correction of vertical permeability estimated by horizontal-well ...

This article was downloaded by: [Sultan Qaboos University] On: 23 July 2013, At: 01:38 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Petroleum Science and Technology Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/lpet20

CORRECTION OF VERTICAL PERMEABILITY ESTIMATED BY HORIZONTAL-WELL PRESSURE TRANSIENT TEST ANALYSIS a

a

A. S. Al-Bemani , F. H. Boukadi & M. H. Al-Jabri a

b

Sultan Qaboos University, Oman

b

Schlumberger, Oman Published online: 07 May 2007.

To cite this article: A. S. Al-Bemani , F. H. Boukadi & M. H. Al-Jabri (1999) CORRECTION OF VERTICAL PERMEABILITY ESTIMATED BY HORIZONTAL-WELL PRESSURE TRANSIENT TEST ANALYSIS, Petroleum Science and Technology, 17:7-8, 829-842, DOI: 10.1080/10916469908949751 To link to this article: http://dx.doi.org/10.1080/10916469908949751

PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

PETROLEUM SCIENCE AND TECHNOLOGY, 17(7&8), 829-842 (1999)

CORRECTION OF VERTICAL PERMEABILITY ESTIMATED BY

Downloaded by [Sultan Qaboos University] at 01:38 23 July 2013

HORIZONTAL-WELL PRESSURE TRANSIENT TEST ANALYSIS

A. S. AI-Bemani*, F. H. Boukadi* & M. H. AI-Jabri**

*Sultan Qaboos University-Oman **Scblumberger-Oman

ABSTRACT Different data are required in order to establish a realistic reservoir model capable of predicting the dynamic field behaviour during the development stage of an oil field. Well testing is considered to be one of the most effective methods for obtaining these reservoir and wellbore data. Numerous analytical models are available and utilised in investigating vertical-well pressure transient tests, on the other hand, horizontal-well pressure transient tests have been considered as more difficult to analyse. In this work, well test data of a horizontal-well are simulated for homogeneous isotropic and anisotropic reservoirs and analysed in order to develop empirical correlations that rectify the vertical reservoir permeability estimated by well testing.

INTRODUCTION The mechanical process of drilling highly accurate horizontal wells is becoming a common practice. The idea of using such wells that increase the

829 Copyright If:I 1999 by Marcel Dekker, Inc.

www.dekker.com

830

AL-BEMANI, BOUKADl, AND AL-JABRI

area of contacted reservoir dates back to the early I940s. At first, there has been little incentive to this technology especially in the presence of hydraulic fracturing as a potential rival. Recently, several studies and experience found that horizontal wells could be used to accelerate production, avoid certain


production problems, and to increase recovery in oil and gas fields. The use of transient well testing for determining productivity of horizontal well becomes a common practice because of the widespread application of this technique.

LITERATURE REVIEW Over the last decade, numerous analytical models have been developed to analyse horizontal-well pressure transient data. The objectives of analysing this data are to obtain useful information about reservoir properties, the producing interval of the drilled length and to estimate mechanical skin factor. Goode and Thambynayagam (1987) first developed an analytical solution for the characteristic transient-pressure response during drawdown and build-up of a horizontal well. The physical model consist of an infinite conductivity horizontal well of a wellbore "r;" and length "L;" located in a homogenous, anisotropic reservoir of a width "h,", length "h,' and uniform thickness of "h," (Fig. I). The reservoir is bounded by upper and lower no flow boundaries. It has been reported in the literature that, interpretation of horizontal-well pressure transient data is a much difficult task than its vertical counterpart


VERTICAL PERMEABILITY ESTIMATES

831

Figure 1: Horizontal Well Configuration

(Kuchuk, 1995). This is because of several reasons such as: • Lack of symmetry beyond the early time. • Effect of the boundaries (lower, upper and side). • Large wellbore volume of a horizontal well. • Pressure variation along the horizontal section. Similar to the pressure transient behaviour of a vertical well intersecting infinite conductive fracture, there are four primary flow regimes (excluding the wellbore storage effects period) that are theoretically possible to be recorded during a drawdown or build-up test in a horizontal well (Goode and Thambynayagm, 1987; Lichtenberger, 1994). Identification of these flow regimes is essential for test planning and interpretation of the pressure transient test data. In many cases, these primary patterns are distorted or

832

AL-BEMANI, BOUKADI, AND AL-JABRI

eliminated because of reservoir heterogeneity, wellbore storage and boundary effect (Lichtenberger, 1994). These flow regimes that are expected to develop within specific time windows depend on the reservoir and fluid properties. Flow regimes can be identified with a diagnostic plot of the pressure transient


data. Goode and Thambynayagm (1987) derived empirical models for estimating the time windows. In chronological order the four flow regimes are identified as: Early Time Radial Flow (ETRF): As the horizontal well is first produced, the pressure transient will move out perpendicular to the wellbore. The flow is radial around the well. This is very similar to a fully penetrated, vertical well in an infinite acting reservoir. On the diagnostic plot, the fully developed first radial flow has a constant derivative. A semilog plot of sandface pressure

"Pwr" vs. time "t" will be a straight line with slope (rn') that yields the horizontal permeability "k;", the vertical permeability "k," and the mechanical skin "sm". The duration of this flow period is normally very short unless the reservoir thickness is large or the vertical permeability is very low. The time to the end of the early-time radial flow period (f"t) can be approximated by: I'if

=

190.0hi

09' r:09'¢J.lC, k,

(1)

Intermediate Time Linear Flow (lTLF): When the length of the horizontal well is much greater than the thickness of the reservoir, a period of linear flow may develop once the pressure transient has reached both the upper and lower

833


boundaries. The reservoir fluid streamlines are parallel to the no-flow boundaries and normal to the wellbore direction at some distance from the wellbore. This flow regime is recognised by the first non-zero slope on the diagnostic plot. A cartesian plot of "Pwr" vs.


(rn") that yields k" hz, or L, and

Sm.

".Ji" will be linear with slope

The duration of this second major flow

regime is directly related to the effective length of the horizontal well. Intermediate time linear flow (I'If) is estimated to end at: I'lf

=

20.8,pJU:, L~

k,

(2)

If this time is less than that calculated in equation I, it may mean that the

length of the horizontal well is not sufficient compared to the thickness of the formation for this flow period to develop. Late Time Radial Flow (LTRF): When the dimensions of the drainage area in the horizontal plane is much larger than Lw, flow towards the horizontal wellbore becomes effectively radial in nature after a long enough time. This situation is similar to the late-time behavior of a vertical well with a vertical fracture. A semilog plot of "Pwr" vs. "t" will be a straight line with slope (rn'") that yields kh and

Sm'

The second radial flow period (also known as

pseudoradial flow) corresponding to the late intermediate time will begin at:

I hif

=

1230.0L~,pJU:, k x

and for a reservoir of finite width, this flow period will end at:

(3)

834


I'if

= 297.0

(

L" + t-: )

2.095

kx

-0.095

t;

¢J1C,

(4)

If the estimated time to the end of the late time radial flow is less than the calculated beginning, then the well is long compared to the distance to the


extremities (Lx" Lxd ) of the reservoir and this radial flow period will not develop. Late Time Linear Flow (LTLF): This final flow pattern occurs when the pressure transient has reached the lateral extremities of the reservoir. Naturally, this flow period will develop only for a reservoir of finite width, and there is a constant pressure source such as aquifer or gas cap. The slope (m?") of the linear section resulting from the pwf vs. .[I on a Cartesian plot

«:»,

yields - - . f.J

In addition to these flow regimes, other flow regimes may also develop (Goode and Thambynayagm, 1987; Lichtenberger, 1994 and Kuchuk, 1995). For example, a hemicylinderical flow period may occur when the well is close to one of the no-flow boundaries. There may also be a spherical flow period if the length of the horizontal well is much smaller than the formation thickness. Therefore, reservoir and wellbore parameters could be estimated accurately after identification of flow regimes. Table 1 below summarises the procedure required:

835

VERTICAL PERMEABILITY ESTIMATES Table 1: Horizontal-Well Pressure Transient Test Analysis Reaioa ETRF

Plot Type Semi-Log

ITLF

Cartesian

LTRF

Semi-Log

LTLF

Cartesian

Parameters Plotted pwfVS. t PwfVS.

Parameters Estimated

~k.k.

.J/

l/JC,ky


II.

~kxky

Pwf vs. t Pwf vs.

.J/

l/JC,k y II.

Determination of the above reservoir parameters accurately is very difficult. Well completion and placement playa very important role in the estimated parameters. Vertical reservoir permeability could be underestimated, as pressure response symmetry near the wellbore is disturbed. Therefore, well placement, during analysis of pressure transient test in horizontal well, should be considered to overcome the additional pressure drop in Z-direction due to k, hence vertical permeability correction. The objective of this study is to

develop

empirical

correlations,

which

relate

the

estimated

vertical

permeability from horizontal-well pressure transient test to the actual vertical permeability for homogeneous isotropic and anisotropic reservoirs.

CONCEPTUAL MODELS AND PROCEDURE In this work, horizontal-well pressure transient test data are simulated using Eclipse-IOO black-oil

simulator.

Two

reservoir

models

of different

836

AL-BEMANI, BOUKADl, AND AL-JABRI


Table 2: Simulator Input (Reservoir, Fluid and Well bore Parameters) Property Permeability Porosity Total Thickness Drainage Radius Number of Layers Initial Reservoir Pressure Bubble-point Pressure Oil Formation Volume Factor Oil Viscosity Total Cornnressibilitv Wellbore Radius Wellbore Damage (skin factor) Horizontal Section Length

Value 3.75 & 37.5 mD 0.25 & 0.30 360 ft 6,280 ft 9 Layers 3,900 psi 3,414 psi 1.4154 rb/stb 0.31 cp 1.494 E-05 psi" 0.5 ft 0 1,848 ft

permeability values are constructed for both homogeneous isotropic and anisotropic reservoirs. The range of permeability is between 3.75 and 37.5 mD.

The anisotropicity is addressed by setting a vertical to horizontal

permeability ratio of "kz/kh=O.l". This anisotropicity ratio is common to most Oman oil fields. Reservoir, fluid and wellbore properties are shown in Table2. The reservoir is divided into nine homogeneous layers. These layers have equal thickness and they are assumed to be in communication. Nine cases of different well penetration "h ~." ratio are considered for every reservoir model. h

Where:

,

P'

h =T , p"

(5)

VERTICAL PERMEABILITY ESTIMATES hp n

:

837

the distance from the closest impermeable boundary (lower or upper) to the depth of penetration

h,

: the total reservoir thickness

Therefore, a total of thirty-six sensitivity runs are simulated to produce both


drawdown and build-up pressure behaviour data. These pressure data are then analysed using the flow regime recognition concept. PanSystem well-testing package is used to estimate the reservoir and wellbore parameters from the pressure behaviour.

Empirical correlations are then produced to relate the

actual permeability to that estimated by analysing well testing data.

DISCUSSION Thirty-six sensitivity runs are simulated to produce pressure transient test data of a horizontal-well drilled and completed in homogeneous isotropic and anisotropic reservoirs. Nine different penetration depths in two different reservoirs of two different permeability/porosity ranges are used. The pressure data are analysed using PanSystem well-testing package. In analysing the tests, diagnostic plots are used to identify the flow regimes. The early-time radial and the late-time radial flow regimes have appeared as straight line with zero slope. The intermediate-time (first) linear flow regime developed between the two radial flow regimes, due to the assumption of a larger horizontal well section in comparison to the reservoir thickness. By analysing the tests, all of the input reservoir and wellbore parameters were estimated correctly except

838



Table 3: Input/Output Vertical Permeability Results Penetrated Layer

h~1I

1 2 3 4 5 6 7 8 9

0.06 0.17 0.28 0.39 0.50 0.39 0.28 0.17 0.06

Input

Isotropic Output

k",.mD

k" mD

3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75

0.94 2.28 2.86 3.16 3.75 3.16 2.84 2.27 0.94

k,./k",

0.251 0.608 0.763 0.843 1.000 0.843 0.757 0.605 0.251

Input

Anisotropic Output k,./k",

k .mD

k", mD

0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375

0.172 0.283 0.336 0.374 0.375 0.373 0.337 0.281 0.176

0.459 0.755 0.896 0.997 1.000 0.995 0.899 0.749 0.469

Table 4: Input/Output Vertical Permeability Results Penetrated Layer

h~1I

I

0.06 0.17 0.28 0.39 0.50 0.39 0.28 0.17 0.06

2 3 4 5 6 7 8 9

Input i: mD 37.5 37.5 37.5 37.5 37.5 37.5 37.5 37.5 37.5

Isotroolc Output k,.Ik", k". mD 8.35 0.223 11.91 0.318 23.73 0.633 32.14 0.857 37.43 0.998 32.12 0.857 23.74 0.633 11.97 0.319 8.35 0.223

Input k""mD 3.73 3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.75

Anisotrooic Output k,.. mD 1.63 2.45 3.23 3.70 3.75 3.69 3.23 2.42 1.63

k,.Ik",

0.437 0.653 0.861 0.987 1.000 0.984 0.861 0.645 0.435

the vertical permeability. The vertical permeability was only estimated as an input value when the penetration depth was in the center of the reservoir (h ~"=0.5). Table 3 and 4 show the comparison between the input k", (to

EclipselOO) and output kze (from PanSystem) for different penetration ratio cases.


1.2

839

fr------,..----------------, y = 0.281 Ln(x) + 1.2301 R' = 0.9697

0.9


0.6

0.3 1-

----

o

0.1

0.2

~

0.3

0.4

0.5

Figure 2: Vertical Permeabilty with Respect to Penetration Ratio for Anisotropic Re...rvolr

The ratio between the estimated vertical permeability k" to the actual one k", can be plotted against the penetration ratio h ~n in order to establish the empirical correlations that correct the estimated vertical permeability. As illustrated in both figures 2 and 3, the actual vertical permeability could be determined within an accuracy of more than 90% using the following equations: Anisotropic reservoirs:

k~

=

k"

(6)

0.28Iln(hpJ + 1.2301

Isotropic reservoirs: k," =

k~,

0.34281n(h pn ) + I.I 544

,

(7)

840


y

= 0.3428Ln(x) + 1.1544 A' = 0.882

0.7


0.4

0.1

1----_----_----_----_---___" o

0.1

0.2

0.3

0.4

0.5

Figure 3: Vertlcal Permeability with Respect to Penetration Ratio for Isotropic Reservoir

The above cases emphasise the errors encountered in estimating the vertical permeability as the horizontal section penetrates any depth but the middle of the reservoir. The calculation of vertical permeability depends on the development of both radial flow regimes. By analysing the first radial flow, the slope of pwr vs. t on a semi-log plot m' yields (kzk h) 112 from the following equation: l62.6q.Jl.{3" m Li;

(8)

Whereas analysing the second radial flow, the slope of pwr vs. t on a semi-log plot rn'" yields kh from the following equation: k. =

l62.6~nJln{3n m h,

(9)


841

The second radial flow develops when the system has not reached the outer boundary and this is similar to that of the vertical-well radial flow behaviour and the permeability estimated from this flow regime is kh or (kxky)ln. In this flow regime, the reservoir thickness and the outer boundary play an important


role in pressure response symmetry in the reservoir, and as the reservoir is large compared to the horizontal section length, the pressure behaviour at this flow regime acts as if the reservoir is infinite. The first radial flow develops when the system has not reached the impermeable upper and lower boundaries. Unless the horizontal section penetrates the middle of the reservoir, the pressure response will detect unsymmetrical pressure behaviour across the well section. This translates into additional pressure drop or larger value of m' and lower value of k, compared to the actual vertical permeability of the system (see equation 8). In this flow regime, the length and the depth of penetration of the horizontal section play an important role in pressure response symmetry in the reservoir. Other than penetration in the middle of the reservoir, the estimated vertical permeability should be corrected.

CONCLUSIONS Similar to its vertical well counterpart, horizontal-well pressure transient test could be analysed using flow regime recognition patterns. Pressure drop due to partial completion (hence higher mechanical skin factor) in vertical-well pressure transient test is also experienced in horizontal-well leading into

842


erroneous estimation of vertical permeability. The closer the depth of penetration to the impermeable layer is the higher the difference between the actual and the estimated permeability. Empirical correlations have been developed to determine the actual permeability from the calculated one from


pressure transient test data of a horizontal-well drilled and completed in either isotropic or anisotropic homogeneous reservoir.

REFERENCES I. Goode, P.A., and Thambynayagam, R.M. 1987. Trans. AIME. December: 683-697. 2. Kuchuk, FJ. 1995. SchlumbergerTechnical Services. U.A.E. 3. Lichtenberger, GJ. 1994. Journal of Petroleum Technology. February: 157-162.

Received: July 11, 1998 Accepted: August 30, 1998