Lumping of continuous mixtures

Another important application of lumping is the lumping of continuous mixtures where an indefinitely large number of species are involved in a reaction [115-125]. Such techniques will be useful especially in processes which involve complex hydrocarbon mixtures such as petroleum feedstocks etc. The discrete system is then represented by a continuum and the lumping by an integration rather than a summation over the original variables. 

As an example we consider an isothermal system containing N different 

If the reaction order is assumed to be constant for all species then the only species dependent parameter is k,. Therefore, a species can be defined by its concentration c,- and its reactivity A ,.  

for N discrete species, the reactant lump can be expressed as 

If N becomes sufficiently large k may be treated as a continuous function and used to designate individual species. The lump C(r) can then be expressed in the integral form 

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