Complex reaction systems are ubiquitous. They are present in numerous chemical and biochemical systems, such as combustion, pyrolysis, nanoparticle synthesis, catalytic conversion of hydrocarbons, and cell metabolism. These systems involve a large number of reactions generating a large set of intermediate species. Automatic network generators allow generation of the exhaustive reaction network; however, the kinetic modeling of these systems is limited by their size and stiffness. Model reduction techniques involving lumping, sensitivity analysis and time-scale analysis can be used to address these challenges [1]. Model reduction using time scale analysis categorizes reactions as fast and slow, imposes pseudo-steady state hypothesis (PSSH) and/or quasi-equilibrium (QE) assumptions for the fast reactions, and generates pseudo-species which evolve in the slow time scale alone. A rigorous framework for performing these tasks for homogeneous reaction systems using singular perturbations was proposed in [2]; for the case of isothermal systems, a low-dimensional model of the slow dynamics can be expressed in terms of a set of pseudo-species obtained as a linear combination of the original species where the transformation matrix belongs to the left null space of the stoichiometric matrix of the fast reactions.

The present study proposes a graph theoretic analysis framework for identification of the pseudo-species evolving in a slow time scale. A directed bipartite graph is used to represent the species and reactions as two disjoint sets for a general chemical reaction network. An edge connecting the two sets represents species participation in a reaction as a reactant or product depending on the edge direction. Cycles consisting of a pair of species participating in fast reactions are identified using a backtracking algorithm [3]. These cycles are closed walks of two species nodes and two reaction nodes. Further, an algorithm that combines the identified cycles to form the pseudo-species, such that the pseudo-species interact with the remaining reaction network through slow reactions only, is developed. The proposed framework is scalable and applicable to heterogeneous systems as well. Three example reaction systems [2, 4] varying from *O*(10^{1}) to *O*(10^{4}) reactions are considered to show the efficacy of the proposed framework.

[1] Okino, M. S., and Mavrovouniotis, M.L. Simplification of Mathematical Models of Chemical Reaction Systems. *Chemical Reviews*, 98(2), 391-408, 1998.

[2] Vora, N., Daoutidis, P. Nonlinear Model Reduction of Chemical Reaction Systems. *AIChE Journal*, 47(10), 2320-2332, 2001.

[3] Tarjan, R. Enumeration of the elementary circuits of a directed graph. *SIAM J. Comput.*, 2(3), 211-216, 1973.

[4] Gerdtzen, Z.P., Daoutidis, P. and Hu, Wei-Shou. Non-linear reduction for kinetic models of metabolic reaction networks. *Metabolic Engineering*, 6(2), 140-154, 2004.

**Extended Abstract:**File Not Uploaded

See more of this Group/Topical: Computing and Systems Technology Division