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5 Validation of the mathematical model 52 The effectiveness of air separation with CMS depends on both equilibrium and kinetic factors; thus, the adsorption pressure should be adjusted to reinforce the effective oxygen adsorption, but to diminish the nitrogen adsorption at the same time. Furthermore, the proper estimation of the contact time of gas and solid phases is of essential importance in the case of kinetically controlled separations. Excessively prolonged duration of adsorption diminishes separation selectivity by approaching the thermodynamic equilibrium state. On the other hand, too short adsorption is not beneficial either, since diffusivity limitations occur. Therefore, the existence of an optimal contact time of phases is expected which greatly depends on applied process conditions, i.e. operating temperature and gas pressure. Since the mass transfer coefficients of oxygen and nitrogen increase with their partial pressures, as presented in Eq. 3.5-6, the thermodynamic equilibrium state is approached faster in the system as the adsorption pressure increases. In the face of this situation, Fig. 5.1.2-2a plots the fractional uptake as a function of time for oxygen and nitrogen. The highest selectivity in the system is expected when the difference of fractional uptake rates attains the maximum. In the case of PSA operation, the contact time of phases is controlled indirectly by the adjustment of the product flow rate and therefore depends on the required product purity level. Furthermore, the occurrence of the peak selectivity at a specific contact time depends on system pressure as well as on temperature. As slopes of kinetic curves would be higher at elevated pressure and temperature due to faster sorption of gases, the selectivity peak shifts towards shorter contact times, as represented in Fig. 5.1.2-2b. Accordingly, when the high-purity nitrogen is generated, the productivity decreases because the system operates in conditions of prolonged contact time of phases, which is located on the right-hand side of the selectivity peak. However, the presented effect of the PSA dynamic behaviour during the generation of a high- purity product will depend considerably on the CMS material and may not occur in every system due to different structure parameters and mass transfer conditions. Referring to Fig. 3.3-3b, the relative error of simulated performance indicators should decrease at higher pressure levels. Although, at the investigated conditions, the trend of the simulation accuracy is not clearly visible, which probably suggests that inaccuracies of other effects are compensated within computed values of the relative error. 5.2 Effect of cycle organisation 5.2.1 Half-cycle time The proper adjustment of the cycle time in a PSA process is the most relevant factor while aiming for a performance improvement. The shape of the mass transfer zone (MTZ) is sensitive to the adsorption duration at high product purities [44]. Thus, in PSA systems, additional effects of the mass axial dispersion and the pressure drop along the fixed-bed should be taken into consideration since the modification of a half-cycle time changes the time span proportion of pressurisation and production steps. The consequences of those effects e.g. premature column breakthrough or reduced working pressure are more pronounced as the half-cycle time is shortened. However, in industrial practice, brief cycle times are aimed for in order to increase the number of cycles per hour of PSA operation and thus boost-up nitrogen productivity. For that reason, the influence of the half-cycle time on PSA performance indicators is investigated in the range of 40 – 60 s. The results are presented in Tab. 5.2.1-1–2 and Fig. 5.2.1-1.PDF Image | Modelling and Simulation of Twin-Bed Pressure Swing Adsorption Plants
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