We present a unified transport model that combines specular, Knudsen and surface diffusion mechanisms, termed the Analytical Diffusion Mechanism (ADiM) model. The ADiM model uniquely describes the transport behaviour of the bulk gas and adsorbed phase taking place in rough and smooth nanopores. Experiments and molecular simulations of nitrogen flow through aligned nanotube-based membranes are used to verify the model. In addition, we explore entrance effects using a suction energy mechanism that is compatible with ADiM and can accelerate gas permeance by an order of magnitude. Finally, ADiM is used to assess the effect of tube size on post-combustion carbon dioxide separation from fossil fuel plants.