Different nano-engineered grazynes have been studied as possible membranes to separate methane (CH4) from carbon dioxide (CO2) by computational simulations based on density functional theory (DFT) and molecular dynamics (MD). The study focuses on the thermodynamics, kinetics, and dynamical aspects associated to the diffusion rates and selectivities in the context of biogas upgrading. Small adsorption energy values have been obtained for three semi-permeable grazynes, with low diffusion energy barriers below 1 eV and getting lower values as the grazyne pore increases. Selectivity estimates are found to decrease with temperature with [1],[1,2]{0,1}-grazyne obtaining the highest CO2 selectivity over CH4 at room temperature, of ca. 17, while, for the rest of grazynes studied, the selectivity falls below 5. MD simulations reveal that selectivities can be larger, up to 39 at high pressures on [1],[2]{2}-grazyne, closely to the value obtained for [1],[2]{(00),2}-grazyne, suiting grazynes membranes for biogas upgrading.