A nonequilibrium molecular dynamics (NEMD) simulation technique is employed to investigate the transport of binary mixtures of hydrogen and methane through a model carbon membrane of varying thickness. Both forced flow simulations under a pressure gradient and isobaric counterdiffusion simulations are conducted in this work. The principal conclusions of these studies are: (i) pore entrance/exit effects may need to be taken into consideration in membrane design for hydrogen/hydrocarbon separations if the length of the controlling pores within the carbon membrane is of the order of one tenth of a micron or less; (ii) viscous (convective) flow contributions to the fluxes of the individual components of the mixture should be negligible for the carbon membranes currently in use; (iii) the cross-coefficients of diffusion appear to play a relatively minor role in the normal (pressure driven) hydrogen/methane membrane separation process however under isobaric conditions the simulation results suggest that hydrogen/methane cross-coupling plays a significant role in hindering the hydrogen counterdiffusion flux within carbon membranes containing long, narrow pores.