First order heterogeneous catalytic

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... 

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 ... 

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... 

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... 

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 ... 

Surface heterogeneity has ever been considered to play a major role on adsorption [desorption] kinetics on [from] real surfaces and on heterogeneous catalytic processes. In fact, the most frequently observed kinetics which deviate from the theoretical first- or second-order ones, i.e. the time-logarithm law commonly known as Elovich equation, have in most cases been interpreted as due to surface heterogeneity. 

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 ... 

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 ... 

The first variable in catalytic hydrogenation is the catalyst. The most commonly used heterogeneous catalysts are platinum, palladium, nickel, rhodium, nickel, and ruthenium. Rylander gave references for the preparation of the most common catalysts, shown in Table 4.14.31 In some cases, salts of transition metals are used rather than the metal itself although the pure metal adsorbed on a support (see above) is also commonly used. Hudlicky presented an order of relative reactivity with propene for groups 8-10 (VIII) transition metal catalysts,341 based on the work of Mann and Lien.342 xhe order given is ... 

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

The adsorption/desorption equilibrium constant for each component is Kf = 0.25 atm and forward is the kinetic rate constant for the forward chemical reaction on the catalytic surface with units of moles per area per time. The reason that forward has the same units as Ehw is because rate laws for heterogeneous catalysis are written in terms of fractional surface coverage by the adsorbed species that participate in the reaction. Langmuir isotherms are subsequently used to express fractional surface coverage of the reacting species in terms of their partial pressures. The best value for the pseudo-first-order kinetic rate constant is calculated from... 

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