## 4 Discussion  
In this section, the RFL process is evaluated using two criteria. The first criterion is the CO\({}_{2}\) adsorption rate per unit volume of the contactor (as an indicator for contactor investment costs) and, secondly, the air-sorbent contacting energy per amount of CO\({}_{2}\) captured (as an indicator for operating energy costs). As the CO\({}_{2}\) adsorption rate is determined by both sorbent properties (such as pore size and volume, particle size, and working capacity) and operating conditions (flow rate and temperature) rather than the reactor type, the adsorption rate of the RFL process is evaluated by comparing with other DAC sorbents published in papers focused on sorbent development. In contrast, the factors for determining the contacting energy are multifaceted, including not only the sorbent property and the operating conditions, but also the reactor type. In this way, the RFL process will be compared with those papers for DAC studying both the sorbent and the reactor. For the studies on the adsorption rate of the adsorbent, normally the comparison among different sorbents is made by comparing the values of \"adsorption half-time\" (\(\text{t}_{50}\)): The time required to reach 50% of the final equilibrium CO\({}_{2}\) capacity [17; 52]. However, \(\text{t}_{50}\) is also dependent on the CO\({}_{2}\) supply rate. The effect of the supply rate on the (observed) adsorption half-time is often not addressed for DAC sorbent screening. Here, we evaluate the adsorption rate of the sorbent used with those reported in literature at comparable supply rate conditions. For this, the stoichiometric time (\(\text{t}_{\text{sto}}\)) concept is used, introduced in Equation (1), which considers the differences both in the CO\({}_{2}\) supply rate and in the sorbent CO\({}_{2}\) capacity among various sorbents. In this way, a fair comparison of the adsorption rates among different sorbents and processes can be made. In line with most literature studies, adsorption half-time (\(\text{t}_{50}\)) is used to represent the adsorption rate here. The corresponding minimum time to reach that 50% of \(\text{q}_{\text{max}}\) is 50% of the stoichiometric time for complete sorbent saturation (\(\text{t}_{\text{sto}}\)). Figure 7 shows the \(\text{t}_{50}\) of the Lewatit sorbent used in this study in comparison to other solid functionalized sorbents tested at air capture conditions from the literature [17; 25; 47; 52]. The operating flows of 188, 206, 273, and 313 m\({}^{3}\)/h studied for Lewatit correspond to the 50% \(\mathrm{t_{sto}}\) values of 22, 18, 16, and 12 min, respectively. Note that other data from the literature listed in Figure 7 were all obtained from experiments at 25 \({}^{\circ}\)C. Considering that there is only a 5 \({}^{\circ}\)C difference in the adsorption temperature (in this study, measurements are done around 20 \({}^{\circ}\)C), the effect of temperature on the adsorption rate among different sorbents is negligible. The 50% \(\mathrm{t_{sto}}\) values (20-22 min) of various PEI/silica are similar to the one for the studied Lewatit sorbent, tested at \(\mathrm{\varphi_{v}}=188\) m\({}^{3}\)/h. However, their \(\mathrm{t_{50}}\) values are much longer than the sorbent used in this study. The reported minimum \(\mathrm{t_{50}}\) of PEI/silica is 196 min and it is around five times longer than the \(\mathrm{t_{50}}\) for Lewatit (33 min). Note that the PEI/silica data were measured using a thermogravimetric analyzer (TGA), while other referred adsorbents were tested in fixed beds. Unlike the comparison with PEI-silica, the comparison of the studied sorbent with AEAPDMS-NFC, HAS6, and FS-PEI-50 is not straightforward due to the large differences in 50% \(\mathrm{t_{sto}}\). Because the \(\mathrm{q_{max}}\) for those sorbents do not differ largely (1.3-1.7 mol/kg), the difference in 50% \(\mathrm{t_{sto}}\) is due to the large difference in their CO\({}_{2}\) supply rate. Figure 7 shows a dashed parity line, representing \(\mathrm{t_{50}}=50\%\)\(\mathrm{t_{sto}}\).