In this work, a fixed-bed adsorption apparatus was developed to carry out adsorption breakthrough curve ex-periments at cryogenic temperatures (between 195 and 273 K) and high pressures (up to 18 bar) to screen adsorbents for the dynamic separation of green hydrogen blended in natural gas grids. Therefore, a series of breakthrough curve experiments of single component CH4 and H2, and their mixtures on the benchmark binder -free zeolite 13X were performed. The equilibrium data obtained were fitted with the virial, dual-site Langmuir, and Langmuir isotherm models. Moreover, the equilibrium data and the isosteric heat of adsorption were compared with the data available in the literature obtained by microcalorimetric, gravimetric, and volumetric methods. The maximum loading obtained for CH4 and H2 at 195 K and 12 bar was 6.95 and 2.08 mol kg-1. The selectivity predicted by the extended dual-site Langmuir was 17.3 for CH4 over H2 at 195 K and 12 bar, considering a binary interaction of a mixture of CH4/H2 (80/20 vol%). Additionally, binary experiments were performed to evaluate the dynamic separation of H2 and CH4 at the mixture ratio H2/CH4 (20/80 % vol.), and data was simulated by using a proper dynamic fixed-bed adsorption mathematical model. Overall, the results pointed out that the novel apparatus provides a reliable tool to collect equilibrium and dynamic information for screening adsorbents targeting the separation of green H2 blended into natural gas grids.