Microkinetic rate

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. 

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. 

Comparison between theoretical predictions and experimental results showed, that, in contrast to the MTBE process, transport processes inside the catalyst were negligible for the TAME process. This is again due to the fact that the microkinetic rate of reaction is one order of magnitude slower than in the MTBE case and is therefore dominating for the operating conditions considered in this study. This was confirmed more rigorously in a recent paper by Higler et al. [39]. 

UHV systems, which are seldom available for such measurements and are time and cost intensive, but also because these more detailed microkinetic rate laws typically simplify to more conventional rate expressions over a chosen range of reaction conditions [6]. 

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

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... 

Table 4 summarizes the rate constants kj - Aj exp(-Ej / RT) for the forward and the reverse reaction derived from our microkinetic analysis of the steady-state and transient experiments with the three catalysts, i.e. Cs-Ru/MgO, Ru/MgO, and Ru/AlaOs catalyst [24]. 

The HTE characteristics that apply for gas-phase reactions (i.e., measurement under nondiffusion-limited conditions, equal distribution of gas flows and temperature, avoidance of crosscontamination, etc.) also apply for catalytic reactions in the liquid-phase. In addition, in liquid phase reactions mass-transport phenomena of the reactants are a vital point, especially if one of the reactants is a gas. It is worth spending some time to reflect on the topic of mass transfer related to liquid-gas-phase reactions. As we discussed before, for gas-phase catalysis, a crucial point is the measurement of catalysts under conditions where mass transport is not limiting the reaction and yields true microkinetic data. As an additional factor for mass transport in liquid-gas-phase reactions, the rate of reaction gas saturation of the liquid can also determine the kinetics of the reaction [81], In order to avoid mass-transport limitations with regard to gas/liquid mass transport, the transfer rate of the gas into the liquid (saturation of the liquid with gas) must be higher than the consumption of the reactant gas by the reaction. Otherwise, it is not possible to obtain true kinetic data of the catalytic reaction, which allow a comparison of the different catalyst candidates on a microkinetic basis, as only the gas uptake of the liquid will govern the result of the experiment (see Figure 11.32a). In three-phase reactions (gas-liquid-solid), the transport of the reactants to the surface of the solid (and the transport from the resulting products from this surface) will also... 

The starting point for microkinetic modeling is the detailed reaction mechanism. Thus, while a conventional kinetic model is formulated as the rate for an apparent gas phase reaction, the surface species are explicitly included in a microkinetic model. 

The input parameters for a microkinetic model may be taken from measured adsorption and reaction rates for the catalyst, measured heats of adsorption together with thermodynamic data for the gas (or liquid-) phase above the catalyst. 

In the washcoat, reaction rates are modeled via global reaction mechanisms. In such a global or macrokinetic reaction mechanism, several microkinetic adsorption, reaction and desorption steps are lumped together, reducing the overall number of kinetic parameters considerably. For some catalysts,... 

In terms of catalytic kinetics, the implications of the dynamic changes in catalyst morphology during methanol synthesis are dramatic. Figure 16a shows the agreement between the predictions of a static microkinetic model and the measured rates of methanol synthesis catalyzed by Cu/ZnO/A1203... 

Fig. 16. (a) Comparison of the calculated rate with the measured rate of methanol synthesis catalyzed by Cu/ZnO/A1203. The calculated rate was obtained from a static microkinetic model, (b) The corresponding comparison estimated by use of a dynamic microkinetic model [adapted from Ovesen et al. (59)]. 

The absorption of ozone from the gas occurred simultaneously with the reaction of the PAH inside the oil droplets. In order to prove that the mass transfer rates of ozone were not limiting in this case, the mass transfer gas/water was optimized and the influence of the mass transfer water/oil was studied by ozonating various oil/water-emulsions with defined oil droplet size distributions. No influence of the mean droplet diameter (1.2 15 pm) on the reaction rate of PAH was observed, consequently the chemical reaction was not controlled by mass transfer at the water/oil interface or diffusion inside the oil droplets. Therefore, a microkinetic description was possible by a first order reaction with regard to the PAH concentration (Kornmuller et al., 1997 a). The effects of pH variation and addition of scavengers indicated a selective direct reaction mechanism of PAH inside the oil droplets... 

The microkinetics of the chemical reaction that takes place is described by da/dt = dbd/dt = —kaabd where kt> is the real chemical reaction rate constant and the index d refers to the dispersed phase. If the components A and B are supplied to the reactor in stoichiometric quantities and... 

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. 

The intrinsic kinetics describes a reaction rate that is not influenced by such transport phenomena therefore, it only depends on the factors concentration, pressure, temperature, and catalyst. For the comparison of the catalytic activity and the investigation of different catalysts, it is necessary to adjust the experimental conditions such that only the intrinsic kinetics is determined. If this is not the case, none of the obtained data are of use. The microkinetics is equivalent to the intrinsic-kinetic, with the difference that it consists of the elementary reactions. 

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