Optimization of the Solution of a Dispersion Model

Alexandru-Nicolae Dimache, Ghiocel Groza, Marilena Jianu, Sorin Perju, Laurențiu Rece, Marta Harničárová and Jan Valíček
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Alexandru-Nicolae Dimache: Department of Hydraulics and Environment Protection, Technical University of Civil Engineering of Bucharest, Bd. Lacul Tei 122-124, 020396 Bucharest, Romania
Ghiocel Groza: Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, Bd. Lacul Tei 122-124, 020396 Bucharest, Romania
Marilena Jianu: Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, Bd. Lacul Tei 122-124, 020396 Bucharest, Romania
Sorin Perju: Department of Hydraulics and Environment Protection, Technical University of Civil Engineering of Bucharest, Bd. Lacul Tei 122-124, 020396 Bucharest, Romania
Laurențiu Rece: Department of Mechanical Technology, Technical University of Civil Engineering of Bucharest, Bd. Lacul Tei 122-124, 020396 Bucharest, Romania
Marta Harničárová: Department of Electrical Engineering, Automation and Informatics, Faculty of Engineering, Slovak University of Agriculture in Nitra, Tr. A. Hlinku 2, 949 76 Nitra, Slovakia
Jan Valíček: Department of Electrical Engineering, Automation and Informatics, Faculty of Engineering, Slovak University of Agriculture in Nitra, Tr. A. Hlinku 2, 949 76 Nitra, Slovakia

Mathematics, 2020, vol. 8, issue 3, 1-11

Abstract: The study of the combination of chemical kinetics with transport phenomena is the main step for reactor design. It is possible to deviate from the model behaviour, the cause of which may be fluid channelling, fluid recirculation, or creation of stagnant regions in the vessel, by using a dispersion model. In this paper, the known general solution of the dispersion model for closed vessels is given in a new, straightforward form. In order to improve the classical theoretical solution, a hybrid of analytical and numerical methods is used. It is based on the general analytic solution and the least-squares method by fitting the results of a tracer test carried out on the vessel with the values of the analytic solution. Thus, the accuracy of the estimation for the vessel dispersion number is increased. The presented method can be used to similar problems modelled by a partial differential equation and some boundary conditions which are not sufficient to ensure the uniqueness of the solution.

Keywords: dispersion model; variable separation method; least-squares method; residence time distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:3:p:318-:d:326744

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