A Nonlinear Approximation for the Pressure Behavior of Heterogeneous Reservoirs

Abstract

Abstract Recent years have seen extensive use of analytical techniques to study pressure behavior in layered, laterally, and radially composite systems. In this paper, we present a new approximate method to describe the transient pressure behavior of heterogeneous reservoirs. The reservoir is subdivided into a collection of subregions with different rock properties embedded in an otherwise homogeneous background that is defined as a homogeneous region, a stack of layers, or a radially symmetric composite structure. However, both the background medium and the anomalous region may exhibit three-dimensional (3D) anisotropy. The proposed method of solution is formulated in the Laplace transform domain wherein both wellbore storage and skin effects can be included in an algebraic fashion. Beginning with the integral equation solution for the pressure diffusion in porous media, we derive a nonlinear approximation with respect to the spatial variations in reservoir properties. This solution may accurately handle high contrasts in reservoir properties as well as large anomalous regions such as deltaic sandstones and sorted channels systems. For small contrasts, the proposed nonlinear approximation reduces to the Born approximation. We present comparison tests with available analytical solutions such as those related to finite-width strips.