Averaging of Equations for Flow and Transport in Random Porous Media

TL;DR

This paper extends a method for deriving averaged equations of flow and transport in random porous media, accommodating more general conditions including bounded domains and non-homogeneous fields, with implications for modeling complex subsurface processes.

Contribution

It significantly broadens the existing approach to include diverse process types, domain boundaries, and non-homogeneous random fields in modeling flow and transport.

Findings

Extended the averaging approach to bounded and unbounded domains.

Analyzed cases with non-homogeneous random fields.

Provided a framework for non-local operators in flow equations.

Abstract

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.