Reaction rates within pore structure

During the last fifteen years there has developed a fairly complete theory of reaction rates within the porous structure of solid catalysts. This theory not only gives us a physical picture of the phenomena occurring within catalyst pores but also provides a mathematical framework which quantitatively describes the phenomena. The results of the theory show that even the most fundamental properties of a catalyst may be influenced by its physical structure. Two catalysts, chemically identical, but having pores of different size, may have different activities, different selectivities, different temperature coefficients of reaction rate, and catalyst poisons may affect the two catalysts in quite different ways. The purpose of this paper is to describe the physical and mathematical picture which leads to these conclusions. 

When diffusion and reaction occur simultaneously within a porous solid structure, concentration gradients of reactant and product species are established. If the various diffusional processes discussed in Section 12.2 are rapid compared with the chemical reaction rate, the entire accessible internal surface of the catalyst will be effective in promoting reaction because the reactant molecules will spread essentially uniformly throughout the pore structure, before they have time to react. Here only a small concentration gradient will exist between the exterior and interior of the particle, and there will be diffusive fluxes of reactant molecules in and product molecules out that suffice to balance the reaction rate within the particle. In... 

Ammonium salts of the zeolites differ from most of the compounds containing this cation discussed above, in that the anion is a stable network of A104 and Si04 tetrahedra with acid groups situated within the regular channels and pore structure. The removal of ammonia (and water) from such structures has been of interest owing to the catalytic activity of the decomposition product. It is believed [1006] that the first step in deammination is proton transfer (as in the decomposition of many other ammonium salts) from NH4 to the (Al, Si)04 network with —OH production. This reaction is 90% complete by 673 K [1007] and water is lost by condensation of the —OH groups (773—1173 K). The rate of ammonia evolution and the nature of the residual product depend to some extent on reactant disposition [1006,1008]. 

This section is concerned with analyses of simultaneous reaction and mass transfer within porous catalysts under isothermal conditions. Several factors that influence the final equation for the catalyst effectiveness factor are discussed in the various subsections. The factors considered include different mathematical models of the catalyst pore structure, the gross catalyst geometry (i.e., its apparent shape), and the rate expression for the surface reaction. 

The reactor feed mixture was "prepared so as to contain less than 17% ethylene (remainder hydrogen) so that the change in total moles within the catalyst pore structure would be small. This reduced the variation in total pressure and its effect on the reaction rate, so as to permit comparison of experiment results with theoretical predictions [e.g., those of Weisz and Hicks (61)]. Since the numerical solutions to the nonisothermal catalyst problem also presumed first-order kinetics, they determined the Thiele modulus by forcing the observed rate to fit this form even though they recognized that a Hougen-Watson type rate expression would have been more appropriate. Hence their Thiele modulus was defined as... 

If the two competing reactions have the same concentration dependence, then the catalyst pore structure does not influence the selectivity because at each point within the pore structure the two reactions will proceed at the same relative rate, independent of the reactant concentration. However, if the two competing reactions differ in the concentration dependence of their rate expressions, the pore structure may have a significant effect on the product distribution. For example, if V is formed by a first-order reaction and IF by a second-order reaction, the observed yield of V will increase as the catalyst effectiveness factor decreases. At low effectiveness factors there will be a significant gradient in the reactant concentration as one moves radially inward. The lower reactant concentration within the pore structure would then... 

Amorphous carbon comprises various combinations of carbon atoms. Charcoalis a typical amorphous form of carbon and is used as a major component of black powder and ballistic modifiers of rocket propellants. Charcoal contains a large number of tiny pores and the total surface area within the structure is approximately 1-3 m mg This surface area plays a significant role as a catalytic surface in various chemical reactions. It is well known that the burning rate of black powder is very fast because of the large surface area of the carbon structure. 

It will be demonstrated in this section that a narrow pore structure limits the reaction rate to an extent which casues the reaction rate to be either proportional to the square root of the specific surface area (per unit mass) or independent of it, depending on the mode of diffusion within the pore structure. Lest this departure of the reaction rate from direct proportionality with specific surface area might be thought to be accounted for in terms of a non-uniform distribution of surface energy over the catalyst surface, it should be pointed out that such in situ heterogeneity is usually only a small fraction of the total chemically active surface and cannot therefore explain the observed effects. 

The porous structure of either a catalyst or a solid reactant may have a considerable influence on the measured reaction rate, especially if a large proportion of the available surface area is only accessible through narrow pores. The problem of chemical reaction within porous solids was first considered quantitatively by Thiele [1] who developed mathematical models describing chemical reaction and intraparticle diffusion. Wheeler [2] later extended Thiele s work and identified model parameters which could be measured experimentally and used to predict reaction rates in... 

Three obvious models which could describe the observed reaction rate are (a) concentration equilibrium between all parts of the intracrystalline pore structure and the exterior gas phase (reaction rate limiting), (b) equilibrium between the gas phase and the surface of the zeolite crystallites but diffusional limitations within the intracrystalline pore structure, and (c) concentration uniformity within the intracrystalline pore structure but a large difference from equilibrium at the interface between the zeolite crystal (pore mouth) and the gas phase (product desorption limitation). Combinations of the above may occur, and all models must include catalyst deactivation. 

For gas-solid heterogeneous reactions particle size and average pore diameter will influence the reaction rate per unit mass of solid when internal diffusion is a significant factor in determining the rate. The actual mode of transport within the porous structure will depend largely on the pore diameter and the pressure within the reactor. Before developing equations which will enable us to predict reaction rates in porous solids, a brief consideration of transport in pores is pertinent. 

The internal structure, comprising pores and surface area, is important for making the active catalytic sites accessible to the reactant molecules. The location of the active species is important for minimizing diffusional resistance since reactants must diffuse within the particle to the active sites and products must diffuse away. Finally, high catalytic surface area and high dispersion of active species are advantageous for maximum reaction rate and utilization of the catalytic components. 

The support has an internal pore structure (i.e., pore volume and pore size distribution) that facilitates transport of reactants (products) into (out of) the particle. Low pore volume and small pores limit the accessibility of the internal surface because of increased diffusion resistance. Diffusion of products outward also is decreased, and this may cause product degradation or catalyst fouling within the catalyst particle. As discussed in Sec. 7, the effectiveness factor Tj is the ratio of the actual reaction rate to the rate in the absence of any diffusion limitations. When the rate of reaction greatly exceeds the rate of diffusion, the effectiveness factor is low and the internal volume of the catalyst pellet is not utilized for catalysis. In such cases, expensive catalytic metals are best placed as a shell around the pellet. The rate of diffusion may be increased by optimizing the pore structure to provide larger pores (or macropores) that transport the reactants (products) into (out of) the pellet and smaller pores (micropores) that provide the internal surface area needed for effective catalyst dispersion. Micropores typically have volume-averaged diameters of 50 to... 

The nature and arrangement of the pores determine transport within the interior porous structure of the catalyst pellet. To evaluate pore size and pore size distributions providing the maximum activity per unit volume, simple reactions are considered for which the concept of the effectiveness factor is applicable. This means that reaction rates can be presented as a function of the key component. A only, hence RA(CA). Various systems belonging to this category have been discussed in Chapters 6 and 7. The focus is on gaseous systems, assuming the resistance for mass transfer from fluid to outer catalyst surface can be neglected and the effectiveness factor does not exceed unity. The mean reaction rate per unit particle volume can be rewritten as... 

Many reactions taking place within catalyst or absorbent pellets in industrial plants are diffusion-limited. Under the typical operating conditions for many absorbents, diffusion of gases into the porous solid occurs in the Knudsen regime. In such circumstances the rate of gas pick-up of these materials is strongly dependent on the pore structure. The pore structure for absorbent pellets that will deliver the most efficient operation of an absorbent bed requires a pervasive system of macropores which provide rapid transport of the gas flux into the centre of the pellet. A network of ramified mesopores branching off the macropores then provides extensive surface area for absorption of gas molecules. Therefore, when manufacturing an absorbent it is necessary to be able to determine the spatial distribution of the macropore network in a product to ensure that the pore structure is the most appropriate for the peirticular duty for which it is intended. 

The sin >lcst flue gas desulfurisation technology is furnace injection, where a dry sorbent is injected into the upper part of the furnace to react with the SO2 in the flue gas. The finely grained sorbent is distributed quickly and evenly over the entire cross section in the upper part of the furnace in a location where the teiiq>erature is in the range of 750-12 50 C. Commercially available and cheap limestone (CaC03) or hydrated lime (Ca(OH)j) is used as sorbent. The sorbent reacts with SO2 and O2 to form CaS04. Below 750 C the reaction rate is too low. At temperatures over 1250 C the surface of the sorbent will be sintered, and the structure of the pores will be destructed, reducing the active surface area, The major part of S02-rcmoval takes place within 1 to 2 seconds. 

In view of evidence such as that in Fig. 8-5, it is unlikely that detailed quantitative descriptions of the void structure of solid catalysts will become available. Therefore, to account quantitatively for the variations in rate of reaction with location within a porous catalyst particle, a simplified model of the pore structure is necessary. The model must be such that diffusion rates of reactants through the void spaces into the interior surface can be evaluated. More is said about these models in Chap. 11. It is sufficient here to note that in all the widely used models the void spaces are simulated as cylindrical pores. Hence the size of the void space is interpreted as a radius 2 of a cylindrical pore, and the distribution of void volume is defined in terms of this variable. However, as the example of the silver, catalyst indicates, this does not mean that the void spaces are well-defined cylindrical pores. 

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