Elementary reaction network modeling

Global Kinetics and Elementary Reaction Network Modeling... 

J. M. Ploeger, P. A. Bielenberg, J. L. DiNaro-Blanchard, R. P. Lachance, J. D. Taylor, W. H. Green and J. W. Tester, Modeling Oxidation and Hydrolysis Reactions in Supercritical Water—Free Radical Elementary Reaction Networks and Their Applications, Combust. Sci. and Tech., 178, 363-398 (2006). 

Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

The very basis of the kinetic model is the reaction network, i.e. the stoichiometry of the system. Identification of the reaction network for complex systems may require extensive laboratory investigation. Although complex stoichiometric models, describing elementary steps in detail, are the most appropriate for kinetic modelling, the development of such models is time-consuming and may prove uneconomical. Moreover, in fine chemicals manufacture, very often some components cannot be analysed or not with sufficient accuracy. In most cases, only data for key reactants, major products and some by-products are available. Some components of the reaction mixture must be lumped into pseudocomponents, sometimes with an ill-defined chemical formula. Obviously, methods are needed that allow the development of simple... 

Using the modeling platform Copasi, the reaction network was encoded in the language SBML and the elementary flux modes were calculated, i.e. minimum sets... 

Mechanistic Modeling. In mechanistic modeling, an intrinsic reaction network is determined, based on the most probable mechanistic description. Rate constants are established individually for these elementary reactions through kinetic measurements. This type of model allows confident extrapolation outside the range of the data base used in its development. 

K-Hexadecane was chosen as model molecule since it is relatively easy to implement and obtain as a pure body. Its reaction network non-exhaustive on Fig. 29—is representative since it includes all the elementary steps involved in the hydrocracking/hydroisomerisation of heavy paraffinic cuts. After reduction, just six kinetic parameters (two for isomerisation, four for cracking) are required to represent this type of network. 

The approach to hydrocarbon cracking taken by the Froment school is to model the actual elementary steps of radicals at the various molecular configurations [38]. These are relatively few initiation hydrogen abstraction from a primary, secondary, or tertiary carbon and radical decomposition by scission of a carbon-carbon bond in /3-position to the unpaired electron. Boolean relation matrices are used to reflect the structures of the hydrocarbon reactants by indicating the existence and location of all their carbon-carbon bonds. Computer software generates reaction networks on the basis of known rate coefficients and activation energies at the various positions. Froment states the number of components in naphtha cracking as around 200, that of radicals as 40, and that of elementary radical steps... 

The proposed theoretical methodology has been applied here to study and rationalize a 15 elementary reaction microkinetic mechanism for the WGSR on Cu(lll) for illustrative purposes. A reaction network has been constructed that incorporates all of the 26 direct RRs that have been previously generated using the conventional methods. Using the electrical circuit analogy the reaction network was subsequently simplified and reduced to a reaction network involving only 3 dominant RRs. An overall rate equation has been developed that reproduces the complete microkinetic model precisely. 

In reality, most chemical reactions consist of numerous elementary reactions combined in reaction networks that are much more difficult to describe. An interesting elementary reaction is a 2-step sequential reaction which is relevant e.g. in modelling thermal separation processes ... 

A vague term, related to Latin machina, used loosely to describe a reaction network, or a reaction sequence, or the stereochemistry of an elementary step. Sometimes called a model. If based on kinetic arguments, it is occasionally called a kinetic mechanism. ... 

The model description of the measured differences in high pressure oxidation is not satisfactory concerning the influence of small wato amounts. Eiiher the model is not complete or th e is a specific solvent effect in addition to the pressure effect on the chemical kinetics. Until now the reaction rate of elementary reactions at high pressure has been measured only in helium [e.g. 32] Calculation of the fugacity coefficients of the HO2 free radical in supCTcritical water also shows specific solvent interactions as a consequence of partial charges [33]. It can be assumed that these inta actions are much lower in supCTcritical carbon dioxide which may lead to somewhat different reaction rates of elementary reactions in the reaction network. 

In microscale model, the reactions generally refer to elementary reaction steps. The reaction network is closely related to the reaction mechanism and could be well obtained by quantum chemistry or ab initio calculations. The corresponding parameters, such as pre-exponential factors and activation energies, could be predicted based on transition state theory (TST) or variational transition state theory (VTST). 

In order to extract more information from the steady-state flux model, extreme pathway analysis (EPA) and elementary mode analysis (EMA) have been developed [14,15]. In these approaches, the metaboHc reaction network is decomposed into a collection of small irreversible functional pathways. When these pathways are weighted and superimposed back together, they are able to form the original metaboHc flux network. By examining the elementary pathways, and using Hnear optimization tools, it is possible to better explore the metaboHc capabilities of a network, and this can also be used to suggest useful metaboHc pathway alterations. 

Models of the ISM consist of a physical framework, that may involve dynamical processes, but certainly involves the timescales of the overall processes being modelled, a chemical context, e.g. the abundances of key species, and a set of ordinary differential equations (odes), that describe the kinetics of the component elementary reactions that make up the network [2]. These odes are of the form ... 

ABSTRACT. A fundamental approach is outlined for the kinetic modeling of complex processes like thermal cracking or catalytic hydrocracking of mixtures of hydrocarbons. The reaction networks are written in terms of radical mechanisms in the first case and of carbenium ion mechanisms in the second case. Since the elementary steps of the networks pertain to a relatively small number of classes, the number of rate coefficients is kept within tractable limits. The reaction networks are generated by computer through Boolean relation matrices. The number of continuity equations is limited by the elimination of radicals or carbenium ions through the pseudo-steady-state approximation. 

The n-octane reaction network consists of 383 elementary chemical steps (52 hydride shifts of the 1.2- and 36 of the 1.3-type, 24 methyl shifts, 96 PCP branching isomerizations, 15 iS-scissions, 75 protonations and 85 deprotonations) involving 14 octanes, 5 paraffinic and 9 olefinic cracking products, 49 octenes, 42 octyl carbenium ions and 6 carbenium ions with a smaller carbon number, disregarding the methyl- and primary carbenium ions, which are known to be less stable. There is, however, no need to consider 383 rate coefficients, since the elementary chemical steps belong to only 6 types when no distinction is made between 1.2 and 1.3 hydride shifts. Yet, since the values of rate coefficients depend upon the structure of the reactant and the product, the true number of parameters depends upon the detail of the structure accounted for in the modeling. 

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