Filtration and Dispersion in a Porous Medium with Multiscale Conductivity and Porosity

Field measurements of conductivity, porosity, etc. have shown their are high heterogeneity, the bounds of such heterogeneity increasing as the scale of observations changes. This has led to the development of fractal models, renormgroup methods, and methods of subgrid modeling. The subgrid modeling approach, associated with problems of the subsurface hydrodynamics, is presented. We consider a single-phase flow of an incompressible fluid through a random porous medium. The joint multi-point probability distribution for porosity and permeability is supposed to be log-normal and satisfy the conditions of the Kolmogorov refined scaling hypothesis. A subgrid model is derived which is similar to the Landau-Lifschitz formula. The theoretical result is compared to the results of the direct numerical modeling and to the results of "ordinary" perturbation theory.