Distribution functions porous catalysts

Pore diffusion can be increased by choosing a catalyst with the proper geometry, in particular the pellet size and pore structure. Catalyst size is obvious (r if pore diffusion limited for the same total surface area). The diameter of pores can have a marked influence on r) because the diffusion coefficient of the reactant Da witl be a function of dp if molecular flow in the pore dominates. Porous catalysts are frequently designed to have different distributions of pore diameters, sometimes with macropores to promote diffusion into the core of the catalyst and micropores to provide a high total area. 

Most of the adsorbents used in the adsorption process are also useful to catalysis, because they can act as solid catalysts or their supports. The basic function of catalyst supports, usually porous adsorbents, is to keep the catalytically active phase in a highly dispersed state. It is obvious that the methods of preparation and characterization of adsorbents and catalysts are very similar or identical. The physical structure of catalysts is investigated by means of both adsorption methods and various instrumental techniques derived for estimating their porosity and surface area. Factors such as surface area, distribution of pore volumes, pore sizes, stability, and mechanical properties of materials used are also very important in both processes—adsorption and catalysis. Activated carbons, silica, and alumina species as well as natural amorphous aluminosilicates and zeolites are widely used as either catalyst supports or heterogeneous catalysts. From the above, the following conclusions can be easily drawn (Dabrowski, 2001) ... 

The computer-reconstructed catalyst is represented by a discrete volume phase function in the form of 3D matrix containing information about the phase in each volume element. Another 3D matrix defines the distribution of active catalytic sites. Macroporosity, sizes of supporting articles and the correlation function describing the macropore size distribution are evaluated from the SEM images of porous catalyst (Koci et al., 2006 Kosek et al., 2005). Spatially 3D reaction-diffusion system with low concentrations of reactants and products can be described by mass balances in the form of the following partial differential equations (Koci et al., 2006, 2007a). For gaseous components ... 

The macro-porosity emacro and the correlation function corresponding to the macro-pore size distribution of the washcoat were evaluated from the SEM images of a typical three-way catalytic monolith, cf. Fig. 25. The reconstructed medium is represented by a 3D matrix and exhibits the same porosity and correlation function (distribution of macro-pores) as the original porous catalyst. It contains the information about the phase at each discretization point— either gas (macro-pore) or solid (meso-porous Pt/y-Al203 particle). In the first approximation, no difference is made between y-Al203 and Ce02 support, and the catalytic sites of only one type (Pt) are considered with uniform distribution. 

Distribution functions are an important statistical tool, and they are used dux>ughout the field of kinetics and reactor analysis. Distribution functions reappear in Chapter 9, as a means of characterizing porous catalysts, and in Chapter 10, as a means of describing fluid flow in nonideal reactors. 

The characterization of the flow in existing DPF materials has been assessed by experiments and macroscopic continuum flow in porous media approaches. However, when it comes to material design it is essential to employ flow simulation techniques in geometrically realistic representations of DPF porous media. Some first applications were introduced in Konstandopoulos (2003) and Muntean et al. (2003) and this line of research is especially important for the development of new filter materials, the optimization of catalyst deposition inside the porous wall and for the design of gradient-functional filter microstructures where multiple functionalities in terms of particle separation and catalyst distribution (for combined gas and particle emission control) can be exploited. 

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... 

Feng, Kostrov and Stewart (1974) reported multicomponent diffusion data for gaseous mixtures of helium (He), nitrogen (N2) and methane (CH4) through an extruded platinum-alumina catalyst as functions of pressure (1 to 70 atm), temperature (300 to 390 K), and terminal compositions. The experiments were designed to test several models of diffusion in porous media over the range between Knudsen and continuum diffusion in a commercial catalyst (Sinclair-Engelhard RD-150) with a wide pore-size distribution. 

A wide variety of analytical probes are used to study, characterize and monitor catalysts and catalyst surfaces. Our intent here is to discuss some of the more common and routine techniques. Much more detail and many more techniques can be found in specialized books 33, 32, 27, 12]. A catalyst functions through the highly specific interactions the active sites have with the reactants. The catalyst might be a metal dispersed on an inert carrier, a polycrystalline or amorphous mixture of metal oxides, or a zeolite (a crystalline and highly porous oxide). The experimentalist is typically interested in the catalyst composition, structure of the catalyst, distribution of active sites, presence of poisons/impurities after the catalyst has been used, and number of active sites parameters that influence the catalytic activity. 

---