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7.6 PSA Case Study Revisited Table 7.11: Optimization results with hybrid filter trust-region algorithm Problem size and computational time No. of variables Total trust-region iterations Optimization CPU time Optimal parameters Adsorption pressure (Ph) Desorption pressure (Pl) Pressurization step time (tp ) Adsorption step time (ta) Adsorption feed flow (ua) Comparison of performance variables N2 purity N2 recovery CO2 purity CO2 recovery 52247 51 1.36 hrs. 300 kPa 40 kPa 35 sec 187.91 sec 12.77 cm/s ROM (AMPL) 99.99% 83.16% 50.29% 98.43% Rigorous model (MATLAB) 99.99% 82.97% 50.01% 97.26% while Table B.4 lists those for the normal subproblem. xk + pk = xk + sk, while Table B.4 shows decisions at xk + vk corresponding to the iteration k. However, CO2 purity and recovery is listed at xk + sk for both tables, since it is observed that for all k, CO2 purity at xk + sk remains same as that at xk + vk. The algorithm begins with the restoration phase of Section I since the inaccurate gradients of ROM yield negative τf . Restoration phase is invoked for every iteration until k = 3, after which feasibility is attained and CO2 purity goes beyond 50%. After k = 3, since τθ = 0, and ROM yield a τf < 0, POD basis augmentation is used. When λ∗ is reduced up to 0.1%, we obtain τf > 0 and thus, proceed for step computation in Section I for 5th iterate (k = 4). Algorithm continues in Section I after this and improves objective until 35th iterate (k = 34). At k = 34, ROM is not able to predict a descent in the objective function even after increasing POD subspace dimension. Hence, algorithm switches to Section II. Eventually, the algorithm terminates after 51st iteration when ∆50 shrinks from 0.031 to 0.008 and goes below ∆min of 0.02. One of the key observations in Table B.3 is the value of tp, which increases steadily in Section I but starts decreasing and hits its lower bound after k = 34, when the algorithm switches to Table B.3 shows decision variables at Chapter 7. Trust-region Framework for ROM-based Optimization 179PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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