## 1 Introduction  
Tight oil and shale gas reservoirs typically have low permeability, making it difficult to achieve high production rates [1]. Hydraulic fracturing technology, as a key technique for reservoir stimulation and production enhancement, has been widely applied and recognized [2; 3]. The core of hydraulic fracturing technology is to fracture the reservoir, creating a complex network of fractures in low-permeability reservoirs to increase the flow channels for oil and gas, thus improving production rates. The stimulated reservoir volume (SRV), which includes the volume of hydraulic fractures and the surrounding area where secondary fractures are formed [4; 5; 6], also includes the activation of natural fractures by hydraulic fracturing, which is crucial for oil and gas production [7; 8; 9; 10; 11].  
The numerical simulation of hydraulic fracturing has made significant progress based on the KGD model [12; 13], PKN model [14; 15], P3D model [16], radial model [17], Pseudo 3-D model [18], and full 3-D model [19]. There are mainly three numerical simulation methods: discrete element method, boundary element method, and finite element method. Among them, the finite element method is widely used due to its high accuracy and the ability to consider the effects of formation parameters, fracturing parameters, and fluid on fracture propagation. It is one of the most widely used numerical simulation methods and can be used to solve nonlinear problems and complex stress-strain problems [20]. The most widely used methods in the finite element method are cohesive zone elements and the extended finite element method. The former has the advantage of eliminatingstress singularity at the fracture tip and high computational efficiency. However, it often requires pre-determined fracture propagation paths and cannot simulate the randomness of real fracture propagation, and the fracture cannot change direction. The latter has the advantage of avoiding the decrease in computational convergence caused by mesh refinement due to stress concentration and the ability to simulate fracture propagation direction changes. However, its computational efficiency is not high, and it cannot form intersecting fractures [21; 22; 23; 24; 25; 26].  
In practical hydraulic fracturing, multiple uncertain parameters increase the difficulty of fracturing design, so it is necessary to study the factors that affect fracturing. Generally, the morphology of fractures is mainly influenced by formation structure, formation stress, and formation mechanical properties. In areas with natural fractures, hydraulic fractures can expand better and form a larger network of fractures [27; 28]. Concentrated stress can also affect the direction of hydraulic fracture propagation, with a greater impact in the horizontal direction and a larger range of influence in the vertical direction [29]. Elastic modulus, Poisson's ratio, tensile strength, displacement, permeability coefficient, and other factors also have different effects on fracture propagation [30; 31; 32; 33], thereby affecting the volume of the fracture network and the production of oil and gas. In actual layered formations, the properties of interlayers also have an impact on the fracturing results, which is often overlooked in many studies. Interactions between interlayers and reservoirs affect fracture propagation and the volume of the fracture network after fracturing.  
Based on the parameters of the target formation in western China, this study establishes a multi-cluster fracture propagation model that considers the properties of interlayers and reservoirs. The model investigates the effects of cluster spacing, cluster number, displacement, elastic modulus, Poisson's ratio, and permeability on the propagation of multi-cluster fractures. It compares the stimulated reservoir volume (SRV) under different influencing factors and analyzes the reasons for the differences, providing reference for subsequent hydraulic fracturing simulation studies.