Poroelastic Response of a Semi-Permeable Borehole Subjected to Non-Hydrostatic In Situ Stresses

Abstract

AbstractIn the existing models of wellbore stability, the borehole wall is idealized as either a fully permeable or a completely impermeable surface. However, the widely observed fact that a shale borehole is permeable to solvent molecules but impermeable to solutes suggests that the borehole wall should be considered as a non-ideal semi-permeable medium. When the wellbore is exposed to the drilling fluid, the dynamic modification of pore pressure on the borehole surface is required to account for fluid entering the formation. In this paper, we present an analytical solution for a semi-permeable borehole subjected to a non-hydrostatic stress in a poroelastic medium, where a Robin boundary condition for pore pressure is adopted, with the fluid flux into the rock matrix being proportional to the pore pressure difference across the borehole wall. Integral transform and load decomposition techniques are employed to assist in the derivation of analytical solutions. The results reveal that, compared to the permeable and impermeable borehole models, the semi-permeable model predicts a sharp difference in the stress and pore pressure fields.