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7.4 PSA Case Study - Post Combustion CO2 Capture Table 7.5: Initial guess for optimization problem (7.31) Decision variable Adsorption pressure (Ph) Desorption pressure (Pl) Pressurization step time (tp) Adsorption step time (ta) Adsorption feed flow (ua) Guess value 150 kPa 50 kPa 50 sec 150 sec 20 cm/sec NLP which is solved in AMPL using IPOPT. We note that to construct a ROM, snapshots are obtained only after CSS is achieved by the rigorous model. Therefore, it is ensured that CSS is satisfied by ROM as well for every trust-region iteration. In other words, CSS is solved internally and is not a part of the infeasibility measure in Problem (7.31). In the subsequent sections, we first compare the accuracy of the reduced-order model at the starting guess x0 for the optimization problem. Next, we solve the optimization problem (7.31) with ZOC for the objective and the purity constraint and monitor if Algorithm I converges to an optimum even when assumption (A3) is not true. Finally, we solve problem (7.31) with FOC. The quality of the dynamic behavior predicted by ROM is compared at the optimum as well. 7.4.3.1 Comparison of Rigorous Model and ROM at the Starting Guess In this section, we validate the accuracy of the ROM and verify how accurately ROM is predicting the dynamic behavior of the original isothermal PSA process at the initial guess x0. Table 7.5 lists the starting guess for our optimization problem (7.31). With 50 spatial finite volumes, we convert the PDAEs in Table 7.1 into DAEs and integrate using ode15s in MATLAB. Cyclic steady state is achieved up to the desired tolerance after simulating the model repeatedly for 50 cycles, and snapshots are collected to generate empirical POD basis. Figure 7.1 shows first six POD basis functions of gas-phase CO2 mole fraction for the adsorption step. The shapes of these functions are quite different since they are empirical in nature. Figure 7.2 shows first 10 singular values for gas-phase CO2 mole fraction and Chapter 7. Trust-region Framework for ROM-based Optimization 152PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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