Stability analysis in shale through deviated boreholes using the Mohr and Mogi-Coulomb failure criteria

Borehole collapse is a commonly encountered wellbore stability problem during drilling in shale. Borehole failures can be reduced by determining the proper mud pressure based on the selection of an appropriate rock failure criterion. Several linear elastic constitutive models have been tested to predict borehole collapse pressure (CP). The fore most used criterion for brittle failure of rocks is the Mohr-Coulomb (M-C), Mogi-Coulomb, Modified Lade and Drucker-Prager. It is seen that either numerical or closed-form analytical solutions of these constitutive models are the preferred way to predict CP. But, closed-form analytical solution for deviated wells under anisotropic stress state is a tedious task and a simple mathematical expression can not be reached. This study evaluated a simplified closed-form M-C analytical solution, including mud cooling effects and compared the results with existing solutions. Existing solution was obtained through the Mogi-Coulomb model. It is a 3D analytical model, using linear elasticity theory to estimate the CP from a rock model. Moreover, a standard work flow of how the Mogi-Coulomb numerical model can be evaluated with triaxial instead of polyaxial test data was reviewed. Shale characterization experimental data were used to estimate model fitting parameters of the Mogi-Coulomb model. Finally, a comparative field case study was carried out to enhance the confidence of using the appropriate material elastic constitutive model for borehole stability analysis. The M-C closed-form analytical solution is providing almost similar prediction as Mogi-Coulomb numerical solution under weak in-situ anisotropy. It was found that well trajectory factors are more vital than the effect of intermediate stress effect on CP.