We develop pore network models of transport and separation of binary and ternary gaseous mixtures, including those involving CO2, CH4, and hydrogen, through silicon carbide and carbon molecular-sieve membranes. A three dimensional network of interconnected pores is used to represent the membrane's pore space, in which the effective pores' radius is distributed according to a pore size distribution (PSD). The connectivity of the pores and the broadness of the PSD are varied in order to study their effect on the transport and separation processes, as are the pressure and temperature in order to understand the effect of the operating conditions. The Maxwell-Stefan equations are used for describing the pore level transport processes, which include Knudsen and hindered diffusion, as well as pore blocking effect and viscous flow. The boundary conditions that are imposed closely correspond to those used in the experimental studies. Good agreement is found between the simulation results and our experimental data for the single and binary gas permeances and separation factors. The results also indicate the fundamental significance to the permselectivity of a membrane of the tail of the PSD, as well as the percolation effect which is manifested through the interconnectivity of the pores that are accessible to the gases.