Dynamic methane charges and discharges of a 2 L adsorbed natural gas (ANG) vessel, filled with two different kinds of adsorbent composite blocks (ACBs), were studied. The two ACBs show the same isothermal stored methane capacity, that is, 100 V/V. The first one is highly conductive but has low permeability, and the second one is highly permeable but has low thermal conductivity. From experimental results, it is shown that the heat transfer phenomena mainly govern the ACB's performance for dynamic methane storage. On the other hand, the coupling between heat and mass transfer within the ACB becomes actual for the dynamic methane discharge process. The simulation model, which was validated here for both the charge and discharge steps and for the two ACBs, was used for a preliminary dimensioning of a real-size ANG vessel.