Pore 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. 

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. 

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. 

Note that this parameter has the same form as the Thiele number which occurs in the theory of diffusion/reac tion in catalyst pores. 

The work of Thiele (1939) and Zeldovich (1939) called attention to the fact that reaction rates can be influenced by diffusion in the pores of particulate catalysts. For industrial, high-performance catalysts, where reaction rates are high, the pore diffusion limitation can reduce both productivity and selectivity. The latter problem emerges because 80% of the processes for the production of basic intermediates are oxidations and hydrogenations. In these processes the reactive intermediates are the valuable products, but because of their reactivity are subject to secondary degradations. In addition both oxidations and hydrogenation are exothermic processes and inside temperature gradients further complicate secondary processes inside the pores. 

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

One must understand the physical mechanisms by which mass transfer takes place in catalyst pores to comprehend the development of mathematical models that can be used in engineering design calculations to estimate what fraction of the catalyst surface is effective in promoting reaction. There are several factors that complicate efforts to analyze mass transfer within such systems. They include the facts that (1) the pore geometry is extremely complex, and not subject to realistic modeling in terms of a small number of parameters, and that (2) different molecular phenomena are responsible for the mass transfer. Consequently, it is often useful to characterize the mass transfer process in terms of an effective diffusivity, i.e., a transport coefficient that pertains to a porous material in which the calculations are based on total area (void plus solid) normal to the direction of transport. For example, in a spherical catalyst pellet, the appropriate area to use in characterizing diffusion in the radial direction is 47ir2. 

A large number of analytical solutions of these equations appear in the literature. Mostly, however, they deal only with first order reactions. All others require solution by numerical or other approximate means. In this book, solutions of two examples are carried along analytically part way in P7.02.06 and P7.02.07. Section 7.4 considers flow through an external film, while Section 7.5 deals with diffusion and reaction in catalyst pores under steady state conditions. 

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). 

This sieve effect cannot be considered statically as a factor that only determines the amount of accessible acid groups in the resin in such a way that the boundary between the accessible and non-accessible groups would be sharp. It must be treated dynamically, i.e. the rates of the diffusion of reactants into the polymer mass must be taken into account. With the use of the Thiele s concept about the diffusion into catalyst pores, the effectiveness factors, Thiele moduli and effective diffusion coefficients can be determined from the effect of the catalyst particle size. The apparent rates of the methyl and ethyl acetate hydrolysis [490] were corrected for the effect of diffusion in the resin by the use of the effectiveness factors, the difference in ester concentration between swollen resin phase and bulk solution being taken into account. The intrinsic rate coefficients, kintly... 

If a transport parameter rc — CS/CL is defined, where Cs is the concentration of C at the catalyst surface, then Peterson134 showed that for gas-solid reactions t)c < rc, where c is the catalyst effectiveness factor for C. For three-phase slurry reactors, Reuther and Puri145 showed that rc could be less than t)C if the reaction order with respect to C is less than unity, the reaction occurs in the liquid phase, and the catalyst is finely divided. The effective diffusivity in the pores of the catalyst particle is considerably less if the pores are filled with liquid than if they are filled with gas. For finely divided catalyst, the Sherwood number for the liquid-solid mass-transfer coefficient based on catalyst particle diameter is two. 

An important application of metal nanoparticles is their use as catalysts on solid supports or in confined media. When the solution containing metal ions is in contact with a solid support, the ions can diffuse in the pores and adsorb on the surface. Therefore, the penetration of the ionizing radiation enables the in situ reduction of metal ions and then the further coalescence of metal atoms inside the confined volumes of porous materials, such as zeolites, alumino-silica-gels, colloidal oxides such as TiOj or polymeric membranes. 

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. 

Figure 1. Dimensions of Ring-Shaped Catalyst Particle with one Sealed End for studying Diffusion in Large Pores.

A catalyst is characterized as a substance which adsorbs reactant. When it is adsorbed it may be transported either by desorption into the pore space or by migration to an adjacent site on the surface. The contribution of surface diffusion must be added to the diffusion in the pore volume to obtain the total mass transport. 

When combined with a solute repulsion factor (1-X) eq 30 was found valid in the range of X below 0.2 using membranes whose pore sizes ranged from 45 to 300A (13). Satterfield, Colton and Pitcher on the other hand studied restricted diffusion in heterogeneous solid almina bead catalysts which possessed a pore radius of 16A, by unsteady diffusion and observed a more severe restriction of the solute diffusion in the pore (14). 

The apparent conversion rate measured as the rate of the formation of the final products is much lower than the rate of reaction (2) due to competition by reaction (4). A complete analysis of mass transfer should include consideration of diffusion (in the pores of the oxide catalyst and in the space between the grains) and of the accompanying reactions of radicals with different species in the gas phase and with surface active sites. This work is presently in progress, and here only a brief discussion is providedThe diffusion coefficient for methyl radicals at the conditions of our... 

Crystalline zeolites have provided a new method to control catalytic selectivity. Called shape selectivity, this control utilizes the restrictive consequences of the molecular size of the zeolite pores . Certain molecules, because of their size and shape, are constrained in their ability to enter or leave zeolite pores. Reactant selectivity occurs when only some of the reactants can diffuse into catalyst pores, for example, linear but not... 

Pore diffusion regime - Diffusion in the pores is the slowest step in this type of catalysis. Reaction takes place mainly on the external surface of the catalysts,... 

In the general case where the active material is dispersed through the pellet and the catalyst is porous, internal diffusion of the species within the pores of the pellet must be included. In fact, for many cases diffusion through catalyst pores represents the main resistance to mass transfer. Therefore, the concentration and temperature profiles inside the catalyst particles are usually not flat and the reaction rates in the solid phase are not constant. As there is a continuous variation in concentration and temperature inside the pellet, differential conservation equations are required to describe the concentration and temperature profiles. These profiles are used with intrinsic rate equations to integrate through the pellet and to obtain the overall rate of reaction for the pellet. The differential equations for the catalyst pellet are two point boundary value differential equations and besides the intrinsic kinetics they require the effective diffusivity and thermal conductivity of the porous pellet. 

As discussed in chapter 5, diffusion through catalyst pores represents a resistance to mass and heat transfer, which gives rise to concentration and temperature gradients within the catalyst pellet. This causes the rate of reaction in the solid phase to be different from that if the bulk phase conditions prevail inside the particle, and the rate of reaction should be integrated along the radius of the pellet to get the actual rate of reaction. 

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