Heterogeneous catalyst effectiveness factor

In the general case of immobilized enzymes not only the internal diffusion addressed above, but also diffusion through the film should be taken into account. Similarly to heterogeneous catalysis the catalyst effectiveness factor for slab geometry and low substrate concentrations (first order kinetics) is decribed by eq. (9.173) in a somewhat different form... 

Heterogeneous catalytic reactors are the most important single class of reactors utilized by the chemical industry. Whether their importance is measured by the wholesale value of the goods produced, the processing capacity, or the overall investment in the reactors and associated peripheral equipment, there is no doubt as to the prime economic role that reactors of this type play in modem industry. The focus of this chapter is the design of heterogeneous catalytic reactors. Particular emphasis is placed on the concept of catalyst effectiveness factors and the implications of heat and mass transfer processes for fixed bed reactor design. 

The first step in heterogeneous catalytic processes is the transfer of the reactant from the bulk phase to the external surface of the catalyst pellet. If a nonporous catalyst is used, only external mass and heat transfer can influence the effective rate of reaction. The same situation will occur for very fast reactions, where the reactants are completely exhausted at the external catalyst surface. As no internal mass and heat transfer resistances are considered, the overall catalyst effectiveness factor corresponds to the external effectiveness factor,... 

Heterogeneous intra and external gradients are included and catalyst effectiveness factors are calculated continuously during the integration. The kinetic rate expressions are intrinsic rates. This is definitely the preferred model, but rigorous modelling of transport processes is tedious for all catalyst sizes and shapes in syngas processes. 

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]. 

Effectiveness Factors for Hougen-Watson Rate Expressions. The discussion thus far and the vast majority of the literature dealing with effectiveness factors for porous catalysts are based on the assumption of an integer-power reaction rate expression (i.e., zero-, first-, or second-order kinetics). In Chapter 6, however, we stressed the fact that heterogeneous catalytic reactions are more often characterized by more complex rate expressions of the Hougen-Watson type. Over a narrow range of... 

More recently, Dupont and coworkers studied the impact of the steric effect in the hydrogenation of monoalkylbenzenes by zerovalent nanoparticles (Ir, Rh, Ru) in the ionic liquid BMI PF6. The results, when compared with those obtained with the classical supported heterogeneous catalysts, showed a relationship between the reaction constants and the steric factors [106]. 

However, the use of the heterogeneous catalysts in applicative enantioselective syntheses has a limited success. Several factors contribute to this situation (1) a long time is required to achieve an effective heterogeneous enantioselective catalyst compared with the homogeneous ones, (2) a more complex structure of the heterogeneous catalyst surface on which centers coexist with different catalytic activity and selectivity, which can lead to undesired secondary reactions, and (3) an increased difficulty to create an effective asymmetric environment and to accommodate it with the multitude of reactions that are interesting to be carried out under enantioselective restrictions. 

Considerable progress has been made within the last decade in elucidating the effects of the microenvironment (such as electric charge, dielectric constant and lipophilic or hydrophilic nature) and of external and internal diffusion on the kinetics of immobilized enzymes (7). Taking these factors into consideration, quantitative expressions have been derived for the kinetic behavior of relatively simple enzyme systems. In all of these derivations the immobilized enzymes were treated as simple heterogeneous catalysts. 

Recall that for a heterogeneous catalytic reactor we had to consider the microscopic concentration profiles around and within a catalyst particle and then elirninate them in terms of the macroscopic position variable z in the reactor design ecpaations (mass transfer limits and effectiveness factors). 

This study employed conventional diffusion-reaction theory, showing that with diffusion-limited reactions the internal effectiveness factor of a heterogeneous catalyst is inversely related to the Thiele modulus. Using a standard definition of the Thiele modulus [100], the observed reaction rate of an immobilized-enzyme reaction will vary with the square root of the immobilized-enzyme concentration in a diffusion-limited system. In this case, a plot of the reaction rate versus the enzyme loading in the catalyst formulation will be nonlinear. 

Note that the results of our simulation via the pseudohomogeneous model tracks the actual plant very closely. However, since the effectiveness factors r]i were included in a lumped empirical fashion in the kinetic parameters, this model is not suitable for other reactors. A heterogeneous model, using intrinsic kinetics and a rigorous description of the diffusion and conduction, as well as the reactions in the catalyst pellet will be more reliable in general and can be used to extract intrinsic kinetic parameters from the industrial data. 

Most textbook discussions of effectiveness factors in porous, heterogeneous catalysts are limited to the reaction A - Products where the effective diffusivity of A is independent of reactant concentration. On the other hand, it is widely recognized by researchers in the field that multicomponent single reaction systems can be handled in a near rigorous fashion with little added complexity, and recently methods have been developed for application to multiple reactions. Accordingly, it is the intent of the present communication to help promote the transfer of these methods from the realm of the chemical engineering scientist to that of the practitioner. This is not, however, intended to be a comprehensive review of the subject. The serious reader will want to consult the works of Jackson, et al. 

If the catalyst is dispersed throughout the pellet, then internal diffusion of the species within the pores of the pellet, along with simultaneous reaction(s) must be accounted for if the prevailing Thiele modulus > 1. This aspect gives rise to the effectiveness factor" problem, to which a significant amount of effort, summarized by Aris ( ), has been devoted in the literature. It is important to realize that if the catalyst pellet effectiveness factor is different from unity, then the packed-bed reactor model must be a heterogeneous model it cannot be a pseudohomogeneous model. 

When gum formation proceeds, the minimum temperature in the catalyst bed decreases with time. This could be explained by a shift in the reaction mechanism so more endothermic reaction steps are prevailing. The decrease in the bed temperature speeds up the deactivation by gum formation. This aspect of gum formation is also seen on the temperature profiles in Figure 9. Calculations with a heterogenous reactor model have shown that the decreasing minimum catalyst bed temperature could also be explained by a change of the effectiveness factors for the reactions. The radial poisoning profiles in the catalyst pellets influence the complex interaction between pore diffusion and reaction rates and this results in a shift in the overall balance between endothermic and exothermic reactions. 

Figure 12-5 (a) Effectiveness factor plot for nth-order kinetics spherical catalyst particles (from Mass Transfer in Heterogeneous Catalysis, hy C. N. Satterfield, 1970 reprint edition Robert E. Krieger Publishing Co., 1981 reprinted by permission of the author), (b) First-order reaction in different pellet geometries (from R. Aris, Introduction to the Analysis of Chemical Reactors, 1965, p. 131 reprinted by permission of Prentice-Hall, Englewood Cliffs, NJ)... 

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