## 2 Materials and Methods
### Radial Flow Reactor Design  
The RFR was designed based on previous results obtained using a fixed-bed reactor (FB) with a sorbent mass of 1-3 g [29]. From those experiments, we found out that the feed rate and external mass transfer do not affect the CO\({}_{2}\) adsorption rate when t\({}_{\text{sto}}\) is 43 min. At this condition (t\({}_{\text{sto}}\) = 43 min), the results showed an overlap of the adsorption rates for the experiments (at 25 \({}^{\circ}\)C, 400 ppm CO\({}_{2}\)) when using 1, 2, and 3 g of sorbent (the feed gas rate was adjusted according to the change in the sorbent mass) using the fixed-bed reactor. This experimental result was used as the design basis to scale up the process to the kilogram sorbent scale in a radial flow reactor. The results of the RFL process will be compared to these fixed-bed-Lewatit (FBL) data used for the design and are presented in Section 3.2. The radial flow reactor is designed for the same stoichiometric time as the one used in the FB. The optimal adsorption time was found to be 0.5-1.5 times the stoichiometric time. For the design of the RFL process, this was adopted, aiming for the RFL design to have the same saturation efficiency, CO\({}_{2}\) capacity, and gas residence time as in the FBL experiment. Specifically, the equivalent gas residence time used in this study is important. This contact time, calculated using the total volume of the sorbent bed (m\({}^{3}\)) over the volumetric flow rate of the feeding gas (m\({}^{3}\)/s), is preferably small to minimize the contact volume and to minimize the risk of supply limitation. Under supply limitations, the rate of sorbent loading is fully determined by the CO\({}_{2}\) supply to the contactor. For the design, a gas residence time of 0.1 s was chosen on the basis of the FB experiments. This contact time is, to the best of our knowledge, the shortest one reported in studies so far [41; 47]. More details on the procedures for the RFR design have been presented previously [29]. An inside view of the RFR is shown in Figure A3 in the Appendix A. The internal and external diameters of the sorbent-packing bed are 154 and 184 mm. The sorbent can be filled from the tubes with a diameter of 20 mm located at the top and emptied from the ball valve at the bottom. The external diameter and height of the reactor are 300 and 585 mm. The sorbent is located axially between two wire meshes ordered from Wire Weaving Dinxperlo (the Netherlands). The height of the sorbent-packing bed is 0.4 m. The porosity of the wire mesh itself is 0.48, which was calculated by Matlab based on a photo taken using a high-speed camera from eScope DP-M01. Figure 2 shows a photo of the RFR and its schematic diagram. The experiment started with desorption by heating the sorbent bed in a flow of nitrogen. To obtain lean sorbent, desorption stopped when the CO\({}_{2}\) outlet concentration was below 10 ppm. In the subsequent adsorption step, ambient air from the surrounding was supplied to the system by a fan (ER 120, [PERSON], The Netherlands). The speed of the fan was controlled by an ABB ACS 150 drive. The volumetric flow of the air supply was measured by a flowmeter from Elster Instrument (Germany). Two CO\({}_{2}\) analyzers (LI-COR L1840A) were used to monitor the CO\({}_{2}\) concentration at the inlet and the outlet (detection range: 0-20,000 ppm; error < 1% of reading). Both analyzers were calibrated just in advance of the first measurement at exactly the same conditions. Four thermocouples were connected to the set-up that measured the temperature of the air supply and the temperature at the top (36 cm), middle (21 cm), and bottom (4 cm) of the bed. To measure the pressure difference between the annular channel and center pipe, a differential pressure transmitter DMD 341 from BD SENSORS (Germany) was utilized; it was connected with two metal tubes whose heights were adjustable. A detailed look at the pressure difference measurement can be found in Figure A4 in Appendix A.