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Chapter 5. Simultaneous Design and Control Optimization of PSA Systems Under Uncertainty such consideration is the high value of fluid superficial velocity, especially during the flow reversal processing steps including blowdown and repressurization with feed, which may result in fluidization of the bed. Another important considera- tion is the sharp rise of bed temperature during the first few PSA cycles in the adsorption stage. Bed temperatures above a certain limit can be detrimental to the adsorbent activity and should be avoided. Consequently, such operational constraints are also incorporated in the overall optimization formulation. In this regard, to ensure that the hydrodynamic regime of the PSA is always under packed bed conditions, superficial fluid velocity at bed ends is constrained to be always less than the minimum fluidization velocity [168]. Similarly, the tempera- tures at bed locations of z/L = 0.25, 0.5, 0.75, 1 (cf. sensors shown in Figure 5.1) is constrained. It is important to note the class of constraints discussed with respect to time. Purity acts as an end point constraint, while velocity and temperature violations, on the other hand should be measured through the complete time horizon of op- eration. The treatment of path constraints for dynamic optimization problem has been a subject of serious attention, specially for the control vector parameteriza- tions (CVP) [159] approach. The complete discretization approach proposed by Cuthrell and Biegler [37] does not suffer from this drawback as the discretized path constraints becomes part of the overall NLP problem. Towards the CVP approach, Feehery and Barton [47] proposed an elegant technique which involves consuming one DOF from the overall list of available DOFs to satisfy a given path constraint. However, the selection criteria to choose this DOF are not unique and rely completely upon the user. For this particular study, we consider an approach where path constraints are converted into end point constraints by defining vio- lation variables for each path constraint [160, 16], as shown below. 117PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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