## 4 Results and Discussion
### Flow and Heat Transfer Characteristics of CP-\(\pi\) RFA  
The distribution of pressure in the adsorbent bed at the cycle steady state (after the eighth cycle) for the CP-\(\pi\) RFA are shown in Figures 7 and 8. During the Pr process, the pressure keeps rising, reaching to the highest point 272.265 kPa. In the initial stage of Ad step, there is an obvious peak of pressure near the outer hole. The number of gas pressure changes a lot with the process of source gas through the adsorber and a result of N\({}_{2}\) caught in the adsorbent bed, while the pressure in the adsorber increases slightly at the end of Ad step. Finally, the highest pressure in the bed is 271.353 kPa. At the end of Cb step, the pressure in the adsorber drops to 101.364 kPa, due to the resistance of the adsorbent layer. After the Cb step, the pressure in the Pu step is relatively stable, which decreases to 101.325 kPa in the major region.  
Figure 6: Pressure changes in the outer channels of CP-\(\pi\) RFA at the cycle steady state.  
Figure 7: Pressure changes in the CP-\(\pi\) RFA at the end of steps of the cycle steady state: (**a**) Pr, (**b**) Ad, (**c**) Cb, (**d**) Pu.  
Figure 9 shows velocity profiles in the adsorbent bed during the process of each step of the cycle steady state for the CP-\(\pi\) RFA. During the Pr step, the gas flow velocity near the outer hole is very high because of the gas enters the adsorber from the outer channel, then due to the resistance of the adsorbent layer, the gas flow velocity decreases from 10.5 m\(\cdot\)s\({}^{-1}\) to 2.2 m\(\cdot\)s\({}^{-1}\). At the Ad step, the gas flow velocity in the adsorbent layer are smaller than those near the outer hole and central hole, which are 5 m\(\cdot\)s\({}^{-1}\) and 2.5 m\(\cdot\)s\({}^{-1}\), respectively. At the Cb step, there is a large pressure reduction on both sides during the initial Cb step. The gas flow velocity near the central hole reaches the peak, about 62 m\(\cdot\)s\({}^{-1}\). This is because the strongly adsorbed components are desorbed from the adsorbent, so the gas flow velocity near the central channel becomes large. With the decrease of the pressure drop between the two sides, the flow velocity of the desorbed gas decreases gradually, same as the radial velocity. At the Pu step, the gas flow velocity in the adsorber gradually decreases along the radial length.  
Figure 8: Pressure profiles in the CP-\(\pi\) RFA in the process of each step of the cycle stead state at the axial central position: (**a**) Pr, (**b**) Ad, (**c**) Cb, (**d**) Pu.  
Figure 10 shows the temperature profiles in the adsorbent layer at the end of the four steps of the cycle steady state for the CP-\(\pi\) adsorber [38]. It is clearly observed that the temperature of the gas-solid two phases at the end of the four steps are all increased and the temperature in the outer hole are all higher than those in the central hole. During the Pr step, the temperature difference between the gas-solid two phases gradually decreases from about 4 K near the outer hole to 2 K near the central hole, while the radial temperature difference in the bed reaches 15 K after the Pr step. During the Ad step, the temperature of the gas-solid two phases in the bed is increased, and the temperature reaches 287 K. During the Cb step, the temperature of the adsorbent decreases from 294 K to 277 K, and the gas phase temperature in the bed is reduced from 304 K in the adsorption state to about 293 K, due to heat transfer during gas desorption. During the Pu step, the temperature of the adsorbent layer decreases from 307 K to 287 K, and the gas phase temperature in the adsorber is reduced from 296 K to 280 K.  
Figure 9: Velocity profiles in the CP-\(\pi\) RFA in the process of each step of the cycle steady state at the axial central position:(**a**) Pr, (**b**) Ad, (**c**) Cb, (**d**) Pu.