Direct air capture can be based on an adsorption system, and the used sorbent (chemisorbents or physisorbents) influences process. In this work, two amine-functionalized sorbents, as chemisorbents, and three different metal organic frameworks, as physisorbents, are considered and compared in terms of some key performance indicators. This was carried out by developing a mathematical model describing the adsorption and desorption stages. An independent analysis was carried out in order to verify data reported in the literature. Results show that the equilibrium loading is a critical parameter for adsorption capacity, energy consumption, and cost. The considered metal organic frameworks are characterized by a lower equilibrium loading (10⁻⁴ mol/kg) compared to chemisorbents (10⁻¹ mol/kg). For this reason, physisorbents have higher overall energy consumptions and costs, while capturing a lower amount of carbon dioxide. A reasonable agreement is found on the basis of the operating conditions of the Climeworks company, modelling the use of the same amine cellulose-based sorbent. The same order of magnitude is found for total costs (751 USD/tonneCO₂ for our analysis, compared to the value of 600 USD/tonneCO₂ proposed by this company).

In this research, an ANOVA analysis and a response surface methodology are applied to analyze the equilibrium of methanol reaction from pure carbon dioxide and hydrogen. In the ANOVA analysis, carbon monoxide composition in the feed, reaction temperature, recycle and water removal through a zeolite membrane are the analyzed factors. Carbon conversion, methanol yield, methanol productivity and methanol selectivity are the analyzed responses. Results show that main factors have the same effect on responses and a common significant interaction is not present. Carbon monoxide composition and water removal have a positive effect, while temperature and recycle have a negative effect on the system. From central composite design, an optimal solution is found in order to overcome thermodynamic limit: the reactor works with a membrane at lower temperature with carbon monoxide composition in the feed equal to 10 mol % and without recycle. In these conditions, carbon conversion, methanol yield, methanol selectivity, and methanol production are, respectively, higher than 60%, higher than 60%, between 90% and 95% and higher than 0.15 mol/h when considering a feed flow rate of 1 mol/h. A comparison with a traditional reactor is also developed: the membrane reactor ensures to have a carbon conversion higher of the 29% and a methanol yield higher of the 34%. Future researches should evaluate an economic analysis about the optimal solution.