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5.3 Case Studies and Computational Results 1 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 950 900 850 800 750 1 700 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 150 100 50 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 0.5 0 structure. Similarly, constraints (5.1f) and (5.1g) ensure that the gas is never expanded by the heavy gas and the feed compressors, respectively. It should be noted that a lower bound of 50 kPa is chosen for the vacuum generated, which is not a substantially high vacuum. Similarly, the chosen upper bound of 1000 kPa for Pads is also reasonably low. Also, it is important to note that a lower bound of 35 kgmol m−2hr−1 is imposed on the total feed flux which is independent of the bed diameter. Thus, with a bigger bed diameter, it will be possible to handle a much higher feed throughput for the same cycle configuration. Hence, as in the case of post-combustion capture case studies, the focus here is to synthesize industrial-scale PSA systems. With 10 temporal finite elements and 10 spatial finite volumes, the optimization problem was solved in AMPL using IPOPT. The optimal profiles for the control variables α(t), β(t), φ(t), Pads(t) and Pdes(t) are shown in Figure 5.1. They are drawn against the cycle time nor- malized between 0 and 1. These profiles suggest an optimal 2-bed 8-step VSA cycle, illustrated in Figure 5.2, which can be deciphered in the following manner. The cycle starts with α(t)=1, β(t) close to 0.67, and φ(t)=1. This suggests bottom reflux from CnB to CoB, a 67% top reflux from CoB to CnB and feed being fed to CoB. From the values of Pads(t) and Pdes(t) for this step, it can be observed that CoB is operating at the feed pressure (700 kPa) while CnB is operating at a vacuum of 50 kPa. Hence, this is an adsorption with a heavy reflux step for 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized cycle time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized cycle time Figure 5.1: Optimal control profiles for case I Chapter 5. Superstructure Case Study: Pre-combustion CO2 Capture 79 Feed(φ) Topreflux(β) Bottomreflux(α) P (kPa) des P (kPa) adsPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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