A Model for Multiphase Flows through Poroelastic Media

Abstract

A continuum model for multiphase fluid mixture flows through poroelastic media is presented. The basic conservation laws developed via a volume averaging technique are considered. Effects of phasic equilibrated forces are included in the model. Based on the thermodynamics of the multiphase mixture flows, appropriate constitutive equations are formulated. The entropy inequality is exploited, and the method of Lagrangian multiplier is used along with the phasic conservation laws to derive the constitutive equations for the phasic stress tensors, equilibrated stress vectors, and the interactions terms. The special cases of wave propagation in poroelastic media saturated with multiphase fluids, and multiphase flows through porous media, are studied. It is shown that the present theory leads to the extended Darcy’s law and contains, as a special case, Biot’s theory of saturated poroelastic media.