Watson kinetic models, Hougen and

Derive a Hougen and Watson kinetic model, assuming that the surface reaction is rate-controlling. 

Examples of Hougen and Watson kinetic models, which are sometimes called Langmuir-Hinshelwood models, can be derived for a great variety of assumed surface mechanisms. See Butt (1980) and Perry s Handbook (1997) for collections of the many possible models. The models usually have numerators that are the same as would be expected for a homogeneous reaction. The denominators reveal the heterogeneous nature of the reactions. They come in almost endless varieties, but all reflect competition for the catalytic sites by the adsorbable species. 

Many theoretical embellishments have been made to the basic model of pore diffusion as presented here. Effectiveness factors have been derived for reaction orders other than first and for Hougen and Watson kinetics. These require a numerical solution of Equation (10.3). Shape and tortuosity factors have been introduced to treat pores that have geometries other than the idealized cylinders considered here. The Knudsen diffusivity or a combination of Knudsen and bulk diffusivities has been used for very small pores. While these studies have theoretical importance and may help explain some observations, they are not yet developed well enough for predictive use. Our knowledge of the internal structure of a porous catalyst is still rather rudimentary and imposes a basic limitation on theoretical predictions. We will give a brief account of Knudsen diffusion. 

Another advantage of forced periodic feed experiments, which has not been fully exploited so far, is that the technique could be used for kinetic model discrimination, a technique in which large deviations could be induced into calculated reponses between rival models under consideration. Hawkins has carried out experiments on oxidation of CO for discriminating between several Hougen and Watson rival models. Cutlip et al have compared experimental forced periodic feed CO oxidation experimental transients with simulations using an elementary step model and compared theory with experiment in studies of the variation of the conversion as a function of time period of the forced oscillation. 

Rate equations for simple reversible reactions are often developed from mechanistic models on the assumption that the kinetics of elementary steps can be described in terms of rate constants and surface concentrations of intermediates. An application of the Langmuir adsorption theory for such development was described in the classic text by Hougen and Watson (/ ), and was used for constructing rate equations for a number of heterogeneous catalytic reactions. In their treatment it was assumed that one step would be rate-controlling for a unique mechanism with the other steps at equilibrium. 

The matrix given in Table XIV shows that there are nine direct mechanisms. Five of these, namely, m2, m5, m7, mg, and m9, were identified by Hougen and Watson. Seventeen different mechanisms with single ratecontrolling steps were modeled and tested for agreement with observed kinetic data. The model corresponding to m7 with s2 as the rate-controlling step was chosen as the recommended rate equation. 

Hougen and Watson [42] suggested analysis of the rate dependency on the partial reactant or the total pressure at low conversion levels, where the product concentrations can be neglected and so-called initial rates are measured. Depending on the assumed rate determining step in the kinetic model a different pressure dependency is predicted, as exemplified in Fig. 13. This allows a direct discrimmination between possible rate expressions of different models. 

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 Hougen-Watson kinetic model that is consistent with the Langmuir-Rideal mechanism can be obtained from the rate law in equations (14-63) and (14-64) via the following modification of each generic term ... 

The feed stream is stoichiometric in terms of the two reactants. Diatomic A2 undergoes dissociative adsorption. Components B, C, and D experience single-site adsorption, and triple-site chemical reaction on the catalytic surface is the rate-controlling feature of the overall irreversible process. This Langmuir-Hinshelwood mechanism produces the following Hougen-Watson kinetic model for the rate of reaction with units of moles per area per time ... 

Two-dimensional diffusion occurs axially and radially in cylindrically shaped porous catalysts when the length-to-diameter ratio is 2. Reactant A is consumed on the interior catalytic surface by a Langmuir-Hinshelwood mechanism that is described by a Hougen-Watson kinetic model, similar to the one illustrated by equation (15-26). This rate law is linearized via equation (15-30) and the corresponding simulationpresented in Figure 15-1. Describe the nature of the differential equation (i.e., the mass transfer model) that must be solved to calculate the reactant molar density profile inside the catalyst. 

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 ... 

Since 1 a is only a function of spatial coordinate r, the partial derivative in (19-38) is replaced by a total derivative, and the dimensionless concentration gradient evaluated at the external surface (i.e., ] = 1) is a constant that can be removed from the surface integral in the numerator of the effectiveness factor. In terms of the Hougen-Watson kinetic model and the dimensional scaling factor for chemical reaction that agree with the Langmuir-Hinshelwood mechanism described at the beginning of this chapter ... 

Consider the Hougen-Watson kinetic model for the production of methanol from CO and H2, given by equation (22-38). Do not linearize the rate expression. Write the rate law in dimensionless form if the chemical reaction is essentially irreversible (i.e., A eq, 00). 

Adsorption Reaction Studies Dehydration of t-butanol on Alumina. Previous work in this laboratory has given encouraging results in arriving at Langmuir-Hinschelwood or Hougen and Watson type kinetic models (2,6,8, ) when the amount of adsorption at reaction conditions has been determined. The typical results presented here repeat some earlier experiments with, however, a much superior apparatus. 

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