Phase field modeling of hydraulic fracturing in porous media formation with natural fracture

In this study, a new coupled fluid flow and fracture phase field evolution model is proposed to simulate hydraulic fracture propagation in porous media with natural fracture. In the proposed model, fracture width is calculated by maximum principal strain criterion, and only when the strain exceeds the critical strain there will be cracks formed, the element permeability is obtained by weighted calculation of fracture permeability and matrix permeability. The coupled fluid flow and stress equilibrium nonlinear equations is solved by the Newton-Raphson (NR) method, and the phase field is solved by Picard iteration method. The model convergence and stability were validated by compared the results of different mesh size and time step cases, respectively. The effectiveness of the model is validated by comparing the fracture width obtained from our numerical model and analytical model. Based on our numerical model, we investigate the influence factors of hydraulic fracture propagation in porous media with natural fracture. The results indicate that the smaller the approaching angle, natural fracture strength and in-situ stress difference, the easier for natural fracture initiating and propagating. Nevertheless, only one wing of the natural fracture can be activated.