The Modeling for Coupled Elastoplastic Geomechanics and Two-Phase Flow With Capillary Hysteresis in Porous Media

We study new constitutive relations employing the fundamental theory of elastoplasticity for two coupled irreversible processes: elastoplastic geomechanics and two-phase flow with capillary hysteresis. The fluid content is additively decomposed into elastic and plastic parts with infinitesimal transformation assumed. Specifically, the plastic fluid content, i.e., the total residual (or irrecoverable) saturation, is also additively decomposed into constituents due to the two irreversible processes: the geomechanical plasticity and the capillary hysteresis. The additive decomposition of the plastic fluid content facilitates combining the existing two individual simulators easily, for example, by using the fixed-stress sequential method. For pore pressure of the fluid in multi-phase which is coupled with the geomechanics, the equivalent pore pressure is employed, which yields the well-posedness of coupled multi-phase flow and geomechanics, regardless of the capillarity. We perform an energy analysis to show the well-posedness of the proposed model. And numerical examples demonstrate stable solutions for cyclic imbibition/drainage and loading/unloading processes. Employing the van Genuchten and the Drucker Prager models for capillary and the plasticity, respectively, we show the robustness of the model for capillary hysteresis in multiphase flow and elastoplastic geomechanics.