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7.4 PSA Case Study - Post Combustion CO2 Capture Table 7.7: Optimization results with ZOC 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 13 35.7 min 203.28 kPa 40 kPa 55.43 sec 161.08 sec 20.8 cm/s ROM (AMPL) 95.81% 85.85% 51.41% 85.11% Rigorous model (MATLAB) 95.99% 85.26% 50.01% 81.74% ROM-based objective function at the center of the trust-region ψkR(0) and at the end of the iteration ψkR(sk) (see Equation (7.10)), the true objective function at the end of the iteration ψ(sk) (see Equation (7.12)), ratio ρk defined in Algorithm I, and the trust-region radius ∆k. We observe that because of the penalty, the focus of the first few iterations of the algorithm is to gain feasibility, although additionally CO2 recovery also improves. Feasibilty is attained in 7th iteration (k=6), after which the penalty formulation is dropped and the purity constraint is moved from the objective function to the constraint section of the trust-region subproblem. Eventually, the algorithm terminates after 13th iteration (k=12) when ∆12 is shrunk further from 0.059 to 0.015, as it becomes less than the ∆min of 0.02. Optimal values of the decision variables together with the optimization CPU time are listed in Table 7.7. CPU time for optimization only accounts for the time taken for all the trust- region iterations, and doesn’t include the time required to calculate snapshots and construct ROM. With 52,247 algebraic variables, algorithm terminated with 13 trust-region iterations and within a reasonable CPU time of 35.7 min. We notice that after algorithm termination, only Pl is at its lower bound, while other decision variables are well within their limits. We Chapter 7. Trust-region Framework for ROM-based Optimization 157PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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