Thermodynamic efficiency of membrane separation of dilute gas: Estimation for CO2 direct air capture application

•The current research activities focus on the throughput of CO2 separation and ignore energy efficiency. The estimation of energy efficiency specific to direct air capture (DAC) has been awaited.•The theoretical limits of energy (exergy) efficiency of separating very dilute gas corresponding to DAC are calculated as a function of the membrane's CO2 separation ratio r. Vacuum swing and continuous pumping schemes are treated.•Efficiency critically depends on the separation ratio r: 0.13 % for r = 10, 2.0 % for r = 100, and 49.9 % for r = 5000 for concentrating 400 ppm CO2.•The energy efficiency of reported CO2 separation simulations and experiments has been thoroughly reviewed, and the candidates for achieving high efficiency are presented. Gas separation technology is crucial for addressing environmental issues like CO2 capture to mitigate climate change. While membrane separation is often cited for its efficiency, accurate estimations are scarce. We present estimations based on classical thermodynamics for very lean CO2 composition (400 ppm), revealing rich details in simple systems and deriving guiding principles. Our main conclusion emphasizes the critical necessity of a high membrane separation ratio, and we discuss candidates for achieving this goal. [Display omitted]