Intrinsic kinetics heterogeneous reactions

Example 10.1 Consider the heterogeneously catalyzed reaction A —> P. Derive a plausible form for the intrinsic kinetics. The goal is to determine a form for the reaction rate that depends only on gas-phase concentrations. 

It is a good idea to run the laboratory reactor without catalyst to check for homogeneous reactions. However, this method does not work when the homogeneous reaction involves reactants that do not occur in the feed but are created by a heterogeneous reaction. It then becomes important to maintain the same ratio of free volume to catalyst volume in the laboratory reactor used for intrinsic kinetic studies as in the pilot or production reactors. 

The pseudohomogeneous reaction term in Equation (11.42) is analogous to that in Equation (9.1). We have explicitly included the effectiveness factor rj to emphasis the heterogeneous nature of the catalytic reaction. The discussion in Section 10.5 on the measurement of intrinsic kinetics remains applicable, but it is now necessary to ensure that the liquid phase is saturated with the gas when the measurements are made. The void fraction s is based on relative areas occupied by the liquid and soUd phases. Thus,... 

Intrinsic Kinetics of Heterogeneous Reactions Involving Solids 255... 

INTRINSIC KINETICS OF HETEROGENEOUS REACTIONS INVOLVING SOLIDS... 

Note that the results of our simulation via the pseudohomogeneous model tracks the actual plant very closely. However, since the effectiveness factors r]i were included in a lumped empirical fashion in the kinetic parameters, this model is not suitable for other reactors. A heterogeneous model, using intrinsic kinetics and a rigorous description of the diffusion and conduction, as well as the reactions in the catalyst pellet will be more reliable in general and can be used to extract intrinsic kinetic parameters from the industrial data. 

In summary, it can be seen for the three-step reaction scheme of this example that the net rate of the overall reaction is controlled by three kinetic parameters, KTSi, that depend only on the properties of the transition states for the elementary steps relative to the reactants (and possibly the products) of the overall reaction. The reaction scheme is represented by six individual rate constants /c, and /c the product of which must give the equilibrium constant for the overall reaction. However, it is not necessary to determine values for five linearly independent rate constants to determine the rate of the overall reaction. We conclude that the maximum number of kinetic parameters needed to determine the net rate of overall reaction is equal to the number of transition states in the reaction scheme (equal to three in the current case) since each kinetic parameter is related to a quasi-equilibrium constant for the formation of each transition state from the reactants and/or products of the overall reaction. To calculate rates of heterogeneous catalytic reactions, an addition kinetic parameter is required for each surface species that is abundant on the catalyst surface. Specifically, the net rate of the overall reaction is determined by the intrinsic kinetic parameters Kf s as well as by the fraction of the surface sites, 0, available for formation of the transition states furthermore, the value of o. is determined by the extent of site blocking by abundant surface species. 

The rate expressions derived above describe the dependence of die reaction rate expressions on kinetic parameters related to the chemical reactions. These rate expressions are commonly called the intrinsic rate expressions of the chemical reactions. However, as discussed in Chapter 1, in many instances, the local species concentrations depend also on the rate that the species are transported in the reaction medium. Hence, the actual reaction rates are affected by the transport rates of reactants and products. This is manifested in two general cases (i) gas-solid heterogeneous reactions, where species diffusion through the pore plays an important role, and (ii) gas-hquid reactions, where interfacial species mass-transfer rate as wen as solubility and diffusion play an important role. Considering the effect of transport phenomena on the global rates of the chemical reactions represents a very difficult task in the design of many chemical reactors. These topics are beyond the scope of this text, but the reader should remember to take them into consideration. 

Suppose that adsorption is much slower than surface reaction or desorption for the heterogeneously catalyzed reaction A P. Deduce the functional form of the pseudohomogeneous, intrinsic kinetics. 

To summarize, transient kinetic experiments are an established and valuable tool in the investigation of heterogeneously catalysed gas phase reactions. For liquid-phase systems, transient studies are much more rare than for gas-phase systems. It is probably related to slower dynamics and the fact that the intrinsic kinetic phenomena can be obscured by mass transfer effects and catalyst deactivation. As an illustration (Figure 8.11) we will consider three-phase continuous hydrogenation of an organic compound leading to two products over a metal catalyst on a structured support (knitted silica). 

Reaction rates correspond to intrinsic kinetics, while generation rates are specific for a particular reaction network. Let us consider as an example (Figure 10.3) the reaction network for a heterogeneous catalytic reaction... 

There are a number of factors which may influence the activity or selectivity of a polymer-immobilized catalyst. Substrate diffusion is but one. This article has reviewed the mathematical formalism for interpreting reaction rate data. The same approach that has been employed extensively in heterogeneous systems is applicable to polymer-immobilized systems. The formalism requires an understanding of the extent of substrate partitioning, the appropriate intrinsic kinetic expression and a value for the substrate s diffusion coefficient. A simple method for estimating diffusion coefficients was discussed as were general criteria for establishing the presence of substrate transport limitations. Application of these principles should permit one to identify experimental conditions which will result in the intrinsic reaction rate data needed to probe the catalytic properties of immobilized catalysts. 

The simulator is able to treat different heterogeneous reaction kinetics, depending on the reaction rate and its character. For example, a detailed model for the heterogeneous catalyst mass-transfer efficiency can be used, which is based on the approach of [99]. When applying this type of kinetic model, the intrinsic kinetics data are needed (see Section 10.3.1). Another way is the pseudohomoge-neous approach with effective kinetics expressions, by which the kinetics description is introduced as source terms into the balance equations (see Eqs. (10.3) and (10.4)). 

In the first part of this book, we have studied the kinetics of homogeneous and heterogeneous chemical reactions as well as the influence of parameters on the reaction rates not taking into account diffusion and mass effects. These phenomena are caused by heat and mass transfer limitations. Therefore, the parameters have been determined under kinetic control regime in the absence of transport phenomena effects. When these phenomena take place, the observed rate is lower than the intrinsic kinetic rate. The effects must be determined separately. 

In the intrinsic heterogeneous catalytic cycle, the reactants are adsorbed on the catalyst surface at specific locations called active sites, and they are activated by chemical interaction with these sites to form the catalyst-reactant complex, thus rapidly transforming on the active site to adsorbed products which subsequently desorb from these sites allowing them to momentarily return to their original state until other reactant molecules adsorb. The simple hypothesis initiating from Langmuir s work on chemisorption [1, 2] forms the basis of the modern theory used in the interpretation of the kinetics of reactions at the catalyst surface ... 

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