A Hyperbolic-Elliptic Model of Two-Phase Flow in Porous Media — Existence of Entropy Solutions

Abstract

We consider the flow of two-phases in a porous medium and propose a modified version of the fractional flow model for incompressible, two-phase flow based on a Helmholtz regularization of the Darcy phase velocities. We show the existence of global-in-time entropy solutions for this model with suitable assumptions on the boundary conditions. Numerical experiments demonstrating the approximation of the classical two-phase flow equations with the new model are presented.