Oscillatory reactions isothermal models

This chapter introduces the simplest chemical kinetic scheme for an isothermal oscillatory reaction in a closed system. This model scheme is used to illustrate concepts of very general importance and applicability. A mathematically deeper analysis is given in chapter 3. 

In chapters 2-5 two models of oscillatory reaction in closed vessels were considered one based on chemical feedback (autocatalysis), the other on thermal coupling under non-isothermal reaction conditions. To begin this chapter, we again return to non-isothermal systems, now in a well-stirred flow reactor (CSTR) such as that considered in chapter 6. 

Another isothermal elementary-step model was developed by Takoudis and Nowobilski (303). They modeled the oscillatory reaction between NO and NH3 on Pt with the following reaction equations ... 

The analysis described in Section 4.6.1 was then applied over a range of ambient temperatures and reaction times for both the isothermal and non-isothermal model. Calculation of the 5, values revealed H2O2 and O3 to be redundant species for both models and at all reaction conditions tested. Table 4.4 shows examples of redundant species calculations from the full non-isothermal scheme at differing parts of the oscillatory trace... 

Fig. 4.6. Comparison of temperature traces from the 22- and 16-step reduced models with the full 47-step non-isothermal model at = 790 K. The removal of reactions 14, 27, 29, 35, 37 and 45 causes only a small decrease in the oscillatory period.

The first attempt in understanding the chemistry of isothermal oscillatory reaction was made by Lotka [20, 21] who proposed a model based on preypredator model, i.e. 

We are thus, in many instances, more interested in the transient behaviour early in a reaction than we are in the more easily studied final or equilibrium state. With this in mind, we shall be concerned in our early chapters with simple models of chemical reaction that can satisfy all thermodynamic requirements and yet still show oscillatory behaviour of the kind described above in a well-stirred closed system under isothermal or non-isothermal conditions. 

In order to model the oscillatory waveform and to predict the p-T locus for the (Hopf) bifurcation from oscillatory ignition to steady flame accurately, it is in fact necessary to include more reaction steps. Johnson et al. [45] examined the 35 reaction Baldwin-Walker scheme and obtained a number of reduced mechanisms from this in order to identify a minimal model capable of semi-quantitative p-T limit prediction and also of producing the complex, mixed-mode waveforms observed experimentally. The minimal scheme depends on the rate coefficient data used, with an updated set beyond that used by Chinnick et al. allowing reduction to a 10-step scheme. It is of particular interest, however, that not even the 35 reaction mechanism can predict complex oscillations unless the non-isothermal character of the reaction is included explicitly. (In computer integrations it is easy to examine the isothermal system by setting the reaction enthalpies equal to zero this allows us, in effect, to examine the behaviour supported by the chemical feedback processes in this system in isolation... 

The application of the basic ideas to real combustion systems is then taken up in Chapters 6 and 7. In Chapter 6, experimental and modelling studies are described which link the mechanistic observations of Chapter 1 to combustion characteristics of fuels studied under laboratory conditions. The experimental emphasis is initially on global combustion phenomena - ignition and oscillatory cool-flames - for a range of hydrocarbons. Section 6.5 then addresses the distribution of products in hydrocarbon oxidation this discussion differs from that in Chapter 1 where the conditions were optimized to allow the investigation of specific reactions. The focus is now on studies of oxidation products over a range of isothermal and non-isothermal conditions, the interpretation of the results in terms of elementary reactions and the use of the experimental data as a detailed test of combustion models. The chapter provides an overview of the success of detailed models in describing combustion phenomena and combustion... 

Rathousky and Hlavacek (1981) presented two mathematical models to illustrate the fact that the influence of adsorbed species on the rate of an isothermal catalytic reaction may lead to a complex dynamic pattern including multiplicity of steady states and oscillatory states. Multiple oscillations and horatian behavior can not be calculated from the models. Rathousky and Hlavacek (1982) studied CO oxidation on Pt/Al203 catalyst and observed changes in oscillations due to the variations in inlet temperature. For a narrow range they observed horatian behavior. Experiments show that interaction of two oscillatory processes cause horatian behavior. 

The model has acted as a useful stimulus. It is the only oscillatory model involving not more than two intermediates and having elementary reaction steps with only first- or second-order kinetics, and also satisfying sudi basic diranical reasonableness as non-native concentrations. However, a chemically satisfactory identification of X and Y with species known to be involved has never been attained it is now widely recognized that the conservative oscillations, to which this model in its isothermal form corresponds, cannot be the basis for those actually observed. ... 

In a recent publication reviewing the status of research into intrinsic oscillations in solid-catalyzed reactions (l ), we emphasized the potential exploitation of combined theoretical and experimental studies of oscillatory behavior for obtaining new insights into catalytic reaction mechanisms and kinetics. In the present paper, we elaborate further on the subject of formulating and analyzing kinetic models which account for oscillatory behavior, and we present some new experimental information for the oscillatory oxidation of CO on a platinum foil. As in reference 1, the analysis here is applied to models describable by two first-order differential equations. The laboratory data reported were obtained from an isothermal gradientless CSTR of void volume h60 cm3 into which there was inserted a platinum foil of area 200 cm2. Continuous measurements were made of the CO2 concentration in the effluent stream. The experimental system is described in detail elsewhere (, . ... 

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