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We tested the MOF framework Cu-BTC for natural gas (NG) storage. Adsorption isotherms of C1–C4 alkanes were simulated applying the Grand Canonical ensemble and the Monte Carlo algorithm in a classical molecular mechanics approach. Experimental monocomponent isotherm of the alkanes was used to validate the force field. We performed multicomponent adsorptions calculations for three different quaternary mixtures of C1–C4 alkanes, matching typical NG streams composition, and predicted theoretical storage capacities, efficiency and accumulation of the NG within that composition. Despite being one of the frameworks with greatest storage capacity of methane, we found that Cu-BTC presented great sensitivity to the variation of the heavier alkanes in NG composition. When we increase the percentage of butane from 0.1% to 0.7% in the mixture, the mass of components retained in the discharge pressure (1 bar) increases from 35 to 60%. We also perform siting and interaction energy investigations and compare the NG storage performance of the Cu-BTC with that of activated carbons. To our knowledge, this is the first study regarding the efficiency of the NG storage in Cu-BTC.