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 nonstationary 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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