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Figure 6.2: First six POD basis functions of methane mole fraction for adsorption since ROM comprises DAEs of only one bed, while the rigorous model is simulated for both beds simultaneously using the Multibed approach. 6.5.3 Comparison of Rigorous Model and ROM at CSS With 35 spatial finite volumes, we convert PDAEs in Table 6.2 to DAEs and integrate using ode15s in MATLAB. Cyclic steady state is achieved up to the desired tolerance after simulating the model repeatedly for 120 cycles, and snapshots are collected to generate empirical POD basis. Figure 6.2 shows POD basis functions of the gas-phase methane mole fraction for the adsorption step. Since these functions are empirical, their shapes are different for all four operating steps. Figure 6.3 shows first 10 singular values for the gas-phase methane mole fraction and temperature for all operating steps. Slopes of the curves show that the singular values decay sharply and the first 5-6 values can accurately capture the dynamic behavior with εPOD as low as 0.1%. Thus, we infer that we can represent all the state variables for all the norm 6.5 Case Study - Hydrogen PSA 0 −0.05 −0.1 −0.15 −0.2 −0.25 0.4 0.3 0.2 0.1 0 −0.1 −0.2 −0.3 0.3 0.2 0.1 0.3 0.2 0.1 1st basis function 2nd basis function 3rd 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 4th basis function Bed Length 5th basis function Bed Length 6th basis function 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 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 Chapter 6. Reduced-order Modeling for Optimization 119 φ φ φφ φφPDF Image | Design and Operation of Pressure Swing Adsorption Processes
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