Shale gas and coalbed methane are energy sources that partly or even mainly consist of methane stored in an adsorbed state in the pores of the organic-rich rock and coal seams. In this study, the graphene nanoslit model is employed to model the nanometer slit pores in shale and coal. The Grand Canonical Monte Carlo (GCMC) and Molecular Dynamics (MD) modelling methods are used to investigate the mechanisms of adsorption and displacement of methane in the slit pore. It was found that the CVFF forcefield resulted in the largest adsorption amount, while the PCFF forcefield resulted in the least. The COMPASS and COMPASS II force fields led to similar results. As the width of the slit pore increases, the adsorption amount of gas molecules increases, and the number density profile of adsorbed methane molecules alters from a single adsorption layer to multi-adsorption layers. The minimum slit pore width at which methane molecules can penetrate the slit pore was found to be 0.7 nm. Moreover, it is demonstrated that by lowering the temperature, the adsorption rate of the methane increases since the adsorption is an exothermic process. Enhancing methane recovery was investigated by the injection of gases such as CO2 and N2 to displace the adsorbed methane. The comparison of adsorption isotherms of gas molecules provided the following order in terms of the amount of adsorption: CO2>CH4>N2.