Model-Based Design of Experiments for Estimating Heat-Transport Parameters in Tubular Reactors
Heat-transport parameters in a two-dimensional heat-transport model are estimated from temperature data of a tubular reactor with a fixed catalyst bed. The reactor design is taken from Adler (Chem. Ing. Tech. 72:555–564, 2000). Using model-based design of
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Abstract Heat-transport parameters in a two-dimensional heat-transport model are estimated from temperature data of a tubular reactor with a fixed catalyst bed. The reactor design is taken from Adler (Chem. Ing. Tech. 72:555–564, 2000). Using model-based design of experiment (DoE), two experimental control variables, the reactor wall temperature and the gas flow density, are optimized to yield minimal parameter uncertainties. Previously in the literature (Bauer, Theoretische und experimentelle Untersuchung zum W¨armetransport in gasdurchstr¨omten Festbettreaktoren, Dissertation, Martin-Luther-Universit¨at, Halle-Wittenberg, 2001; Grah, Entwicklung und Anwendung modularer Software zur Simulation und Parametersch¨atzung in gaskatalytischen Festbettreaktoren, Dissertation, Martin-LutherUniversit¨at, Halle-Wittenberg, 2004), it was suggested that transient heating of the reactor wall (from Ï30 to Ï300°C) yields characteristics in the temperature data that are relevant for estimating heat-transport parameters. It is shown in this work that temperature data from stationary heating at maximum temperature gives much lower parameter uncertainties as when compared to transient heating. This insight allows a significant reduction in the experimental effort. Three to four experiments were previously performed to gather information used to estimate the set of heattransport parameters for a specific catalyst bed. The number can be reduced down to one experiment when the gas flow density is allowed to change over time. Also, the time for a single experiment can further be reduced when the transient heating period is omitted.
A. Badinski () BASF SE, GVM/S Scientific Computing, 67056 Ludwigshafen, Germany e-mail: [email protected] D. Corbett Liquid Crystal Technology Group, Department of Engineering, Parks Road, Oxford OX1 3PJ, UK H.G. Bock et al. (eds.), Model Based Parameter Estimation, Contributions in Mathematical and Computational Sciences 4, DOI 10.1007/978-3-642-30367-8 12, © Springer-Verlag Berlin Heidelberg 2013
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1 Introduction Heat transport plays an important role in the development process for the chemical industry. Tubes that are randomly filled with catalyst particles (e.g. pellets, rings), forming a fixed catalyst bed inside the tube, are often used as chemical reactors. In these reactors, the activity of catalytic reactions is strongly temperature dependent and hot-spots arising from exothermic reactions may lead to catalyst degradation and loss of the catalyst performance. Therefore, a quantitative understanding of the heat transport mechanisms is the basis for a rational design of such tubular reactors. Different mathematical models may be used to model such tubular reactors varying in computational effort. The simplest is the “quasi-homogeneous” model where the gas and solid catalyst phases are considered in one continuously mixed phase [12]. The “heterogeneous” model describes the gas and catalyst as separate continuous phases [2]. The coupling between the two p
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