Reduction kinetic models

Reduction kinetic models (/(a) differential form,g(a) integral, form Eqn. 11.15) 

Phase boundary controlled reaction (contracting area) (l-a)1/2 2(1 - (1 - a)1/2) 

The TPR patterns are very sensitive to the value of the activation energy which is needed for the modelling. Fortunately, this can be calculated separately from a series of experiments in which the heating rate is varied. Kissinger introduced this method in DTA measurements. It will be shown that this method can be generally used in TPR modelling. For the maximum of the TPR peak the following equations hold  

Assuming that /(a) and a are independent of the heating rate and that da/dT is not equal to zero, Eqn. (11.19) can be rewritten as  

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Mineral oil wastewater 03, 03/H202, Oj/uv SBBPR, LVP lamp, 17 W, 80-90% COD reduction. Kinetic modeling 175... 

After the precatalyst is completely converted to the active catalyst Xq, three steps are required to form the desired reduction product. The first step is the coordination of dehydroamino acid (A) to the rhodium atom forming adducts (Xi) and (Xi ) through C=C as well as the protecting group carbonyl. The next step is the oxidative addition of hydrogen to form the intermediate (X2). The insertion of solvent (B) is the third step, removing the product (P) from X2 and regenerating Xq. Hence, the establishment of the kinetic model involves these three irreversible steps. 

Abstract A review is provided on the contribution of modern surface-science studies to the understanding of the kinetics of DeNOx catalytic processes. A brief overview of the knowledge available on the adsorption of the nitrogen oxide reactants, with specific emphasis on NO, is provided first. A presentation of the measurements of NO, reduction kinetics carried out on well-characterized model system and on their implications on practical catalytic processes follows. Focus is placed on isothermal measurements using either molecular beams or atmospheric pressure environments. That discussion is then complemented with a review of the published research on the identification of the key reaction intermediates and on the determination of the nature of the active sites under realistic conditions. The link between surface-science studies and molecular computational modeling such as DFT calculations, and, more generally, the relevance of the studies performed under ultra-high vacuum to more realistic conditions, is also discussed. 

Backman, H., Arve, K., Klingstedt, F. et al. (2006) Kinetic considerations of H2 assisted hydrocarbon selective catalytic reduction of NO over Ag/Al203 Kinetic modelling, Appl. Catal. A 304, 86. 

The kinetic model simulations described above reveal straightforward methods of determining reversibility in chain transfer. In the cases simulated above, a reduction inM in connection with narrowing of the distribution such thatM IM < 2.0 indicates reversible chain transfer. These criteria provide a test for finding suitable combinations of catalyst and chain transfer agent for use in our two-catalyst system. 

A key feature of PdCys as precursors of Pd(0) nanoparticles is that reduction of Pd(II) -> Pd(0) involving C-Pd bond cleavage is required. This accounts for both the high temperatures invariably required and the induction period in the absence of reductants. Rosner et al. have developed a detailed kinetic model of a Heck reaction catalyzed by dimeric palladacycles (Rosner et al. 2001 a,b). This model explains the experimental observations and is consistent with an active species... 

Reports by Li and Zuberbuhler were in support of the formation of Cu(I) as an intermediate (16). It was confirmed that Cu(I) and Cu(II) show the same catalytic activity and the reaction is first-order in [Cu(I) or (II)] and [02] in the presence of 0.6-1.5M acetonitrile and above pH 2.2. The oxygen consumption deviated from the strictly first-order pattern at lower pH and the corresponding kinetic traces were excluded from the evaluation of the data. The rate law was found to be identical with the one obtained for the autoxidation of Cu(I) in the absence of Cu(II) under similar conditions (17). Thus, the proposed kinetic model is centered around the reduction of Cu(II) by ascorbic acid and reoxidation of Cu(I) to Cu(II) by dioxygen ... 

In alkaline solution (pH 11), the complex is present as a p-oxo dimer and ascorbic acid is fully deprotonated. In the absence of oxygen, kinetic traces show the reduction of Fe(III) to Fe(II) with a reaction time on the order of an hour at [H2A] =5xlO-3M. The product [Fen(TPPS)] is very sensitive to oxidation and is quickly transformed to Fe(III) when 02 is added. This leads to a specific induction period in the kinetic traces which increases with increasing [02]. The net result of the induction period is the catalytic two-electron autoxidation of ascorbic acid in accordance with the following kinetic model (23) ... 

The autoxidation of 3,5-di-terf-butylcatechol (H2DTBC) was frequently used to test the catalytic activity of various metal complexes. Speier studied the reaction with [Cu(PY)Cl] (PY = pyridine) in CH2C12 and CHCI3, and reported second-, first- and zeroth-order dependence with respect to Cu(I), 02 and substrate concentrations, respectively (41). The results are consistent with a kinetic model in which the rate determining oxidation of Cu(I) is followed by fast reduction of Cu(II) by H2DTBC. 

Alternative kinetic models were considered for this reaction. Both of them predict rapid reduction of Cu(II) Cu(II) to Cu(I) Cu(I) by H2DTBC and subsequent formation of the Cu(II)(0 -)Cu(II) intermediate in the reaction of the reduced form with 02. The first model assumes that the rate determining formation of the intermediate is followed by a fast, acid assisted dissociation into the oxidized form of the catalyst and H202. In the other model, the rate determining step is the oxidation of H2DTBC by the intermediate. The two models predict... 

Edwards, K. V. Manousiouthakis and T. F. Edgar. Kinetic Model Reduction Using Genetic Algorithms. Comput Chem Eng 22 239-246 (1998). 

Klupinski et al. (2004) conclude that the reduction of nitroaromatic compounds is a surface-mediated process and suggest that, with lack of an iron mineral, reductive transformation induced only by Fe(II) does not occur. However, when C Cl NO degradation was investigated in reaction media containing Fe(II) with no mineral phase added, a slow reductive transformation of the contaminant was observed. Because the loss of C Cl NO in this case was not described by a first-order kinetic model, as in the case of high concentration of Fe(II), but better by a zero-order kinetic description, Klupinski et al. (2004) suggest that degradation in these systems in fact is a surface-mediated reaction. They note that, in the reaction system, trace amounts of oxidize Fe(II), which form in situ suspended iron oxide... 

In practical combustion systems, such as CO boilers, the flue gas experiences spatial and temporal variations. Constituent concentration, streamline residence time, and temperature are critical to determining an efficient process design. Computational fluid dynamics (CFD) modeling and chemical kinetic modeling are used to achieve accurate design assessments and NO, reduction predictions based on these parameters. The critical parameters affecting SNCR and eSNCR design are listed in Table 17.4. 

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