Metal organic framework (MOF) membranes have been widely investigated for gas separation applications. Several MOFs have been recently examined for selective separation of CH. Considering the large number of available MOFs, it is not possible to fabricate and test the CH separation performance of every single MOF membrane using purely experimental methods. In this study, we used molecular simulations to assess the membrane-based CH/CH and CH/CH separation performances of 175 different MOF structures. This is the largest number of MOF membranes studied to date for CH separation. We computed adsorption selectivity, diffusion selectivity, membrane selectivity and gas permeability of MOFs for CH/CH and CH/CH mixtures. Our results show that a significant number of MOF membranes are CH selective for CH/CH separation in contrast to traditional nanoporous materials. Selectivity and permeability of MOF membranes were compared with other membrane materials, such as polymers, zeolites, and carbon molecular sieves. Several MOFs were identified to exceed the upper bound established for polymeric membranes and many MOF membranes exhibited higher gas permeabilities than zeolites and carbon molecular sieves. Examining the structure-performance relations of MOF membranes revealed that MOFs with cavity diameters between 6 and 9 Å, porosities lower than 0.50, and surface areas between 500-1000 m g have high CH selectivities. The results of this study will be useful to guide the experiments to the most promising MOF membranes for efficient separation of CH and to accelerate the development of new MOFs with high CH selectivities.