A novel hybrid hydraulic fracturing phase-field model for porous media

Abstract

This study proposes a novel 2D hybrid hydraulic fracturing phase-field model for simulating the complex fracturing processes in porous media. By coupling Reynolds flow with the cubic law in fractures and Darcy's flow in the low-permeability surrounding reservoir, the fracture-reservoir fluid governing equations are established. To simulate hydraulic fractures, an energy functional for fluid-driven fracture propagation in porous media was developed within a hybrid framework. The proposed functional is based on the interactions between the fluid, fractures, and the surrounding matrix, addressing key issues, such as nonphysical fractures under compression and fracture healing, while maintaining displacement field linearity. Additionally, the proposed functional considers not only the effect of pore water outside the fractures but also the work done by the injection fluid on the internal fracture walls. The fracture width, stress degradation function, fluid leak-off, and strain energy are critical links in hydromechanical–fracture coupling. The above coupled model was discretized using isogeometric analysis and iteratively solved with a staggered scheme. Six 2D examples were used to evaluate the model's validity, computational capability, and hydraulic fracturing behaviour. The results showed that the proposed model can reasonably capture the highly nonlinear hydraulic fracturing process in shale reservoirs, including matrix deformation, fracture propagation, injection fluid flow inside fractures, pore water seepage outside fractures, and fluid leak-off.