Numerical Simulation of Three-Phase Flow in Heterogeneous Porous Media

We describe an efficient numerical simulator, based on an operator splitting technique, for three-phase flow in heterogeneous porous media that takes into account capillary forces, general relations for the relative permeability functions and variable porosity and permeability fields. Our numerical procedure combines a non-oscillatory, second order, conservative central difference scheme for the system of hyperbolic conservation laws modeling the convective transport of the fluid phases with locally conservative mixed finite elements for the approximation of the parabolic and elliptic problems associated with the diffusive transport of fluid phases and the pressure-velocity calculation. This numerical procedure has been used to investigate the existence and stability of nonclassical waves (also called transitional or undercompressive waves) in heterogeneous two-dimensional flows, thereby extending previous results for one-dimensional problems.