Hydrodynamic Dispersion for Fluid Filtration Through a Porous Medium with Random Macroscopic Inhomogeneities

We study the convective diffusion of passive admixtures in the course of forced fluid filtration through a porous medium with frozen random inhomogeneities of macroscopic parameters. During the fluid filtration, the parameter inhomogeneities lead to spatially irregular flows and are responsible for dispersion of the fluid particles, which causes convective diffusion that is additional to molecular diffusion. In contrast to the molecular diffusion, this diffusion is anisotropic and directly proportional to the filtration flow velocity. We consider the inhomogeneities of both permeability and porosity of the medium and report on analytical results for the most common options of their statistical properties. It was assumed that the inhomogeneities are relatively small and their autocorrelation function decays with the distance r not slower than 1/ r β , where β > 1. Direct numerical simulation for different cases confirmed the validity of the restrictions we adopted and the correctness of the analytical findings.