A THEORY OF MIXTURE ON FLOWS THROUGH POROUS MEDIA

This article utilizes the theory of mixtures to formulate the flow of fluids through porous media. The flow is regarded as a non-equilibrium transport process of the mixture, and the effects of immiscibility and mass exchanges between the constituents are considered. Capillary pressure relations and the effective stress relation are introduced as the closure equations. Problems of the Darcy flow, non-Darcy flow and flow in the double-medium are elucidated systematically. Linear and nonlinear equations that govern the macroscopic motion of the fluids, including the thermo-dynamical coupled effects, are developed. The present theory is consistent with the classical.