Transport in Porous Media 11: 187-199, 1993. 187 9 1993 Kluwer Academic Publishers. Printed in the Netherlands. Research Note: Diffusion in Isotropic and Anisotropic Porous Systems: Three-Dimensional Calculations M. QUINTARD LEPT-ENSAM (URA CNRS), Esplanade des Arts et Mdtiers, 33405 Talence Cedex, France (Received: 17 May 1991) Abstract. Effective diffusion coefficients were calculated numerically for three-dimensional unit cells representative of different unconsolidated porous media. These numerical results were compared with the experimental results of Kim for packed beds of glass spheres, mica particles, and an artificial porous medium composed of mylar disks. These three-dimensional numerical results confirm that the porosity is the essential parameter for the determination of the effective diffusion coefficient in the case of unconsolidated isotropic systems. In the case of anisotropic systems, better agreement is obtained between numerical predictions and actual data when the unit cell is three-dimensional rather than two- dimensional. This emphasizes the fact that three-dimensional unit cells feature more realistic geometrical properties which are needed to accurately describe anisotropic systems. Key words. Effective diffusion tensor, volume averaging 3D numerical models, anisotropic systems, periodic systems. 1. Introduction The calculation of effective diffusion coefficients for porous media, given the geometrical characteristics, has received renewed attention because of the recent progress in both computer hardware and porous medium imaging techniques (such as X-ray tornography, NMR imaging). It is not unrealistic to try to compute directly transport properties given the description of a real porous system. Still, three- dimensional computations are very demanding in terms of computer resources, therefore calculations are restricted to unit cells involving a few particles. These unit cells must be representative, in some sense, of the real structure to give effective diffusion coefficients close to the actual measurements. This question was extensively studied by Kim et al. (1987) based on experiments and numerical solutions of the closure problem associated with the determination of the effective diffusion coefficients. However, computations were carried out on two-dimensional structures while the experimental data were obtained from truly three-dimensional porous systems (packing of spheres, disks, and mica particles). The two-dimensional studies of Kim et al. (1987) were extended to three-dimension by Saez et al. (1991) using parallelepipeds in planar configurations. The purpose of this work is to present more realistic results based on the systems studied by Kim et al.