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6.5 Case Study - Hydrogen PSA Table 6.12: Optimization results for Case II Problem size and computational time No. of variables No. of constraints Total no. of iterations Total CPU sec. Optimal parameters High operating bed pressure (PH) Low operating bed pressure (PL) Pressurization step time (tp) Adsorption step time (ta) Feed velocity (ufeed) Regeneration velocity (ureg) Comparison of performance variables H2 purity H2 recovery CH4 purity CH4 recovery thus a minus sign is used for ureg. We solve after discretizing ROM in the temporal dimension. Optimization results along with the CPU time is shown in Table 6.12. Within the bounded region, an optimum hydrogen recovery of 15.11% is obtained. As in the previous case, optimization is computationally efficient and the problem gets solved in only 184 CPU seconds. The rigorous model is also simulated at the optimal values of the decision variables to validate optimization results from AMPL. Purities and recoveries obtained from the rigorous model simulation are also listed in Table 6.12. We observe that these values are quite close to the ones obtained after ROM-based optimization, indicating that the ROM is predicting the dynamic behavior reasonably accurately at the optimum as well. As in the previous case, we also compare gas-phase methane mole fraction profiles for the rigorous model simulation and ROM optimization in Figure 6.9. Barring small oscillations in the adsorption step, profiles match reasonably accurately, thus showing that ROM’s behavior is fairly close to the dynamic behavior predicted by rigorous model at the optimum. 43040 43034 13 184.493 510 kPa 140 kPa 4 sec 51 sec 0.11 m/s -0.0495 m/s ROM (AMPL) 0.9986 0.1511 0.9507 0.1827 Rigorous model (MATLAB) 0.9974 0.1509 0.9495 0.1826 the optimization problem in AMPL using IPOPT Chapter 6. Reduced-order Modeling for Optimization 130PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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