Percolation in two-scale porous media

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field. The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation threshold for the three-dimensional media is a decreasing function of the variance and correlation length of the threshold field. A simplified model predicts these trends in 3d; moreover, it suggested some effects in 2d which were all numerically verified. Received 17 August 2000     

Transport properties of compact clays. II. Diffusion

An experimental system was constructed in order to measure the diffusion coefficient in three types of porous media, namely mica, sodic montmorillonite, and natural compact clay. Several salts at various concentrations were used for the measurements in order to investigate the influence of these factors. Influence of porosity was also studied. In a first approximation, all the results can be summarized by a simple Archie's law independent of the clay and of the solute. The diffusion and electric formation factors have also been systematically compared; they generally agree for large porosities, while they disagree for small porosities for clay and montmorillonite.     

Transport Properties of Compact Clays

Conductivity and permeability of model and natural clays have been studied experimentally. Local properties such as porosity and zeta potentials were measured as functions of the electrolyte solutions. Whenever possible, experimental data were compared to numerical data obtained for random packings of grains of arbitrary shape, and a good agreement was found between them. Copyright 2001 Academic Press.     

Permeability of Self-Affine Fractures

The permeability of self-affine fractures with various roughness exponents H is investigated by direct three-dimensional numerical simulations. A scaling behavior with an exponent H is exhibited in the self-affine scale range. Permeability can be related to the fractional open area and to the percolation probability by simple models.     

Transport Properties of Compact Clays: I. Conductivity and Permeability

Conductivity and permeability of model and natural clays have been studied experimentally. Local properties such as porosity and zeta potentials were measured as functions of the electrolyte solutions. Whenever possible, experimental data were compared to numerical data obtained for random packings of grains of arbitrary shape, and a good agreement was found between them.     

Nuclear magnetic resonance diffusion with surface relaxation in porous media

Nuclear magnetic resonance (NMR) diffusion simulations with surface relaxation were performed numerically in unconsolidated and consolidated porous media by a random walk technique. Two uniform and nonuniform models of surface relaxation were proposed and compared. The apparent diffusion coefficient and extinction function were determined and studied in the fast, slow and intermediate diffusion regimes of relaxation. According to theoretical predictions, it was observed that the extinction function does not depend on surface relaxivity parameter rho 2 in the slow diffusion regime. The apparent diffusion coefficients are independent of rho 2 in the fast diffusion regime and tend to be superposed onto a single curve in the slow one. The evolution of the apparent diffusion coefficients is gathered by a reduced representation in the fast diffusion regime.     

Pierre M. Adler and Jean-François Thovert: Fractures and Fracture Networks.

Transport in Porous Media -     

Under the Volcano: Unsaturated Flow and Induced Variations of Electromagnetic and Gravitational Fields

A number of electric and magnetic signals have been observed on La Fournaise volcano, which are attributed to electrokinetic effects induced by the heavy rains which fall in this area. A general modeling of the flow in the unsaturated and saturated zones is proposed for an arbitrary topography, arbitrary spatial distributions of physical properties, and arbitrary rains. This flow generates an electrical field and an associated current which itself induces a variable magnetic field. Variations of water masses inside the volcano are also determined to predict gravity variations. Saturation, electric, magnetic, and gravity fields are given and discussed for various rain distributions including real ones.