Manufacturing membrane materials with high selectivity and permeability is quite desirable but practically not possible, since the permeability and selectivity are usually inversely proportional. From the viewpoint of reducing the cost of CO₂ capture, module performance is even more important than the performance of membrane materials itself, which is affected by the permeance of the membrane (P, stagecut) and selectivity (S). As a typical example, when the mixture with a composition of 13% CO₂ and 87% of N₂ is fed into the module with 10% stage cut and selectivity 5, in the 10 parts of the permeate, CO₂ represents 4.28 parts and N₂ represents 5.72 parts. In this case, the CO₂ concentration in the permeate is 42.8% and the recovery rate of CO₂ in this first separation appears as 4.28/13 = 32.9%. When permeance and selectivity are doubled, however, from 10% to 20% and from 5 to 10, respectively, the CO₂ concentration in the permeant becomes 64.5% and the recovery rate is 12.9/13 = 99.2%. Since in this case, most of the CO₂ is separated, this may be the ideal condition. For a given feed concentration, the CO₂ concentration in the separated gas decreases if permeance is larger than the threshold value for complete recovery at a given selectivity. Conversely, for a given permeance, increasing the selectivity over the threshold value does not improve the process further. For a given initial feed gas concentration, if permeance or selectivity is larger than that required for the complete separation of CO₂, the process becomes less efficient. From all these considerations, we can see that there exists an optimum design for a given set of conditions.