## 1 Introduction
With these requirements in mind, different contacting methods were evaluated, all based on forced convective flow. The results are presented in Appendix A, Figure 14. It was found that the CO\({}_{2}\) sorbents were saturated much faster and with a much higher removal efficiency--in a classical (axial) fixed-bed contactor and in a fluidized bed--when compared with the use of a parallel-flow fixed bed, which (on its turn) displays a much lower pressure drop. The faster loading rate allows for more cycles per day and hence increased productivity and lower CapEx. Moreover, a fixed-bed reactor seems better suited than a fluidized-bed reactor for capturing CO\({}_{2}\) from air because of the possibility of operating at a lower pressure drop and allowing for a more compact design. A fluidized bed requires not only a gas distributor (with an additional pressure drop) to ensure an even gas distribution, but also a freeboard zone for gas-solid separation. Additionally, fluid beds have a lower contacting efficiency due to bubble formation. In selecting the operating conditions, the selection of the gas over sorbent ratio (GSR) and the adsorption process time is important, but not straightforward. For the first one, there is a trade-off between the CO\({}_{2}\) supply (sufficient CO\({}_{2}\) supply requires a high air flow rate) and the pressure drop (low pressure drop requires a low air flow rate). The selection of the adsorption time is finding the best trade-off between the gas capture efficiency and the solid conversion (also called sorbent saturation efficiency). A high gas capture efficiency corresponds with high reaction rates, normally found at low sorbent saturations at short adsorption times. A high sorbent saturation efficiency requires a long adsorption time, resulting in a lower system productivity, as the loading rate typically decreases with loading, but a lower energy penalty per kg of CO\({}_{2}\) for sorbent heating during sorbent regeneration. To represent the GSR, here, we use a parameter called the stoichiometric time. This parameter represents the general mass balance and is defined by the following expression:  
\[\mathrm{t_{sto}}=\frac{\mathrm{m_{S}\cdot q_{max}}}{\varphi_{V}\cdot\mathrm{O_{ CO2}}}\;. \tag{1}\]Here, m\({}_{\text{s}}\) (kg) represents the mass of the sorbent, q\({}_{\text{max}}\) (in g CO\({}_{2}\) per kg sorbent) represents the maximum CO\({}_{2}\) amount adsorbed by the sorbent, \(\varphi_{\text{v}}\) (m\({}^{3}\) s\({}^{-1}\)) represents the volumetric flow of gas introduced to the reactor, and \(\rho_{\text{CO2}}\) (g m\({}^{-3}\)) represents the concentration of CO\({}_{2}\) in the gas entering the reactor. Equation (1) shows that parameter t\({}_{\text{sto}}\) is inversely proportional to the GSR. Earlier work showed that the optimal stoichiometric time for CO\({}_{2}\) air capture using the sorbent used in this study is in the range of 15-45 min, with the optimal adsorption time being equal to 0.5-1.5 times the stochiometric time t\({}_{\text{sto}}\)[29]. The experimental data supporting those findings were firstly obtained from a fixed-bed reactor with 1-3 g of sorbent. Then, those optimal operating conditions were derived based on a total cost analysis considering the contacting energy, the regeneration energy, and the sorbent cost [29]. With the fixed-bed type as the optimal contacting method as well as the proper operating conditions, the next step is to select an adsorber to scale up the process to a scale of several kilograms of sorbent. A traditional scale-up of the axially-fixed-bed reactor used for the 1-3 g scale would result in a 'pancake-shaped' flat-bed contactor due to the low pressure drop requirement, occupying a large footprint area and giving rise to difficulties in proper feed gas distribution. In this respect, a radial flow reactor (RFR) was considered to be a good option. Radial flow reactors were introduced and developed for large-scale chemical plants in the late 1960s and early 1970s [30].