An improved phase-field model for oil–water two-phase flow and mixed-mode fracture propagation in hydraulic fracturing

An improved novel phase-field model is proposed for describing fracture propagation, effectively characterizing the interactions between oil–water two-phase fluids and solids as well as mixed-mode fracturing. This model encompasses equations for two-phase flow stress balance, fluid flow, and a complex mode fracture phase-field specific to two-phase flow. Within the fluid flow equations, the capillary pressure caused by the oil–water interface during the fluid loss process in the matrix is accounted for, and the anisotropic relative permeability during fluid flow is linked to normalized saturation. The driving forces for fracture propagation in the phase-field are categorized into Mode I and Mode II forces, with the contribution from the oil–water two-phase fluid attributed to the Mode I (tensile) driving force. The model uses finite element numerical discretization and the Newton-Raphson iterative method to establish a numerical iteration format, employing an implicit-explicit staggered solution scheme. Additionally, the model is used to investigate several key factors. It assesses the impact of different intersection angles on fracture propagation in naturally porous media. It also studies the effect of different natural fracture permeabilities on hydraulic fracture propagation. Finally, the model analyzes the propagation patterns of hydraulic fractures under different perforation phase angles.