Catalytic effectiveness factor

A temperature gradient would also be expected. For an isothermal case, with rj set equal to 1, multiple steady-state solutions may be found (see Figure 10), and the concentration gradient is very significant at temperatures above 427°C (800°F). The non-isothermal catalytic effectiveness factors for positive order kinetics under external and internal diffusion effects were studied by Carberry and Kulkarni (8) they also considered negative order kinetics. 

In Figure 7.2 is a simple representation of gradients for several cases of relative mass transfer/reaction rates. Since these gradients are established when transport rates become finite, the net effect is to reduce the overall rate of reaction due to the lower incident concentration of reactant within the catalyst as compared to external surface (or bulk) concentration. The net activity of the catalyst is diminished, and it is common to define this quantitatively in terms of the catalytic effectiveness factor, given by... 

If we wish to express these results for gas-liquid reactions in strict analogy to those for the catalytic effectiveness factor, then the solutions of equation (7-107) can... 

This sequence of steps should be familiar, since they are the same as those developed in Chapter 7 for the derivation of the catalytic effectiveness factor. Here we are interested primarially in steps 13, although there is one more case of chemical reaction to be considered. This one requires more analysis than before. To this point we have been sailing along not much more. 

Cassiere, G. and Carberry, J.J. (1973) Interphase catalytic effectiveness factor activity, yield and non-isothermality. Chem. Eng. Educ., 7 (1), 22—26. 

The methods used for modeling-supported PTC systems are all based on the standard equations developed for porous catalysts in heterogeneous catalysis (Chapter 6). These are expressed in terms of an overall effectiveness factor that accounts both for the mass transfer resistances outside the supported catalyst particles (film diffusion resistance, expressed as a Biot number) and within them (intraparticle diffusional resistance, expressed in terms of a Thiele modnlns). Then, for any given solid shape, the catalytic effectiveness factor can be derived as a function of the Thiele modulus A. Thus, for a spherical support solid, we have... 

Carberry, J.J. (1961) The catalytic effectiveness factor under nonisothermal conditions. AIChE J., 7, 350-351. 

Where, tIc is overall catal54ic effectiveness factor. The overall catalytic effectiveness factor for a spherical catalyst particle can be expressed as ... 

When the operating temperature exceeds ca 93°C, the catalytic effects of metals become an important factor in promoting oil oxidation. Inhibitors that reduce this catalytic effect usually react with the surfaces of the metals to form protective coatings (see Metal surface treatments). Typical metal deactivators are the zinc dithiophosphates which also decompose hydroperoxides at temperatures above 93°C. Other metal deactivators include triazole and thiodiazole derivatives. Some copper salts intentionally put into lubricants counteract or reduce the catalytic effect of metals. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

By changing Ser 221 in subtilisin to Ala the reaction rate (both kcat and kcat/Km) is reduced by a factor of about 10 compared with the wild-type enzyme. The Km value and, by inference, the initial binding of substrate are essentially unchanged. This mutation prevents formation of the covalent bond with the substrate and therefore abolishes the reaction mechanism outlined in Figure 11.5. When the Ser 221 to Ala mutant is further mutated by changes of His 64 to Ala or Asp 32 to Ala or both, as expected there is no effect on the catalytic reaction rate, since the reaction mechanism that involves the catalytic triad is no longer in operation. However, the enzyme still has an appreciable catalytic effect peptide hydrolysis is still about 10 -10 times the nonenzymatic rate. Whatever the reaction mechanism... 

The relative importance of the potential catalytic mechanisms depends on pH, which also determines the concentration of the other participating species such as water, hydronium ion, and hydroxide ion. At low pH, the general acid catalysis mechanism dominates, and comparison with analogous systems in which the intramolecular proton transfer is not available suggests that the intramolecular catalysis results in a 25- to 100-fold rate enhancement At neutral pH, the intramolecular general base catalysis mechanism begins to operate. It is estimated that the catalytic effect for this mechanism is a factor of about 10. Although the nucleophilic catalysis mechanism was not observed in the parent compound, it occurred in certain substituted derivatives. 

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

Oxidation kinetics over platinum proceeds at a negative first order at high concentrations of CO, and reverts to a first-order dependency at very low concentrations. As the CO concentration falls towards the center of a porous catalyst, the rate of reaction increases in a reciprocal fashion, so that the effectiveness factor may be greater than one. This effectiveness factor has been discussed by Roberts and Satterfield (106), and in a paper to be published by Wei and Becker. A reversal of the conventional wisdom is sometimes warranted. When the reaction kinetics has a negative order, and when the catalyst poisons are deposited in a thin layer near the surface, the optimum distribution of active catalytic material is away from the surface to form an egg yolk catalyst. 

In analyzing various proposed catalytic effects we will have to specify an assumed mechanism and examine its energetics. Comparing the relative contributions to (Ag - Agfage) from different catalytic factors should tell us which of them are really important. Of course, if the assumed mechanism is incorrect we will be asking a somewhat irrelevant question. 

The previous chapters taught us how to ask questions about specific enzymatic reactions. In this chapter we will attempt to look for general trends in enzyme catalysis. In doing so we will examine various working hypotheses that attribute the catalytic power of enzymes to different factors. We will try to demonstrate that computer simulation approaches are extremely useful in such examinations, as they offer a way to dissect the total catalytic effect into its individual contributions. 

Engberts [3e, f, 9, 29] investigated the influence of metal ions (Co, Ni, Cu +, Zn +) on the reaction rate and diastereoselectivity of Diels-Alder reaction of dienophile 31 (Table 6.5, R = NO2) with cyclopentadiene (32) in water and organic solvents. Relative reaction rates in different media and the catalytic effect of Cu are reported in Table 6.5. 10 m Cu(N03)2 accelerates the reaction in water by 808 times, and when compared with the uncatalyzed reaction in MeCN by a factor of 232 000. 

The pseudohomogeneous reaction term in Equation (11.42) is analogous to that in Equation (9.1). We have explicitly included the effectiveness factor rj to emphasis the heterogeneous nature of the catalytic reaction. The discussion in Section 10.5 on the measurement of intrinsic kinetics remains applicable, but it is now necessary to ensure that the liquid phase is saturated with the gas when the measurements are made. The void fraction s is based on relative areas occupied by the liquid and soUd phases. Thus,... 

The ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

The differences between faces usually are small. The reaction rates observed at the different faces as a rule are of the same order of magnitude and differ by no more than a factor of 3 to 5. Significant catalytic effects where one of the faces is tens of times more (or fess) active than the other single-crystal faces of the same metal are rare. One of the few examples is the reduction of CO2 on platinum which occurs with the formation of a strongly bound chemisorbed product (called reduced CO2). At the... 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

---