Thermo-poroelastodynamic response of a borehole in a saturated porous medium subjected to a non-hydrostatic stress field

Abstract

A thermo-poroelastodynamic (TPED) model incorporating the thermo-osmosis and thermal-filtration phenomena is used to analyze the transient response of a borehole subject to a non-hydrostatic stress field. The coupled TPED model is developed on the basis of equations of motion, fluid flow, heat transfer and constitutive equations so as to couple the stress wave, pressure wave and thermal wave in early times. Poroelastodynamics (PED) and thermo-elastodynamics (TED) models correspond two particular cases of the current model. The borehole problem is decomposed into the superposition of an axisymmetric mode and an asymmetric mode, corresponding to axisymmetric and deviatoric loadings, respectively. The semi-analytical solutions in the Laplace transform space are inverted numerically to obtain time-dependent displacement, pore pressure, temperature and stresses. Comparisons are performed among different sub-models to examine the influence of thermal effect on the response of pore pressure and stresses as well as the influence of pore water on the response of stress components. A direct comparison among the dynamic, quasi-static and static models shows that inertial effect is very important in the early times and it contributes to the early-time wave behavior.