First order heterogeneous catalytic reaction

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... 

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... 

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

Consider a straight tube of radius R with circular cross section and expensive metal catalyst coated in the inner wall. Reactant A is converted to products via first-order irreversible chemical reaction on the catalytic surface at r = R. Hence, diffusion of reactant A in the radial direction, toward the catalytic surface, is balanced by the rate of consumption of A due to heterogeneous chemical reaction. The boundary condition at the mathematically well-defined catalytic surface (i.e., r = R) is... 

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. 

For catalytic reactions carried out in the presence of a heterogeneous catalyst, the observed reaction rate could be determined by the rate of mass transfer from the bulk of the reaction mixture and the outer surface of the catalyst particles or the rate of diffusion of reactants within the catalyst pores. Consider a simple first order reaction its rate must be related to the concentration of species S at the outer surface of the catalyst as follows ... 

Two important ways in which heterogeneously catalyzed reactions differ from homogeneous counterparts are the definition of the rate constant k and the form of its dependence on temperature T. The heterogeneous rate equation relates the rate of decline of the concentration (or partial pressure) c of a reactant to the fraction / of the catalytic surface area that it covers when adsorbed. Thus, for a first-order reaction,... 

Given any complex system of heterogeneous catalytic first order reactions the mass balance on a differential volume element of the reactor at the height h yields the following system of differential equations for the j-th reaction component i) for the bubble phase... 

This expression still includes the effect of longitudinal dispersion. It is identical to Eq. (6-41), except that the rate for a homogeneous reaction has been replaced with the global rate XpPs per unit volume for a heterogeneous catal)dic reaction. In Sec. 6-9 Eq. (6-41) was solved analytically for first-order kinetics to give Eq. (6-45). Hence that result can be adapted for fixed-bed catalytic reactors. The first-order global rate would be... 

In the framework of this description an attempt to model an effect of spatial non-uniformity of real catalytic systems was made (Bychkov et al., 1997). It was assumed that reaction proceeds in a heterogeneous system represented by two active infinite plane surfaces and in the gas gap between them. Surface chemistry was treated as for the Li/MgO catalyst (see Table III). Because of substantial complexity of the kinetic scheme consisting of several hundred elementary steps, the mass-transfer was described in this case as follows. The whole gas gap was divided into several (up to 10) layers of the same thickness, and each of them was treated as a well-stirred reactor. The rate of particle exchange between two layers was described in terms of the first-order chemical reaction with a rate constant ... 

U sing polymers was one of the very first methods in order to heterogenize the catalyst in a homogeneous catalytic reaction. Thus, thanks to these supports, the catalyst acquires the property of insolubility while maintaining its catalytic performance [39-42]. Some authors synthesized phosphonated resins, such as polystyrene, and used them as a ligand in several rhodium and platinum complexes. Thus, hydrogenation [43, 44], hydrosilylation [45], and hydroformylation of olefins were catalyzed. 

Kinetics. If the kinetics and mechanism of the reaction in homogeneous solution are known, they can be translated at least approximately into the heterogenized system [30,37]. The principal difference between the homogeneous and heterogenized reactions is that the catalyst is distributed uniformly over the entire system in the former, but is concentrated in a part of it in the latter, a distinction of physics rather than chemistry. Provided the reaction is first order in the catalyst, as is usually true, the same amount of catalytically active species—say, hydrogen ions or complexed cobalt metal atoms—could be expected to produce approximately the same rate in both systems. This is a very crude, but useful hypothesis to start with. Complicating facets of the heterogenized reactions are ... 

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