Séminaire Théorie

Mardi 27 Septembre 2016 à 11h00.

The Archie law in a model of diffusion in porous media

''The diffusion coefficient D of a gas or of a solute in porous media is frequently related to the porosity  by the Archie law (1942) as D/D0  m, where D0 is the coefficient in a free medium and m is called cementation exponent, with experimental values ranging from  1.3 to  5. This relation was originally used to fit data for the analogous problem of electrical conductivity in saturated solution. The Archie law with a broad range of exponents m may be explained by effective medium theories applied to models of disordered solids. Here I introduce a model of random walks in a lattice that represents a mi- cro/nanoporous granular solid with randomly distributed macropores. Step rates de- pend only on the target site: 1 to macropore, p to interfacial solid, and q to bulk solid, with q  p  1. Steps may be allowed only to nearest neighbor sites or also extended to next nearest neighbors sites. For q  0.1p, D/D0 approximately fits the Archie law up to low porosity. For larger q/p, D/D0 saturates as  decreases, and for smaller q/p, D/D0 deviates to very small values due to confinement of tracers to clusters of P and I sites. The effective exponent m increases as p decreases, but does not depend on q. This shows that interfacial diffusion is the rate limiting mechanism of the problem. Smaller p is associated to a higher degree of compaction of the solid grains, which provides a consistent stochastic interpretation of the cementation concept.''