Darcy, Forchheimer, Brinkman and Richards : classical hydromechanical equations and their significance in the light of the TPM

Abstract

In hydromechanical applications, Darcy, Brinkman, Forchheimer and Richards equations play a central role when porous media flow under saturated and unsaturated conditions has to be investigated. While Darcy, Brinkman, Forchheimer and Richards found their equations mainly on the basis of flow observations in field and laboratory experiments, the modern Theory of Porous Media allows for a scientific view at these equations on the basis of precise continuum mechanical and thermodynamical investigations. The present article aims at commenting the classical equations and at deriving their counterparts by the use of the thermodynamical consistent Theory of Porous Media. This procedure will prove that the classical equations are valid under certain restrictions and that extended equations exist valid for arbitrary cases in their field.