(1) Department of Mathematics, Campus Box 170, Denver, CO, 80217-3364, U.S.A.;(2) Center for Applied Math, Math Sciences Building, Purdue University, West Lafayette, IN, 47907, U.S.A.
Abstract:
In this paper, we derive a Forchheimer-type equation for two-phase flow through an isotropic porous medium using hybrid mixture theory. Hybrid mixture theory consists of classical mixture theory applied to a multiphase system with volume averaged equations. It applies to media in which the characteristic length of each phase is small relative to the extent of the mixture. The derivation of a Forchheimer equation for single phase flow has been obtained elsewhere. These results are extended to include multiphase swelling materials which have nonnegligible interfacial thermodynamic properties.