Determination of steady states of tank and recycle tubular reactors using homotopy and parametric continuation methods

Marek Berezowski

doi:10.1515/ijcre-2023-0211

Article

Determination of steady states of tank and recycle tubular reactors using homotopy and parametric continuation methods

Marek Berezowski

Published/Copyright: December 18, 2023

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From the journal International Journal of Chemical Reactor Engineering Volume 22 Issue 3

Abstract

This work concerns the application of the homotopy method to solve the mathematical model of a non-adiabatic chemical continuous stirred tank reactor (CSTR) and tubular reactor with mass recycle (TRR) (Berezowski 2000. Spatio-temporal chaos in tubular chemical reactors with the recycle of mass, Chaos, Solitons & Fractals, vol. 11, no. 8, pp. 1197–1204). This method was associated with the parametric multivariable continuation algorithm. Thanks to this, this method can automatically find all the multiple steady states of the reactor model without the need to use any iteration. The parametric continuation method is used to determine a curve whose each point is a solution of the tested model. Therefore, the starting point must be very precisely designated so that it lies on this curve. Otherwise, the result is a graph that deviates from the correct graph. However, this condition is not required when the homotopy method is also introduced into the calculations. The starting point can then be a point with any coordinates. Different curves are also obtained, but the homotopy method ensures that each of them passes through the point where the parameter p = 1. The solution we are looking for in the model is just such a point. This is undoubtedly a big advantage resulting from the combination of both above-mentioned methods.

Keywords: chemical tank reactor; tubular recycle reactor; multiple steady states; homotopy method; parametric continuation method

Corresponding author: Marek Berezowski, Faculty of Chemical Engineering and Technology, Cracow University of Technology, 30-155 Kraków, ul. Warszawska 24, Poland, E-mail: marek.berezowski@pk.edu.pl

Research ethics: Not applicable.
Author contributions: The author have accepted responsibility for the entire content of this manuscript and approved its submission.
Competing interests: The author states no conflict of interest.
Research funding: None declared.
Data availability: Not applicable.

References

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Received: 2023-11-12

Accepted: 2023-12-03

Published Online: 2023-12-18

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Articles in the same Issue

https://doi.org/10.1515/ijcre-2023-0211

Keywords for this article

chemical tank reactor; tubular recycle reactor; multiple steady states; homotopy method; parametric continuation method