The adsorption properties of CO₂, N₂ and CH₄ in all-silica zeolites were studied using molecular simulations. Adsorption isotherms for single components in MFI were both measured and computed showing good agreement. In addition simulations in other all silica structures were performed for a wide range of pressures and temperatures and for single components as well as binary and ternary mixtures with varying bulk compositions. The adsorption selectivity was analyzed for mixtures with bulk composition of 50:50 CO₂/CH₄, 50:50 CO₂/N₂, 10:90 CO₂/N₂ and 5:90:5 CO₂/N₂/CH₄ in MFI, MOR, ISV, ITE, CHA and DDR showing high selectivity of adsorption of CO₂ over N₂ and CH₄ that varies with the type of crystal and with the mixture bulk composition.