Modeling the Critical Pressure Below which Sand Production will Occur based on Extended Mogi-Coulomb Failure Criterion

Sand production is of great concern in the Oil and Gas industry because of the economical, operational and technical problems that come with the phenomenon. Several sand prediction models are available in the literatures, but little or no consideration has been given to non-linearity of failure criterion used to develop the sand prediction models. Hence, a non-linear form of Mogi-Coulomb failure criterion was adopted in this research to develop a sand prediction model and simple sand prediction software. The most used rock failure criteria developed over the years for analyzing brittle failure of rocks is Mohr-Coulomb failure criterion. Published literatures have shown deficient in some field scenarios. Reason for these deficiencies was largely associated with the implicit assumption made in Mohr-Coulomb criterion that, the intermediate principal stress (σ2) has no influence on rock strength. So, this criterion is only based on the maximum and minimum principal stresses (σ1 and σ3) and only applicable to rock failure under conventional triaxial stress states (σ1 > σ2 = σ3). However, for a polyaxial stress state σ1 > σ2 > σ3), studies have proved that the intermediate principal stress (σ2) has a pronounced effect on rock strength and should not be neglected. Hence, Mohr–Coulomb criterion is relatively conservative in predicting sanding onset and therefore not very accurate for sand prediction models. As a result, this research presents a simple 3D sand prediction model based on Extended Mogi-Coulomb criterion that considered the non-linear relationships between most of field parameters when considering rock failure. The extended Mogi-Coulomb criterion is a nonlinear or parabolic form of Mogi-Coulomb criterion which accounts for the influence of the intermediate principal stress on rock strength and also very suitable for weak rocks. A fourth order polynomial equation was derived from first principle by combining both constitutive stress laws and the parabolic Mogi-Coulomb failure criterion. Then, Matlab software was used to develop a script and solution to the equation. And finally, the model solution was used to build simple graphic user interface software called ‘A.I Sand Predicton’ using Java programming language. Model verification was carried out by simulating several data available in the literatures and the solution was observed consistent with field observations. The solution of the critical wellbore pressure calculated using the "A.I Sand Predicton Software" was also found consistent with solution from Matlab and Mathematica softwares, respectively, which makes the software validated and reliable. Also, the case study shows that the critical wellbore pressure reduces as the strength parameters a, b, and c of the Extended Mogi-Coulomb criterion increases. Hence, the analytical model developed in this research using the extended Mogi-Coulomb criterion can reliably and accurately predict onset sand production.