A theory for wave propagation in porous rocks saturated by two-phase fluids under variable pressure conditions

In this work we present an extension of Biot s theory to describe wave propagation in elastic and viscoelastic porous solids saturated by two-phase fluids for arbitrarily fixed confining and pore pressure conditions. As the fluids are immiscible, the model takes into account capillary forces. Appropriate bulk and pore volume compressibilities are defined in terms of the coefficients in the stress-strain relations, which lead to a generalization of the classic effective pressure laws for the case of single-phase fluids. Using a Lagrangian formulation, the coupled equations of motion for the solid and the fluid phases are also derived, including dissipative effects due to matrix viscoelasticity and viscous coupling between the solid and fluid phases, which are used to model the levels of wave attenuation and dispersion observed in rocks. Four different body waves can propagate in this type of media, three compressional waves and one shear wave. The sensitivity of the phase velocities and quality factors to variations in saturation and effective pressure in a sample of Boise sandstone saturated by a gas-water mixture is presented and analyzed. Our results suggest that a combined analysis of such measurable quantities can be used as indicators of the saturation and pressure states of a hydrocarbon reservoir.