Wave Propagation in Poroelastic Media Saturated by Two Fluids

Abstract

A theory of wave propagation in isotropic poroelastic media saturated by two immiscible Newtonian fluids is presented. The macroscopic constitutive relations, and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations and assuming small deformations. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy’s law. The coefficients of macroscopic constitutive relations are expressed in terms of measurable quantities in a novel way. The theory demonstrates the existence of three compressional and one rotational wave. The third compressional wave is associated with the pressure difference between the fluid phase and dependent on the slope of the capillary pressure-saturation relation.