Thermal pore pressures and stresses in a partially saturated porous medium: A local thermal non-equilibrium model

Abstract

This work first describes a local thermal non-equilibrium (LTNE) model for investigating thermally induced deformations and stresses in a porous medium partially saturated with a wetting fluid and a non-wetting fluid. The LTNE model assumes that the two fluid phases experience the same temperature variation, which is different from that of the solid matrix in a continuum material particle. The temperature differential between the solid and fluid contributes to the thermally induced fluid content variations for both the wetting and non-wetting fluids. The LTNE model is subsequently employed to examine the thermally induced pore pressures and stresses around a cylindrical hole in an infinite partially saturated porous medium subjected to a uniform temperature variation at the hole boundary. Closed-form, asymptotic short-time solutions for the temperatures, thermal pore pressures, and thermal stresses are obtained using the Laplace transform technique. For a partially saturated porous medium with the non-wetting fluid saturation close to its residual saturation (i.e., porous flow is dominated by the wetting fluid), the numerical results indicate that partial saturation increases the thermal pore pressure of the wetting fluid as well as the thermal radial stress under LTNE. Compared with the results under local thermal equilibrium (LTE), the thermal pore pressures are reduced by LTNE in the partially saturated medium. In the meantime, LTNE leads to slightly higher thermal radial stress.