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Home / 2023 issue 5 / Method for identification of cell models of fluidized bed reactor based on discrete analogues of Boltzmann equation

Method for identification of cell models of fluidized bed reactor based on discrete analogues of Boltzmann equation

V.P. Zhukov, A.N. Belyakov, N.S. Shpeynova, E.A. Shuina, I.D. Aksakovskiy

Vestnik IGEU, 2023 issue 5, pp. 83—89

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Abstract in English: 

Background. The most complex models with the high quality of the results obtained are, as a rule, more expensive in terms of developer qualifications and computational resources. During process design, a detailed description of the object is often not required, and the accuracy of the results obtained should not be higher than the accuracy of the measuring instruments used. Thus, the optimal combination of simplicity and quality of the mathematical description of technological processes is an urgent task of mathematical modeling.

Materials and methods. To identify a cell model developed based on the theory of Markov chains, data obtained by solving discrete models of the Boltzmann equation are used.

Results. A method to identify cell models of a fluidized bed reactor has been developed using data obtained based on solving discrete models of the Boltzmann equation. The adequacy of the identified model of a fluidized bed reactor has been verified. An approach to develop computational support for a cell model based on the theory of Markov chains is presented.

Conclusions. The analysis of the results obtained has shown an adequate description of the processes in fluidized bed reactors in terms of cell models. The models are developed based on the theory of Markov chains and identified based on the results obtained within the framework of discrete models of the Boltzmann equation. The proposed method to identify and verify cell models provides the possibility to obtain simultaneously acceptable indicators of model simplicity and the accuracy of calculation of the design and operating parameters of fluidized bed reactors. 

References in English: 
  1. Barantseva, Е.A. Mizonov, V.E., Khokhlova, Yu.V. Protsessy smeshivaniya sypuchikh materialov: modelirovanie, optimizatsiya, raschet [Processes of mixing bulk materials: modeling, optimization, calculation]. Ivanovo, 2008. 116 р.
  2. Mizonov, V.E., Zhukov, V.P., Berthiaux, H., Bernotat, S. Application of multi-dimensional Markov chains to model kinetics of grinding with internal classification. International journal of mineral processing,  2004, vol. 74, pp. 307–315.
  3.  Ogurtsov, A.V. Modelirovanie istiraniya chastits v kipyashchem sloe na osnove teorii tsepey Markova [Simulation of abrasion of particles in a fluidized bed based on the theory of Markov chains]. Izvestiya vysshikh uchebnykh zavedeniy. Seriya: Khimiya i khimicheskaya tekhnologiya, 2003, vol. 46, no. 7, pp. 64–66.
  4.  Berthiaux, H., Mizonov, V., Zhukov, V. Application of the Theory of Markov Chains to Model Different Processes in Particle Technology. Powder Technology, 2005, vol. 157, no. 1–3, pp. 128–137.
  5.  Aloyan, R.M., Fedosov, S.V., Mizonov, V.E. Teoreticheskie osnovy matematicheskogo modelirovaniya mekhanicheskikh i teplovykh protsessov v proizvodstve stroitel'nykh materialov [Simulation of abrasion of particles in a fluidized bed based on the theory of Markov chains]. Ivanovo, 2011. 255 p.
  6. Samarskiy, A.A. Matematicheskoe modelirovanie: Idei. Metody. Primery [Mathematical modeling: Ideas. Methods. Examples]. Moscow: Fizmatlit, 2001. 320 p.
  7.  Zhukov, V.P., Belyakov, A.N. Modelirovanie sovmeshchennykh geterogennykh protsessov na osnove diskretnykh modeley uravneniya Bol'tsmana [Modeling of combined heterogeneous processes based on discrete models of the Boltzmann equation]. Teoreticheskie osnovy khimicheskoy tekhnologii, 2017, vol. 51, no. 1, pp. 78–84.
  8. Vulis, L.A. Teoriya i raschet magnitogazodinamicheskikh techeniy v kanalakh [Theory and calculation of magnetogasdynamic flows in channels]. Moscow: Atomizdat, 1971. 384 p.
  9. Mizonov, V., Zhukov, V., Bernotat, S. Simulation of Grinding: New Approaches. Ivanovo, 1997. 108 p.
  10. Belyakov, A.N., Zhukov, V.P., Vlasyuk, A.A., Barochkin, A.Е. Raschet mnogomernykh sovmeshchennykh protsessov izmel'cheniya, klassifikatsii v sypuchikh sredakh [Calculation of multidimensional combined processes of grinding, classification in bulk media]. Svidetel'stvo o gosudarstvennoy registratsii programmy dlya EVM № 2010612671 [Certificate of state registration of computer program № 2010612671], 2010.
  11. Zhukov, V.P., Barochkin, A.E., Belyakov, A.N., Sizova, O.V. Analiz i sovershenstvovanie metodov resheniya diskretnykh modeley uravneniya Bol'tsmana [Analysis and improvement of methods for solving discrete models of the Boltzmann equation]. Vestnik IGEU, 2021, issue 6, pp. 62–69.
  12. Babukha, G.L., Rabinovich, M.I. Mekhanika i teploobmen potokov polidispersnoy gazovzvesi [Mechanics and heat exchange of polydisperse gas suspension flows]. Kiev, 1969. 219 p.
  13. Mizonov, V., Mitrofanov, A., Ogurtzov, A., Tannous, K. Modeling of Particle Concentration Distribution in a Fluidized Bed by Means of the Theory of Markov Chains. Particulate Science and Technology, 2014, vol. 32, no. 2, pp. 171–178.
Key words in Russian: 
идентификация, ячеечная модель, теория цепей Маркова, дискретные модели уравнения Больцмана, реактор кипящего слоя
Key words in English: 
Identification, cell model, Markov chain, discrete models of Boltzmann equation, fluidized bed reactor
The DOI index: 
10.17588/2072-2672.2023.5.083-089
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