Reaction mechanism microkinetic model

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. 

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,... 

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,... 

In 2001, Mirodatos et al. [89] stressed the importance of transient studies as an alternative to steady continuous reactor operations. A combination of microkinetic analysis together with transient experiments should allow the determination of the global catalytic conversion from elementary reaction steps. Prerequisite for such analysis is the correlation of experimental data with the data of a model. Compliance between the data helps to derive the reaction mechanism. 

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). 

The proposed theoretical methodology has been applied here to study and rationalize a 15 elementary reaction microkinetic mechanism for the WGSR on Cu(lll) for illustrative purposes. A reaction network has been constructed that incorporates all of the 26 direct RRs that have been previously generated using the conventional methods. Using the electrical circuit analogy the reaction network was subsequently simplified and reduced to a reaction network involving only 3 dominant RRs. An overall rate equation has been developed that reproduces the complete microkinetic model precisely. 

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. 

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. 

Also, quantum mechanical approaches, such as DFT, can be used to estimate thermochemical parameters, like enthalpies and entropies, as well as kinetic parameters like activation energies and frequency factors of chemical reactions. The microkinetic analysis is then a way to incorporate the basic surface chemistry in the kinetic modelling. 

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. 

A microkinetic reaction model was constructed to elucidate the intrinsic reaction mechanism and to provide insight into the processes occurring in the reactor. CHEMKiN software [50] was used to accommodate this model. The PrOx reaction mechanism describing the detailed gas-phase and surface chemical kinetics was constmcted from previously published work [51] and adapting the rate parameters to our experimental results. The model is composed of eight adsorption reactions, eight desorption reactions and 12 surface reactions with nine gas-phase species (N2, O, O2, CO2, H, OH, CO, H2, H2O) and eight surface species [Pt(s), 0(s), H(s), OH(s), H20(s), C(s), CO(s), CO2 (s)]. 

Microkinetics as defined by Dumesic, is the examination of catalytic reactions in terms of elementary chemical reactions that occur on the catalytic surface and their relation with each other and with the surface during a catalytic cycle. This definition can easily be expanded into covering non-catalytic systems as well. Microkinetics, for the most part, has focused on analysis or understanding of the reaction mechanism. The approach, however, also holds the promise of being used to aid in the synthesis of new materials. Microkinetic modeling is now an important tool for many of the practicing reaction engineers. This approach enables one to formulate and follow the detailed concentration profile for most if not all of the reaction intermediates. 

Microkinetic modeling predicts thermodynamic properties for species and kinetic parameters of elementary steps of a mechanism, as described in subsequent sections. The kinetic parameters, that is, sticking coefficient (5 ) of a species, preexponential factor (Ajp, and activation energy as well as the change in enthalpy (Aff ) and entropy (A5°) in each elementary step at 298 K on Pt(lll) are also presented in Table 8.1. Here, stands for reaction index and f for forward. This mechanism will be used throughout this chapter to illustrate the capabilities of microkinetic modeling tools. 

The previous sections described techniques employed for parameter estimation. These thermodynamic and kinetic parameters are input to a microkinetic model that is solved numerically to describe material balances in a chemical reactor (e.g., a PFR). This section describes tools for the subsequent model analysis, which can be used in multiple ways. Initially during mechanism development, they can be used to assess which reactions and reactive intermediates are important in the model, which helps the modeler to focus on important features of the surface reaction mechanism. During this process, simulated macroscopic observables, for example, global reaction orders and apparent activation energies can be compared directly to experimental data. Then, once the model describes experimental data reasonably well, analytical tools can be used to develop further insights into the reaction mechanism, with apphcations that include catalyst design [50]. 

Two important quantities that are often evaluated from a microkinetic model are the reaction order with respect to each reactant and the apparent activation energy. Both quantities can be estimated from experiments using flow reactors [53,54], which makes them valuable parameters in validating and fine-tuning a model. Reaction order data are also some of the best indicators of the kinetics of the mechanism, and agreanent with experimental orders is a good indication that the model is capturing the correct kinetics. 

In this chapter, an overview of microkinetic modeling was given. Microkinetic modeling aims at understanding how surface structure and adsorbate properties at the molecular level affect thermodynamic and kinetic phenomena at the macroscale. Inputs to microkinetic modeling via first-principles and semiempirical methods were discussed, followed by an explanation of several microkinetic analysis tools. The modeling of the WGS reaction on platinum was presented as an example of using these tools in the assessment of the surface reaction mechanism. 

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