Membrane separation may substitute conventional energy intensive technologies, and it could have cost benefits and lower environmental footprints. Several membrane processes have been developed to achieve higher purity and recovery of products. This study uses a generic membrane superstructure (or system) that facilitates all possible inter- and intra-connections among different membrane stages (or units) which are arranged in series-parallel configurations. The developed mathematical model for the membrane system is a mixed integer non-linear programming (MINLP) problem. The mathematical model is implemented in AMPL, and BARON solver is used to solve it. The MINLP model of the membrane system can choose membrane from a Membrane Database, which has a number of polymeric and inorganic (graphene, carbon molecular sieve, zeolite and metal-organic frameworks) membranes. In this work, two industrial case studies of gas separation are considered: post-combustion CO2 capture and biogas upgradation by CO2 removal. The selection of CO2 removal technology depends on plant location, production capacity and product quality specifications. The chosen applications have challenges in terms of energy consumptions, economics and environmental burden. The separation performance of the membrane system is evaluated and compared for same membrane in all membrane stages. Two optimization problems were solved for each membrane: minimization of total area of membranes and minimization of total mechanical power. For both applications, best performing membranes were identified to target the minimum separation cost.