Hougen-Watson approach

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 approach) [15] and the approach is sometimes made simpler by using so-called virtual pressures [16] (cf. Chapter 3). 

For a simple reaction A B occurring on single sites and with the reaction between adsorbed species as the rate determining step the classical Hougen Watson approach leads to [Froment Bischoff, 1990] ... 

In Chapters 3 and 4 the Langmuir-Hinshelwood-Hougen-Watson approach to heterogeneous catalysis was discussed. Such an approach supposes that usually there is one rate determining step (adsorption, surface reaction or desorption) and that the other steps are in quasi-equilibria. 

The Langmuir-Hinshelwood/Hougen-Watson approach is not limited to monomolecular reactions. It can be quite easily extended toward bimolecular and even more complex reactions. In equation 68 different terms can be recognized as... 

Froment [1987a, 1987b] further extended the Hougen-Watson approach to complex reactions such as hydrocracking and illustrated the derivation of the rate equations not only reflecting the chemisorption of the reacting species, but also the effect of some of the species on the nature and properties of the actives sites, as encountered, for example, in Co/Mo catalysis. 

This approach was applied to data obtained by Hausberger, Atwood, and Knight (17). Figure 9 shows the basic temperature profile and feed gas data and the derived composition profiles. Application of the Hougen and Watson approach (16) and the method of least squares to the calculated profiles in Figure 9 gave the following methane rate equation ... 

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... 

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. 

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. 

The greatest barrier in the application of the Multicomponent Fowler-Guggenheim or Bragg-Williams Lattice gas model to, a practical situation like Pet-reforming, is the absence of experimental interaction parameters. In the simulations of the earlier sections, representative values were used. In general, for an n component system, we need to fix n(n+l) / 2 interaction parameters of the symmetric W matrix (91 for a 13 component Model ). Mobil has used successfully a 13 lump KINPTR model(5), which essentially uses a Hougen-Watson Langmuir-Hinshelwood approach. This results in a psuedo-monomolecular set of reactions, which is amenable to matrix analysis. 

A catalysed reaction is a result of several steps involving adsorption on active sites, reaction between sites and desorption fi om sites. Following Langmuir-Hinselwood-Hougen-Watson (LHHW) approach, the reaction rate has the form ... 

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 approach 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 based on the work of Weisz and Hicks (63)]. Because 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 of rate expression would have been more appropriate. Hence, their Thiele modulus was defined as... 

The validity of the approach is also discussed in a paper by Boudart [1986]. Certainly, the nonuniformity of catalytic surfaces, revealed by data on the heats of chemisorption, is a reality, but does this mean that a reaction necessarily senses this nonuniformity — that the reaction is structure sensitive That depends on the reaction itself, but also on the operating conditions. It may be that the reaction requires only one (or perhaps two) metal atoms or actives sites to proceed, but also that the operating conditions lead to a surface which is almost completely covered by species, so that the nonuniformities are no longer felt. In such a case the use of Hougen-Watson rate equations, based on the Langmuir isotherm, is "... not only useful, but it is also correct. In all cases their use provides physical intuition, improvable rate equations and mechanistic insight unattainable through empirical rate laws [Boudart, 1986]. Since then, further support for this point of view has been published. 

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