Catalytic effective diffusivity

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. 

For the purposes of this illustrative example, we wish to calculate the combined and effective diffusivities of cumene in a mixture of benzene and cumene at 1 atm total pressure and 510 °C within the pores of a typical TCC (Thermofor Catalytic Cracking) catalyst bead. For our present purposes, the approximation to the combined diffusivity given by equation 12.2.8 will be sufficient because we will see that the Knudsen diffusion term is the dominant factor in determining the combined diffusivity. 

Acidic micro- and mesoporous materials, and in particular USY type zeolites, are widely used in petroleum refinery and petrochemical industry. Dealumination treatment of Y type zeolites referred to as ultrastabilisation is carried out to tune acidity, porosity and stability of these materials [1]. Dealumination by high temperature treatment in presence of steam creates a secondary mesoporous network inside individual zeolite crystals. In view of catalytic applications, it is essential to characterize those mesopores and to distinguish mesopores connected to the external surface of the zeolite crystal from mesopores present as cavities accessible via micropores only [2]. Externally accessible mesopores increase catalytic effectiveness by lifting diffusion limitation and facilitating desorption of reaction products [3], The aim of this paper is to characterize those mesopores by means of catalytic test reaction and liquid phase breakthrough experiments. 

Spiro [27] has derived quantitative expressions for the catalytic effect of electron conducting catalysts on oxidation-reduction reactions in solution in which the catalyst assumes the Emp imposed on it by the interacting redox couples. When both partial reaction polarization curves in the region of Emp exhibit Tafel type kinetics, he determined that the catalytic rate of reaction will be proportional to the concentrations of the two reactants raised to fractional powers in many simple cases, the power is one. On the other hand, if the polarization curve of one of the reactants shows diffusion-controlled kinetics, the catalytic rate of reaction will be proportional to the concentration of that reactant alone. Electroless metal deposition systems, at least those that appear to obey the MPT model, may be considered to be a special case of the general class of heterogeneously catalyzed reactions treated by Spiro. 

Microbes tend to form flocks as they grow, into which nutrients and dissolved oxygen must diffuse. The rate of growth thus depends on the diffusional effectiveness. This topic is developed by Atkinson (1974). Similarly enzymes immobilized in gel beads, for instance, have a reduced catalytic effectiveness analogous to that of porous granular catalysts that are studied in Chapter 7. For the M-M equation this topic is touched on in problems P8.04.15 and P8.04.16. 

The oxidation of compound A according to the reaction A - B is to be conducted over spherical catalytic particles of radius rp = 0.4 cm. The concentration distribution of A within each particle is described by the relation C(r) = 4 x 10 4r2 mol/cm5, where r is the radial position within the particle. Given that the effective diffusivity Dctt = (1007i) 1 cm2/s, find the rate of the chemical reaction. 

The major results of this study are consistent with a simple picture of mordenite catalysts. An increase in effective pore diameter, whether by extraction or exchange, will increase the rate of transport of reactant and product molecules to and from the active sites. However, aluminum ions are necessary for catalytic activity as aluminum is progressively removed by acid extraction, the number of active sites and the initial activity decrease. Coke deposition is harmful in two ways coke formation as the reaction proceeds will cause a decrease in effective pore diameter and effective diffusivity, and coke deposited on active sites will result in a chemical deactivation as well. 

SBY, yet the HDN activities of the catalysts are almost the same, especially for Mo-Ni / Zr-Si-Al catalyst. It is well known that not only surface chemistry of the support but also geometrical factors, like the surface area and pore-size distribution, are of major importance for performance of HDN catalyst. The pores are not only paths for reactants and products but also influence the deposition of the active metals during preparation. Mo-Ni/Zr-Si-Al catalyst has bigger surface area (over 600 M2/g) than SBY(240 M2/g), from the point of effective diffusivity, Zr-Si-Al is better than SBY. If the acidity of Zr-Si-Al support was increased properly by some modification methods, the synthesis samples would be a good HDN catalytic materials. 

Several other low temperature investigations, two in air (41, 55) and two in steam (37,44) > are interesting from the standpoint of showing the complications that arise when diffusion, catalysis, and product inhibition of the surface become important. Long and Sykes (46, 47) have studied catalytic effects for C -f H20 and C -f C02 reactions and propose slightly different mechanisms for catalysis by transition metals and by alkali metals. 

Information relating to the diffusion of metal-bearing compounds in catalytic materials at reaction conditions has been obtained indirectly through classic diffusion and reaction theory. Shah and Paraskos (1975) calculated effective diffusitivities of 7 x 10-8 and 3 x 10-8 cm2/sec for V and Ni compounds in reduced Kuwait crude at 760°F. These low values may be indicative of a small-pore HDS catalyst. In contrast, Sato et al. (1971) report that the effective diffusivity of vanadium compounds was one-tenth that of the nickel compounds on the basis of metal deposition profiles in aged catalysts. This large difference may be influenced by relative adsorption strengths not explicitly considered in their analysis. 

Hydrides. According to X-ray and neutron diffraction and metallographic studies of the Nb-H system,524 the H may be considered a lattice gas with phase transitions. In the a-, a -, j6-, and -phases of the system, H occupies tetrahedral interlattice positions. Whereas direct reaction between niobium metal and hydrogen occurs only after repeated activation of the metal by hydrogen absorption at ca. 7 atm and 350 °C, NbH2 is formed at temperatures as low as 22 °C in mixtures of LaNi5H6 7 and Nb.525 The extraordinary catalytic effect of the lanthanum-nickel complex is attributed to the presence of surface-absorbed atomic hydrogen species which are able to diffuse into the niobium lattice. There has been a review of the T a-H system.526... 

The effective diffusivity Dn decreases rapidly as carbon number increases. The readsorption rate constant kr n depends on the intrinsic chemistry of the catalytic site and on experimental conditions but not on chain size. The rest of the equation contains only structural catalyst properties pellet size (L), porosity (e), active site density (0), and pore radius (Rp). High values of the Damkohler number lead to transport-enhanced a-olefin readsorption and chain initiation. The structural parameters in the Damkohler number account for two phenomena that control the extent of an intrapellet secondary reaction the intrapellet residence time of a-olefins and the number of readsorption sites (0) that they encounter as they diffuse through a catalyst particle. For example, high site densities can compensate for low catalyst surface areas, small pellets, and large pores by increasing the probability of readsorption even at short residence times. This is the case, for example, for unsupported Ru, Co, and Fe powders. 

Instead, they proposed a time on stream theory to model the catalyst deactivation. However, in an earlier work by Voorhies (2), a linear correlation between conversion and coke on catalyst for fixed-bed catalytic cracking was derived. Rudershausen and Watson (3) also observed the similar behavior. Coke on catalyst can reduce the activity by covering the active sites and blocking the pores. The effects of pore size on catalyst performance during hydrotreating coal oils in trickle-bed reactors have been studied experimentally by Ahmed and Crynes (4) and by Sooter (5). The pore size effects in other studies are also reported 7, 8). Prasher et al. (9) observed that the effective diffusivities of oils in aged catalysts were severely reduced by coke deposition. 

The main reaction i.e, benzene hydrogenation occuring inside porous Ni-catalyst pellets is accompanied by poisoning reaction in which the thiophene presented in the feed stream reacts irtevcrsibly with the catalytic active sites. An analysis was made assuming isothermal behaviour [7], the same effective diffusivity for reactant and poison and that the steady-state continuity equation represents a good approximation at all times [8,9]. Under these conditions the mass balances for benzene, thiophene and catalyst activity are... 

Production of larga crystals. The effective diffusivity of these products would be low and unfavorable for their use in catalytic reactions. 

The rate of solute diffusion in liquids in porous materials becomes observably lower than would be expected from Equation 3.27 when the solute molecular size becomes large with respect to the pore size. This phenomena can be important for catalytic processing of heavy liquid petroleum fractions [25]. In the case of liquid transport through finely porous materials, the effective diffusivity can be expressed as [26]... 

A quantitative description of heterogeneous catalytic reactors for design, scaling-up, control or optimization purposes requires several parameters. Some of them, including the effective diffusivity and some parameters for the transport models and also the intrinsic chemical rate, should be determined in special experiments. 

Some coals contain an ash in addition to carbon, moisture, and volatiles. To obtain a conservative estimate, one should assume that a porous ash shell is retained during the burning of the combustible material. This ash may, of course, have a catalytic effect on the heterogeneous carbon combustion reactions however, it is a cause for additional diffusion resistance. 

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. 

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