Darcy’s Law for Flow in Porous Media and the Two-Space Method

Abstract

A common problem in engineering and science is to derive simple equations governing complicated phenomena. Often complicated governing equations are known, but they are too difficult to analyze. An example of a simplified equation is Darcy’s law, which describes flow of a viscous fluid through a porous medium. The more complicated equation for the same phenomenon is the Navier-Stokes equation. As an example of a general method for simplifying equations, This chapter shows how to derive Darcy’s law from the Navier-Stokes equation. Simplified equations are often called “homogenized equations,” and the procedure of replacing the original equations by them is often called “homogenization.” The chapter discusses the two-space method for deriving simplified equations by using an example of the flow of a compressible viscous fluid through a rigid porous medium.