Path-dependent thermoplastic solution for wellbore stress analysis

Abstract A time-dependent solution is presented for the evolution of elastoplastic stress concentration around a wellbore subjected simultaneously to time-dependent thermal gradients relative to the far-field formation. Rock deformation is described using the incremental theory of plasticity with consideration of strain hardening. The thermal strains due to transient heat transfer toward the wellbore are solved for and incorporated into the formulation of rock stress evolution. Results demonstrate that the history of thermal strains shapes the stress path trajectory and consequently the long-term stress state at the wellbore wall. Conventional shear failure analysis based solely on elastic yield is shown to be overly conservative in defining the wellbore breakout limit of the drilling mud weight. Allowing plastic deformation beyond elastic yield results in a substantially lower value for this limit. The magnitude of wellbore contraction is strongly affected by strain hardening. Consequently, accurate characterization of the rock hardening behavior is essential for determining the lower bound of the drilling mud weight when a plastic model is used for wellbore stability analysis.