Lei Jin

Forward constraining of the magnitude of SHmax on a stress polygon using wellbore failures observed from deviated wells requires the orientation of SHmax known a priori. This orientation can be separately determined from, e.g., wellbore failures in vertical/near-vertical wells. Unfortunately, in the case where image logs are available only in highly deviated wells, SHmax orientation cannot be independently determined as the impact of wellbore trajectory on wellbore failures can be significant. In this study, we propose a new method for simultaneously determining the magnitude and orientation of SHmax as well as two rock strength variables using wellbore failures in arbitrarily deviated wells. This method fully accounts for the inter-dependence among the unknown variables and fully considers the impact of wellbore trajectory on wellbore failures. It is associated with two key assumptions: (1) the size of the breakout coincides with the plastic yield zone; (2) the stress redistribution due to plastic strain is negligible, and the yield function reaches a maximum value at the breakout center and reaches zero at the breakout edges. Based on these assumptions, we set up a constrained optimization at each breakout. The objective function is chosen based on the yield function at the breakout center, and the constraints are imposed based on frictional equilibrium, the presence or lack of drilling induced tensile fractures, and the breakout width. The Drucker-Prager yield criterion and the 3D Griffith tensile failure criterion were chosen for our method. We then employ the interior-point algorithm for performing the optimization and compute the Hessian matrix using the quasi-Newton method for second-derivative test and selection of the local extremum. This optimization process can be easily executed for all breakouts. Finally, we demonstrate the application of our new method using breakout data from a deviated wellbore and show that it is able to overcome the limitations of the conventional method.