On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media

The purpose of this paper is to examine the 3D effect on flows at high velocities through homogeneous porous media. Results of numerical simulations of a steady incompressible Newtonian fluid flowing through a 2D and a 3D periodic porous media performed at various Reynolds numbers are presented. The flow patterns are described and the pressure and the shear stress at the fluid/solid surface are analyzed. In accordance with the macroscopic momentum balance equation applied to each periodic cell, the viscous and the pressure drags exerted by the solid grain on the fluid are calculated and their contributions to the deviation from Darcy's law are evaluated. Based on the analysis of flow structures and the evolution of the pressure and the viscous drags, three laminar flow regimes are identified: Darcy, transition and strong inertia. It is shown that the transition zone for the 3D-flow is very narrow in comparison with that of the 2D-flow. As a consequence, the non-Darcy 3D-flow is correctly modeled by Forchheimer's equation. This explains the success of this equation in interpreting most of the experiments performed in real (3D) porous media. (C) 2004 Published by Elsevier Ltd.