Stability analysis and uncertainty modeling of vertical and inclined wellbore drilling through heterogeneous field

Abstract

A stochastic two-dimensional geomechanical model developed by the authors and presented herein is used to analyze wellbore stability in heterogeneous formations. It consists of a finite element model and assumes linear elastic and isotropic material behavior under the plane strain state. The model simulates the stress state around vertical and inclined wellbore when a formation is submitted to internal drilling fluid pressure. This new state of stress may lead to rock failure, which is analyzed through a failure criteria. Since the exact variation of formation's mechanical properties is not known, a spatially correlated field is used to evaluate the variability of a rock mechanical material property. The correlation between each pair of finite elements is determined by a covariance function. A two-dimensional spatially correlated field is used to verify the correlation between the elements of a vertical wellbore. A different approach, however, is necessary to model inclined wellbores. Once the direction and inclination of a wellbore are defined, a three-dimensional spatially correlated field becomes necessary to best simulate the formation field. Simulations using the stochastic model proposed herein and considering constant elastic modulus have been compared. It is observed that when considering the same elastic modulus along the field, the area of the plastic zone is symmetric at the borehole wall; when using the stochastic model, however, the plastic zone area surrounding the well is not symmetric; thus, the most vulnerable plastic zone may lead to premature failure. Stochastic simulations have been carried out with different heterogeneous fields for vertical and inclined wells, and distributions of the total plastic zone areas are obtained for each case. Based on the stochastic field probabilistic analysis, a distribution function is presented, which aims to define a stability framework analysis to best assist a decision making process in determining if a mud pressure is operationally acceptable or not.