A Mathematical Model And Application Of Saturated Chemo-thermo Poroelastic Media

In the framework of Biot’s theory, a weighted average of temperatures for solid and fluid phases is used to establish a mathematical model for fluid saturated chemo-thermo-poroelastic media. The temperatures for solid and fluid phases, pore pressure, thermal stresses and chemo-thermal stress around a cylindrical hole or a spherical cavity in an infinite fluid saturated porous medium under various boundary conditions are investigated by employing Laplace transform technique. The work is mainly on:First, we assume that the pore fluid comprises of two chemical species including solute and solvent, a mathematical model for fluid saturated chemo-thermo-poroelastic media undergoing local thermal non-equilibrium (LTNE) is established.The decoupling governing equations of pore pressure, variation of the solute mole fraction and solid displacement are deduced under the irrotational displacement field. For two typical engineering problems, namely a cylindrical hole or a spherical cavity in an infinite fluid saturated poroelastic medium, the solutions of temperature field, variation of the solute mole fraction and pore pressure are obtained by using the Laplace transform technique for the case of different boundary conditions. Finally, Numerical results for two porous materials (clay and sandstone) are presented to examine the effects of LTNE on the temperatures, pore pressure, variation of the solute mole fraction and thermal stresses around the hole and the difference between thermal effects, chemical effects and chemo-thermo effects. The results show that:1) when the parameter Sp (Sparrow number) is small (≈0.35) and Biot numbers is moderate (≈1.0), the effects of LTNE are very apparent. The peaks for pore pressure and absolute value of radial thermal stresses are two and three times (sandstone) or four and five times (clay) bigger than the corresponding peak values of the classical poroelasticity.2) When the temperature and variation of the solute mole fraction change together, the pore pressure and thermal stresses are dominantly affected by chemical effects rather than thermal effects. Considering the effects of chemical or chemo-thermal effects, the peak of pore pressure and absolute value of total stress are at the same magnitude. In the case of only considering the thermal effects, for the sandstone material, the peak pore pressure is less than the absolute value of total stress.