An Analytical Elasto-Plastic Analysis for Stability of Axisymmetric Wellbore Available to Purchase

In this paper, a general shear strain hardening and softening Drucker-Prager model based on the existing triaxial compression test results has been introduced to model the rock behaviour which captures well the mechanical characteristic of typical soft rock formations. This elastoplastic model is then adopted to develop a rigorous analytical solution for the drained wellbore drilling problem subjected to in-plane isotropic stress field, and to simulate the borehole collapse failure. It is found that the wellbore boundary value problem can be reduced to solving a system of first order ordinary differential equations in the plastic zone, with the radial, tangential, and vertical stresses as well as the volumetric strain and plastic shear strain being the five basic unknowns. The illustration numerical example shows the distributions of stress components and volumetric strain around the borehole, in addition to the evolving plastic deviatoic strain and stress path for a rock point at the borehole surface due to the wellbore drilling. The critical mud pressures necessary to prevent borehole collapse, predicted by the elastoplastic analysis based on different wellbore instability criteria, are compared with the value corresponding to the elastic theory, which are found to be considerably lower.