## 5 Conclusions  
This study uses a cohesive element model to investigate the morphological characteristics of hydraulic fracturing with multiple clusters. It discusses the research and analyzes the effects of three fracturing construction parameters (cluster spacing, the number of clusters, and displacement) and three geomechanical parameters (elastic modulus, Poisson's ratio, and permeability) on the behavior, morphology, and stimulated reservoir volume (SRV) of fracture propagation. The main conclusions are as follows:  
1. At the initial stage of fracturing, the edge fracture starts to propagate when the injection pressure reaches 47.85 MPa, while the mid fracture starts to propagate at an injection pressure of 49.31 MPa. This indicates that there is a certain interaction between the fractures during the fracturing process. The propagation of the mid fracture in terms of width and height is influenced by the edge fracture. With the same amount of fracturing fluid injection, the length of the mid fracture will be greater than that of the edge fracture. 2. When the cluster spacing is small, the mid fracture is greatly influenced by the edge fracture, resulting in a lower height and narrower width than the predetermined maximum values. As the cluster spacing increases, the width and height of the mid fracture increase, while the length decreases. The situation is the opposite for the edge fracture. The more clusters there are, the more pronounced the interaction between the fractures, especially the influence of the edge fracture on the mid fracture. With a larger displacement, more fracturing fluid enters the formation, resulting in an increased length, width, and height of the edge fracture. However, the mid fracture is influenced by the edge fracture, leading to a decrease in width and an increase in length. 3. The elastic modulus has a significant impact on the edge fracture. As the ratio of elastic moduli increases, the width of the edge fracture decreases while the length increases. When the ratio of elastic moduli is small, the mid fracture is longer and narrower. When the ratio of elastic moduli is large, the length of the mid fracture decreases while the width increases, but the impact is relatively small. As the ratio of Poisson's ratios increases, the morphology of the edge fracture changes less, while the width of the mid fracture increases and the length decreases. When the ratio of Poisson's ratios reaches a certain value, the influence on the fractures is basically negligible. An increase in the ratio of permeabilities allows more fracturing fluid to enter the formation, reducing the interaction between fractures. This has a minimal impact on the edge fracture, while promoting a better expansion of the mid fracture. 4. An increase in cluster quantity and displacement leads to an increase in the SRV in both the reservoir and the interlayer. As the cluster spacing increases, the interaction between fractures decreases, causing the fractures to transition from vertical expansion to forward expansion, resulting in a larger SRV in the reservoir. A higher ratio of elastic moduli leads to a decrease in the overall SRV, but an increase in the SRV in the reservoir and a decrease in the SRV in the interlayer. This is beneficial for reservoir exploitation. The ratio of Poisson's ratios and the ratio of permeabilities between the interlayer and the reservoir have a relatively small impact on the SRV in both the interlayer and the reservoir. Conceptualization, X.Z., X.L. and L.L. ; methodology, X.Z., X.L. and L.L. ; software, X.Z. ; formal analysis, X.Z. ; investigation, X.Z. ; resources, X.Z., X.L. and L.L. ; data curation, X.Z. ; writing--original draft preparation, X.Z. ; writing--review and editing, L.L. ; visualization, X.Z. ; supervision, X.L. ; project administration, X.L. and L.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding.