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7.7 Conclusions Table 7.12: Perturbation results for Algorithm II Optimal value 300 40 35 187.91 187.91 12.77 12.77 CO2 purity∗ 303 50.13% 39 49.82% 33 50.03% 190.91 50.49% 184.91 49.51% 13.77 52.53% 11.77 47.61% CO2 recovery∗ 97.31% 97.63% 97.34% 96.77% 97.57% 94.94% 98.48% Perturbed value Ph (kPa)† Pl (kPa)† tp (sec)† ta (sec) ta (sec) ua (cm/s) ua (cm/s) ∗Optimal CO2 recovery: 97.26%, CO2 purity: 50.01%, †at bound purity. Moreover, perturbing ta and ua in both directions either improves CO2 recovery while diminishing its purity, or vice-versa. Therefore, we can safely conclude that the algorithm converged to a local optimum. Finally, in Figure 7.6, we also present a comparison between the gas-phase CO2 mole frac- tion profiles at the optimum, obtained from the final valid tangential subproblem iteration, and from the rigorous model simulation in MATLAB. Profiles are nearly identical which confirms that ROM is predicting physically correct dynamic behavior of the system during optimization. 7.7 Conclusions Trust-region based methodology provides an excellent adaptive framework to systematically utilize reduced-order models for optimization since it not only restricts the validity zone of the reduced-order model, but also provides a robust and globally convergent algorithm. Therefore, we develop trust-region based algorithms and explore both exact penalty-based and filter-based approaches to handle general equality and inequality constraints in the original optimization problem. First, exact penalty trust-region algorithm is demonstrated for a 2-bed 4-step isothermal PSA process. We illustrate that executing the algorithm with only Zero-order Correction cannot ensure convergence to the local optimum of the original optimization problem, and thus conclude that FOC with exact gradient information is necessary for convergence. With Chapter 7. Trust-region Framework for ROM-based Optimization 181PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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