## 4 Discussion
### Effect of Cluster Spacing  
Keeping other parameters constant, three pre-existing fractures are established with distances between fractures of 15 m, 17.5 m, 20 m, 22.5 m, and 25 m, respectively. The influence of different cluster spacing conditions on fracture morphology is analyzed and studied. The simulation results are shown in Figures 6 and 7. From Figure 6, it can be observed that the height of the edge fracture reaches its maximum value. The fracture width-height curves show little difference between cluster spacings of 15 m and 17.5 m. The curves for cluster spacings of 22.5 m and 25 m overlap each other. The height of the mid fracture increases with the increase in cluster spacing. The compression effect is minimal at a cluster spacing of 25 m, resulting in the maximum fracture width. The compression effect is maximum at a cluster spacing of 15 m, resulting in the smallest fracture width, and the height does not reach its maximum value. As the cluster spacing increases, the fracture width increases, reaching its maximum at a cluster spacing of 25 m. When the cluster spacing is too small, there is a significant difference in the width of the mid fracture, with a difference of 81% between the maximum and minimum widths. In contrast, the difference between the maximum and minimum widths of the edge fracture is only 24%. Figure 7 illustrates the relationship between fracture width and half-length. When the cluster spacing is 15 m and 17.5 m, the initial width of the mid fracture is small and the half-length is long due to the compression effect from the edge fracture. As the fracture half-length increases, the influence of the edge fracture on the mid fracture weakens, resulting in an increasing width. At the front end of fracture propagation, the width decreases to zero. The edge fracture, on the other hand, has a shorter fracture half-length due to the influence of  
Figure 5: Shows the curve of pore pressure variation at the injection point during fracture propagation. (**a**) The variation in pore pressure at the injection point of the edge fracture. (**b**) The variation in pore pressure at the injection point of the mid fracture. fluid loss into the formation during the expansion of the mid fracture, but it has a larger initial width. When the cluster spacing is 20 m, 22.5 m, and 25 m, the compression effect on the mid fracture weakens, leading to an increased initial width and more fluid loss into the formation. As a result, the fracture half-length decreases. The difference in the fracture width-half-length curves is not significant between cluster spacings of 22.5 m and 25 m. The influence of fluid loss into the formation at the front end of the fracture from the mid fracture weakens the compression effect on the edge fracture, resulting in the curves of fracture width-half-length for the edge fracture and the mid fracture overlapping each other. When the fracture spacing is small, the edge fracture has a significant impact on the mid fracture. As the fracturing fluid is continuously injected, the edge fracture exerts compression on the mid fracture. This causes the width of the injection point of the mid fracture to decrease, while the width of the injection point of the edge fracture is larger. However, under the action of the fracturing fluid, the force for the mid fracture to expand forward increases, resulting in a longer half-length compared to the edge fracture. At the same time, the fracturing fluid loss into the formation at the front end of the mid fracture hinders the forward expansion of the edge fracture to some extent, resulting in  
Figure 6: Illustration of the relationship between fracture width and height. (**a**) Relationship between width and height of the edge fracture. (**b**) Relationship between width and height of the mid fracture. Figure 7: Illustration of the relationship between fracture width and half-length. (**a**) Relationship between width and half-length of the edge fracture. (**b**) Relationship between width and half-length of the mid fracture.