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7.4 PSA Case Study - Post Combustion CO2 Capture Pressurization Adsorption Depressurization Desorption 2222 10 10 10 10 0000 10 10 10 10 −2 −2 −2 −2 10 10 10 10 −4 −4 −4 −4 10 10 10 10 −6 −6 −6 −6 10 10 10 10 0 5 10 0 5 10 0 5 10 0 5 10 (a) Singular values for gas−phase mole fraction of CO (on log scale) 2 Pressurization Adsorption Depressurization Desorption 2222 10 10 10 10 0000 10 10 10 10 −2 −2 −2 −2 10 10 10 10 −4 −4 −4 −4 10 10 10 10 −6 −6 −6 −6 10 10 10 10 0 5 10 0 5 10 0 5 10 0 5 10 (b) Singular values for superficial velocity (on log scale) Figure 7.2: Singular values of mole fraction of CO2 and superficial gas velocity of λ∗. We discretize the DAEs of the reduced-order model in time with 20 finite elements and 3 collocation points for all four operating steps, and the resulting algebraic equations are solved with IPOPT. The initial conditions for the process are taken as decision variables and reduced CSS conditions (shown in Table 7.4) are solved simultaneously with the model equations in AMPL. Figure 7.3 compares the profiles of gas-phase CO2 mole fraction obtained after inte- grating the rigorous model till CSS is achieved, and after solving the algebraic equations of ROM with reduced CSS conditions. We observe a significant match between the profiles, thus indicating that ROM is predicting the dynamics quite precisely. As another basis to verify ROM’s accuracy, we compare purities and recoveries of nitrogen and CO2 for both rigorous model and ROM at CSS for this starting guess. Table 7.6 lists such a comparison. It can be observed that the values obtained from ROM are fairly close to the ones obtained after integrating the rigorous model even with relatively large λ∗ = 0.05. Chapter 7. Trust-region Framework for ROM-based Optimization 154PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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