## 5 Verification Work  
Some model validation work was conducted to verify the validation of simulating the hydraulic fracture interaction with natural fractures using the coupled pore fluid diffusion and stress analysis along with global cohesive element.  
Firstly, we compared the simulation results with a triaxial hydraulic fracturing experiment in the laboratory. A true triaxial fracturing system was used to perform hydraulic fracturing on synthetic rock specimens that had been strictly prepared and cured (Figure 23). The cubic model block with a side length of 300 mm was located in a confining pressure loading device, which was used to simulate the field stress conditions. Three independent double cylinder hydraulic pump sets provided dynamic confining pressure loading. The test parameters referred to the field test parameters and were calculated by similarity criteria. The vertical, maximum, and minimum horizontal principal stresses were 9.8 MPa, 10.5 MPa and 8.6 MPa, respectively. The hydraulic fluid injection pressure was controlled by the hydraulic pump of the hydraulic fracturing assembly. The injection rate was 1 mL/s. As a control group, a fluid-solid coupled model was established with the same parameters used in the experiment, and the simulation result was compared with the experimental result. The results showed that the bottom hole pressure curve obtained by the numerical simulation was highly consistent with the bottom hole pressure curve in the experiment, shown in Figure 24a. The breakdown pressure and steady pressure obtained from the simulation were 17.38 MPa and 9.92 MPa relatively, which were very close to the experimental results of 15.18 MPa and 10.08 MPa. It proved that simulating the hydraulic fracturing using coupled pore fluid diffusion and stress analysis is credible.  
Another model was used to verify the accuracy of the interaction between hydraulic fractures and natural fractures. Different scenarios might occur in the interaction of a hydraulic fracture and a pre-existing natural fracture in naturally fractured shale reservoirs [23,51,52]. The hydraulic fracture may deflect into the natural fracture under the influence of the pre-existing fracture, or it may cross directly without being impacted by the natural fracture. The numerical model was built to simulate the intersection behavior of a hydraulic fracture and a single pre-existing natural fracture. A cohesive pore pressure element was inserted into the model to serve as the natural fracture, and coupled pore fluid diffusion and stress analysis were used to simulate the solid-fluid problem. By changing the in situ horizontal stress difference and the approximation angle, different propagation behaviors of hydraulic fractures were obtained. The numerical results and the experimental results are shown in Figure 24b. Square data denote that the hydraulic fracture crossed the  
Figure 22: The bottom hole pressure under different cementing strengths of natural fractures.  
natural fracture, while triangle data denote that the hydraulic fracture was captured and deflected to the direction of the natural fracture. At a small approaching angle, the experimental results and the simulation results showed that hydraulic fractures were deflected. When the approaching angle was 60\({}^{\circ}\), the numerical results showed that the hydraulic fracture deflected under 2 MPa in situ stress difference and crossed under 4 MPa in situ stress difference. At higher approaching angles, the numerical results agreed with the experimental results that the hydraulic fractures crossed the natural fracture. In general, the simulation cases were consistent with the experimental cases in the literature [53]. This shows that it is effective to simulate fracture intersection behavior by using cohesive element combined with coupled pore fluid diffusion and stress analysis.