A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity

The mechanical behavior of porous media is largely governed by the interactions among coexisting components. These interactions occur through interfaces. In this paper, a continuum theory of multiphase porous media is developed that can be used to characterize the interactions among various components. Central to the theory is the implementation of the dynamic compatibility conditions microscopically representing the constraints on the pressure jumps across the interfaces. It is shown that capillary relaxation processes are thermodynamically associated with the changes in the volume fractions of fluids. A linear model is developed by a formal linearization of the proposed theory. For fully saturated conditions, the linearized theory reduces to the Biot's poroelasticity model. A procedure to evaluate the material constants is presented for the porous media with two fluids. The linear model is utilized to analyze the propagation of acoustic waves in an unsaturated rock. The theoretical results are compared with the experimental data available in the literature. (C) 2002 Elsevier Science Ltd. All rights reserved.