Graphene has enormous potential as a unique molecular barrier material with atomic layer thickness, enabling new types of membranes for separation and manipulation. However, the conventional analysis of diffusive transport through a membrane fails in the case of single layer graphene (SLG) and other 2D atomically thin membranes. In this work, analytical expressions are derived for gas permeation through such atomically thin membranes in various limits of gas diffusion, surface adsorption, or pore translocation as the rate-limiting step. Gas permeation can proceed via direct gas-phase interaction with the pore, or interaction via the adsorbed phase on the membrane exterior surface. A series of van der Waals force fields allows for the estimation of the energy barriers present for various types of graphene nanopores. These analytical models will assist in the understanding of molecular dynamics and experimental studies of such membranes.