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Membranes provide an efficient method for treating flue gases to capture CO2 from various point sources, achieving high recovery and purity rates. However, the lack of systematic process-level design tools has limited the translation of advanced membrane materials into large-scale technical and economic metrics. Thus, in this study, we present a superstructure model for the design of membrane-based carbon capture, both from highly energy-intensive industries and from power plants. The superstructure model enables the flexible design and global optimization of multi-stage membrane systems. Multiple membranes are compared under technical performance indicators (specific energy and specific area), while the already commercialized polymeric membranes Polaris and PolyActive are taken into consideration for estimating their economic performance. The presented framework establishes a robust link between material innovation and optimal process design, providing a key tool for the large-scale deployment of membrane-based carbon capture.