Langmuir—Hinshelwood—Hougen—Watson

The problem posed by Eq. (6.22), without the additional complication of the O dependence, is a classical problem in heterogeneous catalysis. The usual approach it to use Langmuir isotherms to describe reactant (and sometimes product) adsorption. This leads to the well known Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics.3 The advantage of this approach is... 

Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics, 21 Nernst, 95... 

Such rate expressions are often termed Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations and are widely used in chemical engineering [see Froment and BischofT (79)]. The usual procedure is to postulate plausible mechanisms without considering cycles, as in Example 1. In such cases it may be desirable to develop the complete list of possible direct mechanisms even if further considerations can rule out some as being unlikely. The following example illustrates a typical case. 

Butt and Petersen (1988) extended the Langmuir—Hinshelwood—Hougen—Watson kinetics to involve the varying activity (as a result of catalyst deactivation with time) to describe... 

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. 

The form of the resulting expression differs from the gas phase reaction rate expressions due to the presence of a denominator which represents the reduction in rate due to adsorption phenomena and of which the individual terms represent the distribution of the active sites among the possible surface complexes and vacancies. These expressions are termed the Langmuir-Hinshelwood-Hougen-Watson (LHHW) rate expressions. 

For a reaction of such complexity as methanation (or FTS) an exact kinetic theory is actually out of the question. One has to introduce one or more approximations. The usual assumption made is that one reaction step is rate determining (r.d.s.) and other steps are in equilibrium or steady state. Adsorption equilibria are described by Langmuir formulas (Langmuir-Hinshelwood, Hougen-Watson... 

The results can be interpreted in terms of Langmuir-Hinshelwood-Hougen-Watson kinetics. Styrene adsorbs more strongly than octenes and, as a consequence, only after styrene has been converted does the formation of octanes proceed at a high rate. The... 

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 ... 

As already mentioned, the denominator of Langmuir-Hinshelwood-Hougen-Watson rate equations is composed of additive terms, each being proportional to one state of coverage the leading " 1" to the number of vacant sites, and each other term K, pt to the number of sites occupied species i. Thus, if a macs exists, all terms but one are negligible and if any lacs exist, their terms are negligible. 

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. 

There are currently two available different ways in which one might use the predicted kinetic information on elementary reaction steps 1) the conventional Langmuir-Hinshelwood-Hougen-Watson (LHHW) approach [3], in which an explicit rate expression might be derived based on the common, but rather arbitrary. 

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