Examples of Reaction Models

To avoid having to refer continually to other texts, and to ensure that the reader appreciates that the techniques used in the formation of reaction models are common to all branches of reaction engineering, this chapter begins by introducing some basic concepts of reaction kinetics. (For a more detailed treatment the reader should consult Refs. 1-4.) We will then derive some simple kinetic relationships and discuss reaction models and experimental methods of obtaining numerical values for the kinetic constants involved. The chapter concludes by giving two examples of reaction models, one for the reduction of hexavalent uranium to a four-valent state and the other for electrosynthesis of p-anisidine from nitrobenzene. 

We will derive a typical expression for a reaction model and then consider ways of obtaining the necessary numerical values for the constants and variables in the expression. The chapter concludes with two examples of reaction models, one for an inorganic and the other for an organic. 

The two examples of reaction models presented in Section 3.2.3 should acquaint readers enough with the principle of setting up a reaction model that they can apply the principle to any synthesis. The difference between a reaction mechanism and a reaction model (mentioned in Section 3.2) should now be clear. 

The examples of the model studies presented show how the meshing of modern surface techniques with reaction kinetics can provide valuable Insights Into the mechanisms of surface reactions and serve as a useful complement to the more traditional techniques. Close correlations between these two areas holds great promise for a better understanding of the many subtleties of heterogeneous catalysis. 

After introducing some types of moving-particle reactors, their advantages and disadvantages, and examples of reactions conducted in them, we consider particular design features. These relate to fluid-particle interactions (extension of the treatment in Chapter 21) and to the complex flow pattern of fluid and solid particles. The latter requires development of a hydrodynamic model as a precursor to a reactor model. We describe these in detail only for particular types of fluidized-bed reactors. 

Mathematical models based on physical and chemical laws (e.g., mass and energy balances, thermodynamics, chemical reaction kinetics) are frequently employed in optimization applications (refer to the examples in Chapters 11 through 16). These models are conceptually attractive because a general model for any system size can be developed even before the system is constructed. A detailed exposition of fundamental mathematical models in chemical engineering is beyond our scope here, although we present numerous examples of physiochemical models throughout the book, especially in Chapters 11 to 16. Empirical models, on the other hand, are attractive when a physical model cannot be developed due to limited time or resources. Input-output data are necessary in order to fit unknown coefficients in either type of the model. 

Models for biochemical switches, logic gates, and information-processing devices that are also based on enzymic reactions but do not use the cyclic enzyme system were also introduced [76,115,117-122]. Examples of these models are presented in Table 1.3. It should also be mentioned that in other studies [108,112-114,116], models of chemical neurons and chemical neural networks based on nonenzymic chemical reactions were also introduced. 

Another example of reactions at interfaces that is only now being recognized, due to the lack of suitable experimental techniques in the past, is that of species such as SOz and NOz at liquid interfaces. As discussed in Chapters 7 and 8, there is increasing evidence that the reactions of such species at the air-water interface can be fast relative to that in the bulk and may have unique reaction mechanisms compared to those in the bulk or gas phases. Given the paucity of data on such processes at the present time, they are generally not included in present models of aerosol growth. How-... 

The kinetic equations are useful as a fitting procedure although their basis - the homogeneous system - in general does not exist. Thus they cannot deal with segregation and island formation which is frequently observed [27]. Computer simulations incorporate fluctuation and correlation effects and thus are able to deal with segregation effects but so far the reaction systems under study are oversimplified and contain only few aspects of a real system. The use of computer simulations for the study of surface reactions is also limited because of the large amount of computer time which is needed. Especially MC simulations need so much computer time that complicated aspects (e.g., the dependence of the results on the distribution of surface defects) in practice cannot be studied. For this reason CA models have been developed which run very fast on parallel computers and enable to study more complex aspects of real reaction systems. Some examples of CA models which were studied in the past years are the NH3 formation [4] and the problem of the universality class [18]. However, CA models are limited to systems which are suited for the description by a purely parallel ansatz. 

Some reactions are brought about by the action of heat alone, for example the thermal decomposition of carbonates, and baking bread and other materials. These constitute a special class of solid reactions somewhat akin to the progressive conversion type of reaction models but with the rate limited by the rate of heat penetration from the exterior. 

Numerous modeling studies of CVD reactors have been made and are summarized in recent review papers (I, 212). Table 3 in reference 212 lists major examples of CVD models up to mid-1986. Therefore, rather than giving an exhaustive list of previous work, Table V presents a summary of the major modeling approaches and forms the basis for the ensuing discussion, which is most appropriately handled in terms of two groups (1) hot-wall LPCVD systems and (2) cold-wall, near-atmospheric-pressure reactors. In LPCVD reactors, diffusion and surface reaction effects dominate, whereas in cold-wall reactors operated at near-atmospheric pressures, fluid flow and gas-phase reactions are important in predicting performance, as discussed earlier in relation to transport phenomena. 

EXAMPLES OF RECENT MODELLING STUDIES OF ENZYMIC REACTIONS... 

The Langmuir-Hinshelwood kinetic model describes a reaction in which the rate-limiting step is reaction between two adsorbed species such as chemisorbed CO and 0 reacting to form C02 over a Pt catalyst. The Mars-van Krevelen model describes a mechanism in which the catalytic metal oxide is reduced by one of the reactants and rapidly reoxidizd by another reactant. The dehydrogenation of ethyl benzene to styrene over Fe203 is another example of this model. Ethyl benzene reduces the Fe+3 to Fe+2 whereas the steam present reoxidizes it, completing the oxidation-reduction (redox) cycle. This mechanism is prevalent for many reducible base metal oxide catalysts. There are also mechanisms where the chemisorbed species reacts... 

Over the last three decades, two general approaches have been proposed in the literature for describing the interactions of sulfate in soils. The first approach is that of a chemical nature where thermodynamic interrelationships with speciation of cations and anions present in soil solution and the interaction with the soil surface are the major mechanisms. These models may be referred to as chemical models. Examples of such models include that of Cosby et al. (1986), Reuss and Johnson (1986), De Vries et al. (1994), among others. A common feature of these models is that both ion exchange and aluminum hydrolysis reactions are similar. Their capability of quantifying these processes varies according to whether the interactions are... 

In catalytic stepwise reactions, which involve more complex elementary transformations than scheme (4.4), the rate-determining parameters can be identified through similar considerations. Several examples of simple model schemes of catalytic transformations are given following. These schemes often are used for the microkinetic analysis of particular catalytic transformations and help to reveal the influence of various factors. 

Some aspects of fluidized-bed reactor performance are examined using the Kunii-Levenspiel model of fluidized-bed reactor behavior. An ammonia-oxidation system is modeled, and the conversion predicted is shown to approximate that observed experimentally. The model is used to predict the changes in conversion with parameter variation under the limiting conditions of reaction control and transport control, and the ammonia-oxidation system is seen to be an example of reaction control. Finally, it is shown that significant differences in the averaging techniques occur for height to diameter ratios in the range of 2 to 20. 

Examples of Recent Modelling Studies of Enzymic Reactions. - A key... 

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