Analytical Model of Wellbore Stability Analysis of Inclined Well Based on the Advantageous Synergy among the Five Strength Criteria

Abstract

The proper drilling mud density is vital for wellbore stability maintenance, which relies on both stress distribution on the borehole wall and rock strength. Thus, the selection of rock strength criterion is vital for wellbore stability analysis (WSA), and several strength criteria have been developed and employed to perform WSA, but the real collapse pressure does not comply with any single strength criterion. Therefore, to accurately predict the critical mud weight against wellbore collapse, an analytical model of WSA was proposed for inclined wells based on the advantageous synergy among the five types of strength criteria, such as the Mohr-Coulomb criterion, Mogi-Coulomb criterion, Drucker-Prager criterion, modified Wiebols-Cook criterion, and modified Lade criterion. The predicted results among these analytical and five conventional models were compared under three kinds of typical stress regimes, such as normal, strike-slip, and reverse faults. Finally, five kinds of typical oil and gas field data were collected to further verify the accuracy of this new model. The results indicated that different models predicted different collapse pressure, owing to the Mohr-Coulomb criterion ignoring the intermediate principal stress ( ${\sigma }_2$ ), so as to always give the greatest collapse pressure, followed by the present analytical model and the Mogi-Coulomb criterion, while the other three types of strength criteria gave different results, because of the difference in the influence of ${\sigma }_2$ , while the present analytical model integrated the advantageous synergy among the five strength criteria. The prediction error of the conventional analytical model ranges from 9.4 to 34.2% with an average of 22.1%, while the prediction error of this new model ranges from 2.3 to 12.5% with an average of 7.1%, so that the present analytical model has much higher accuracy than that of any single strength criterion. In addition, this new analytical model can be simplified as the conventional analytical model by adjusting the weight coefficients.