Heterogeneous catalytic reactions estimation

The development of methods for the kinetic measurement of heterogeneous catalytic reactions has enabled workers to obtain rate data of a great number of reactions [for a review, see (1, )]. The use of a statistical treatment of kinetic data and of computers [cf. (3-7) ] renders it possible to estimate objectively the suitability of kinetic models as well as to determine relatively accurate values of the constants of rate equations. Nevertheless, even these improvements allow the interpretation of kinetic results from the point of view of reaction mechanisms only within certain limits ... 

The Langmuir adsorption isotherm provides a simple mechanistic picture of the adsorption process and gives rise to a relatively simple mathematical expression. It can also be used to obtain a crude estimate of specific surface areas. More important, from the viewpoint of the chemical engineer, it serves as a point of departure for formulating rate expressions for heterogeneous catalytic reactions. 

Interpretation of the mechanisms of the hydrocarbon desorption reactions mentioned above was considered (31,291) with due regard for the possible role of clay dehydration. While this water evolution process is not regarded as a heterogeneous catalytic reaction, it is at least possible that water loss occurs at an interface (293) so that estimations of preexponential factors per unit area can be made. On this assumption, Arrhenius parameters (in the units used throughout the present review) were calculated from the available observations in the literature and it was found (Fig. 9, Table V, S) that compensation trends were present in the kinetic data for the dehydration reactions of illite (+) (294), kaolinite ( ) (293,295 298), montmorillonite (x) (294) and muscovite (O) (299). If these surface reactions are at least partially reversible,... 

Walter et al. [84] discussed several common experimental methods to estimate the influence of internal mass transfer resistances on the observed rates of heterogeneous catalytic reactions. For example, when the reaction temperature is varied, because the intrinsic reaction rate increases more strongly with temperature than the rate of diffusion, the influence of mass transfer becomes more important and the observed apparent activation energy decreases as the temperature increases effects of temperature on selectivity may be more complex. 

The problem whether the periodical operation of a technical reactor with input concentrations which change periodically provides higher selectivities and yields than stationary operating was examined with the example of benzene oxidation into malein anhydride [103], A rather complex example was the oxide-hydrogenation of isobutyric aldehyde to methacrolein [100], Based on dynamic experiments a reaction scheme is proposed and estimation of kinetic parameters of the main reaction using an Eley-Rideal type rate equation was carried out. The examples revealed that the wave-front analysis provides valuable qualitative and quantitative kinetic information of heterogeneous catalytic reactions. 

Suppose that we were asked to estimate the amount of catalyst required to reach a final n-Cs conversion of 55%. From Chapter 3, the design equation for an ideal stirred-tank reactor with a heterogeneous catalytic reaction taking place is... 

In this chapter, we revisit the subject of reaction/transport interactions in heterogeneous catalysts, this time from a quantitative standpoint. The topic must be examined from two perspectives. First, a researcher that is studying the kinetics of a heterogeneous catalytic reaction (or reactions) must ensure that his or her experiments are free of transport effects. In other words, the experiments must be conducted under conditions where intrinsic chemical kinetics determines the reaction rate(s). The researcher may have to make calculations to estimate the magnitude of heat and mass transport influence. He or she may also have to carry out diagnostic experiments in order to define a region of operation where transport does not affect the reaction rate and selectivity. 

In many cases, it is necessary to estimate the rate at which a heterogeneous catalytic reaction wfll proceed, if it is controlled by external mass transfer. Alternatively, it may be necessary to estimate the concentration difference (Ca,b — Ca ) and the temperature difference (7b — T ) that are required to sustain a known or measured rate of reaction. Calculations of Ca3 — Ca,s and Tb — Tg are the only way to evaluate the influence of external transport when definitive diagnostic experiments are not feasible. Calculations such as these can be performed using Eqns. (9-38) and (9-40), provided that the transport coefficients kc and h are known, or can be obtained from correlations. 

For homogeneous systems, a = 1, while for heterogeneous catalytic reactions = Wcat/ hi =/7b simple kinetic models analytical solutions are possible, while numerical solutions provide a general approach to model simulation and parameter estimation. 

At present we have evidence for the complexity of higher temperature adsorption/desorption phenomena while, in general, the kinetic characteristics observed for many catalytic reactions are perhaps deceptively simple. The estimations of the concentrations of the participating surface intermediates are, in contrast, experimentally very difficult. Mechanistic investigations of many heterogeneous catalytic processes yield insufficient information to allow clear distinctions to be drawn between alternative reaction modelsf 125). 

A ratio of Cas to the rate of catalytic reaction under steady-state conditions (r) gives a rough estimation for the reaction time scale. For typical heterogeneous catalytic processes applied for the production of bulk chemicals and petrochemicals, this value is estimated to be 10-2—101 s (Fig. 5). The changes of the reaction rate caused by the side processes of catalyst modification can take considerably longer. This is attributed to the higher capacity of substances in the catalyst bulk phase that can be involved in side interactions and to a slow rate of side processes in comparison with the stages of the catalytic cycle. 

By applying an appropriate perturbation to a relevant parameter of a system under equilibrium, various frequency modulation methods have been used to obtain kinetic parameters of chemical reactions, adsorption-desorption constants on surfaces, effective diffusivities and heat transfer within porous solid materials, etc., in continuous flow or batch systems [1-24]. In principle, it is possible to use the FR technique to discriminate between all of the kinetic mechanisms and to estimate the kinetic parameters of the dynamic processes occurring concurrently in heterogeneous catalytic systems as long as a wide enough frequency range of the perturbation can be accessed experimentally and the theoretical descriptions which properly account for the coupling of all of the dynamic processes can be derived. 

Estimation of the kinetic parameters using experimental data and requiring a mass transfer limited, heterogeneous catalytic liquid phase reaction model, which comprises implicit algebraic and ordinary differential equations. 

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