Numerical simulation of hydraulic–natural fracture interaction based on the continuous–discontinuous element method

Shale reservoirs commonly contain numerous geological discontinuities, such as natural fractures, faults, and lithological interfaces. These discontinuities significantly influence the formation of hydraulic fracture networks. Therefore, to investigate the impact of different natural fracture parameters on fracture network development, this study establishes a stress-seepage-fracture multi-field coupling model for fractured reservoirs based on the continuous-discontinuous algorithm. The effects of natural fracture angle, stress difference, natural fracture strength, and injection rate on fracture network morphology, injection pressure, and fracture complexity are systematically analyzed. The results indicate that the natural fracture angle and stress difference jointly control fracture propagation patterns. At high natural fracture angles and high stress differences, hydraulic fractures tend to directly cross natural fractures. Additionally, as natural fracture strength increases, the difficulty of natural fracture activation gradually rises, while the number of branch fractures increases. Under high injection rates, the fluid pressure builds up rapidly, facilitating better activation of natural fractures. Meanwhile, as the injection rate increases, the growth rate of fracture complexity accelerates significantly. However, under the same injected volume, the fracture complexity is highest at 0.001 m³/s and lowest at 0.01 m³/s. This study aims to provide guidance for understanding the interaction mechanisms between hydraulic and natural fractures and optimizing fracturing design parameters.