Chemical reaction kinetics catalyst effects

All these factors are functions of the concentration of the chemical species, temperature and pressure of the system. At constant diffu-sionai resistance, the increase in the rate of chemical reaction decreases the effectiveness factor while al a constant intrinsic rate of reaction, the increase of the diffusional resistances decreases the effectiveness factor. Elnashaie et al. (1989a) showed that the effect of the diffusional resistances and the intrinsic rate of reactions are not sufficient to explain the behaviour of the effectiveness factor for reversible reactions and that the effect of the equilibrium constant should be introduced. They found that the effectiveness factor increases with the increase of the equilibrium constants and hence the behaviour of the effectiveness factor should be explained by the interaction of the effective diffusivities, intrinsic rates of reaction as well as the equilibrium constants. The equations of the dusty gas model for the steam reforming of methane in the porous catalyst pellet, are solved accurately using the global orthogonal collocation technique given in Appendix B. Kinetics and other physico-chemical parameters for the steam reforming case are summarized in Appendix A. 

In this work reactor modeling and experimentation have been combined to study the warm-up period of exhaust gas catalytic converters. The influence of structural modifications may be effectively studied numerically provided that an accurate model for the catalytic converter is available. Such a model can guide the converter design provided that the description of the chemical reaction kinetics is tuned for the catalyst at hand. 

These pioneers understood the interplay between chemical equiUbrium and reaction kinetics indeed, Haber s research, motivated by the development of a commercial process, helped to spur the development of the principles of physical chemistry that account for the effects of temperature and pressure on chemical equiUbrium and kinetics. The ammonia synthesis reaction is strongly equiUbrium limited. The equiUbrium conversion to ammonia is favored by high pressure and low temperature. Haber therefore recognized that the key to a successful process for making ammonia from hydrogen and nitrogen was a catalyst with a high activity to allow operation at low temperatures where the equiUbrium is relatively favorable. 

Kinetic investigation of the reaction of cotarnine and a few aromatic aldehydes (iV-methylcotarnine, m-nitrobenzaldehyde) with hydrogen eyanide in anhydrous tetrahydrofuran showed such differences in the kinetic and thermodynamic parameters for cotarnine compared to those for the aldehydes, and also in the effect of catalysts, so that the possibility that cotarnine was reacting in the hypothetical amino-aldehyde form could be completely eliminated. Even if the amino-aldehyde form is present in concentrations under the limit of spectroscopic detection, then it still certainly plays no pfi,rt in the chemical reactions. This is also expected by Kabachnik s conclusions for the reactions of tautomeric systems where the equilibrium is very predominantly on one side. 

Notice that in the region of fast chemical reaction, the effectiveness factor becomes inversely proportional to the modulus h2. Since h2 is proportional to the square root of the external surface concentration, these two fundamental relations require that for second-order kinetics, the fraction of the catalyst surface that is effective will increase as one moves downstream in an isothermal packed bed reactor. 

The analysis of simultaneous diffusion and chemical reaction in porous catalysts in terms of effective diffusivities is readily extended to geometries other than a sphere. Consider a flat plate of porous catalyst in contact with a reactant on one side, but sealed with an impermeable material along the edges and on the side opposite the reactant. If we assume simple power law kinetics, a reaction in which there is no change in the number of moles on reaction, and an isothermal flat plate, a simple material balance on a differential thickness of the plate leads to the following differential equation... 

In chemical equilibria, the energy relations between the reactants and the products are governed by thermodynamics without concerning the intermediate states or time. In chemical kinetics, the time variable is introduced and rate of change of concentration of reactants or products with respect to time is followed. The chemical kinetics is thus, concerned with the quantitative determination of rate of chemical reactions and of the factors upon which the rates depend. With the knowledge of effect of various factors, such as concentration, pressure, temperature, medium, effect of catalyst etc., on reaction rate, one can consider an interpretation of the empirical laws in terms of reaction mechanism. Let us first define the terms such as rate, rate constant, order, molecularity etc. before going into detail. 

The philosophy used to develop detailed chemical kinetic mechanisms for gas-phase reactions can, in principle, be extended to treat heterogeneous reactions, provided diffusion is also considered in the final analysis. Clearly, the problem in heterogeneous catalysis is considerably more complex because of the close proximity of a large number of atoms and their collective effect on reaction kinetics and mechanisms, and the inevitable variation of catalyst structure with time—for example, as a result of sintering and poisoning. 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

The model includes fundamental hydrocarbon conversion kinetics developed on fresh catalysts (referred to as start-of-cycle kinetics) and also the fundamental relationships that modify the fresh-catalyst kinetics to account for the complex effects of catalyst aging (deactivation kinetics). The successful development of this model was accomplished by reducing the problem complexity. The key was to properly define lumped chemical species and a minimum number of chemical reaction pathways between these lumps. A thorough understanding of the chemistry, thermodynamics, and catalyst... 

Of interest in applied kinetics is the study of chemical reactions taking place in flow systems which are hydrodynamically simple, so that the kinetics effects may be properly calculated. A simple example is the flow (with flat velocity profile v0 in the z direction) of a fluid through a circular tube the fluid is an inert material S containing a small quantity of substance A. The inside of the cylindrical tube is coated with a catalyst which converts A into B according to a first-order reaction, with k as reaction-rate constant. Let it then be desired to obtain the percentage of conversion after the fluid has flowed through the reactor tube of length L and radius R. 

The problem of calculating reaction rate is as yet unsolved for almost all chemical reactions. The problem is harder for heterogeneous reactions, where so little is known of the structures and energies of intermediates. Advances in this area will come slowly, but at least the partial knowledge that exists is of value. Rates, if free from diffusion or adsorption effects, are governed by the Arrhenius equation. Rates for a particular catalyst composition are proportional to surface area. Empirical kinetic equations often describe effects of concentrations, pressure, and conversion level in a manner which is valuable for technical applications. 

In several experiments, in particular the study by Temkin and co-workers [224] of the kinetics in ethylene oxidation, slow relaxations, i.e. the extremely slow achievement of a steady-state reaction rate, were found. As a rule, the existence of such slow relaxations is ascribed to some "side reasons rather than to the purely kinetic ("proper ) factors. The terms "proper and "side were first introduced by Temkin [225], As usual, we classify as slow "side processes variations in the chemical or phase composition of the surface under the effect of reaction media, catalyst deactivation, substance diffusion into its bulk, etc. These processes are usually considered to require significantly longer times to achieve a steady state compared with those characterizing the performance of chemical reactions. The above numerical experiment, however, shows that, when the system parameters attain their bifurcation values, the time to achieve a steady state, tr, sharply increases. 

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