Well Test Analysis in Gas-Condensate Reservoirs

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AbstractPublished analyses of well tests in gas-condensate

reservoirs when pressure drops below the dew point areusually based on a two-zone radial composite model,representing regions of condensate drop-out around thewellbore and of initial gas composition away from the well.

Laboratory experiments, on the other hand, suggest that threedifferent mobility zones could exist: (1) an outer zone awayfrom the well, with the initial liquid condensate saturation; (2)a zone nearer to the well, with increased condensate saturationand lower gas mobility; and (2) a zone in the immediatevicinity of the well with high capillary number whichincreases the gas relative permeability, resulting in a recoveryof much of the gas mobility lost from condensate blockage.This paper investigates the existence of this latter zone in welltest data. An example of well test analysis is discussed, whichillustrates the difficulty of identifying such a zone as, in manycases, build-up and/or drawdown data are dominated bywellbore phase redistribution effects. Where the three zones

can be identified, data are analyzed using a three-zone radialcomposite model to yield a complete characterization of thenear-wellbore effects, and in particular the knowledge of thevarious components of the total skin effect: mechanical skin;rate-dependent two-phase skin; and skin due to gas condensateblockage. The existence of the three zones and the results of the analysis are verified with a compositional simulator whererelative permeability depends on capillary number.

IntroductionGas condensate reservoirs exhibit a complex behavior d

to the existence of a two-fluid system, reservoir gas and liqucondensate1- 4. Three main problems are caused by liquid droout when wells are produced below the dew point, namely

non-reversible reduction in well productivity; a lemarketable gas; and condensate-blocked pipelines.

Consequently, many laboratory5,6,11,12,33 theoretical1,2,4,9

and field investigations10, 15-23 have been conducted over tlast forty years to try to understand condensate reservoir flobehavior. It has been found that, when reservoir pressuaround a well drops below the dew point pressure, retrogracondensation occurs and three regions are created wdifferent liquid saturations14,24,25. Away from the well, an ouregion has the initial liquid saturation; next, there is intermediate region with a rapid increase in liquid saturatiand a corresponding decrease in gas relative permeabiliLiquid in that region is immobile. Closer to the well, an inn

region forms where the liquid saturation reaches a criticvalue, and the effluent travels as a two-phase flow wconstant composition (the condensate deposited as pressudecreases is equal to that flown towards the well). There malso exist a fourth region in the immediate vicinity of the wwhere low interfacial tensions at high rates yield a decrease the liquid saturation and an increase of the gas relatipermeability1,9. The first, third and fourth regions shouappear as three different permeability zones in a well test. Texistence of the fourth region is particularly important aswould counter the reduction in productivity due to liqudropout. This “velocity stripping26” has been inferred frolaboratory experiments and numerical simulations but the

has been little evidence of it from well test data published date.

The present paper presents preliminary results from a stuaimed at developing a better understanding, both qualitativeand quantitatively, of near-wellbore effects in gas condensareservoirs from well testing. In the study, the conditions of texistence of the different mobility zones due to condensadropout are investigated by analyzing well test data fronumerous gas condensate fields with different characteristiand correlating them to the various reservoir and fluproperties. Particular emphasis is on the identification of t

SPE 62920

Well Test Analysis in Gas-Condensate ReservoirsA. C. Gringarten, A. Al-Lamki, S. Daungkaew, Centre for Petroleum Studies, Imperial College of Science, Technology &Medicine, London, UK; R. Mott, AEA Technology; T. M. Whittle, Baker Hughes



2 A C. GRINGARTEN, A. AL-LAMKI, S. DAUNGKAEW, R. MOTT, T. M. WHITTLE SPE 62

enhanced gas relative permeability region around the well, asit remains a key uncertainty in well deliverability forecasting1,

10, 23. The overall objective of the study is to develop newmethods for predicting well productivity in gas condensatereservoirs.

Previous work

There are relatively few publications dealing with welltesting in gas condensate reservoirs1, 10, 11, 15, 17, 19, 21. Publishedinterpretations are performed mainly on build-up data, becausedrawdown data are usually affected by flow rate fluctuations,and in the particular case of gas condensate wells, by noisedue to condensate unloading in the wellbore. Analyses usepressure1, 12, 17, single-phase pseudo-pressure11, 12, 21 or two-phase pseudo-pressures10, 12, 19. The latter, which require goodexperimental measurements of relative permeability curves(rare for gas condensate systems) yield homogeneous lookingderivatives and give access to the mechanical skin only.

Single-phase pseudo-pressure, on the other hand, yield,often composite-shaped derivatives below the dew point.

These usually resemble curve (a) in Figure 1 and suggest theexistence of two mobility-zones, one in the vicinity of thewellbore with reduced gas effective permeability due to liquiddropout, and one away from the well, with single phase gaswhere the reservoir pressure is still above the dew point.Analysis of such build-up data with a two-region compositemodel provides the total skin and a 2-phase (condensateblockage) skin19. The non-Darcy coefficient is often estimatedby matching drawdown or rate data with a simulator which

includes non-Darcy flow, by adjusting the parameter β of theForcheimer equation1, 10.

There has been no published well test data exhibiting aregion of increased gas mobility in the immediate vicinity of

the wellbore (the fourth region mentioned in the introduction)which should yield a response similar to curve (b) in Figure 1.The only mention of the possible existence of such a zone infield data is found in Ref. 20, where the authors had toincorporate liquid velocity stripping in their simulator tomatch DST drawdown data from the Britannia field.

Simulation studiesBefore proceeding with the analysis of field data, a number

of simulations were performed with a compositional simulator(techSIM from AEA Technology), in order to verify theconditions of the existence of the three mobility zonesdescribed above and to develop an understanding of the

derivative shapes to be expected in a well test27

. The simulatorcalculates the fluid PVT properties using an equation-of-state(EOS) and varies condensate and gas relative permeabilities asa function of the capillary number, Nc, according tocorrelations developed by Henderson et al.

28,29. The simulationmodel represents a single-well in a homogeneous, radialreservoir of uniform thickness. The reservoir characteristicsare constant and are shown in Table 1. The model consists of 40 cells with an outer radius of 11,950 ft to insure that noboundary effects are seen in the simulated well tests. Near thewellbore, the cells are small to simulate the gas-condensatenear-wellbore behavior accurately. The cell size increases

logarithmically away from the wellbore. The model does naccount for wellbore storage and mechanical skin.

The simulation runs are designed to show the gacondensate behavior under different production conditions. all cases, the initial reservoir pressure is set to just above tdew point pressure, so that the liquid-phase condensate format the start of production. An example of a pressure-rahistory for a simulation run is shown in Fig. 2. This rconsists of 10 periods of alternating draw-downs and build-u(1DD, 2BU, 3DD, 4BU,…, 9DD, and 10BU). The fidrawdown is extended (100 days) to allow for the condensato accumulate in the near-well bore region, and the subsequeperiods are ten days long. Variations of this production histare run with different rates, gas-oil relative permeabilmodels, and fluid compositions.

Fig. 3 shows how the liquid condensate (So) builds around the wellbore during the first production period, 1Dwith and without capillary number (Nc) effects. Capillanumber effects reduce the condensate saturation around twell and in the reservoir. As time increase, the reduction

greater in the immediate vicinity of the wellbore and tsaturation takes a ‘doughnut’ shape around the well. Tcorresponding gas relative permeability, shown in Figure exhibits a minimum between 10 and 100 feet in our examplemaximum corresponding to the single phase gas away frothe well and an intermediate value in the few feet around twell. These are the three mobility regions discussed in tintroduction and should yield three stabilizations on tderivative.

The derivatives of the shut-in period, 2BU, following tinitial, extended drawdown, are shown in Figure 5 in terms single-phase pseudo-pressure, with and without Nc effects. expected from the condensate saturation distribution (Figu

3), the early-time mobility is much lower without Nc effethan with Nc effects. The three stabilizations on the derivatiwith Nc effects are not obvious, but should exist as indicatedFigure 5, based on the gas relative permeability distribution Figure 4. There should be only two stabilizations without Neffects.

Figure 5 is for a lean gas. The same test was simulated fa rich gas and the gas relative permeability distributions acompared in Figure 6. The rich gas does not show a minimuand the corresponding derivative should have twstabilizations only, as illustrated in Figure 7.

The simulation study thus confirms that, when capillanumber effects are important, the pressure derivative shou

exhibit three stabilizations. In our example, the differencbetween the various stabilizations are very small: tpermeability thickness selected was 1000 mD.ft, which seemto be the limit beyond which well productivity is no longaffected by condensate deposition30. Lower permeabilithickness values should yield greater contrast betwestabilization levels.

Impact of wellbore dynamicsWhen looking at field data, it becomes obvious that o

reason for the lack of well tests showing a zone of increasgas mobility around the wellbore is that such data are difficu



SPE 62920 WELL TEST ANALYSIS IN GAS-CONDENSATE RESERVOIRS 3

to identify with confidence. When they may exist, they arealso likely to be hidden by wellbore phase redistributioneffects. Phase redistribution occurs when different phases flowin different directions in the wellbore. Typical examples areoil and water, gas and water, gas and liquid condensate, andoil and gas in gas-lifted wells. It creates an increase in thewellbore storage coefficient and may be present in drawdownsor in build-up’s. This is different from a phase change, whichcreates a decrease in the wellbore storage coefficient in abuild-up and an increase in the drawdown. The impact of phase change on the pressure behavior is usually limited toearly times whereas an increase in wellbore storage due tophase redistribution may dominate the test for many hours.

Recognizing the existence of wellbore phase redistributionis important because it can create derivative shapes whichcould be easily misinterpreted as they are similar to whatwould be obtained with double porosity, partial penetration orcomposite behaviors. Typical derivative shapes due to phaseredistribution (whether in a drawdown or in a build-up) areshown in Figure 8. Curve (5) in Figure 8 corresponds to the

denser phase being re-injected into the formation.An example of how phase redistribution can affectmultiphase flow pressure behavior and therefore the analysisof the data is shown in Figure 9. Figure 9 is a log-log plot of rate normalized pressure and pressure derivative for adrawdown and the following build-up in a North Sea wellproducing oil and water (Well A). Rate normalized means thatthe pressure change and the derivative have been divided bythe applicable rate so that the derivatives stabilize at the samelevel during radial flow in all the flow periods. In Figure 9, thedrawdown and build-up derivatives are different at earlytimes, as the well was open at the surface for the drawdown,and shut-in downhole for the build-up. They also, however,

differ at late times, with different apparent radial flowstabilizations. Interpretation of production logs run duringboth drawdown and build-up points to reverse water flow inthe wellbore during build-up. This suggests that the build-up isentirely dominated by increasing wellbore storage andtherefore is not interpretable. Analysis in this example has tobe performed on the drawdown.

The same phenomena is often seen in gas wells producingwater. Figure 10 shows the pressure and rate history during awell test in a dry gas well in Canada (Well B). One build-upand five drawdowns are presented on the rate-normalised log-log plot of Figure 11. Data in Figure 11 are plotted in terms of normalized pseudo-pressure10. The drawdown called “Flow

period 2” is at the beginning of the test, and is followed by thebuild-up (Flow period 4). All drawdowns in Figure 11 exceptthe one corresponding to Flow period 15 exhibit similarshapes (except for differences in skin and wellbore storage atearly times) and tend towards the same derivative radial flowstabilization at late times. The behavior of the build-up (Flowperiod 4) and of the drawdown Flow period 15, on the otherhand, are very different. This can be explained as follows:during a drawdown, a mixture of gas and water droplets flowsup the well. When the well is shut-in, the droplets remainsuspended for a little while and then drop down, creating aliquid cushion at the bottom of the well which may even be

reinjected into the reservoir, by gravity or by expansion of tgas at the top of the well. This results in an increase wellbore storage effects which could dominate the entbuild-up behavior and render the analysis impossible. Thdoes not happen in drawdowns unless the concentration denser fluid in the wellbore is such that it cannot be lifted the gas to the surface. This would occur in drawdowns wlow flow rates, or in drawdowns following a previodrawdown at a higher rate, such as Flow period 15. In tparticular example of Figure 11, although the shape of tbuild-up resemble that of a composite behavior, the build-upentirely dominated by wellbore phase redistribution and ninterpretable: analysis with a composite model wouoverestimate the gas mobility by a factor 3. Here agaanalysis must be performed on the drawdowns (Flow peri2).

Phase redistribution is also present in drawdowns abuild-up’s from gas condensate wells. Figure 12 is a ratnormalized log-log plot of drawdown data (Flow periods 14, 15 and 18) for a North Sea lean gas condensate well (W

C). Pressures and derivatives are expressed in terms of singphase normalized pseudo-pressure10. Drawdown data aobviously dominated by increasing wellbore storage. Ashould be expected, this effect seems more pronounced aappears to last longer for low flow rates (Flow periods 14and 15). The higher rate drawdown Flow period 18 seems leaffected compared to the other drawdowns. Its derivative similar to that for the build-up’s, Flow periods 8, 18 and 2shown in Figure 13. Close inspection of the build-up’s showthat they also are affected by phase redistribution in the peri1 to 10 hours, so it is possible that the drawdown Flow peri17 is affected as well. This has to be taken into account whperforming the analysis.

Early time well test behavior of gas condensate weOne of the objective of our study is to confirm t

existence of “velocity stripping” in gas condensate wells frowell test data. This refers to an enhanced gas mobility zonehigh rates in the immediate vicinity of the wellbore due high capillary numbers. We are therefore looking fderivatives exhibiting a three-region composite behavisimilar to curve (b) in Figure 1. As discussed in the previosection, the challenge is to avoid data affected by wellbophase redistribution.

Data for Well C in Figure 13 seem to show a three-regicomposite behavior and therefore could be interpreted

quantify the three mobility zones defined in the introductioThe analysis is best performed on the drawdown data Floperiod 17, as it is the longest period of the test and shows moof the various composite features. The final derivatistabilization, corresponding to the mobility of the gas with tinitial condensate saturation, is easy to locate, slightly belothe last data points after 100 hours. The derivative stabilizaticorresponding to the increased condensate saturation equally easy to locate, at the level of the derivative humaround 10 hours. The location of the derivative stabilizaticorresponding to the enhanced gas mobility, on the other hanis much more difficult to find. It must be between the oth




two, and therefore cannot correspond to the minimum at 1hour. This minimum must correspond to wellbore phaseredistribution effects, as suggested by the shapes of the build-up’s in Figure 14. There is therefore a significant uncertaintyin this particular example.

When a choice has been made for the first stabilization, theanalysis can be performed with a three region compositemodel31 (Figure 15), based on a solution by Satman, et al.32.The log-log match with such a model is shown in Figure 16:(1) represents the three-region composite model with nowellbore storage and skin; (2) is the same solution for constantwellbore storage; and (3) is the changing wellbore storagesolution. The latter also provides a good match on thesuperposition plot and for the simulation of the entire test. Theinternal and external radii of the condensate “doughnut” are100 and 500 feet, respectively.

Another example of the possible existence of threederivative stabilizations is shown in Figure 17. The data arefrom Well D, another North Sea lean gas condensate reservoir.They can be interpreted with either a two-region or a three-

region composite model. Both analyses give parameter valueswhich are reasonable. The complete analysis is shown inFigures 18 to 20 (respectively, Horner match, simulation, andskin versus rate plots). It yields all the components of the skinfactor.

Discussion and ConclusionsThis paper presents the preliminary results of a systematic

study of well tests in gas condensate reservoirs. One of theprimary objectives is to investigate the conditions of theexistence of the different mobility zones due to condensatedropout and velocity stripping.

It was found that phase redistribution is a major problem inanalyzing the data. It not only reduces the amount of dataavailable for analysis, but may also create drawdown or build-up shapes that can easily be misinterpreted for reservoirbehaviors.

Examples have been shown that seem to exhibit threestabilizations on the derivative, corresponding to threemobility zones: (1) an outer zone away from the well, withthe initial liquid condensate saturation; (2) a zone nearer to thewell, with increased condensate saturation and lower gasmobility; and (2) a zone in the immediate vicinity of the wellwith high capillary number which increases the gas relativepermeability, resulting in a recovery of much of the gas

mobility lost from condensate blockage.These results have to be considered with caution, however,until more systematic evidence of such behavior becomesavailable.

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10-3 10-2 10-1 1 10 102 103

Elapsed time (hours)

m n

( p ) c h a n g e a n d d

e r i v a t i v e ( p s i )

103

102

10

1

Gas with lower condensatesaturation (stripping)

High condensate

Saturation (liquid drop-out)

Gas with initial

Condensate saturation

(a)

(b)

Fig. 1: Schematic of pressure and derivative composite behavior:(a) two-region composite; (3) three-region composite

0

500

1000

1500

2000

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R a t e ( m m s c f / d )

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Rate (mmscf/d)

1DD 3DD 5DD 7DD 9DD2BU 4BU 6BU 8BU 10B

Fig. 2: Rate & Pressure History Example for the Simulation Runs.

0.1 1 10 100 1000 10000

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0

0.05

0.1

0.15

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0.3

S o

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with Nc

0.1days

1day

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100days0.1day

100days

Fig. 3: Saturation distribution in the reservoir during the firstextended drawdown

0.82

0.88

0.94

1

0.1 1 10 100 1000 1000


R e l a t i v e P e r m e a b i l i t y ,

k r g

0.1 day

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Reduction with time

Fig. 4: Gas relative permeability distribution in the reservduring the first extended drawdown

Without Nc

With Nc

10-4 10-3 10-2 10-1 1 10

Elapsed time (days)

m ( p ) c h a n g e ( 1 0 - 6 p s i 2 / c p )

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102

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1

Fig. 5: Log-log pressure derivatives for the build-up following tfirst extended drawdown

0

0.1

0.2

0.30.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100 1000 10


k r g

Rich gas

Lean gas

Fig. 6: Gas relative permeability distribution for lean and rgases during the first extended drawdown




10-4 10-3 10-2 10-1 1 10

Elapsed time (days)

m ( p ) c h a n g e

( 1 0 - 6 p s i 2 / c p )

102

10

RICH GAS

LEAN GAS

Fig. 7: Log-log pressure derivatives for the build-up following thefirst extended drawdown

Elapsed time, ∆∆∆∆t ( hours) N o r m a l i z e d P s e u d o - P r e s s u r e D e r i v a t i v e (

p s i )

Radial FlowStabilisation

Reinjection ofcondensate cushion

10-3 10-2 10-1 1 10 102 103

104

103

102

10

1

(3)

(2)

(1)

(4)

(5)

Fig. 8: Log-log derivative plots, increasing wellbore storage dueto phase redistribution in the wellbore

Drawdown

Build-up

10-3 10-3 10-2 10-1 1 10 102


104

103

102

10

R a t e n o r m a l i z e d p r e s s

u r e c h a n g e a n d d e r i v a t i v e ( k P a )

Radial Flow Stabilization

Fig. 9: Log-log plot, oil/water Well A, showing increasing wellborestorage due to phase redistribution in the wellbore during build-up

Time from the start of the test (hours)

P r e s s u

r e ( p s i a )

F l ow R a

t e ( M s cf / D )

Flow Periods:

20 40 60 80 100

4000

3000

2000

1000

40000

30000

20000

10000

0

(14)(4)(3)(2)(1) (12)(11)(9) (15)

Fig. 10: Pressure and rate test history, dry gas Well B

10-3 10-2 10-1 1 10 102

104

103

102

10


R a t e n o r m a l i z e d m n

( p ) c h a n g e a n d d e r i v a t i v e ( p s i )

7

9

2

11

154

Current (Drawdown) or

Previous (Build-up) Rate

20,000Mscf/D

28,000

31,400

32,600

13,000

31,400

Flow

Period

7

9

2

11

15

4

Type

Dd

Dd

Dd

Dd

Dd

Bu

Radial flow

stabilization

Fig. 11: Log-log plot, dry gas Well B, showing increasing wellbostorage due to phase redistribution in the wellbore during buiup and decreasing rate drawdown

103

102

10

1

R a t e n o r m a l i z e d m n ( p ) c h a n g e a n d d e r i v a t i v e ( p s i )

FP 18 (DD 57.5 MScf/D)

FP 14 (DD 38 MScf/D)

FP 15 (DD 47 MScf/D)

FP 7 (DD 45 MScf/D)

10-3 10-2 10-1 1 10 102 103


Fig. 12: Log-log plot, gas condensate Well C, showing increaswellbore storage due to phase redistribution in the wellboduring low rate drawdowns




103

102

10

1


( p ) c h a n g

e a n d d e r i v a t i v e ( p s i )

10-3 10-2 10-1 1 10 102 103



FP 18 BU (DD 57.5 MScf/D)

FP 8 BU (DD 45 MScf/D)

FP 21 BU (DD 38 MScf/D)

Fig. 13: Log-log plot, gas condensate Well C, showing little phaseredistribution in the wellbore during build-up’s and high ratedrawdown

103

102

10

1

R a t e

n o r m a l i z e d m n


10-3 10-2 10-1 1 10 102 103


High condensateSaturation (liquid drop-out)

Gas with initial

Condensate

SaturationGas with lowercondensate

saturation (stripping)

?

Fig. 14: Log-log Diagnostic Plot for Well C

r 1

r 2

Gas with initialCondensate saturation

(kh / µ)3, (φµcth)3

Gas with lowercondensatesaturation (stripping)


High condensate

Saturation (liquid drop-out)


Fig. 15: Schematic of three-region composite model

103

102

10

1


( p ) c h a n g

e a n d d e r i v a t i v e ( p s i )

10-3 10-2 10-1 1 10 102 103



Gas with initial

Condensate

Saturation

High condensateSaturation (liquid drop-out)

Gas with lowercondensate

saturation (stripping)

(2)(3)

(1)

Fig. 16: Analysis of gas condensate Well C with the three-regcomposite model (Log-log Match)

2-Region composite: r1=365 ft; (kh/ µ)1/2=0.24; (φµct)1/2=0.32

3-Region composite:r1= 33 ft; (kh/ µ)1/2=2.7 ; (φµct)1/2=1.9r2=322 ft; (kh/ µ)2/3=0.32; (φµct)2/3=0.33

104

103

102

10

m n


10-2

10-1

1 10 102

103


Fig. 17: Analysis of gas condensate Well D with the three-regicomposite model (Log-log Match)

1000

2000

3000

4000

5000

6000

7000

8000

0 10000 20000 30000 40000 N o r m a l i s e d P s e u d o

P r e s s u r e ( p s i a )

Superposition Function (Mscf/D)

2-Region composite

3-Region composite

Fig. 18: Analysis of gas condensate Well D with the three-regicomposite model (Horner Match)



SPE62920 WELL TEST ANALYSIS IN GAS-CODENSATE RESERVOIRS 9

1000

2000

3000

4000

5000

6000

100 110 120 130 140 150 160 170

P r e s s u r e ( p

s i a )

Elapsed time (hrs)

Fig. 19: Analysis of gas condensate Well D with the three-regioncomposite model (Horner Match)

35.0

35.4

35.8

36.2

36.6

37.0

4200 4600 5000 5400 5800 6200

S k i n

Gas Rate (Mscf/D)

Total Skin, Rate Dependent = 37Total Skin, Rate Independent = 31

Mechanical and Completion Skin = 27Turbulence Factor = 0.000948 D/Mscf

Fig. 20: Skin versus rate, Well D

Parameters Value

Porosity 0.1

Absolute permeability 10 mD

Net-to-gross ratio 1

Conate water saturation 0.15

Wellbore radius 0.25 ft

Top Depth 8500ft

Initial Reservoir Pressure (lean gas) 3600 psia

Initial reservoir Pressure (rich gas) 6400 psia

Table 1: Parameters for simulations

Documents

Well Test Analysis in Gas-Condensate Reservoirs