Kinetics, porous catalyst

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

Oxidation kinetics over platinum proceeds at a negative first order at high concentrations of CO, and reverts to a first-order dependency at very low concentrations. As the CO concentration falls towards the center of a porous catalyst, the rate of reaction increases in a reciprocal fashion, so that the effectiveness factor may be greater than one. This effectiveness factor has been discussed by Roberts and Satterfield (106), and in a paper to be published by Wei and Becker. A reversal of the conventional wisdom is sometimes warranted. When the reaction kinetics has a negative order, and when the catalyst poisons are deposited in a thin layer near the surface, the optimum distribution of active catalytic material is away from the surface to form an egg yolk catalyst. 

Many theoretical embellishments have been made to the basic model of pore diffusion as presented here. Effectiveness factors have been derived for reaction orders other than first and for Hougen and Watson kinetics. These require a numerical solution of Equation (10.3). Shape and tortuosity factors have been introduced to treat pores that have geometries other than the idealized cylinders considered here. The Knudsen diffusivity or a combination of Knudsen and bulk diffusivities has been used for very small pores. While these studies have theoretical importance and may help explain some observations, they are not yet developed well enough for predictive use. Our knowledge of the internal structure of a porous catalyst is still rather rudimentary and imposes a basic limitation on theoretical predictions. We will give a brief account of Knudsen diffusion. 

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... 

Effectiveness Factors for Hougen-Watson Rate Expressions. The discussion thus far and the vast majority of the literature dealing with effectiveness factors for porous catalysts are based on the assumption of an integer-power reaction rate expression (i.e., zero-, first-, or second-order kinetics). In Chapter 6, however, we stressed the fact that heterogeneous catalytic reactions are more often characterized by more complex rate expressions of the Hougen-Watson type. Over a narrow range of... 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve very slow binding steps. In these cases, the mass-transfer parameter k is replaced... 

HETEROGENEOUS CATALYSIS KINETICS IN POROUS CATALYST PARTICLES... 

Heterogeneous Catalysis Kinetics in Porous Catalyst Particles 199... 

These TPD techniques reflect the kinetics (not thermodynamics) of adsorption, and are quite useful for determining trends across series of catalysts, but are often not suitable for the derivation of quantitative information on surface kinetics or energetics, in particular on ill-defined real catalysts. Besides averaging the results from desorption from different sites, TPD detection is also complicated in porous catalysts by simultaneous diffusion and readsorption processes [58],... 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Weisz, P. B., and Goodwin, R. D. (1963). Combustion of carbonaceous deposits within porous catalyst particles. I. Diffusion controlled kinetics. J. Catal. 2, 397. 

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... 

A reaction A R is to take place on a porous catalyst pellet (dp = 6 mm, = 10" m /m cat s). How much is the rate slowed by pore diffu-sional resistance if the concentration of reactant bathing the particle is 100 mol/m and the diffusion-free kinetics are given by... 

It is desirable to list the sequence of space and point steps which together constitute global adsorption. This is not a new concept and such descriptions have frequently been presented (I, 14), particularly for fluid reactions on porous catalyst particles. The first space process, axial dispersion, is not a part of the. sequence, but it does affect the observed kinetics, and is logically considered as a space process. Its significance depends upon the reciprocal of the axial Peclet number, EJ(2R)v. The sequential steps are ... 

The kinetic and thermodynamic selectivity factors are quantities which are functions of the chemistry of the system. When an active catalyst has been selected for a particular reaction (often by a judicious combination of theory and experiment) we ensure that the kinetic and thermodynamic factors are such that they favour the formation of desired product. Many commercial processes, however, employ porous catalysts since this is the best means of increasing the extent of surface at which the reaction occurs. Chemical engineers are therefore interested in the effect which the porous nature of the catalyst has on the selectivity of the chemical process. 

The starting point of a number of theoretical studies of packed catalytic reactors, where an exothermic reaction is carried out, is an analysis of heat and mass transfer in a single porous catalyst since such system is obviously more conductive to reasonable, analytical or numerical treatment. As can be expected the mutual interaction of transport effects and chemical kinetics may give rise to multiple steady states and oscillatory behavior as well. Research on multiplicity in catalysis has been strongly influenced by the classic paper by Weisz and Hicks (5) predicting occurrence of multiple steady states caused by intrapellet heat and mass intrusions alone. The literature abounds with theoretical analysis of various aspects of this phenomenon however, there is a dearth of reported experiments in this area. Later the possiblity of oscillatory activity has been reported (6). 

Several quantitative analyses of the effect of intraparticle heat and mass transport have been carried out for parallel, irreversible reactions [1]. Roberts and Lamb [2] have worked on the effect of reversibility on the selectivity of parallel reactions in a porous catalyst. The reaction selectivity of a kinetic model of two parallel, first order, irreversible reactions with a second order inhibition kinetic term in one of them has also been investigated [3]. 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

Using 324 measuring points taken at temperatures between 35 and 75 °C, hydrogen concentrations between 1.6 10-3 and 11.0 10-3 mol NdnT3 and oxygen concentrations between 1.7 10 3 and 7.3 10 3 mol Ndm-3, a kinetic expression for the reaction was determined on the basis of a Langmuir-Hinshelwood model (Figure 2.30). The Mears criterion was applied to verify that no mass transfer limitation was to be expected for the system from the gas phase to the non-porous catalyst ... 

Figure 3. Transition from the kinetic regime to the diffusion-controlled regime of a heterogeneous catalytic fluid-solid reaction carried out on a porous catalyst.

Probably, for most slurry reactor applications, information on the value of the product kLa is sufficient for design purposes. In some cases, however, information on the individual parameters a and/or ki, can be useful. For instance, the reactor capacity will depend on a, rather than on the product k a, if the reaction is so fast that all conversion takes place within the stagnant film (film theory) around the gas bubbles. For first-order conversion kinetics in the porous catalyst particles this will occur for... 

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