In this work, a comprehensive pore-network model is developed for simulation of multicomponent diffusion through a porous media. In a pore-network model, the porous media structure is considered to be a three-dimensional regular network of nodes and the pores that are connecting them to each other. In this paper, a pore-network model was used to compute the diffusivity of natural gas, which consists of methane, water, and mercaptan, on zeolite 13X. Zeolite 13X is used in the temperature swing adsorption (TSA) process in South Pars in the Middle East. The effective diffusivity of these gases is achieved according to Knudsen diffusion, molecular diffusion, viscous flow, and surface diffusion conditions on three-dimensional networks simultaneously. Results were compared with reported data from literature and were in good agreement with them. In this modeling, the effect of the pore volume reduction on the cross-section area of pores, which may result in reduction in diffusivity of pores, has been considered. Also, the effects of pressure, temperature, and Z connectivity on effective diffusivity of multicomponent gas have been investigated.