Hinshelwood-Hougen-Watson models

In the interest of generality, we consider hypothetical reactions and derive rate equations for a few typical LHHW models. As the Langmuir isotherm is the basis of all LHHW models, we begin by a simple derivation of this isotherm. 

Langmuir isotherm Unlike in homogeneous reactions where the rate is proportional to the reactant concentration (say, [A]), in catalytic reactions, it is proportional to the surface concentration [A]j. Since [AJ is not usually known, it is convenient to express it in terms of [A] by equating the rates of adsorption and desorption for the reaction  

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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... 

Venimadhavan (1994) presented the heterogeneous kinetics for methyl acetate synthesis. He has developed a Langumuir - Hinshelwood - Hougen-Watson model to represent reaction kinetics. Isothermal batch kinetic experiments were performed using heterogeneous catalyst (Amberlyst 15) at temperatures of 313 K - 323 K. Also, independent binary adsorption experiments were performed to estimate the adsorption equilibrium constants. 

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. 

This is a mathematical expression for the steady-state mass balance of component i at the boundary of the control volume (i.e., the catalytic surface) which states that the net rate of mass transfer away from the catalytic surface via diffusion (i.e., in the direction of n) is balanced by the net rate of production of component i due to multiple heterogeneous surface-catalyzed chemical reactions. The kinetic rate laws are typically written in terms of Hougen-Watson models based on Langmuir-Hinshelwood mechanisms. Hence, iR ,Hw is the Hougen-Watson rate law for the jth chemical reaction on the catalytic surface. Examples of Hougen-Watson models are discussed in Chapter 14. Both rate processes in the boundary conditions represent surface-related phenomena with units of moles per area per time. The dimensional scaling factor for diffusion in the boundary conditions is... 

The most important characteristic of this problem is that the Hougen-Watson kinetic model contains molar densities of more than one reactive species. A similar problem arises if 5 mPappl Hw = 2CaCb because it is necessary to relate the molar densities of reactants A and B via stoichiometry and the mass balance with diffusion and chemical reaction. When adsorption terms appear in the denominator of the rate law, one must use stoichiometry and the mass balance to relate molar densities of reactants and products to the molar density of key reactant A. The actual form of the Hougen-Watson model depends on details of the Langmuir-Hinshelwood-type mechanism and the rate-limiting step. For example, consider the following mechanism ... 

Summary of Parametric Sensitivity Results on the Effectiveness Factor for Langmuir-Hinshelwood Mechanisms and Hougen-Watson Models... 

Problem. Think about the overall strategy that must be implemented to account for the effect of interpellet axial dispersion on ihe outlet concentration of reactant A when Langmuir-Hinshelwood kinetics and Hougen-Watson models are operative in a packed catalytic tubular reactor. Residence-time distribution effects are important at small mass transfer Peclet numbers. 

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. 

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