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6.5 CaseStudy-HydrogenPSA............................. 112 6.5.1 PSAProcessandModelEquations..................... 112 6.5.2 Reduced-orderModel ............................ 115 6.5.3 ComparisonofRigorousModelandROMatCSS. . . . . . . . . . . . . 119 6.5.4 ROM-based Optimization within a Trust-region . . . . . . . . . . . . . . 124 6.5.4.1 Case I: Optimization without velocities . . . . . . . . . . . . . 124 6.5.4.2 CaseII:Optimizationwithvelocities . . . . . . . . . . . . . . 129 6.6 Conclusions...................................... 133 7 Trust-region Framework for ROM-based Optimization 134 7.1 Introduction...................................... 135 7.2 OptimizationProblem ................................ 137 7.2.1 Trust-regionSubproblem .......................... 137 7.2.2 Correction (scaling) for Objective and Constraints . . . . . . . . . . . . 138 7.3 Penalty-basedTrust-regionAlgorithm ....................... 141 7.3.1 PenaltyFormulation ............................. 141 7.3.2 Trust-regionAlgorithm ........................... 143 7.3.3 ConvergenceandOptimality ........................ 145 7.4 PSACaseStudy-PostCombustionCO2 Capture . . . . . . . . . . . . . . . . 146 7.4.1 PSAProcessandModelEquations..................... 146 7.4.2 Reduced-orderModel ............................ 149 7.4.3 OptimizationusingAlgorithmI....................... 151 7.4.3.1 Comparison of Rigorous Model and ROM at the Starting Guess 152 7.4.3.2 Optimization with Zero-order Correction . . . . . . . . . . . . 156 7.4.3.3 Optimization with First-order Correction . . . . . . . . . . . . 159 7.5 HybridFilterTrust-regionAlgorithm........................ 162 7.5.1 Motivation .................................. 162 7.5.2 Filter ..................................... 164 CONTENTS CONTENTS viiiPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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