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 obta, in 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.

Rapid evaporation-driven chemical pre-concentration and separation on paper

“…In porous media, the volumetric flow rate q per unit cross-sectional area is linked to the gradient in pressure P using Darcy's Law [53]:…”

Validity of Darcy's law under transient conditions

“…Many subsequent experiments, both in the laboratory and in the field, have shown its validity for steady-state conditions. Because of the law's importance, both for the management of ground-water resources and for its relevance to petroleum production, vigorous efforts have been made to give it a substantial theoretical basis (Gray and O'Neill, 1976).…”

Fragment de description de la physique des transferts thermiques dans le sous-sol

“…Nous ne nous étendrons pas davantage sur ce problème de changement d'échelle dont on trouvera une analyse beaucoup plus détaillée dans les références [1], [2], [3], [4] et [5] notamment. -le transfert de chaleur associé à la diffusion thermique dont on peut montrer qu'il peut se mettre sous la forme: -le transfert de matière associé à la diffusion moléculaire dont on peut montrer également qu'il peut se mettre sous la forme: …”