Lumping, mechanism reduction

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 are other lumping techniques for linear kinetics, such as cluster analysis observer theory , singular perturbation , and intrinsic lowdimensional manifolds. Recently, Androulakis treated kinetic mechanism reduction as an integer optimization problem with binary variables denoting the existence and nonexistence of reactions and species. The technique is amenable to uncertainty analysis. 

Tomlin, A.S., Tur yi, T. Mechanism reduction to skeletal form and species lumping. In Battin-Leclerc, F., Blurock, E., Simmie, J. (eds.) Development of Detailed Chemical Kinetic Models for Cleaner Combustion, pp. 447-466. Springer, Heidelberg (2013b)... 

Sikalo et al. (2014) compared several options for the application of genetic algorithms to mechanism reduction, exploring the trade-off between the size and accuracy of the resulting mechanisms. Information on the speed of solution was also taken into account, so that, for example, the least stiff system (Sect. 6.7) could be selected. An automatic method for the reduction of chemical kinetic mechanisms was suggested and tested for the performance of reduced mechanisms used within homogeneous constant pressure reactor and burner-stabilised flame simulations. The flexibility of this type of approach has clear utility when restrictions are placed on the number of variables that can be tolerated within a scheme in the computational sense. However, the development of skeletal mechanisms is rarely the end point of any reductiOTi procedure since the application of lumping or timescale-based methods can be applied subsequently. These methods will be discussed in later sections. 

Several of the mechanism reduction methods discussed so far (see Sects. 7.2—7.6) result in a smaller reaction mechanism, which is a subset of the original detailed mechanism obtained by the removal of redundant species and reactions. Other methods provide a smaller mechanism cruisisting of lumped species and/or lumped reaction steps (Sect. 7.7). A further group of methods was then discussed which identify fast timescales within the model (see Sects. 7.8 and 7.9), and the resulting reduced model is a new set of differential equations with accompanying algebraic equations. In some cases these equatiruis can be converted back to a reaction... 

Whilst the mechanism of the process of size reduction is extremely complex, in recent years a number of attempts have been made at a more detailed analysis of the problem. If a single lump of material is subjected to a sudden impact, it will generally break so as to yield a few relatively large particles and a number of fine particles, with relatively few particles of intermediate size. If the energy in the blow is increased, the larger particles will be of a rather smaller size and more numerous and, whereas the number of fine particles will be appreciably increased, their size will not be much altered. It therefore appears that the size of the fine particles is closely connected with the internal structure of the material, and the size of the larger particles is more closely connected with the process by which the size reduction is effected. 

It is worth noting that some cyclic molecules play an important role in the mechanism. Another interesting feature results from the use of lumped compounds. The lumping of different species into a single pseudocompound causes a reduction in the complexity of the reacting system. For example, the 4 isomers of the branched C6 paraffins are lumped into a single pseudo-compound the 12 alkylbenzenes from C9 to C2o are described by three pseudo-compounds, C9, C1S and C20, etc. 

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. 

So far, the main aims of research into lumping have been to try and find mathematical procedures which apply to any general reaction system, and provide an automatic algorithm for reduction. It is not clear yet whether or not such a technique will ever exist which can be applied for any mechanism. Certainly if a method is to be developed it will have to be founded on rigorous mathematical principles. Quite a large amount of... 

For the reduction of chemical mechanisms, reaction-rate analysis has probably the largest record of success. A novel way for the inspection of rates is based on the study of algebraic-rate sensitivities and the Jacobian matrix. These methods can be used for the automatic identification of redundant species and reactions, to produce a reduced mechanism consisting of a subset of the original mechanism. The use of algebraic manipulation in techniques such as the QSSA and lumping, make the production of a reduced mechanism essential and make subsequent calculations as simple as possible. 

This chapter aims to describe the methods of automatic generation of the detailed mechanisms of the oxidation and combustion reactions of alkanes as well as the techniques of reduction of these mechanisms by the lumping of the species and of the reactions. 

FOURNET R., WARTH V., GLAUDE P.A., BATTIN-LECLERC F., SCACCHI G., COME G.M., Automatic Reduction of Detailed Mechanisms of Combustion of Alkanes by Chemical Lumping, Int. J. Chem. Kin., 32, 36 (2000). 

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. 

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