Reaction detailed kinetics model

Chapter 10 begins a more detailed treatment of heterogeneous reactors. This chapter continues the use of pseudohomogeneous models for steady-state, packed-bed reactors, but derives expressions for the reaction rate that reflect the underlying kinetics of surface-catalyzed reactions. The kinetic models are site-competition models that apply to a variety of catalytic systems, including the enzymatic reactions treated in Chapter 12. Here in Chapter 10, the example system is a solid-catalyzed gas reaction that is typical of the traditional chemical industry. A few important examples are listed here ... 

In this work, a detailed kinetic model for the Fischer-Tropsch synthesis (FTS) has been developed. Based on the analysis of the literature data concerning the FT reaction mechanism and on the results we obtained from chemical enrichment experiments, we have first defined a detailed FT mechanism for a cobalt-based catalyst, explaining the synthesis of each product through the evolution of adsorbed reaction intermediates. Moreover, appropriate rate laws have been attributed to each reaction step and the resulting kinetic scheme fitted to a comprehensive set of FT data describing the effect of process conditions on catalyst activity and selectivity in the range of process conditions typical of industrial operations. 

The detailed kinetic description of a chemical process is a primary feature for both the industrial practice and the comprehension of the reaction mechanism. The development of a kinetic model able to predict at the same time the reactants conversion and the products distribution (i.e., a detailed kinetic model) is a prerequisite for the design, optimization, and simulation of the industrial process. Also, the detailed description of process kinetics allows the ex post evaluation of the goodness of the mechanistic scheme on the basis of which the model itself is developed, making possible the collection of further insight in the chemistry of the process. 

On account of this, the difficulties associated with developing a detailed kinetic model for the FTS, able to describe at the same time the rate of formation of all the reaction products, are obvious. It is therefore not surprising that several efforts have been devoted through the years to simplify the kinetic mechanism of the FTS. 

Development of a Detailed Kinetic Model 16.3.2.1 The Reaction Scheme... 

A key feature of PdCys as precursors of Pd(0) nanoparticles is that reduction of Pd(II) -> Pd(0) involving C-Pd bond cleavage is required. This accounts for both the high temperatures invariably required and the induction period in the absence of reductants. Rosner et al. have developed a detailed kinetic model of a Heck reaction catalyzed by dimeric palladacycles (Rosner et al. 2001 a,b). This model explains the experimental observations and is consistent with an active species... 

The presence of ascorbic acid as a co-substrate enhanced the rate of the Ru(EDTA)-catalyzed autoxidation in the order cyclohexane < cyclohexanol < cyclohexene (148). The reactions were always first-order in [H2A]. It was concluded that these reactions occur via a Ru(EDTA)(H2A)(S)(02) adduct, in which ascorbic acid promotes the cleavage of the 02 unit and, as a consequence, O-transfer to the substrate. While the model seems to be consistent with the experimental observations, it leaves open some very intriguing questions. According to earlier results from the same laboratory (24,25), the Ru(EDTA) catalyzed autoxidation of ascorbic acid occurs at a comparable or even a faster rate than the reactions listed in Table III. It follows, that the interference from this side reaction should not be neglected in the detailed kinetic model, in particular because ascorbic acid may be completely consumed before the oxidation of the other substrate takes place. 

In order to determine the errors that may be introduced by the Zeldovich model, Miller and Bowman [6] calculated the maximum (initial) NO formation rates from the model and compared them with the maximum NO formation rates calculated from a detailed kinetics model for a fuel-rich (isothermal system was assumed and the type of prompt NO reactions to be discussed next were omitted. Thus, the observed differences in NO formation rates are due entirely to the nonequilibrium radical concentrations that exist during the combustion process. Their results are shown in Fig. 8.1, which indicates... 

In order to develop a suitable kinetic model of the full NH3-N0-N02/02 SCR reacting system, first the active reactions depending on N0/N02 feed ratio and temperature were identified then a dedicated study was performed aimed at clarifying the catalytic mechanism of the fast SCR reaction on the basis of such a reaction chemistry a detailed kinetic model was eventually derived, whose intrinsic rate parameters were estimated from global non-linear regression of a large set of experimental transient runs. 

The chapter ends with a case study. Four different reduced kinetic models are derived from the detailed kinetic model of the phenol-formaldehyde reaction presented in the previous chapter, by lumping the components and the reactions. The best estimates of the relevant kinetic parameters (preexponential factors, activation energies, and heats of reaction) are computed by comparing those models with a wide set of simulated isothermal experimental data, obtained via the detailed model. Finally, the reduced models are validated and compared by using a different set of simulated nonisothermal data. 

Only a few studies have tackled the problem of deriving a detailed kinetic model of the phenol-formaldehyde reactive system, mainly because of its complexity. In recent years, a generalized procedure has been reported in [11,14] that allows one to build a detailed model for the synthesis of resol-type phenolic resins. This procedure is based on a group contribution method and virtually allows one to estimate the kinetic parameters of every possible reaction taking place in the system. 

The personal experience of the authors allows us to conclude that, in most cases, the development of a suitable comprehensive kinetic model is not limited by the development of a mathematical model but by the limitations of the experimental measurements. In fact, in chemical kinetics the experiments are very often expensive, in terms of time and money, and not all the kinetically relevant reaction intermediates can be measurable and even defined in their chemical structure. Thus, the testing of more detailed kinetic models may be hindered by the availability of experimental data. 

The initial decomposition chemistry involves unimolecular reactions. This was the conclusion of the first gas-phase kinetics study [84] and has been repeatedly confirmed by subsequent bulb and shock-tube experiments [85, 86]. That first study used shock heating to induce thermal decomposition [84], The data were interpreted in terms of simple C-N bond fission to give CH2 and N02. A more extensive and definitive shock-tube study was reported by Zhang and Bauer in 1997 [85]. Zhang and Bauer presented a detailed kinetics model based on 99 chemical reactions that reproduced their own data and that of other shock-tube experiments [84, 86]. An interesting conclusion is that about 40% of the nitromethane is lost in secondary reactions. 

Figure 3. Reaction trajectories calculated using a detailed kinetics model. Symbols...

A number of research groups have used SIFT instruments for measurements directed toward IS chemistry. The Birmingham group of Adams and Smith, the inventors of the SIFT technique [16], was particularly active in this regard and a major focus of their SIFT measurements was the systematic study of reactions of hydrogenated ions, e.g. CH,, CjH,, NH , HnS+, HnCO+ etc., with numerous molecular species [18]. Further contributions by this group include detailed studies of isotope exchange in ion-neutral reactions, studies for which the SIFT is eminently suited, since the ion source gas and the reactant gas are not mixed. From these studies and detailed kinetic models of interstellar ionic reactions, it is now understood that the observed enhancement of the rare isotopes (e.g. D, 13C) in some IS molecules is due to the process of isotope fractionation in ion-neutral reactions [19]. 

Detailed kinetic models almost never include all species that are known to be present in the reactor. As an example, it is well known to everyone who has used a gas chromatograph with a flame-ionization detector, that ions are present in hydrocarbon flames. However, mechanisms for methane flames do not, in general, include the reactions of ions. The fact is that implicitly reduced mechanisms are used more often than not in modelling work understanding how objectively reduced mechanisms can be generated is, therefore, of primary importance. 

A detailed kinetic model for n-butane combustion has also been reported by Kojima [234] comprising 700 reversible reactions. Although this may prove to be a useful development, it has not been the subject of chemical validation, having been used only to simulate ignition delays for n-butane in a shock tube and in a rapid compression machine. In the absence of complementary chemical tests, the prediction of ignition delay really constitutes an application rather than a test of a comprehensive kinetic scheme. 

The effects of a variation of the main reaction parameters temperature, nitrous oxide partial pressure and benzene partial pressure were studied as a first step towards a detailed kinetic model, as this is required for the design of an industrial hydroxylation reactor. The choice of the proper reaction conditions can significantly increase phenol production [6],... 

In most enzyme-catalyzed reactions two or more substrates are involved, such as in the enzyme-catalyzed aldol reaction, the cyanohydrin reaction or enzyme-catalyzed peptide synthesis (examples used before). For many reaction schemes kinetic models have been derived using the steady-state assumption. Some important reaction mechanisms and the corresponding rate equations are summarized in Table 7-1. An approach to the steady-state method and a detailed discussion of the resulting kinetic models is difficult and is not the aim of this chapter. 

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