On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media

Abstract

Macroscopic balance equations for components, momentum and energy are established for a multiphase flow with diffusion, chemical reactions, heat transfer and exchanges of components between phases in a porous medium. These equations are established separately for each fluid phase, for the solid part of the medium, and for interfaces, by starting from the corresponding equations valid at the pore level and taking their mean value around each point. Then macroscopic entropy balance equations are derived. The entropy source density shows clearly the generalized fluxes and forces which appear in the problem, and suggests how to choose phenomenological equations. A simple example illustrating the method is given in the last paragraph, for a single phase flow with heat transfer in a porous medium. One obtains a generalized form of Darcy's equation. Rigorous conditions along the interfaces and contact lines in a multiphasic medium are given in Appendix.