On the general equations for flow in porous media and their reduction to Darcy's Law

Abstract

A technique of local averaging is applied to obtain general equations which describe mass and momentum transport in porous media. The averaging is performed without significantly idealizing either the porous medium or the pertinent fluid mechanical relations. The resulting general flow equation is simplified to treat flow of a Newtonian fluid in a slowly deforming solid matrix for two special cases. For flow in an isotropic medium where convective and inertial terms are important, an equation is developed which is dependent only on five medium parameters which could be evaluated by experiment. Flow in an anisotropic medium is also analyzed, and the general equation is reduced to Darcy's law when the convective and inertial terms are neglected.