TDistinguished

Author Series

Well Testing and Interpretationfor Horizontal Wells

Fikri J. Kuchuk, SPE, Schlumberger Technical Services Inc.

Summary

The use of transient well testing for determining reservoir parametersand productivity of horizontal wells has become common because ofthe upsurge in horizontal drilling. Initially, horizontal well tests wereanalyzed with the conventional techniques designed for verticalwells. During the last decade, analytic solutions have been presentedfor the pressure behavior of horizontal wells. New flow regimes havebeen identified, and simple equations and flow regime existence cri­teria have been presented for them. The flow regimes are now usedfrequently to estimate horizontal and vertical permeabilities of thereservoir, wellbore skin, and reservoir pressure.

Although the existing tools and interpretation techniques may besufficient for simple systems, innovation and improvement of thepresent technology are still essential for well testing of horizontalwells in many reservoirs with different geological environmentsand different well-completion requirements.

Introduction

This paper reviews testing and interpretation methods for hori­zontal wells. Since Renney's! article in 1941, many articles dealingwith reservoir engineering, PI, and well-testing aspects of horizon­tal wells have appeared in the literature. 1-12 In the last decade, manypapers have been published on the pressure behavior of horizontalwells in single-layer, homogeneous reservoirs.Jr-" Recently,numerous papers on interpretation of horizontal well test data21- 26

and on the behavior of horizontal wells in naturally fractured 27- 29

and layered30•31 reservoirs have appeared.Because of the uncertainty of regulating flow rate or keeping it

constant for drawdown tests in general and buildup tests (particularlyat early-times), the use of production logging tools to measure down­hole flow rate during pressure well tests has increased in the lastdecade. These tools have increased the scope of pressure-transientwell testing by providing new measurements. Drawdown tests, forwhich it has often been difficult to keep the flow rate constant, cannow provide the same quality of information as buildup tests. Thus,the possibility of obtaining reliable information about the well/reser­voir system by using characteristic features of both transient tests(drawdown and buildup) has increased considerably. This is particu­larly crucial for horizontal wells, where the early-time transient dataare the most sensitive to the vertical permeability and skin if the well­bore storage effect is minimized. Recently, production logging and

Copyright 1995 Society of Petroleum Engineers

This paper is SPE 25232. Distinguished Author Series articles are general, descriptive pa­pers that summarize the state of the art in an area of technology by describing recent develop­ments for readers who are not specialists in the topics discussed. Written by individuals rec­ognized as experts in the area, these articles provide key references to more definitive workand present specific details only to illustrate the technology. Purpose: to inform the generalreadership of recent advances in various areas of petroleum engineering. A softboundanthology, SPE Distinguished Author Series: Dec. t98t-Dec. 1983. is available from SPE'sBook Order Dept.

36

downhole shut-in have been combined'? to acquire reliable pressure/rate data during drawdown and buildup tests.

Nonaxisymmetric drilling-fluid invasion and the long, snakelikecompleted wellbore make the cleanup process difficult, particularlytoward the tips of horizontal wells. Therefore, it is important toobtain flow profiles and the effective well length, which is oftenmuch less than the drilled length, for the interpretation of horizontalwell tests. The effective well length is important for determiningdamage skin and the vertical permeability. Production logging forhorizontal wells is now usually conducted with a coiled-tubing sys­tem. 32 The fluid profiles also provide information about standingwater and wellbore crossflow, both common phenomena.V Unfor­tunately, the wellbore crossflow during buildup tests makes inter­pretation difficult. In many instances, the pressure data may notreveal any information about the wellbore cross flow. The wellboretemperature profiles are often useful tools for determining wellborecrossflow for buildup tests.

Significant progress has been made over the last decade in devel­oping forward analytical models and interpretation techniques forhorizontal wells. Many flow regimes predicted by the theory, whichare essential for system identification, have been observed in thefield examples. However, testing horizontal wells is sill challengingin terms of measurements and interpretation. The field experiencedocumented in the last decade indicates that interpreting tests fromhorizontal wells is much more difficult than for vertical wells.

The objective of this paper to present solutions and to describeproblems in pressure-transient testing and interpretation for hori­zontal wells rather than to provide a scholarly review of the litera­ture on the subject.

Flow Regimes for Horizontal Wells

Let us consider a horizontal well (Fig. I) completed in an anisotrop­ic reservoir, which is infinite in the x and y directions. The formationpermeabilities in the principal directions are denoted by kx =ky =kHand kz = kv, with a thickness, h, porosity, fjJ, compressibility, Ct, andviscosity,,u. The well half-length is 4. the radius is rw, and the dis­tance from the wellbore to the bottom boundary is z.,.. The boundaryconditions at the top and bottom (in the z direction) of the system areeither no flow and/or constant pressure. For this horizontal well ina single-layer reservoir, we provide simple equations for obtainingpermeabilities and skins. There are usually several flow regimeswith different durations because of the partially penetrated nature ofhorizontal wells and multiple boundary effects. For instance, as Fig.2 shows, we may observe three radial (pseudoradial) flow regimesfor a horizontal well in a vertically bounded single-layer reservoir.The flow regimes for horizontal wells have been investigated bymany authors,I4-18 and specific methods have been proposed toidentify flow regimes and their durations under ideal conditions.

January 1995• JPT

derivativesEx. 2

. _ ~.

10-4

0.1

10pressure

Zw

~

x

ky

Lo~l(

Fig. 1-Horizontal well model.

III Z

J--_L:_y--~.....H-Lw

III

~------------------""""""

h

and the damage skin as

mIl = 162.6qll/2 jkHkvLw ••• ••••• ••••• •••••• •••••• (1)

s ~ 1.151[ ~:,. + 3.2275 + 2 log 1'(

. . .. .. . . . .. . . .. .. (2)~v ) (AA)]+ 4 - + - log --- ,kH ¢Ilc,r~

TABLE 1-RESERVOIR PARAMETERS FOREXAMPLES SHOWN IN FIG. 3.

h kH kv i; ZwExample .Q!L (md) (md) J!!L J!!L .

~1 100 100 10 500 20 0.001462 100 100 1 500 20 0.003893 100 100 5 500 5 0.001944 40 100 5 500 20 0.001975 200 200 1 500 20 0.00530

• Where fwD = (fW/ 2Lwl(1+ jk~kV) -

k - ¢Il c, [2 (h )2]v - 0.00026377Ctsjb e

max zw. - z., • . (4)

where lsfbe is the time to feel the second (farthest) boundary effect.In practice. Eqs. 3 and 4 may not be reliable because the ¢Ilcr prod­uct may not be accurately known . Nevertheless, they can be usedqualitatively. Alternatively. because Eqs. 3 and 4 provide two piecesof information. they may also be used to provide constraints on thepositions of the boundaries. This information is useful when the

where tsnbe is the time to feel the effect of the nearest boundary. or

where q is the constant flow rate, !i.PIhr = Po- Pw(t= I hour) fordrawdown tests, and !i.Plhr=Pw(!i.t= 1 hour) - (!i.t- 0) for builduptests. Pw at 1hour for both tests is obtained from the semilog, Horner,or derivative plot.

In principle, the geometric mean permeability j kHkvand damageskin may be obtained from the first radial flow regime. provided thaIthe wellbore pressure during this regime is not affected by wellborestorage and/or boundaries. The anisotropy ratio is needed for calcu­lati7 damage skin from Eq. 2. However, because the dependenceon kH/k v is logarithmic. its effect on the damage skin estimationwill usually be small.

The vertical permeability may be obtained from the time of onsetof the deviation of the pressure or pressure deri vative from this flowregime as (in oilfield units)

k - ¢Il c, . 2 2V - 00002637 t mm [zw.(h - zw)], (3)

. "I. snbe

Fig. 3-Derivatives for Examples 1 through S and pressure forExampleS.

10-2

Third radial

_J ._.

Time

Fig. 2-Radial flow regimes for a horizontal well.

First radial

7-r

Hemi-radial

-....r--.

First Radial Flow Regime. The first flow pattern for horizontalwells is elliptic-cylindrical. After some time. the elliptic-cylindricalflow regime becomes pseudoradial, as shown in Fig. 2. This radialflow around the wellbore may continue until the effect of the nearestboundary is felt at the wellbore. It may not develop if the anisotropyratio. kH/kV. is large. The behavior of this regime is similar to the ear­ly-time behavior of partially penetrated wells. The derivatives forall examples, for which the well/reservoir parameters are given inTable 1 (see Ref. 18), clearly indicate (Fig. 3) the first radial flowregime . The slope of the semilog straight line can be expressed as

Log-log plots ~f the change in the wellbore pressure. !i.p...•associated with type curves have been used extensively as diagnosticand interpretation tools since the early 1970's.9 In the early 1980·s.Bourdet et al.33 showed that a combined log-log plot of pressure andpressure derivative is a better diagnostic and interpretation tool thana pressure plot alone for comparing measured transient data with themodel responses. In this paper. the pressure change and pressurederivative are denoted by !i.Pw and dPw/d In t. respectively.

10

OJ.2:Cii>

.~

o

JPI' • January 1995 37

location of one of the boundaries changes with time, such as whenthe gas cap moves downward or when there is an unknown continu­ous shale above or below the well.

Second Radial Flow Regime. This is a hemicylindrical flowregime, as shown in Fig. 2, that follows the first radial flow. Thisflow regime may occur when the well is not centered with respectto the no-flow top and bottom boundaries. In some cases, only thisflow regime may be observed without the first flow regime. Theslope obtained from this flow regime is two times larger than thatobtained from the first regime. Thus,

mrz = 2m rl (5)

and

s ~ 2302{";;~. + 32275 + IO{ (1 + fj;) ;:]

- log ( ,/,kHkVz) } . . (6)-r/lctrw

As in the first radial flow regime, the geometric mean permeabilityj kH/k v and damage skin may be obtained from this flow regime.

Intermediate-Time Linear Flow Regime. If the horizontal well ismuch longer than the formation thickness, this flow regime maydevelop after the effects of the upper and lower boundaries are feltat the wellbore. As Fig. 3 shows, the derivative for Example 4 exhib­its a linear flow regime for almost one logarithmic cycle because theformation thickness (Table I) is short (40 ft). The slope of the linearstraight line (plot of pressure vs. the square root of time) is given by

mil = (8.128q/2Lwh)j/l/kJIPc, (7)

and the skin by

S = (2LwjkHk v/141.2q/l)!1POhr + 2.303

where !1POhr is the intercept. Note that if bo. jkv/kH (h/Lw), is notsmall, then the linear flow regime will not take place because theflow will spread out significantly from the ends of the well beforethe effects of the top and bottom boundaries are seen.

Third (Intermediate) Radial Flow Regime. After the effects of thetop and bottom boundaries are felt at the wellbore, a third radial flowpattern will develop (Fig. 2) in the x-y plane. This regime does notexist for wells with a gas cap or aquifer. The semilog straight-lineslope is

mr3 = 162.6q/l/kHh (9)

and the skin is

(10)

where S, ~ - 2303 IO{~~. (1 + jf;}- (~~.)]

- fj; L(t - ~v + ~~) (11)

38

Eq. 11 is valid only for no< 2.5. The full expression given byKuchuk et ai.18 should be used when ro ~ 2.5.

The start of this flow regime can be written as18

tv = 20, (12)

where tv = 0.0002637kHt/cjJ/lctL~ (13)

The start ofthe third radial flow regime defined by Eq. 12 is some­what subjective. Clonts and Ramey,13 Goode and Thambynaya­gam.!" Ozkan et ai.,16 and Odeh and Babu17 presented differentexpressions for the start of the third regime. Although it can be usedonly qualitatively to determine an upper bound to the horizontalpermeability (see Fig. 3), Eq. 12 is a good approximation for thestart of the third radial flow regime. However, for bo~ 1, Eq. 12becomes crude, as shown by Curves 2 and 5 in Fig. 3. For these twoexamples, the start times are actually less than those obtained fromEq. 12. For large anisotropy ratios, ho may become large, and thestart of the radial flow regime could be much larger than thatobtained from Eq. 12.

Other flow regimes may also develop, depending on the outerboundaries in the x and y directions and the well geometry. Forexample, a spherical flow regime may occur if a horizontal well ismuch shorter than the formation thickness.

Constant-Pressure Boundary. If the top or bottom boundary is ata constant pressure, a steady-state pressure is achieved at the well­bore. The total skin can then be expressed as

s = (jkHk v Lw/374.4q/l)!1Pss - 2.303

I[

8h (nzw) (h - zw) fj;H]X og ( ~)cot 2h + --r::- kv '

nr; 1 + ,;kv/kH

...................... (14)

where !1pss is the pressure difference between the well pressure andconstant pressure at the boundary. The height of the formation maybe estimated from the time lcbp- at which the wellbore pressurebecomes steady state, as

h = 0.01 jkvtCbP/cjJ/lCt, (15)

where tcbp is the time to reach the steady-state pressure at the well­bore. Alternatively, if h is known, this equation may be used to esti­mate the vertical permeability.

Interpretation

Horizontal test well data may be interpreted in two steps: the first isthe identification of the boundaries and the main features, such asfaults and fractures, of the model from flow regime analyses. Unlikemost vertical wells, well test measurements from horizontal wellsare usually affected by nearby shale strikes and lenses and by topand bottom boundaries at early times. The second step is to estimatewell/reservoir parameters and to refine the model that is obtainedfrom flow regime analyses.

The graphical type curve procedure is practically impossible forthe analysis of horizontal well test data because usually more thanthree parameters are unknown, even for a single-layer reservoir.Thus, along with the flow regime analyses, nonlinear least-squarestechniques are usually used to estimate reservoir parameters. Inapplying these methods, one seeks not merely a model that fits agiven set of output data (pressure, flow rate, and/or their derivatives)but also knowledge of what features in that model are satisfied bythe data. Evaluation of model features can be done iteratively duringestimation and by the diagnostic tools mentioned above (identifyingflow regimes). However, if the uncertainties about the model can beresolved with the diagnostic tools, the estimation can be carried outwith a greater confidence at a minimal cost. For instance, if the loca­tions of the lower and upper boundaries are known or identified

January 1995· JPT

Fig. 5-The permeability and thickness distributions for thenine-layer reservoir.

Layered Reservoirs. Most oil and gas reservoirs are often layered(stratified) to various degrees because of sedimentation processesover long geologic times. The geologic characterization of layeredreservoirs and their evaluation have received increasing attention inrecent years because of the widespread use of 3D seismic and high­resolution wire line logs.

Understanding the pressure-transient behavior of layered reser ­voirs is important because of the strong influence that layering hason the productivity of horizontal weIIs.12 However, single-layermodels are often used for the interpretation of weII-test data fromlayered reservoirs. Recently, an interesting example-" was pres­ented to examine the behavior of a horizontal weII in a nine-layerreservoir and in two equivalent single-layer reservoirs. The nine­layer system consists of nine different-thickness horizontal layerswith high and low horizontal and vertical penneabilities randomlydistributed among the layers (Fig. 5) . In this nine-layer reservoir,each layer is a laterally and vertically continuous flow unit that com­municates vertically (formation crossflow) with adjacent layersin the z direction. The horizontal well is completed in the middleof the fifth layer. For computation of the single-layer response,we used the thickness-weighted arithmetic average horizontalpermeability < kH > = [k7= j(kH);h;]/h, and the harmonic aver­age vertical nneability < kv > = hr7k7=lhj(kvl; or < kv > =

k7=1 (kHkv);hjhr (the < kHkv > curve in Fig. 6), where lit =

k7=AAs shown in Fig . 6, the derivatives for these three cases clearly

indicate the first radial flow regime before the effects of the bottom

100

~ kH

!iJ kv

806040

permeability, md

20a

20-~

1O~

5Vl~ ~~~~~~~~~~~g) 15 ·'.:·.:·:·::·\,:x";-,:·x

~ 20 ~:£ 5~

105~:il-~

15.Fractured Reservoirs. Many horizontal weIIs have been drilled infractured reservoirs, such as Respo Mare" and Austin Chalk,23 toincrease production. The solutions presented for horizontal wells innaturaIIy fractured (double-porosity) reservoirs are a simple exten­sion of homogeneous single-layer solutions.27-29 Although thedouble-porosity model may work for late-time behavior, it does notwork at early- and middle-time intervals unless the fracture densityis very high and its conductivity is low.

1000

from the flow regime analyses, the horizontal and vertical pennea­Lilities and damage skin can beestimated with a greater confidence.

The wellbore volume of horizontal wells is usually larger thanthose of vertical wells. Field observations indicate that wellborestorage may vary considerably as pressure builds up. The effect ofwellbore storage can be easily eliminated or reduced if the down­hole flow rate is measured and analyzed with the bottornhole pres­sure. As stated, a downhole shut-in tool should be used for builduptests, particularly for low-productivity wells, to minimize the weII­bore storage effect.

It is well known that the estimated parameters for horizontal wellsare strongly correlated. For instance, vertical permeability and well­bore storage are strongly correlated. Skin is correlated to both kHand ky. As recommended by Kuchuk et al.,21 it may be necessary toconduct a short drawdown test and a long buildup test for flowingwells to estimate these parameters confidently. These two testsshould be carried out sequentially. For shut-in weIIs, the drawdownshould be long enough to minimize the effect of producing time.Fig, 4 presents pressure derivatives for two drawdown and two72-hour buildup tests with a 24-hour producing time for the samesystem with different vertical penneabilities. For the drawdowntests, derivatives are taken with respect to the logarithmic of the testtime. For buildup tests, derivatives are taken with respect to the log­arithm of the Homer time (tp +6. t}/6.t, where tp is the producingtime and 6.t is the test time].

As Fig. 4 shows, even for a 24-hour producing time, the effect isvisible. The behavior of the low-vertical-permeability case is notdrastically different from that of the high-vertical-permeabilitycase. A 24-hour producing time is about the minimum time requiredto flow the well for these two systems. The drawdown derivativetype curves without skin and storage for these two systems are pres­ented in Fig. 3 as Example 1 (ky = 10 md) and Example 2 (ky = Imd). Note that none of the flow regimes that are clearly visible inFig . 3 can be identified in Fig. 4 because of the weIIbore storage andskin effects. Although these are noise-free synthetic data, the thirdradial flow regime is hardly identifiable even at 72 hours. This prob­lem would become much more pronounced for real tests . If thedownhole flow rate is measured or a downhole shut-in device isused, the identifiable data interval would then be increased.

--nine-layer• harmonic <ky>

-----harmonic <kHky>

'Rgj'.~

.~... 100QJ

"0

--DO for kv=10md

11 BU for kv=lO md

---.- DD for kv = 1 md

o BU for ky= 1 md 100

10°time, hr

Fig. 4-Comparison of derivatives for drawdowns and buildUpsfor different vertical permeabllities.

Fig. 6-Comparison of derivatives for layered and equivalenthomogeneous single-layer systems.

JPT • January 1995 39

and top no-flow boundaries. After a transition period, all curves flat­ten, indicating a late-time radial flow regime. This occurs becauseduring this period the horizontal well behaves as a point-source wellin the x-y plane. As Fig. 6 shows, the behavior of the nine-layer res­ervoir is completely different from that for a reservoir with twoequivalent single layers, except for the late-time radial flow regime,which evolves in 100 hours. Note that the shape of the derivative ofthe nine-layer case is similar to that of the single-layer case givenby Example I (Fig. 3). Consequently, identification of such a layersystem may not be possible and may also lead to an incorrect inter­pretation, particularly in estimating the vertical permeability and thedistance to the boundaries. As Fig . 6 also shows, it is difficult to saywhich averaging techniques work better for vertical permeability.Therefore, a multilayer reservoir generally cannot be treated as anequivalent single-layer system, except when the permeability varia­tions are small .30 .

In addition, the behavior of the gas and water zones may differfrom that of the constant-pressure boundary condition, and theeffect of a gas cap or a water zone should not automatically beassumed as a constant-pressure boundary.P

Conclusions

Over the last decade, significant progress has been made in develop­ing forward analytical models and interpretation techniques for hor­izontal wells. The effects of the top and the bottom boundaries, suchas no-flow and/or constant-pressure boundaries, on the transientbehavior of horizontal wells have been recognized. Flow regimeshave been presented for system identification and for estimation ofa number of reservoir parameters.

A wide variety of testing equipment (hardware) for vertical wellshas been adapted for testing horizontal wells. Production loggingand/or downhole shut-in have been used successfully to acquire reli­able pressure and rate data for drawdown and buildup tests. Produc­tion logging tools usually have been run with a coiled-tubing system.

Field experience indicates that the interpretation of well testsfrom horizontal wells is much more difficult than for vertical wells .A large anisotropy ratio and the existence of multiple boundarieswith unknown distances to the wellbore increase the complexity ofthe interpretation. Minimizing the well bore storage effect is crucialfor system identification and parameter estimation.

The pressure derivative is shown to be an effective system identi­fication tool that can also provide initial approximations of the non­linear estimation. Relying solely on nonlinear estimation withoutdiagnostics may lead to an erroneous model and estimates.

The behavior of a multilayer reservoir with a horizontal well can­not be treated as an equivalent single-layer system with averageproperties.

Nomenclature

c/ = total compressibility, Lt2tm, psi - I

h = thickness, L, ftk= permeability, L2, mdL = length, L, ftm= slopen = number of layersp= pressure, mlLt2, psiq = flow rate, L3tt, RB/Dr = radius, L, ftS= skint = time, t, hours

x, y,z= coordinates, L, ftJl = viscosity, mILt, cpljJ = porosity, fraction

SubscriptsD = dimensionlessH = horizontalhr= hour

i = layer number1= linear0= initial or original

40

p = producingr= radial

ss = steady-statet= totalv= verticalw= well

wf= flowing pressure (drawdown)x, y,z= coordinate indicator

Acknowledgments

I am grateful to Schlumberger for permission to publish this paper.I am indebted to P.A. Goode, R .M. Thambynayagam, and DJ.Wilkinson for their contributions to horizontal well testing.

References

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January 1995• JIYI'

SI Metric Conversion Factors

Canadian SPEICIM/CANMET IntI.Conference on Recent Advances inHorizontal Well Applications, Calgary, March 20-23.

Fikri J. Kuchuk is ch ief reservo ir engineer for SchlumbergerMiddle East in Dubai. He was a sen ior scientist and a groupleader at Schiumberge r-Doll Research Center, Ridgefield , CT,and conducted research in pressure transient testing , inverseproblem, flow through porous media, and downhole pressureand flow rate measurements. He was a consulting professor inthe Petroleum Engineer ing Dept. of Stanford U. during1988-1994. Kuchuk was the recipient of the 1994 ReservoirEngi­neering Award. He was the Program Chairman for the 1993Annual Technical Conference and Exhibition and has chairedmany SPEtechnical committees.

E-OI =mE-04 =,um2

E+OO = kPa

ft x 3.048*md x 9.869 233psi x 6.894 757

"Conva rsion factor is exact.

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JPT • January 1995 41