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4.4 Case Studies and Computational Results the bed length to 5 meters. A desired CO2 purity of at least 95% is chosen. Besides this, we impose a lower bound on feed flux Qfeed, in the absence of which the optimizer may force the feed fraction φ(t) to zero in order to maximize CO2 recovery. Finally, we add the equation for power consumption (3.15b) to the optimal control problem. A 72% efficiency is assumed for all the compressors and the vacuum generator unit [30]. As in the previous case, we fix the flue gas inlet pressure Pf eed to 300 kPa to achieve a reasonable Qf eed . The following large-scale NLP results after complete discretization of state and control variables in the optimal control problem. max CO2 recovery (from Equation (3.14d)) s.t. c(w) = 0 (fully discretized Equations (3.2)-(3.13)) CO2 purity ≥ 0.95 (from Equation (3.14b)) Qfeed,L+Qfeed,H ≥80kgmolm−2hr−1 Pads ≥ Pd Pdes ≤ Pfeed Pa ≥ Pfeed 0 ≤ α(ti), β(ti), φ(ti) ≤ 1 ∀ti 20sec≤Tc ≤2400sec 101.32 kPa ≤ Pads(ti) ≤ 600 kPa ∀ti Pdes(ti) ≥ 50 kPa ∀ti (4.2) As in the previous case study, c(w) is the set of completely discretized PDAEs with CSS condition. We choose a lower bound of 50 kPa for the vacuum generated, which is not a substantially high vacuum. Similarly, the chosen upper bound of 600 kPa for Pads is also not substantially high. No bounds are specified for the purity and the recovery of nitrogen. We impose a lower bound of 80 kgmol m−2 hr−1 on the total feed flux. Because the bound is not on the feed throughput, a bigger diameter PSA bed will be able to handle much higher feed throughput and the optimal configuration need not change. For instance, for a 3 meter bed diameter, one PSA column will be able to handle a significantly high feed throughput of 565 kgmol/hr for the same optimal configuration. Also note that the value of 80 kgmol m−2 hr−1 is significantly higher than feed flux chosen in the literature studies in Table 4.1, as the focus here is to synthesize industrial scale PSA systems. The NLP was solved in AMPL with 26 temporal finite elements and 20 spatial finite Chapter 4. Superstructure Case Study: Post-combustion CO2 Capture 57PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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