Dynamics of porous saturated media, checking of the generalized law of Darcy

Abstract

The homogenization process applied to fi ne periodic deformable saturated porous medium under dynamic solicitations leads to the macroscopic description. This method enables us to perform a complete calculation of the effective parameters. The main fact is that the farmulation so obtained-similar to Biot's results-exhibits a generalized example of Darcy's law which contains all the dynamic couplings between the two phases. After recalling the main facts of the subject this work presents some properties of the generalized Darcy coefficient and an experimental checking. An agreement between experimental and numerical results using the homogenization process is obtained.

Frequency-dependent viscous flow in channels with fractal rough surfaces

“…Despite the great variability of the pore microgeometries considered in the literature [15][16][17][18] , it is generally found, both experimentally and numerically, that the normalized dynamic permeabilityk(ω) matches reasonably well a scaling function 19,20 which depends on a characteristic frequency ω c and a similarity parameter, M . Remarkably, M is usually found to be almost configuration independent and close to unity, as long as the pore surface is locally smooth 19,21,22 .…”

Computation of the dynamic thermal dissipation properties of porous media by Brownian motion simulation: Application to an open-cell aluminum foam

“…As a result, this models an infinitely large matrix as if the porous structure within the unit cell were replicated in all other unit cells, without discontinuities in the porous structure between one unit cell and the one adjacent. It can be proved from homogenization techniques 19 that this approach is valid if and only if the fundamental condition of scale separation is respected, that is, l / L Ӷ 1, where l is the characteristic dimension of the heterogeneities, L is the macroscopic characteristic dimension, and l / L is a measure of the separation of scales. This means that the microscopic characteristic length must be small compared to the macroscopic sample size and to the physical phenomenon characteristic size.…”

Using a Poroelastic Theory to Reconstruct Subsurface Properties: Numerical Investigation

“…Poroelastic theories have since been derived and improved by many authors (e.g. Auriault et al, 1985;Geertsma & Smith, 1961;Johnson et al, 1987).…”