Diffusion in catalyst pellets

Vrentas, JS Duda, JL, Diffusion in Polymer-Solvent Systems, in. Construction of Deborah Number Diagrams, Journal of Polymer Science Polymer Physics Edition 15,441,1977. Wakao, N Smith, JM, Diffusion in Catalyst Pellets, Chemical Engineering Science 17, 825, 1962. 

In connection with multiphase diffusion another poorly understood topic should be mentioned—namely, the diffusion through porous media. This topic is of importance in connection with the drying of solids, the diffusion in catalyst pellets, and the recovery of petroleum. It is quite common to use Fick s laws to describe diffusion through porous media fJ14). However, the mass transfer is possibly taking place partly by gaseous diffusion and partially by liquid-phase diffusion along the surface of the capillary tubes if the pores are sufficiently small, Knudsen gas flow may prevail (W7, Bl). 

Wakao N, Smith JM (1962) Diffusion in catalyst pellets, Chem Eng Sci 17 825-834... 

The importance of diffusion in catalyst pellets can often be determined by measuring the effect of pellet size on the observed reaction rate. In this exercise, consider an irreversible first-order reaction occurring in catalyst pellets where the surface concentration of reactant A is C s = 0.15 M. 

S.C. Reyes and E. Iglesia, Effective diffusivities in catalyst pellets New model porous structures and transport simulation techniques, J. Catal. 129 457 (1991). 

There are a number of books that discuss internal diffusion in catalyst pellets however, one of the first books that should be consulted on this and other topics on heterogeneous catalysis is... 

L. B. Rothfeld, Gaseous Counter Diffusion in Catalyst Pellets, ... 

Mesoscale Modeling for Reaction-Diffusion in Catalyst Pellet 296... 

H. Hofmann Industrial process kinetics and parameter estimation, Adv.Chem.Ser. 109(1972)519-534 /2/ P. Trambouze, H. van Landeghem and J.P. Wauquier Les reac-teurs chimiques. Edition Technip, Paris 1984 /3/ H. Hofmann, G. Emig and W. Rdder The use of an integral reactor with sidestream-analysis for the investigation of complex reactions, EFCE Publ.Ser. 37(1984)4 19-426 /4/ S. Yagi and D. Kunii Studies on the effective thermal conductivities in packed beds, AIChE J. (1957)373-381 /5/ D. Kunii and J.M. Smith Heat transfer characteristics of porous rocks, AIChE J. (1960)71-78 /6/ N. Wakao and J.M. Smith Diffusion in catalyst pellets, Chem.Eng.Sci. 17(1962)825-834... 

Unlike the diffusion in catalyst pellets, molecular as well as eddy (turbulent) diffusion causes the mass dispersion in fixed-beds. The effective molecular diffusivity may be obtained by simply multiplying the gas molecular diffusivity by the factor s/k, where the tortuosity factor k is often taken as 1.5. The theory on eddy diffusivity is not well established. Therefore, the effective diffusivities are often correlated in the following form ... 

C.T. Wang and J.M. Smith, Tortuosity Factors for Diffusion in Catalyst Pellets, AICHE Journal (1983) 132-136. 

Despite the very restricted circumstances In which these equations properly describe the dynamical behavior, they are the starting point for almost all the extensive literature on the stability of steady states in catalyst pellets. It is therefore Interesting to examine the case of a binary mixture at the opposite limit, where bulk diffusion controls, to see what form the dynamical equations should take in a coarsely porous pellet. 

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. 

Obviously, the structure of a catalyst surface in any reaction system is important since it defines the catalyst itself. In residuum processing the pore structure is as critical. As shown in the following section, the pore structure influences the diffusion characteristics of metal-bearing molecules and thus the spatial distribution of metal deposits in catalyst pellets. The spatial distribution in turn affects the activity of the catalyst and the useful life of the reactor bed. 

While catalytic HDM results in a desirable, nearly metal-free product, the catalyst in the reactor is laden with metal sulfide deposits that eventually result in deactivation. Loss of catalyst activity is attributed to both the physical obstruction of the catalyst pellets pores by deposits and to the chemical contamination of the active catalytic sites by deposits. The radial metal deposit distribution in catalyst pellets is easily observed and understood in terms of the classic theory of diffusion and reaction in porous media. Application of the theory for the design and development of HDM and HDS catalysts has proved useful. Novel concepts and approaches to upgrading metal-laden heavy residua will require more information. However, detailed examination of the chemical and physical structure of the metal deposits is not possible because of current analytical limitations for microscopically complex and heterogeneous materials. Similarly, experimental methods that reveal the complexities of the fine structure of porous materials and theoretical methods to describe them are not yet... 

Metal deposition in hydrotreating of heavy oils is one of the most important phenomenon causing catalyst deactivation. Present work focuses on the modeling of hydrodemetallisation catalyst deactivation by model compound vanadyl-tetraphenylporphyrin. Intrinsic reaction kinetics, restrictive diffusion and the changing catalyst porous texture are the relevant phenomena to describe this deactivation process. The changing catalyst porous texture during metal depositon can be described successfully by percolation concepts. Comparison of simulated and experimental metal deposition profiles in catalyst pellets show qualitative agreement. 

The general approach for modelling catalyst deactivation is schematically organised in Figure 2. The central part are the mass balances of reactants, intermediates, and metal deposits. In these mass balances, coefficients are present to describe reaction kinetics (reaction rate constant), mass transfer (diffusion coefficient), and catalyst porous texture (accessible porosity and effective transport properties). The mass balances together with the initial and boundary conditions define the catalyst deactivation model. The boundary conditions are determined by the axial position in the reactor. Simulations result in metal deposition profiles in catalyst pellets and catalyst life-time predictions. 

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. 

Luss, D., Diffusion—Reactioninteractions in Catalyst Pellets p. 239 in Chemical Reaction and Reactor Engineering, Marcel Dekker, New York, 1987. 

Intraparticle Diffusion and External Mass-Transfer Resistance For typical industrial conditions, external mass transfer is important only if there is substantial intraparticle diffusion resistance. This subject has been discussed by Luss, Diffusion-Reaction Interactions in Catalyst Pellets, in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Dekker, 1987. This, however, may not be the case for laboratory conditions, and care must be exerted in including the proper data interpretation. For instance, for a spherical particle with both external and internal mass-transfer limitations and first-order reaction, an overall effectiveness factor r, can be derived, indicating the series-of-resistances nature of external mass transfer followed by intraparticle diffusion-reaction ... 

Note that in the limit of external diffusion control, the activation energy 0b,—>0, as can be shown when substituting Eq. (7-110) inEq. (7-108). For more details on how to represent the combined effect of external and intraparticle diffusion on effectiveness factor for more complex systems, see Luss, "Diffusion-Rection Interactions in Catalyst Pellets. Heat-Transfer Resistances A similar analysis regarding external and intraparticle heat-transfer limitations leads to temperature... 

Vanadium deposition profiles in catalyst pellets have been determined by various researchers (14-30). For this purpose porphyrinic model compounds and industrial feedstocks are used. The used catalyst are mainly conventional hydrotreating catalysts with narrow pores. Therefore, metal deposition profiles show mainly deposition in the outer shells of the catalyst pellets (M- or U-shaped profiles), indicating that the metal deposition process is diffusion limited. 

To describe the mass diffusion processes within the pores in catalyst pellets we usually distinguish three fundamentally different types of mass diffusion mechanisms [64, 49, 48] ... 

Our examination of diffusion and reaction in catalyst pellets. showed that many case.s the reactant concentration near the center of the particle was virtual zero. If this condition were to occur in a hydrogel, the cells at the center would di Consequently, the gel thickne.ss needs to be designed to allow rapid transport oxygen. 

Luss. D.. "Diffusion—Reaction Interactions in Catalyst Pellets," p. 239 in Clierri-iful Retictiim anj Rem tar Eagtiteeiing. New York Marcel Dekker. 1987. 

In our laboratories extensive studies on the catalytic hydrogenation of aromatic nitrocompounds, as an example of the catalytic three-phase reactions, have been carried out in reactors of different types - e g. see [8-10]. In all cited cases the time consumed for kinetic investigations had a very significant contribution to the total experimental effort [11-13]. Particularly for the hydrogenation over palladium on alumina catalyst, the experimental investigations leading to the detection and quantitative description of internal diffusion resistances in catalyst pellets have taken a lot of time. 

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