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... 

Examples of Hougen-Watson kinetic models, which are also called Langmuir-Hinshelwood models, can be derived for a great variety of assumed surface mechanisms. See Butt and Perry s Handbook (see Suggestions for Further reading in Chapter 5) 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. 

In addition to the assumptions implicit in the use of the Langmuir isotherm the following assumption is applicable to all Hougen-Watson models the reaction involves at least one species chemisorbed on the catalyst surface. If reaction takes place between two adsorbed species, they must be adsorbed on neighboring sites in order for reaction to occur. The probability of reaction between adsorbed A and adsorbed B is assumed to be proportional to the product of the fractions of the sites occupied by each species (0A9B). Similar considerations apply to termolecular reactions occurring on the surface. 

Hougen-Watson Models for the Case of Equilibrium Adsorption. This section treats Hougen-Watson mathematical models for cases where the rate limiting step is the chemical reaction rate on the surface. In all cases it is assumed that equilibrium is established with respect to adsorption of all species. 

Hougen- Watson Models for Cases where Adsorption and Desorption Processes are the Rate Limiting Steps. When surface reaction processes are very rapid, the overall conversion rate may be limited by the rate at which adsorption of reactants or desorption of products takes place. Usually only one of the many species in a reaction mixture will not be in adsorptive equilibrium. This generalization will be taken as a basis for developing the expressions for overall conversion rates that apply when adsorption or desorption processes are rate limiting. In this treatment we will assume that chemical reaction equilibrium exists between various adsorbed species on the catalyst surface, even though reaction equilibrium will not prevail in the fluid phase. 

The analyses developed in this section are readily extended to reactions with different stoichiometries. Regardless of whether an adsorption or a desorption process is rate limiting, the resulting rate expressions may be written in the typical Hougen-Watson fashion represented by equation 6.3.30. A comprehensive summary of such relations has been developed by Yang... 

ILLUSTRATION 6.1 DEVELOPMENT OF A HOUGEN-WATSON RATE EXPRESSION FOR A HETEROGENEOUS CATALYTIC REACTION... 

It has been suggested that the rate limiting step in the mechanism is the chemisorption of propionaldehyde and that the hydrogen undergoes dissociative adsorption on nickel. Determine if the rate expression predicted by a Hougen-Watson model based on these assumptions is consistent with the experimentally observed rate expression. 

Ender these conditions the Hougen-Watson model is consistent with the experimentally observed rate expression. 

Studies of the influence of total pressure on the initial reaction rate for pure reactants present in stoichiometric proportions provide a means of discriminating between various classes of Hoqgen-Watson models. Isolation of a class of probable models by means of plots of initial reaction rate versus total pressure, feed composition, and temperature constitutes the first step n developing a Hougen-Watson rate model. Hougen (14) has considered the influence of total pressure for unimolecular and bimolecular surface reactions the analysis that follows is adopted from his monograph. 

Studies of the effect of pressure on initial rates limit the possible Hougen-Watson rate expressions to certain classes. Subsequent studies using nonstoichiometric feeds and inerts and product species in the feed mixture further serve to determine the exact form of the reaction rate expression. 

We should also point out that the adsorption equilibrium constants appearing in the Hougen-Watson models cannot be determined from adsorption equilibrium constants obtained from nonreacting systems if one expects the mathematical expression to yield accurate predictions of the reaction rate. One explanation of this fact is that probably only a small fraction of the catalyst sites are effective in promoting the reaction. 

Is the experimental data consistent with this rate expression If so, what is the value of the rate constant What type of Hougen-Watson model gives rise to this form for the rate expression ... 

In studies of the temperature dependence of the reaction, the rate goes through a maximum (at fixed PA and PB) at a temperature near 400 °K. How do you interpret these facts in terms of the Hougen-Watson framework ... 

I. Derive equations relating the initial reaction rate (7 0) to the total pressure (71) for each of the above cases when the sulfur dioxide and oxygen are initially present in equimolar amounts. Do this using the Hougen-Watson mechanistic models. Show your derivations. 

Effectiveness Factors for Hougen-Watson Rate Expressions. The discussion thus far and the vast majority of the literature dealing with effectiveness factors for porous catalysts are based on the assumption of an integer-power reaction rate expression (i.e., zero-, first-, or second-order kinetics). In Chapter 6, however, we stressed the fact that heterogeneous catalytic reactions are more often characterized by more complex rate expressions of the Hougen-Watson type. Over a narrow range of... 

The reactor feed mixture was "prepared so as to contain less than 17% ethylene (remainder hydrogen) so that the change in total moles within the catalyst pore structure would be small. This reduced the variation in total pressure and its effect on the reaction rate, so as to permit comparison of experiment results with theoretical predictions [e.g., those of Weisz and Hicks (61)]. Since the numerical solutions to the nonisothermal catalyst problem also presumed first-order kinetics, they determined the Thiele modulus by forcing the observed rate to fit this form even though they recognized that a Hougen-Watson type rate expression would have been more appropriate. Hence their Thiele modulus was defined as... 

Buzzi-Ferraris, G., and Donati, G. 1974. A powerful method for Hougen-Watson model parameter estimation with integral conversion data. Chem. Eng. Sci. 29 1504-9. 

Hydrogenation of octenes occurs with surface reaction controlling (Hougen Watson, Chemical Process Principles, p 943, 1947). The rate equation is... 

Langmuir-Hishelwood-Hougen-Watson (LHHW) formulation, 21 341 Langmuir isotherm, 1 592-593, 626 11 169 Langmuir monolayer formation, 17 56 Lanham Act, 25 259, 261, 265 Lanicor, molecular formula and structure, 5 98t... 

The hyperbolic model types have very commonly been used in the analysis of kinetic data, as discussed in Section I. Such applications are sometimes justified on the theoretical bases already alluded to, or simply because models of the form of Eq. (2) empirically describe the existing reaction-rate data. Considerably more complex models are quite possible under the Hougen-Watson formalism, however. For example, Rogers, Lih, and Hougen (Rl) have proposed the competitive-noncompetitive model... 

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