Analysis of the Impact of Clusters on Productivity of Multi-Fracturing Horizontal Well in Shale Gas

Shale gas reservoirs with nanoporous media have become one of the primary resources for natural gas development. The nanopore diameters of shale reservoirs range from 5 to 200 nm, with permeability ranging from 1 × 10−9 to 1 × 10−6 μm2. The natural gas production from shale gas reservoirs is low, necessitating the use of multi-stage hydraulic fracturing in horizontal wells. Segmented multi-cluster perforation fracturing is an effective method for shale gas extraction in these wells. The number of clusters significantly impacts the productivity of horizontal wells. Therefore, it is essential to analyze the impact of cluster numbers on fracture productivity in shale gas reservoir development. In this study, the equivalent flow resistance method was applied to establish a productivity model for multi-stage hydraulic fracturing horizontal wells in shale gas reservoirs considering diffusion and slip. An approximate analytical solution was obtained, and the effects of cluster length, diffusion coefficient, and fracture network permeability on productivity were analyzed. The results show that gas production gradually increases with the increase in the number of clusters and cluster length. However, as the number of clusters increases, the interference between clusters leads to a decrease in the productivity of individual clusters. As the fracture permeability, fracture network permeability, and diffusion coefficient increase, shale gas production also gradually increases. The permeability of the fracture network has the greatest impact on productivity. These research results are beneficial for the design of clusters in horizontal well fracturing and are of great importance for the development and production of shale gas reservoirs.