A New Finite volume Framework for Numerical Simulation of Two-Phase Flow in Porous Media

Simultaneous flow in porous media occurs in a large variety of engineering fields, such az enhanced oil recovery EOR by water flooding. In petroleum industry applications the nonlinear partial differential equations governing the multiphase flow through porous media are solved currently, almost exclusively by finite difference methods. In this study, the two phase flow through aporous medium is numerically studied. The governing Darcy eduations are discretized via a control volume aproach and the continuity equation is used to obtian the phase saturations. The pressure eguations are solved implicitly, while, an exlicit scheme is selected for obtianing the phase saturations. In order to maintain the problem generality, the effects of capillary pressure as well as the fluid compressibility is considered in the mathematical model. An unstructured traingular grid is used to enhance the solution accuracy around the injection and production wells. Also, utilizing the Fourier stability analysis, an adaptive time stepping is selected to optimize the computational effort is solution of the unsteady equations. At each time step, the Shilthuis material balance conditions are checked for the whole domain in order to ensure of the solution validity. The mesh independency of implemented model in computer program is verified by investigating the solution of a test case problem with different number of computational cells. Results show good agreement with the findings of conventional finite difference methods.