Diffusion in catalysts

For the first assumption, the value of Kw for the shift appears to be too high. It must be this high because it is necessary to make C02 appear while both C02 and CO are being consumed rapidly by methanation. The data may be tested to see if the indicated rate appears unreasonable from the standpoint of mass transfer to the gross catalyst surface. Regardless of the rate of diffusion in catalyst pores or the surface reaction rate, it is unlikely that the reaction can proceed more rapidly than material can reach the gross pill surface unless the reaction is a homogeneous one that is catalyzed by free radicals strewn from the catalyst into the gas stream. 

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. 

Thus, considering diffusion in pores leads to very similar results to those we obtained when describing diffusion in catalyst particles. 

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). 

Tortuosity Factors for Diffusion in Catalysts at 65 atm, as reported by Butt [39]... 

Thus far, however, the influence of diffusion in catalyst pores on the observed rates has been neglected. The method of incorporating this factor was indicated by Wheeler (57). For the exchange experiments, no corrections have to be made. For the equilibration experiments at relatively high temperatures, however, the data appear to be substantially modified. 

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

Information about transport diffusion in catalyst particles can also be deduced during the initial, unsteady state period of a permeation experiment. In this stage, the number of molecules passing the plug of catalyst per unit time will increase from zero until the rate of permeation characterizing the steady state behavior is attained. In the limit t - oo, the total amount of molecules which have permeated in the time interval 0... t is given by the relation [1,2, 12]... 

The TEOM is a promising tool for investigation of the influence of coke on adsorption and diffusion in catalysts. As a consequence of high flow rates of the carrier gas through the sample bed, the technique minimizes the external mass and heat transfer limitations in transient experiments without affecting the accuracy of the measurements. The data are not influenced by buoyancy and flow patterns, which are significant when conventional methods are used. 

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. 

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... 

A series of CoMo/Alumina-Aluminum Phosphate catalysts with various pore diameters was prepared. These catalysts have a narrow pore size distribution and, therefore, are suitable for studying the effect of pore structure on the deactivation of reaction. Hydrodesulfurization of res id oils over these catalysts was carried out in a trickle bed reactor- The results show that the deactivation of reaction can be masked by pore diffusion in catalyst particle leading to erro neous measurements of deactivation rate constants from experimental data. A theoretical model is developed to calculate the intrinsic rate constant of major reaction. A method developed by Nojcik (1986) was then used to determine the intrinsic deactivation rate constant and deactivation effectiveness factor- The results indicate that the deactivation effectiveness factor is decreased with decreasing pore diameter of the catalyst, indicating that the pore diffusion plays a dominant role in deactivation of catalyst. 

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

Hiramitsu Y, Sato H, Hosomi H, Aoki Y, Harada T, Sakiyama Y, Nakagawa Y, Kobayashi K, Hori M (2009) Influence of humidification on deterioration of gas diffusivity in catalyst layer on polymer electrolyte fuel cell. J Power Sources 195 435-444... 

In CSTRs the source of non-kinetic influences is often the recirculation rate. In principle this can be varied in a given reactor. All too often, however, the reactor is simply operated at its maximum recirculation rate and it is assumed that this yields ideal CSTR behaviour. Many procedures exist for calculating when diffusion or heat transfer effects are expected to cause distortions. None of these are better than the experimental test, and most are not as good. This is particularly true in the case of pore diffusion in catalysts. However, calculational methods can give an idea of whether trouble of this kind is to be expected, and encourage one to perform the experimental tests. 

In Chapter 1, Fyfe, Mueller, and Kokotailo describe the applications of solid-state NMR to the study of zeolite molecular sieve catalysts and related systems. Zeolites provide an apt arena in which to demonstrate the capabilities of modern techniques such as sample spinning, cross-polarization, and multidimensional correlation spectroscopy. In Chapter 2, Karger, and Pfeifer consider the question of molecular diffusion in catalyst systems. Applications of NMR techniques such as imaging, lineshape analysis, relaxation, pulsed field gradient echo spectroscopy, and NMR tracer exchange are described and compared with other, more traditional techniques such as radioactive tracing. In Chapter 3, Haw discusses the use of NMR to probe catalytic processes, showing how the combination of temperature control with novel NMR probes makes it possible to elucidate reaction mechanisms in situ. 

Table 7,2 Porosity and tortuosity factors for diffusion in catalysts.

Table 8.2 Computations Using Orthogonal Collocation Diffusion in Catalyst Particle...

Taking into account this estimation, Ostrovskii and Bukhavtsova [8] have considered the simplified model of reaction/diffusion in catalyst particle under capillary condensation. According to Equation (23.7), we can suppose that diffusion limitation inside the globule (Figure 23.1) is negligible, even in the case where it is filled with liquid. Then the diffusion/reaction equation has the form... 

An interesting approach to better diffusion in catalyst is also coating of microporous APO precursors on the mesoporous SBA-15 structure, bringing the weak acid-base characteristics to the resulting mesoporous materials, and that the acid-base properties of these materials can be modified by the aging treatment in glycol (162). 

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

---