Species Lumping

Algorithmic approaches have also been developed that attempt to define mathematical rules for the selection of lumped groups as well as methods for the determination of reaction rates for the new reactions of the lumped species. Such methods have the advantage that they are based on formal principles and therefore do not rely on chemical knowledge or a priori assumptions about the chemical reactivity of the original species. They may, however, require the application of quite stringent mathematical restrictions that make wide application difficult and may result in a reduced model form that cannot easily be cast in terms of a set of 

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The species which are unknown and have not been identified as one of the major chemical lump such as alkanes, phenols and aromatics are lumped together as unidentified. However, the species in this lump include saturated and unsaturated cycloalkanes with or without side chains, which resembles the naphthenes, a petroleum refinery product group. A number of well known species in coal liquid are not mentioned in this lumping scheme. Such as heterocyclic compounds with sulfur, nitrogen or oxygen as the heteroatom, and other heteroatora containing species. Some of these compounds appear with aromatics (e.g. thiophenes, quinolines) and with phenols (e.g. aromatic amines), and most of them are lumped with the unidentified species lump. 

A linear algebraic system of rate equations for the fast species results, which can be solved a priori. Hence a strongly reduced (in the number of species to be treated) system is obtained. This concept originates from astrophysical applications and from Laser physics. It is in some instances also referred to as collisional-radiative approximation , for the fast species, lumped species concept , bundle-n method or intrinsic low dimensional manifold (ILDM) method in the literature. We refer to [9,12,13] for further references on this. 

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)... 

In terms of species lumping, we can now see that it is possible to define a new set of variables which define the lumped species... 

If the function h is linear, then in chemical kinetics, this approach would be termed linear species lumping and is essentially a formalisation of the chemical lumping approach described in the previous section. In the linear case the transformation is simply a matrix multiplication operation ... 

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