Study of structure of flows of a technological apparatus using the theory of random functions

Authors

DOI:

https://doi.org/10.15587/2706-5448.2021.225023

Keywords:

flow hydrodynamics, dynamic characteristics, autocorrelation function, cross-correlation function, Wiener-Hopf equation, integral and differential distribution function.

Abstract

The object of research is the structure of flows in the absorber of hydrogen chloride. One of the most problematic areas in the study of flow hydrodynamics in chemical-technological devices are both technological and technical difficulties, when the device is exposed to random disturbances and/or the supply of a standard indicator is impossible due to a violation of the technological regulations.

A method for studying the hydrodynamic structure of flows in a shelf absorber of hydrogen chloride of the «Korobon-KA» type (Germany) in the normal operation of a chemical apparatus using the theory of random functions is proposed. An industrial experiment was carried out on the operating equipment to determine the input and output concentrations of the components of the gas flow. The absorber of hydrogen chloride is considered as a one-dimensional object, at the input of which a random function acts – the concentration of hydrogen chloride in the input stream, and at the output there is a random variable – the concentration of hydrogen chloride in the output stream. The method for determining hydrogen chloride and chlorine in a gas stream is based on the absorption of chlorine by a solution of potassium iodide, followed by titration of the released iodine with sodium thiosulfate. In parallel, portions of acid were sampled at the inlet and outlet, and then the density and temperature of the hydrochloric acid solutions were determined.

An algorithm for calculating the impulse function estimates is developed. The obtained experimental data are smoothed. As a result of processing the experimental data, autocorrelation and cross-correlation functions were obtained, the Wiener-Hopf equation was solved, and the impulse weight function was obtained. Having calculated the moments of the obtained impulse weight function, it was proved that the structure of flows in the «Korobon-KA» absorber can be satisfactorily described by the ideal displacement model. The calculations were carried out in software environments MathCAD, Matlab.

According to the results obtained, the proposed method for determining the hydrodynamic structure of flows will find application in the study of chemical-technological devices, when the object is exposed to random disturbances and the supply of a standard indicator is impossible due to violation of technological regulations. This makes it possible to find the parameters of flow hydrodynamics in the apparatus in the mode of its normal operation.

Author Biographies

Yurii Beznosyk , National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute»

PhD, Associate Professor

Department of Automation Hardware and Software

Liudmyla Bugaieva, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute»

PhD, Associate Professor

Department of Cybernetics Chemical Technology Processes

References

  1. Kafarov, V. V., Glebov, M. B. (2018). Matematicheskoe modelirovanie osnovnykh protsessov khimicheskikh proizvodstv. Moscow: Iurait, 403.
  2. Bendat, J. S., Piersol, A. G. (2010). Random Data: Analysis and Measurement Procedures. Wiley, 640. doi: http://doi.org/10.1002/9781118032428
  3. Volgin, V. V., Karimov, R. N. (1979). Otsenka korreliatsionnykh funktsii v promyshlennykh sistemakh upravleniia. Moscow: Energiia, 80.
  4. Balakirev, V. S., Dudnikov, E. G., Tsirlin, A. M. (1967). Eksperimentalnoe opredelenie dinamicheskikh kharakteristik promyshlennykh obektov upravleniia. Moscow: Energiia, 232.
  5. Vrentas, J. S., Vrentas, C. M. (2007). Axial conduction with boundary conditions of the mixed type. Chemical Engineering Science, 62 (12), 3104–3111. doi: http://doi.org/10.1016/j.ces.2007.03.009
  6. Vrentas, J. S., Vrentas, C. M. (2015). Dependence of Heat Transfer in a Circular Tube with Prescribed Wall Flux on Peclet Number and on Heating Length. Chemical Engineering Communications, 202 (7), 964–970. doi: http://doi.org/10.1080/00986445.2014.883975
  7. Lawrie, J. B., Abrahams, I. D. (2007). A brief historical perspective of the Wiener–Hopf technique. Journal of Engineering Mathematics, 59 (4), 351–358. doi: http://doi.org/10.1007/s10665-007-9195-x
  8. Cozzolino, D. (2014). The use of correlation, association and regression to analyse processes and products. Mathematical and Statistical Approaches in Food Science and Technology. Oxford, 19–30. doi: http://doi.org/10.1002/9781118434635.ch02
  9. Kozub, D. J., Macgregor, J. F., Wright, J. D. (1987). Application of LQ and IMC controllers to a packed‐bed reactor. AICHE Journal, 33 (9), 1496–1507. doi: http://doi.org/10.1002/aic.690330909
  10. Rakoczy, R., Masiuk, S., Kordas, M. (2010). Application of statistical analysis in the formulation of sewage treatment plant mathematical model. Inż. Ap. Chem., 49 (4), 64–65.
  11. Sandrock, C., de Vaal, P. L. (2009). Dynamic simulation of Chemical Engineering systems using OpenModelica and CAPE-OPEN. Computer Aided Chemical Engineering, 26, 859–864. doi: http://doi.org/10.1016/S1570-7946(09)70143-9
  12. Bugaieva, L. M., Boiko, T. V., Beznosyk, Yu. O. (2017). Systemnyi analiz khimiko-tekhnolohichnykh kompleksiv. Kyiv: Interservis, 254.
  13. Khimicheskaia apparatura iz grafitovykh materialov: katalog spravochnik (2008). Sovmestnoe rossiisko-germanskoe predpriiatie OOO «Donkarb grafit».
  14. Verlan, A. F., Sizikov, V. S. (1986). Integralnye uravneniia: metody, algoritmy, programmy. Kyiv: Naukova dumka, 543.
  15. Tikhonov, A. N., Arsenin, V. Ia. (1979). Metody resheniia nekorrektnykh zadach. Moscow: Nauka, 285.
  16. Golovanchikov, A. B., Dulkina, N. A. (2009). Modelirovanie struktury potokov v khimicheskikh reaktorakh. Volgograd: VolgGTU, 240.
  17. Gelperin, N. I., Pebalk, V. L., Kostanian, A. E. (1977). Struktura potokov i effektivnost kolonnykh apparatov khimicheskoi promyshlennosti. Moscow: Khimiia, 264.

Downloads

Published

2021-02-27

How to Cite

Beznosyk , Y., & Bugaieva, L. (2021). Study of structure of flows of a technological apparatus using the theory of random functions. Technology Audit and Production Reserves, 1(3(57), 16–20. https://doi.org/10.15587/2706-5448.2021.225023

Issue

Vol. 1 No. 3(57) (2021): Chemical engineering

Section

Measuring Methods in Chemical Industry: Reports on Research Projects

License

Copyright (c) 2021 Yurii Beznosyk , Liudmyla Bugaieva

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.