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Gas injection displacement is a widely used technique to enhance the recovery of coal methane (CH4) or oil reservoirs. Additionally, this method plays a crucial role in effectively developing CH4 resources in a closed goaf. In the present study, the distribution characteristics of fissures in a closed goaf were determined using a physical simulation test, and the connected fissure network was extracted and modeled. Further, CH4 extraction numerical simulation tests were conducted on the connected fissure network under gas injection conditions. The migration and distribution characteristics of CH4 were analyzed in the connected fissure network under different gas injection conditions, including gas injection position, gas injection rate, and gas injection type. The research also evaluated the impact of different gas injection conditions on CH4 production in vertical wells. Finally, a model was developed to determine characteristic parameters for CH4 production in vertical production wells, which were calculated and compared across different gas injection conditions. Results revealed a negative correlation between CH4 volume fraction and gas injection time in vertical wells under different gas injection conditions, contrary to the S-type growth curve. Gas injection positions significantly influenced the migration and distribution of gas within the connected fissure network, with higher CH4 productivity and production efficiency in the gas injection position P2 compared to P1. The increase in the gas injection rate enhanced CH4 production efficiency, albeit having little effect on CH4 productivity. Gas injection types yielded no significant influence on CH4 production efficiency, although CH4 productivity was lower with 100% CO2 injection compared to 100% N2 and mixed gas. This investigation provides the foothold for enhancing the recovery of CH4 in closed goafs and contributes to the progress of carbon emission reduction technology in coal mining areas. [ABSTRACT FROM AUTHOR]