Dynamic kinetic models

The aim of the present section is to illustrate the procedures employed for the derivation of dynamic kinetic models appropriate for simulation of exhaust aftertreatment devices according to the converter models illustrated in the previous section. In particular, it will be shown how to derive global reaction kinetics which are based on a fundamental study aimed at the elucidation of the reaction mechanism. In principle, this approach enables a greater model adherence to the real behavior of the reacting system, which should eventually afford better results when validating the model in a wide range of operating conditions, as typically required for automotive applications. 

Such quantitative dynamic models are difficult and expensive to develop, this is why they are rarely available. A simpler approach is reasonable that uses quantitative information on observable rates of some hypothetical processes on the surface. A dynamic kinetic model can be presented as follows [2] ... 

Development of dynamic kinetics models is most effective when transient kinetic experiments combined with physico-chemical methods of investigation of catalyst surface. There are examples of models that describe well the dynamic processes on the catalyst, such as studies by Balzhinimaev et. al. [15], Sadhankar and Lynch [16], Jobson et. al, [17]. Once a model of dynamic processes on catalyst surface is devised, it can further be used for numerical optimization of the periodically forced reactor. Invariance of such model, where all equations and parameters are independent on time at every space scale such as pellet, catalyst bed or reactor at any time, simplifies the further scale up. 

Fig. 5. Effect of cycle period and inlet SO2 concentration on the performance of flow reversal reactor. (1-3) SO2 conversion predicted with dynamic kinetic model, (l -3 ) SO2 conversion predicted with steady-state kinetic model. (1,1 ) 9 % SO2 in the reactor inlet, (2,2 ) 6 % SO2, and (3,3) 3 % SO2.

Also, the study of the reaction kinetics under unsteady-state conditions (i) may provide relevant information concerning the mechanism of the reaction and (ii) allow to decouple the study of the kinetics of the reactants adsorption-desorption from that of the surface reaction under representative conditions (95,97,102). For all the above-mentioned applications, reliable engineering analysis and reactor modeling calls for a dynamic kinetic model of the SCR reaction. 

A global, dynamic kinetic model of NO-NO2/NH3 reactions for vanadia-based catalysts, with high level of detail, closely reflecting all the mechanistic steps discussed in Reference (15), was first published by Chatteijee and coworkers (130). The model could adequately describe the effects of the NO2/NOX feed ratio on transient and steady-state NO conversions, as well as on the selectivity of the SCR process to NH4NO3 and N2O, in the relevant range of temperatures for diesel exhaust after-treatment. 

In a companion paper (117), the dynamic model of Reference (116) has been completed with account of the SO2 oxidation reaction. For this purpose transient SO2 conversion data were collected over a commercial V-W/Ti02 honeycomb catalyst during SO2 oxidation experiments, involving step changes in temperature, area velocity, and feed composition (SO2, O2, H2O and NH3) with respect to typical DeNOx conditions. Characteristic times of the system response were of a few hours, and peculiar SO3 emission peaks were noted upon step increments of reaction temperature and H2O feed content. All the data could be successfully fitted by a dynamic kinetic model based on the assumption that buildup-depletion of surface sulfate species is rate controlling (see eg. Figure 17). Finally, it was shown that the dynamic model of the SCR monolith reactor in Reference... 

The BET treatment is based on a kinetic model of the adsorption process put forward more than sixty years ago by Langmuir, in which the surface of the solid was regarded as an array of adsorption sites. A state of dynamic equilibrium was postulated in which the rate at which molecules arriving from the gas phrase and condensing on to bare sites is equal to the rate at which molecules evaporate from occupied sites. 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

Chemical dynamics and modeling were identified as important research frontiers in Chapter 4. They are critically important to the materials discussed in this chapter as well. At the molecular scale, important areas of investigation include studies of statistical mechaiucs, molecular and particle dynamics, dependence of molecular motion on intermolecular and interfacial forces, and kinetics of chemical processes and phase changes. 

In this work, the MeOH kinetic model of Lee et al. [9] is adopted for the micro-channel fluid dynamics analysis. Pressure and concentration distributions are investigated and represented to provide the physico-chemical insight on the transport phenomena in the microscale flow chamber. The mass, momentum, and species equations were employed with kinetic equations that describe the chemical reaction characteristics to solve flow-field, methanol conversion rate, and species concentration variations along the micro-reformer channel. 

The contribution of different crystal planes to the overall surface area of the particle can thus be calculated and is shown in Fig. 8.12(b). The results have been included in a dynamical micro-kinetic model of the methanol synthesis, yielding a better description of kinetic measurements on working catalysts [C.V. Ovesen, B.S. Clausen, J. Schiotz, P. Stoltze, H. Topsoe and J.K. Norskov, J. Catal. 168 (1997) 133]. 

GP 1] [R 1] A kinetic model for the oxidation of ammonia was coupled to a hydro-dynamic description and analysis of heat evolution [98], Via regression analysis and adjustment to experimental data, reaction parameters were derived which allow a quantitative description of reaction rates and selectivity for all products trader equilibrium conditions. The predictions of the model fit experimentally derived data well. 

Blaauboer BJ (2003) The integration of data on physicochemical properties, in vitro-derived toxicity data and physiologically based kinetic and dynamic as modelling a tool in hazard and risk assessment. A commentary. Toxicol Lett 138(1-2) 161-171... 

As a third example let us consider the growth kinetics in a chemostat used by Kalogerakis (1984) to evaluate sequential design procedures for model discrimination in dynamic systems. We consider the following four kinetic models for biomass growth and substrate utilization in the continuous baker s yeast fermentation. 

Monomer concentrations Ma a=, ...,m) in a reaction system have no time to alter during the period of formation of every macromolecule so that the propagation of any copolymer chain occurs under fixed external conditions. This permits one to calculate the statistical characteristics of the products of copolymerization under specified values Ma and then to average all these instantaneous characteristics with allowance for the drift of monomer concentrations during the synthesis. Such a two-stage procedure of calculation, where first statistical problems are solved before dealing with dynamic ones, is exclusively predetermined by the very specificity of free-radical copolymerization and does not depend on the kinetic model chosen. The latter gives the explicit dependencies of the instantaneous statistical characteristics on monomers concentrations and the rate constants of the elementary reactions. 

Model dynamics were forced to steady state by setting derivatives for the melt complexes in Eq. (61) to zero (Bunimovich et al., 1995). This should make the model behave as though the steady-state kinetic model... 

Timm, Gilbert, Ko, and Simmons O) presented a dynamic model for an isothermal, continuous, well-mixed polystyrene reactor. This model was in turn based upon the kinetic model developed by Timm and co-workers (2-4) based on steady state data. The process was simulated using the model and a simple steady state optimization and decoupling algorithm was tested. The results showed that steady state decoupling was adequate for molecular weight control, but not for the control of production rate. In the latter case the transient fluctuations were excessive. 

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