A Local Thermal Nonequilibrium Poroelastic Theory for Fluid Saturated Porous Media

Abstract

In the classical thermo-poroelasticity theory of porous media, local thermal equilibrium between the solid and fluid phases is assumed. In many transient heat conduction/pore pressure diffusion problems, however, the rate of heat transfer between the solid and fluid may not be fast enough to achieve local thermal equilibrium, i.e., the solid and fluid may undergo different temperature variations, which induces additional pore pressure and thermal stresses. This work presents the basic thermo-poroelasticity equations for porous media undergoing local thermal nonequilibrium (LTNE). In the LTNE thermo-poroelasticity theory, the temperatures of solid and fluid phases are governed by the LTNE heat transfer theory. A weighted average of temperatures for the solid and fluid phases is used to formulate the constitutive equations. The theory is subsequently applied to a cylindrical hole in an infinite porous medium subjected to uniform fluid pressure and temperature at the hole boundary. The asymptotic short time solutions of temperature, pore pressure and thermal stresses are obtained using the Laplace transform technique. The numerical results show that the temperature, pore pressure and thermal stresses are significantly influenced by the LTNE effects.