Transient kinetics modeling

The Bodenstein steady state approximation is widely applied in catalysis. At the same time this approximation is often not valid and the dynamics should be taken into accout. Transient kinetic modelling as well as oscillation reactions will be considered in Chapter 8. 

Liu W. and Flytzani-Stephanopoulos M. 1995. Total oxidation of carbon monoxide and methane over transition metal-fluorite oxide composite catalysts, J. Catal., 153, 304-316. Sedmak G., HoCevar S. and Levee J. 2004. Transient kinetic model of CO oxidation over a... 

The objective of the modelling work is to construct a transient kinetic model, which allows to give an adequate description of the measured N2, CO, NO, O2, CO2, N2O, and NO2 concentrations at the reactor outlet with a given inlet in time. 

The transient kinetic model of the standard SCR reaction over a commercial V-based catalyst for vehicles reported in Reference (101) is the only treatment available so far accounting both for the redox nature of the SCR catalytic mechanism and for the ammonia inhibition effect. It relies on a dual-site redox scheme, whereby ammonia is first adsorbed onto acidic sites, but reacts with NO on different redox sites associated with the vanadium component. The redox sites can, however, be blocked by excess ammonia. Adopting a Mars-Van Krevelen formal approach, the following modified redox (MR) rate expression was derived (27) ... 

Concerning other catalysts, Malmberg and co-workers have presented a transient kinetic model for NH3 SCR of NO over a Fe-zeolite catalyst (110),... 

Based on the above general model, Shi et al. [33] has proposed a transient kinetic model to describe the contamination of the PEM anode catalyst layer by H2S present in the fuel feed stream. Figure 6.5 shows flie model-predicted cell voltages in comparison with experimental results. It can be seen that their model provides an excellent fit with the experimental results. 

NibbeUce, R., Nievergeld, A., Hoebink, J., et al. (1998). Development of a transient kinetic model for the CO oxidation by O2 over a Pt/Rh/Ce02/K-Al203 three-way catalyst, Appl. Catal. B Environmental, 19, pp. 245-259. 

The corresponding reactions of transient Co(OEP)H with alkyl halides and epoxides in DMF has been proposed to proceed by an ionic rather than a radical mechanism, with loss of from Co(OEP)H to give [Co(TAP), and products arising from nucleophilic attack on the substrates. " " Overall, a general kinetic model for the reaction of cobalt porphyrins with alkenes under free radical conditions has been developed." Cobalt porphyrin hydride complexes are also important as intermediates in the cobalt porphyrin-catalyzed chain transfer polymerization of alkenes (see below). 

In the gas phase, the reaction of O- with NH3 and hydrocarbons occurs with a collision frequency close to unity.43 Steady-state conditions for both NH3(s) and C5- ) were assumed and the transient electrophilic species O 5- the oxidant, the oxide 02 (a) species poisoning the reaction.44 The estimate of the surface lifetime of the 0 (s) species was 10 8 s under the reaction conditions of 298 K and low pressure ( 10 r Torr). The kinetic model used was subsequently examined more quantitatively by computer modelling the kinetics and solving the relevant differential equations describing the above... 

Have we pushed the use of time resolved transient absorption with kinetic modeling to its limit We think not. Studies of the temperature dependence of hole transport in hairpins such as 3GAZ should provide additional details about the mechanism of this processes. The use of donor-acceptor triplexes... 

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. 

With the above-described heat transfer model and rapid solidification kinetic model, along with the related process parameters and thermophysical properties of atomization gases (Tables 2.6 and 2.7) and metals/alloys (Tables 2.8,2.9,2.10 and 2.11), the 2-D distributions of transient droplet temperatures, cooling rates, achievable undercoolings, and solid fractions in the spray can be calculated, once the initial droplet sizes, temperatures, and velocities are established by the modeling of the atomization stage, as discussed in the previous subsection. For the implementation of the heat transfer model and the rapid solidification kinetic model, finite difference methods or finite element methods may be used. To characterize the entire size distribution of droplets, some specific droplet sizes (forexample,.D0 16,Z>05, andZ)0 84) are to be considered in the calculations of the 2-D motion, cooling and solidification histories. 

Watanabe and Ohnishi [39] have proposed another model for the polymer consumption rate (in place of Eq. 2) and have also integrated their model to obtain the time dependence of the oxide thickness. Time dependent oxide thickness measurement in the transient regime is the clearest way to test the kinetic assumptions in these models however, neither model has been subjected to experimental verification in the transient regime. Equation 9 may be used to obtain time dependent oxide thickness estimates from the time dependence of the total thickness loss, but such results have not been published. Hartney et al. [42] have recently used variable angle XPS spectroscopy to determine the time dependence of the oxide thickness for two organosilicon polymers and several etching conditions. They did not present kinetic model fits to their results, nor did they compare their results to time dependent thickness estimates from the material balance (Eq. 9). More research on the transient regime is needed to determine the validity of Eq. 10 or the comparable result for the kinetic model presented by Watanabe and Ohnishi [39]. 

Kinetic modeling of the transient absorption spectra is necessary in order to obtain estimates of the lifetimes and rate constants associated with the evolution of the intermediates observed during the dissociation. A detailed description of the modeling may be found in our work on the picosecond photodissociation of the natural car-boxy- and oxy- heme complexes (3,4). The model is designed to treat the dissociation as a series of first or second order steps indicated in pathways I and II, ones that are consistent with the transient absorption data and with arguments based on bottlenecks... 

This represents the typical feed mixture to SCR converters when no oxidation precatalyst is applied, as for instance in the case of NOx abatement from stationary sources. With such a feed mixture the main deNOx reaction occurring over V-based catalysts is the so-called standard SCR (R6 in Table V). Transient experiments in a wide range of temperatures (50-550°Q were performed in order to develop a suitable kinetic model of the NH3-N0/02 reacting system. The study of the standard SCR kinetics was particularly focused on the characteristics that are critical for mobile applications, namely the behavior during transient operation and the reactivity in the low temperature region. 

In order to develop a suitable kinetic model of the full NH3-N0-N02/02 SCR reacting system, first the active reactions depending on N0/N02 feed ratio and temperature were identified then a dedicated study was performed aimed at clarifying the catalytic mechanism of the fast SCR reaction on the basis of such a reaction chemistry a detailed kinetic model was eventually derived, whose intrinsic rate parameters were estimated from global non-linear regression of a large set of experimental transient runs. 

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