An Analytical Pressure-Transient Model for Multilayered, Composite Reservoirs With Pseudosteady-State Formation Crossflow

Abstract

ABSTRACT Reservoir deposition occurs over geologic periods of time. Although reservoirs are assumed homogeneous for simplicity of analysis, most reservoirs are heterogeneous in nature. Some common forms of heterogeneity are the presence of layers and the presence of different zones of fluids and/or rocks in the formation. In this study, a new analytical solution for multi-layered composite reservoirs with pseudosteady state interlayer crossflow has been developed. Fluid flow in the reservoir has been treated as a generalized eigenvalue problem. The developed analytical solution for an n-layered composite reservoir is applicable for any irregularly-shaped discontinuity boundary, and for closed, constant-pressure and infinite outer boundary conditions. This new solution is computationally very efficient. Using eigenvalues and eigenvectors of the system, this method requires solution of an order of magnitude fewer simultaneous equations as compared to other methods proposed in the literature. This method is also very versatile and can handle multiple composite regions (more than two), and partially-penetrating wells subject to bottom-water and/or gas-cap drives for well testing purposes. This analytical model has been validated by comparing the results with those of some simple, well-known models in the well testing literature. Solution methodology and future possibilities of the new solution have also been discussed.