Novel phase field model of hydraulic fracture propagation in poroelastic media and numerical investigation of interaction between hydraulic fracture and natural fracture

A novel numerical model is established to study the hydraulic fracture extend in poroelastic media with natural fractures based on the phase field method. In this new model, the poroelasticity parameter (Biot's coefficient, Biot's modulus, and porosity) of rock is a function of the phase field value. Therefore, a new phase field evolution equation is derived. The finite element numerical discretization method and Newton–Raphson (NR) iterative method are adopted to establish the corresponding numerical solution iterative scheme. The stability and correctness of the model were verified by a series of numerical simulation cases. The fluid pressure within the fracture, the fracture length, and the fracture width calculated by the model that regards the poroelasticity parameter as a constant would be larger, longer, and smaller, respectively, compared with those calculated by the model established in this study. The effect of certain formation factors and engineering factors on the intersection behavior between hydraulic fracture and natural fracture is investigated based on the established model.