Catalytic multicomponent diffusion

When modeling phenomena within porous catalyst particles, one has to describe a number of simultaneous processes (i) multicomponent diffusion of reactants into and out of the pores of the catalyst support, (ii) adsorption of reactants on and desorption of products from catalytic/support surfaces, and (iii) catalytic reaction. A fundamental understanding of catalytic reactions, i.e., cleavage and formation of chemical bonds, can only be achieved with the aid of quantum mechanics and statistical physics. An important subproblem is the description of the porous structure of the support and its optimization with respect to minimum diffusion resistances leading to a higher catalyst performance. Another important subproblem is the nanoscale description of the nature of surfaces, surface phase transitions, and change of the bonds of adsorbed species. 

Rieckmann and Keil (1997) introduced a model of a 3D network of interconnected cylindrical pores with predefined distribution of pore radii and connectivity and with a volume fraction of pores equal to the porosity. The pore size distribution can be estimated from experimental characteristics obtained, e.g., from nitrogen sorption or mercury porosimetry measurements. Local heterogeneities, e.g., spatial variation in the mean pore size, or the non-uniform distribution of catalytic active centers may be taken into account in pore-network models. In each individual pore of a cylindrical or general shape, the spatially ID reaction-transport model is formulated, and the continuity equations are formulated at the nodes (i.e., connections of cylindrical capillaries) of the pore space. The transport in each individual pore is governed by the Max-well-Stefan multicomponent diffusion and convection model. Any common type of reaction kinetics taking place at the pore wall can be implemented. 

At present two models are available for description of pore-transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[4,5] and the Dusty Gas Model (DGM)[6,7]. Both models permit combination of multicomponent transport steps with other rate processes, which proceed simultaneously (catalytic reaction, gas-solid reaction, adsorption, etc). These models are based on the modified Maxwell-Stefan constitutive equation for multicomponent diffusion in pores. One of the experimentally performed transport processes, which can be used for evaluation of transport parameters, is diffusion of simple gases through porous particles packed in a chromatographic column. 

One other textbook deserves a special mention. The book by G. Froment and K. Bischoff, Chemical Reactor Analysis and Design, aims not to be easy but elegant, introducing the reader directly to the advanced theories of reaction engineering and to the frontiers of research by including complex reaction networks, advanced models for catalytic systems, multicomponent diffusion, and the surface renewal theory for gas-liquid contact. The book is excellent for students who wish to become scientists in chemical reaction engineering. 

Work in the area of simultaneous heat and mass transfer has centered on the solution of equations such as 1—18 for cases where the stmcture and properties of a soHd phase must also be considered, as in drying (qv) or adsorption (qv), or where a chemical reaction takes place. Drying simulation (45—47) and drying of foods (48,49) have been particularly active subjects. In the adsorption area the separation of multicomponent fluid mixtures is influenced by comparative rates of diffusion and by interface temperatures (50,51). In the area of reactor studies there has been much interest in monolithic and honeycomb catalytic reactions (52,53) (see Exhaust control, industrial). Eor these kinds of appHcations psychrometric charts for systems other than air—water would be useful. The constmction of such has been considered (54). 

In PEMFCs, the membrane electrode assembly (MEA, Eig. 15.2a) is a multilayer sandwich composed of catalytic layers (CLs) where electrochemical reactions take place, gas-diffusion media providing access of gases to the CLs, and a proton exchange membrane (PEM) such as Nafion . The CL is a multiphase multicomponent medium comprising ... 

In the preceding section, we explained that the bulk diffusion of oxide ion plays an important role in the enhancement of the catalytic activity of the multicomponent bismuth molybdate systems. Here, another important role of the oxide ion migration in increasing the stability of the catalyst system is introduced. 

Diffusion measurements under nonequilibrium conditions are more complicated due to the difficulties in ensuring well defined initial and boundary conditions. IR spectroscopy has proved to be a rather sensitive tool for studying simultaneously the intracrystalline concentration of different diffusants, including the occupation density of catalytic sites [28], By choosing appropriate initial conditions, in this way both co- and counterdiffusion phenomena may be followed. Information about molecular transport diffusion under the conditions of multicomponent adsorption may also be deduced from flow measurements [99], As in the case of single-component adsorption, the diffusivities arc determined by matching the experimental data (i.e. the time dependence of the concentration of the effluent or the adsorbent) to the corresponding theoretical expressions. 

Diffusivities are often measured under conditions which are far from those of catalytic reactions. Moreover, corresponding to their different nature, the various measuring techniques are limited to special ranges of application. The possibility of a mutual transformation of the various diffusivities would therefore be of substantial practical relevance. Since each of the coefficients of self-diffusion and transport diffusion in single-component and multicomponent systems refers to a particular physical situation, one cannot expect that the multitude of information contained in this set of parameters can in general be adequately reflected by a smaller set of parameters. Any correlation which might be used in order to reduce the number of free parameters must be based on certain model assumptions. 

Catalytic systems are inherently multicomponent. An attractive method for determining the difFusivities in multicomponent systems is Fourier transform (FT) PFG NMR spectroscopy, which allows the simultaneous determination of the self-difFusivities of the individual components in a. mixture. If the chemical shifts of the individual species are sufficiently different, the Fourier transform of the spin echo yields separate peaks for the various adsorbates, and then similar to normal PFG NMR the attenuation of the separate peaks with increasing applied field gradient intensity yields the self-diffusivities. Because the technique can also be applied at elevated temperatures, it provides the opportunity for in-situ diffusion measurements under reaction conditions. The experiment also yields the time dependence of the relative concentrations of the reactant and product molecules and thus the intrinsic reaction rate. 

Step 12. Use the thermal energy and mass balances for multicomponent reactive mixtures to analyze diffusion and chemical reaction in nonisothermal catalytic pellets. 

A recent review on intraparticle diffusion in multicomponent catalytic reactions is by Schneider [153]. 

Yu. F. Zuev, A. B. Mirgorodskaya, B. Z. Idiatullin, Structural properties of microheterogeneous surfactant-based catalytic system. Multicomponent self-diffusion NMR approach, Appl. magnetic resonance, 2004, 27, 489-500. 

For all steady-state applications, the Stefan velocity is identically zero (there is no etching or deposition in steady-state catalytic combustion). Given the ID dimensionality of the stagnation-flow problem, a full multicomponent transport approach for the diffusion velocities is computationally manageable ... 

Catalyst selection should be based on catalyst reactivity, reaction selectivity, and physical properties such as particle size, density, and resistance to attrition. For process development, heat and mass transfer phenomena together with reactivity and physical properties of catalysts must be taken into account. The catalytic process begins with gas reactant transferring to the catalyst outer surface and subsequent intraparticle diffusion of the reactant through the pores of the catalyst. Reactants then absorb onto the catalyst surface and react to form product. These products desorb from the surface, and, through intraparticle diffusion, the products exit from the pores and outer catalyst surface. Consider the example of the ammoxidation of propylene to produce acrylonotrile over multicomponent molybdenum/bismuth catalysts ... 

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