Catalytic reaction models

J. W. Evans. Kinetic phase transitions in catalytic reaction models. Langmuir 7 2514-2519, 1991. 

Lyberatos, G., Kuszta, B. and Bailey, J. E., 1984, Discrimination and identification of dynamic catalytic reaction models via introduction of feedback. Chem. Engng Sci. 39, 739-750. 

Realistic analysis of fixed-bed reactor experiments requires calculation of interfacial states. Laboratory reactors are typically much shorter than full-scale units and operate with smaller axial velocities, producing significant departures of the iiiterfacial states from the measurable values in the mainstream fluid and consequent difficulties in establishing catalytic reaction models. Interfacial temperatures and partial pressures were calculated with jn and jo- and used in estimating reaction model parameters, in a landmark paper by Yoshida. Ramaswami. and Hougen (1962). Here we give an updated analysis of interfacial states in fixed-bed reactor operations for improved treatment of catalytic reaction data. 

Case Study 11.3 Gas-Solid (Catalytic) Reaction Modeling of a Complex... 

Real surfaces have point defects and steps while the interfaces in simulations are usually ideal. Defects play a very important role in electrochemical and catalytic reactions. Models need to be developed that are able to account for the electronic structure near these defects. First steps in this direction have been made [98, 99, 284]. 

Bowen, J.H., Gas-solid, non-catalytic reaction models, Trans. IChemE, 52. T282-T284 (1974). 

NakatsujI H 1987 Dipped adcluster model for chemisorptions and catalytic reactions on metal surface J. Chem. Phys. 87 4995-5001... 

NakatsujI H, Nakal H and Fukunishi Y 1991 Dipped adcluster model for chemisorptions and catalytic reactions on a metal surface Image force correction and applications to Pd-02 adclusters J. Chem. Phys. 95 640-7 NakatsujI H and Nakal H 1992 Dipped adcluster model study for the end-on chemisorption of O2 on an Ag surface Can. J. Chem. 70 404-8... 

NakatsujI H 1997 Dipped adcluster model for chemisorption and catalytic reactions Prog. Surf. Sci. 54 1... 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

Mechanistic Models. A general theory of the mechanism for the complete heterogeneous catalytic oxidation of low molecular weight vapors at trace concentrations in air does not exist. As with many catalytic reactions, however, certain observations have led to a general hypothesis (17). 

Reaction Kate. The kinetics for a single catalytic reaction can be modeled as... 

Several titanium(IV) complexes are efficient and reliable Lewis acid catalysts and they have been applied to numerous reactions, especially in combination with the so-called TADDOL (a, a,a, a -tetraaryl-l,3-dioxolane-4,5-dimethanol) (22) ligands [53-55]. In the first study on normal electron-demand 1,3-dipolar cycloaddition reactions between nitrones and alkenes, which appeared in 1994, the catalytic reaction of a series of chiral TiCl2-TADDOLates on the reaction of nitrones 1 with al-kenoyloxazolidinones 19 was developed (Scheme 6.18) [56]. These substrates have turned out be the model system of choice for most studies on metal-catalyzed normal electron-demand 1,3-dipolar cycloaddition reactions of nitrones as it will appear from this chapter. When 10 mol% of the catalyst 23a was applied in the reaction depicted in Scheme 6.18 the reaction proceeded to give a yield of up to 94% ee after 20 h. The reaction led primarily to exo-21 and in the best case an endo/ exo ratio of 10 90 was obtained. The chiral information of the catalyst was transferred with a fair efficiency to the substrates as up to 60% ee of one of the isomers of exo3 was obtained [56]. 

The development of methods for the kinetic measurement of heterogeneous catalytic reactions has enabled workers to obtain rate data of a great number of reactions [for a review, see (1, )]. The use of a statistical treatment of kinetic data and of computers [cf. (3-7) ] renders it possible to estimate objectively the suitability of kinetic models as well as to determine relatively accurate values of the constants of rate equations. Nevertheless, even these improvements allow the interpretation of kinetic results from the point of view of reaction mechanisms only within certain limits ... 

The kinetics of a complex catalytic reaction can be derived from the results obtained by a separate study of single reactions. This is important in modeling the course of a catalytic process starting from laboratory data and in obtaining parameters for catalytic reactor design. The method of isolation of reactions renders it possible to discover also some other reaction paths which were not originally considered in the reaction network. 

In a later publication, Kolbel et al. (K16) have proposed a less empirical model based on the assumption that the rate-determining steps for a slurry process are the catalytic reaction and the mass transfer across the gas-liquid interface. When used for the hydrogenation of carbon monoxide to methane, the process rate is expressed as moles carbon monoxide consumed per hour and per cubic meter of slurry ... 

Farkas and Sherwood (FI, S5) have interpreted several sets of experimental data using a theoretical model in which account is taken of mass transfer across the gas-liquid interface, of mass transfer from the liquid to the catalyst particles, and of the catalytic reaction. The rates of these elementary process steps must be identical in the stationary state, and may, for the catalytic hydrogenation of a-methylstyrene, be expressed by ... 

Such a model should take into account at least the following phenomena Mass transfer across gas-liquid interface, mass transfer to exterior particle surface, catalytic reaction, flow and axial mixing of gas phase, and flow and axial mixing of liquid phase. 

The effect of alkali presence on the adsorption of oxygen on metal surfaces has been extensively studied in the literature, as alkali promoters are used in catalytic reactions of technological interest where oxygen participates either directly as a reactant (e.g. ethylene epoxidation on silver) or as an intermediate (e.g. NO+CO reaction in automotive exhaust catalytic converters). A large number of model studies has addressed the oxygen interaction with alkali modified single crystal surfaces of Ag, Cu, Pt, Pd, Ni, Ru, Fe, Mo, W and Au.6... 

R.M. Lambert, F. Williams, A. Palermo, and M.S. Tikhov, Modelling alkali promotion in heterogeneous catalysis in situ electrochemical control of catalytic reactions, Topics in Catalysis 13, 91-98 (2000). 

The model postulates two significant resistances in series diffusion through the growing shell ( R.jyp) and polymerization at the catalyst surface (R(jat catalytic reaction resistance,... 

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