The microscopic competitive adsorption mechanism of methane (CH4) and carbon dioxide (CO2) is of fundamental significance for CO2 sequestration with enhanced gas recovery (CS-EGR) in clay-rich shale gas reservoirs, which is still in a preliminary research stage. In this study, the Na-montmorillonite models with various pore sizes and water densities were generated to gain insights into the CO2/CH4 competitive adsorption behaviors using the combined molecular dynamics and grand canonical Monte Carlo simulations. The effects and corresponding mechanisms of clay pore size, structure heterogeneity and water content on CO2/CH4 adsorption capacity, contribution of selectivity and isosteric adsorption heat were discussed in detail. Simulation results show that the Na-montmorillonite clay favors the preferential adsorption of CO2 over CH4, and the preferential adsorption of CO2 reduces with increasing clay pore size and pressure. Adsorbility factor is the major contribution for the CO2 /CH4 adsorption selectivity in dry clay models, while the contribution of volumetric factor enhances with rising pore heterogeneity caused by increasing water content and decreasing pore size. The physical pore heterogeneity in the upper near-wall region resulted from Na+ distribution, associated with the difference of CO2/CH4 dynamic diameter is one reason for the asymmetrical CO2/CH4 density profiles, while the strong affinity between CO2/Na+ and substituted Al atoms in the upper tetrahedron is the other reason. Interestingly, a later increase of CO2/CH4 adsorption selectivity with further rising water density is observed, which is due to the solvation of Na+ in interlayer water phase, re-exposing some high energy adsorption sites for CO2 adsorption. This result provides implication that the CS-EGR efficiency can be potentially improved by increasing the water content in clay. This study gains deep insights into the CO2/CH4 competitive adsorption mechanism in montmorillonite clay at microscopic scale, and can open new potentials for tuning the application of CS-EGR in clay-rich shale gas reservoirs.