Porous solids with channel sizes that are not much above the size of small hydrocarbons can yield extremely large adsorption selectivity. Our Grand Canonical Monte-Carlo simulations indicate exceptionally high selectivity for the separation of methane, ethane and propane from natural gas. At 250 K the C3H8/CH4 separation on MIL-127 at low pressure has a selectivity of more than 1000 and the C3H8/CH4 separation on CNT (9,9) is even above 2000. This is due to the strong molecule lattice interaction in narrow channels which leads to large enthalpies of adsorption. The Arrhenius law for the Henry coefficients is analysed in order to show that the effect is due to this enthalpy rather than to steric reasons.