A control volume based finite element method for simulating incompressible two-phase flow in heterogeneous porous media and its application to reservoir engineering

Abstract

Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces. Discontinuity of velocity field leads this method not to conserve mass locally. Moreover, the accuracy and stability of a solution is highly affected by a non-conservative method. In this paper, a three dimensional control volume finite element method is developed for two-phase fluid flow simulation which overcomes the deficiency of the standard finite element method, and attains high-orders of accuracy at a reasonable computational cost. Moreover, this method is capable of handling heterogeneity in a very rational way. A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution. The accuracy and efficiency of the method are verified by simulating some waterflooding experiments. Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.