The porosity of clay minerals is dominated by nanoscale pores that provide a large surface area for physical and chemical interactions with the surrounding fluids, including gas adsorption. Measuring gas adsorption at subsurface conditions is difficult, because elevated pressures are required and the interactions between the supercritical gas and the clay are relatively weak. Here, we report on the measurement of adsorption isotherms of CO2 and CH4 on the source clay Na-montmorillonite (SWy-2) at different temperatures (25–115°C) over a wide range of pressures (0.02–25 MPa). The experimental observations are thoroughly analysed by considering both net and excess adsorbed amounts, and by extracting adsorption metrics, such as the Henry's constants and enthalpy of adsorption. The results consistently indicate that SWy-2 favours adsorption of CO2 over CH4 with selectivity, S≈5.5. The experimental data are successfully described using a Lattice Density Functional Theory (LDFT) model. The adsorption energetics estimated by the model compare well with the experimentally obtained enthalpy of adsorption. It is further shown that even at the highest pressure the pore space of the clay is only partially filled and that the degree of saturation increases upon approaching the critical temperature of the gas. The ability of the LDFT model to reveal pore-dependent adsorption behaviours demonstrates its potential against empirical models, such as the Langmuir equation, which fail at capturing the complexities of supercritical gas adsorption at subsurface conditions.