Deactivation kinetics rate equation

Evaluation of F(x) for Second Order Deactivation. As mentioned earlier for the case of second order decay F(x) cannot be derived analytically, however numerical calculation of F(x) or Its evaluation from simulated rate data Indicates that the function defined In Equation 11 provides an excellent approximation. This was also confirmed by the good fit of model form 12 to simulated polymerization data with second order deactivation. Thus for second order deactivation kinetics the rate expression Is Identical to Equation 12 but with 0 replacing 02. 

Kinetic Rate Lam y/Vfateriat Balance reaction/deactivation/ reactor design equation, heat/mass transpat/ fluid-flow model,... 

Prior to the kinetic experiments, possible deactivation phenomena of the catalytic system were checked by recycling experiments with prenal and citral as substrates. These results provide not only important hints on the form of the rate equation, but also on which reaction is convenient for long-term investigations in the loop reactor. After the reaction, the aqueous and organic phases were separated and the catalyst phase was reused without further purification. Results on the hydrogenation of prenal are shown in Fig. 7. The reaction rate clearly decreases if the catalyst phase is reused. According to GC analysis and H-NMR studies, this can be attributed to the fact that the product of the reaction, prenol, is highly soluble in water. Consequently, a simple phase... 

For ideal radical polymerization to occur, three prerequisites must be fulfilled for both macro- and primary radicals, a stationary state must exist primary radicals have to be for initiation only and termination of macroradicals only occur by their mutual combination or disproportionation. The rate equation for an ideal polymerization is simple (see Chap. 8, Sect. 1.2) it reflects the simple course of this chain reaction. When the primary radicals are deactivated either mutually or with macroradicals, kinetic complications arise. Deviations from ideality are logically expected to be larger the higher the concentration of initiator and the lower the concentration of monomer. Today termination by primary radicals is an exclusively kinetic problem. Almost nothing has been published on the mechanism of radical liberation from the aggregation of other initiator fragments and from the cage of the... 

Using the resin, asphalt (R+AT) and aromatics (AR) separated from an atmospheric rcsid oil (ARO) as fc stocks, we have investigated the effects of catalytic coke additive coke (Cgdd) on the cracking activity of a commercial FCC catalyst in a fixed bed (FB) and a rixed fluid bed (FFB) pilot units. Correlations between catalyst activity (a) and coke on catalyst (Q.) have been developed. A catalyst deactivation model, which is useful in modeling of cracking reaction kinetics, has been derived through rate equations of coke formation. 

Deactivation Kinetics A separable form of rate equation was used for the poisoning reaction, first order with poison concentration and active sites, respectively. Similar forms have been used elsewhere (Richardson, 1971 Baiker et al -, 1966 Zrncevic and Gomzi, 1983) From previous studies done on the thiophene... 

For the evaluation of the kinetic equation for the deactivation kinetics the asumption was made, that for a deactivated catalyst the same kinetic modd is valid and the rate constants do not change with time on stream. Therefore reaction kinetics and ci eac-... 

If we assume that the reaction between the surface bound molecule and toluene is rate detemuning step, we arrive at the expression shown in Equation 2 for the deactivation kinetics. 

The predominance of kinetic studies have assumed uniform sites on the catalyst surface. However, it has long been recognized that many catalyst surfaces exhibit non-uniform sites. Boudart and Djega-Mariadassou [3] have discussed the kinetics of non-uniform surfaces and conclude that "a non-uniform surface behaves catalytically. .like a uniform surface..", and that "rate equations are similar for a given mechanism on a uniform or non-uniform surface". This result justifies "the common practice of neglecting non-uniformity of catalytic surfaces in kinetic studies". However, it appears that uniform catalyst sites catmot adequately explain catalyst deactivation phenomena. The objective of the present study was to explain deactivation in terms of a model based on a variable activation energy site distribution on the catalyst. 

These are rapid, simple reactors that offer economy of feed and provide protection against process deactivation. A typical scheme is given in Fig. 7.26. The operation is transient so that concentrations change over the surface. Kinetic interpretations are difficult for any but first-order rate equations. Pulse reactors do have utility in poison titration measurements, in determining activities of the fresh surface, and for following surface conditioning. 

Deactivation Kinetics A separable form of rate equation was used... 

Often deactivation is expressed in terms of time. This is not the true variable, as it could lead to incomplete predictions. More correctly, the deactivation function has to be expressed in terms of the deactivating agent the coke precursor or the poison, which means that the amount of coke (or poison) on the catalyst site should be known. The determination of a rate equation for the formation of the coke precursor is thus an integral part of the kinetic study of the process. 

The effect of deactivation on the kinetics of the main reaction is thus modeled by the single activity factor which multiplies the surface reaction rate constant. The rate of deactivation, as suggested by the data of Table 3.5, would be represented in a separate rate equation with the precise form depending on the mechanism of deactivation. For example, if poisoning were the mechanism of deactivation in a scheme such as (XXVI), then... 

The result here concerning separability seems to be rather pessimistic in fact. Maybe a curve-fit variable of. s would serve just as well. How might we be able to test this Would it really be worth the effort Also, the appearance of IS in the main reaction makes the rate equation nonlinear. Does this mean that separable kinetics for deactivation will not work for nonlinear kinetics ... 

Several factors and assumptions are built into equation (7-97). The most noticeable is the time variation of this term will be important if the rate of the deactivation is rapid compared to the rate of the main reaction, that is if k. The most important assumption in equation (7-97), however, is that the deactivation kinetics are separable hence the activity factor s in the reaction rate term. Finally, since A disappears in both of the reactions in the parallel scheme, the overall rate constant is given by the sum shown above. For the series scheme, of course, some changes will have to be made that, by now, one hopes will be obvious. 

A series of Cu- and Cu-Ln-ZSM-5 (Ln= Ce, Sm) were prepared by ionic-exchange of ZSM-5 with various copper salts. These catalysts were subjected to TG-DSC measurements coupled with mass spectrometry analysis in the presence of a 30 ml min flow of NO. The fitting of these experimental curves with rate equations led to the determination of the kinetic parameters. The correlation of these parameters with catalytic, FTIR, and XPS data provided a model of deactivation of these catalysts in NO decomposition. 

Another important consideration in the FCC unit model is the deactivation of catalyst as it circulates through die unit Previous work has used two different approaches to model catalyst activity time on stream and coke on catalyst [49]. Since the 21-lump includes discrete lumps for the kinetic and metal cokes, this work uses a coke-on-catalyst approach to model catalyst deactivation. In addition, this work includes a rate equation in the kinetic network for coke balance on the catalyst. The general deactivation function due to coke, coke> is given by Eq. (4.4). 

The kinetic network in Figure 5.7 includes separate pathways for N5 and N6 components and accounts explicitly for light production (C1-C5). This is critical to maintaining a good prediction of light gas components from industrial models. In addition, the adsorption factors include terms to account for hydrogen content, total pressure and adsorbed hydrocarbons. Additional work by Taskar et al. [4, 5] modifies this network to include the effects of catalyst deactivation. Table 5.4 shows the key rate equations for each class and the deactivation factor due to Taskar et al. 

In the simplest case, the catalytic activity is proportional to the number of active sites Nt, intrinsic rate constant and the effectiveness factor. Catalyst deactivation can be caused by a decrease in the number of active sites, changes in the intrinsic rate constant, for example, changes in the ability of surface sites to promote catalysis, and by degradation in accessibility of the pore space. When the reaction and deactivation rates are of different magnitudes, the reactions proceed in seconds, while the deactivation can require hours, days, or months moreover, the deactivation does not affect the selectivity. The concept of separable deactivation kinetics is applied. The reaction rates and deactivation are treated by different equations. A quantity called activity, (a), is introduced to account for changes during the reaction. 

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