Membrane-based carbon capture offers an energy-efficient and environmentally friendly alternative to conventional absorption-based processes, yet adoption remains limited by its performance with dilute CO 2 sources such as natural gas power plants. Here we present a techno-economic assessment of pyridinic-graphene membranes—porous graphene membranes hosting pyridinic nitrogen—that yield increasingly high CO 2 permeance and selectivity as CO 2 concentration in the feed decreases. This unique behaviour substantially reduces energy consumption, process footprint and capture costs, even when considering the non-ideal effects such as concentration polarization and pressure drops. Using uncertainty-aware cost modelling, including membrane cost, electricity prices, contingency factors and learning curves, we show that capture costs can reach US$50–100 per ton CO 2 for natural gas power plants and as low as US$25–50 per ton CO 2 for coal and cement plants, positioning this technology favourably against state-of-the-art capture processes. Our work bridges material innovation with process optimization, highlighting the role of advanced membrane materials and process design in cost-effective carbon capture for diverse industrial sectors.