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Ph (kPa) Ph (kPa) Pl (kPa)† tp (sec) tp (sec) ta (sec) ta (sec) ua (cm/s) ua (cm/s) 203.28 203.28 40 55.43 55.43 7.4 PSA Case Study - Post Combustion CO2 Capture Table 7.8: Perturbation results with ZOC CO2 purity∗ 206.28 50.28% 200.28 49.72% 39 50.44% 57.43 49.97% 53.43 50.04% 161.08 164.08 50.14% 161.08 158.08 49.87% 20.8 21.8 50.32% 20.8 19.8 49.65% CO2 recovery∗ 82.01% 81.47% 82.71% 81.68% 81.81% 81.39% 82.09% 80.77% 82.77% Optimal value Perturbed value ∗Optimal CO2 recovery: 81.74%, CO2 purity: 50.01%, †at bound also report the purities and recoveries of nitrogen and CO2 as obtained from AMPL after final optimization iteration, and from the rigorous model MATLAB simulation at the optimum. We recall that the ROM is constructed with a threshold tolerance λ∗ = 0.05. With this λ∗, ROM compares fairly well with the rigorous model. In order to verify if the algorithm terminated at an optimal point, we follow the analysis presented in section 6.5.4.1 and perturb decision variables from their optimal values. In partic- ular, we provide a positive perturbation to variables at their upper bounds and negative to the ones at their lower bounds, and record the change in CO2 purity and recovery. For decision variables not at their bounds, we provide both positive and negative perturbations. Since the CO2 purity constraint is active at the termination, the termination point can be proven opti- mal if, with such perturbations, we either improve CO2 recovery and simultaneously decrease its purity, or vice-versa is true for all the decision variables. Moreover, if we improve both CO2 purity and recovery for the parameters at their bounds, termination point is optimal. However, if CO2 purity and recovery both improve for a decision variable not at a bound, or if they both decrease for a variable at either of its bounds, the termination point is not optimal. Perturbation results for this case are shown in Table 7.8. It can be observed that the CO2 purity and recovery both improve when Ph is perturbed from 203.28 kPa to 206.28 kPa, and tp is perturbed from 55.43 sec to 53.43 sec. This shows that the point at which algorithm Chapter 7. Trust-region Framework for ROM-based Optimization 158PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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