Catalysts, general diffusion effects

Here, we consider the general case of a porous catalyst, where the internal diffusion effect is included in the effectiveness factor (//,). 

Thus diffusion limitations decrease the yield twofold. These results may be generalized to include interface and intraparticle diffusion for bidisperse catalysts [5]. The effect of diffusion limitation on the concentration distribution over the reactor length can be calculated from Equations 8.24, 8.29 and 8.33. An example of such calculations is shown in Figure 8.4 for the case CM = 0, DtA = D and kjkx = 0.1. Although the rate of... 

The problem of the optimal particle shape and size is crucial for packed bed reactor design. Generally, the larger the particle diameter, the cheaper the catalyst. This is not usually a significant factor in process design - more important are the internal and external diffusion effects, the pressure drop, the heat transfer to the reactor walls and a uniform fluid flow. 

The solid phase could be a reactant, product, or catalyst. In general the decision on the choice of the particle size rests on an analysis of the extra-and intra-particle transport processes and chemical reaction. For solid-catalyzed reactions, an important consideration in the choice of the particle size is the desire to utilize the catalyst particle most effectively. This would require choosing a particle size such that the generalized Thiele modulus < gen, representing the ratio of characteristic intraparticle diffusion and reaction times, has a value smaller than 0.4 see Fig. 13. Such an effectiveness factor-Thiele modulus analysis may suggest particle sizes too small for use in packed bed operation. The choice is then either to consider fluidized bed operation, or to used shaped catalysts (e.g., spoked wheels, grooved cylinders, star-shaped extrudates, four-leafed clover, etc.). Another commonly used procedure for overcoming the problem of diffu-sional limitations is to have nonuniform distribution of active components (e.g., precious metals) within the catalyst particle. 

In general, supported metal catalysts are less effective than Raney metal modified catalysts, and the enantioselectivities of supported catalysts are near to those of the Raney catalysts only in the cases when large amounts of metal are found on the surface of the support This can be explained, at least in the cases of bulk metal catalysts, as a consequence of an increase in crystallite sizes and diffusion of the tartaric acid modifier into the pores during modification of the catalyst (Sachtler " ). Detailed consideration of this problem is in discussed in Chapter 5. 

The general theoretical approach is to develop the mathematical equations for simultaneous mass transfer and chemical reaction, as the reactants and products difHise into and out of the porous catalyst. When reaction occurs simultaneously with mass transfer within a porous structure, a concentration gradient is established. Since interior surfaces are thus exposed to lower reactant concentrations than surfaces near the exterior, the overall reaction rate throughout the catalyst particle under isothermal conditions is less than it would be if there were no mass transfer limitations. As will be shown, the apparent activation energy, the catalyst selectivity, and other important observed characteristics of a reaction are also dependent upon the structure of the catalyst and the effective diffusivity of reactants and products (Charles and Thomas, 1963). 

For diffusion-affected reactions, the generalized internal effectiveness factor for fresh catalyst, tjq, can be used to arrive at the following overall pellet effectiveness for uniform chemical deactivation ... 

Active matrix contributes significantly to the overall performance of the FCC catalyst. The zeolite pores are not suitable for cracking of large hydrocarbon molecules generally having an end point > d00 [-(482°C) they are too small to allow diffusion of the large molecules to the cracking sites. An effective matrix must have a porous structure to allow diffusion of hydrocarbons into and out of the catalyst. 

J. Wood, L. F. Gladden 2003, (Effect of coke deposition upon pore structure and self-diffusion in deactivated industrial hydroprocessing catalysts), Appl.Cat. A General, 249, 241. 

Ordinary or bulk diffusion is primarily responsible for molecular transport when the mean free path of a molecule is small compared with the diameter of the pore. At 1 atm the mean free path of typical gaseous species is of the order of 10 5 cm or 103 A. In pores larger than 1CT4 cm the mean free path is much smaller than the pore dimension, and collisions with other gas phase molecules will occur much more often than collisions with the pore walls. Under these circumstances the effective diffusivity will be independent of the pore diameter and, within a given catalyst pore, ordinary bulk diffusion coefficients may be used in Fick s first law to evaluate the rate of mass transfer and the concentration profile in the pore. In industrial practice there are three general classes of reaction conditions for which the bulk value of the diffusion coefficient is appropriate. For all catalysts these include liquid phase reactions... 

Bulk or forced flow of the Hagan-Poiseuille type does not in general contribute significantly to the mass transport process in porous catalysts. For fast reactions where there is a change in the number of moles on reaction, significant pressure differentials can arise between the interior and the exterior of the catalyst pellets. This phenomenon occurs because there is insufficient driving force for effective mass transfer by forced flow. Molecular diffusion occurs much more rapidly than forced flow in most porous catalysts. 

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