Introduction: Carbon dioxide (CO2) enhanced gas recovery represents a viable strategy for sequestering CO2 while concurrently augmenting gas production from subsurface reservoirs. Gas reservoirs, as inherent geological formations, are optimal repositories for gaseous compounds, rendering them suitable for CO2 storage. Nevertheless, the economic viability of pure CO2 storage necessitates integration with oil and gas recovery mechanisms to facilitate widespread CO2 utilization.Method: This study addresses the complexities of CO2 enhanced gas recovery through a comprehensive approach that combines theoretical model and numerical simulations. A numerical model is developed to simulate three-component diffusion involving CO2, and methane (CH4) in a two-phase system comprising gas and water.Results: The investigation systematically explores the process of enhanced CH4 extraction and CO2 injection into the reservoir and examines the influencing factors on extraction. Simulation results reveal a power-law decrease in CH4 production rate, stabilizing at a constant extraction rate. Enhanced CH4 extraction benefits from increased porosity, with higher porosity levels leading to greater CH4 extraction. Permeability augmentation positively influences CH4 production, although with diminishing returns beyond a certain threshold. The CO2 injection rate shows a direct proportionality to CH4 production. However, elevated CO2 injection rates may increase reservoir pressure, potentially causing cap rock damage and CO2 gas flushing.Discussion: This study contributes valuable theoretical insights to the field of CO2 enhanced gas recovery engineering, shedding light on the intricate dynamics of multi-component fluid transport processes and their implications for sustainable CO2 utilization.