Scaling Concepts in Porous Media

Abstract

Scaling concepts in disordered matter should be of use to the physics of porous media (POM)1. The applications of such media are numerous, ranging from hydrogeology, oil industry, chromatography and filtration, and justify the lasting interest for this physics2. We will focus our attention towards the effect of disorder in POM and, more precisely, that of multiple scales in the geometry of the fluid(s) penetrating them; but we will also recall some basic properties of POM. Geometrical disorder in POM has several origins: There is a strong contrast between the material properties of the solid phase and the fluid one(s) penetrating it. The pore space can range from homogeneous to very heterogeneous (e.g. from sintered materials obtained with a relatively uniform particle size distribution to fractured rocks presenting an irregular distribution of cracks of variable size, aperture...). Heterogeneous POM often present a large range of geometrical scales. In multiple phase flows, the distribution of the fluid phases contained in the POM introduces additional heterogeneities and multiplicity of scales. Local heterogeneities like those due to roughness or of chemical nature (e.g. presence of clays in sandstones) control the wetting properties in polyphasic flows. We will not consider this last class of parameters which, nevertheless, are of dramatic practical importance. Chemical surface effects can also model the properties of walls in random field problems: the advancing front of a wetting fluid on an heterogeneous surface (or, possibly, in a porous material made of wettable and non wettable properties) displays some characteristic features (rough interfaces, hysteresis) of R.F. systems4 discussed in the article by Villain.