## 6 Summary and Conclusions  
In this paper, a global cohesive model was established to simulate the natural fracture network in a reservoir. The propagation patterns of a hydraulic fracture in a natural fracture network were investigated. The propagation, bifurcation, and intersection of a hydraulic fracture under different in situ horizontal stress differences, the tensile strengths of rock, and cementing strengths of natural fractures were studied. The fracture parameters such as  
Figure 24: (**a**) Result comparison between the numerical simulation and the physical experiment. (**b**) Result comparison between the numerical simulation and the simulation in the reference.  
Figure 23: Schematic of the triaxial hydraulic fracturing test system used in the experiment.  
length and maximum aperture and the effective area of the fracture path were quantitatively evaluated. The results can be briefly concluded as follows:  
1. The global cohesive model can achieve non-prefabricated propagation of hydraulic fractures in a natural fracture network. This contributes a fracture simulation close to that in a real situation and benefits the understanding of the role that natural fractures play in induced-fracture propagation.
2. Step-by-step propagation patterns of hydraulic fractures showed that the hydraulic fracture tips were attracted by local natural fractures under low in situ stress difference. This led to bifurcations and secondary fractures at the intersection of fractures and, thus, contributed to the complexity of the induced fracture network. The influence of natural fractures on the overall trend of fracture propagation was limited when the in situ stress difference increased.
3. An effective area that indicated the influenced area of induced fractures was defined. It was higher when the horizontal in situ stress difference was at a low level, due to the formation of secondary fractures. When the in situ stress ratio was 1.12, the length of the main hydraulic fracture reached its maximum.
4. The mechanical properties of rock and natural fractures have impacts on the propagation of induced fractures. With the increase in the tensile strength of rock and the cementing strength of natural fractures, the induced fracture became less complicated due to the high cracking energy, and the length of the main fracture decreased. In addition, the higher tensile strength of rock increased the initiation pressure of the induced fracture, while the cementing strength of the natural fractures showed no impact on it.  
The results of the study can be utilized to explain various hydraulic fracturing behaviors in reservoirs that developed with rich natural fractures. It allows for the prediction of induced fracture propagations as well as the connection with natural fractures. The method can be utilized for related fracturing design, in general. In the future, the anisotropy of rock and the temperature stress field should be considered in study to obtain results that fit real situations.  
Conceptualization, Y.L.; methodology, Y.H.; simulation, Y.L.; validation, Y.L.; writing--original draft preparation, Y.L.; writing--review and editing, Y.K. All authors have read and agreed to the published version of the manuscript.  
This work is supported by the National Natural Science Foundation of China (No. 52174004), the National Key Research and Development, Program of China (No. 2018 YFC0808401), and the Fundamental Research Funds for the Central Universities (2042022 kf1025).  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.