Hydraulic fracturing phase-field model in porous viscoelastic media

The mechanical behavior of shale exhibits pronounced time-dependent nonlinearity. Existing phase-field models are inadequate for evaluating the fluid-driven fracture propagation process in porous viscoelastic media. In this study, a new viscoelastic phase-field model for fluid-driven fracture propagation was introduced based on a thermodynamically consistent framework using the Maxwell–Wiechert model to describe viscoelastic constitutive behavior, with the bulk and shear moduli expanded using the Prony series. Volumetric deviatoric splits were used for both elastic and viscous energies. The fluid flow in both the fracture and the matrix adhered to Darcy's law. Additionally, the phase-field driving force considers the combined influence of rock elastic, viscous, and fluid energies. The numerical calculation iteration format was constructed using finite element discretization and the Newton–Raphson (NR) iterative method. A staggered iteration algorithm was applied to address the displacement, pressure, and phase-field problems. This method not only accurately simulates mechanical cyclic loading but also models the extension of multiple hydraulic fractures in homogeneous reservoirs and hydraulic fracture propagation in fractured reservoirs.