## 1 Introduction
In a radial flow reactor, the sorbent is packed in a coaxial cylindrical annulus and divides the contactor into two gas chambers; one part is called the center pipe and the other one is called the annular channel. In a radial flow reactor, the gas phase passes through the sorbent bed in the radial direction. Note that the small-scale fixed bed is essentially a representative unit cell for the gas phase passing the sorbent in a radial flow reactor. A radial flow reactor can be easily scaled up without significantly increasing the footprint, as it merely needs to increase the height of the cylindrical shape of the reactor instead of its diameter. The configurations of the RFR can be divided into z-type and \(\pi\)-type configurations according to the direction of the inflow and outflow. A z-type RFR has the gas inflow and outflow in the same direction, whereas the inflow and outflow in a \(\pi\)-type RFR are in opposite directions. A \(\pi\)-type RFR is chosen in this study because it has a more uniform flow distribution than that of the z-type [31]. Figure 1 shows the configurations of the reactor types mentioned above. At present, RFRs have not been investigated for the application of CO\({}_{2}\) direct air capture. In the past two decades, RFRs were studied in some research papers and patents for, e.g., (1) configurations for a uniform flow distribution [31; 32; 33], (2) the application of catalytic reactions to produce naphtha [34; 35], xylenes [36], methanol [37], or hydrogen [38], and (3) the application of air purification (prior to the cryogenic air separation unit) [39]. No other studies evaluated RFRs for DAC using a supported amine sorbent. [PERSON] et al. estimated the operational cost by modeling the economic performance of a DAC process in a monolithic contactor unit coated with amino-modified silica adsorbent [40]. [PERSON] and [PERSON] estimated for a plate-type adsorber on the basis of experimental data in a lab-scale fixed-bed reactor (17 mm in diameter, 50 cm in length) using a supported amine sorbent, resulting in a total cost a total cost of 150-200 USD/ton CO\({}_{2}\)[13]. [PERSON] et al. evaluated air capture using 1 kg of  
Figure 1: Configurations for (**a**) a flat-bed reactor (**b**) a z-type radial flow reactor (RFR), and (**c**) a \(\pi\)-type RFR. polyethylenimine (PEI)-silica sorbent in a bubbling fluidized bed. On the basis of their experimental results, a conceptual design for CO\({}_{2}\) air capture was proposed, for which the operating cost was estimated to be 152 USD/t-CO\({}_{2}\)[41]. In addition to that, [PERSON] et al. evaluated a small-scale monolithic cylinder (2.5 cm in diameter, 10.2 cm in length), impregnated with PEI and suggested an operating cost of 100 USD/t-CO\({}_{2}\)[23]. In this paper, we focus on the process development in the application of CO\({}_{2}\) direct air capture in a radial flow reactor (RFR) using a commercial supported amine sorbent, Lewatit VP OC 1065 (Lewatit), in short: the RFL process (RFR reactor with Lewatit VPOC 1065 as adsorbent). The RFL process is operated at a sorbent scale of 2 km; this is the first time that such a reactor type and such a scale of the sorbent are investigated for the application of CO\({}_{2}\) air capture. The aim of this paper is an experimental feasibility study of the RFL process. Next to design validation, the RFR is operated as fixed-bed and as (intermittently and continuously) operating moving-bed. The RFL process performance is compared with other sorbents and processes for DAC, indicating that the RFL process is an attractive technology for capturing CO\({}_{2}\) directly from ambient air.