Developing a technique for improving the efficiency of iterative methods for the calculation of the multicomponent rectification process

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.85372

Keywords:

mathematical modeling, multicomponent rectification, iteration methods, the θ-method of convergence, mobile control

Abstract

Studies of the technological base of mobile control over the processes of rectification are based on determining the concentration and temperature profiles of the installation in the established regime at different coordinates of the point of application of controlling influence.

A problem of the calculation of static characteristics of the process is in the iterative determination of such concentrations of components in the bottoms so that the bidirectional calculations, based on them, and carried out to the control section of a rectifying column, make it possible to obtain identical results. The θ-method is the effective technique for the provision of convergence of such calculations. However, when calculating multi-plate rectifying columns with several feeding inputs, in which the separation of multicomponent mixtures occurs, it is necessary to use a simple procedure for the reduction in time spent searching for the solution.

The problem of reducing the necessary number of iterations is solved by the exponentiation of coefficient θ, which is determined by the introduced tuning parameter of the algorithm. The extreme dependence of the number of iterations on this exponent is proven.

Performed calculations of the column for separating the multicomponent product of the MTBE synthesis proved that the proposed modification of the θ-method of convergence of iterative calculations of the operating modes of rectifying columns makes it possible to reduce the time, necessary for the search for the solution, by 50 %. In this case, it is not necessary to obtain high quality of initial approximations of compositions of the separation products. The method is characterized by high stability and workability in a wide range of change in the input magnitudes. 

Author Biographies

Anton Sheikus, Ukrainian State University of Chemical Technology Gagarina ave., 8, Dnipro, Ukraine, 49005

Postgraduate student

Department of Computer Integrated Technology and Metrology

Elena Belobrova, Ukrainian State University of Chemical Technology Gagarina ave., 8, Dnipro, Ukraine, 49005

Senior Lecturer

Department of Economic Cybernetics

 

Yaroslav Dovgopoliy, Ukrainian State University of Chemical Technology Gagarina ave., 8, Dnipro, Ukraine, 49005

Postgraduate student

Department of Computer Integrated Technology and Metrology

Igor Levchuk, Ukrainian State University of Chemical Technology Gagarina ave., 8, Dnipro, Ukraine, 49005

PhD, Associate professor

Department of Computer Integrated Technology and Metrology

Valeriy Korsun, National Mining University Karl Marx ave., 19, Dnipro, Ukraine, 49600

Doctor of Technical Sciences, Professor, Head of Department

Department of Metrology and Information-Measuring Technologies

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Published

2016-12-14

How to Cite

Sheikus, A., Belobrova, E., Dovgopoliy, Y., Levchuk, I., & Korsun, V. (2016). Developing a technique for improving the efficiency of iterative methods for the calculation of the multicomponent rectification process. Eastern-European Journal of Enterprise Technologies, 6(2 (84), 38–44. https://doi.org/10.15587/1729-4061.2016.85372