Lumping analysis of chemical reaction systems



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Kinetic modeling of complex reaction networks involving a large number of species usually requires lumping several of the species into a smaller number of reactive groups. The complexity of a model is governed not only by mathematical considerations but much more by accessibility of experimental information and the objectives of the model. This work investigates the effect of temperature on the reaction rate of grouped species which are consumed by parallel nth order irreversible reactions. It is shown that when the activation energies of the individual reactions is about equal, the temperature effect can be described by an Arrhenius expression. However, when the activation energies of the various reactions are widely spread, the Arrhenius dependence may not be adequate unless one assumes that the activation energy of the lump may be temperature and conversion dependent. Under these conditions, the Arrhenius temperature dependence is, at best, a rough approximation and it is very important to define exactly the experimental method of determining the activation energy. Widely different activation energies for the pseudocomponent may be obtained from different experimental techniques which yield the same value for a single reactant. Next, the exact and approximate lumping of many parallel first order competing reactions has been analyzed. The applicability of empirical rate expressions to describe the behavior of lumped concentrations is examined. Exact lumping requires complete specifications of reacting species and rate constants. When this information is not available, bounds on the lumped concentration may be derived using limited experimental information. The bounds enable to determine the quality of lumping and guide the manner in which species should be grouped together. The bounds can also test the lumping in recycle reactors. A more general approach to lumping has been shown to be based on the constancy of lump selectivity. This work also analyzes the lumping of consecutive reaction networks. Once again, the applicability of empirical rate expressions to determine lumped concentrations has been examined. Bounds for the various lumped concentrations have been developed which in turn provide criteria regarding how various species ought to be grouped in a lump. This method has been applied to determine the adequacy of lumping in the case of chlorination of n-decane. Finally, the lumping of the above two reaction networks in a continuous flow stirred tank reactor is examined. The lumpability conditions are shown to be exactly the same as those obtained when reactions are carried out in batch reactors.