Structural averaging of flow processes in nonhomogeneous porous media

Abstract

The problem of constructing macroscopic analogs for the equations describing processes in nonhomogeneous porous media is considered. The classical results of the theory relate to the case in which the averaging procedure leads to the smoothing of the coefficients describing the inhomogeneity without modifying the structure of the equations of the process. It is natural to call such averaging coefficient averaging. In this paper another approach — structural averaging, in which the type of the equations themselves or their qualitative structure is modified, is investigated. In the overwhelming majority of cases, in addition to a small scale of inhomogeneity, these systems also contain one or more small (large) parameters reflecting important differences in the properties of the individual components of the medium or the physical components of the transport process itself. A typical example of the structural averaging problems generated by processes in highly nonhomogeneous media and, moreover, processes with nonequivalent diffusion and convective transport is investigated. The methods of asymptotic averaging [1,2] are employed. Processes in highly nonhomogeneous media were investigated in [3–6]. Studies [4, 8, 9] are concerned with the averaging of convection-diffusion systems.