Averaging of Equations for Flow and Transport in Random Porous Media.

In the papers (Shvidler, 1985 and 1993, and Shvidler and Karasaki, 1999, 2001, 2005, and 2008) we developed an approach for finding the exactly averaged equations of flow and transport in porous media. We studied for steady state flow with sources and also analyzed unsteady flow and nonreactive solute transport in unbounded domains with stochastically homogeneous conductivity random fields. In the base of the approach is the existence of appropriate random Green's functions and relevant linear random operators. Examination of random fields with global symmetry makes it possible to describe some different types of averaged equations with non-local unique vector or tensor operators. In this paper we substantially extend the approach and study more general processes in bounded or unbounded fields of any dimensions and examine the cases where the random fields of conductivity and porosity are stochastically homogeneous or non-homogeneous.