We report the results of extensive equilibrium molecular dynamics simulation of adsorption of ternary gas mixtures in a class of model nanoporous materials, namely, carbon molecular sieve membranes (CMSMs), which are being utilized for separation of gas mixtures. We use a novel three-dimensional molecular pore network model for CMSMs based on Voronoi tessellation of the simulation cell. The simulations with such a model allow us to investigate the effect of the morphology of the pore space, i.e., its pore size distribution and pore connectivity, on the adsorption isotherms. We also extend a statistical mechanical theory of adsorption of single gases and their binary mixtures, recently developed by us, to ternary mixtures and use the results of the molecular simulations to test its accuracy. The theory is shown to provide very accurate predictions for the simulation results over wide ranges of the temperature and porosity of the membrane. The performance of the theory is also compared with that of another theory of adsorption based on a virial expansion.