## 1 Introduction
Climeworks is expecting to reduce the cost from 600 USD/tonneCO\({}_{2}\) to 100 USD/tonneCO\({}_{2}\) by 2030, while a more optimistic forecast is proposed by Global Thermostat, with suggested costs of 15-50 USD/tonneCO\({}_{2}\) for the near future [53]. Such costs appear to be unrealistic. From the considered literature analysis, it is evident that there is a gap to conduct an independent and complete analysis to evaluate some important KPIs, such as costs (operating and capital) and energy consumption of a number of important DAC technologies, including chemisorption and physisorption, based on the design of DAC process. Of the two, physisorption has hitherto received less attention from the research community. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Physisorbent**} & \multicolumn{2}{c}{**Adsorption Capacity**} & \multirow{2}{*}{**Reference**} \\ \cline{2-3} \cline{4-4}  & **CO\({}_{2}\)** & **H\({}_{2}\)O** & \\ \hline SIFSIX-3-Ni & \(1.8\times 10^{-1}\) & 5.17 & [PERSON] et al. [50] \\ HKUST-1 & \(5\times 10^{-2}\) & 9.89 & [PERSON] et al. [39] \\ Mg-MOF-74 & \(1.4\times 10^{-1}\) & 9.50 & [PERSON] et al. [51] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Adsorption capacity of some physisorbents from ambient air at 49% of relative humidity. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Literature Work/Team**} & **Actual Cost** & **Future Cost** \\  & **(USD/tonneCO\({}_{2}\))** & **(USD/tonneCO\({}_{2}\))** \\ \hline [PERSON] et al. [53] & & \(6.3\times 10^{1}\)–\(8.6\times 10^{1}\) \\ [PERSON] and [PERSON] [54] & \(4.3\times 10^{1}\)–\(4.94\times 10^{2}\) & \\ [PERSON] et al. [18] & \(9.1\times 10^{1}\)–\(2.27\times 10^{2}\) & \\ [PERSON] et al. [55] & \(6\times 10^{1}\)–\(1.9\times 10^{2}\) & \\ [PERSON] [56] (Climeworks) & \(6\times 10^{2}\) & \(1\times 10^{2}\) \\ [PERSON] [57] (Global Thermostat) & & \(1.5\times 10^{1}\)–\(5\times 10^{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimated costs for adsorption technology. The work of [PERSON] et al. [58] reports a comparison between some MOFs and amine-functionalized sorbents to evaluate costs and energy consumptions; however, their research is not based on design calculation but multi-objective optimization without any correlation between design parameters. Other research on adsorption technology are concerned with the sensitivity analysis of operating parameters [59; 60], regeneration methodology [61], new adsorbent bed [62], and thermodynamics [63]. This proposed work, following a design procedure, compares the theoretical performance and techno-economics of two amine-functionalized sorbents, SI-AEATPMS ([N-(2-aminoethyl)-3-aminopropyl]trimethoxysilane (AEATPMS) grafted on silica gel) and APDES-NFC-FD (3-aminopropylthethyldiethoxysilane (APDES) on nanofibrilated cellulose (NFC)), in addition to three different MOFs (MIL-101, MOF-177, MOF-5), with the aim to capture CO\({}_{2}\) from dry air, by using an adsorption system based on temperature swing for regeneration. We are supposing conditions without the relative humidity of air due to limitations in the literature data for the selected sorbents. In any case, this assumption reduces the energy consumption of the desorption stage for chemisorbents and to ensure a higher capture efficiency for physisorbents. SI-AEATPMS and APDES-NFC-FD are considered because they were suggested by the Climeworks company for DAC systems. MOF-5, MOF-177, and MIL-101 are taken into account because they have already been used in the literature for carbon dioxide capture with good performances and advantages compared to other sorbents (high adsorption capacity, thermally stable, and good strength to withstand pressures) [64; 65]. As the most investigated in the literature and in real applications for CO\({}_{2}\) capture, these sorbents can provide a good representation of the whole families of sorbents.