Transition to chaos in the oscillating co oxidation on Pt/Al2O3

Kapička, Jiří; Marek, M.

doi:10.1016/0039-6028(89)90359-2

Cited by 13 publications

(7 citation statements)

References 10 publications

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“…Both synchronous periodic and aperiodic oscillations of CO, CO 2 , and temperature on individual pellets were observed . A reproducible transition from simple periodic oscillations via a sequence of period-doubling bifurcations to deterministic chaos was also observed …”

Section: Resultsmentioning

confidence: 81%

“…18 A reproducible transition from simple periodic oscillations via a sequence of period-doubling bifurcations to deterministic chaos was also observed. 19 Oscillations and period-doubled oscillations have been found in the above lumped (CSTR) spatially 1D model for higher temperatures, when only the kinetic relations for CO oxidation (reactions 1-5 in Table 1) are used. An example of such nonlinear behavior is shown in Figure 1, where the CO oxidation lightoff and then a switch from the stationary to the periodic (oscillatory) solution at higher temperature can be seen.…”

Section: Co Oxidationmentioning

confidence: 89%

“…Thus, the above kinetic model based on nonstationary kinetics predicts a qualitatively similar evolution of outlet conversions as sequences of regimes observed in experiments. 18,19 The outlet CO concentrations for two types of periodic regimes arising in the PFR at constant inlet oxygen concentrations are shown in Figure 3. For inlet O 2 concentrations equal to 0.67%, a single periodic regime shown in Figure 3a is observed.…”

Section: Co Oxidationmentioning

confidence: 99%

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Modeling of Three-Way-Catalyst Monolith Converters with Microkinetics and Diffusion in the Washcoat

Kočí

Kubı́ček

Marek

2004

Ind. Eng. Chem. Res.

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Two models of catalytic monolith reactor with diffusion in the washcoat are described, employing the nonstationary kinetics of CO and hydrocarbon oxidation, NO x reduction, and oxygen storage with 23 reaction steps. The first model describes the dynamic behavior in a short monolith (recirculation reactor or CSTR), and the second one is a spatially two-dimensional nonstationary model of the monolith with plug flow. The models are used to demonstrate the qualitative agreement between the observed nonlinear dynamics of CO oxidation, including hysteresis and periodic and period-doubled oscillations, and earlier experiments. The effects of transport parameters within the washcoat on the monolith lightoff and on the outlet conversions are simulated. Computed spatiotemporal concentration patterns of reaction intermediates within the washcoat layer are used to discuss the oxidation and reduction functions of the three-way-catalyst monolith.

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Section: Resultsmentioning

confidence: 81%

Section: Co Oxidationmentioning

confidence: 89%

Section: Co Oxidationmentioning

confidence: 99%

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Modeling of Three-Way-Catalyst Monolith Converters with Microkinetics and Diffusion in the Washcoat

Kočí

Kubı́ček

Marek

2004

Ind. Eng. Chem. Res.

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“…For the CO oxidation on Pt/ AI2O3, Kapidka and Marek found a drift through a period doubling sequence. 1 Another example is the electrodissolution of copper where the working electrode was slowly covered by a film of CuCl.2 Since the time scale of the oscillations was short with regard to the time scale of the formation of the film, short fragments of the time series could be regarded as stationary, which allowed Fourier analysis and the construction of attractors and Poincard maps.…”

Section: Introductionmentioning

confidence: 99%

Periodic perturbation of a drifting heterogeneous catalytic system

Liauw¹,

Koblitz²,

Jaeger³

et al. 1993

J. Phys. Chem.

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The investigation of the dynamic behavior of chemical systems by experiments can be seriously impeded by a drift of variables. Sometimes, this drift is taken advantage of by considering it as an autonomous change of a bifurcation parameter. As an example, this approach is applied to the dynamic behavior of the oscillatory oxidation of formic acid over Pd/A1203. The system is driven with a periodic variation of the reactor temperature with constant frequency and an amplitude of just 0.25 K. With the catalyst temperature changing autonomously, a drift from quasi-periodicity through various entrainment bands is observed. It is shown through a simulation with the simple circle map that this experiment is essentially equivalent to a classical entrainment experiment.A phase multistability is observed within the 1:l entrainment band which is reminiscent of the behavior of an extended sine map.

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“…It should be mentioned in this context, that with CO oxidation on polycrystalline Pt catalysts near atmospheric pressure conditions, not only more or less regular periodic rate oscillations were found, but that chaotic temporal behavior was also identified in a number of studies [136][137][138][139].…”

Section: Oxidation Of Carbon Monoxide On Other Surfacesmentioning

confidence: 99%

Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

Ertl

2008

Handbook of Heterogeneous Catalysis

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The rate of a catalytic reaction is governed by the underlying mechanism, i.e. the sequence of elementary reaction steps, and depends on the external control parameters such as the concentrations (= partial pressures) p j of educt and product species and temperature T, if transport processes are excluded in this context. More specifically, usually the adsorbed species are assumed to be randomly distributed over the surface, and their concentrations (= coverages) θ i are described within a mean-field approximation so that the reaction rate (= number of molecules r formed per unit time, dn r /dt t ) is given by dn r dt = f θ i , T ( ) (1) whereby the coverages θ i are in turn determined by a set of differential equations (modeling the individual steps of adsorption, desorption and surface reaction) of the typeProper treatment then requires that additional constraints given by heat and mass balance are taken into consideration.Under flow conditions with the external control parameters being kept fixed, usually the reaction proceeds at steady state with constant rate, i.e., dn r /dt = constant and dθ i /dt = 0. Due to the nonlinear character of the quoted differential equations, this has, however, not necessarily to be the case; the kinetics may -for certain ranges of parameters -become oscillatory or even irregular (chaotic). Such systems are typically far away from equilibrium, and (i) By far the most detailed insights into the underlying mechanisms and the general phenomenology of spatio-temporal self-organization were obtained in studies with well-defined single crystal surfaces by applying the arsenal of modern surface physical methods.(ii) Single crystal studies are usually conducted with bulk samples under low pressure conditions (≤ 10 -4 mbar)where the temperature changes associated with varying reaction rate are negligible. In addition, the mean-free path of gaseous molecules is comparable or even larger than the dimensions of the reaction vessel, which is operated as a continuous flow reactor. Hence, concentration gradients in the gas phase are practically instantaneously (≤ 10 -3 s)transmitted. Analysis of such experiments is thus appreciably simplified.(iii) Experiments with polycrystalline, i.e. "real", catalysts are usually conducted at elevated partial pressures (≥ 1 mbar) under which the heat released by the reaction may lead to noticeable temperature variations. The resulting thermokinetic effects may become dominating, so that even the nonuniformity of the surface chemistry is masked and quite novel phenomena may arise. Ideally, the reaction is conducted in a way, which may be described by a continuously stirred tank reactor (CSTR), i.e., perfect mixing ensures that the concentrations are everywhere identical.However, frequently a concentration profile exists along the reactor, which is hence rather of the plug-flow type. It is thus evident that heat and mass transfer limitations may play important roles with such systems.Generally, an extended system such as a single crystal surface, or even more ...

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Transition to chaos in the oscillating co oxidation on Pt/Al2O3

Cited by 13 publications

References 10 publications

Modeling of Three-Way-Catalyst Monolith Converters with Microkinetics and Diffusion in the Washcoat

Modeling of Three-Way-Catalyst Monolith Converters with Microkinetics and Diffusion in the Washcoat

Periodic perturbation of a drifting heterogeneous catalytic system

Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

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