Analysis of wave propagation in non-isothermal poroelastic solids saturated by two-phase fluids

Abstract

SUMMARY This work presents a model to characterize the behaviour of waves propagating in non-isothermal poroelastic solids saturated by two-phase fluids. The dynamic differential equations include the poroelasticity and heat equations with the solid, fluid and thermal fields combined using coupling terms. A plane wave analysis shows that five waves can propagate, three compressional, one fast (P1) and two slow (P2, P3), a shear fast (S) and a thermal slow (T). P2, P3 and T are diffusive waves at low frequencies, while P1 and S behave as propagating waves. The T wave is coupled with the compressional waves and uncoupled with the S wave. The plane wave analysis applied to a real sandstone saturated with gas–water mixtures compares phase velocities and attenuation factors for two-phase and effective single-phase fluids, considering or neglecting the coupling terms. It is observed that P1 and P2 waves have higher velocities for coupled cases, while P3 and T waves exhibit the opposite behaviour. Furthermore the plane wave analysis is performed in the coupled case for oil–water and gas–water two-phase fluids, with compressional waves exhibiting higher velocities for gas–water than for oil–water mixtures. The propagation of waves in a 1-D thermo-poroelastic medium saturated by a gas–water mixture is presented and analysed using a finite element procedure. Considering temperature may become important in high-pressure high-temperature hydrocarbon and geothermal reservoirs.