Kinetics scheme Reaction network

Post-Gel Examples. In addition to affecting the pre-gel viscosity, the presence of water (or humidity during cure) can also affect the cure response and final network structure formed in urethane coatings. Using reactions R1-R4, the following kinetic scheme can be written for cure of polyol-urethane coatings in the presence of humidity ... 

A kinetic description of large reaction networks entirely in terms of elementary reactionsteps is often not suitable in practice. Rather, enzyme-catalyzed reactions are described by simplified overall reactions, invoking several reasonable approximations. Consider an enzyme-catalyzed reaction with a single substrate The substrate S binds reversibly to the enzyme E, thereby forming an enzyme substrate complex [/iS ]. Subsequently, the product P is irreversibly dissociated from the enzyme. The resulting scheme, named after L. Michaelis and M. L. Menten [152], can be depicted as... 

If the number of components is very large, a mixture can be regarded as continuous and sharp distinctions between individual components are not made. Methods for dealing with stoichiometry, thermodynamics and kinetics for continuous mixtures are discussed by Aris and Gavalas [33]. An indication is given that rules for grouping in such mixtures depend on the nature of the reaction scheme. Wei and Kuo [34] considered ways in which species in a multicomponent reaction mixture could be lumped when the reaction network was composed of first-... 

A number of mechanistic modeling studies to explain the fluid catalytic cracking process and to predict the yields of valuable products of the FCC unit have been performed in the past. Weekman and Nace (1970) presented a reaction network model based on the assumption that the catalytic cracking kinetics are second order with respect to the feed concentration and on a three-lump scheme. The first lump corresponds to the entire charge stock above the gasoline boiling range, the second... 

Another approach is to conduct competitive experiments with binary mixtures in which the complete reaction pathway is developed according to a reaction scheme like that of Scheme 1 described in the beginning of this review or like those shown in Figs. 12-15. Much of the confusion found in past reports of the kinetics of dibenzothiophene and its alkylated derivatives has come from incomplete deconvolution of the reaction network. Selectivity is often reported as the ratio of the yields of biphenyls (direct sulfur extraction) to the yields of cyclohexylbenzenes (hydrogenative route). As discussed in Section IV, cyclohexylbenzenes are produced via two different routes and, unfortunately, even low-conversion studies do not circumvent this confusion. To illustrate how conclusions can often be confused if the wrong model is used, some examples of reported competitive inhibition experiments will be discussed. 

Thus, considering the Fe-assisted PC conversion of phenol, the observable effect is that phenol produces many intermediate species from the start of the reaction regardless of the pathways involved in the production of such intermediates. It can thus be concluded that the Fe-assisted PC oxidation of phenol can be equally represented with a series-parallel reaction scheme, as it was for the unpromoted PC reaction. All the steps described above are summarized in Figure 10, a reaction scheme based on observable species. It must be emphasized that although the reaction network describes both unpromoted PC and Fe-assisted PC reactions, the values of the kinetic constants will be different for both systems. 

On the basis of acquired kinetic data, a general reaction network for reduced and sodium modified Ru-Sn/Si02 catalysts is proposed in Scheme 1... 

Unfortunately this principle is very often disregarded, or is not taken into account in modeling. We have to stress, however, that only thermodynamically consistent kinetic schemes correctly vector the overall process simulation. Moreover, the faster the reaction in the forward direction, the sooner is the equilibration. That means that disregarding of reverse reactions can distort the whole reaction network. 

As an example of the derivation of kinetic equations we will consider the hydrogenation of butadiene (J.Goetz, R.Touroude, D.Yu. Murzin, Kinetic aspects of selectivity and stereoselectivity for the hydrogenation of buta-1,3-diene over a palladium catalyst, Ind. Eng. Chem. Res., 35 (1996) 703). The overall reaction network, which was used for kinetic modeling is presented in Figure 4.2. In this scheme the addition of hydrogen to anti and syn - adsorbed diene molecules is assumed, producing but-l-ene trails- and cis but-2-ene are formed from anti and syn adsorbed diene respectively. There could also be a conformational interconversion of adsorbed buta-1,3-diene. 

Complex kinetic schemes cannot be handled easily, and, in general, a multidimensional search problem must be solved, which can be difficult in practice. This general problem has been considered for first-order reaction networks by Wei and Prater [13] in their now-classical treatment. As described in Ex. 1.4-1, their method defines fictitious components, B , that are special linear combinations of the real ones, Aj, such that the rate equations for their decay are uncoupled, and have solutions ... 

In biological systems, kinetic schemes for selectivity augmentation are widespread but are usually built upon highly sophisticated interwoven reaction networks. Naturally, this finding obviates easy adaptation and implementation into abiotic mimicks. though the principles seem clear, and attractive applications to artificial chemical flux systems are readily envisaged. 

The approach in which each reaction step is studied in isolation, in order to describe the chemistry involved correctly, and in which the resulting kinetic parameters of each step are then used as kinetic input to describe the overall kinetic scheme, gave good results. The Arrhenius law was satisfied (between 568 to 648 K) and the complete chemical network was fitted well. 

Kinetics and Mechanism. The isoparaffins are intermediate compounds in the reforming reaction network, as shown in (Scheme 1) for n-heptane. At very low conversion, isomers are the main products. In the reaction of n-heptane on Pt/Al203, at zero conversion the isomers are the 52% in moles of the products, whereas at high conversion (95%), cracking products are the main products and the isomers yield is 3%, which shows that after being formed, the isomers are converted by successive steps (19). There is a maximum in the formation of i-hexanes both as a function of space velocity (19) and as a function of temperature (6,20). The equilibrium between ra-C6 and methylpentanes is rapidly established, but this is not true for the dimethylbutanes (8,11). This observation indicates that there is a very low kinetic constant for the transformation of single branched into doubly branched isomers (8). 

Once defined the reaction network that describes the different investigated reacting systems and understood the main features of the reaction mechanisms, consistent kinetic schemes and rate expressions were derived, as extensively described in the following. In order to estimate the rate parameters in such expressions, transient experimental data collected over the powdered SCR catalyst were analyzed... 

Reaction Network and Kinetic Scheme Over the SCR Component... 

In recent years, kinetic studies have concentrated on the HDS of dibenzothio-phene (DBT) derivatives as these species are by orders of magnitude less reactive than sulfur species such as thioles, sulfides, and thiophene, or benzothiophene (Figure 5.1.22). The reaction network of hydrodesulfurization is illustrated in Scheme 6.8.2 for the example of HDS of DBT on CoMo. 

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