Comparative study of computational methods for the solution of the two-dimensional reservoir flow equations

Abstract

Several methods have been developed for solving the system of linear equations that arise in approximating the solution of two-dimensional reservoir flow equations. Those methods solve the system of linear equations either directly or iteratively. In this thesis a comparative study of the most commonly used methods is made. The study includes a full analysis of each method plus a comparison of the computing efficiencies in terms of both the computation times and the memory space requirements. It also includes a discussion of grid ordering techniques that have appeared in the literature. The test problem used in the comparison is a homogeneous, two-phase (oil-water), two-dimensional five-spot water flooding. A simple two-phase three dimensional reservoir simulator was used. The results showed D4-Gaussian Elimination method to be the most efficient of the direct methods while the Point Successive Over-relaxation method was the most efficient among the iterative techniques. Nested Factorization method had the fastest convergence of all the iterative techniques.