Model Langmuir-Hinshelwood-Hougen-Watson

Langmuir-Hinshelwood-Hougen-Watson model (LHHW)... 

A typical Langmuir-Hinshelwood-Hougen-Watson model for the reversible gas-phase reaction A R+S taking place on a solid catalyst is given by... 

In general, the use of Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type of rate equation for representing the hydrogenation kinetics of industrial feedstocks is complicated, and there are too many coefficients that are difficult to determine. Therefore, simple power law models have been used by most researchers to fit kinetic data and to obtain kinetic parameters. 

Herzfeld and Langmuir-Hinshelwood-Hougen-Watson cycles, could be formulated and solved in terms of analytical rate expressions (19,53). These rate expressions, which were derived from mechanistic cycles, are phrased, however, in terms of the formation and destruction of molecular species without the need for computing the composition of reactive intermediates. Thus, these expressions are the relevant kinetics required for molecular models and are rooted to the mechanistic cycles only implicitly by the mechanistic rate constants. The molecular model, in turn, transforms a vector of reactant molecules into a vector of product molecules, either of which is susceptible to thermodynamic analysis. This thermodynamic analysis helps to organize these components into relevant boiling point or solubility product classes. Thus the sequence of mechanistic to molecular to global models is intact. 

In heterogeneous catalysis these models are generally referred to as the Langmuir-Hinshelwood-Hougen-Watson (LHHW) models. The term Michaelis-Menten kinetics is often used in homogeneous catalysis, enzyme reactions and reactions of microbial systems. 

Exemplary results of modeling processes inside the catalytic layer are presented in Fig. 9. The solid lines show the dependency of the overall effectiveness factor on the relative distribution of the catalyst between the comers and the side regions. The two cases represent two levels of the first-order rate constants, with the faster reaction in case (b). As expected, the effectiveness factor of the first reaction drops as more catalyst is deposited in the comers. The effectiveness factor for the second reaction increases in case (a) but decreases in case (b). The latter behavior is caused by depletion of B deep inside the catalytic layer. What might be surprising is the rather modest dependency of the effectiveness factor on the washcoat distribution. The explanation is that internal diffusion is not important for slow reactions, while for fast reactions the available external surface area becomes the key quantity, and this depends only slightly on the washcoat distribution for thin layers. The dependence of the effectiveness factor on the distribution becomes more pronounced for consecutive reactions described by Langmuir-Hinshelwood-Hougen-Watson kinetics [26]. 

Recently a rigorous quantitative model was developed in order to describe promotional and, more generally, catalytic kinetics [130,147]. The model can be viewed as an extension of classical Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics. 

The models described above are termed Langmuir-Hinshelwood-Hougen-Watson (LHHW) models, named after the scientists that contributed a lot to the development of these engineering models. The characteristics of these models are that adsorption follows the Langmuir isotherm, and that reaction takes place between adsorbed species. Sometimes, one distinguishes Eley Rideal models, whereby a molecule reacts directly from the gas phase with a surface complex ... 

Skrzypek el al. mode (19H5) Skrzypek el al. (1985) developed this model based on the Langmuir-Hinshelwood-Hougen-Watson kinetic model to explain the non-monotonic behaviour observed by Calder-bank (1974). They suggested that the reaction rate behaviour can be related to the Langmuir-Hinshelwood kinetic model for bimolecular reactions, where the surface reaction between o-Xylene and oxygen chemisorbed on the active centers is the rate determining step. The rate of appearance of various components can be written as ... 

The rate of oXylene disappearance in Figure 5.10 shows a maximum illustrated when plotted against p-Xylene initial concentration such dependence of reaction rate cannot be explained by a redox mechanism but by a Langmuir-Hinshelwood, Hougen-Watson (LH-HW) model such as equation (5.78) which describes the reaction behaviour with a characteristic maximum as shown in Figure 5.10. 

Microkinetic modeling is a framework for assembling the microscopic information provided by atomistic simulations and electronic structure calculations to obtain macroscopic predictions of physical and chemical phenomena in systems involving chemical transformations. In such an approach the particular catalytic reaction mechanism is expressed in terms of its most elementary steps. In contrast to the Langmuir-Hinshelwood-Hougen-Watson (LHHW) formulations, no rate-determining mechanistic step (RDS) is assumed. 

Langmuir-Hinshelwood-Hougen-Watson (LHHW) Models... 

The strategy for predicting the temporal evolution of a complex chemical reaction described in this section is based on the application of mass balances and symmetry relations between concentration dependences, starting from extreme initial values of the concentrations. The results obtained may be very useful for advanced analysis of complex chemical reactions and can be applied to the analysis of linear models of reversible reactions in plug-flow reactors and in the linear vicinity of nonlinear complex reversible reactions both in batch reactors (closed systems) and in plug-flow reactors. They can also be applied to the analysis of pseudomonomolecular models of the Langmuir-Hinshelwood-Hougen-Watson type for reversible reactions. 

As pointed out by Levenspid (2000), the usual procedure to study the kinetics of surface-catalyzed reactions is to propose a mechanism based on the Langmuir-Hinshelwood-Hougen-Watson (LHHW) model, derive the corresponding equation, and then fit it to the data at hand. If the fit is good, researchers often claim that thqr have found the actual mechanism. This procedure is questionable, as shown by Topic 4.5.4. It would be better to state that our experimental results are formally described (within the range of the investigated reaction conditions) by the selected kinetic equation (probably out of several possible others). 

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