## 3 Results and Discussion
### Performance of the Fixed-Bed RFL

Table 3: Comparison of the experimental conditions in the fixed bed reactor and in the radial flow reactor. sorbent at the adsorption time \(t\), \(q_{eq}\) is the equilibrium capacity at inlet conditions, and \(q_{des}\) represents the residual capacity after desorption. Figure 3 shows that the variation of the \(\eta_{\text{S}}\) curve and the \(\eta_{\text{G}}\) curve with time are opposite. The intersection points of both curves are found at exactly the stoichiometric time. This finding that \(\eta_{\text{G}}\) equals \(\eta_{\text{S}}\) at the stoichiometric time was presented previously [29]. It can be noticed from Figure 3 that the point where the \(\eta_{\text{S}}\) and \(\eta_{\text{G}}\) curves cross is at a marginally larger value for the RFR due to the variations in temperature, CO\({}_{2}\) concentration, and humidity. The \(\eta_{\text{S}}\) and \(\eta_{\text{G}}\) at \(t=\)\(\text{t}_{\text{sto}}\) are 61% for the RFR and 56% for the FB contactor. This limited difference between the RFR and the FB results indicates a successful scale-up, especially considering all of the differences listed in Table 3 and, most importantly, the completely different geometric designs of the two contacts. The results show once more that the proportional increases of the sorbent amount and the air flow lead to similar efficiencies, despite the large variation of the superficial velocity (0.1 m/s for the FB and 0.23 m/s for the RFR). It also confirms that external mass transfer does not govern the rate of the adsorption process under the studied conditions shown in Figure 3. Hence, the stoichiometric time is found to be a good scale-up criterion for the DAC application, suggesting a predictable \(\eta_{\text{S}}\) curve variation with time. This curve can be used to calculate the working capacity (when \(q_{eq}\) is known from the adsorption isotherm) in relation to the choice of the adsorption time. With this, the required sorbent amount can be estimated. In the design and scale-up of fixed bed processes, three major aspects are typically considered, namely pressure drop, sorbent deactivation, and temperature control (heat effects) [48]. The RFL process shows a relatively low pressure drop (see Section 3.1) which will be compared to other CO\({}_{2}\) air capture processes in Section 4. In addition to that, the adsorbent is stable over at least one month of operation under air capture conditions [43] as well as during 300 h of testing under the flue gas capture [46]. Additionally, in these RFL process tests, we did not find any reduction in the CO\({}_{2}\) working capacity of the adsorbent (see Figure A7). Temperature control and heat effects for the studied RFL process are discussed below. Figure 4a shows the breakthrough curve and the CO\({}_{2}\) concentration at the inlet for a typical adsorption experiment in RFR. This experiment was operated with the air flow rate of 206 m\({}^{3}\)/h, in which the CO\({}_{2}\) concentration varied from 430 to 440 ppm and the RH content is around 40%. In the breakthrough curve, the CO\({}_{2}\) concentration increased immediately after adsorption start-up. The entire breakthrough curve shows a fast adsorption rate in the initial phase and slows down in the subsequent phase. The CO\({}_{2}\) concentration at the outlet reaches 97% of the inflow concentration in the first 2 h at a sorbent capacity of 1.26 mol/kg, but it takes another hour to achieve the maximum capacity (1.33 mol/kg). The studied sorbent was also tested in the gram-scale fixed-bed reactor under the comparable conditions (20 \({}^{\circ}\)C, RH 40%, 426 ppm), which demonstrated a similar maximum capacity (1.30 mol/kg). For the same experiment, the temperature ranged from 19 to 21\({}^{\circ}\)C, as illustrated in Figure 4b. Some fluctuations in the temperature of the inflow are observed, which are presumably caused by the varying number of people working in the lab, affecting ventilation rate, inlet temperature, and inlet CO\({}_{2}\) concentration.