In this thesis, we have particular interest in the hydrogen recovery from a hydrogen/hydrocarbon refinery waste mixture. Hydrogen is one of the clean, affordable and environmentally friendly energy sources. However, the current industry is not focused on the production or use of hydrogen as an energy carrier or a fuel for energy generation. Membrane separations are an economic alternative to either pressure swing adsorption separations or cryogenic separations. Transport across thin membranes can produce chemical and physical separations at a relatively low price. Thus, the diffusion of fluid gas-mixtures inside a porous material is an important factor in membrane separations. This research involves the mathematical modelling of adsorption and diffusion in microporous carbon membranes and particularly the Selective Surface Flow (SSF) carbon membranes developed by Air Products and Chemicals, Inc. Molecular simulations are used to predict the performance of the SSF membranes for hydrogen/hydrocarbon mixture separation under realistic conditions of temperature pressure and bulk gas compositions. Non-Equilibrium Molecular Dynamics (NEMD) gives a fully rigorous account of the dynamics of adsorption and diffusion at an atomic level, by integrating the equations of motion of adsorbed molecules interacting with each other, and with the surface, according to specified intermolecular potentials. In the NEMD simulations performed, it is assumed that all the pores in the membranes are identical, unconnected and open to the surface. However, this single-pore assumption is unlikely to occur in a real material. A real membrane contains pores of different sizes, connected together in a pore network, allowing the possibility of connectivity effects that are not accommodated by a single-pore model. Thus, the fundamentals of critical path analysis (CPA) are used to characterise the pore network structure. The CPA shows that species are selectively transported essentially through distinct sub-networks within the pore network of the membrane. The simulation results are compared with experimental permeabilities obtained from the Air Products selective surface flow membrane for a mixture of hydrogen/methane, relevant to the e.g. recovery of hydrogen from catalytic reformer offgas.