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Membrane processes are emerging as an attractive alternative to absorption for carbon capture, thanks to the high energy efficiency and modularity. To assess the real potential of membrane technology at a large scale, operating conditions need to be optimized in combination with the selected material. In this work, for the first time, we report the results of the techno-economic optimization of a double-stage membrane process for post-combustion carbon capture in the presence of a wide range of membranes, corresponding to several combinations of CO2 permeance and CO2/N2 selectivity. The optimization maps identify impact of various performance parameters on the cost. Also, the optimization results are used to chart out targets for permeance and selectivity, beyond which a further improvement does not result in cost reduction. Overall, this work gives important insights into the impact of membrane performances on the techno-economic feasibility of the optimized capture process and into the performance targets to make the technology more competitive.