Microkinetic model catalysts

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]. 

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. 

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. 

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... 

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,... 

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... 

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]. 

In the following example, we use a simple microkinetic model of CO oxidation on Pt together with the reconstructed porous catalyst to follow the evolution of local concentration profiles within the porous structure. The reaction-diffusion problem of the CO oxidation on the Pt/y-Al203 porous catalyst... 

These relationships, when incorporated into microkinetics models of catalytic reaction cycles, enable remarkable new predictive insights into the control of heterogeneously catalyzed reactions. Predictive models of catalytic activity as a function of catalyst composition as well as reaction conditiorvs have been constructed (22-24). The resultant volcano curves can be considered to be an application of the Sabatier principle (25,26). 

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). 

The experimental results have been used as a basis for building kinetics models 110-113). Carbon formation kinetics has also been included in the microkinetics models. The models assume that the carbon filaments are formed by carbon atoms diffusing through bulk nickel crystallites. Recent investigations have also indicated that surface diffusion processes can be more important than was believed in the filament formation mechanism 114). When the irreducible heat transfer limitation was taken into account, providing an improved estimate of the real catalyst surface temperature, the model was able to predict both our own kinetics data 110 113) as well as the intrinsic kinetics reported by Xu and Froment 115) for the reaction in the presence of a similar catalyst (nickel on Mg-Al203 spinel). 

Another test of validity is to check the performance of the model against experimental rate data obtained far from equilibrium. The microkinetic model presented in Table 7.3.1 predicts within a factor of 5 the turnover frequency of ammonia synthesis on magnesia-supported iron particles at 678 K and an ammonia concentration equal to 20 percent of the equilibrium value. This level of agreement is reasonable considering that the catalyst did not contain promoters and that the site density may have been overestimated. The model in Table 7.3.1 also predicts within a factor of 5 the rate of ammonia synthesis over an Fe(lll) single crystal at 20 bar and 748 K at ammonia concentrations less than 1.5 percent of the equilibrium value. 

Key Words Ethylene epoxidation, Silver, Bimetallic catalyst design, Copper, Density functional theory, Microkinetic modeling. 2008 Elsevier B.v. 

Motivated by the idea of rational catalyst design, we take advantage of the computational efficiency of DFT methods to examine a variety of Ag-containing bimetallic catalysts. We focus initially on the branching reactions of the OME since these have been shown to control selectivity [9]. Initial screening based solely on OME reactions suggests several promising bimetallic combinations. However, if one considers a more complete microkinetic model, copper stands out for its ability to enhance the selectivity of silver-based bimetallic catalysts. 

FIGURE 8.11 Predictions of ethylene oxide (EO) selectivity on different bimetallic Ag,4M, catalysts from the microkinetic model. Two pre-exponential factors were adjusted to correctly capture the experimental EO selectivity on pure Ag. 

Here S represents a vacant site on the surface of the catalyst. The set of elementary reactions generated under these constraints for the WGS reaction is presented in Table 1. To simplify the resulting analysis, in what follows we further disregard two of the elementary reactions from this microkinetic model, namely... 

Numerical simulations and analyses were performed for both the continuous stirred-tank reactor (CSTR) and the plug-flow reactor (PER). A comparison between the microkinetic model predictions for an isothermal PFR and the experimental results [13], is presented in Fig. 2 for the following conditions commercial low temperature shift Cu catalyst loading of 0.14 g/cm total feed flow rate of 236 cm (STP) min residence time r = 1.8 s feed composition of H20(10%), CO(10%), C02(0%), H2(0%) and N2(balance). As can be seen, the model can satisfactorily reproduce the main features of the WGSR on Cu LTS catalyst without any further fine-tuning, e.g., coverage dependence of the activation energy, etc, which is remarkable and provides proof of the adequacy of the... 

The wider utilization of microkinetic models is somewhat retarded by the vast amount of information needed about interactions of chemical intermediates with complex, heterogeneous catalysts. The microkinetic approach has been applied to numerous diverse chemistries including cracking, hydrogenation, hydrogenolyis, hydrogenation, oxidation reactions and ammonia synthesis to name a few. 

Microkinetic modeling assembles molecular-level information obtained from quantum chemical calculations, atomistic simulations and experiments to quantify the kinetic behavior at given reaction conditions on a particular catalyst surface. In a postulated reaction mechanism the rate parameters are specified for each elementary reaction. For instance adsorption preexponential terms, which are in units of cm3 mol"1 s"1, have been typically assigned the values of the standard collision number (1013 cm3 mol"1 s 1). The pre-exponential term (cm 2 mol s 1) of the bimolecular surface reaction in case of immobile or moble transition state is 1021. The same number holds for the bimolecular surface reaction between one mobile and one immobile adsorbate producing an immobile transition state. However, often parameters must still be fitted to experimental data, and this limits the predictive capability that microkinetic modeling inherently offers. A detailed account of microkinetic modelling is provided by P. Stoltze, Progress in Surface Science, 65 (2000) 65-150. 

In the present paper, we will discuss in some detail the results of methanol synthesis catalyst since in this case, the dynamic changes occurring in the catalyst structure have been described in some detail and it has been possible to use this insight to formulate a dynamic microkinetic model. 

In the following section, we will discuss the kinetic implications of the dynamical changes in catalyst morphology during methanol synthesis. First, we will present an analysis of steady state kinetic experiments using a static, microkinetic model where it is assumed that the number of sites are constant. Then, we will introduce the dynamic aspect into the microkinetic modeling and also discuss some recent transient experiments. 

Comparison of the calculated rate with the measured rate of methanol synthesis over a Cu/ZnO/AhOs catalyst. The calculated rate is obtained from the static microkinetic model. Inlet gas compositions 12% CO, 2.1% CO2, 85.9% H2 (solid circle), 17 9% CO, 6.7% CO2, 75.4% H2 (empty triangle) [21]. 

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... 

---