Characterization Of Heterogeneous Porous Media

by Mostafa FOURAR

Ecole des Mines de Nancy

Laboratoire d'Energétique et de Mécanique Théorique et Appliquée
Parc de Saurupt, 54042 Nancy Cedex, France

The objective of this study is to test a new approach to characterize heterogeneous porous media by using the inertia effect. Indeed, at high Reynolds number, the flow through porous media is governed by the Forchheimer equation (1914) which includes two-terms: a linear term to account for the viscous effect and a quadratic term to account for the inertia effect. Both terms depend on the characteristics of the porous media by means of the intrinsic permeability and the inertia coefficient. Determination of these parameters and those characterizing dispersion in porous media (tracer flow) may lead to a better characterization of the heterogeneity. To this end, numerical simulations were performed using 3DSL simulator. However, as 3DSL allows to simulate only flows at low Reynolds number (Darcy's law, 1856), I defined an equivalent permeability of the medium as follows:

For all the simulations, I supposed that the inertia coefficient is constant b_ÿ = b₀. Values of K_ÿ were generated using GSLIB (Deutsch and Journel, 1998) and a lognormal distribution with a mean permeability K and a variance σ²_ln(K). Different realizations were performed with N_x = N_y = 50 and different values of the correlation length in the x-direction (L = 0,2.5,5,10,15,20). Numerical simulations were also performed for homogeneous and stratified porous media.

For more information please contact Mostafa Fourar or see http://www.mines.inpl-nancy.fr/~fourar.