Analysis and numerics for multiphase flow in porous media

Abstract

This chapter addresses some developments of analysis and numerics for multiphase flow in porous media. Mathematical properties and numerical analysis for a degenerate elliptic–parabolic partial differential system that describes the flow of two incompressible, immiscible fluids in porous media are discussed. The objective of porous media simulation is to understand the complex chemical and physical fluid flow and transport processes occurring in a porous medium sufficiently well to be able to optimize the recovery of hydrocarbon. A numerical model is determined that has the required properties of accuracy and stability and that produces solutions representing the basic physical features as well as possible without introducing spurious phenomena associated with the specific numerical scheme. A computer code capable of efficiently performing the necessary computations for the numerical model is developed. The processes of multiphase flow and transport involve convection, or physical transport, of fluids through a heterogeneous porous medium. The equations used to simulate them at a macroscopic level are variations of Darcy's law.