Deactivation equation

In addition to [A ] being qiiasi-stationary the quasi-equilibrium, approximation assumes a virtually unperturbed equilibrium between activation and deactivation (equation (A3.4.125)) ... 

Perphthalic acid <550SC(3)619) is an even milder reagent that works even at —20 to 20 °C. Performic, permaleic and pertrifluoroacetic acids are strong oxidizing agents and they are recommended for AT-oxidation of the least reactive substrates. The last of the three is the most commonly used, especially for the oxidation of highly deactivated substrates (Scheme 16) such as perchloropyridine (electronic deactivation) (74MI20501) and 2,6-dibromopyridine (electronic and steric deactivation) (equation 35). 

Complete reforming kinetics have been developed for several commercial catalysts, including those used in Mobil reformers. Since KINPTR affects Mobil s business strategy, the complete reforming kinetics are proprietary. However, as an example, KINPTR C6 kinetics will be presented for UOP s R16H platinum-rhenium-alumina catalyst. Both the hydrocarbon conversion and the deactivation equations [Eqs. (36), (40)] can be directly applied to the C6 system. For the C6 hydrocarbon conversion, Eq. (40) becomes... 

The deactivation parameters aij are determined by integrating the kinetic deactivation equations ... 

The module AGING controls the integration of the catalyst deactivation equations. 

A simple deactivation equation was used for a fixed bed reactor ... 

Figure IB displays relative catalytic activity (RA) - in terms of pseudo first-order rate constants, corrected for coke content, related to the fresh, sulfided catalyst vs carbon content. The individual HDS, HVD and CNH activities all decrease with increasing carbon content, the order of deactivation being HYD < HDS < CNH. (The results for relative HDN activities followed closely those of CNH, and are not shown). Relative activities fall off less sharply as coke content increases. Because of the limited set and scatter of the data, a definitive deactivation correlation could not be obtained. Best fit curves to the data were constructed from a power-deactivation equation in C (1), and are shown by the solid curves in Fig. IB.

L All x -i daia, obtained at timeS On-stream of 0-6 seconds, can be fitted to it deactivation equation of the form of eqn 1 or 3 with a value of d for each interval of lime-on-stream. 

Catalyst deactivation is often characterized through empirical parameters. Some authors (refs, 5-8) have used parameters like tolerance, toxicity, susceptibility or initial deactivation which are directly obtained from the experimental deactivation curves. In other cases (refs. 9-11), experimentally found deactivation equations have been employed as an approximation of the actual deactivation law (linear, hyperbolic, exponential or power equations). While the use of such a kind of parameters provide useful information on the catalyst sensitivity to a given poison, the approach of obtaining the deactiv-... 

Case II. No primary radical termination. The termination of chain radicals occurs by degradative chain transfer and by combination with the resulting radicals besides the normal processes of mutual deactivation. Equation (P6.32.7) can then be written as... 

Rates of this kind are of relatively little use, as it is impossible to sieve out isothermal sets of rates at constant activity. It would take many experiments at different conditions to make available a sufficient data set to allow the sieving out of isothermal data at constant activity. Such data would, however, allow us to compare sets of isothermal rates at a variety of activities and from this determine the parameters of the deactivation equation. Unfortunately, the number of experiments required for this procedure to be applied presents a serious handicap. The method cannot be made compatible with rapid data acquisition. Fortunately, there is a way out of the dilemma. It is possible to unravel decay properties by other much simpler and less laborious means. The method described below (see also Grenier, (1997)) requires as few as two experiments using the decaying catalyst. 

Due to the similarity of the catalyst and of the characteristics of the deactivation in the transformation of methanol and of ethanol, eq. (5) has been taken as a basis for the establishment of possible deactivation equations for the transformation of ethanol into hydrocarbons. In eq. (5), X is the mass fraction (based on the organic components in the reaction medium) of the lumps of the kinetic scheme that can be considered coke precursors. This is the way in which the composition of the reaction medium is commonly expressed in the literature for the kinetic study of the processes of transformation of methanol on a HZSM-5 zeolite [8,12-14,16] and on a SAPO-34 [9]. In eq. (5), activity, a, is defined as the ratio between reaction rate at t time and at zero time ... 

Figure 7.23 Types of relationships encountered with porous catalysts. Curve A is the result for nonselective deactivation for equations (vi) and (xvi). Curve B is for uniform deposition of poison with (po large and antiselective deactivation, equation (v). Curves C and D are for selective deactivation, equation (xiv), with Q = 10 and 100, respectively. [After A. Wheeler, Advan. Catal., 3, 249 with permission of Academic Press, New York, NY, (1951).]...

The experiments were analyzed by the following deactivation equation [58]... 

All the balances have accumulation, convection, axial dispersion, and reaction terms. The equations include liquid holdup, Bi, and superficial liquid velocity, w. Langmuir-type rate equation, for the main reaction, Equation 15.4, included also an activity correction term a. Kst and in Equations 15.5-15.7 indicate the adsorption parameters for stearic acid and heptadecene, respectively. Equation 15.4 corresponds to a monomolecular transformation of stearic acid via the adsorption of the reactant to the main product. Adsorption terms for stearic acid and heptadecene were used, since both of these compounds contain functional groups enabling adsorption on the active sites of the catalyst Reaction rates were assumed not to be limited by heptadecane adsorp-UoiL Thus, the adsorption term of heptadecane was n ected. In line with the experimental observations indicating catalyst deactivation. Equation 15.4 (Table 15.2) was modified to incorporate the decrease in catalyst activity. In particular, the activity was assumed... 

The rate of the radiative deactivation (equation 11) that yields the photons used to measure tiie emission as a function of time depends on [ >D ]t. Since [T>D ]t depends on the observed rate constant, the decay of the emission depends on the decay of the excited state and thus on the observed rate constant and not only on the radiative rate constant. 

These deactivation equations are not easy to prove, but have been successful in describing several olefin polymerization processes with Ziegler-Natta and metallocene catalysts. 

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