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rigorous mathematical models. Very few studies in the literature have tried to address this issue. All of these studies suggest simplistic formulations to determine minimum number of beds required in a PSA process for given kinds and fixed sequences of operating steps. Chiang [46] proposed simple arithmetic- based heuristics, while Smith et al. [177] extended Chiang’s work to propose a mixed-integer nonlinear programming (MINLP) based approach to obtain optimal number of beds required to execute a fixed sequence of operating steps. Smith et al. [178, 179] also suggested a 3-step scenario to design an industrial PSA system, but again with a known cycle of operating steps. Recently, Nikoli`c et al. [136, 137] proposed a state-task network (STN) based framework to determine optimal number of beds. However, STN developed wasn’t exhaustive and missed many basic steps. It is clear that novel PSA cycle sequences are anticipated for upcoming applications as well as for high-efficiency separation for current applications. Although process designers commonly resort to simplified and specific models for the PSA process of interest, and utilize simplistic descriptions in order to achieve satisfactory designs, accurate and reliable industrial design requires more challenging effort which is systematic and rigorous. 1.2.2 Computationally-efficient Simulation/Optimization Another research challenge, as briefly mentioned in the previous section, relates to developing computationally-efficient strategies to simulate and optimize PSA systems goverened by rig- orous mathematical models. The behavior in each bed is described by partial differential and algebraic equations (PDAEs) in space and time, constructed from conservation of heat, mass, and momentum augmented by transport and equilibrium equations. Such hyperbolic equa- tions involve high nonlinearities arising from non-isothermal effects and nonlinear adsorption isotherms, with solution profiles represented by steep adsorption fronts. As a result, opti- mization of PSA systems for either design or operation presents a significant computational challenge to current optimization techniques and nonlinear programming algorithms [31]. 1.2 Research Challenges with PSA Chapter 1. Introduction 5PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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