Abstract: The morphology of fracture propagation in hydraulic fracturing plays a crucial for exploiting oil, gas, and geothermal energy in deep rock formations. To address fracture propagation in hydraulic fracturing in deep rock formations, this article establishes a stress-seepage coupling model based on the phase field method theory, Biot’s porous elastic medium mechanics theory, and seepage mechanics theory. The equations were discretized using the finite element method, and the Newton-Raphson (NR) and the separated coupling methods were employed to enhance calculation accuracy. The reliability of the model was verified by comparing the numerical simulation results with laboratory tests and numerical simulations based on the numerical manifold method (NMM), and comparing numerical solution with the theoretical analytical solution. In this study, we utilize the established model to investigate the effects of in-situ stress difference, fracture spacing, and injection flow rate on the propagation of double fractures perpendicular to the direction of maximum principal stress in hydraulic fracturing. The results demonstrate that the increase of in-situ stress difference leads to a higher deflection angle of the fracture propagation path and more propagation branches. Smaller fracture spacing facilitates easier fracture penetration, while larger spacing increases the deflection angle and propagation length. Additionally, a larger injection flow rate increases fracture propagation length and speed. Understanding the impact of different factors on fracture propagation establishes valuable theoretical foundations for optimizing complex fracture networks in deep rock formations through hydraulic fracturing.

Key words: phase field method, hydraulic fracturing, porous media, fracture propagation, numerical simulation