A compatible boundary element approach with geologic modeling techniques to model transient fluid flow in heterogeneous systems

Abstract

Multi-scale and arbitrarily shaped heterogeneous systems based on geological interpretation of structures, facies, and architectures in a piece-wise manner of variation are solved by a boundary element method (BEM) with systematic partition and coupling strategies. This technique extends the BEM to be compatible with geological models to obtain highly accurate pressure and production transients of multiple wells without finer grid sizes or smaller time steps. Comparisons to analytical solutions, existed BEM approaches, and semianalytical methods have validated this work in aspects of subdividing strategies and modeling accuracy. In this approach, two options are available to divide the reservoir into locally homogeneous subsystems: first is to partition along existed interface boundaries between different geo-bodies or structures and thus result in multiple irregular subsystems; the second is to subdivide the domain into identical rectangular subsystems and a few irregular subsystems as needed, and assign heterogeneity like finite difference or element simulators do. Each subsystem with uniformly average properties is then formulated in integral equations and systematically coupled with adjacent subsystems along interface boundaries to obtain solutions. Examples of calculating pressure and production transients of a fluvial system demonstrate its compatibility with both object and pixel based geologic modeling techniques. Pressure derivatives are very sensitive to geological facies with different rock properties. This work shows promises to develop BEM-based simulators.