Lumped reaction mechanism

All these steps can influence the overall reaction rate. The reactor models of Chapter 9 are used to predict the bulk, gas-phase concentrations of reactants and products at point (r, z) in the reactor. They directly model only Steps 1 and 9, and the effects of Steps 2 through 8 are lumped into the pseudohomoge-neous rate expression, a, b,. ..), where a,b,. .. are the bulk, gas-phase concentrations. The overall reaction mechanism is complex, and the rate expression is necessarily empirical. Heterogeneous catalysis remains an experimental science. The techniques of this chapter are useful to interpret experimental results. Their predictive value is limited. 

Preliminary work showed that first order reaction models are adequate for the description of these phenomena even though the actual reaction mechanisms are extremely complex and hence difficult to determine. This simplification is a desired feature of the models since such simple models are to be used in numerical simulators of in situ combustion processes. The bitumen is divided into five major pseudo-components coke (COK), asphaltene (ASP), heavy oil (HO), light oil (LO) and gas (GAS). These pseudo-components were lumped together as needed to produce two, three and four component models. Two, three and four-component models were considered to describe these complicated reactions (Hanson and Ka-logerakis, 1984). 

In the washcoat, reaction rates are modeled via global reaction mechanisms. In such a global or macrokinetic reaction mechanism, several microkinetic adsorption, reaction and desorption steps are lumped together, reducing the overall number of kinetic parameters considerably. For some catalysts,... 

Section 4.10 includes a brief survey of global reaction mechanisms, which have generally been obtained in a less formal way and with no direct link to the comprehensive mechanism. These skeleton mechanisms have played a major role in the development of our understanding of combustion. In the present context, the Shell model of autoignition [8] provides an excellent example, based on the underlying chemistry and providing a minimal basis for a description of the overall dynamics. An ultimate aim of reduction and lumping techniques is to provide models of this type, but with well-defined links to the comprehensive mechanism. 

The novelty in the work of Ranzi et al. is the automatic simplification of the large detailed reaction mechanism obtained by lumping both the species and the reactions. Isomers with similar kinetic behaviour were considered as single-lumped species (see Section 4.7.3 for a discussion of chemical lumping). Parallel reaction routes were lumped together based on kinetic assumptions. Finally, the model parameters were fitted to the predictions of the complete scheme. 

Lumping and Mechanism Reduction It is often useful to reduce complex reaction networks to a smaller reaction set which still maintains the key features of the detailed reaction network but with a much smaller number of representative species, reactions, and kinetic parameters. Simple examples were already given above for reducing simple networks into global reactions through assumptions such as pseudo-steady state, rate-limiting step, and equilibrium reactions. 

There is in fact sufficient knowledge available on the elementary steps involved in the reaction mechanisms to allow automatic generation of the entire network and the reaction intermediates, which run into several tens of thousands (Baltanas and Froment, 1985). In retrospect, and given a few fairly reliable assumptions, late lumping of the species and the reaction intermediates is possible (Vynckier and Froment, 1991). 

Most reactions in petroleum processing have so may reactants that their individual modeling is out of question. In such cases, the participants can be lumped into one or more supercomponents (lumps), the mixture can be treated mathematically as a continuum, or kinetics can be based on conversion not of individual molecules, but of reactive configurations that the reactants have in common. Only this last method can account for the actual reaction mechanism. 

In the light of the rate models obtained it may be of interest to speculate as to possible reaction mechanisms in the dehydrogenation and hydrogenation of butane-butenes system. The system may be described tentatively by lumping the cis- and trans-2-butenes as,... 

Two a priori lumped kinetic models were discussed in Chapter VIII the pH, YH model for pyrolyses and the COX and COLE model for oxidations. These models are basic models as they have the morphology which must be obeyed by all detailed reaction mechanisms of pyrolysis and oxidation. 

As has already been seen, these a priori lumped kinetic models account for the macroscopic properties of the reactions, such as cool flames, the delays of autoignition... but without being able to relate them to the chemical structure of the reactants. In other words, they are incapable of describing both qualitatively and quantitatively the formation of individual molecules, such as the toxic substances (carbon monoxide, aldehydes, butadiene, aromatics, PAHs, soot) or the tropospheric pollutants (nitrogen and sulphur oxides, unburnt hydrocarbons, various oxygenated compounds), produced by the burning of fuels. There is therefore a strong requirement to develop detailed reaction mechanisms, likely to predict both the kinetic and chemical characteristics of these reactions. 

Table 4 Lumped primary mechanism for the oxidation of an alkane propagation reactions. Units mol, cm, s, kJ.

Table 5 gives the propagation reactions (not including metatheses) of the lumped primary mechanism of the oxidation of n-pentane. It must be noted that this scheme only includes 4 free radicals instead of 24 for the detailed mechanism 3 pentyl radicals, 3 peroxy radicals, 9 hydroperoxypentyl radicals and 9 hydroperoxypentyl-peroxy radicals the dihydroperoxypentyl radicals have not been considered. 

This computer program carries out the reduction of detailed mechanisms using the Quasi- Stationary-State Approximation (QSSA). When the negligible species have been eliminated and the quasi-stationary species identified, the algorithm looks for a set of independent reactions allowing the quasi-stationary concentrations to be calculated by applying the QSSA. Lumped reactions are obtained by a linear combination of elementary reactions of the detailed mechanism. 

This computer program generates detailed primary mechanisms of oxidation and combustion reactions of alkanes and lumped secondary mechanisms of the primary products formed. It is interfaced with the KERGAS reaction database and the THERGAS, KINBEN and KINCOR computer programs. It produces reaction models (mechanisms, thermodynamic and kinetic data) which can be used directly in the CHEMKIN computer programs. 

SPYRO is a computer program for calculating a steamcracking reactor with hydrocarbon loads ranging from ethane to the naphthas. The computer program contains a detailed reaction mechanism for the pyrolysis of molecules containing from 1 to 4 carbon atoms and lumped mechanisms for larger species. The approach developed by the authors has been validated industrially. 

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