Mathematical Model of Multiphase Flow through Porous Media

Introduction

In general, multiphase flows concern the flow of two or more immiscible fluids (phases) in a porous media. These are of immense practical relevance to subsurface contamination and remediation techniques. A distinguishing feature of multiphase flow, in comparison to single phase flow, is the existence of interfaces between fluids. At the microscopic (pore) scale, these interfaces are known to influence the system behavior by supporting non-zero stresses such that the pressures at the adjacent phases are not equal. Thus, to make a reliable mathematical model, it is necessary to identify and understand physical processes at microscopic scale and to describe their manifestation at the macroscopic (core) or field scale. The connection of the flow physics between these two scales can be understood by so-called upscalling. In the following the mathematical model is presented most part of which can also be found in [73, 72, 74].