In our study on sub-critical hydrocarbon permeation in activated carbon, a minimum in the total permeability (B_T) at low pressure has been observed for only long-chain hydrocarbons such as n-hexane and n-heptane. Such an observation suggests that the minimum appearance depends on the properties of permeating vapors as well as the porous medium. In this paper a permeation model is presented to explain the minimum behavior with the allowance of the collision-reflection factor in the Knudsen diffusivity to be a function of surface loading. Surface diffusion was found to be very significant compared to other transport mechanisms such as Knudsen diffusion and gaseous viscous flow at low pressures. Since the gaseous viscous flow contributes negligibly to the B_T at low pressures, the minimum appearance in the B_T is mainly attributed to the interplay between Knudsen diffusion and surface diffusion. Also, the molecular structure of adsorbates plays an important role in the minimum appearance.