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7.4 PSA Case Study - Post Combustion CO2 Capture following POD basis representation for velocity to make the adsorption feed velocity ua visible during optimization, as we consider it a decision variable: j=1 model in Table 7.1 on to these POD basis functions. 7.4.3 Optimization using Algorithm I In this section we apply the exact penalty trust-region algorithm on a ROM-based optimization problem which maximizes CO2 recovery subject to a constraint on CO2 purity. For optimiza- tion, we consider five decision variables, high pressure Ph up to which the bed is pressurized and at which the adsorption step takes place, low pressure Pl for the depressurization and des- orption steps, step time for pressurization and depressurization tp, and that for adsorption and desorption ta, and finally, feed velocity during the adsorption step ua. The DAE-constrained optimization problem is described as below R M u (x, t) = ua + auj (t)φuj (x) for adsorption step. Table 7.4 shows DAEs of the reduced-order model obtained after Galerkin projection of the max CO2 recovery (from Equation (7.25)) s.t. CO2 purity ≥ 0.5 (from Equation (7.23)) 101.32 kPa ≤ Ph ≤ 300 kPa 40 kPa ≤ Pl ≤ 101.32 kPa 35sec≤tp ≤150sec 50sec≤ta ≤400sec 10 cm/sec ≤ ua ≤ 30 cm/sec (7.31) Here, a lower bound of 50% is reasonable for CO2 purity since we are using Skarstrom cycle to extract CO2, which lacks any kind of a step that enriches CO2 concentration in the bed. Thus, we cannot achieve high CO2 purity with this 2-bed 4-step cycle. However, our focus here is to illustrate the exact penalty trust-region algorithm for optimization using ROMs with the help of this case study. We also note that in order to improve CO2 purity and recovery, we allow vacuum depressurization and desorption steps as the bounds for Pl lie in the vacuum range. Problem (7.31) is solved by using the ROM-based trust-region subproblem repeatedly. We discretize the DAEs of the ROM in the temporal dimension and convert it into a standard Chapter 7. Trust-region Framework for ROM-based Optimization 151PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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