Microkinetic expressions

Microkinetic Expressions Derivation of Volcano Curve 9 A closed expression for 9c can be deduced ... 

Using microkinetic expressions, we have discussed the most important catalytic concepts that describe heterogeneous catalytic reactions. We have related these concepts with the energies, entropies, and transition-state features that are accessible through current state-of-the-art DFT techniques. 

The preceding examples demonstrate the possibihty of the deduction of microkinetic expressions for the stationary rates of various stepwise cata lytic processes followed by thermodynamic analysis of the obtained expres sions. It is obvious, however, that the analysis is only meaningful when the said stationary states are stable in respect to the concentrations of the cata lytic intermediates. 

In Section 2, we begin our analysis with a presentation of analytic microkinetics expressions that relate activity and selectivity to elementary rate constants of simplified mechanistic models of the Fischer-Tropsch... 

We initially present microkinetics expressions assuming "Ci formation via direct CO dissociation while assuming that removal of adsorbed oxygen atoms, Oads/ is fast. Oads is removed by reaction with Fl2 or possibly with CO, which we do not explicitly consider in the microkinetics model. The product of the first pathway, water, can deactivate the Fischer-Tropsch catalyst, as has been investigated extensively (41). 

APPENDIX B. MICROKINETICS EXPRESSIONS FOR THE FISCHER-TROPSCH REACTION... 

The study of reaction kinetics in flow reactors to derive microkinetic expressions also rehes on an adequate description of the flow field and well-defined inlet and boundary conditions. The stagnation flow on a catalytic plate represents such a simple flow system, in which the catalytic surface is zero dimensional and the species and temperature profiles of the estabhshed boundary layer depend only on the distance from the catalytic plate. This configuration consequently allows the application of simple measurement and modehng approaches (Sidwell et al., 2002 Wamatz et al., 1994a). SFRs are also of significant technical importance because they have extensively been used for CVD to produce homogeneous deposits. In this deposition technique, the disk is often additionally forced to spin to achieve a thick and uniform deposition across the substrate (Houtman et al., 1986a Oh et al., 1991). 

We shall now utilize the microkinetic expressions for individual elementary surface processes, as described in the previons section, in order to establish a model for describing fnll catalytic cycles. A heterogeneous catalytic process always includes a number of elementary steps happening in sequence one after the other. If the reaction occurs over a surface, for example, the reactants first need to be adsorbed on the surface, then move into the vicinity of each other through diffusion processes, then react with each other forming the products, and finally desorb. Sometimes, the adsorbed reactants need to undergo various activation steps before being able to react with each other. 

We will illustrate first the physical chemistry that determines the temperature of the maximum rate for methane formation and then extend the analysis to the FT reaction. The lumped microkinetics expression for the rate of methane production is given by Eq. (16.21). 

In microkinetics, overall rate expressions are deduced from the rates of elementary rate constants within a molecular mechanistic scheme of the reaction. We will use the methanation reaction as an example to illustrate the... 

This study presents kinetic data obtained with a microreactor set-up both at atmospheric pressure and at high pressures up to 50 bar as a function of temperature and of the partial pressures from which power-law expressions and apparent activation energies are derived. An additional microreactor set-up equipped with a calibrated mass spectrometer was used for the isotopic exchange reaction (DER) N2 + N2 = 2 N2 and the transient kinetic experiments. The transient experiments comprised the temperature-programmed desorption (TPD) of N2 and H2. Furthermore, the interaction of N2 with Ru surfaces was monitored by means of temperature-programmed adsorption (TPA) using a dilute mixture of N2 in He. The kinetic data set is intended to serve as basis for a detailed microkinetic analysis of NH3 synthesis kinetics [10] following the concepts by Dumesic et al. [11]. 

In contrast to so-called microkinetic analyses, an important aspect of chemical reaction engineering involves the use of semiempirical rate expressions (e.g., power law rate expressions) to conduct detailed analyses of reactor performance, incorporating such effects as heat and mass transport, catalyst deactivation, and reactor stability. Accordingly, microkinetic analyses should not be considered to be more fundamental than analyses based on semiempirical rate expressions. Instead, microkinetic analyses are simply conducted for different purposes than analyses based on semiempirical rate expressions. In this review, we focus on reaction kinetics analyses based on molecular-level descriptions of catalytic processes. 

Some specific features of catalytic reactions, which are identified via the microkinetic analysis and are what make catalytic and noncatalytic reac tions qualitatively different, are discussed following. One is possible nonco incidence of the rate limiting steps (the process bottleneck ) and rate determining steps, the parameters of the latter being directly present in the expressions that describe the stationary rate of the stepwise process. 

To compete with the empirical models (Temkin and improved expressions) for the best fit to experimental data cannot be the prime objective of the microkinetic approaches. Rather, they are means of checking whether our knowledge and understanding of the elementary steps correspond to the reality of catalysts under industrial synthesis conditions. 

Microkinetic modeling is a framework for assembling the microscopic information provided by atomistic simulations and electronic structure calculations to obtain macroscopic predictions of physical and chemical phenomena in systems involving chemical transformations. In such an approach the particular catalytic reaction mechanism is expressed in terms of its most elementary steps. In contrast to the Langmuir-Hinshelwood-Hougen-Watson (LHHW) formulations, no rate-determining mechanistic step (RDS) is assumed. 

In the dynamic, microkinetic model, it is furthermore taken into account that the rate of methanol synthesis is different over the three low index facets [21]. The observed rate of the methanol synthesis for a given catalyst is therefore an average of the rates over the exposed facets and can be expressed as... 

In the third part of this chapter, the experimental determination and the detailed theoretical analysis of reaction kinetics obtained at catalysts used in RD processes are discussed. For reliable column design, activity based microkinetic rate expressions are applied successfully to heterogeneously catalyzed processes. By increasing the particle size of heterogeneous catalysts to be used in RD processes, mass-transport resistances can become relevant and have to be considered for reliable column simulations. This is exemplified by the industrially relevant syntheses of the fuel ethers MTBE and ETBE. 

The microkinetics of this reaction were investigated in detail by Rehfinger and Hoffmann [7]. These authors proposed the following rate expression in terms of liquid-phase activities the derivation is described in Section 5.4.3... 

When formulating a microkinetic rate expression r(T,x) one has to account for the sorption equilibria of the reaction components between the liquid phase and the active catalyst phase. For this purpose, since the liquid-phase reaction mixtures have a strongly non-ideal behavior, one should use generalized Langmuir sorption isotherms in terms of liquid-phase activities as proposed first in the pioneer work of Rehfinger and Hoffmann [45]. According to these authors, the sorption equilibria of the N species A on one active site S is given by... 

For the simulation of RD columns in which the chemical reactions take place at heterogeneous catalysts, it is important to keep in mind that a macrokinetic expression (5.55) has to be applied. Therefore, the microkinetic rate has to be combined with the mass transport processes inside the catalyst particles. For this purpose a model for the multicomponent diffusive transport has to be formulated and combined with the microkinetics based on the component mass balances. This has been done by several authors [50-53] by use of the generalized Maxwell-Stefan equations. 

Sundmacher and Qi (Chapter 5) discuss the role of chemical reaction kinetics on steady-state process behavior. First, they illustrate the importance of reaction kinetics for RD design considering ideal binary reactive mixtures. Then the feasible products of kinetically controlled catalytic distillation processes are analyzed based on residue curve maps. Ideal ternary as well as non-ideal systems are investigated including recent results on reaction systems that exhibit liquid-phase splitting. Recent results on the role of interfadal mass-transfer resistances on the attainable top and bottom products of RD processes are discussed. The third section of this contribution is dedicated to the determination and analysis of chemical reaction rates obtained with heterogeneous catalysts used in RD processes. The use of activity-based rate expressions is recommended for adequate and consistent description of reaction microkinetics. Since particles on the millimeter scale are used as catalysts, internal mass-transport resistances can play an important role in catalytic distillation processes. This is illustrated using the syntheses of the fuel ethers MTBE, TAME, and ETBE as important industrial examples. 

Power law model also provides good kinetic fit for the low-temperature WGS catalysts. Ovensen et al. [53] proposed microkinetic model based on surface redox mechanism and also evaluated the macroscopic power law kinetic model which was found to be an excellent representation of the kinetic data. Koryabkina et al. [54] determined the kinetic parameters for power law expression using catalysts based on copper over different supports. These authors suggested that there was a strong inhibition on the reaction rate by the products. They also proposed that the kinetics could be explained by a redox mechanism. The kinetic parameters obtained from different works are summarized in Table 9.5. 

In general, a mechanism for any complex reaction (catalytic or non-catalytic) is defined as a sequence of elementary steps involved in the overall transformation. To determine these steps and especially to find their kinetic parameters is very rare if at all possible. It requires sophisticated spectroscopic methods and/or computational tools. Therefore, a common way to construct a microkinetic model describing the overall transformation rate is to assume a simplified reaction mechanism that is based on experimental findings. Once the model is chosen, a rate expression can be obtained and fitted to the kinetics observed. 

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