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Chapter 5. Simultaneous Design and Control Optimization of PSA Systems Under Uncertainty final CSS conditions to the initial bed conditions and the transient behavior of the processing steps, as a result of bed interconnections. Furthermore, the time instants at which the different effluent variables are stored can be different from the time instants at which the temporal information is required during the influent seeking process step. To resolve this, the interpolation schemes are employed [84, 69]. 5.1.2.3 Complete Discretization Approach In complete discretization approach proposed by Nilchan and Pantelides [104], the underlined PDAE based model is completely discretized in spatial as well as time domain resulting in a large system of nonlinear algebraic system of equations, which can be solved by a suitable NLP solver. To enforce the CSS conditions, its equation (Eq. 5.1) is included in the overall model formulation itself. Similar to the unibed formulation defined in section 5.1.2.2, only a single bed is mod- eled. Consequently, and since each processing step can have different duration, the equations are written in the time offsets form instead of usual time formu- lations. Similar to the direct determination approach, this method also requires a good initial guess to the non linear system of equations. However, in contrast to the direction determination approach it also require initial guess for the tem- poral profiles of the variables, which can be a challenging issue. This is usually generated by a single cycle simulation. It is important to note that all of the CSS acceleration approaches to optimize PSA mainly focuses on predicting the final CSS correctly [68, 69]. The intermedi- ate states towards the CSS evolution, are either not evaluated or are fictitious in nature, which for the case of control studies are of importance. In this work, the traditional dynamic optimization approach was considered as more suitable for control studies and is employed, where the model is integrated in time towards a 107PDF Image | Operation and Control of Pressure Swing Adsorption Systems
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