A mathematical model of the adsorber was developed using the Toth equation. Microporous mordenite was synthesized to confirm model validation. The structure and characteristics of the obtained sorbent were confirmed by SEM, N2 adsorbtion, XRD and XRF methods. Adsorption of the hydrogen-methane mixture on H-form of synthesized mordenite was carried out at the pressure of 2 MPa and the temperature range of 20–35 °С.