Polynomial filtration laws for low Reynolds number flows through porous media

In this work we use the method of homogenization to develop a filtration law in porous media that includes the effects of inertia at finite Reynolds numbers. The result is much different than the empirically observed quadratic Forchheimer equation. First, the correction to Darcy’s ∗The research of A.M. was partially supported by the GDR MOMAS (Modélisation Mathématique et Simulations numériques liées aux problèmes de gestion des déchets nucléaires) (PACEN/CNRS, ANDRA, BRGM, CEA, EDF, IRSN) as a part of the project ”Modèles de dispersion efficace pour des problèmes de Chimie-Transport: Changement d’échelle dans la modélisation du transport réactif en milieux poreux, en présence des nombres caractéristiques dominants. ” . It was initiated during the stay of A.M. as Visiting Researcher at the ICES, University of Austin in May 2007, supported through the J. T. Oden Faculty Fellowship.