Thermoporoelastic response of a semi-permeable wellbore subjected to convective cooling and non-hydrostatic in situ stresses

Existing models of wellbore stability idealize the borehole wall as either a perfectly permeable or an entirely impermeable surface. The widespread observation that a shale borehole allows solvent molecules to pass through but impedes solutes suggests that the borehole wall should be regarded as a non-ideal semi-permeable medium. To address the magnitude and rate of fluid penetration into the formation when a semi-permeable wellbore is exposed to a non-isothermal drilling fluid quantitatively, this work develops analytical solutions for a semi-permeable borehole undergoing convective cooling and far-field non-hydrostatic in situ stresses in the framework of fully coupled thermoporoelasticity. Integral transform and load decomposition techniques are employed to facilitate the derivation of analytical solutions. The results show that, in contrast to the permeable or impermeable borehole models, the semi-permeable model predicts significantly different stress and pore pressure fields. The transient evolution of temperature, pore pressure, and stresses is predominantly governed by two non-dimensional numbers: the Biot number B-i and a newly identified number pi(f) that characterizes the capability of shale to transport fluid across the solid-fluid interface.