Based on the theory of phase field method

a model of fracture propagation in porous elastic formation is established. In the proposed model

the fluid flow in the porous rock obeys Darcy’s seepage law

and the permeability of rock is anisotropic and a function of the maximum principal strain. The convergence of the model is verified by comparing the results of three different time steps cases. Meanwhile

based on the proposed model

the effects of the in-situ stress difference

intersection angle

injection rate

and fracturing fluid viscosity on the intersection behaviour of hydraulic and natural fractures are investigated. The results indicate that: ① The hydraulic fracturing can solely make one side of the natural fracture open; ② The smaller the intersection angle and in-situ stress difference

the easier the hydraulic fracture is to open the natural fracture; ③ Increasing injection rate is beneficial to completely open the natural fractures

therefore

in the process of fracturing construction

the construction displacement should be increased as much as possible under the conditions of wellhead equipment and underground string strength; ④ The injection pressure increases with the increase of injection rate and fluid viscosity. Finally

the reliability of this model is verified by comparing the simulation results of this model with those of previous laboratory experiments.