CO2–H2O Co-Adsorption in Continuous TVSA Direct Air Capture: Process-Level Thermodynamic Implications for Energy Demand and Exergy Efficiency

Abstract Solid-sorbent direct air capture (DAC) processes employing temperature–vacuum swing adsorption (TVSA) inherently operate under humid conditions, yet the process-level thermodynamic consequences of humidity remain insufficiently characterized. This work extends a previously established dry-cycle equilibrium-stage TVSA framework by explicitly incorporating CO2–H2O co-adsorption through the weighted-average dual-site Toth (WADST) model coupled with the Guggenheim–Anderson–de Boer (GAB) formulation, using Lewatit VP OC 1065 as the representative DAC sorbent. The resulting equilibrium-stage framework embeds humidity-dependent equilibrium loadings, differential heats of adsorption, effective sorbent heat capacities, and an explicit product-gas conditioning step, enabling a thermodynamically consistent assessment of humidity effects on continuous TVSA operation. Across the investigated operating window, humidity produces competing thermodynamic effects: increasing adsorber feed-gas relative humidity enhances equilibrium CO2 loading and cyclic CO2 working capacity, thereby reducing the specific solids circulation requirement, while simultaneously causing a much stronger increase in H2O uptake and net H2O transport. Species-resolved energy analysis shows that the resulting regeneration penalty becomes increasingly dominated by the H2O heat-of-adsorption contribution, outweighing the benefit of enhanced CO2 working capacity and leading to increased regeneration energy demand and reduced regeneration exergy efficiency. Because water released during regeneration must subsequently be removed from the desorber off-gas, product-gas conditioning introduces an additional thermodynamic tradeoff between attainable CO2 purity and conditioning duty. Stage-wise analysis further reveals that humidity alters the spatial distribution of regeneration by localizing H2O removal within the uppermost equilibrium desorber stage while increasingly front-loading CO2 desorption. Overall, the extended equilibrium-stage framework provides a thermodynamic benchmark for evaluating sorbent performance, reactor concepts, and water-management strategies, while demonstrating that humidity-enhanced CO2 adsorption does not necessarily translate into improved cycle-level thermodynamic performance when accompanied by substantial cyclic water uptake and release.