An analytical solution to wellbore stability using Mogi-Coulomb failure criterion

Abstract

Deep wellbores/boreholes are generally drilled into rocks for oil and gas exploration, monitoring of tectonic stresses purposes. Wellbore and tunnel in depth are generally in true triaxial stress state, even if the ground is under axisymmetric loading condition. Stability of such wellbores is very critical and collapse of wellbore must be avoided. Mogi-Coulomb failure criterion is a better representation of rock strength under true triaxial condition. In this paper, an analytical solution is proposed using Mogi-Coulomb failure criterion. The solution is obtained for rock mass exhibiting elastic-perfectly plastic or elastic-brittle-plastic behaviour considering in-plane isotropic stresses. The proposed solution is then compared with exact analytical solution for incompressible material and experimental results of thick-wall cylinder. It is shown that the results obtained by the proposed analytical solution are in good agreement with the experimental results and exact analytical solution. A reduction of about 13%–20% in plastic zone from the proposed closed-form solution is observed, as compared to the results from the finite element method (FEM) based Mohr-Coulomb criterion. Next, the influences of various parameters such as Poisson's ratio, internal pressure (mud weight), dilation angle, and out-of-plane stress are studied in terms of stress and deformation responses of wellbore. The results of the parametric study reveal that variation in the out-of-plane stress has an inverse relation with the radius of plastic zone. Poisson's ratio does not have an appreciable influence on the tangential stress, radial stress and radial deformation. Dilation angle has a direct relation with the deformation. Internal pressure is found to have an inverse relation with the radial deformation and the radius of plastic zone. © 2019 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences