Abstract
Under study is the mathematical model describing the inverse temperature hysteresis as well as the self-sustained oscillations in the CO oxidation over a palladium catalyst in an chemical stirred tank reactor (CSTR). We consider the reaction dynamics under temperature-programmed conditions: At first, the temperature T of the CSTR monotonically increases (due to outside heating) and then it decreases to the initial value. As the temperature goes up, on the surface and in the bulk of the catalyst two palladium oxide forms appear and then, while the temperature decreases, the catalyst reduces to its original state. The mathematical model of nonstatinary processes in such a CSTR is the piecewise continuous system of nonlinear ordinary differential equations (ODE), i.e, a discrete-continuous system. Using the theory of dynamical systems and bifurcation theory as well as numerical methods, we study the structure of the maximal families of the steady states and periodic solutions in dependence on temperature. For the system under study some sufficient conditions are given under which an inverse hysteresis is observed on the dependence of the conversion of the main reagent versus T. Moreover, as temperature decreases, there are self-oscillations of the reaction rate and CO conversion on the lower back branch of the hysteresis. The parameters of the model are found such that the experimental data are qualitatively described.
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Acknowledgment
The authors express their gratitude to E. M. Slavinskaya and A. I. Boronin (Boreskov Institute of Catalysis) for the important recommendations in the course of the development of mathematical model and the helpful discussions of the obtained results presented in the article.
Funding
The authors were supported by the Boreskov Institute of Catalysis SB RAS (the budget projects nos. AAAA-A17-117041710084-2 and AAAA-A17-117041710076-7) and the Sobolev Institute of Mathematics SB RAS (project no. I.1.5.3).
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Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2019, Vol. XXII, No. 4, pp. 44–53.
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Lashina, E.A., Chumakova, N.A. & Chumakov, G.A. Self-Sustained Oscillations on the Back Branch of the Inverse Hysteresis in a Mathematical Model of Catalytic CO Oxidation over Palladium. J. Appl. Ind. Math. 13, 663–671 (2019). https://doi.org/10.1134/S1990478919040094
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DOI: https://doi.org/10.1134/S1990478919040094