Theory and analytical solutions to wellbore problems with hardening/softening Drucker-Prager models

Recognizing and quantifying the elasto-plastic nature of underground formations is critical for various subsurface operations such as drilling, stimulation, production, injection, and storage. In the case of geological CO2 storage, for instance, it is key to identify storage sites characteristics and pumping parameters that lead to safe and perennial CO2 trapping. In this work, we investigate different rock hardening/softening behaviors with the Drucker-Prager model: cohesion hardening/softening, friction hardening/softening, and their combination, jointed hardening/softening. Our focus is to solve the elasto-plastic deformation analytically in the vicinity of a wellbore. The three hardening/softening formulations predict different mechanical responses and stress-paths for solving the same wellbore problem with excavation. The analytical solutions for 2D axisymmetric problems with different hardening laws are provided in this study and verified with corresponding numerical results. This approach can be used to interpret field observations and calibrate experimental data with more comprehensive models. These new laws are implemented and benchmarked in GEOS, an open-source advanced numerical simulator of subsurface formations. This study enhances our understanding of subsurface rock's elasto-plastic behavior and offer analytical references for interpretating experimental measurements and developing numerical simulations for solving wellbore problems.