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max H2 recovery (from Equation (6.34)) s.t. ROM Equations (6.36)-(6.41) H2 purity ≥ 0.998 (from Equation (6.32)) 480kPa≤PH ≤520kPa 130kPa≤PL ≤170kPa 3 ≤ tp ≤ 7 47≤ta ≤53 (6.42) Here bounds on decision variables define the trust-region. We discretize ROM in the temporal dimension and the resulting large-scale NLP is solved in AMPL using IPOPT. Optimal values Chapter 6. Reduced-order Modeling for Optimization 124 6.5 Case Study - Hydrogen PSA to compare the accuracy of ROM. Values obtained from ROM developed with the 5-rank approximation are accurate up to 3 decimal places and can be considered identical to the true values for all practical purposes. 6.5.4 ROM-based Optimization within a Trust-region In this section, we demonstrate how a ROM can be used to perform computationally efficient optimization within a trust-region around the root-point where ROM is constructed. In par- ticular, we utilize the reduced-order model in Table 6.6 to maximize hydrogen recovery subject to a purity constraint and tight bounds on the decision variables which form the trust-region. As discussed before, such tight bounds are essential as ROM loses its accuracy as we go further away from the root-point. Table 6.8 shows decision variables considered for the optimization problem and their values at which the ROM is constructed. We consider two separate cases for optimization. In the first case, we do not consider feed and regeneration velocities as decision variables, while they are included as decision variables in the second case. Optimization results for both cases are discussed further. We also perform optimization without a trust-region and demonstrate why such a bounded region is essential when ROM is used for optimization. 6.5.4.1 Case I: Optimization without velocities With feed and regeneration velocities held fixed at their root-point values, we solve the following ROM-based optimization problem.PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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