Natural gas demand has increased rapidly across the globe in the last decade, and it is set to play an important role in meeting future energy requirements. Natural gas is mainly produced from fossil fuel and is a side product of crude oil produced beneath the earth’s crust. Materials hazardous to the environment, like CO2, H2S, and C2H4, are present in raw natural gas. Therefore, purification of the gaseous mixture is required for use in different industrial applications. A comprehensive computational fluid dynamics (CFD) model was proposed to perform the separation of natural gas from other gases using membrane modules. The CFD technique was utilized to estimate gas flow variations in membrane modules for gas separation. CFD was applied to different membrane modules to study gas transport through the membrane and flux, and to separate the binary gas mixtures. The different parameters of membrane modules, like feed and permeate pressure, module length, and membrane thickness, have been investigated successfully. CFD allows changing the specifications of membrane modules to better configure the simulation results. It was concluded that in a membrane module with increasing feed pressure, the pressure gradient also increased, which resulted in higher flux, higher permeation, and maximum purity of the permeate. Due to the high purity of the gaseous product in the permeate, the concentration polarization effect was determined to be negligible. The results obtained from the proposed CFD approach were verified by comparing with the values available in the literature.