Gas-gas separation, to purify natural gas, is simulated using a membrane supported by a porous medium. Removing acidic gasses from the natural gas is gaining attention recently. Computational fluid dynamics simulations are conducted for asymmetric multi-component fluid flows in a channel. The flow system consists of a circular cross-section channel bounded by a porous layer which supports the membrane wall. The Navier-Stokes equations model the flow in the channel, while the flow in the porous medium is modeled by both the Darcy's law and the extended Darcy's law. Mass transport equations, including mass diffusion of mixtures of two gasses (CO2 and CH4), are employed to determine the concentration distribution. The membrane will be modeled as a functional surface; where the flux of each component will be determined based on the local partial pressure of each species, composition, and permeability and selectivity of the membrane. The effect of the porous medium on the membrane performance will be determined for a wide range of Reynolds number. The performance of the system will be measured by maximum mass separation with minimal frictional losses.