, thepost frac build-up test and production decline analysis hadfairly reliable results after numerous iterations but failed toprovide the information in a timely fashion that could beutilized for the completion and fracture design, optimization,and execution. The other techniques simply failed becausegood wellbore-reservoir communication was not established.As a result, not until the impulse-fracture injection tests wereconducted were the desired permeability test objectivesachieved with reduced shut-in times and costs. Modificationsto the technique further reduced both shut-in times and coststo obtain good reliable reservoir permeability in these tight

formation gas reservoirs.The subsequent sections will detail the testing chronologyused in the Western Canadian Sedimentary Basin to determinereliable estimates of reservoir permeability. This chronologywill include a discussion of the methods employed,operational procedures, and costs associated with the tests. Asummary of the tests conducted, results, costs, and anassessment of the successful permeability test criteria forapplication to tight gas are included as Table I located at theend of the paper.

Test 1: Post Frac BUT & Production Decline AnalysisThe first set of tests conducted included performing aconventional post frac build-up test and subsequent productiondecline analysis to determine reservoir permeability. A water-frac stimulation (treated water with friction reducer andnitrogen) was conducted on this well with 12.6 mkg of

proppant placed. After the fracture stimulation, the well wasflowed for six days to clean-up prior to performing a single-point flow and buidup test. After the initial clean-up periodthe well was flowed for 30 hours then shut-in for an extendedpressure build-up test.

Figure 1 is a plot of the rate and pressure response for thepost fracture stimulation flow and build-up test. Note, the wel

was flowed for nearly six days following the fracturestimulation, however, it is doubtful whether this extended flowperiod was adequate to totally recover the load fluids andclean-up the fracture.

Figure 2 shows the interpretation of the build-up tesresponse. As shown on this figure, a well defined unit slope inthe data prior to 0.1 hours indicates the wellbore storagedominated period. Following the transition out of thewellbore storage flow period, a fairly well developed -slopeperiod starts at about 100 hours and lasts until the end of thepressure buildup test at 326.5 hours (13.6 days). This -slopedata is indicative of a finite conductivity fracture. The finiteconductivity fracture is consistent with the low proppantconcentrations and volumes pumped in this well, the results ofthe pre-fracture design simulation, and the post-fracture matchof the treating pressures. It should be noted that no flowperiods exist in this build-up data that clearly define effectiveformation permeability or effective fracture half-length. As aresult, permeability and fracture half-length must bedetermined from an iterative model history match of the

pressure response.This lack of obvious constraint on permeability and

fracture half-length implies that there is no unique solution tothis build-up. However, the best understanding of the data canonly be achieved by investigating a number of differensolution iterations of the data. The best match of the build-uppressure data is shown in Figure 2 with the best match oformation permeability of 0.011 md while the effectivefracture half-length exhibited following the six day post fracclean-up period was 60 meters with an FCDof 5.

Figure 1: Rate and Pressure Response From Post Frac Build -Up (Test 1)

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In general, the quality of the match is extremely good.Derivative features and the pressure response are matchedwell. This fracture description (short half-length and lowconductivity) can only be viewed as consistent with thefracture design expectations if it is assumed that fracture

clean-up was not complete prior to this pressure buildup test.To test this as a possibility and to confirm the permeability

level obtained from the pressure buildup interpretation, thelong-term performance data from this well was historymatched. The match approach was to constrain thepermeability to the build-up interpretation (0.011 md) andattempt to match the performance data by gradually increasingthe fracture half-length and effective fracture conductivitywith time. This was accomplished by utilizing a threedimensional, numeric, single phase, finite difference simulator(GAS3D). This approach has been utilized extensively tomatch fracture clean-up well performance in the East Texas(Cotton Valley) Formation.47-49

Figure 3 shows the match of the first 100 days of rate-timeperformance data obtained in this manner. The simulator uses

the measured wellhead pressures, translated to bottomholepressures with the Cullendar and Smith method, as theimposed production constraints. Obviously, the quality of thematch is quite good. The fracture half-length has beenincreased from 62 m at the beginning of the simulation toapproximately 215 m at the end. This was done in three stepswith minimal fracture conductivity change (+/- 5%) requiredover time.

Though this is not a unique solution to the post fractureproduction analysis, it does provide a solution that fits both the

early time fracture clean-up period as well as later timeproduction period when the full effective fracture half-lengthis achieved. Though non-unique the production match stronglysupports the formation permeability determination of 0.011md and implies the fracture was cleaning up for monthsfollowing the fracture stimulation. Though after a number o

iterations a fairly reliable interpretation of permeability wasobtained with the post-frac build-up and production data. TheBUT and production decline analysis were not timely forcompletion and fracture optimization purposes or coseffective due to the lengthy shut-in and production deferrment

Test 2: Perforation Inflow Diagnostic (PID) TestOn the next well a Perforation Inflow Diagnostic (PID) teswas conducted. A service rig was put on the well, tubingtripped in, and the cement displacement water was circulatedout and displaced with nitrogen. A perforating and test stringwas run with Tubing Conveyed Perforating (TCP) gunsbeneath a retrievable packer to reduce the size of the wellbore

storage chamber. The guns were oriented and the packer setDue to restrictions in the packers available for the casing usedand the need for oriented perforations, this exercise was verydifficult, time consuming, and costly to execute.

Pressure gauges were connected to the drop bar used todetonate the perforating guns. A plug was set in the tubing tofurther reduce the chamber size and the well was then left shuin for 6 days. Due to low inflow, there was no definitiveindication that the guns had fired until the packer was unseand the guns tripped out of the hole. Inspection confirmed thatthe perforating guns had fired, yet poor inflow resulted. Wasthis poor inflow due to low permeability and reservoir qualityor to poor wellbore-reservoir connection? The first test took10 days total and cost $84,000 with no reliable results

obtained. In addition, this test not only failed to provide coseffective results it also failed the operational simplicitycriterion due to the elaborate test string utilized.

Figure 4 shows a plot of bottomhole pressure and gas flowrate versus time for this test. As shown, the pressure had buil

up to less than half of the anticipated reservoir pressure. Thepetrophysical permeability expectation was well in excess othe pressure response seen in this well. As a result, poorwellbore-reservoir communication rather than poor reservoirquality was viewed as the likely cause of the anamolous

Figure 2: Post Frac Build-Up Test History Match (Test 1)

Figure 4: Rate and Pressure response (Test 2)

0

2000

4000

6000

8000

10000

12000

0 20 40 6 0 80 100 12 0

Time (Hrs.)

Pr

essure(kPa)

0

0.1

0.2

0.3

0.4

0.5

0.6

P

Qsc(N)

Figure 3: Post Frac Production History Match (Test 1)

0

200

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600

800

1000

12001400

1600

1800

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0 20 40 60 80 100 120Time, Days

Rate,

MscfD

0

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pressure behavior.

Test 3: Impulse Test with NitrogenThe next test conducted on a nearby well was an impulseinjection test with nitrogen. This test was chosen because itwas believed that it would better address the wellbore-

reservoir communication issue. Once again, a service rig hadto be utilized to execute this test. In addition, an elaborate teststring was utilized to complete all functions at once asrequired. The TCP guns, packer, and other elements of the teststring were tripped in the hole. The cement displacementwater was circulated out of the hole and displaced withnitrogen. Attempts were made to orient the perforating guns inthe direction of maximum horizontal stress and set the packersimultaneously. After 2 days, the operation was stopped andthe packer was set with the guns in the incorrect orientation. Awellhead isolation tool had to be installed at surface due to thehigh pressures needed for the test. The well was pressured upwith nitrogen to well in excess of reservoir pressure. Thisdetonated the pressure actuated TCP guns and initiated the

test. Once again, there was no definitive indication that theguns had detonated as no pressure losses were visible on thesurface gauges for the first several hours. The well was leftshut in for 6 days and remained in wellbore storage throughoutthe test. As a result, no permeability information was obtained.The cost of the test was $128,000. This cost included theassociated well work described previously in addition to therental of a tree saver for the extremely high test pressures.

Test 4: Closed Chamber Drill-Stem Test (CCDST)The next test conducted was a PID/ Closed Chamber DST.This test consisted of displacing the well to nitrogen andwireline perforating with the well open to the atmosphere.Once perforated, a plug was set in the casing immediatelyabove the permanent downhole pressure gauge (restricting thesample chamber to approximately 1 m3. Once again concernsover the lack of wellbore-reservoir communication wereevident as the well built to one percent of reservoir pressure inthe first nine days and only to fifty one percent of reservoirpressure over the course of seven months. Because of low

inflow and production deferrment, the test was finally abortedat a cost of $106,000. Though operationally simple, the teswas still not cost effective and failed to provide useablepermeability results.

Figure 5 shows a log-log diagnostic plot of the pressure andderivative response for this test. As shown, it took well over

300 hours to get out of wellbore storage much less into radialflow. It should be noted that extensive simulation work wasconducted to analyze this data. The pressure response in thiswell does not fit any classic slug test type curve and as aresult, no reasonably unique solution was obtained.

Test 5: Impulse-Fracture Injection TestAs a result of the concerns over wellbore-reservoircommunication and costs that had been encountered duringthe first three more conventional tests. The next test attemptedwas an Impulse-Fracture Injection Test and After ClosureAnalysis38. This test and analysis technique has beensuccessfully applied in low to moderate permeabilityapplications throughout the world.

The test was conducted by perforating, then running in atubing string, packer, and fluid control valve to providedownhole shut-off to reduce the chamber size. The packer wasset, and fluid was injected down the tubing to break down theformation. Injection was stopped immediately afterbreakdown. Leak-off rates were sufficiently low that nopressure bleed off could be seen when the pump was stoppedbefore breakdown. A pressure testing truck could, thereforebe used for the breakdown as only very low pump rates werenecessary.

Once broken down, the well was shut-in and the pressuredecline monitored for five days. This test provided estimatesof permeability at a cost of $62,000. In addition, the

breakdown procedure ensured good wellbore-reservoicommunication.

Figure 6 shows a plot of bottom hole pressure versus timefor the breakdown and pressure decline. As shown, the wel

broke down at 39 MPa and declined to 20 Mpa over the nextfifty-seven hours.

Figure 7A and 7B show the After Closure Analysis flowregime identification plot and pseudo-radial flow analysis plotrespectively. As these figures show, pseudo-radial flow wasachieved and a reliable permeability estimate of 0.008 md wasdetermined.

The permeability interpreted from this data is viewed as areliable estimate for several reasons. First, the pressure

Figure 5: Log-Log diagnostic Plot (Test 4 CCDST)

ta, hr

Derivative,

106kPa

2/Pa.s

,

106kPa

2/Pa.s

10-1 1 101 102 103 104

10-2

10-1

1

101

102

Storage 1

Figure 6: Pressure Response From Test 5 Impulse-Fracture Injection Test

BHP(MPa)

20.0

25.0

30.0

35.0

Time (min)0 500 1000 1500 2000 2500 3000 3500

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response seen was a classic impulse test response. Secondly,the pseudo-radial flow period was readily identifiable with theanalyses procedures38 undertaken, and finally the estimates of

permeability obtained in this manner proved to be a muchbetter fit with the actual well performance. Though reliableresults were obtained, additional modifications wereundertaken to the Impulse-Fracture Injection Test procedure tomake the technique more cost effective.

Tests 6-12: Modified Impulse-Fracture InjectionDue to the good permeability results and ensured

communication between the wellbore and reservoir, the nextseries of tests consisted of conducting a modified form of theImpulse-Fracture Injection Test44. The reasons for themodifications were to reduce the costs further and to improvethe interpretability of the data. The interpreted permeability is

proportional to the total fluid injection volume so the fluidvolumes must be determined accurately which can be aproblem when injecting such small fluid volumes. On theother hand, the time to pseudo-radial flow is directly related tothe square of the fracture half-length. Double the size of thecreated fracture during the injection test and you quadrupal thetime to get to pseudo-radial flow. As a result, the test wasmodified so that the injection volume could be increased forbetter volume accuracy without creating a larger fracture. Thiswas achieved by conducting a step down injection test (shownin Table 2) as proposed and advanced by Nolte. The modifiedtest included multiple injection rates with each injection step

consisting of an equal volume of fluid injected. This mighentail, for example pumping 2 BPM (0.32 m3/min) for 1minute, 1 BPM (0.16 m3/min) for 2 minutes, 0.67 BPM (0.11m3/min) for 3 minutes, and 0.5 (0.05 m3/min) BPM for 4minutes.

Following the step down test the wells were shut-in from

two to six days until pseudo-radial flow was achieved. In all ofthe Modified Impulse-Fracture Injection Tests, reliable resultswere achieved at a fraction of the cost of the moreconventional pressure transient tests with the average cost toconduct one of these tests averaging $15,000. It should benoted that these costs include reperforating the wells, when theentire interval can be perforated and tested the costs have beenon the order of $7,000.

Figures 8A and 8B show the diagnostic flow regimeidentification plot and pseudo-radial flow analysis for one ofthe Modified-Impulse-Fracture Injection Tests, respectivelyAs shown, a definitive pseudo-radial flow period is identified(Figure 8A) and a reservoir permeability of 0.008 md isinterpreted (Figure 8B). It should be noted that the costsreported in US$ and are for an application in a semi-remotelocation. Table I summarizes the permeability test chronology

Figure 8A: Flow Regime Identification Plot (Test 7 MIFIT)

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

d

P=(P-Pi)anddP'

500

1000

2000

5000

10000

20000

50000

1/F-L^22.0 5.0 10 20 50 100 200 500

dP

dP/dP'

dP'

Figure 8B: After Closure Analysis Interpretation (Test 7 MFIT)

P(t)KPa

20000

25000

30000

FRorFL0.0 0.2 0.4 0.6

P(t)vsFR

P(t)vsFL

FR:190070.0 FL:0.0

Radial FlowP i (K Pa ) = 1 79 99 .9 7

Volume (CuM)= 2.00

M-R(KPa) = 190070.0kh/mu = 5.32

kh (md-ft) = 0.11k (md) = 0.008

P(t)KPa

20000

25000

30000

FRorFL0.0 0.2 0.4 0.6

P(t)vsFR

P(t)vsFL

FR:190070.0 FL:0.0

Radial FlowP i (K Pa ) = 1 79 99 .9 7

Volume (CuM)= 2.00

M-R(KPa) = 190070.0kh/mu = 5.32

kh (md-ft) = 0.11k (md) = 0.008

Figure 7A: Flow Regime Identification Plot (Test 5 IFIT):

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

dP=(P-Pi)anddP'

0.0

20

0.0

50

0.2

0

0.5

0

1.0

2.0

5.0

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20

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100

1/F-L^20.0020 0.0100 0.050 0.20 0.50 1.0 2.0 5.0 10 20 50 100 2 00

dP

dP/dP'

dP'

19.5

Less Smoothing Mor e Smoothing

PRes

Figure 7B: After Closure analysis Interpretation (Test 5 IFIT)

P(t)MPa

20

25

30

35

FR or FL-0.014 -0.007 0.000 0.007 0.014 0.021 0.028 0.035 0.042

P(t) vs FR

P(t) vs FL

FR:828.9 FL:0.0

Radial FlowP i (M Pa ) = 1 9. 20Volume (CuM) =0.34

M-R (MPa) = 828.9kh/mu = 0.53k h ( md -f t) = 0 .0 1k (md) = 0.003

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results, and assessment of the permeability test criteria foreach test conducted. As shown, the Modified Impulse-FractureInjection test with After Closure Analysis achieved allobjectives admirably.

Case History 2: Ricinus (Viking) Field

Geologic Setting:The Viking Formation of Southwest Alberta is a Cretaceous(Late Albian), sand-prone deposit overlying the Joli Foushale/Mannville Group and below the Westgate shale on theColorado Group. The formation can be divided into threemajor cycles, the lower two of which occur regionally with theupper cycle confined to the Bearberry, Alberta area.

The lowermost Viking cycle is dominated by sand and isregressive, consisting of two unconformity-boundedprogradational wedges comprised of storm-dominatedshoreface and offshore shelf sediments. The middle Vikingcycle is also regressive and is capped by an unconformityformed following sea-level fall and erosion into underlyingdeposits. In the Bearberry area an additional Upper Viking

transgressive cycle occurs, consisting of coarse-grained sandsand conglomerates delivered to the basin margin during thesea-level lowstand and subsequently reworked into offshorebars and tidal channels during subsequent transgression.These coarsest sediments exhibit the best reservoir quality andnow occur as E-W trending bodies within the transgressiveViking. Permeability in the Viking Formation ranges from 0.1to 10 md.

Determination of Reservoir Permeability:The second case history is an interesting comparison of the

use of the open-hole Modular Dynamic Formation Tester(MDT) and After Closure Analysis technique applied to pre-

frac diagnostic pressure decline data. The MDT estimates ofpermeability were determined prior to running productioncasing and as a result, were useful in making dry hole versusset pipe decisions. Though timely, interpretation of this datacan be highly subjective due to multiple phase flow of drillingmud filtrate and gas (this example) and the inability toestablish the correct/equivalent downhole flow rate.

The After Closure Analysis technique employed for theevaluation of the mini-frac pressure decline data though not astimely as the MDT, was still timed adequately to favorablyimpact fracture design and execution. In addition, thisexample highlights another application for the After ClosureAnalysis (ACA) Technique as a part of pre-fracture

stimulation diagnostic testing. Note, that this method ofdetermining permeability is less geared for application to trulytight formation gas reservoirs due to the time it takes toachieve pseudo-radial flow. The subsequent sections detail theevaluation of the MDT and ACA techniques employed in theRicinus (Viking) Field.

The Viking Formation in the area is an extremely complexreservoir(s) with a conglomeratic section overlying asandstone interval. The numerous thrust sheets, reservoirjuxtaposition, and interwell communication make knowledgeof reservoir pressure prior to setting pipe paramount tooptimized field development.

The Modular Formation Dynamics Tester (MDT) isperfectly fit for this purpose. The MDT is an openhole toothat is used to isolate a one-meter interval, produce and/orinject fluids, while monitoring bottomhole pressure. Thoughthe tool can be utilized to conduct flow and build-up tests or todetermine in-situ stresses, it was used in the Ricinus Field to

conduct flow and build-up tests to determine reservoirpressure and permeability.Figure 9 highlights the tool configuration used for the

Viking Formation. It should be noted that due to an eight-degree dogleg in this particular well the full tool configurationcould not be utilized. The dogleg further restricted the rigid

tool length and knuckle joints (i.e. labeled AH-107 in Figure9) were required. In addition, the tool run in the Ricinus welconsisted of a tension and compression sub (CTS-B1), atelemetry cartridge (TCC-BF), and a gamma ray sonde (SGTL). Below the knuckle joint is the power supply (MRPC), thepump off (MRPO) and flow (MRF_C) controller, and the livefluid analyzer (LFA). Below the flow analyzer are two TAMpackers (MRPA) that are one meter apart. Once run, thepackers are used to straddle the zone of interest (zero point of

Figure 9: Modular Formation Dynamics Tester (MDT)

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the tool is between packer elements), formation fluids are thenproduced or wellbore fluids injected in the formation and thepressure monitored.

Multiple packer sets, flow, and build-up tests weresuccessfully conducted in the Ricinus well of interest.However, only one of the Viking intervals tested is detailed in

this case history.Figure 10 shows the bottom hole pressure versus time

chart for two flow and build-up tests conducted using the

MDT in the Viking conglomerate. As shown, the pressure wasdrawn down from hydrostatic to 3900 KPa and built back upto 10400 KPa during the first flow and shut-in sequence anddrawndown to 4900 KPa and built up to 10300 KPa during thesecond sequence. The first flow period lasted only 5 minutesand nearly 2.5 liters of drilling mud was produced during thistime period. Subsequently, the tool was shut-in and thepressure build-up monitored for nearly an hour. Following thistest and to validate its results, the tool was opened up and anadditional 30.0 liters of drilling mud, gas cut mud, and gas

were produced during a 41-minute flow period. Next, the toolwas again shut-in and the pressure was allowed to build fornearly three hours. During this time, the pressure built fromthe instantaneous shut-in pressure of 4900 KPa to 10300 KPa.

Next, the second extended flow and build-up test wasinterpreted to determine the reservoir permeability andpressure. To evaluate the build-up test a log-log diagnosticplot and conventional horner plot were developed. Note,however,, the conventional interpretation of the data is mademore difficult because both drilling mud and gas were

produced during the extended flow period. Two methods wereemployed for the analysis of this data. First, a downhole gasflow rate was estimated and used in a conventional horneranalysis and secondly, the test was assumed to be an impulse

test even though the shut-in time to flow time (tsi/ti) ratio wasonly 4.

Figures 11A and 11B show the log-log diagnostic plot andhorner analysis for method 1. As shown, the data wastransitioning from wellbore storage to pseudo-radial flow atthe end of the test. Further, the horner analysis with thedownhole gas flow rate assumption (Method 1) indicated areservoir permeability of 0.07md.

Figure 11A: Flow Regime Identification Plot (Method 1)

dm(P)(psi^2/cpe-06)

0.5

0

1.0

2.0

5.0

10

20

50

100

200

dTeq(hours), Tp = 2188.80.0020 0.0050 0.020 0.050 0.10 0.20 0.50 1.0 2.0 5.0

Figure 12B: Impulse Analysis (Method 2)

P(t)MPa

10

11

12

13

14

FR or FL0.0 0.5 1.0 1.5 2.0 2.5

P(t) vs FR

P(t) vs FL

FR:0.4 FL:0.0

Radial FlowPi (MPa) = 9.88Volume (Liters) =30.00

M-R (MPa ) = 0.4kh/mu = 22.40k h ( md -f t) = 0 .3 4k (md) = 0.102

Figure 11B: Horner Analysis (Method 1)

m(p)(psi^2/cpe-06)

60

80

100

120

140

160

(tp+dt)/dt

200 500 2000 10000 50000 500000 5000000

P* = 10469.715 KPakh = 0.234 md-ftk = 0. 071 mdSkin = 71.456Flow Eff = 0.078

Figure 12A: Flow Regime Identification Plot (Method 2)

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

dP=(P-Pi)anddP'

0.0

100

0.0

500.1

0

0.2

0

0.5

0

1.0

2.0

5.0

10

1/F-L^20.50 1.0 2.0 5.0 10 20

dP

dP/dP'

dP'

9.9

L es s S moo th in g Mo re Smo othi ng

PRes

Figure 10: MDT Pressure Response (Repeated Flow/Build-up Tests)

Pressure(KPa)

0

4000

12000

20000

28000

Time (min)100 200 300

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Next, method 2 was employed to interpret the data. Figures12A and 12B show a flow regime identification plot andpseudo-radial flow analysis plot, respectively for the impulseassumption (Method 2). As shown the analyses resulted in anestimated formation permeability of 0.10 md.

Following the MDT, production casing was run and the

well was completed in the Viking Formation interval ofinterest and fracture stimulated. As part of the pre-frac testingon this well a fluid displacement and a mini-frac test wereconducted. Though the mini-frac test and pressure declinemonitoring was aborted prematurely due to operationalconsiderations, After Closure Analysis was applied to the fluiddisplacement pressure decline data in an attempt to determineestimates of reservoir pressure and permeability. Note, thatthis data collection utilized a dead string to monitorbottomhole pressure.

Figures 13A and 13B shows the flow regime identificationplots and the analysis of pseudo-radial flow using the After

Closure Analysis Technique, respectively. This analysisestimated a permeability of 0.13 md for this interval. Thus, allanalyses were in good agreement. It should be noted that thewell went on a vacuum shortly after the apparent pseudo-radial flow period was achieved.

Comparison of MDT to After Closure AnalysisThe Modular Dynamic Formation Tester (MDT) performedadmirably in this and subsequent wells to determine both

reservoir pressure and permeability. The true value in this toois that the required reservoir information can be obtained priorto setting pipe and completing the well. In one of the Vikingapplications, the use of the MDT tool and subsequent analysisresults precluded setting pipe and conducting completionoperations in Viking intervals that had already been depleted

by offset wells saving millions of dollars in pipe andcompletion costs. Benefits from such timely data collectionare easy to quantify.

In one application in the Viking Formation the MDTtesting cost $118,000 for multiple MDT runs and $130,154 forrig time and rental charges for a total cost of $248,154. Inanother application with fewer intervals to interpret the toocost only $113,000 to run (MDT and rig charges). Given thatthe tool saved running production casing and multiplecompletions in a severely depleted reservoir in one applicationand eliminated up to five completions in another it was easy tocost justify this application of the MDT as its use saved nearly$1,500,000.

Though extremely beneficial, there still is some inheren

difficulty in interpreting the results of the data collected withthe tool. What is the correct/appropriate downhole gas flowrate to utilize in the interpretation? This multi-phaseinterpretation problem can be negated in future MDT testshowever, by using the MDT tool in an Impulse-FractureInjection Test mode to breakdown the formation and monitorthe decline to pseudo-radial flow using the instantaneoussource solutions developed by Gu et al38 and Nolte40-41.

Case History 3: Almond Formation, Wamsutter FieldGeologic Setting:

The Wamsutter Field is a Tight Formation Gas field located inSouthwestern Wyoming with a resource base that covers over

2,000 square miles. The field is roughly centered on theWamsutter Arch, which is a broad structural high that mayhave been uplifted as late as Paleocene time. Production in thefield is primarily from the Almond Formation, anoverpressured sandstone/siltstone/shale sequence in the UpperCretaceous Mesaverde Group. The field has produced around2 TCF to date, with over 3 TCF additionally recoverable.

Most of the sands found in the Almond Formation arelenticular and fluvial in origin with a marginal marineexposure. The average grain size is fine to very fine grained inindividual fluvial beds of from a few inches to tens of feetThe gross pay section consists of lenticular stacked sands (6-12 pay sands in each wellbore), most of which are of 60-200

acres in size, with 0.005-0.100 md permeability. The Almondsection is slightly overpressured at 0.52 psi/ft reservoirpressure.

Modified Impulse-Fracture Injection Tests:The final case history is the interpretation of pressure andpermeability for the Almond Formation of the MeseverdeGroup. More conventional pressure transient analysistechniques have been employed over the years, but are littleused today due to the time and cost involved. Conventionapressure transient tests in these low permeability reservoirsgenerally require long flow flow periods (days), longer shut-in

Figure 13B: After Closure Analysis Interpretation (Fluid Displacement Test)

P(t)MPa

15

20

25

30

35

FR or FL

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

P(t) vs FR

P(t) vs FL

FR:43.1 FL:0.0

Radial FlowP i (M Pa ) = 1 1. 70

Volume (CuM) =33.66

M -R (M Pa ) = 4 3. 1k h/mu = 4 29. 50k h (md -f t) = 6 .4 4k (md) = 0 .1 31

Figure 13A:Flow regime Identification Plot (Fluid Displacement Test)

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

dP=(P-Pi)anddP'

5.0

10

20

50

1/F-L^21.0 2.0 5.0 10

dP

dP/dP'

dP'

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

dP=(P-Pi)anddP'

5.0

10

20

50

1/F-L^21.0

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

dP=(P-Pi)anddP'

5.0

10

20

50

1/F-L^21.0 2.02.0 5.0 105.0 10

dP

dP/dP'

dP'

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periods (days to weeks), downhole shut-off tools to reducewellbore storage effects, and cost tens of thousands of dollars.More recently, log analysis and petrophysical correlations oflog and core porosity and permeability have been utilized inWamsutter Field development. These methods haveshortcomings as well, and well performance is often poorly

predicted by these log-core correlations. As a result, thecompletions are difficult to optimize, and the economics of thefield development program suffer.

As an aid in determining permeability in-situ and testingthe log-core correlations used previously, the ModifiedImpulse-Fracture Injection Test and After Closure Analysistechnique were employed. This test was conducted byidentifying and perforating a well bounded Almond sandinterval and breaking down the formation with the ModifiedImpulse-Fracture Injection (step down) procedure. Oncebroken down, the well was shut-in and the pressure declinemonitored for approximately two days. This test gaveexcellent results and cost only $2,000. The reduced costoccurred due to the low pressures encountered as compared tothe Canadian examples and the ability to utilize a small skidmounted centrifugal pump equipped with an accurateflowmeter and surface pressure transducer. Figure 14 shows alog montage for a Wamsutter Field well where one of theAlmond sands was isolated and tested through the use of theModified Impulse-Fracture Injection Test. The interval testedis highlighted on the figure with an arrow.

Figures 15A and 15B shows the flow regime diagnosticplot and the interpretation of the pseudo-radial flow period forthe Wamsutter Field test, respectively. As shown in (15A) agood pseudo-radial flow period was established in this test asdetermined by the pressure and first derivative declining at anegative unit slope and the second derivative flattening at avalue of 1.

Figure 15B shows the test interpretation of 0.003 md forthe Wamsutter test. Also, note that the reservoir pressuredetermined was 5610 psi. A sidewall core plug taken from thesame interval showed 0.035 md Klinkenberg correctedpermeability to air at 800 psi confining stress. It is important

to note that while core derived permeabilities represent areservoir thickness of less than one foot the Modified Impulse-

Fracture Injection Test measures the average permeability ofthe entire sand thickness encountered and communicatedduring the test.

Numerous such tests were conducted on a number oAlmond Formation intervals in the Wamsutter FieldIndividual sands tested ranged from 7 to 56 feet thick, withpermeabilities from 0.001 to 0.090 md. Reservoir pressuregradients ranged from 0.434 to 0.795 psi/ft. These test resultare being coupled with log derived data and a correlation willbe developed between reservoir permeability from theImpulse-Fracture Injection Tests and effective hydrocarbonporosity to more accurately estimate reservoir permeability foroptimizing completion designs in the future.

Conclusions1. The application of Modified Impulse-Fracture

Injection Tests and After Closure Analysistechniques can be a time and cost effective meansof determining reservoir permeability andpressure in tight formation gas reservoirs,

2. By conducting the impulse test above fracturingpressure, communication with the reservoir canbe ensured, providing a distinct advantage overconventional impulse, slug test, and/or closedchamber DST,

Figure 15A: Flow Regime Identification Plot (Almond MIFIT)

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

dP=(P-Pi)an

ddP'

5.0

10

20

50

100

200

50

0

1000

5000

1/F-L^22.0 5.0 10 20 50 100 200 500 1000

dP

dP/dP'

dP'

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

dP=(P-Pi)an

ddP'

5.0

10

20

50

100

200

50

0

1000

5000

1/F-L^22.0

dP/dP'

0.2

0

0.5

0

1.0

2.0

5.0

dP=(P-Pi)an

ddP'

5.0

10

20

50

100

200

50

0

1000

5000

1/F-L^22.0 5.05.0 10 2010 20 5050 100 200100 200 500 1000500 1000

dP

dP/dP'

dP'

Figure 15B: After Closure analysis Interpretation (Almond MIFIT)

P(t)psi

6000

6500

7000

7500

8000

8500

9000

FR or FL-0.2 0.0 0.2 0.4 0.6

P(t) vs FR

P(t) vs FL

FR:106261.0 FL:0.0

Radial FlowP i ( ps i) = 5 6 10 .0 0

Volume (M-Gal) =0.43

M-R (psi ) = 106261.0kh/mu = 1.37k h ( md -f t) = 0 .0 3k (md) = 0.003

Figure 14: Log for The Almond Formation Test (MIFIT)

GR, APIUn its0 2 0 010 0

Neutron, Phi0 1 .000.50

Resistivity, Ohms0 1 0050.00

GR, APIUn its0 2 0 010 0

Neutron, Phi0 1 .000.50

Resistivity, Ohms0 1 0050.00

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3. The application of Modified Impulse-FractureInjection Test Procedures (breakdown proceduresutilizing a step-down approach as advocated byNolte) is particularly important in tight formationgas reservoir applications,

4. Determination of reservoir permeability and

pressure is critical to optimum field development,well completions, and fracture stimulation. TheModified Impulse-Fracture Injection Test is aviable means of determining formationpermeability,

5. Formation permeability obtained from theModified Impulse-Fracture Injection Test can beused to improve permeability predictions fromlog-core correlations.

AcknowledgementsThe authors wish to thank the management of BP and BP-Canada Energy Company for permission to publish this work.In addition, the authors wish to thank Dr. Ken Nolte for his

continued development and tireless advocation of this valuabletechnology.

Nomenclature

A = area, L2

F t( ) = time function, Eq. 18, dimensionless

L t( ) = time function, Eq. C-5, dimensionless

N = number of spatial cells, dimensionlessP = defined by C-28, T

R t( ) = time function, Eq. C-9, dimensionless

E'

=plane strain modulus, M / LT2

CR = reservoir fluid-loss coefficient, L / T1/2

CT = total fluid-loss coefficient, L / T1/2

F t*

( ) = t F tc ( ) , Eq. C-27, T1/2

G*

= G-axis intercept, dimensionless

MR = recession multiplier for tc , dimensionless

Pg =press. fcn. for gas res. (App. D) , M / LT2

Sp = spurt value, L

T = tDxf , dimensionless res. time for a fracture

Tc = Tevaluated at tc, dimensionless

Tknee = Tevaluated at tknee, dimensionless

Tp = Tevaluated at tp, dimensionless

Vf = volume of fracture, L3

Vf p = volume of fracture at tp, L3

Vi = volume of fluid injected, L3

VLp = volume of fluid lost at tp, L3

VLT = total volume of fluid lost, L3

a = 1/2 length, Eq. A-7, L

i j k, , = indices, dimensionless

s =prior time (App. C), L, or dimless skin (App. D)

cf = fracture compliance, L / M / LT2

ct = reservoir total compressibility, LT M2 /

e = exponent or symbol in Eq. B-10, dimensionless

fC = CT-component offx , dimensionless

fR = recession fraction, Fig. 3, dimensionlessfV = volume fraction for proppant, dimensionless

fL = fraction of fluid loss because of spurt, dimensionless

fpad = pad volume fraction, dimensionless

fx =xfa/xf, dimensionless

f = spurt-component offx , dimensionless

g tD( ) = loss function, Eq. A- 22, dimensionless

g0 = g( )0

h = reservoir height , L

hf = fracture height, L

h0 = initial fracture height, L

k =permeability, L2 x = distance from wellbore, Lw = fracture width, L

mH = Horner slope, M / LT2

mL = linear-flow slope,p vs F, M / LT2

mLL = log-log slope, App. D (dimensionless)

mR = radial flow slope,p vs F2, M / L T2

p =pressure, M / LT2

p*

= corrected slope of G-plot, M / L T2

pD = dimensionless reservoir pressure

pR =pressure of reservoir beyond filtrate,M / L T2

pc = fracture closure pressure, M / LT2

pf = fracture pressure, M / LT2

pi = initial reservoir pressure, M / L T2

qi = injection rate, L / T3

t = time since pumping began, T

tD = dimensionless time for radial flow (App. D)

tR = time of recession (App. B) and of ramp (App. D), T

ta = apparent time, or time of fracture arrival, T

tc = time of fracture closure, T

tknee = time of transition-flow knee, T

tp = time of pumping, T

xf = final fracture half-length, L

xf a = apparent value of,xf,L

xt = fracture half-length at time, t, L

t = t tp , time since end of pumping, T

tc = t tc p , time for closure period, T

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tc*

= t fc R( )= 0 , time with no recession, T

td = ( ) /t t tc c , dimensionless time since closure

tD = t tp/ , dimensionless time since end pumping

pR = p pR i , press. difference in reservoir, M / LT2

pRD

=

dimensionless simulation pressure, Eq. B-3pT = p pc i , total pressure difference at closure, M / L T

2

pf = p pf c , net fracturing-pressure, M / LT2

= time exp. for propagation, Eq. B-4, dimensionless

= spatial-averaging coeff., Eq. A-27, dimensionless

= factor for app. time = 2 in Eq. A-11; 16 2/ in Eq.18

= difference, or ( / )g022 for Eqs. A-22 to 25, dimless

= dimensionless pressure difference, Eq. C-24

= exponent for prop schedule, Eq. A-31

=porosity, dimensionless

= reservoir diffusivity, L / T2

= spurt coefficient, Eq. A-12, dimensionless

* = upper bound for , defined by Eq. C-25, dimless = reservoir fluid viscosity, M /LT

= dimenless time difference for simulation, Eq. B-12 = Vf p/Vi, dimensionless

= dimensionless prior time for simulation = dimensionless time current time for simulation = fluid loss flux, L/T

= ramp rate, L / T3 2

= dimensionless distance for simulation

c

= equivalent dim. close time with recession, Eq. A-21

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Table 1: Case History One- Summary of Tests, Results, Costs, And As sessment of TFG Permeability Test Criteria

Tst#

Test Type Permmd

CorePerm

md

ActualCost

M$

Cost ProductionDeferrment

Timeliness OperationalSimplicity

1 Post Frac BUT 0.011 5 Very Good Poor Very Poor Excellent

1 Prod Decline 0.011 0 Excellent Excellent Very Poor Excellent

2 CCDST NA 84 Very Poor Fair Good Poor

3 N2Impulse NA 128 Very Poor Fair Good Very Poor

4 PID+ NA 106 Very Poor Very Poor* Good Poor

5 I-FIT & ACA 0.003 0.010 62 Poor Excellent Excellent Excellent

6 MI-FIT & ACA 0.0078 0.015 15 Very Good Excellent Excellent Very Good

7 MI-FIT & ACA 0.008 0.008 15 Very Good Excellent Excellent Very Good

8 MI-FIT & ACA 0.0068 7 Very Good Excellent Excellent Very Good




12 MI-FIT & ACA 0.0552 0.076 7 Very Good Excellent Excellent Very Good* PID was aborted without results, extension of shut-in time to nearly seven months resulted in significant production deferment

Table 2: Modified Impulse-Fracture Injection Test Example Procedure

StageInjection

Rate,BPM

InjectionTime,min

CumulativeTime,min

StageVolume,

Bbls

CumulativeVolume,

Bbls

1 2.00 1 1 2 2

2 1.00 2 3 2 4

3 0.67 3 6 2 64 0.50 4 10 2 8

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