The propagation of hydraulic fractures is highly influenced by the geological structure of the reservoir in unconventional reservoirs, such as natural fractures. In this paper, a new fluid–solid coupling dynamic model was built which presents the failure mechanism of hydraulic fracture with pre-existing simple and complex natural fractures. The cohesive element method and the maximum principal stress fracture criterion were used in the new model. An analysis was conducted to investigate the impact of various factors, including encounter angle, in situ stress, elastic modulus, and Poisson’s ratio, on the propagation of hydraulic fractures. The simulation results indicate that the encounter angle and the in situ stress are the main factors affecting the fracture morphology. When the encounter angle and the in situ stress difference are small, hydraulic fractures propagate along natural fractures. When the elastic modulus is small, it is advantageous for the advancement of both hydraulic and natural fractures. The Poisson’s ratio has a slight effect on the fracture propagation pattern.

There are many natural fractures in shale reservoirs, changes in hydraulic fracture extension patterns. In the paper, a multi-fracture extension finite element model for horizontal wells in shale reservoirs under the disturbance of natural fractures is established by combining the actual geological parameters and construction parameters of a horizontal well multi-fracturing operation in X oilfield to analyze the effects of the difference in geostress, elastic modulus, angle of natural fractures, and the number of natural fracture groups on the hydraulic fracture extension. The results show that with the increase in ground stress difference and natural fracture angle, hydraulic fractures are more likely to penetrate the natural fractures; with the increase in elastic modulus, the fracture stress and tip stress increase, the volume of rupture unit, the fracture extension width and the pore pressure concentration area decrease, and it is easy to form a long and narrow fracture; with the increase in the number of fracture groups, the connectivity of reservoir fractures increases, the extension of fractures is stronger, and it is easier to form a complex fracture network.

Conventional fracturing design generally only considers the propagation of a single fracture in homogeneous storage, but the heterogeneity characteristics of the reservoir and the development of complex natural fractures will affect the fracturing effect. In order to study the horizontal well fracture propagation law under the synergistic effect of complex natural fracture reservoir heterogeneity, the globally embedded cohesive element finite model is established, and the heterogeneous reservoirs are built by Python programming. The influencing factors of multi-fracture propagation with heterogeneous reservoirs are analyzed, including the in situ stress difference, the injection rate of fracturing fluid, the perforation spacing, and the perforating clusters number. The results show that the heterogeneity and the natural fracture of the reservoir will affect the in situ stress distribution and propagation direction. When the in situ stress difference is low, the reservoir heterogeneity and natural fractures have a great influence on the fracture morphology. With the increase in injection rate, the fracture length and fracture width increase. With the in situ stress difference increase, the fracture deflection angle decreases. With the increase in fracturing fluid injection rate, the fracture length increases. The number of hydraulic fractures communicating with natural fractures increases with the natural fracture number and the number of perforation clusters under the synergistic effect of complex natural fracture and reservoir heterogeneity.