Overall effectiveness factor catalytic reactions

Exemplary results of modeling processes inside the catalytic layer are presented in Fig. 9. The solid lines show the dependency of the overall effectiveness factor on the relative distribution of the catalyst between the comers and the side regions. The two cases represent two levels of the first-order rate constants, with the faster reaction in case (b). As expected, the effectiveness factor of the first reaction drops as more catalyst is deposited in the comers. The effectiveness factor for the second reaction increases in case (a) but decreases in case (b). The latter behavior is caused by depletion of B deep inside the catalytic layer. What might be surprising is the rather modest dependency of the effectiveness factor on the washcoat distribution. The explanation is that internal diffusion is not important for slow reactions, while for fast reactions the available external surface area becomes the key quantity, and this depends only slightly on the washcoat distribution for thin layers. The dependence of the effectiveness factor on the distribution becomes more pronounced for consecutive reactions described by Langmuir-Hinshelwood-Hougen-Watson kinetics [26]. 

There can be, however, no doubt that in catalytic processes, purely physical factors play an important role, in addition to the chemical valence forces. This is particularly true for the solid catalysts of heterogeneous reactions for which the properties of surfaces, as the seats of catalytic action are of prime importance. The total surface areas, the fine structure of the surfaces, the transport of reactants to and from surfaces, and the adsorption of the reactants on the surfaces, can all be considered as processes of a predominantly physical nature which contribute to the catalytic overall effect. Any attempt, however, to draw too sharp a line between chemical and physical processes would be futile. This is illustrated clearly by the fact that the adsorption of gases on surfaces can be described either as a mere physical condensation of the gas molecules on top of the solid surface, as well as the result of chemical affinities between adsorbate and adsorbent. Every single case of adsorption may lie closer to either one of the hypothetical extremes of a purely physcial or of a purely chemical adsorption, and it would be misleading to maintain an artificial differentiation between physical and chemical factors. 

As mentioned earlier, if the rate of a catalytic reaction is proportional to the surface area, then a catalyst with the highest possible area is most desirable and that is generally achieved by its porous structure. However, the reactants have to diffuse into the pores within the catalyst particle, and as a result a concentration gradient appears between the pore mouth and the interior of the catalyst. Consequently, the concentration at the exterior surface of the catalyst particle does not apply to die whole surface area and the pore diffusion limits the overall rate of reaction. The effectiveness factor tjs is used to account for diffusion and reaction in porous catalysts and is defined as... 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

Paul Weisz suggested in a lucid note published in 1973 that cells, and indeed even entire organisms, have evolved in a way that maintains unity effectiveness factor [24]. That is, the size of the catalytic assembly is increased in nature as the overall rate at which that assembly operates decreases, and the relationship between characteristic dimension and activity can be well approximated by the observable modulus criterion for reaction limitation. It is possible that Weisz s arguments may fail under process conditions, and internal gradients within a compartment or cell may be important. However, at present it appears that the most important transport limitations and activities in cells are those that operate across cellular membranes. Therefore, to understand and to manipulate key transport activities in cells, it is essential that biochemical engineers understand these membrane transport processes and the factors influencing their operation. A brief outline of some of the important systems and their implications in cell function and biotechnology follows. 

In our discussion of surface reactions in Chapter 11 we assumed that each point in the interior of the entire catalyst surface was accessible to the same reactant concentration. However, where the reactants diffuse into the pores within the catalyst pellet, the concentration at the pore mouth will be higher than that inside the pore, and we see that the entire catalytic surface is not accessible to the same concentration. To account for variations in concentration throughout the pellet, we introduce a parameter known as the effectiveness factor. In this chapter we will develop models for diffusion and reaction in two-phase systems, which include catalyst pellets and CVD reactors. The types of reactors discussed in this chapter will include packed beds, bubbling fluidized beds, slurry reactors, and trickle beds. After studying this chapter you will be able to describe diffusion and reaction in two- and three-phase systems, determine when internal pore diffusion limits the overall rate of reaction, describe how to go about eliminating this limitation, and develop models for systems in which both diffusion and reaction play a role (e.g., CVD). 

As a rule, the asymmetric catalytic reaction is part of a more extensive multi-step synthesis. This is particularly pronounced for the cases where the active substance is the goal of the development work (categories A and D), but also for the more simple intermediates described in B and C. This means that the catalytic step has to be integrated into the overall synthesis and therefore, the route selection is a very important phase of process development. Very detailed discussions of this aspect can be found, e.g., in the contributions of Wirz et al. (p. 385, 399), Netscher et al. (p. 71) or Caille et al. (p. 349). It is important to realize that the effectiveness of the catalytic step is only one, albeit often an important, factor but that it is the cost of the overall synthesis which is decisive for the final choice as to which route will be chosen. The comparison of competing routes is not always easy and different approaches can be found in the contributions of Blaser et al. (p. 91), Pes-ti and Anzalone (p. 365), or Singh et al. (p. 335). In some cases, the overall synthesis is actually designed around an effective enantioselective transformation as for example described for the metolachlor process by Blaser et al. (p. 55). This situation will become rarer when more catalysts with well described scope and limitations will be commercially accessible. 

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... 

Gas-solid reactions between a fluid and a solid are important in a number of applications such as coal gasification, metallic ore processing, and catalyst regeneration. They are related in many aspects to the gas-solid catalytic reactions we have treated in developing the concepts of catalytic effectiveness, but differ in the very important aspect that the solid itself (in the form of a porous matrix) is one of the reactants. Since the solid phase itself is involved in reaction, often conditions of diffusion/ reaction change with time of reaction and the overall process is an unsteady-state one. As with effectiveness factors, many variants on a theme can be envisioned, i.e., is the reaction fast or slow, does the particle porosity (hence D ff) change with reaction, are boundary layer transport effects of importance, etc. We will present in some detail the developments of Wen concerning these questions [C.Y. Wen, Ind. Eng. Chem., 60, 34 (1968) H. Ishida and C.Y. Wen, Amer. Inst. Chem. Eng. J., 14, 311 (1968)]. 

Heterogeneous catalytic reactions involve by their nature a combination of reaction and transport processes, as the reactant must be first transferred from the bulk of the fluid phase to the catalyst surface. In Figure 11.2, the combined reaction and transport processes are shown schematically for a fast exothermic chemical reaction within a porous catalyst. If the rate of the intrinsic reaction is comparable to the rate of transport processes, significant concentration profiles of the reactants and products will develop. In addition, the temperature of the catalyst particle will be different from that of the bulk fluid. With increasing temperature, the influence of transport phenomena becomes more important and finally limits the overall reaction rate. This has detrimental influences on product yield and selectivity, and may lead to high overtemperatures of the catalyst and its fast deactivation [6]. The influence of transport phenomena is commonly characterized by an effectiveness factor as defined in Eq. (11.2). 

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,... 

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