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.