Closed-form solution of stress state and stability analysis of wellbore in anisotropic permeable rocks

This work aims to develop a closed-form solution of stress state around wellbore drilled in the anisotropic permeable rocks taking into account the transient effect of fluid flow. For this purpose, a simplified method was adopted to solve the anisotropic hydraulic diffusion equation. Knowing the explicit transient evolution of pore pressure, the hydraulic and hydro-mechanical potentials were proposed through which stress state around wellbore are determined thanks to the use of the well-known complex potential approach. The validity of this closed-form solution was verified by comparing with the result obtained from the numerical simulation. By combining the analytical solution of stresses on well wall with a chosen anisotropic failure criterion of rock mass, the stability analysis of wellbore was carried out. Through the parametric study, we elucidated the influence of different factors on the safe mud pressure window notably the anisotropic poro-elastic properties, the anisotropic strength of the rock masses as well as the anisotropic initial stress state and the inclined bedding plane of formation.