A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures, characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids, is proposed. In this model, the driving force for the phase field consists of both tensile and shear components, with the fluid contribution primarily manifesting in the tension driving force. The displacement and pressure are solved simultaneously by an implicit method. The numerical solution’s iterative format is established by the finite element discretization and Newton-Raphson (NR) iterative methods. The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks, and the limitations of the hydraulic fracture expansion phase-field model, which only considers mode I fractures, are revealed. In addition, the influence of matrix mode II fracture toughness value, natural fracture mode II toughness value, and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.