Abstract

Naturally fractured reservoirs normally exhibit high horizontal permeability anisotropy. Orientation of anisotropy, degree of anisotropy, and maximum/minimum permeabilities are required to describe the reservoir flow anisotropy. These parameters are normally obtained from interference testing. A series of sensitivity study was conducted to investigate the reliability of these estimated parameters from an interference analysis. The results show that interference test analysis gives reliable estimate of the orientation of anisotropy. However, the degree of anisotropy, maximum/minimum permeabilities, and total compressibility are very sensitive if the degree of permeability anisotropy is high and if the well configuration is unfavorable. Among the above parameters, the degree of anisotropy is the least reliable.

Introduction

A reservoir which permeability varies with direction is considered as anisotropic permeability reservoir. Permeability anisotropy can be caused by many factors but is primarily caused by sedimentary processes or by tectonics. Tectonics plays important role on the stress pattern in the rock, which in turn controls the orientation and opening/closure of natural fractures. Thus, tectonics can cause significant horizontal permeability anisotropy.

In naturally fractured reservoirs the flow direction will be dominant along the open fractures which are normally oriented in a certain preferred direction. Elkin and Skov 1 applied anisotropic permeability in their analysis of interference test to infer the fracture trend in the Spraberry field, Texas. Later, Parson 2 showed that the gross behaviour of a regular fracture-matrix system is analytically equivalent to that of an anisotropic permeable medium.

Interference testing is commonly analyzed by the type-curve matching procedures of Papadopulos-Ramey.3,4 Our past experience indicated that estimated permeability anisotropy can be erratic for some unknown reasons. The objective of this study, thus, is to investigate the reliability of permeability anisotropy estimation using the type-curve matching procedures. Two published field interference data are also analyzed to reinforce the theoretical study.

Interference Analysis Using Type-Curve Matching

Theory of interference testing is well explained in Refs. 3 through 5. A brief description is given below to provide necessary background, definitions, and notations.

Pressure Distribution.

Pressure response in a homogeneous anisotropic reservoir can be described by the exponential-integral solution: 4,5

Equation 1

Here, ke is the geometric mean permeability defined by

Equation 2

and kr is the radial directional permeability defined by

Equation 3

where kHmax and kHmin are horizontal maximum and minimum principal permeabilities, respectively, and ? is the angle between observation well and horizontal maximum permeability axis with respect to active well. Eq. 1 is applicable when the following assumptions are hold:

  1. the reservoir is homogeneous anisotropic;

  2. the active-well/ observation-well system is infinite-acting;

  3. single-phase fluid flow;

  4. fully penetrated well;

  5. constant fluid and rock properties; and

  6. negligible gravity effect.

Pressure Distribution.

Pressure response in a homogeneous anisotropic reservoir can be described by the exponential-integral solution: 4,5

Equation 1

Here, ke is the geometric mean permeability defined by

Equation 2

and kr is the radial directional permeability defined by

Equation 3

where kHmax and kHmin are horizontal maximum and minimum principal permeabilities, respectively, and ? is the angle between observation well and horizontal maximum permeability axis with respect to active well. Eq. 1 is applicable when the following assumptions are hold:

  1. the reservoir is homogeneous anisotropic;

  2. the active-well/ observation-well system is infinite-acting;

  3. single-phase fluid flow;

  4. fully penetrated well;

  5. constant fluid and rock properties; and

  6. negligible gravity effect.

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