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 cri-teria 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 hori-zontal wells. Since Renney's! article in 1941, many articles dealing with reservoir engineering, PI, and well-testing aspects of horizon-tal wells have appeared in the literature.1-12In 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 data2 1- 26 and on the behavior of horizontal wells in naturally fractured27- 29 and layered30•31reservoirs 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 down-hole 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/reser-voir system by using characteristic features of both transient tests (drawdown and buildup) has increased considerably. This is particu-larly crucial for horizontal wells, where the early-time transient data are the most sensitive to the vertical permeability and skin if the well-bore 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 pa-pers that summarize the state of the art in an area of technology by describing recent develop-ments for readers who are not specialists in the topics discussed. Written by individuals rec-ognized 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 sys-tem.32_{The fluid profiles also provide information about standing} water and wellbore crossflow, both common phenomena.V Unfor-tunately, the wellbore crossflow during buildup tests makes inter-pretation 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 devel-oping 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 hori-zontal wells rather than to provide a scholarly review of the litera-ture on the subject.

Flow Regimes for Horizontal Wells

Let us consider a horizontal well (Fig. I) completed in an anisotrop-ic reservoir, whanisotrop-ich is infinite in thexandydirections. The formation permeabilities in the principal directions are denoted bykx

=

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 dis-tance from the wellbore to the bottom boundary isz.,..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.

derivatives Ex.2

.

_

~.

10-4

0.1

10

pressure

Zw

~

x

ky

L

o

~l(

Fig. 1-Horizontal well model.

I I I

Z

J--_L:_y--~

...

H-Lw

I I I

~---""""""

h

and the damage skin as

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

s

~

1.151[

~:,.

+

3.2275

+

2 log

1'(

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

~

v )

(AA)]

+

4 -

+

-

log - - - , kH ¢Ilc,r~

TABLE 1-RESERVOIR PARAMETERS FOR

EXAMPLES SHOWN IN FIG.3.

h

_kH

kv i; Zw Example

_.Q!L

(md) (md)

_J!!L

_J!!L

_~

.

1 100 100 10 500 20 0.00146 2 100 100 1 500 20 0.00389 3 100 100 5 500 5 0.00194 4 40 100 5 500 20 0.00197 5 200 200 1 500 20 0.00530 • WherefwD =(fW/2Lw

l(1

+jk~kV) -k_{v -}- _0.00026377Ct¢Il c, [2 (h )2] sjb emax zw. - z., • . (4)

wherelsfbe is the time to feel the second (farthest) boundary effect. In practice. Eqs. 3 and 4 may not be reliable because the¢Ilcr prod-uct 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. This information is useful when the wheretsnbeis the time to feel the effect of the nearest boundary. or where qis the constant flow rate,!i.PIhr=Po- Pw(t= I hour) for drawdown tests, and!i.Plhr=Pw(!i.t=1 hour) - (!i.t-0) for buildup tests.Pwat 1 hour for both tests is obtained from the semilog, Horner, or derivative plot.

In principle,the geometric mean permeabilityjkHk_vand 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 calcu-lati7 damage skin from Eq.2. However, because the dependence on kH/k_vis 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 - ¢Ilc, . 2 2

V - 00002637 t mm [zw.(h - zw)], (3)

. "I.snbe

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

10-2

Thirdradial

_

J

._.

Time

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

7

-

_r

Hemi-radial

-

..

..

r

--

.

First Radial Flow Regime. The first flow pattern for horizontal wells is elliptic-cylindrical.Aftersome 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.Itmay not developif the anisotropy ratio.kH/kV.is large.The behaviorof this regime issimilar to the ear-ly-time behavior of partially penetrated wells. The derivativesfor 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 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. Bourdetetal.33showed 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.PwanddPw/dInt.respectively.

10 OJ .2: Cii > .~

o

JPI' • January 1995 37

location of one of the boundaries changes with time, such as when the gas cap moves downward or when there is an unknown continu-ous 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,

mrz = _{2m rl} (5)

and

s

~

2302{

";;~.

+

32275

+

IO{

(1

+

f j ; ) ;:]

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

-r/lctrw

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.Ifthe 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 exhib-its 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/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 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 thex-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/kHh (9)

and the skin is

(10)

where S,

~

- 2303

IO{

~~.

(1

+

jf;}-

(~~.)]

- f j ;

L(t -

~v

+

~~)

(11)

38

Eq. 11 is valid only for

no

<2.5. The full expression given by

Kuchuket 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 some-what subjective. Clonts and Ramey,13 Goode and

Thambynaya-gam.!" Ozkan et ai.,16 and Odeh and Babu17presented 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 thex 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. Ifthe top or bottom boundary is at

a constant pressure, a steady-state pressure is achieved at the well-bore. The total skin can then be expressed as

s

= _{(jkHk v Lw/374.4q/l)!1Pss - 2.303} I [ 8h (nz w) (h - zw) fj;H] X og ( ~)cot

2h

+

--r::-

k_{v '} nr; 1

+

,;kv/kH . . . (14)

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

h

=

0.01jkvtCbP/cjJ/lCt, (15)

wheretcbpis the time to reach the steady-state pressure at the

well-bore. Alternatively, ifhis known, this equation may be used to

esti-mate 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 loca-tions of the lower and upper boundaries are known or identified

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

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 high-resolution 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 pres-ented to examine the behavior of a horizontal weII in a nine-layer

reservoir and in two equivalent single-layer reservoirs.The

nine-layer system consists of nine different-thicknesshorizontal 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 com-municates 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

aver-age vertical nneability

<

_{kv >}= hr7k7=lhj(kvl;or

<

_{kv >}=

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

100

~

kH

!iJ

kv

80

60

40

permeability, md

20

a

20-~

1O~

5

Vl~ ~~~~~~~~~~~ g)

15

·'.:·.:·:·::·\,:x";-,:·x

~

20

~

:£

5~

10

5~:il-~

1 5 .

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 exten-sion 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-timeintervals unless the fracture density

is very high and its conductivity is low.

1000

from the flow regime analyses,the horizontal and vertical

pennea-Lilities and damage skin canbeestimated 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 beeasily eliminated or reduced if the

down-hole flow rate is measured and analyzed with the bottorndown-hole pres-sure. As stated, a downhole shut-in tool should be used for buildup

tests, particularly for low-productivity wells,to minimize the

weII-bore storage effect.

It is well known that the estimated parameters for horizontal wells are strongly correlated. For instance, vertical permeability and

well-bore 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

log-arithm of the Homer time (tp+6.t}/6.t,wheretp is the producing

time and6.tis 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-hourproducing 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

pres-ented 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

prob-lem 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 thenbeincreased.

--nine-layer

• harmonic <ky>

---harmonic <kHky>

'R

gj'

.~

.~

... 100

QJ "0 --DO for kv=10md 11 BUfor kv=lOmd ---.- DD for kv=1md o BUfor ky=1md

100

10°

time, hr

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

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

and top no-flow boundaries. After a transition period, all curves flat-ten, indicating a late-time radial flow regime. This occurs because during this period the horizontal well behaves as a point-source well

in thex-yplane. As Fig.6shows, the behavior of the nine-layer

res-ervoir is completely different from that for a resres-ervoir with two equivalent single layers, except for the late-time radial flow regime,

which evolves in100hours. 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 inter-pretation, particularly in estimating the vertical permeability and the distance to the boundaries. AsFig.6also 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 varia-tions 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-pressureboundary.P

Conclusions

Over the last decade, significant progress has been made in develop-ing forward analytical models and interpretation techniques for hor-izontal 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 reli-able pressure and rate data for drawdown and buildup tests. Produc-tion 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 identi-fication tool that can also provide initial approximations of the non-linear estimation. Relying solely on nonnon-linear estimation without diagnostics may lead to an erroneous model and estimates.

The behavior of a multilayer reservoir with a horizontal well

can-not be treated as an equivalent single-layer system with average

properties.

Nomenclature

c/ = total compressibility,Lt2tm,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, L3tt,_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= dimensionless H= horizontal hr= hour i= layer number 1= linear 0= initial or original

40

p= producing r= radial ss = steady-state t= total

v=

vertical w= well

wf= flowing pressure (drawdown) x,y,

z

= coordinate indicator

Acknowledgments

Iam grateful to Schlumberger for permission to publish this paper.

Iam indebted to P.A. Goode,R.M.Thambynayagam, and DJ.

Wilkinson for their contributions to horizontal well testing.

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SI Metric Conversion Factors

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Fikri J. Kuchuk is chief reservo ir engineer for Schlumberger Middle East in Dubai. He wasa sen ior scientist and a group leader atSchiumberge r-DollResearch Center,Ridgefield ,CT, and conducted research in pressure transienttesting,inverse problem,flow through porousmedia,and downhole pressure and flowratemeasurements.He was a consultingprofessorin the Petroleum Engineer ing Dept. of Stanford U. during

1988-1994.Kuchuk was the recipient of the 1994ReservoirEngi

-neering Award. He was the Program Chairman for the 1993

Annual Technical Conferenceand Exhibitionand has chaired many SPEtechnical committees.

E-OI =m E-04

=,um

2 E+OO =kPa ft

x

3.048* md x 9.869233 psi x 6.894757

"Convarsionfactor is exact.

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