Phase-field model of hydraulic fracturing in thermoelastic–plastic media

In this study, we present a thermodynamically consistent thermo-fluid–solid–elastic–plastic phase-field model to accurately capture the propagation process of hydraulic fracture in deep shale. The developed model takes into account the degradation of the thermoelastic–plastic parameters, strain hardening, mixed-mode fracture, and thermal convection. The model incorporates an uncorrelated Drucker–Prager constitutive model with a nonlinear saturated strain function to capture the deformation behavior of shale. The driving force of the fracture integrates the effects of elastic, plastic dissipative, fluid, and thermal energies of the rock. The model is constructed in a numerical computation iteration format using finite element discretization and Newton–Raphson iteration. To solve the coupled problem more efficiently, a staggered iteration algorithm is adopted to solve the displacement, pressure, temperature, and phase fields. Several numerical results are extracted and compared with the analytical solution results and experimental test data to demonstrate the accuracy and validity of the proposed model. In addition, the propagation behavior of hydraulic fractures in thermoelastic–plastic reservoirs with homogeneous, natural fractures or layering is investigated, and the results show that the model can capture complex fracture propagation patterns.