Poroelastic Solutions of a Semipermeable Borehole under Nonhydrostatic In Situ Stresses within Transversely Isotropic Media

Prevalent models addressing wellbore stability typically oversimplify the borehole wall, characterizing it as either perfectly permeable or entirely impermeable. However, the widely observed behavior of a shale borehole, permitting solvent molecules, while restricting solutes, underscores the necessity of recognizing the borehole wall as a nonideal semipermeable medium—a medium that selectively allows certain molecules to pass through, while blocking others. This paper presents a poroelastic solution for a semipermeable borehole subjected to nonhydrostatic stresses within a fluid-statured transversely isotropic medium. The analytical solutions in the Laplace domain are derived through the combined application of integral transform and load decomposition techniques. Numerical examples are presented to explore the influence of both semipermeability and material anisotropy on temporal evolution of pore pressure and poroelastic stresses surrounding the wellbore. The results show that, for a semipermeable wellbore under Mode 2 loading, which accounts for perturbations in pore pressure, changes in Young’s modulus ratio and Poisson's ratio have minimal influence on the distribution of pore pressure surrounding the wellbore. However, the circumferential stress exhibits a high sensitivity to alterations in Young’s modulus ratio and Poisson's ratio. The impact of mechanical anisotropy on circumferential stress becomes increasingly significant as time progresses. In contrast, for a semipermeable wellbore under Mode 3 loading that accounts for deviatoric stresses, both mechanical anisotropy and borehole semipermeability significantly shape the pore pressure near the wellbore at early times, while mechanical anisotropy does not noticeably affect circumferential stress. Additionally, the results underscore a noticeable disparity in the stress and pore pressure fields predicted by the semipermeable model in comparison with both permeable and impermeable borehole models. This highlights the importance of considering the nonideal semipermeable nature of shale boreholes in wellbore stability analyses.