Convective cooling/heating induced thermal stresses in a fluid saturated porous medium undergoing local thermal non-equilibrium

Abstract

Local thermal non-equilibrium (LTNE) may have profound effects on the pore pressure and thermal stresses in fluid saturated porous media under transient thermal loads. This work investigates the temperature, pore pressure, and thermal stress distributions in a porous medium subjected to convective cooling/heating on its boundary. The LTNE thermo-poroelasticity equations are solved by means of Laplace transform for two fundamental problems in petroleum engineering and nuclear waste storage applications, i.e., an infinite porous medium containing a cylindrical hole or a spherical cavity subjected to symmetrical thermo-mechanical loads on the cavity boundary. Numerical examples are presented to examine the effects of LTNE under convective cooling/heating conditions on the temperature, pore pressure and thermal stresses around the cavities. The results show that the LTNE effects become more pronounced when the convective heat transfer boundary conditions are employed. For the cylindrical hole problem of a sandstone formation, the thermally induced pore pressure and the magnitude of thermal stresses are significantly higher than the corresponding values in the classical poroelasticity, which is particularly true under convective cooling with moderate Biot numbers. For the spherical cavity problem of a clay medium, the LTNE effect may become significant depending on the boundary conditions employed in the classical theory.