Microkinetic Reaction Simulation

Measurement techniques for the resolution of concentration and temperature profiles in chemical reactors with heterogeneously catalyzed gas-phase reactions are a very useful tool not only for a better understanding of the reaction sequence and derivation of reaction kinetics but also for the elucidation of the coupling between catalytic reaction kinetics and mass and heat transport. The combination of numerical simulations of the reactive flow in catalytic reactors incorporating microkinetic reaction schemes and those recently developed invasive and noninvasive in situ techniques can today support the optimization of reactor design and operating conditions in industrial applications. 

Figure 3.10. Schematic representation of the elementary steps used in microkinetic simulations of the reduction of NO on supported metal particles [23]. The mechanism represented here incorporates adsorption and desorption steps, surface reactions such as NO dimerization and dissociation and N2, N20 and C02 formation, surface oxidation, and mobility of adsorbates. (Figure provided by Professor Libuda and reproduced with permission from Elsevier, Copyright 2005).

The microkinetic analysis is certainly a scientifically interesting approach which will contribute to the identification and selection of catalytic compounds even in more complex situations as described above. One problem still to be solved is the experimental procurement and/or estimation of the parameters used in microkinetic simulations, which limits the wide applicability of the method. Providing kinetic parameters for a complex reaction network from kinetic experiments for an analogous catalyst is a time-consuming process. Despite the availability of modem experimental equipment and efficient computers, a complex reaction demands at least one man year of work [51]. The estimation of parameters by ab initio or semiempirical methods has to be considered with caution because ideal surfaces are usually assumed. 

Recent simulations by Marin and coworkers (56,57) seem to confirm Equations (12b) and (12c). A single-event microkinetics (SEMK ) model was used to analyze data characterizing Fischer-Tropsch catalysis on iron. The authors reported an activation energy of only 57 kj/mol for CO dissociation, whereas activation energies for the chain-growth reaction and termination reaction leading to alkane or alkene formation were found to be 45,118, and 97 kJ/mol, respectively. 

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. 

P.Stolze, Microkinetic simulation of catalytic reactions, Progress in Surface Science, 65 (2000) 65. 

The Reaction Mechanism Microkinetic Analysis, Monte Carlo Simulation, and Multiple Steady States... 

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. 

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. 

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]. 

Legal limits for the emissions of the main pollutants in the automobile exhaust gases are becoming more and more strict The development of new and advanced catalytic converters demands not only experimental work, but also extensive and detailed modelling and simulation studies. The models become more complex, when all the important physical and chemical phenomena arc considered. Particularly the use of non-stationary kinetic models (microkinetics) with surface deposition of reaction components (Jirtit et al., 1999, e.g.) and the incorporation of diffusion effects in porous catalyst structure lead to a large system of partial differential equations. 

The results of simulations of TWC model with microkinetics and diffusion resistance within the washcoat enable the interpretation of the dynamics of surface coverages and overal reactions and can serve for the improvement of the washcoat design. It has been found that not only multiple steady states (hysteresis) but also various types of periodic and complex spatiotemporal concentration patterns can exist in the monolith. Thorough analysis of bifurcations and transitions among existing patterns is numerically demanding task due to dimension of the problem. 

Microkinetic modehng 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 pre-exponential terms, which are in units of cm mol s have... 

Voltammetry is an important tool for evaluating electrochemical and electro-catalytic processes. In a voltammetric experiment, the potential of a working electrode is varied with time relative to a reference electrode. The current of the working electrode is measured and reported as a function of potential. If the potential is swept linearly with time, peaks or waves are observed, which can be attributed to the various electrochemical processes possible in the system. For comparison with experiment, DFT calculated energetics can be used to predict voltammetry results in much the same way microkinetic models are used to predict catalytic kinetics. In the sections above, we have discussed DFT methods to calculate elementary reaction or adsorption free energies as a function of electrode potential. These free energy differences can be used to calculate potential dependent equilibrium constants. Section 3.2.5 will present a method to calculate potential dependent activation barriers. With these values for all possible elementary reaction steps, we could use microkinetic modeling to simulate voltammetry and compare with experiment. 

With an assumed value of 3, a potential dependent activation barrier is determined. This potential dependent barrier was used within a microkinetic model for the overall borohydride oxidation reaction, which allowed for simulation of a borohydride oxidation LSV." A value of near to 0.5 was found to provide a simulated voltammogram that matched experiment, though the same value was used for all reaction steps as an approximation. 

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