## 4 Discussion
For results that lie on the parity line, their adsorption rates are equal to the supply rates, implying marginal mass transfer and reaction kinetics limitations (in other words: Supply rate limitation). This is the case for HAS6 and FS-PEI-50, which are tested at very slow supply rates. Those supply rates are considered less attractive for practical application because they lead to much longer adsorption times as well as fewer cycle numbers. The adsorption half-time of HAS6 was constrained by mass transfer through the pores due to its morphology characters according to [17]. In comparison, the Lewatit sorbent has larger pores (38 vs. 4.9 nm) and larger pore volume (0.2 vs. 0.11 mL/g) than those for HAS6. From this comparison, we may expect that the adsorption rate for Lewatit will be faster than that for HAS6 in the applied \(\mathrm{t_{sto}}\) range for Lewatit. For a relative fast supply rate, like that for both AEAPDMS-NFC and Lewatit, the \(\mathrm{t_{50}}\) lies above the dashed line, indicating some extents of rate limitation in the mass transfer, the intrinsic reaction, or both. These limitations increase when the supply rate increases. The AEAPDMS-NFC sorbent, tested at a smaller supply rate, already deviates more (in the vertical direction) from the parity line in Figure 7 than the sorbent used in this work. It therefore seems plausible that at comparable supply conditions, in the range of 15-30 minutes for 50% of \(\mathrm{t_{sto}}\), this difference will be significantly larger, underlining the fast adsorption rate of the Lewatit sorbent. Figure 7: The relationship between the CO\({}_{2}\) and water sorbent saturation half-time (\(\mathrm{t_{50}}\)) and the stoichiometric time (50% \(\mathrm{t_{sto}}\)) for Lewatit VP OC 1065 (data: See Figure 7 in Appendix A) compared with those of other air capture sorbents studied by [17; 25; 47; 52]. Note that the \(\text{t}_{50}\) values for water adsorption using the studied sorbent and its relation to 50% \(\text{t}_{\text{sto}}\) are also shown in Figure 7. The short \(\text{t}_{\text{sto}}\) values are due to the much higher water content in air compared to \(\text{CO}_{2}\). Those two results for water are in line with the results of \(\text{CO}_{2}\) adsorption using the studied sorbent. This indicates that the water adsorption, shown in Figure 5, is also fast. Overall, it can be summarized that the sorbent used shows a good performance with respect to the adsorption rate for DAC in comparison with other sorbents reported in the literature. Moving forward to the evaluation of the RFL process regarding the contacting energy, Table 4 shows the comparison of the adsorption characteristics among various DAC systems, all using supported amine sorbents. The results listed for this work are calculated using the data shown in Figure 7. The operating conditions in the present study were selected based on an optimization strategy presented in an earlier study [29]. The conditions for other studies [40; 41; 53] were taken from the respective studies at conditions selected by the respective authors for their technical/economic assessment. We recalculated the \(\text{t}_{\text{sto}}\) values for these studies, and the results (included in Table 4) show that the conditions in this work (24-43 min) are within the range covered by the references (14-101 min). For the selected cases, it is observed that the pressure drop and the electricity consumption for the RFL process are significantly lower than the sorbent circulation process using PEI-silica and a circulating fluidized bed reactor [41]. The process using TRI-PE-MCM-41 in a monolithic contactor possessed the lowest pressure drop in this comparison, but required a longer adsorption time, presumably caused by a long \(\text{t}_{\text{sto}}\)[40]. A longer adsorption time decreases the number of cycles per day and the reactor productivity, and eventually increases the sorbent and the reactor costs. Furthermore, monolithic contactors require time (and energy) for heating/cooling taking place in the same contactor.