Order heterogeneous catalytic reactions

As a first approximation a convective term in the film region has been negleted, u is the superficial gas velocity and u f denotes the gas velocity at minimum fluidization conditions. Tne specific mass transfer area a(h) is based on unit volume of the expanded fluidized bed and e OO is the bubble gas hold-up at a height h above the bottom plate. Mathematical expressions for these two latter quantities may be found in detail in (20). The concentrations of the reactants in the bubble phase and in film and bulk of the suspension phase are denoted by c, c and c, respectively. The rate constant for the first order heterogeneous catalytic reaction of the component i to component j is denoted... 

In this chapter we will discuss the results of the studies of the kinetics of some systems of consecutive, parallel or parallel-consecutive heterogeneous catalytic reactions performed in our laboratory. As the catalytic transformations of such types (and, in general, all the stoichiometrically not simple reactions) are frequently encountered in chemical practice, they were the subject of investigation from a variety of aspects. Many studies have not been aimed, however, at investigating the kinetics of these transformations at all, while a number of others present only the more or less accurately measured concentration-time or concentration-concentration curves, without any detailed analysis or quantitative kinetic interpretation. The major effort in the quantitative description of the kinetics of coupled catalytic reactions is associated with the pioneer work of Jungers and his school, based on their extensive experimental material 17-20, 87, 48, 59-61). At present, there are so many studies in the field of stoichiometrically not simple reactions that it is not possible, or even reasonable, to present their full account in this article. We will therefore mention only a limited number in order for the reader to obtain at least some brief information on the relevant literature. Some of these studies were already discussed in Section II from the point of view of the approach to kinetic analysis. Here we would like to present instead the types of reaction systems the kinetics of which were studied experimentally. 

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 results obtained indicate the interpretation of fractional reaction orders frequently obtained in experimental studies of heterogeneous catalytic reactions. 

In earlier work, it was found for borides, silicides and nitrides that specific activity, expressed as total rate of methane consumption per unit surface area, plummeted with increasing surface area of the catalyst samples.1718 The same relationship was also found for transition metals carbides (Figure 16.4). It should be noted the dependence of specific activity on surface area rather than catalyst composition is unusual for heterogeneous catalytic reactions. In addition, it can be found that the reaction order in the oxidant is perceptibly in excess of 1 (Tables 16.8 and 16.9). Such an order is hard to explain in terms of common mechanism schemes for heterogeneous catalytic oxidative reactions. 

The apparent rate constant in (2.10), which is obtained by multiplying a true rate constant kc and the square root of an equilibrium constant, Keq, can show a law of dependence on temperature different from the simple Arrhenius law. In some cases, even a negative temperature dependence can be observed. Moreover, if both mechanisms (2.6) and (2.7)-(2.8) are active in parallel, the observed reaction rate is the sum of the single rates, and an effective reaction order variable from 1 /2 to 1 can be observed with respect to reactant A. Variable and fractionary reaction orders can be also encountered in heterogeneous catalytic reactions as a consequence of the adsorption on a solid surface [6],... 

In this chapter, we will review the reaction dynamics studies which has been performed on supported model catalysts in order to unravel the elementary steps of heterogeneous catalytic reactions. In particular we will focus on the aspects that cannot be studied on extended surfaces like the effect of the size and shape of the metal particles and the role of the substrate in the reaction kinetics. In the first part we will describe the experimental methods and techniques used in these studies. Then we present an overview of the preparation and the structural characterization of the metal particle. Later, we will review the adsorption studies of NO, CO and 02. Finally, we will review the two reactions that have been investigated on the supported model catalysts the CO oxidation and the NO reduction by CO. 

A different model [11] that can be used to obtain the kinetics equation for a pyrolytic reaction is adapted from the theory developed for the kinetics of heterogeneous catalytic reactions. This theory is described in literature for various cases regarding the determining step of the reaction rate. The case that can be adapted for a pyrolytic process in solid state is that of a heterogeneous catalytic reaction with the ratedetermining step consisting of a first-order unimolecular surface reaction. For the catalytic reaction of a gas, this case can be written as follows ... 

In order to study reactions in liquid phase, it is necessary to develop new experimental techniques that will allow operando spectroscopy and transient studies of liquid phase heterogeneous catalytic reactions. Essential for such technique is a reactor module. Chromolith HPLC column (Merck) [1] with sihca foam in a polymer cartridge is suitable as a reactor for transient experiments because the high surface area silica foam can act as support with relatively low pressure drop. However, thermal stability of this HPLC column is limited to low temperatures because of the polymer housing (<150°C). It is... 

Thus, the mechanism of catalytic processes near and far from the equilibrium of the reaction can differ. In general, linear models are valid only within a narrow range of (boundary) conditions near equilibrium. The rate constants, as functions of the concentration of the reactants and temperature, found near the equilibrium may be unsuitable for the description of the reaction far from equilibrium. The coverage of adsorbed species substantially affects the properties of a catalytic surface. The multiplicity of steady states, their stability, the ordering of adsorbed species, and catalyst surface reconstruction under the influence of adsorbed species also depend on the surface coverage. Non-linear phenomena at the atomic-molecular level strongly affect the rate and selectivity of a heterogeneous catalytic reaction. For the two-step sequence (eq.7.87) when step 1 is considered to be reversible and step 2 is in quasi-equilibria, it can be demonstrated for ideal surfaces that... 

In a heterogeneous catalytic reaction, the intraparticle efTectiveness for a first-order reaction within a spherical catalyst ate steady state is [63]... 

Some heterogeneous catalytic reactions are carried out in the supercritical phase, in order to increase catalyst activity and life through in-situ regeneration of surfaces with tuning of operation conditions. For example, supercritical fluids are capable of dissolving carbon that may otherwise be deposited on the catalyst in the absence of the supercritical solvent. 

The complications of heterogeneous catalytic reactions are such that each specific case must be considered individually, and few if any are really fully understood. There are, however, a few fundamental aspects that can be considered in order to get an overall picture of what individual molecular processes may be involved (Fig. 9.6). Those fundamentals include (1) the initial physical adsorption process, (2) possible surface diffusion of the adsorbed species, (3) chemisorption processes (e.g., bond breaking, if it is involved), (4) chemical reaction between adsorbed species and (5) desorption of the product. All or only some of those steps (or perhaps others not mentioned) may be involved in a given catalytic process. Any one of them may be the rate-determining step. 

Almost all commercial heterogeneous catalytic reactions are conducted with a contact time of at least several seconds. Many require much longer contact time. There are, however, a few commercial catalytic processes in which the reaction is completed in a very short time (order of milliseconds). These very fast reactions are usually affected by heat- and mass-transport resistances. They are usually carried out either on catalytic gauzes or on a reticulated structure or monolith coated with a very thin washcoat on which a catalyst is impregnated. 

The negative reaction order in ligand L has implications for truly complex mass-transfer effects. In particular, lower mass-transfer rates can actually increase the overall observed reaction rate. This issue of negative reaction orders is seldom observed or mentioned in the context of stoichiometric and heterogeneous catalytic reactions. But it is frequently noted in homogeneous catalytic studies. Chaudhari has discussed this problem in detail for the gas-liquid mass-transfer control of CO in the hydroformylation reaction (21). 

As already mentioned, in the overwhelming majority of heterogeneous catalytic reactions, the zone where the chemical reaction occurs is limited to the interface between the solid and fluid phases, thus the material of the bulk solid, which is not in direct contact with the fluid phase, is not involved. This means that, in general, it is necessary to prepare a catalyst with a large proportion of active metal atoms exposed at the surface. In order to increase their number, it is possible to support the metal on a high surface-area oxide (alumina, silica, zeolites). It is then... 

Numerous methods are used to create materials with specific surface properties and most commercial supports are already available in a variety of surfiice area-pore size combinations which are somewhat interrelated in such a way that large pore supports typically have a reduced surface area. In heterogeneous catalytic reactions, it is important to have control over both the surface area and the pore size in order to achieve the highest possible catalytic activity. 

The so-called two-step sequence method is that the derivation of reaction rate expression only requires to consider two key steps for a reaction involving multielementary steps. Only the rate constants or equilibrium constants of the two key steps appear in rate expression, which are of clear physical meaning. In order to determine the key steps, a concept of most abundant reaction intermediate (Mari) must be introduced. Mari is an intermediate of maximum concentration among all reactive intermediates invovled in the reaction, and the concentration of other intermediates can be ignored. Based on the concepts of both rate determining step and most abundant reaction intermediate, the mechanisms of many catalytic reactions can be simplified to two-step sequences for the derivation of kinetic equations. In order to explain the rules for the treatment of heterogeneous catalytic reaction kinetics by simplest two-step sequences method, two examples are given as follows ... 

Analysis In most heterogeneous catalytic reactions, rate laws are expressed in terms of partial pressures instead of concentration. However, we see that through the use of the ideal gas law we could easily express the partial pressure as a function of concentration then conversion in order to express the rate law as a function of conversion. In addition, for most all heterogeneous reactimis you will usually find a term like (1 + + K Pg +, ..) in the denominator of the rate law, as will be... 

In this chapter, we revisit the subject of reaction/transport interactions in heterogeneous catalysts, this time from a quantitative standpoint. The topic must be examined from two perspectives. First, a researcher that is studying the kinetics of a heterogeneous catalytic reaction (or reactions) must ensure that his or her experiments are free of transport effects. In other words, the experiments must be conducted under conditions where intrinsic chemical kinetics determines the reaction rate(s). The researcher may have to make calculations to estimate the magnitude of heat and mass transport influence. He or she may also have to carry out diagnostic experiments in order to define a region of operation where transport does not affect the reaction rate and selectivity. 

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