## 3 Results and Discussion
### Performance of the Fixed-Bed RFL  
In this section, experimental work was carried out using a fixed-bed mode of operation for the RFL process, aiming to study the RFR:  
1. CO\({}_{2}\) adsorption performance at a larger scale (2 kg) in the RFR in comparison with the results obtained on small scale (1 g) in the FB on which the RFR design is based;
2. CO\({}_{2}\) breakthrough and temperature profiles during a typical CO\({}_{2}\) adsorption test;
3. the rates of CO\({}_{2}\) and water adsorption. For a fair comparison, the RFR reactor was operated at the same stoichiometric time (t\({}_{\text{sto}}\)) of 43 min as the original FB tests with only 1 g of sorbent. The experimental conditions are listed in \begin{table}
\begin{tabular}{c c} \hline \hline
**Adsorption** & \\ \hline Sorbent mass (kg) & 1.7 \\ Flow rate (m\({}^{3}\)/h) & 41–313 \\ CO\({}_{2}\) concentration (ppm) & 429–464 \\ Relative humidity (\%) & 40–65 \\ Temperature (\({}^{\circ}\)C) & 19–22 \\ \hline Desorption & \\ \hline Nitrogen purge (m\({}^{3}\)/h) & 3 \\ Temperature (\({}^{\circ}\)C) & 120 \\ Duration (h) & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Working conditions for experimental work for testing RFR in fixed-bed mode. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Sorbent mass in buffer (kg) & 2.4 \\ Air flow rate (m\({}^{3}\)/h) & 188 \\ CO\({}_{2}\) concentration (ppm) & 436 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental conditions for the moving-bed RFR tests. Table 3. Note that although the two reactors were operated at the same t\({}_{\text{sto}}\), there is a difference of more than 1000 times in parameters such as air flow and sorbent hold up and a difference of 500 times in the geometric aspect ratio of the bed thickness over the contacting area ratio. Furthermore, it is important to note that the experimental determined maximum capacities are different, due to the fact that the FB experiments were carried out with dry,'synthetic' air of exactly 400 ppm CO\({}_{2}\), whereas the RFR was operated inside the high-pressure laboratory of the University of Twente using the real lab air with 60% relative humidity (RH) and a slightly elevated CO\({}_{2}\) content (here: 452 ppm). Figure 3 shows the comparison of the two reactors regarding their adsorption performance with respect to the gas capture efficiency (\(\eta_{\text{G}}\)) and the sorbent saturation efficiency (\(\eta_{\text{S}}\)). The first parameter is calculated from the experimentally determined CO\({}_{2}\) concentration in the gas leaving the reactor. using the following equation:  
\[\eta_{\text{G}}(t)=\frac{C_{CO2,in}\cdot t-\int_{0}^{t}C_{CO2,out}dt}{C_{CO2,in} \cdot t}. \tag{2}\]  
The latter is calculated as:  
\[\eta_{\text{S}}(t)=\frac{q_{t}-q_{des}}{q_{\alpha}-q_{des}}. \tag{3}\]  
In Equation (2), \(C_{CO2,in}\) and \(C_{CO2,out}\) represent the concentration of CO\({}_{2}\) in the inlet gas and outlet gas streams of the reactor. In Equation (3), \(q_{t}\) (g/kg sorbent) represents the adsorbed CO\({}_{2}\) capacity of the  
Figure 3: Comparison of the adsorption performance between the RFR and fixed bed (FB) using sorbent saturation efficiency (\(\eta_{\text{S}}\)) and gas capture efficiency (\(\eta_{\text{G}}\)) under the conditions listed in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Units** & **Fixed Bed** & **Radial Flow** \\ \hline Air flow rate & m\({}^{3}\)/h & 0.072 & 188 \\ Contacting area & m\({}^{2}\) & 2.0\(\times\) 10\({}^{-4}\) & 0.23 \\ Aspect ratio (thickness/area) & m/m\({}^{2}\) & 49.7 & 0.065 \\ Temperature & \({}^{\circ}\)C & 25 & 20 \\ Mass of the sorbent & g & 1 & 1720 \\ CO\({}_{2}\) inlet concentration & ppm & 400 & 452 \\ Stoichiometric time, t\({}_{\text{sto}}\) & min & 43 & 43 \\ Relative humidity, RH & \% & 0 & 60 \\ Superficial velocity & m/s & 0.1 & 0.23 \\ Max. working capacity & mol/kg & 0.9 & 1.5 \\ \hline \hline \end{tabular}
\end{table}