Time scale decomposition in complex reaction systems: A graph theoretic analysis

•A graph-theoretic framework is presented for time scale decomposition of complex reaction networks.•The framework identifies the species that evolve only in the slow time scale.•An algorithm implementation using bi-partite graph representation of the reaction network is discussed.•The framework is automated, generic and scalable to large reaction networks.•An application to two reaction systems showing the computational advantage for model reduction is discussed.

The formulation of a kinetic model for a complex reaction network typically yields reaction rates which vary over orders of magnitude. This results in time scale separation that makes the model inherently stiff. In this work, a graph-theoretic framework is developed for time scale decomposition of complex reaction networks to separate the slow and fast time scales, and to identify pseudo-species that evolve only in the slow time scale. The reaction network is represented using a directed bi-partite graph and cycles that correspond to closed walks are used to identify interactions between species participating in fast/equilibrated reactions. Subsequently, an algorithm which connects the cycles to form the pseudo-species is utilized to eliminate the fast rate terms. These pseudo-species are used to formulate reduced, non-stiff kinetic models of the reaction system. Two reaction systems are considered to show the efficacy of this framework in the context of thermochemical and biochemical processing.