15. Gas Well Testing Field Case Studies

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Chapter 15Gas W ell TestingField Case Studies

15.1 IntroductionThis chapter presents various field case studies in low, high permeability,and fractured carbonate gas wells including summary, conclusions, and rec-ommendations. It also includes a gas well test evaluation sheet, state reportforms, and various cross plotting techniques before and after workovers.

15.2 Gas W ell Test Evaluation SheetWell Data and Basic Parameters

Filed name aaaa-~ Well name bbbbZone number cccc-Interval feetReservoir datum feet ssEstimated reservoir pressure psiaReservoir temperature 0RNet hydrocarbon thickness feetGas saturation fractionPorosity fractionFluid viscosity cPCompressibility psi" 1Hydrocarbon porosity fractionFluid gradient psi/ftZ-factor Well radius feetDrainage radius feetCumulative production prior to test mmcf


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G a s C o m p o s i t i o n"Gas IH 2SI CO 2 IN 2 IC i I C 2 IC 3 11C4 In C 4 I iC 5 In C 5 IC 6 I C 7 +compositionM o I % I I 1 1 1 1 1 1 1 1 1 1

Well Test DataChoke size I Rate I Duration I Cumulative I Final BHP I Final THP(-/64") (mmcfd) (min) tim e(h r) (psia) (psia)

Amerada DataAmerada no. Serial no. Last calibrated data Depth of Amerada

Interpreted data:MBH correction: tp (hr)tpDA (dimensionless time)Buildup slope m(mmpsia 2/cP)if(Pwfo) (mmpsia2/cP)f (Pwf) At=i (mmpsia 2/cP)

Calculated data:1.632 x 10% cTkh = , md - ftmk = kh/h

, ' = i . i 5 i r ( * > i * - * Q ^ > _ l o g k + 3 . 2 3 1L rn < t > h i x c tr l Jm(Ap)j' = 0.867 m /Ap =


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Pressure data:HPi) =F = 4ntDA

Af is(Pwf) = f(pR) = eF

15.3 Shallow Low -Pressure and Highly ProductiveGas ReservoirsThe following example illustrates how to determine the stabilized deliver-ability curve and AOF.

Example 15-1 Determining StabilizedDeliverability Curve and AO F fromthe Test DataA gas well produces from a shallow low-pressure, highly productive reser-voir. The well has been tested by a multirate test and the results are plotted inFigure 15-1. One and one-half durations of each flow period was enough toreach stabilization of flow ing wellbore pressure. In fact, it was observed thatpressures stabilized almost instantaneously after each rate change.Solution The log-log backpressure plot gives a straight line which definesa backpressure exponent n = 1 /slope = 0.56. The backpressure coefficient is

Gas flow rate, mmscfdFigure 15-1. Linear plot for determining high-velocity effect on gas wellperformance.

Intercepts = 0.00145Indicates pressure loss due to steadystate skin s

Slope, B = 0.001607Indicates pressure loss due tohigh velocity flow Dqsc


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calculated from the curve asC = 8.0 x 10 6( l l ,200)a 5 6 = 43,204 scf/day/psia2

The backpressure equation then is qsc = 43 ,204(p | / ^ ) 0 ' 5 6 and the absoluteopen flow is 45.538 mmscfd. A Cartesian plot of Ap2/q sc versus qsc (Figure15-1) gives a straight line (except for a small deviation and the low rate point).The intercept of the line is A = 0.00145 psia2/scfd/D and the slope isB = 1.607 x 10-3 P d i a 2 / S C Mmmscfd

or, when expressed in scf/d,* = 1 . 6 0 7 x l 0 - 9 p S i a 2 / S C f d / dscfd/d

The low n value and the high B value indicate large rate-dependent skin. Theslope B in Figure 15-1 indicates the significance of the high-velocity effect onthe productivity of the well. A large slope implies large rate-dependent skin.The intercept A is related to steady-state skin factor. If the rate needs to bewritten in terms of flow ing pressure, the quadratic equation can be solved asfollows:^A2+ 4B(pl-p2wf)-Aqsc = YB^(0.00145)2 +4(1.607 x I O " 9 ) ^ - plf) - 0.00145

= 2(1.607 x 10"9)This equation can be used to calculate the AOF for this example.

15.4 Recom mended Form of Rules of Procedurefor Backpressure Tests Required by StateRegulatory BodiesAll backpressure tests required by a state regulatory body shall be conductedin according with the procedures set out by the state regulatory body exceptfor those wells in pools where special testing procedures are applicable.1"3The calculations shall be made in the manner prescribed in the appropriate testexamples. The observed data and calculations shall be reported on the pre-scribed forms. Gas produced from wells connected to a gas transportationfacility should not be vented to the atmosphere during testing. When an accu-rate test can be obtained only under conditions requiring venting, the volumevented shall be the minimum required to obtain an accurate test. All surface


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pressure readings shall be taken with a dead weight gauge. Under special con-ditions where the use of a dead weight gauge is not practical, a properly cali-brated spring gauge may be used when authorized by the state regulatory body.Subsurface pressures determined by the use of a properly calibrated pressurebomb are acceptable. The temperature of the gas column must be accuratelyknown to obtain correct test results; therefore a thermometer well should beinstalled in the wellhead. Under shut-in or low-flow-rate conditions, the ex-ternal temperature may distort the observed wellhead temperatures. Wheneverthis situation exists the mean annual temperature should be used.15.5 Appropriate State Report Form s

The appropriate state report forms are as follows.Texas Gas W ell12

Uses tubing pressures Square root chart entries for gas measurement GE system dialogue Answers transferred to G-1 form

New M exico G as W ell1'2 Uses tubing pressures Deviated well UCS system dialogue Answers transferred to preprinted state form C-122

Oklahoma G as W ell3 Uses casing pressures Single-point test Case No. 1 assigned to input data GE system dialogue Answers presented in report form

Offshore Gas Well Using IOC C P rocedure3 Uses bottom-hole pressures UCS system dialogue Answers presented in report form for natural gas Oklahoma


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15.6 Stimulation Efforts Evaluation, Sum mary,and RecommendationsThis section presents theoretical and practical aspects of methods used todetermine absolute open flow potential (AOF), formation permeability, overallskin factors, average reservoir pressure, and gas in place in low- and high-permeability gas reservoirs. Test analysis methods examined include deliver-ability, Horner, type curves, and reservoir limit test analysis. It also includesa brief summary, conclusions, and recommendations of two field case stud-

ies. One case is for a low-permeability gas reservoir; the other is for a high-permeability gas reservoir. These two cases demonstrate well test analysisapplications in low- as well as high-permeability gas reservoirs.Low -Permeability Gas W ell, Nilam Gas Field, IndonesiaCase Studies: Nilam Gas Field, W ell # N-38/gas, Zone GSO A

N ilam gas field is in Kalim antan , Indon esia, and is "offshore." Th e reservo iris 12,950 ft deep and consists of layers of clay and sandstone. The overallthickness is about 52 ft with average porosity of about 14 to 20%.

The empirical deliverability equations areqsc = 1.3152 x 10" 6 (~p2R - plh) (wellhead conditions)qsc = 0.5997 x 10~ 6 (~p2R - plf) (bottom-hole conditions)Stabilized flow equations are also developed using the LIT(\J/) approach to

estima te deliverability potential of this gas w ell against any sandface pr essu re.The values of exponent n = 1 and formation perm eability = 8.274 mD indi-cate, that it is a low-permeability gas reservoir (see Table 15-1 for a summaryof results).The laminar-inertial-turbulent (LIT) flow equations are^(PR) ~ is(Pwh) = 45 .5574 s cq + 2.1429q 2 c (wellhead conditions)is(pR) - if(pwf) = 9l.S213qsc + 0.1785 q)c (bottom-hole conditions)

Returning again to the Forscheimer equation, ~ p\ p^ = Aqsc + Bq2c, khis small (339.23 mD), A qsc becomes large, and the B q2c term can becomenegligible (not necessarily zero) when co m pared to the lam inar pressure dro pterm. We could then w rite qsc = j(~p2R P^f)1'0-Calculate the following quantitiesnJ2 S> = 76.145inY^q = 27.087


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Table 15-1Summary of Results

Wellhead Bottom-hole Flow rate Choke sizepressure (psia) pressure (psia) (mmscf/d) (inch)Shut-in 2388 3700 R a t e l 2015 3144 2.397 16Rate 2 1640 2566 5.214 24Rate 3 1365 2158 6.144 32Rate 4 1015 1836 7.186 48Extended rate 1015 1721 6.148 32

Final shut-in 2388 3700 n 1.0 1.0C 1.3152 x 10"6 0.5997 x 10~6 mmscfd/psiaAOF 7.50 8.21 mmscfd

Table 15-2Specific Results of Pressure Buildup Analysis Using Four Rate TestsParameters Estimated values Remarks

qsc 6.148 mmscfdVKPvv/i) 690xl0 6 p s i a 2 / c Pxjf(Vwfo) 669xl06psia2/cPm 21.0x106 psia2/cPkh 339.23 mD-ftk 8.274 mDs ' +16 .869 Apparent skins +3 .649 True skin SeeTable 15-3D 2.137511 Turbulent factor SeeTable 15-3\lr(AP)skin 64.44 mmpsia2/cP 995psia True skinxjf(Pi) 861.12 mmpsia2/cP 3955 psia From Horner plot

xJr(PR) 772.0 m mpsia2/ cP 3702 psiaStatic gradient 0.110psi/ft

J 2 < 1 2= ! 6 0 . 0 8 8^TY xq = 441.037

Solving by the least square method, we gets = +3.649 (true skin)

D = 2.137511 (turbulent factor)Figure 15-2 shows a graphical method to estimate true skin factor.


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Table 15-3Evaluation of True Skin andTVirbulent FactorGas flow rate # 1 2 3 4 5Gasflowrate^mmscfd 2.397 5.214 6.144 7.186 6.148T/r(Pw/l),mmpsia2/cP 770 765 752 745 650^ (P w /o) ,mmpsia2/cP 592.45 418.12 306.21 227.88 201.25m, mmpsia2/cP/cycle 15 20 21 22 21Jch,mD-ft 185.163 302.078 339.00 378.480 339.229K,mD 4.516 7.366 8.268 9.231 8.279S', apparent skin 8.748 14.842 16.728 18.958 16.869

Gas flow rate q, mmscfdFigure 15-2. Apparent skin factor s' versus gas flow rate.

Radius ofInvestigationAt the beginning of the middle transient regime (MTR), At =1 hr, 102 ft.

At the end of the middle transient regime (MTR), At =10 hr, 321 ft. Thusa significant fraction of the well's drainage area has been sampled and itspermeability is 6.282 mD.

AtAr = 147.12 hr, 1233 ft.At Ar = 468.78 hr, 2200 ft which is equal to the assumed re.

True skin s = 3.80Apensknfaos'


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Reservoir limit:m* = 0.29412 x 106 psia2/cP/hrV p = 2.59288 x 1011 scf (gas filled pore volume of the reservoir)

Basis on p t = 3965 psiaConclusions and Recomm endations

A Homer plot using pseudopressure was used to obtain reservoir parameters.This completion has fair permeability to gas and positive true skin factor,indicating an undamaged well.Overall, the results of analysis are reasonable and can be accepted as reliable.Based on this analysis, it can be concluded that:

The completion would probably benefit from stimulation. Test procedures were suitable for this well. Production could continue from this reservoir at this gas well using a32/64 inch choke size.

High-Permeability Gas Well: Batak Gas Field, IndonesiaCase Studies: Batak Gas Field, Well # B-9U gas, Zone F-I

Batak gas field is in Kalimantan, Indonesia, and is "offshore." The reservoiris 5500 ft deep and consists of layers of sand and limestone. The overallthickness is about 68 ft with average porosity of about 15 to 22% .The empirical deliverability equations are

q sc = 0.00095(~p2R - plh) '69 (wellhead conditions)qsc = 0.00473 (~p2R - plf)M (bottom-hole conditions)

Stabilized flow equations are also developed using the LIT(VO approach toestimate deliverability potential of this gas well against any sandface pressure.The values of exponent n = 0.69 (wellhead conditions), n = 0.61 (bottom-hole conditions), respectively, and permeability = 920 mD indicate that it is ahigh-permeability gas well. See Table 1 5 ^ for a summary of results.The laminar-inertial-turbulent (LIT) flow equations areIT(PR) ~ is(Pwh) = I.lSlSq sc + 0.2677q

2sc (wellhead conditions)

^(PR) - f(Pwf) = 0.6430#5C + 0.0597^2c (bottom-hole conditions)


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Table 15-4S u m m a r y of Results

Wellhead Bottom-hole Flow rate Choke sizepressure (psia) pressure (psia) (mmscf/d) (inch)Shut-in 2602 3795 R a te l 2567 3774 1.446 16Rate 2 2532 3757 6.681 24Rate 3 2317 3723 15.790 32Rate 4 2281 3717 16.566 48Extended rate 2463 3754 10.822 32Final shut-in 2602 3795 n 0.69 0.61C 0.00095 0.00473 mmscfd/psia2AOF 49.07 110.03 mmscfd

Table 15-5Specific Results of Pressure Buildup Analysis: Two-Rate Test

Units Buildup # 1 Buildup # 2qsc mmscfd 16.566 10.822ir(Pwfi) mmpsia2/cP 834.85 838.55ir(Pwfo) mmpsia2/cP 816.51 827.90m mmpsia2/cP 0.40 0.35kh mD-ft 45,284.82 33,809.17k mD 1053.14 786.26s' Apparent skin +39 .25 +27 .57s True skin +5 .57D Turbulent factor 2.03308^-(AP)1S^n mmpsia2/cP 1.6975 psia (true skin)\/f (Pi) mmpsia2/cP 839.33786 psia from Horner Plotis(PR) mmpsia2/cPStatic gradient psi/ft 0.116

Returning again to the Forscheimer equat ion ~p\ - p f = Aqsc + Bqfc, kh islarge (920.0 mD),A qsc becomes small , and we would have 1 /2 2 \ -61qsc= V B ^ P R ~ Pwf*

It is clear then that it is not necessary for flow to be completely turbulentthroughout the reservoir for the slope (n) to be equal to 0.5.


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Conclusions and RecommendationsA Horner plot using pseudopressure was used to obtain reservoir parameters.This completion has high permeability to gas and positive true skin factor,indicating an undamaged well.Overall, the results of analysis are reasonable and can be accepted as reliable.Based on this analysis, it can be concluded that: The completion would benefit very little from stimulation. Test procedures were suitable for this gas well. Restrictions caused by turbulent effects are occurring in this well. Larger tubing size is recommended. Production could continue from this reservoir at this well using a 3 2/64inch choke size.

15.7 Form ation Characteristics from FracturedCarbonate Gas ReservoirsField Case Study for Analyzing Buildup TestsHaving Two Slopes

Special pressure responses from well tests must be analyzed in light of allavailable information. Adams et al.4 have presented a complete evaluation ofa fractured carbonate gas reservoir. In a conventional buildup plot, two slopeswere observed, with the first one having a higher value than the second one(Figure 15-2). After a detailed analysis, they concluded that the matrix perme-ability could be evaluated from the first slope, and the m ean permeability of thematrix-fracture system could be evaluated from the second slope. Their resultsusing this criterion were reasonable when compared with known geologic andcore data. The use of special pressure responses for buildup tests in a fracturedcarbonate gas reservoir will be illustrated with an example using the methodproposed by Adams et al.4Example 15-2 Analyzing Buildup Test with Two Slopes in a Fractured Car-bonate (CO3) ReservoirFigure 15-4 shows a buildup for well A, which is located in a fracturedcarbonate reservoir. The figure shows three straight lines. Figure 15-3 showspermeability variation of core data for this well. Gas properties are as fol-lows: T = 900F; psc = 15.025 psia; T sc = (60 + 460) = 5200R; qg =0.548 mmscfd; h = 160 ft; rw = 0.3 ft; \x g = 0.0131 cP; 0 = 0.03 fraction;c t =0 . 0 0 0 9 p s i "1 .Solution Figure 15-4 shows a buildup plot of Xogi^ 1) versus x/f(p).This figure shows three straight lines, with their corresponding slopes, the


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Cumulative sample frequency, %Figure 15-3. Core permeability variation for gas well (after Adams eta/.).4

extrapolated value of ij/(p) at infinite shut-in, and ty(pws)\hr at 1hr. Adamset al. carried out the interpretation asfollows (seeTable 15-6).

1. Thematrix permeability kmwas calculated from_ 57.92 x l0 6qscPpST

mihTsc_ 57.92 x .548 x 15.025 x (90+460)~ 26.0 x 106x 160 X = 0.121mD (15-1)

2. The skin factor swas calculated froms =1.151\fiPhhr - fiPwf) - logJ ^ , +3.231

1 1[(98.7-37.4) xlO6^ = 11 51L 26.0x10^

0.12 ]~ g 0.03 x 0.0131 x 0.0009 x 0.32 + ' J= 1.151 [2.358 - 7.019 - 3.23] = -1.131

VerticalFv= (0.0047 - 0.002) / 9.9947

= 0.96

HorizontalFA = (0 . 2 - 0 . 0 1 ) / 0 . 2 =0.95

AbouepmbymD


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The ratio fe/^i equals 2.48. Since the drainage area is known to be780,000 sq ft, the dimensionless producing time can be calculated from

_ 0.000264Jfc2f _ 0.000264 x 0.3 x 1570 _tDA = (f)iJict A = 0.03 x 0.0131 x 0.00063 x 780,000 = '(15-3)

*The dimensionless correction to ^r(P) is 1.2 from curve III of FigureB-3 for the case of a 2:1 rectangle.

* _ m,2x correctionxlr(p) xl/(p) =^V } ^yy) 2.303

ilr(p) = 159.0 x 106 - 5.5 x 106 = 153.5 mmpsia2/cP

4. The reservoir flow efficiency can be calculated fromxlf(p)-xjf{pwf)-QM9mxs1 1 , = f(p) - f{pwf)

_ 153.5 - 37.5 - 0.869 x 26.0(-1.131) _ , o g~ 153.5 - 37.4 ~ ( }

5. The distance x to the change in permeability can be calculated from

k2 L m2 4>V>ctrl

0.3~ 1 O g 0.03 x 0.0131 x 0.0009 x 0.32 + 3 ' 2 3


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Consequently x/rw = 292 and x = 87.6 ft. This distance to change inpermeability can also be compared from4

/ x \ 2 _ AtD A2V-^-*!)w ~HW)x W (i5 7)JC/rw = 322 and JC = 96.6 ft. The values of x calculated by two methodsare of the same order of magnitude and consequently it can be concludedthat the change of k is about 90 ft from the wellbore.

15.8 Buildup Interpretations Beforeand After WorkoversIn practice, it is desirable to get as much information as possible from a

pressure buildup test. Trying as many crossplotting techniques as possible cando this. The buildup data before and after workover were obtained in variouszones, block III, Benuang Gas Field, and South Sumatra, Indonesia. Fieldexamples are reproduced here because of their practical implications.

Buildup Data Completely Controlled by AfterflowFigure 15-5 shows a conventional plot of shut-in pressure versus log of

shut-in time. The pressure buildup data are completely controlled by afterflow.

At, hoursFigure 15-5. is(P) versus Af-Semilog plot.

Condition ratio = 3.9No work over is recommended

Improved conditionsAround the wellbore

Curved


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Interpretation would be based on conventional radial flow equations, usingwhat appears to be the straight-line portion of the curve A. The conditionratio using as a basis this straight line is 3.9 and indicates improved con-ditions around the wellbore. Under these conditions, no workover would beattem pted in this w ell. Figu re 15 -6 sh ow s a plot of shut-in pres sure versus shut-in time in Cartesian coordinates. A straight line is obtained, which indicatesthat the buildup data are entirely dominated by wellbore storage (afterflow).Figu re 15 -7 sho ws a log-log plot of pres sure differential versu s tim e. A straight

S-npeueV(p)

Ay/,mmpa/cP

At, hoursFigure 15-6. if (P) versus Af-Cartesian coordinate crossplot (fractured gaswell).

Buildup data dominated bywellbore storage (afterflow)

Straight line of slope 1.0(45) indicates afterflow

At, hoursFigure 15-7. Log A ^ ve rsu s log At Log-log plot (fractured g a s well).

Straight line indicatesbuildup data entirelydominated by after-

flow


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Shut-in time At, hoursFigure 15-8. is(P) versus log Af-Semilog plot .

line with a unit slope is obtained, which also indicates that the buildup dataare dominated by afterflow.

Pressure Buildup Data with Long Afterflowand Beginning of Linear F lowFigure 15-8 shows a conventional semilog plot of shut-in pressure versustime. The apparent straight line A allows the calculation of a condition ratiogreater than 1 and a negative skin. U nder these con ditions no w orkover shouldbe attemp ted. The analys is, how ever, was followed by cross plotting the shut-inpressure versus time in Cartesian coordinates. The plot revealed a straight linefor the first 25 hr (Figure 15-9), which was indicative of afterflow.Figure 15-10 is a log-log cross plot of incremental pressure Ap (shut-inpressure flowing pressu re) versu s tim e. A straight line of unit slope w as no tappa rent during the first 40 hr of shut-in. A bse nce of such a straight line po ints

to the possible presence of skin on the face of the fracture. Starting at 40 hr,there is a straight line of half-unit slope , w hich is indicative of linear flow. Theinterruption of the straight line is attributed to change of pumps and or skindamage on the surface of the fracture around the wellbore. Figure 15-11 isa plot of pressure differential versus square root of shut-in time on Cartesiancoordinates. This type of cross plot results in a straight line, in which linearflow dominates. The intercept of the straight line at zero shut-in time equalsthe pressure drop due to skin. The slope of the straight line can calculatethe length of the fracture or the formation permeability depending on whichparam eter can be reasonably assum ed. In this case the com bination of all plots

\(P)m

a/cP

Before work overCondition ratio < 1Skin factor is negative

Curve A


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Shu t-in time At, hoursFigure 15-10. Log A P versus log A f - lo g - lo g plot (fractured gas well).

provided valuable information and led to the recom m endation of a stimu lationjob . Figure 15-12 shows the results of a pressure survey after the workover insemilog coordinates.Figure 15 -13 shows a straight-line portion on Cartesian coordinates, w hichis indicative of afterflow. This period ended after 16 hr shut-in. Figure 15-14shows a log-log cross plot of pressure differential versus time. A straight line

Aymmpa/cP

VjZ(P)ma/cP

25 degreeStraight-line of slope is( 0.5 (26 ) indicateslinear flow

25 degreeBefore work over

Shut-in time At, hoursFigure 15-9. f(P) versus shut-in timeCartesian coordinate plot (fracturedgas well).

Straight-line portionIndicates afterflow

Before work over


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SnpuVjZ(P)

Aymmpa/cP

Before work over

(At)05 , hours05Figure 15-11. A ^ ve rsu s V ^ Af-S pecialized plot (fractured g a s well).

Shut-in time At, hoursFigure 15-12. \j/(P) versus log Af-Semilog plot (gas well).

w ith unit slope is obtained w hich e nds at 20 hr. Th is unit slope is indicative ofafterflow. Another straight line is obtained after 20 hr. The slope of this line is0.5 and indicates that flow beco m es predo m inantly linear.Figure 15-15 shows a Cartesian cross plot of pressure differential versussquare root of shut-in time. The resulting straight line indicates the presence

After work overCu rv ed


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S-npeue\P)

S-npeue\P)

After work over

Straight-line portionIndicates afterflow

Period could alter 16 hours shut-in

Shut-in time At, hoursFigure 15-13. A ^ versu s Af -C ar te si an coordinate plot (fractured g as well).

Shut-in time At, hoursFigure 15-14. x/r(P) versus log Af-Semilog plot (gas well).

After work over

St-line of slope = 0.5Indicates linear flow

St-line of slope = 45Indicates afterflow


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S-npeue/(F

After work over

Shut-in time (Atf\ (hours )0 5Figure 15-15. \/r(P) versus At Cartesian co ordina te plot (fractured g a s well).

of linear flow. The intercept at zero shut-in time is equivalent to the pressurechange due to skin, and in this case is negative indicating that the stimulationjo b was successful. N ote: Th e variety of cross plots presen ted in this case led torecom m end stimu lation of a well with dam age and resulted in damag e rem ovaland improved conditions around the wellbore.

Pressure Buildup Data Controlled for a Short PeriodFigure 15-16 shows the conventional semilog plot and the "first glance"straight line. Figure 15-17 shows a cross plot of shut-in pressure versus time

in Cartesian coordinates. The lack of a straight line at early times indicatesthat the afterflow period dies very quickly. Figure 15-18 shows a log-logplot of pressu re differential (shut-in pressu re flowing pressure) versus time.A straight line of half-unit slope is obtained which indicates linear flow. Alsonotic e that the unit slope straight line, indicative of we llbore storage , is miss ing.Figure 15-19 shows a Cartesian cross plot of pressure differential (shut-inpressure flowing pressu re) versus sq uare root of shut-in tim e. A con tinuo usstraight line is obtained which indicates the predominance of linear flow. Theintercept of this line at zero time is negative, indicating improved conditionsaround the wellbore.


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\P)mmpa/cP

\Pmmpa/cP

First glance st-line

C u r v e d

Shut-in time At, hoursFigure 15-16. is (P) versus Af-Semilog plot (fractured gas well).

Lack of a st-line early times indicatesthat after flow period dies very quickly

Afterflow period dies very quickly

Shut-in time At, hoursFigure 15-17. V (P ) ve rsu s A f- C ar te si an coo rdina te plot (fractured g a s well).


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Aymmpa/cP

Ay/mmpa/cP

No wellbore storage effect

St-line of slope = 0.5Indicates linear flow

Figure 15-18. Log Axj/ versus log At Log-log plot (fractured g a s well).

Intercept is negative indicating improvedconditions around the wellbore

Figure 15-19. A\[r versus +/At Specialized plot (fractured g a s well).

Pressure Buildup Data Show ing a Sm all AfterflowFigure 15-20 shows a conventional semilog cross plot which results intwo straight lines name d A and B . Figure 15 -21 shows a Cartesian cross plotof shut-in pressure versus time which indicates no early straight line and,


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Shut-in time At, hoursFigure 15-20. is(P) versus log Af-Semilog plot (fractured gas well).

consequently, that the afterflow period dies rapidly. Figure 15-22 shows alog-log cross plot of pressu re differential (shut-in pressu re flowing p res -sure) versus shut-in time. There are a few early-scattered points and then astraight line in the half-unit slope, w hich indicates linear flow. In the late por-tion there is a slightly curved lin e, which in dicates the presen ce of radial flow.Finally, a plot of pressure differential (Ap) versus square root of shut-in timeis shown in Figure 15-23. There is a very clear straight line, which suggestslinear flow, followed by a curved portion when radial flow is attained. Thestraight-line portion A of Figure 15-20 can calculate formation permeabil-ity using radial flow theory. With the slope of Figure 15-23 , its intercept atzero shut-in, and the formation permeability determined from Figure 15-20,we can calculate the fracture length and pressure drop with a good degree ofaccuracy.

St-line BSt-line A

S-npeuemmpa/cP


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S-npeuemmpa/cP

Avjmmpa/cP

No early straight lineAfterflow period dies rapidly

Shut-in time At, hoursFigure 15-21. f{P) versus t Cartesian co ordina te plot (fractured g a s well).

Curved line indicatingRadial flow

St-lineofslope = 0.5Indicating linear flow

Shut-in time At, hoursFigure 15-22. Log Ax/r versus log Af-Log-log plot (fractured gas well).


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S-npeuemmpa/cP

(4/>)Skin = - 1 5 p s iCurved portionIndicating radial flow

St-line indicatinglinear flow

Shut-in time, hoursFigure 15-23. A^ versus At Cartesian coordinate plot (Fractured gas well).

References and Additional Read ing1. Back Pressure Test for Natural Gas Wells, revised edition. Railroad Com-mission of Texas, 1951.2. Interstate Oil Compact Commission (1962). M anual of Back Pressure Test-ing of Gas Wells.3. Kansas State Corporation Commission (1959). M anual of Back PressureTesting of Gas Wells.4. Adams, A. R., Ramey, H. J., and Burgass, R. J., "Gas Well Testing in aFracture Carbonate Reservoir," /. Petroleum Technol. (Oct. 1988), 1187-1194.5. Earlougher, R. C , and Ramey, H. J., J r., Miller, F. G., and Mueller, T. D.,"Pressure Distribution in Rectangular Reservoirs," J. Petroleum Technol.(1960)20, 199-208.

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15. Gas Well Testing Field Case Studies

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