A poroelastic solid saturated by a three-phase fluid

Abstract

A theory to describe the propagation of waves in a poroelastic solid saturated by a three-phase fluid is presented and anlyzed. The model takes into account the existence of two capillary and three relative permeability functions, assumed to depend on the non-wetting fluid saturations. A plane wave analysis predicts the existence of four compressional waves, denoted as P1, P2, P3 and P4, and one shear wave, all of them suffering attenuation and dispersion effects. A numerical example showing the behaviour of all waves as function of saturation and frequency in a sample of Nivelsteiner sandstone saturated by water, oil and gas is presented.