A porothermoelastic solution for the inclined borehole in a transversely isotropic medium subjected to thermal osmosis and thermal filtration effects

Given that the hydraulic boundary conditions at the wellbore wall are identified as permeable (PBC) and impermeable (IMPBC) and that the assumption of plane strain holds, the present paper formulates an analytical solution, which is based on fully coupled linear porothermoelastic model with the thermal osmosis and thermal filtration effects, in Laplace space domain. The solution is available for the cases that the wellbore axis of inclined wellbore is perpendicular to the isotropic plane of the transversely isotropic medium under non-hydrostatic stress condition. The wellbore problem is decomposed into axisymmetric and deviatoric loading cases. The numerical results of the time-dependent distributions of field variables are obtained by virtue of performing the inversion technique for Laplace transforms. The sensitivity analyses are performed on the key parameters to thermal osmosis and thermal filtration effects. The effect of thermal filtration on temperature is also illustrated. The numerical comparative analyses in the present paper examine the influence of material anisotropy of poromechanical parameters and thermal properties, which embody in porothermoelastic-osmosis-filtration model and common porothermoelastic one, on the thermally induced pore pressure and stresses. Finally, an integrated geomechanical wellbore stability model is developed to investigate the compressive and tensile failure extents of horizontal wells. The model is involved with three aspects, i.e. the coordinates transformations pertaining to wellbore and weak plane systems, the criteria to evaluate the shear failure (including intact rock and weak plane) as well as tensile fracture, and the fully coupled porothermoelastic analytical solution. The developed porothermoelsatic analytical solution can provide a theoretical basis for multiple of aspects including the inversion of in-situ stress, geothermal reservoir stimulation and petroleum drilling design.