A thermo-poroelasticity model for partially saturated porous media

Abstract

This work describes a thermo-poroelasticity model for a porous medium filled by two immiscible fluids in the framework of the Biot theory of poroelasticity. Local thermal equilibrium is assumed, i.e., the solid, the wetting fluid and the nonwetting fluid experience the same temperature variation in a continuum material particle. The constitutive relations in the present model include the thermally induced fluid content variations for both the wetting and nonwetting fluids. The model is employed to study the thermo-poroelastic responses of a borehole in a partially saturated, infinite porous medium subjected to a uniform temperature variation at the borehole boundary. The Laplace transform technique is used to obtain closed form, short time solutions for the thermally induced pore pressure and stress fields around the borehole. The analytical solutions indicate that the pore pressures of both the wetting and nonwetting fluids around the borehole at short times are characterized by the complementary error functions with the time scaled by partial saturation parameters as well as the thermal diffusivity of the porous medium. The numerical results for a porous medium dominantly filled by the wetting fluid indicate that the peak thermal pore pressure of the wetting fluid is much higher than that in the corresponding porous medium fully saturated by the wetting fluid while the thermal fluid content variation of the wetting fluid becomes lower due to partial saturation. Partial saturation also increases the thermal radial stress but the thermal hoop stress is relatively insensitive to partial saturation.