Well Testing and Interpretation for Horizontal Wells

T

Distinguished Author Series

Well Testing and Interpretation for Horizontal Wells Fikri J. Kuchuk, SPE, Schlumberger Technical Services Inc. Summary

The use of transient well testing for determining reservoir parameters and productivity of horizontal wells has become common because of the upsurge in horizontal drilling. Initially, horizontal well tests were analyzed with the conventional techniques designed for vertical wells. During the last decade, analytic solutions have been presented for the pressure behavior of horizontal wells. New flow regimes have been identified, and simple equations and flow regime existence criteria have been presented for them. The flow regimes are now used frequently to estimate horizontal and vertical permeabilities of the reservoir, wellbore skin, and reservoir pressure. Although the existing tools and interpretation techniques may be sufficient for simple systems, innovation and improvement of the present technology are still essential for well testing of horizontal wells in many reservoirs with different geological environments and different well-completion requirements. Introduction

This paper reviews testing and interpretation methods for horizontal wells. Since Renney's! article in 1941, many articles dealing with reservoir engineering, PI, and well-testing aspects of horizontal wells have appeared in the literature. 1-12 In the last decade, many papers have been published on the pressure behavior of horizontal wells in single-layer, homogeneous reservoirs.Jr-" Recently, numerous papers on interpretation of horizontal well test data 2 1- 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 (particularly at early-times), the use of production logging tools to measure downhole flow rate during pressure well tests has increased in the last decade. These tools have increased the scope of pressure-transient well testing by providing new measurements. Drawdown tests, for which it has often been difficult to keep the flow rate constant, can now 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 data are 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 work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering. A softbound anthology, SPE Distinguished Author Series: Dec. t98t-Dec. 1983. is available from SPE's Book 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, snakelike completed wellbore make the cleanup process difficult, particularly toward the tips of horizontal wells. Therefore, it is important to obtain flow profiles and the effective well length, which is often much less than the drilled length, for the interpretation of horizontal well tests. The effective well length is important for determining damage skin and the vertical permeability. Production logging for horizontal wells is now usually conducted with a coiled-tubing system. 32 The fluid profiles also provide information about standing water and wellbore crossflow, both common phenomena.V Unfortunately, the wellbore crossflow during buildup tests makes interpretation difficult. In many instances, the pressure data may not reveal any information about the wellbore cross flow. The wellbore temperature profiles are often useful tools for determining wellbore crossflow for buildup tests. Significant progress has been made over the last decade in developing forward analytical models and interpretation techniques for horizontal wells. Many flow regimes predicted by the theory, which are essential for system identification, have been observed in the field examples. However, testing horizontal wells is sill challenging in terms of measurements and interpretation. The field experience documented in the last decade indicates that interpreting tests from horizontal wells is much more difficult than for vertical wells. The objective of this paper to present solutions and to describe problems 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 formation permeabilities in the principal directions are denoted by kx = ky = kH and kz = kv, with a thickness, h, porosity, fjJ, compressibility, Ct, and viscosity,,u. The well half-length is 4. the radius is rw , and the distance from the wellbore to the bottom boundary is z.,.. The boundary conditions at the top and bottom (in the z direction) of the system are either no flow and/or constant pressure. For this horizontal well in a single-layer reservoir, we provide simple equations for obtaining permeabilities and skins. There are usually several flow regimes with different durations because of the partially penetrated nature of horizontal wells and multiple boundary effects. For instance, as Fig. 2 shows, we may observe three radial (pseudoradial) flow regimes for a horizontal well in a vertically bounded single-layer reservoir. The flow regimes for horizontal wells have been investigated by many authors,I4-18 and specific methods have been proposed to identify flow regimes and their durations under ideal conditions. January 1995• JPT

10 I I I

pressure

ky

Z

L

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

Ex. 2

derivatives

x

~l(

I I I

""""""

~.

_

~

o

h

.

Zw

~------------------

0.1 10-4

Fig. 1-Horizontal well model.

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

Third radial

_J ._.

10

~v

+ OJ

.2:

Cii >

.~

7

o

-r

Hemi-radial

-....r--. First radial

10-2

Time

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

Log-log plots ~f the change in the wellbore pressure. !i.p...• associated with type curves have been used extensively as diagnostic and 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 and pressure derivative is a better diagnostic and interpretation tool than a pressure plot alone for comparing measured transient data with the model responses. In this paper. the pressure change and pressure derivative are denoted by !i.Pw and dPw/d In t. respectively. First Radial Flow Regime. The first flow pattern for horizontal wells is elliptic-cylindrical. After some time. the elliptic-cylindrical flow regime becomes pseudoradial, as shown in Fig. 2. This radial flow around the wellbore may continue until the effect of the nearest boundary is felt at the wellbore. It may not develop if the anisotropy ratio. kH/kV. is large. The behavior of this regime is similar to the early-time behavior of partially penetrated wells. The derivatives for all examples, for which the well/reservoir parameters are given in Table 1 (see Ref. 18), clearly indicate (Fig. 3) the first radial flow regime . The slope of the semilog straight line can be expressed as mIl

= 162.6qll/2 jkHkvL w

••• ••••• ••••• •••••• ••••••

and the damage skin as

s

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

JPI' • January 1995

(1)

4

-

kH

+

)-

(AA)]

log - - ¢Ilc,r~

,

. . .. .. . . . .. . . .. .. (2)

where q is the constant flow rate, !i.PI hr = Po- Pw(t= I hour) for drawdown tests, and !i.Plhr= Pw(!i.t= 1 hour) - (!i.t- 0) for buildup tests. Pw at 1 hour for both tests is obtained from the semilog, Horner, or derivative plot. In principle, the geometric mean permeability j kHk v and damage skin may be obtained from the first radial flow regime. provided thaI the wellbore pressure during this regime is not affected by wellbore storage and/or boundaries. The anisotropy ratio is needed for calculati7 damage skin from Eq. 2. However, because the dependence on kH/k v is logarithmic. its effect on the damage skin estimation will usually be small. The vertical permeability may be obtained from the time of onset of the deviation of the pressure or pressure deri vative from this flow regime as (in oilfield units)

k V -

where

¢Il c, . 2 2 00002637 t mm [zw. (h - zw)], . "I. snbe

tsnbe

(3)

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

k v -- 0.00026377Ct ¢Il c,

max [2 zw. (h - z., )2]• .

(4)

sjb e

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 used qualitatively. Alternatively. because Eqs. 3 and 4 provide two pieces of information. they may also be used to provide constraints on the positions of the boundaries. Thi s information is useful when the TABLE 1-RESERVOIR PARAMETERS FOR EXAMPLES SHOWN IN FIG. 3.

kH

h Example

.Q!L

(md)

kv (md)

1 2 3

100 100 100 40 200

100 100 100 100 200

10 1 5 5 1

4 5

i;

Zw

J!!L J!!L 500 500 500 500 500

20 20 5 20 20

.

~

0.00146 0.00389 0.00194 0.00197 0.00530

l(1+ jk~kV) -

• Where fwD = (f W / 2L w

37

location of one of the boundaries changes with time, such as when the 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 flow regime, as shown in Fig. 2, that follows the first radial flow. This flow regime may occur when the well is not centered with respect to the no-flow top and bottom boundaries. In some cases, only this flow regime may be observed without the first flow regime. The slope obtained from this flow regime is two times larger than that obtained from the first regime. Thus, (5)

mrz = 2m rl

and

s

~ 2302{";;~. + 32275 + IO{ (1 +

- log (

fj;) ;:]

,/,kHk Vz) } . . -r/lctrw

(6)

As in the first radial flow regime, the geometric mean permeability j kH/k v and damage skin may be obtained from this flow regime. Intermediate-Time Linear Flow Regime. If the horizontal well is much longer than the formation thickness, this flow regime may develop after the effects of the upper and lower boundaries are felt at the wellbore. As Fig. 3 shows, the derivative for Example 4 exhibits a linear flow regime for almost one logarithmic cycle because the formation thickness (Table I) is short (40 ft). The slope of the linear straight line (plot of pressure vs. the square root of time) is given by mil

= (8.128q/2L wh)j/l/kJIPc,

Eq. 11 is valid only for no < 2.5. The full expression given by ~ 2.5. Kuchuk et ai. 18 should be used when The start of this flow regime can be written as 18

ro

tv

= 20,

(12)

where tv = 0.0002637kHt/cjJ/lctL~

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 Babu 17 presented different expressions for the start of the third regime. Although it can be used only qualitatively to determine an upper bound to the horizontal permeability (see Fig. 3), Eq. 12 is a good approximation for the start of the third radial flow regime. However, for bo ~ 1, Eq. 12 becomes crude, as shown by Curves 2 and 5 in Fig. 3. For these two examples, the start times are actually less than those obtained from Eq. 12. For large anisotropy ratios, ho may become large, and the start of the radial flow regime could be much larger than that obtained from Eq. 12. Other flow regimes may also develop, depending on the outer boundaries in the x and y directions and the well geometry. For example, a spherical flow regime may occur if a horizontal well is much shorter than the formation thickness. Constant-Pressure Boundary. If the top or bottom boundary is at a constant pressure, a steady-state pressure is achieved at the wellbore. The total skin can then be expressed as

s= X

(jkHk v L w/374.4q/l )!1Pss - 2.303

Iog

[ nr; ( 1

w) 8h ~)cot (nz 2h + (h - zw) fj;H] kv ' + ,;kv/kH ...................... (14)

S = (2L wjkHk v/141.2q/l)!1POhr

where !1pss is the pressure difference between the well pressure and constant pressure at the boundary. The height of the formation may be estimated from the time lcbp- at which the wellbore pressure becomes steady state, as

+ 2.303

h where !1POhr is the intercept. Note that if bo. jkv/k H (h/L w), is not small, then the linear flow regime will not take place because the flow will spread out significantly from the ends of the well before the effects of the top and bottom boundaries are seen. Third (Intermediate) Radial Flow Regime. After the effects of the top and bottom boundaries are felt at the wellbore, a third radial flow pattern will develop (Fig. 2) in the x-y plane. This regime does not exist for wells with a gas cap or aquifer. The semilog straight-line slope is

m r3 = 162.6q/l/k Hh

(9)

and the skin is

(10)

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

38

--r::-

(7)

and the skin by

- fj;

(13)

L(t - ~v + ~~)

(11)

= 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 is the identification of the boundaries and the main features, such as faults and fractures, of the model from flow regime analyses. Unlike most vertical wells, well test measurements from horizontal wells are usually affected by nearby shale strikes and lenses and by top and bottom boundaries at early times. The second step is to estimate well/reservoir parameters and to refine the model that is obtained from flow regime analyses. The graphical type curve procedure is practically impossible for the analysis of horizontal well test data because usually more than three parameters are unknown, even for a single-layer reservoir. Thus, along with the flow regime analyses, nonlinear least-squares techniques are usually used to estimate reservoir parameters. In applying these methods, one seeks not merely a model that fits a given set of output data (pressure, flow rate, and/or their derivatives) but also knowledge of what features in that model are satisfied by the data. Evaluation of model features can be done iteratively during estimation and by the diagnostic tools mentioned above (identifying flow regimes). However, if the uncertainties about the model can be resolved with the diagnostic tools, the estimation can be carried out with 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

from the flow regime analyses, the horizontal and vertical penneaLilities and damage skin can be estimated with a greater confidence. The well bore volume of horizontal wells is usually larger than those of vertical wells. Field observations indicate that well bore storage may vary considerably as pressure builds up. The effect of wellbore 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 buildup tests, particularly for low-productivity wells, to minimize the weIIbore storage effect. It is well known that the estimated parameters for horizontal wells are strongly correlated. For instance, vertical permeability and wellbore storage are strongly correlated. Skin is correlated to both kH and ky. As recommended by Kuchuk et al.,21 it may be necessary to conduct a short drawdown test and a long buildup test for flowing wells to estimate these parameters confidently. These two tests should be carried out sequentially. For shut-in weIIs, the drawdown should be long enough to minimize the effect of producing time. Fig, 4 presents pressure derivatives for two drawdown and two 72-hour buildup tests with a 24-hour producing time for the same system with different vertical penneabilities. For the drawdown tests, derivatives are taken with respect to the logarithmic of the test time. For buildup tests, derivatives are taken with respect to the logarithm of the Homer time (tp +6. t}/6.t, where tp is the producing time and 6.t is the test time]. As Fig. 4 shows, even for a 24-hour producing time, the effect is visible. The behavior of the low-vertical-permeability case is not drastically different from that of the high-vertical-permeability case. A 24-hour producing time is about the minimum time required to flow the well for these two systems. The drawdown derivative type curves without skin and storage for these two systems are presented in Fig. 3 as Example 1 (ky = 10 md) and Example 2 (ky = I md). Note that none of the flow regimes that are clearly visible in Fig . 3 can be identified in Fig. 4 because of the weIIbore storage and skin effects. Although these are noise-free synthetic data, the third radial flow regime is hardly identifiable even at 72 hours. This problem would become much more pronounced for real tests . If the downhole flow rate is measured or a downhole shut-in device is used, the identifiable data interval would then be increased. Fractured Reservoirs. Many horizontal weIIs have been drilled in fractured reservoirs, such as Respo Mare" and Austin Chalk,23 to increase production. The solutions presented for horizontal wells in naturaIIy fractured (double-porosity) reservoirs are a simple extension of homogeneous single-layer solutions. 27-29 Although the double-porosity model may work for late-time behavior, it does not work at early- and middle-time intervals unless the fracture density is very high and its conductivity is low.

1000

Layered Reservoirs. Most oil and gas reservoirs are often layered (stratified) to various degrees because of sedimentation processes over long geologic times. The geologic characterization of layered reservoirs and their evaluation have received increasing attention in recent 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 has on the productivity of horizontal weIIs. 12 However, single-layer models are often used for the interpretation of weII-test data from layered reservoirs. Recently, an interesting example-" was presented to examine the behavior of a horizontal weII in a nine-layer reservoir and in two equivalent single-layer reservoirs. The ninelayer system consists of nine different-thickness horizontal layers with high and low horizontal and vertical penneabilities randomly distributed 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 layers in the z direction. The horizontal well is completed in the middle of the fifth layer. For computation of the single-layer response, we used the thickness-weighted arithmetic average horizontal permeability < kH > = [k7= j(kH);h;]/h, and the harmonic average vertical nneability < k v > = hr7k7=lhj(kvl; or < k v > = k7=1 (kHkv);hjh r (the < kHk v > curve in Fig. 6), where lit =

k7=A

As shown in Fig . 6, the derivatives for these three cases clearly indicate the first radial flow regime before the effects of the bottom

20-~ 1O~ Vl~ g)

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

~ 20 ~

:£ 5~ 10

5~:il-~

~

kH

!iJ

kv

15.

a

20

40

60

80

100

permeability, md Fig. 5-The permeability and thickness distributions for the nine-layer reservoir.

--DO for kv=10md 11

BU for kv=lO md

---.- DD for kv = 1 md o

BU for ky= 1 md

100

'R gj' .~

.~...

QJ

--nine-layer

100

• harmonic -----harmonic

"0

10° time, hr Fig. 4-Comparison of derivatives for drawdowns and buildUps for different vertical permeabllities. JPT • January 1995

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

39

and top no-flow boundaries. After a transition period, all curves flatten, indicating a late-time radial flow regime. This occurs because during this period the horizontal well behaves as a point-source well in the x-y plane. As Fig. 6 shows, the behavior of the nine-layer reservoir is completely different from that for a reservoir with two equivalent single layers, except for the late-time radial flow regime, which evolves in 100 hours. Note that the shape of the derivative of the nine-layer case is similar to that of the single-layer case given by Example I (Fig. 3). Consequently, identification of such a layer system may not be possible and may also lead to an incorrect interpretation, particularly in estimating the vertical permeability and the distance to the boundaries. As Fig . 6 also shows, it is difficult to say which averaging techniques work better for vertical permeability. Therefore, a multilayer reservoir generally cannot be treated as an equivalent single-layer system, except when the permeability variations are small .30 . In addition, the behavior of the gas and water zones may differ from that of the constant-pressure boundary condition, and the effect of a gas cap or a water zone should not automatically be assumed 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, such as no-flow and/or constant-pressure boundaries, on the transient behavior of horizontal wells have been recognized. Flow regimes have been presented for system identification and for estimation of a number of reservoir parameters. A wide variety of testing equipment (hardware) for vertical wells has been adapted for testing horizontal wells. Production logging and/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 tests from horizontal wells is much more difficult than for vertical wells . A large anisotropy ratio and the existence of multiple boundaries with unknown distances to the wellbore increase the complexity of the interpretation. Minimizing the well bore storage effect is crucial for 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 without diagnostics 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 average properties. Nomenclature c/ = total compressibility, Lt 2tm , psi - I

h = thickness, L, ft k= permeability, L2, md L = length, L, ft m= slope n = number of layers p= pressure, mlLt 2, psi q = flow rate, L 3tt, RB/D r = radius, L, ft S= skin t = time, t, hours x, y, z = coordinates, L, ft Jl = viscosity, mILt, cp ljJ = porosity, fraction Subscripts D= H= hr= i= 1= 0=

40

dimensionless horizontal hour layer number linear initial or original

p = producing

r= radial ss = steady-state t= total v= vertical w= 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 \. Renney, L.: " Drilling Wells Horizontally," Oil Weekly (Jan. 20,1941 ) 12. 2. Giger, EM., Reiss, L.H., and Jourdan, A.P.: "Reservoir Engineering Aspects of Horizontal Drilling ," paper SPE 13024 presented at the 1984 SPE Annual Technical Conference and Exhibition, Houston, Sept. 16-19. 3. Giger, EM.: "Horizontal Wells Production Techniques in Heterogeneous Reservoirs," paper SPE 13710 presented at the 1985 SPE Middle East Oil Technical Show, Bahrain , March 11-14. 4. Reiss, L.H.: "Production From Horizontal After 5 Years," 1PT (Nov. 1987) 1411; Trans. , AIME, 283. 5. Sherrard. D.W., Brice, B.W., and MacDonald , D.G.: "Application of Horizontal Wells at Prudhoe Bay," 1PT(Nov. 1987) 1417. 6. King, G.R. and Ertekin, T.: "Comparative Evaluation of Vertical and Horizontal Drainage Wells for the Degasification of Coal Seam s," SPERE (May 1988) 720 . 7. Babu, O.K. and Odeh, A.S.: "Productivity of a Horizontal Well," SPERE (Nov. 1989) 417 . 8. Joshi, S.D.: "Augmentation of Well Productivity With Slanted and Horizontal Wells," 1PT (June 1988) 729 ; Trans., AIME 285. 9. Karcher, BJ., Giger, EM ., and Combe , J.: "Some Practical Formulas to Predict Horizontal Well Behavior," paper SPE 15430 presented at the 1986 SPE Annual Technical Conference and Exhibition, New Orleans, Oct . 5-8. 10. Goode, P.A. and Kuchuk, FJ.: "Inflow Performance of Horizontal Wells," SPERE(Aug. 1991) 319. I \. Goode , P.A. and Wilkinson, OJ.: "Inflow Performance of Partially Open Horizontal Wells," 1PT(Aug. 1991) 983. 12. Kuchuk, FJ. and Saaedi, J: "Inflow Performance of Horizontal Wells in Multilayer Reservoirs," paper SPE 24945 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, DC, Oct. 4-7. 13. Clonts, M.D. and Ramey, HJ. Jr.: "Pressure Transient Analysis for Wells with Horizontal Drainholes,' paper SPE 15116 presented at the 1986 SPE California Regional Meeting, Oakland, April 2--4. 14. Goode, P.A. and Thambynayagam, R.M.: "Pressure Drawdown and Buildup Analysis for Horizontal Wells in Anisotropic Media," SPEFE (Dec . 1987) 683; Trans., AIME , 283. 15. Daviau, E et al .: "Pressure Analysis for Horizontal Wells," SPEFE (Dec . 1988) 716. 16. Ozkan, E., Raghavan, R., and Joshi, S.D. : " Horizontal Well Pressure Analysis," SPEFE (Dec. 1989) 567; Trans .• AIME , 287. 17. Odeh, A.S. and Babu, O.K.: "Transient Flow Behavior of Horizontal Wells: Pressure Drawdown and Buildup Analysis," SPEFE (March 1990) 7; Trans ., AIME, 289, 18. Kuchuk, FJ . et al .: "Pressure-Transient Behavior of Horizontal Wells With and Without Gas Cap or Aquifer," SPEFE (March 1991) 86; Trans ., AIME. 291. 19. Rosa, AJ and Carvalho, R.S.: " A Mathematical Model for Pressure Evaluation in an Infinite-Conductivity Horizontal Well," SPEFE (Dec. 1989) 559. 20. Ozkan . E. and Raghavan , R.: " Performance of Horizontal Wells Subject to Bottomwater Drive," SPERE (Aug . 1990) 375; Trans .• AIME, 289, 2\. Kuchuk, FJ. et al.: "Pressure Transient Analysis for Horizontal Wells," JPT (August 1990) 974; Trans., AIME, 289. 22. Abbaszadeh, M. and Hegeman, P.: " Pressure-Transient Analysis for a Slanted Well in a Reservoir With Vertical Pressure Support," SPEFE (Sept. 1990) 277; Trans ., AIME, 289. 23. Lichtenberger, GJ.: "Pressure Buildup Test Results From Horizontal Wells in the Pearsall Field of the Austin Chalk," paper SPE 20609 presented at the 1990 SPE Annual Technical Conference and Exhibit ion, New Orleans, Sept. 23-26 .

January 1995• JIYI'

24. Rosenzweig, U., Korpics, D.C., and Crawford, G.E.: "Pressure Transient Analysis of the JX-2 Horizontal Well, Prudhoe Bay, Alaska," paper SPE 206 10 presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 23-26. 25. Shah, P.C., Gupta , D.K., and Deruyck, B.G.: "Field Application of the Method for Interpretation of Horizontal-Well Transient Tests," SPEFE (March 1994) 23. 26. Suzuki, K. and Nanba, T.: "Horizontal Well Test Analysis System," paper SPE 206 13 presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 23-26. 27. Carvalho, R.S. and Rosa, AJ .: ''Transient Pressure Behavior for Horizontal Wells in Naturally Fractured Reservoir," paper SPE 18302 presented at the 1988 SPE Annual Techn ical Conference and Exhibition, Houston, Oct. 2- 5. 28. Williams, E.T. and Kikani, 1.: "Pressure Transient Analysis of Horizontal Wells in a Naturally Fractured Reservoir," paper SPE 206 12 presented at the 1990 SPE Annual Technical Confere nce and Exhibition, New Orleans, Sept. 23- 26. 29. Aguilera, R. and Ng, M.e.: "Transient Pressure Analysis of Horizontal Wells in Anisotropic Naturally Fractured Reservoirs," SPEFE (March 199 1) 95. 30. Kuchuk, FJ.: "Pressure Behavior of Horizontal Wells in Multilayer Reservoirs With Crossflow,' paper SPE 22731 presented at the 1991 SPE Annual Technical Conference and Exhibition, Dallas, Oct. 6-9. 3 1. Suzuki, K. and Namba, T.: "Horizontal Well Pressure Transient Behavior in Stratified Reservoirs," paper SPE 22732 presented at the 1991 SPE Annual Technical Confe rence and Exhibition, Dallas, Oct. 6-9. 32. Domzalski, S. and Yver, J.: "Horizontal Well Testing in the Gulf of Guinea," Oil Field Review (April 1992) 42. 33. Bourdet, D. et al.: "A New Set of Type Curves Simplifies Well Test Analysis," World Oll (May 1983). 34. Kuchuk, FJ . and Kader, A.S: "Pressure Behavior of Horizontal Wells in Heterogeneous Reservoirs," paper HWC94-25 presented at the 1994

JPT • January 1995

Canadian SPEICIM /CA NMET IntI. Conference on Recent Adva nces in Horizontal Well Applications, Calgary, March 20-23.

SI Metric Conversion Factors

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

E-OI =m E-04 =,um 2 E+OO = kPa

"Conva rsion factor is exact.

Fikri J. Kuchuk is ch ief reservo ir engineer for Schlumberger Middle East in Dubai. He was a sen ior scientist and a group leader at Schiumberge r-Doll Research Center, Ridgefield , CT, and conducted research in pressure transient testing , inverse problem , flow through porous media , and downhole pressure and flow rate measurements. He was a consulting pro fessor in the Petroleum Engineer ing Dept. of Stanford U. during 1988-1994. Kuchuk was the recipient of the 1994 Reservoir Engineering Award. He was the Program Chairman for the 1993 Annual Technical Conference and Exhibition and has chaired many SPE technical committees.

41