Molecular reaction schemes

In molecular reaction schemes, only stable molecular reactants and products appear short-lived intermediates, such as free radicals, are not mentioned. Nearly all the reactions written are considered as pseudo-elementary processes, so that the reaction orders are equal to the mol-ecularities. For some special reactions (such as cocking) first order or an arbitrary order is assumed. Pseudo-rate coefficients are written in Arrhenius form. A systematic use of equilibrium constants, calculated from thermochemical data, is made for relating the rate coefficients of direct and reverse reactions. Generally, the net rate of the reversible reaction 

Some lumped constituent reactions can also be added to the molecular scheme in order to account for some complex features of global reaction (e.g. tar formation). 

The parameters of molecular reaction schemes include the Arrhenius parameters of rate coefficients and sometimes some stoichiometric coefficients and some reaction orders. 

Molecular reaction schemes have a long history of use in the design of pyrolysis coils. Since the pioneer works of Myers and Watson [46] and Schutt [47] on propane pyrolysis, improved by Snow and Schutt [48], molecular reaction schemes have been applied to the modelling of the pyrolysis of light and heavy hydrocarbons [38, 49—56]. Froment and co-workers have extensively promoted molecular reaction schemes in a series of papers [57—61] a brief account can be found in a book by Froment and Bischoff [25]. 

The building of a molecular reaction scheme may be done by analyzing the stoichiometric and kinetic results about the reaction under consideration, but also by means of theoretical considerations of the structure, thermochemistry and kinetics. 

Molecular reaction schemes have a long history of use in the design of pyrolysis coils. Since the pioneer works of Myers and Watson [46] and Schutt [47] on propane pyrolysis, improved by Snow and Schutt 

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Pseudo-kinetic Lumped constituents models Molecular reactions schemes... 

Theoretical considerations may also help to build up a reaction scheme. The principle of smallest change of structure states that only a few chemical bonds may be broken or formed in a single chemical step. This principle is mainly used in mechanistic modelling, but gives indications about the filiation of constituents. The knowledge of the equilibrium constants allows us to eliminate some reactions. Finally, if a detailed reaction mechanism has been postulated on firmly established experimental and theoretical grounds, it may be simplified to a molecular reaction scheme. 

Let us first note that the quality of a fit of correct models (comprehensive models can be assumed to be correct) to experiments generally increases when the number of parameters increases. But this is compensated for by increasing uncertainties in the parameter estimates. In other words, for a given amount of experimental results, only a limited number of parameters (or combinations of parameters) can be estimated with reasonable accuracy. A tentative rule of thumb could be stated for a given type of experiment, the number of rate coefficients that can be estimated from experimental results is nearly equal to the number of independent stoichiometries. (This rule is clearly true for molecular reaction schemes.) In general, except for very simple experiments where elementary processes have been quasi-isolated, the number of kinetic parameters far exceeds the amount of experimental information. Thus, only a few model parameters can be estimated. 

A more sophisticated approach is given by the so-called molecular reaction schemes. These schemes give a true picture of the stoichiometry and thermochemistry and describe the primary, secondary, etc. kinetic nature of reaction products. Though the rate coefficients of molecular reaction schemes are pseudo rate coefficients, they can generally be expressed in an Arrhenius form and do not depend too much on operating conditions however, they must be determined for each particular type of system and cannot be derived from fundamental kinetic parameters in the literature. 

In conclusion, pseudo-kinetic models cannot be extrapolated beyond the range of the experimental data they are derived from, cannot incorporate the progress achieved in the whole field of fundamental chemical kinetics, both experimental and theoretical, and cannot be used for designing new reactors. In all these domains, mechanistic simulation is obviously superior, at least theoretically, and this seems also to be true in practice. Indeed, Goossens et al. [77—79] have carried out a comparison of the value for prediction of their mechanistic model and of the molecular reaction schemes proposed by Ross and Shu [55] and Sundaram and Froment [60]. Goossens et al. concluded that there is an actual superiority of the mechanistic model. Froment himself now seems to agree with this conclusion since, after having developed the molecular reaction schemes with co-workers [57—61], he and Sundaram [186] have lately proposed free radical schemes for pyrolysis reactions. 

Implicit to our considerations are a number of assumptions regarding the molecular details of the individual elementary reaction steps. The analysis of the kinetics presented here employed a simplified molecular reaction scheme. Our approach aimed at formulating explicit relationships between those elementary reaction rate constants that determine selectivity. 

Figure 2. Molecular reaction scheme for the catalytic cracking of n-hexane.

Figure 1. Molecular reaction scheme for metal extraction into SF using protonated ligands.

Table 1 Molecular reaction scheme and kinetic parameters for the thermal cracking of ethane... 

The kinetic model used here has been developed by Sundaram and Froment [18] by a rigorous screening between several plausible molecular reaction schemes on the basis of thermodynamic considerations and statistical tests on the kinetic parameters. The scheme, together with the kinetic parameters, is given in Table 1. It should be added that the kinetic parameters for the reverse reactions (2) and (5) have been obtained from equilibrium data. 

MOLECULAR REACTION SCHEME AND KINETIC PARAMETERS FOR THE THERMAL CRACKING OF ETHANE ... 

Reaction Model, The molecular reaction scheme is taken from Sundaram and Froment (22). The model is composed of 5 reactions related to the main products,namely, ethylene,hydrogen, methane and propylene, and is summarized below... 

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