Hinshelwood approach

The theoretical calculations described have recently been supported by an extraordinary kinetic analysis conducted by Vanrysellberghe and Froment of the HDS of dibenzothiophene (104). That work provides the enthalpies and entropies of adsorption and the equilibrium adsorption constants of H2, H2S, dibenzothiophene, biphenyl, and cyclohexylbenzene under typical HDS conditions for CoMo/A1203 catalysts. This work supports the assumption that there are two different types of catalytic sites, one for direct desulfurization (termed a ) and one for hydrogenation (termed t). Table XIV summarizes the values obtained experimentally for adsorption constants of the various reactants and products, using the Langmuir-Hinshelwood approach. As described in more detail in Section VI, this kinetic model assumes that the reactants compete for adsorption on the active site. This competitive adsorption influences the overall reaction rate in a negative way (inhibition). 

Kinetic investigations have been reported for the hydrogenation of a variety of substrates [29,30]. Typically, the reaction is between zero- and first-order for hydrogen and, especially at higher concentrations of nitro arene, zero-order in substrate. A Langmuir-Hinshelwood approach (reversible adsorption of reactants and intermediates on the metal surface) is usually chosen for kinetic analysis, quite often with good agreement. 

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. 

In considering kinetic models which can display oscillatory behaviour, it is useful to recall the Langmuir-Hinshelwood approach to a simple reaction such as the oxidation of CO, taking place in a closed system and consider the commonly adopted assumptions ... 

For the case where 5 = 2, this expression reduces to the simple exponential form of Arrhenius. For values of 5 greater than 2, it yields a much larger probability of reaction than one would obtain from the normal Arrhenius form. The enhancement may be several orders of magnitude. For example, when 5 = 10 and E/RT = 30, the ratio of the probability factor predicted by Hinshelwood s approach to that predicted by the conventional Arrhenius method is (30)" /4 = 3.375 X 10". The drawback of the approach is that one cannot accurately predict 5 a priori. When one obtains an apparent steric factor in excess of unity, the Hinshelwood approach can often be used in interpretation of the data. 

Langmuir-Hinshelwood approach, with irreversible reaction as further alternative applied to chemical and enzymatic reactions (fc 2 = 0). 

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