An Experimental Measurement of the Permeability of Deformable Porous Media
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AN EXPERIMENTAL MEASUREMENT OF THE PERMEABILITY OF DEFORMABLE POROUS MEDIA
A. AMBARI,* B. GAUTHIER-MANUEL** AND E. GUYON*** *Ecole Hassania des Travaux Publics, B.P. 1008 Casablanca, MARCO **Laboratorie d'Electrochimie des Solides, La Bouloie, 25030 BESANCON CEDEX ***Laboratoire HMP, E.S.P.C.I., 10, rue Vauquelin, 75005 PARIS FRANCE.
ABSTRACT Knowledge of the evolution of the permeability of cement throughout the course of hydration provides a suitable means to evaluate the evolution of the pore structure. The main difficulty is to measure permeability without disturbing the tenuous structure of the material at the beginning of the hydration. We have developed a differential permeability technique in which the applied flow is sufficiently weak that the structure of the medium is not disturbed. As an example of application of this technique we present measurement of the evolution of the critical permeability during a sol-gel transition.
INTRODUCTION The flow of a viscous fluid through a porous medium, and more generally the study of the transport properties within these media, are of considerable interest. On the fundamental side, understanding these properties belong to the general class of problems of transport in random geometries, the object of many studies. On the applied side, porous media problems are met in various fields of science: hydrology (partially and fully saturated soils, spread of pollutants); assisted recovery in oil fields; chemical engineering (filters, chromatography on gels, heterogeneous catalysis); and biophysics (transport across membranes). A first geometric characteristic of a porous system is the porosity 0, which is the volume fraction of the voids. The specific area S (area/unit volume) may be determined from adsorption isotherms. Both parameters can also be determined from stereological studies on random cuts if the medium is homogeneous and isotropic. However, these parameters alone do not fully characterize the pore size or, in particular, its connectivity. The permeability k introduced by H. Darcy [1]17 more than one century 2 ago is a geometric coefficient (homogeneous to (length) ) that relates the average flow rate per unit area in a permeable medium, Q, to an applied pressure gradient for a fluid of viscosity n: Q - -(k/q)Vp
(1)
This linear relation is obtained from a complex averaging of the viscous flow through the medium, as described by the Stokes equation. The average is taken on a representative elementary volume that is large compared with the pore size [2]. The relation is only valid at low Reynolds numbers (Re < a few units where Re-pk.v/n, v is a local velocity and k is of order of the pore size). A number of empirical formula relate the permeability to geometric characteristics of the porous media. The classical is the Kozeny-Carman [3] formula, which can be established for a random network of tubes having a 17
1n this original work, the ratio (k/*) was considered as the permeability The permeability, k, should be referred to as the (the Darcy permeability). sp
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