With the increasing demand for alternative fuels the storage of natural gas (NG) in adsorbents like metal organic frameworks (MOFs) will become more important. In order to use MOFs as storage media in fuel delivery systems, the optimization of mass and energy transfer of the system is crucial. For rapid NG filling of a tank, molecules need to reach the adsorption sites within a reasonable time while the heat of adsorption should be dissipated to the environment. In this article, mass transfer in shaped bodies of MOFs was determined by permeability measurements and pulsed field gradient (PFG) NMR spectroscopy. The heat dissipation was also experimentally measured and both data sets were used to set up a theoretical density function theory model to predict the behavior of MOFs for NG storage.