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Chapter 5. Simultaneous Design and Control Optimization of PSA Systems Under Uncertainty optimization procedures. In this regard, three key methodologies, the complete discretization approach proposed by Nilchan and Pantelides [104], the unibed formulation from Kumar et al. [84], and the CSS direct determination approach [39] employed in the work of Jiang et al. [68], are discussed here in detail. 5.1.2.1 Direct Determination Approach This approach employs numerical procedures to directly obtain the CSS, instead of solving the full scale PSA model, cycle by cycle. It starts by posing CSS as a two point boundary condition, as shown in Eq. 5.1, requiring the final state of the system to be exactly the same as the state after one complete PSA cycle. ej = yp(tcycletime)j − yp0j = 0 (5.1) gj Here, j is the iteration counter, yp0 is the initial state of the PSA system, while gj represents the PSA operational constraints which must be satisfied at the CSS such as the purity constraint. In general, yp is composed of n PSA variables, such as temperature, species concentration distributed over m grid points across the bed, as shown in Eq. 5.2. yp11 yp12 ... yp1n yp yp ... yp 21 22 2n yp = (5.2) yp31 ... ... yp3n . ... ypm1 ... ... ypmn Next, Newton method is applied on the Eq. 5.1, yielding a working formula for the evaluation of new estimate of the PSA CSS, as mentioned in Eq. 5.3. It is important to note that this method converges quadratically to the CSS, given 104PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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