FRACTAL AND SUPERDIFFUSIVE TRANSPORT AND HYDRODYNAMIC DISPERSION IN HETEROGENEOUS POROUS-MEDIA

We review and discuss diffusion and hydrodynamic dispersion in a heter ogeneous porous medium. Two types of heterogeneities are considered. O ne is percolation disorder in which a fraction of the pores do not all ow transport to take place at all. In the other type, the permeabiliti es of various regions of the pore space are fractally distributed with long-range correlations. Both systems give rise to unusual transport in which the mean square displacement [r2(t)] of a particle grows nonl inearly with time. Depending on the heterogeneities and the mechanism of diffusion and disperison, we may have fractal transport in which [r 2] grows slower than linearly with time, or superdiffusive transport i n which [r2] grows faster than linearly with time. We show that percol ation models can give rise to both types of transport with scale-depen dent transport coefficients such as diffusivity and dispersion coeffic ients, which are consistent with many experimental observations.