## 4 Results and Discussion
### Modeling and Validation of PSA Cycle
\[\text{P/F ratio}=\frac{v_{g}|_{z=L,at~{}\text{{PG step}}}}{y_{H_{2},feed}v_{g} |_{z=0,at~{}\text{{AD step}}}} \tag{23}\]  
where \(v_{g}|_{z=L,at~{}\text{{PG step}}}\) is the gas flow rate at the outlet during the PG step; \(y_{H_{2},feed}\) is the molar fraction in the feed gas; and \(v_{g}|_{z=0,at~{}\text{{AD step}}}\) is the gas flow rate at the inlet during the AD step. The PSA cycle model is validated by analyzing the bed pressure variations during the 20 th cycle, as illustrated in Figure 7. Between 2850 and 2890 s, the AD step takes place in the adsorption bed, maintaining a pressure of approximately 10 bar to facilitate the adsorption of impurity gases. From 2890 to 2900 s, the DPE step occurs, during which the pressure rapidly drops and then briefly stabilizes after equalization. Between 2900 and 2925 s, the BD step is carried out, reducing the bed pressure quickly to around 1 bar (atmospheric pressure). During 2925-2965 s, the PG step is performed, with the exhaust valve remaining open and the pressure maintained near atmospheric levels. From 2965 to 2975 s, the PPE step takes place, functioning as the reverse of the DPE step. Finally, during 2975-3000 s, the FP step begins, reintroducing the feed gas into the bed and increasing the pressure back to 10 bar. The performance of the PSA process is evaluated based on hydrogen purity and recovery:  
\[\text{Purity}(\%)=\frac{\int_{0}^{t_{AD}}c_{H_{2}}v_{g}|_{z=L}dt}{\sum_{i=1}^{ t_{AD}}\int_{0}^{t_{AD}}c_{i}v_{g}|_{z=L}dt}\times 100\% \tag{24}\]  
\[\text{Recovery}(\%)=\frac{\int_{0}^{t_{AD}}c_{H_{2}}v_{g}|_{z=L}dt-\int_{0}^{ t_{DC}}c_{H_{2}}v_{g}|_{z=L}dt}{\int_{0}^{t_{AD}}c_{H_{2}}v_{g}|_{z=0}dt+\int_{0}^{ t_{FP}}c_{H_{2}}v_{g}|_{z=0}dt}\times 100\% \tag{25}\]  
where \(t_{AD}\), \(t_{PG}\), and \(t_{FP}\) are the time of the AD step, PG step, and FP step, respectively; \(v_{g}|_{z=L}\) is the outlet velocity of the gas; and \(v_{g}|_{z=0}\) is the inlet velocity of the gas. Figure 8 presents the variation in hydrogen purity and recovery over the entire PSA cycle. Prior to the start of the cycle, pure H\({}_{2}\) is fed into the adsorption bed until the  
Figure 7: Pressure variation in the adsorption bed in the 20 th cycle (symbol: experimental data from Ref. [28]; line: simulation result). adsorbent reaches saturation, fully filling the bed with hydrogen. As a result, at the end of the first cycle, the outlet H2 purity approaches about 100%, and the recovery is relatively high. However, with each subsequent cycle, the incomplete regeneration of the adsorbent allows small amounts of impurity gases to exit with the H2 during the adsorption step. This causes a gradual decline in both purity and recovery. By approximately the fifth cycle, the recovery begins to stabilize; from the tenth cycle onward, the purity also stabilizes, indicating that the PSA process has reached a steady state. The simulated purity values show good agreement with the experimental data. However, discrepancies in recovery are observed during the third to fifth cycles, potentially due to experimental errors. In general, the simulated recovery is slightly higher than the experimental values, possibly due to unmeasured H2 losses during experiments, leading to a lower observed recovery. Overall, the simulated H2 purity and recovery trends align well with the experimental results. Following a dual-bed, six-step PSA process applied to a lean hydrogen mixture (N2/CO2/H2/CO = 44.6/35.4/19.9/0.1 mol%), a hydrogen product with 97.03% purity and 48.60% recovery is achieved. Although the operating conditions in this study differ from those used in other works, the simulation result of hydrogen performance is acceptable, higher than the purity of 96.03% on the CuBTC/zeolite 13X layered bed and the recovery of 48.4% on zeolite 13X obtained by Ref. [25]. However, there is a gap between this work and Ref. [29].