Practical Aspects of Well Test Analysis Under Composite Reservoir Situations
Authors: Ambastha A.K. 
Published: March 2010

Abstract
Well test analysis using a composite reservoir model has become popular because of the flexibility provided by a composite reservoir model in visualizing numerous reservoir situations. A composite reservoir model is useful for analysing transient pressure data from acidization and fluid injection projects, oil or gas reservoirs with rock or fluid property contrasts) and geothermal reservoirs with thermal discontinuities. In the simplest case, a composite reservoir model is helpful in all reservoir situations, where we can consider the reservoir to be composed of two regions of different properties. Therefore, well test analysis based on a composite reservoir model is aimed at obtaining estimates of reservoir properties and skin factors corresponding to bath the inner and outer region data.

Introduction
Though linear, spherical(3), and elliptical(1–6) composite models have been discussed in the literature a radial(7–17) composite model has been a popular model to analyse well test data from a variety of reservoir situations. Generally, a two-region, radial composite reservoir model is used in practice (see Figure 1). In a two-region, composite reservoir idealization the reservoir is considered to be composed of two regions of different properties. The well may be producing (or injecting) at a constant rate and may exhibit wellbore storage and skin effects. The variable R denotes the discontinuity (or front) radius. There may also be a skin at the discontinuity. The dimensionless pressure solution, in Laplace space, for such a situation has been presented in References (9) and (11). Title Laplace space solution is inverted to the real space using Stehfest algorithm (1–8).
Well test analysis based on a radial, two-region composite reservoir model is aimed at obtaining estimates of discontinuity radius, and reservoir properties and skin factors corresponding to both the inner and outer region data. Problems associated with estimating discontinuity radius (or swept volume for fluid injection projects) have been discussed before(9.10,14.19.20). This paper addresses the issues related to data misinterpretation, and consequent misinterpretations of reservoir characteristics and skin factors, while analysing well test data using a radial, two-region composite reservoir model. All results presented in this paper have been generated using the solution presented in Reference (11).

Ideal Model Response
Figure 2 shows drawdown semi-log pressure derivative (PwD = d Pwd I d In tD) responses for a well located in an infinite, two-region, radial composite reservoir. The pressure derivative responses are graphed as a function of tRD with M and Fs as parameters. All variables are identified in the Nomenclature. Figure 2 applies for CD = S = sr = 0 situations. Pressure derivative responses are shown for several possible combinations of mobility and storativity ratios, which may be equal to, less than, or greater than unity. For two-region composite reservoir situations, Figure 2 shows that at early times an infinite-acting radial flow regime corresponding to the inner region mobility appears. The early time infinite-acting radial flow regime is identified as that portion of the responses where PWD has a constant value equal to one-half. Dimensionless pressure response during the early-time infinite-acting radial flow regime is expressed as: