Darcy's Law for a Heterogeneous Porous Medium
Francisco Duarte Moura Neto, Severino T. Melo · Journal of Porous Media · 2001
We consider slow viscous flow of a Newtonian fluid through a spatially varying porous medium. Applying the method of homogenization in a heterogeneous porous medium constructed by a microscopic, locally periodic structure we are able to derive an appropriate form of Darcy's law. This is a macroscopic relationship between the average fluid velocity and the overall pressure and external force mediated by a heterogeneous permeability tensor. A simple explicit example, which is amenable to analytical resolution and which exhibits part of the complexity of a general situation, is considered.