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.

Based on the existing research results, a theoretical fracture model of strata under the compound impact of static and harmonic dynamic load is improved, and the fracture characteristic parameters (stress intensity factor, T-stress, and fracture initiation angle) under the two far-field stress are determined according to the crack dip angle. Additionally, the effects of harmonic dynamic load on the distribution of the stress field and the fracture characteristic (the crack initiation angle, the fracture degree, the number of fracture units, and the fracture area) are further calculated and discussed by theoretical model solution, extended finite element simulation, and the secondary development of the simulation module, respectively. The research results show that the far-field stress, stress intensity factor, and T-stress vary in harmonic form with time under the compound impact of static and harmonic dynamic loads. The frequency of dynamic load affects the number of reciprocal fluctuations of stress intensity factor and T-stress as well as the crack initiation time, but has less influence on the crack initiation angle and fracture degree. While the amplitude of dynamic load affects the stress intensity factor, the extreme value of T-stress and fracture characteristics of the crack. This study has theoretical guiding significance for parameters’ optimization and realization of resonance impact drilling technology.

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.