Thermodynamically constrained energy optimization of multistage membrane CO2 capture cascades

Multistage membrane cascades offer a modular and electrified route for CO2 capture, but their performance is strongly governed by nonlinear transport, competitive multicomponent permeation, inter-stage pressure coupling, and thermodynamic limits. These effects are often simplified or neglected in conventional stage-decoupled membrane optimization studies, which can lead to operating strategies that are numerically attractive but physically inconsistent. In this work, a thermodynamically constrained, multistage vacuum-driven membrane framework is developed for CO2 separation from dilute air, O2-depleted air, and flue-gas feeds. The model couples nonlinear solution-diffusion transport with competitive CO2/O2/N2 permeation and treats stage-specific permeate pressures as optimization variables. Experimental pseudo-multistage data are used for validation, while a Physics-Informed Neural Network (PINN) is incorporated to interpolate across feed CO2 and O2 compositions and generate continuous operating maps that are not directly available from discrete experiments. Multi-objective optimization using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is then applied to quantify trade-offs between CO2 purity and specific energy consumption. The results reveal two distinct operating regimes. Under ultra-dilute air conditions, CO2 enrichment is primarily feed-limited, and vacuum intensification provides only marginal improvement because of the severe thermodynamic penalty associated with low CO2 partial pressure. In contrast, flue-gas feeds operate in a driving-force-dominated regime, where optimized stage-wise pressure allocation substantially improves enrichment efficiency. For the optimized five-stage flue-gas configuration, the Pareto knee achieves CO2 purity above 40 vol% at a specific energy consumption of approximately 1.4–1.5 MWh t CO2−1. Sensitivity analysis confirms that feed CO2 concentration and N2 dilution dominate system performance, whereas vacuum pressure acts mainly as a fine-tuning variable once the feed-composition regime is fixed. Economic scaling further shows that capture cost varies linearly with electricity price, with SEC as the dominant cost driver. Overall, the proposed framework provides a quantitative basis for screening multistage membrane configurations, interpreting feed-composition effects, constructing physics-consistent operating maps, and guiding the design of electrified CO2 capture systems.