Wellbore Failure Modelling Using a Modified Drucker-Prager Criterion

Abstract

The failure around the wellbore is studied using a modified form of Drucker-Prager failure criterion (MDP). The MDP has a linear shear failure envelope in the meridian plane and a curve-sided triangular failure curve in the deviatoric plane which can be controlled by the yield stress ratio (K). The model is compatible with the rock strength measurements under true-triaxial stress conditions similar to the modified Lade (MLa) failure criterion. The MDP is used for stress modelling and wellbore stability analyses. The stress modelling is done by calculating the magnitude of maximum horizontal stress (SHmax) from the observed failure in the image log. The stress modelling result is compared with the results from the Mohr-Coulomb (MC), Drucker-Prager (DP), and modified Lade (MLa) criteria. The MDP is also used for wellbore stability analysis using both analytical and numerical (finite element) approaches. The analytical approach is used to conduct a sensitivity analysis to investigate the impact of well trajectory on minimum required mud weight. The finite element analysis is conducted to investigate the dimension of the breakout developed under different mud weights. The results are compared against the other failure criteria. The SHmax magnitude calculated from the MDP model falls between the MC and DP. The analysis shows that the MDP with K = 0.778 is compatible with the MLa results for a rock with an internal friction angle close to 30° for both SHmax magnitude modelling and minimum required mud weight calculations for the wellbore stability analysis. The results from the finite element analyses shows that the calculated breakout widths and depths using the MDP model falls between the MC and DP models. The analysis shows that in the presented case, although the calculated breakout width is large, the depth and amount of failed material around the wellbore are relatively small to create any wellbore instability problems. Hence, a mud weight relatively lower than calculated required mud weight from the analytical approach can be used in practice to drill the well. The results show the importance of considering the depth of the breakouts in the mud weight design.