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Membrane-based carbon capture offers an energy-efficient and environmentally-friendly alternative to conventional absorption-based processes, yet remains limited by its performance with dilute CO₂ sources such as natural gas power plants. We present a techno-economic assessment of a pyridinic-N-substituted graphene membrane that yields increasingly high CO₂ permeance and selectivity, as feed concentration decreases. This unique behavior substantially reduces energy consumption, process footprint, and capture costs. Using uncertainty-aware cost modeling, including membrane cost, electricity prices, contingency factors, and learning curves—we show that capture costs can reach 25–50 per ton CO₂ for coal and cement plants, positioning this technology favorably against state-of-the-art absorption and adsorption processes. Our work bridges material innovation with process optimization, and highlights the role of advanced membrane materials and process design in driving cost-effective, scalable CO₂ capture solutions for diverse industrial applications.