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It is clear that the mathematical model of pressure swing adsorption processes is described by coupled nonlinear partial differential and algebraic equations distributed in space and time with periodic boundary conditions that connect the processing steps together, and high nonlineari- ties arising from non-isothermal effects and nonlinear adsorption isotherms. Also, the solution of such convection dominated hyperbolic PDAEs is governed by steep adsorption fronts. Con- sequently, a large number of spatial finite volumes are generally required to capture dynamic behavior with steep fronts. As a result, optimization of such systems for either design or operation represents a significant computational challenge to the current DAE optimization techniques and nonlinear programming algorithms. Although sophisticated optimization strategies have been developed and applied to PSA systems with a significant improvement in the performance of the process (such as the complete discretization based approach by Nilchan [138] for optimization of a bench-scale and a rapid PSA process, a mixed-integer nonlinear programming based approach by Smith et al. [177, 178, 179] to minimize number of beds, an SQP-based approach by Ko et al. [110, 111] to optimize PSA and fractionated vacuum PSA processes, an SQP-based approach by Jiang et al. [99] with direct sensitivities to obtain derivatives for the optimization problem, and the complete discretization approach with the interior-point nonlinear solver IPOPT applied in chapter 4 and 5 for the case studies related to the superstructure optimization), even the most efficient of these approaches can usually be quite expensive and prohibitively time-consuming. For instance, we report a CPU time of 12.6 hrs. for case II, and 4.5 hrs. for case III of the post- combustion capture case study in sections 4.4.2 and 4.4.3, respectively. Even for just 10,500 variables in the optimization problem, CPU time was as high as 52 min. for case I, and 66 min. for case II of the pre-combustion capture case study in section 5.3.1 and 5.3.2, respectively. Jiang et al. [100] reported a CPU time of 50-200 hrs. on a 2.4 GHz linux machine for a 5-bed 11-step PSA process optimization to maximize hydrogen recovery. Multiobjective optimization of a simple single bed air drying PSA process by Sankararao et al. [157] took 720 hrs. on a 2.99 6.1 Motivation 6.1 Motivation Chapter 6. Reduced-order Modeling for Optimization 97PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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