Solutions to a model for compressible immiscible two phase flow in porous media

Abstract

In this article, we study the existence of solutions to a nonlinear degenerate system modelling the displacement of two-phase compressible immiscible flow in a three dimensional porous media. The aim of this work is to treat the model with its general form with the whole nonlinear terms. Especially, we consider the case where the density of each phase depends on its corresponding pressure. We derive new energy estimates on velocities, saturations and pressures to treat the degeneracy of the system. A compactness result is shown for degenerate systems.

Keywords

• Degenerate system
• nonlinear parabolic system
• compressible flow
• porous media