A Finite-Element Method for Reservoir Simulation

Abstract

Several previous studies have applied finite-element methods to reservoir simulation problems. Accurate solutions have been demonstrated with these methods; however, competitiveness with finite difference has not been established for most nonlinear reservoir simulation problems. In this study a more efficient finite-element procedures is presented and tested. The method is Galerkin-based, and improved efficiency is obtained by combining Lagrange trial functions with Lobatto quadrature in a particular way. The simulation of tracer performance, ion exchange preflush performance, and adverse mobility ratio miscible displacements is considered. For the problems considered, the method is shown to yield accurate solutions with less computing expense than finite differences or previously proposed finite-element techniques. For the special case of linear trial functions, the method reduces to a five-point central difference approximation. In contrast to previously reported results, this approximation is found to simulate adverse mobility ratio displacements without grid orientation sensitivity, provided a sufficiently fine grid is used.