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GHz Pentium IV machine. This gives a strong motivation to develop cost-efficient and robust optimization strategies for PSA processes. Moreover, for flowsheet optimization, incorporation of dynamic PSA models with other steady-state models in the flowsheet requires much faster approaches for integrated optimization. Model reduction is a powerful tool that permits systematic generation of cost-efficient representations of large-scale systems that, in particular, result from the discretization of the PDEs. Antoulas et al. [11] provide an overview of numerous model reduction techniques which can be applied to large-scale PDE based systems. In particular, over the past decade, proper orthogonal decomposition (POD) has been developed as a powerful model reduction approach that provides an accurate reduction of the large spatially distributed models to much smaller models, and have resulted in an extensive list of articles. Berkooz et al. [27] provide a detailed list of such articles. Chatterjee [45] explains the concept and applications of POD in a clear and concise manner. POD (also known as Karhunen-Lo ́eve approximation) based reduced-order modeling technique is ubiquitous and has been applied for a multitude of applications. It has been extensively used in obtaining low-dimensional models for efficient simulation [116, 117, 128, 131, 153] and control [12, 26, 115, 147] in fluid dynamics. Yuan et al. [210] developed reduced-order models for bubbling fluidized beds. Armaou et al. [13] utilized the concept of POD for a diffusion reaction process, while Theodoropoulou et al. [185] extended the applications of ROM-based modeling to chemical vapor deposition. Park et al. [141] applied Karhunen-Lo ́eve approximation to a nonlinear heat conduction equation defined on an irregular domain. Shvartsman et al. [162] utilized POD for generating ROMs for MOVPE reactor. Couplet et al. [56], Favier et al. [68], and Galletti et al. [82] developed calibrated reduced-order modeling techniques using POD for the laminar and turbulent flow problems. Cao et al. [39] developed a POD-based reduced order model for analysis of a detailed model of the upper tropical Pacific Ocean. Gunzburger et al. [89] developed a generic framework to incorporate boundary conditions having multiple parameters in a POD-based ROM of time- dependent PDEs. The framework addresses both homogeneous and nonhomogeneous boundary 6.1 Motivation Chapter 6. Reduced-order Modeling for Optimization 98PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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