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7.4 PSA Case Study - Post Combustion CO2 Capture −0.1 −0.2 −0.3 −0.4 1st basis function 2nd basis function 3rd basis function 0 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 0.6 0.4 0.2 0 −0.2 −0.5 −0.4 0 0.5 1 0 0.5 1 0 0.5 1 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 Bed Length 4th basis function Bed Length 5th basis function −0.4 0.4 0.2 0 −0.2 −0.4 Bed Length 6th basis function 00 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 0 0.5 1 0 0.5 1 0 0.5 1 Bed Length Bed Length Bed Length −0.6 Figure 7.1: First six POD basis functions of CO2 mole fraction for adsorption superficial gas velocity for all the operating steps. From the slopes of the curves, it is clear that the singular values decay fairly sharply. For this case study, we choose a threshold error tolerance λ∗ of 0.05 (cf. (6.10) and section 6.2.4). For εP OD (M ) ≤ λ∗ to hold true, we obtain norm M = 2, 4, 1, and 3 for pressurization, adsorption, depressurization, and desorption steps, respectively. In other words, with such few basis functions error in projection can be at most 5%. We purposely choose a slightly higher value of 0.05 for the threshold tolerance since it is observed that with a low value of λ∗ (say 0.01 or 0.001), ROM incorporates those POD basis functions which do not contribute much towards predicting the dynamics, thus causing the DAE system of the ROM to become ill-conditioned. Moreover, with these values of M, ROM comprises a mere 70 DAEs, while the rigorous model contains a total of 1400 DAEs. Hence, we obtain a significant model reduction as ROM is 1/20th of the rigorous model with this choice Chapter 7. Trust-region Framework for ROM-based Optimization 153 φφ φφ φφPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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