## 3 Validation
### Validation of Breakthrough Curves on Adsorption Beds
\begin{table}
\begin{tabular}{l c c} \hline \hline
** adsorbent** & **AC** & **Zeolite 13X** \\ \hline Particle radius, \(R_{p}\) [m] & 0.00085–0.0012 & 0.0010–0.0011 \\ Particle density, \(\rho_{p}\) [kg/m\({}^{3}\)] & 750 & 1050 \\ Bulk density, \(\rho_{b}\) [kg/m\({}^{3}\)] & 558 & 751 \\ Bed porosity, \(\epsilon_{b}\) & 0.256 & 0.284 \\ Total porosity, \(\epsilon_{z}\) & 0.698 & 0.673 \\ Heat capacity, \(C_{\rm{eff}}\) [1/kg/K] & 1570 & 1100 \\ Pore volume [cm\({}^{3}\)/g] & 0.46 & 0.39 \\ Total surface area [m\({}^{2}\)/g] & 1306.4 & 742.9 \\ \hline
**Algorithm bed** & & \\ \hline Length, \(L\) [m] & 1.0 & \\ Inside diameter, \(d_{b}\) [m] & 0.021 & \\ Thickness of wall, \(\phi_{b}\) [m] & 0.0022 & \\ Heat capacity of wall, \(C_{\rm{eff}}\) [1/kg/K] & 502.8 & \\ Density of wall, \(\rho_{b}\) [kg/m\({}^{3}\)] & 7830 & \\ Thermal conductivity of wall, \(K_{w}\) [W/m/K] & 16 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of adsorbents and adsorption bed [28]. Figure 1: Adsorption isotherms of (**a**) CO\({}_{2}\), (**b**) N\({}_{2}\), (**c**) CO, and (**d**) H\({}_{2}\) on AC and zeolite 13X at 293 K, 308 K, and 323 K (symbol: experimental data from Refs. [26; 27]; line: TD DSL fitting). Figure 2: Breakthrough curves and residuals on (**a**) AC single-layer bed, (**b**) zeolite 13X single-layer bed, and (**c**) AC/ zeolite 13X = 6:4 layered bed at 10 bar and 3 LSTP/min (full symbol: experimental data from Ref. [28]; line: simulation results; open symbol: residuals). A comparison of the breakthrough times indicates that zeolite 13X is more efficient in removing N\({}_{2}\) and CO. Additionally, the higher roll-up of CO on the zeolite 13X bed suggests that zeolite 13X has a higher adsorption affinity for impurity gases. The CO roll-up phenomenon refers to the increase in the CO molar fraction at the outlet that exceeds its inlet molar fraction. This occurs due to competitive adsorption in multi-component gas mixtures, where the strongly adsorbed adsorbate (CO\({}_{2}\)) displaces the weakly adsorbed adsorbate (CO) from the adsorbents' surface, causing the desorption of the weakly adsorbed adsorbate. Although CO\({}_{2}\) penetrates later on zeolite 13X, [PERSON] pointed out that during the pressure swing between 1 bar and the feed pressure, the working capacity of CO\({}_{2}\) on zeolite 13X is much smaller than that on AC [28]. Solving this issue through vacuum pressure adsorption (VPSA) would significantly increase the cost. Therefore, hydrogen purification is performed using an AC/zeolite 13X layered bed configuration. As shown in Figure 2c, the breakthrough of impurity gases and the roll-up of CO on the layered bed have been significantly improved. To assess the accuracy of the simulation results, residual analysis of the breakthrough curves is conducted and presented in Figure 2. Minor discrepancies, such as the height of the CO roll-up and the breakthrough rate of CO\({}_{2}\), may come from idealized model assumptions. Despite these deviations, the good agreement between the experimental data and simulation results validates the model and supports its application in PSA cycle studies.