Lumping analysis, reaction kinetics

Wei s later work with J. C. Kuo on lumping and that of Li and Rabitz at Princeton [Chem. Eng. Sci. 44,1413, (1959)] also opened up an important area of formal kinetics. See also Bischoff and Coxson, Lumping strategy. l.E.C. Res. 26,1329 2151, (1983). J. E. Bailey [Lumping analysis of reactions in continuous mixtures. Chem. Eng. J. 3, 5261 (1962)]. forged an important link between continuous mixtures and lumps. 

Three general strategies have been pursued for model order reduction lumping, sensitivity analysis, and time-scale analysis. Lumping, the most common method, groups the reactants into a smaller number of pseudo-species. The grouping may be based on some set of physical properties, or on the reactivity of the compound. Lumping is useful when only limited measurements and information are available about specific reaction kinetics and detailed chemical composition in a lumped model, most information about specific reactions and species is concealed. 

It is in the area of approximate lumping that the distinction between the meaning of lumping, as used in this article, and of overall kinetics, possibly becomes a fuzzy one. For instance, the analysis of many parallel irreversible first-order reactions, to be briefly discussed in the next section, has been called lumping in the literature, though it is not in any sense an exact (Wei-Kuo) lumping, nor an approximate one One chooses to consider only one lump, as given later by Eq. (97) but the qualitative kinetic behavior of the lump in no way resembles that of the... 

Now, some difficulties may appear around the reactor. The inspection of the heat recovery system reveals a rather complicated structure. To simplify this first analysis, the whole heat recovery system is lumped in a single unit, called FEHE, which is the abbreviation for Feed-Effluent-Heat-Exchanger. However, coding the reactor remains difficult. Selecting a Plug Flow Reactor (PFR) model, close to physical reality, requires kinetics. Again, we can simplify the analysis by assuming the main reactions close to equilibrium in a first unit R1 (REQUIL) followed by a second unit R2 (RSTOIC) that... 

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. 

Therefore, it is good engineering practice to use in reactor models so-called effective parameters by lumping several basic mechanisms or reaction steps into an overall phenomenon described by one single term in the respective reactor or reaction model. In this way, the parameters are always bound to the model equations by which they have been defined. The parameter values determined by regression analysis cannot be used independently in other model equations like physical properties, flow velocity etc., measurable independently without any model definition. This fundamental dilemma has some consequences in kinetic data analysis and parameter estimation that should always be kept in mind ... 

---