Hougen and Watson kinetics

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. 

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. 

In other instances, reaction kinetic data provide an insight into the rate-controlling steps but not the reaction mechanism see, for example, Hougen and Watson s analysis of the kinetics of the hydrogenation of mixed isooctenes (16). Analysis of kinetic data can, however, yield a convenient analytical insight into the relative catalyst activities, and the effects of such factors as catalyst age, temperature, and feed-gas impurities on the catalyst. 

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. 

It is assumed throughout that an expression for the rate of reaction in terms of the local thermodynamic variables is available. The derivation of such expressions is no easy task (see for example Hougen and Watson, 1947) and there are some commercial reactions for which no sound kinetic expression is known. Nor is it always easy to get at those that are being used, for often a company will guard... 

The performance of a catalyst will often deteriorate as the catalyst becomes coated with carbon or poisoned with impurities from the process stream. This may be reflected by introducing a parameter t into the kinetic expression, r(c,T r). This parameter might be the time elapsed since the installation of the catalyst or the total volume of reactants passed since its regeneration. The question is considered by Hougen and Watson (1947), who give expressions for the dependence of r on r. The particular form does not concern us here we assume that a satisfactory expression has been developed. We want to know how the control of an adiabatic reactor should depend on r. 

A higher form of interpretation of the effect of solvents on the rate of heterogeneously catalyzed reactions was represented by the Langmuir-Hinshelwood kinetics (7), in the form published by Hougen and Watson (2), where the effect of the solvent on the reaction course was characterized by the adsorption term in the kinetic equation. In catalytic hydrogenations in the liquid state kinetic equations of the Hougen-Watson type very frequently degrade to equations of pseudo-zero order with respect to the concentration of the substrate (the catalyst surface is saturated with the substrate), so that such an interpretation is not possible. At the same time, of course, also in these cases the solvent may considerably affect the reaction. As is shown below, this influence is very adequately described by relations of the LFER type. 

Kinetics of reactions on more than one site are more complex. A general formalism for single-step surface reactions and rate control by the reaction, adsorption of a reactant, or desorption of a product has been developed by Hougen and Watson ... 

Chemical engineering thermodynamics, while certainly initiated by H. C. Weber s book in 1935, was launched in the 1940 s with the texts by Dodge in 1944, then by Hougen and Watson, and finally by J. M. Smith. Canadian adaptation was rapid (and virtually complete by the early 1950 s), much more so than in the area of applied kinetics where it took almost another decade and the successive and increasing impact of the texts by Hougen and Watson, Walas, J. M. Smith, and O. Levenspiel. 

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. 

The use of Langmuir isotherms to interpret kinetic data was proposed by Hinshelwood [2] and discussed at length by Hougen and Watson [3]. Surface reaction rates are assumed to depend on the fraction of sites covered by different species. If the surface is at adsorption-desorption equilibrium, the equations for etc. are used in the rate expressions, and the surface... 

Only 3 years later, in 1947, Hougen and Watson published Kinetics and Catalysis (Chemical Process Principles Part 3), which forms the basis of modem chemical reaction engineering. In the same year, W. Robert Marshall and Robert L. Pigford prMi h A Applications of Differential Equations to Chemical Engineering Problems, illustrating applications of mathematics to many areas of chemical engineering. Up to a certain point, it constituted the first step toward the systematic process design. 

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