Dual site Langmuir Hinshelwood model

The error model used in the minimization is based on the hypothesis that the residuals have zero mean and are normally distributed. The first is easily checked, the latter is only possible when sufficient data points are available and a distribution histogram can be constructed. An adequate model also follows the experimental data well, so if the residuals are plotted as a function of the dependent or independent variable(s) a random distribution around zero should be observed. Nonrandom trends in the residuals mean that systematic deviations exist and indicate that the model is not completely able to follow the course of the experimental data, as a good model should do. This residual trending can also be evaluated numerically be correlation calculations, but visual inspection is much more powerful. An example is given in Fig. 12 for the initial rate data of the metathesis of propene into ethene and 2-butenc [60], One expression was based on a dual-site Langmuir-Hinshelwood model, whereas the other... 

A second possibility to arrive to a similar first-order kinetics is starting from a dual site Langmuir-Hinshelwood model with oxygen adsorbed strongly in dissociative form while methane is adsorbed weakly ... 

The model considers the noble-metal catalyzed oxidation reactions of CO, two hydrocarbons of differing reactivities and H2, and the reaction kinetics was described by the global rate expressions of the dual-site Langmuir-Hinshelwood type [2]. 

Pignet and Schmidt have fitted a Langmuir-Hinshelwood model for non-competitive dual-site adsorption and with dissociative oxygen adsorption ... 

The basic problem can be stated as follows minimize an objective function fjx), where x is a vector variable comprising the parameters to be estimated, andXx) is the sum of squares to be minimized. For instance, in the oxidation of carbon monoxide, already mentioned in Chapter 4 and discussed in more detail in Chapter 11 (and in [Asprey, 1997]), the following Langmuir-Hinshelwood Dual Site Dissociative Adsorption Model is used to fit experimental data ... 

For SR of higher hydrocarbons, Rostrup-Nielsen " and Tottrup " postulated a Langmuir-Hinshelwood-Houghen-Watson (LHHW) kinetic model. It was assumed that the hydrocarbon chemisorbs on a dual catalytic site, followed by successive a-scission of the C-C bond. The resulting Ci species react with adsorbed steam to form H2 and CO. The expressions were lit to data for SR of n-Cv on a Ni/MgO catalyst at 500°C the overall rate expression is " " ... 

Recently, Praharso et al also developed a Langmuir-Hinshelwood type of kinetic model for the SR kinetics of i-Cg over a Ni-based catalyst. In their model, it was assumed that both the hydrocarbon and steam dissociatively chemisorb on two different dual sites on the catalyst surface. The bimolecular surface reaction between dissociated adsorbed species was proposed as the ratedetermining step. The following generalized rate expression was proposed ... 

In their pioneering work Dodd and Watson (3) correlated the dehydrogenation data by Langmuir-Hinshelwood rate models and found that a dual-site surface rate-controlling model is most plausible. Noda and co-workers (21) and more recently Carra and his colleagues (2) obtained essentially the same results as Dodd and Watson (3) for the chromia-alumina catalyzed dehydrogenation of n-butane. As Table I shows, somewhat different values for the orders of power function models are quoted in the references using this method of correlation. 

However, as the reaction proceeds, the add adsorption term might have to be introduced and in such an event the reaction kinetics would be represented by a dual site mechanistic, such as Langmuir-Hinshelwood (LH) model. 

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