Rate dual site model

Figure 6. Calculated vs. observed rate—dual site model...

This equation gives (0) = 0, a maximum at =. /Km/K2, and (oo) = 0. The assumed mechanism involves a first-order surface reaction with inhibition of the reaction if a second substrate molecule is adsorbed. A similar functional form for (s) can be obtained by assuming a second-order, dual-site model. As in the case of gas-solid heterogeneous catalysis, it is not possible to verify reaction mechanisms simply by steady-state rate measurements. 

At low 7t, the denominator simplifies to unity in each case and both models are linear in n. For sufficiently high n, the parenthesis in the denominator approaches Ketv, the initial rate for the dual-site model then approaches zero, and that of the single-site model approaches a constant value. Thus the plot of the experimental data will indicate that the dual-site model is preferable if a maximum exists in the data, or that the single-site model is preferable if a horizontal high-pressure asymptote exists. Hence, for the data of Franckaerts and Froment (FI) shown in Fig. 2, the dual-site model is preferred over the single-site model. 

By using only simple hand calculations, the single-site model has been rejected and the dual-site model has been shown to represent adequately both the initial-rate and the high-conversion data. No replicate runs were available to allow a lack-of-fit test. In fact this entire analysis has been conducted using only 18 conversion-space-time points. Additional discussion of the method and parameter estimates for the proposed dual-site model are presented elsewhere (K5). Note that we have obtained the same result as available through the use of nonintrinsic parameters. 

In many reactions it has been demonstrated that more than one site is involved in the catalytic process. This is particularly often the case for dissociation reactions. The same procedure as depicted above for a single site model can be used for the derivation of the rate expression for a dual site model, but the result is somewhat different. This is exemplified for the following dissociation reaction A 2B, which is thought to proceed according to the three step sequence ... 

In the case of the dual site model the initial rate even passes through a maximum if the surface reaction step is rate determining (cf. Eqn. (3.24)). 

A dual-site model for the storage and the release of NH3 over a Fe-zeolite catalyst has been proposed by Colombo et al. [23]. The acid sites where ammonia is either weakly adsorbed or physisorbed are denoted as Site-1 while the strong adsorption sites are denoted as Site-2. The following rate expressions describe the rates of ammonia adsorption/desorption for each site ... 

The model considers the noble-metal catalyzed oxidation reactions of CO, two hydrocarbons of differing reactivities and H2, and the reaction kinetics was described by the global rate expressions of the dual-site Langmuir-Hinshelwood type [2]. 

The Q (initial reaction rate) plots were presented in Fig. 19. Note again that the data may be correlated well by straight lines for both models. The C2 values are correlated by the solid lines of Fig 20. Note that the dual-site values can again be correlated by a straight line, but that the single-site values of C2 show a definite curvature. Alternatively, the 0.975 atm value of the single-site C2 could be rejected, and the three high-pressure points... 

Recently, Praharso et al also developed a Langmuir-Hinshelwood type of kinetic model for the SR kinetics of i-Cg over a Ni-based catalyst. In their model, it was assumed that both the hydrocarbon and steam dissociatively chemisorb on two different dual sites on the catalyst surface. The bimolecular surface reaction between dissociated adsorbed species was proposed as the ratedetermining step. The following generalized rate expression was proposed ... 

The error model used in the minimization is based on the hypothesis that the residuals have zero mean and are normally distributed. The first is easily checked, the latter is only possible when sufficient data points are available and a distribution histogram can be constructed. An adequate model also follows the experimental data well, so if the residuals are plotted as a function of the dependent or independent variable(s) a random distribution around zero should be observed. Nonrandom trends in the residuals mean that systematic deviations exist and indicate that the model is not completely able to follow the course of the experimental data, as a good model should do. This residual trending can also be evaluated numerically be correlation calculations, but visual inspection is much more powerful. An example is given in Fig. 12 for the initial rate data of the metathesis of propene into ethene and 2-butenc [60], One expression was based on a dual-site Langmuir-Hinshelwood model, whereas the other... 

Note that the mathematical form of the model implies that the rate-limiting step is a dual-site surface reaction between chemisorbed hydrogen and chemisorbed butyraldehyde, and that the reverse reaction is the monomolecular dehydrogenation of chemisorbed butanol. Models of this sort should not be overinterpreted from a mechanistic standpoint. Kinetics models are at best ambiguous indicators of mechanism in that several models typically fit the data equally well. 

A palladium-hydrogen-mordenite catalyst with a 10.8/1 silica/alumina mole ratio was evaluated for the hydroisomerization of cyclohexane. The rate of reaction followed a first-order, reversible reaction between cyclohexane and methylcyclopentane. The energy of activation for this reaction between 400° and 500°F was 35.5 it 2.4 kcal/mole. Cyclohexane isomerization rates decreased with increasing hydrogen and cyclohexane-plus-methylcyclopentane partial pressure. These effects are compatible with a dual-site adsorption model. The change of the model constants with temperature was qualitatively in agreement with the expected physical behavior for the constants. 

In order to confirm their proposed mechanism (surface reaction between chemisorbed benzene and chemisorbed hydrogen), poisoning experiments were employed using thiophene as a poison. This showed that the deactivation rate decreases with increasing hydrogen and benzene partial pressures, and hence they concluded from their data that hydrogen and benzene are both chemisorbed on the catalyst surface and their proposed dual-site adsorption kinetic model is suitable to describe the hydrogenation of benzene on nickel. 

Zmcevic and Rusic (1988) used commercial nickel on a silica-alumina catalyst (code Rl-10, manufactured by BASF) containing 21% Ni. They proposed a mechanism based on the dual site adsorption model followed by a bimolecular surface reaction which is the rate-controlling step for the formation of cyclohexane from benzene. The rate equation obtained has the form ... 

In their pioneering work Dodd and Watson (3) correlated the dehydrogenation data by Langmuir-Hinshelwood rate models and found that a dual-site surface rate-controlling model is most plausible. Noda and co-workers (21) and more recently Carra and his colleagues (2) obtained essentially the same results as Dodd and Watson (3) for the chromia-alumina catalyzed dehydrogenation of n-butane. As Table I shows, somewhat different values for the orders of power function models are quoted in the references using this method of correlation. 

This rate-limiting step is third order in the forward direction (i.e., adsorption) and second order in the reverse direction (i.e., desorption). Since two active sites are required for dual-site adsorption, one predicts that the kinetic model is proportional to the square of the vacant-site fraction. Substitution for a from (14-144) leads to... 

The transient kinetic model of the standard SCR reaction over a commercial V-based catalyst for vehicles reported in Reference (101) is the only treatment available so far accounting both for the redox nature of the SCR catalytic mechanism and for the ammonia inhibition effect. It relies on a dual-site redox scheme, whereby ammonia is first adsorbed onto acidic sites, but reacts with NO on different redox sites associated with the vanadium component. The redox sites can, however, be blocked by excess ammonia. Adopting a Mars-Van Krevelen formal approach, the following modified redox (MR) rate expression was derived (27) ... 

Concerning the rate expressions, extending the dual-site Redox kinetics already presented for the NH3-NO/O2 reacting subsystem, a new global kinetic model for the full NH3-NO/NO2 SCR reacting system was derived. 

In the case of the Standard SCR reaction (R.6 or R.8), a dual-site Mars-Van Krevelen rate expression assuming that NH3 blocks the red-ox sites for NO activation was adopted in line with previous work performed over both vanadium-based [30, 36] and Fe-zeolite catalysts [12], in order to explain the observed inhibiting effect of NH3 on such a reaction at low temperatures. The model has been then extended to include also the SCR reactivity in the presence of excess NO2 and particularly to describe also the reactivity of N2O (R.14 and R.15). 

Only the catalyst dual reaction center site model to be discussed in Section 16.4.2 will be able to restore high conversion with low values of rate of chain growth termination. 

Figure 16.21 convincingly shows the advantage of the dual reaction center site model over the single reaction center site model at high value of a. This is the condition in which the rate of CO consumption becomes inhibited by the... 

A longer implies a decrease in CO dissociation rate or decrease in k. In case 4, a increases, kj has to decrease unless the rate of C-C bond formation sharply increases. The increase in rate of CO consumption is consistent with an increase in number of reactive centers. A decrease of kj affects CO conversion negatively, unless CO dissociation is slow compared to the rate of C-C bond formation (polymerization model Umit). However, a faster rate of CO dissociation counteracts the increase of The increase in CO consumption and decrease of k, are consistent with dual reaction center site model. The addition of promoting reducible oxides may lead to the presence of dual reaction center sites, resolving the... 

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