Catalysts activity factor

For the catalyst activity factor (aj), several models have been proposed, depending on the origin of catalyst deactivation, that is, sintering, fouling, or poisoning. The following differential equation can semiempiricaUy represent different kinds of... 

In practice, it generally will be found that one-dimensional models are entirely adequate for optimization, provided that they are validated in some kind of pilot-scale tubular reactor. Validation comprises the adjustment of parameters in the reactor model equations so that observed and predicted temperature and concentration profiles match as closely as possible. Typical parameters are the relative catalyst activity factors Bj and, if necessary, the overall heat-transfer coefficient, U. A statistically-designed set of experiments in the pilot-plant is invaluable for model validation, and such a set was used in this project. 

If progressive deactivation is a factor, it may be desirable to describe the Bj catalyst activity factors as functions of axial distance ana catalyst age. In any event, the final design must be checked over a realistic range of catalyst activities to ensure operability and performance over the projected life of the catalyst. 

Figure 4.64 Catalyst activity factor and equilibrium metals content.

Beta distribution shape parameter Catalyst activity factor... 

The catalyst activity factor (< ,) is time-dependent. The following difierential equation represents semi-empiricaUy different kinds of separable deactivation functions ... 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Under polymerisation conditions, the active center of the transition-metal haHde is reduced to a lower valence state, ultimately to which is unable to polymerise monomers other than ethylene. The ratio /V +, in particular, under reactor conditions is the determining factor for catalyst activity to produce EPM and EPDM species. This ratio /V + can be upgraded by adding to the reaction mixture a promoter, which causes oxidation of to Examples of promoters in the eadier Hterature were carbon tetrachloride, hexachlorocyclopentadiene, trichloroacetic ester, and hensotrichloride (8). Later, butyl perchlorocrotonate and other proprietary compounds were introduced (9,10). 

For commercial appHcation, catalyst activity is only one of the factors to be considered. Equally important is catalyst life, but Htde has been pubHshed on this aspect. Partly because of entrainment losses and partly through loss of acid as volatile triethyl phosphate, the catalyst loses activity unless compensating steps are taken. This decline in activity can be counteracted by the periodic or continuous addition of phosphoric acid to the catalyst during use, a fact that seems to have been disclosed as early as 1940 (94). A catalyst subjected periodically to acid addition could remain in service indefinitely, according to a report by Shell (91). A later Shell patent (85) states that complete reimpregnation with acid is required every 200 mn-days. 

In other instances, reaction kinetic data provide an insight into the rate-controlling steps but not the reaction mechanism see, for example, Hougen and Watson s analysis of the kinetics of the hydrogenation of mixed isooctenes (16). Analysis of kinetic data can, however, yield a convenient analytical insight into the relative catalyst activities, and the effects of such factors as catalyst age, temperature, and feed-gas impurities on the catalyst. 

Suppose that catalyst pellets in the shape of right-circular cylinders have a measured effectiveness factor of r] when used in a packed-bed reactor for a first-order reaction. In an effort to increase catalyst activity, it is proposed to use a pellet with a central hole of radius i /, < Rp. Determine the best value for RhjRp based on an effective diffusivity model similar to Equation (10.33). Assume isothermal operation ignore any diffusion limitations in the central hole, and assume that the ends of the cylinder are sealed to diffusion. You may assume that k, Rp, and eff are known. 

The activity in aliphatic alkylation of all the alkaline and ammonium salts of H4SiWi204o and H3PW12O40 are compared in Table 4. A deactivation factor, R %, measuring the decrease of the catalyst activity after 65 min is also reported... 

The results obtained with different amines cannot be explained merely on the effects of amine basicity. Thus, to obtain complete hydrogenation of Q to DHQ, the basicity has to be tailored by other factors such as the steric hindrance of the amine and its electronic interaction with the catalyst active sites this seems to be favored by the presence of an electron-rich aromatic ring. Of note, the positive effect of substituted aromatic amines, with a 49% DHQ yield being obtained for ethylanilines, is independent of the substituent position of the alkyl group. 

The task of developing a suitable catalyst for commercial applications involves many considerations, ranging from obvious factors like catalyst activity and selectivity to variables like the catalyst shape and the composition of the binder used in a pelletizing process. This section is devoted to a discussion of these considerations and of the techniques involved in manufacturing industrial catalysts. 

There are several factors that may be invoked to explain the discrepancy between predicted and measured results, but the discrepancy highlights the necessity for good pilot plant scale data to properly design these types of reactors. Obviously, the reaction does not involve simple first-order kinetics or equimolal counterdiffusion. The fact that the catalyst activity varies significantly with time on-stream and some carbon deposition is observed indicates that perhaps the coke residues within the catalyst may have effects like those to be discussed in Section 12.3.3. Consult the original article for further discussion of the nonisothermal catalyst pellet problem. 

This relation is plotted as curve Bin Figure 12.11. Smith (66) has shown that the same limiting forms for are observed using the concept of effective dififusivities and spherical catalyst pellets. Curve B indicates that, for fast reactions on catalyst surfaces where the poisoned sites are uniformly distributed over the pore surface, the apparent activity of the catalyst declines much less rapidly than for the case where catalyst effectiveness factors approach unity. Under these circumstances, the catalyst effectiveness factors are considerably less than unity, and the effects of the portion of the poison adsorbed near the closed end of the pore are not as apparent as in the earlier case for small hr. With poisoning, the Thiele modulus hp decreases, and the reaction merely penetrates deeper into the pore. 

Since its discovery in 1980,7 the Sharpless expoxidation of allylic alcohols has become a benchmark classic method in asymmetric synthesis. A wide variety of primary allylic alcohols have been epoxidized with over 90% optical yield and 70-90% chemical yield using TBHP (r-BuOOH) as the oxygen donor and titanium isopropoxide-diethyl tartrate (DET, the most frequently used dialkyl tartrate) as the catalyst. One factor that simplifies the standard epoxidation reaction is that the active chiral catalyst is generated in situ, which means that the pre-preparation of the active catalyst is not required. 

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