Catalytic reactions pore diffusion effects

The conversion of cyclohexanes to aromatics is a highly endothermic reaction (AH 50 kcal./mole) and occurs very readily over platinum-alumina catalyst at temperatures above about 350°C. At temperatures in the range 450-500°C., common in catalytic reforming, it is extremely difficult to avoid diffusional limitations and to maintain isothermal conditions. The importance of pore diffusion effects in the dehydrogenation of cyclohexane to benzene at temperatures above about 372°C. has been shown by Barnett et al. (B2). However, at temperatures below 372°C. these investigators concluded that pore diffusion did not limit the rate when using in, catalyst pellets. 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

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. 

Inert gas pressure, temperature, and conversion were selected as these are the critical variables that disclose the nature of the basic rate controlling process. The effect of temperature gives an estimate for the energy of activation. For a catalytic process, this is expected to be about 90 to 100 kJ/mol or 20-25 kcal/mol. It is higher for higher temperature processes, so a better estimate is that of the Arrhenius number, y = E/RT which is about 20. If it is more, a homogeneous reaction can interfere. If it is significantly less, pore diffusion can interact. 

Zeolites have ordered micropores smaller than 2nm in diameter and are widely used as catalysts and supports in many practical reactions. Some zeolites have solid acidity and show shape-selectivity, which gives crucial effects in the processes of oil refining and petrochemistry. Metal nanoclusters and complexes can be synthesized in zeolites by the ship-in-a-bottle technique (Figure 1) [1,2], and the composite materials have also been applied to catalytic reactions. However, the decline of catalytic activity was often observed due to the diffusion-limitation of substrates or products in the micropores of zeolites. To overcome this drawback, newly developed mesoporous silicas such as FSM-16 [3,4], MCM-41 [5], and SBA-15 [6] have been used as catalyst supports, because they have large pores (2-10 nm) and high surface area (500-1000 m g ) [7,8]. The internal surface of the channels accounts for more than 90% of the surface area of mesoporous silicas. With the help of the new incredible materials, template synthesis of metal nanoclusters inside mesoporous channels is achieved and the nanoclusters give stupendous performances in various applications [9]. In this chapter, nanoclusters include nanoparticles and nanowires, and we focus on the synthesis and catalytic application of noble-metal nanoclusters in mesoporous silicas. 

This situation is termed pore-mouth poisoning. As poisoning proceeds the inactive shell thickens and, under extreme conditions, the rate of the catalytic reaction may become limited by the rate of diffusion past the poisoned pore mouths. The apparent activation energy of the reaction under these extreme conditions will be typical of the temperature dependence of diffusion coefficients. If the catalyst and reaction conditions in question are characterized by a low effectiveness factor, one may find that poisoning only a small fraction of the surface gives rise to a disproportionate drop in activity. In a sense one observes a form of selective poisoning. 

The analysis of the literature data shows that zeolites modified with nobel metals are among perspective catalysts for this process. The main drawbacks related to these catalysts are rather low efficiency and selectivity. The low efficiency is connected with intracrystalline diffusion limitations in zeolitic porous system. Thus, the effectiveness factor for transformation of n-alkanes over mordenite calculated basing on Thiele model pointed that only 30% of zeolitic pore system are involved in the catalytic reaction [1], On the other hand, lower selectivity in the case of longer alkanes is due to their easier cracking in comparison to shorter alkanes. 

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... 

For liquid-phase catalytic or enzymatic reactions, catalysts or enzymes are used as homogeneous solutes in the hquid, or as sohd particles suspended in the hquid phase. In the latter case, (i) the particles per se may be catalysts (ii) the catalysts or enzymes are uniformly distributed within inert particles or (hi) the catalysts or enzymes exist at the surface of pores, inside the particles. In such heterogeneous catalytic or enzymatic systems, a variety of factors that include the mass transfer of reactants and products, heat effects accompanying the reactions, and/or some surface phenomena, may affect the apparent reaction rates. For example, in situation (iii) above, the reactants must move to the catalytic reaction sites within catalyst particles by various mechanisms of diffusion through the pores. In general, the apparent rates of reactions with catalyst or enzymatic particles are lower than the intrinsic reaction rates this is due to the various mass transfer resistances, as is discussed below. 

Reactions influenced by mass transport If the rate of a reaction is influenced by mass transport, the effect of the pressure both on the rate of the chemical reaction and on the rate of mass transport must be taken into account. As an example, a heterogeneous catalytic reaction governed by the rate of diffusion within the pores of the catalyst is considered. 

From the foregoing dicussion it is apparent that residuum hydroconversion processes can be influenced adversely by pore diffusion limitations. Increasing the catalyst porosity can alleviate the problem although increased porosity is usually accompanied by a decrease in total catalytic surface area. Decreasing the catalyst particle size would ultimately eliminate the problem. However, a different type of reaction system would be required since the conventional fixed bed would experience excessive pressure drops if very fine particles were used. A fluidized system using small particles does not suffer from this limitation. However, staging of the fluidized reaction system is required to minimize the harmful effects that backmixing can have on reaction efficiency and selectivity. 

We have used CO oxidation on Pt to illustrate the evolution of models applied to interpret critical effects in catalytic oxidation reactions. All the above models use concepts concerning the complex detailed mechanism. But, as has been shown previously, critical. effects in oxidation reactions were studied as early as the 1930s. For their interpretation primary attention is paid to the interaction of kinetic dependences with the heat-and-mass transfer law [146], It is likely that in these cases there is still more variety in dynamic behaviour than when we deal with purely kinetic factors. A theory for the non-isothermal continuous stirred tank reactor for first-order reactions was suggested in refs. 152-155. The dynamics of CO oxidation in non-isothermal, in particular adiabatic, reactors has been studied [77-80, 155]. A sufficiently complex dynamic behaviour is also observed in isothermal reactors for CO oxidation by taking into account the diffusion both in pores [71, 147-149] and on the surfaces of catalyst [201, 202]. The simplest model accounting for the combination of kinetic and transport processes is an isothermal continuously stirred tank reactor (CSTR). It was Matsuura and Kato [157] who first showed that if the kinetic curve has a maximum peak (this curve is also obtained for CO oxidation [158]), then the isothermal CSTR can have several steady states (see also ref. 203). Recently several authors [3, 76, 118, 156, 159, 160] have applied CSTR models corresponding to the detailed mechanism of catalytic reactions. 

The molecular size pore system of zeolites in which the catalytic reactions occur. Therefore, zeolite catalysts can be considered as a succession of nano or molecular reactors (their channels, cages or channel intersections). The consequence is that the rate, selectivity and stability of all zeolite catalysed reactions are affected by the shape and size of their nanoreactors and of their apertures. This effect has two main origins spatial constraints on the diffusion of reactant/ product molecules or on the formation of intermediates or transition states (shape selective catalysis14,51), reactant confinement with a positive effect on the rate of the reactions, especially of the bimolecular ones.16 x ... 

As described in Section 4.1.1.2, in most catalytic reactions, the reactant molecules diffuse through a boundary layer and through the pores to the active center, react, and diffuse back. If the velocity of any of these two diffusion processes is smaller than the conversion of the reactants at the active center, the overall reaction rate for the whole process is limited by the mass transport and not by the chemical reaction. If the reaction is influenced by mass transport effects, a comparison of the catalytic activity of different catalysts is impossible ... 

The acid properties of zeolites can be modified by various treatments ion exchange, dealumination etc. which can be carried out in different ways. As was shown for the most classical methods, the effect of these treatments on the characteristics of the acid sites is generally complex. Indeed they provoke also modifications of the pore system which can favor or limit the diffusion of reactant and product molecules hence influence the catalytic properties. All these effects being well-known, it is relatively easy to tailor zeolites for obtaining active, stable and selective catalysts for desired reactions. 

The whole of the internal surface area of a porous catalyst will be available for the catalytic reaction if the rates of diffusion of reactant into the pores, and of product out of them, are fast compared with the rate of the surface reaction. In contrast, if the reactant diffuses slowly but reacts rapidly, conversion to product will occur near the pore entrances and the interior of the pores will play no role in the catalysis. Ion exchange resins are typical examples of catalysts for which such considerations are important (cf. Sect. 2.3). The detailed mathematics of this problem have been treated in several texts [49-51] and we shall now quote some of the main theoretical results derived for isothermal conditions. The parameters involved tend to be those employed by chemical engineers and differ somewhat from those used elsewhere in this chapter. In particular, the catalyst material (active + support) is present in the form of pellets of volume Vp and the catalytic rates vv are given per unit volume of pellet (mols m 3). The decrease in vv brought about by pore diffusion is then expressed by an effectiveness factor, rj, defined by... 

While the above criteria are useful for diagnosing the effects of transport limitations on reaction rates of heterogeneous catalytic reactions, they require knowledge of many physical characteristics of the reacting system. Experimental properties like effective diffusivity in catalyst pores, heat and mass transfer coefficients at the fluid-particle interface, and the thermal conductivity of the catalyst are needed to utilize Equations (6.5.1) through (6.5.5). However, it is difficult to obtain accurate values of those critical parameters. For example, the diffusional characteristics of a catalyst may vary throughout a pellet because of the compression procedures used to form the final catalyst pellets. The accuracy of the heat transfer coefficient obtained from known correlations is also questionable because of the low flow rates and small particle sizes typically used in laboratory packed bed reactors. 

In terms of catalysis, important equilibrium processes include low-temperature gas adsorption (capillary condensation) and nonwetting fluid invasion, both of which are routinely used to characterize pore size distribution. Static diffusion in a Wicke-Kallenbach cell characterizes effective diffusivity. The simultaneous rate processes of diffusion and reaction determine catalyst effectiveness, which is the single most significant measure of practical catalytic reactor performance. 

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 most of the acid sites are located in pores of molecular size the rate and the selectivity of catalytic reactions depend not only on the intrinsic properties of the sites but also on the pore structure. A zeolite catalyst selects the reactant or the product by their ability to diffuse to and from the active sites (reactant and product selectivity). Steric constraints in the environment of the sites limit or inhibit the formation of intermediates or transition states (restricted transition state selectivity) [24,25]. The strong polarizing interaction between zeolite crystallites and adsorbed molecules leads to an unusually high concentration of the reactants in the pores. This concentration effect causes an enhancement of the rates of bimolecular reaction steps over monomolecular reaction steps [26]. 

Often the global reaction rate of heterogeneous catalytic reactions is affected by the diffusion in the pore and the external mass-transfer rate of the reactants and the products. When the diffusion in the pores is not fast, a reactant concentration profile develops in the interior of the particle, resulting in a different reaction rate at different radial locations inside the catalytic pelet. To relate the global reaction rate to various concentration profiles that may develop, a kinetic effectiveness factor is defined [1, 3,4,7, 8] by... 

The effectiveness factor, rj, is defined as the ratio of the reaction rate with pore diffusion resistance to the reaction rate without pore diffusion resistance (i.e., all of the active catalytic sites are restricted to the external surface of the particle). In mathematical terms... 

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