TY - JOUR

T1 - Self-Sustained Oscillations on the Back Branch of the Inverse Hysteresis in a Mathematical Model of Catalytic CO Oxidation over Palladium

AU - Lashina, E. A.

AU - Chumakova, N. A.

AU - Chumakov, G. A.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - CSTR reactor

KW - discrete-continuous dynamical system

KW - heterogeneous catalytic reaction

KW - inverse hysteresis

KW - self-sustained oscillations

UR - http://www.scopus.com/inward/record.url?scp=85078947891&partnerID=8YFLogxK

U2 - 10.1134/S1990478919040094

DO - 10.1134/S1990478919040094

M3 - Article

AN - SCOPUS:85078947891

VL - 13

SP - 663

EP - 671

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -