Microkinetic modeling

Fundamental Concepts in Heterogeneous Catalysis, First Edition. Jens K. N0rskov, Felix Studt, Frank Abild-Pedersen and Thomas Bligaard. 

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The single-event microkinetic concept ensures the feedstock independence of the kinetic parameters [8]. Present challenges in microkinetic modelling are the identification of catalyst descriptors accounting for catalyst properties such as acidity [10,11] and shape selectivity [12,13]. 

Determine the values of the descriptors from step 1 that yield optimal catalytic activity. This determination can, again, be made empirically, via microkinetic modeling, or via Sabatier analysis. 

S. Storsaeter, D. Chen and A. Holmen, Microkinetic modelling of the formation of Cj and C2 products in the Fischer-Tropsch synthesis over cobalt catalysts, Surf. Sci., 2006, 600, 2051-2063. 

In the case of heterogeneous catalysis, a DCKM or microkinetic model must incorporate the added dimension of adsorbed chemical species as well as active versus non-active sites. To obtain the full predictive capability from reactant influent to product effluent, all possible reactions in the system, both heterogeneous and homogeneous, must be accounted for. To properly understand the catalytic reaction sequence, it is possible that seemingly unimportant intermediates on the surface may be what initiate gas phase reactions. To begin this elucidation, the surface chemical species and their properties must be known. 

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. 

One of the important conclusions of the microkinetic modeling is that even large changes in some parameters do not affect the overall agreement between model and experiment much. 

Figure 4.32. Methanol decomposition over Pt as determined from a microkinetic model. Adapted...

The microkinetic models in this section are built upon BEP-relations of the type described above. It will be shown that an underlying BEP-relation in general leads to the existence of a volcano relation. We shall also use the microkinetic models in combination with the universal BEP-relation to explain why good catalysts for a long range of reactions lie in a surprisingly narrow interval of dissociative chemisorption energies. 

A simple tool is described, which provides a conceptual framework for analyzing microkinetic models of heterogeneous reactions. We refer to this tool as the Sabatier Analysis . The Sabatier Analysis of the microkinetic models developed in this section suggests that the clustering of good catalysts can be explained by the combination of the universal BEP-relation and activated re-adsorption of synthesis products onto the catalyst. 

The same microkinetic model can be used to investigate how the reactivity of the optimal catalyst changes with other reaction conditions such as temperature or pressure. In Figure 4.35, the dependence of the turnover frequency on temperature is shown. For high temperatures, the optimal catalyst moves out towards the more reactive surfaces. Figure 4.36 shows the dependence of the turnover frequency on the pressure of the more important reactant. The position of the optimal catalyst for... 

Figure 4.38. Sabatier volcano-curve The limiting case of the exact numerical solution of the microkinetic Model 1.

Detailed microkinetic models are available for CO, H2 and HC oxidation on noble metal(s) (NM)/y-Al203-based catalysts (cf., e.g. Chatterjee et al., 2001 Harmsen et al., 2000, 2001 Nibbelke et al., 1998). The model for CO oxidation on Pt sites includes both Langmuir-Hinshelwood and Eley-Rideal pathways (cf., e.g., Froment and Bischoff, 1990). Microkinetic description of the hydrocarbons oxidation is more complicated, particularly due to a large number of different reaction intermediates formed on the catalytic surface. Simplified mechanisms, using just one or two formal surface reaction steps,... 

The microkinetic models provide quite detailed description of the transients in catalyst operation. However, the number of balanced species and reaction steps is quite high for a realistic exhaust gas composition, due to the explicit consideration of all surface-deposited reaction intermediates. The models using microkinetic reaction schemes may also exhibit quite complex non-linear dynamic behavior (cf., e.g., Kubicek and Marek, 1983 Marek and Schreiber,... 

Olsson et al. focused on microkinetic models aiming to describe in detail the transient steps in the NOx storage and reduction process. First, the NO oxidation sub-model on Pt/y-Al203 and Pt/Ba0/y-Al203 was developed (Olsson et al., 1999), then the NOx storage sub-model (Olsson et al., 2001) and finally the mean-field microkinetic NOx storage and reduction model (Olsson et al.,... 

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)]. 

A model for the riser reactor of commercial fluid catalytic cracking units (FCCU) and pilot plants is developed This model is for real reactors and feedstocks and for commercial FCC catalysts. It is based on hydrodynamic considerations and on the kinetics of cracking and deactivation. The microkinetic model used has five lumps with eight kinetic constants for cracking and two for the catalyst deactivation. These 10 kinetic constants have to be previously determined in laboratory tests for the feedstock-catalyst considered. The model predicts quite well the product distribution at the riser exit. It allows the study of the effect of several operational parameters and of riser revampings. 

This has in turn been related to the relative stability of the OMME compared to the ethylene reactant and the epoxide product [11]. It has been argued that the relative instability of the OMME intermediate on Ag compared to Group VIII metals is the main origin of the unique activity of Ag as an effective epoxidation catalyst. Whether this simple interpretation is correct remains to be seen and will require considerable further investigations. In our current studies, we propose to shed light on the competitive partial oxidation and total oxidation channels with ab initio derived microkinetic modeling [61]. 

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