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in the solution given by the ROM increases as we go further away from the root-point. There- fore, it is invalid to use a particular ROM for the optimization problem (6.22), i.e., Problem (6.23) cannot be defined for the entire decision variable space. However, we assume a reason- able accuracy for the ROM in a confidence region (or “trust-region”) around root-point, and write Problem (6.23) only for that trust-region to benefit from the computational advantage offered by ROMs. Hence, we define tighter bounds on decision variables in Problem (6.23) to ensure algorithm remains close to the root-point. Computationally-efficient optimization is then performed using ROM and the optimal solution obtained becomes the new root-point where ROM can be updated with new snapshots. Problem (6.23) is then solved again with a new trust-region around this new root-point. A systematic adaptive scheme based on such a repetitive strategy will be developed in the next chapter. In the subsequent sections, we il- lustrate ROM-based optimization within a neighborhood of the root-point with the help of an example of the hydrogen PSA process. Since this forms a key step in the adaptive optimization algorithm, we explore it in detail. 6.5 Case Study - Hydrogen PSA 6.5.1 PSA Process and Model Equations We consider a 2-bed 4-step hydrogen PSA process which extracts hydrogen from a feed mixture comprising 30% hydrogen and 70% methane. In particular, the process is a Skarstrom cycle shown in Figure 2.3, and described in detail in section 2.4.1. The target process for this case study is bench-scale as described in Ko et al. [110, 111]. Design specifications and simulation conditions are listed in Table 6.1. We make following assumptions to develop a mathematical model for this process 1. All of the gases follow the ideal gas law. 2. There are no radial variations in temperature, pressure and concentrations of the gases in the solid and the gas phase. 6.5 Case Study - Hydrogen PSA Chapter 6. Reduced-order Modeling for Optimization 112PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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