Lumping via Stochastic Assembly

This lumping approach, introduced by Klein and coworkers, deals with reaction systems involving large molecules whose structures are very difficult, if not impossible, to characterize. A case in point is asphaltenes, the portion of a resid that is aromatic-soluble and paraffinic-insoluble. Lumping is achieved by assuming that the reactivity of such large molecules is dominated by the reactivities of a small number of functional groups on the molecules. A 

For the pyrolysis of asphaltenes, Klein s approach basically consists of the following steps (1) construction of an ensemble of reactant molecules based on characterization data, (2) development of lumped kinetics for a set of reactive functionalities, and (3) coupling of ensemble with lumped kinetics. This first step is stochastic while the rest are deterministic. Each of the steps is briefly described below. 

A simple way of constructing each molecule in the ensemble is to cormect ring systems (aromatic or naphthenoaromatic) with alkyl chains in a linear fashion subject to stoichiometric constraints. It is easier to construct an ensemble of liquid molecules than solid molecules. The latter requires modeling of three-dimensional structures. 

The second step assumes that the reactivity of the ensemble is dominated by a few selected functionalities. The task then is to determine the reaction kinetics for each of the functional groups. Here the art of lumping applies in order to keep the number of kinetic lumps small. Information on reaction pathways and kinetics can be independently obtained from experiments using representative model compounds. For example, butyl benzene pyrolysis may serve as a model system for the pyrolysis of alkyl aromatics moieties in resids. 

The final step is to couple the lumped kinetics with the stochastically constructed ensemble. One then follows the reactions by updating the composition of the ensemble as the reactions proceed. The initial reaction 

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