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 closedform 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.
A main aspect of wellbore stability analysis is the selection of an appropriate rock failure criterion. Several linear elastic methods have been used to predict or describe at which stresses or stress conditions failure occur in a formation. The most popular models that have been used are Mohr- Coulomb (M-C), Mogi-Coulomb, modified Lade and Drucker-Prager. The principle used to predict borehole failures through those models are quite similar, but the involvement of principal stresses in the material failure process is different from model to model. For example, M-C does not consider the effect of intermediate principal stress while Mogi-Coulomb and modified Lade do. Several authors studied the performance of each constitutive model and discussed their goodness and limitations [1, 2, 4-9, 19, 21]. It is obvious that intermediate strength effects can not be ignored to estimate borehole collapse risk under strong anisotropic in-situ stress state. A 3D failure criterion related model is therefore required to account for polyaxial stress effects on collapse pressure prediction (CPP). The Mogi-Coulomb linear elastic model accounts for s2 effects on CPP. A closed form 3D elastic analytical solution  worked well in conjunction with linear M-C elastic model and modified Lade criterion. Thus, it will be interesting to evaluate this developed model with other solutions. In general, 3D failure criteria that contain numerous parameters, or which require numerical evaluation, are difficult to apply in practice, particularly for wellbore stability problems.