Shortest paths in chemical kinetic applications

A computational model for the determination of important reaction pathways in a system of reaction equations is presented. The reaction scheme is treated as a bipartite directed graph where the vertices are the species and the reactions. An edge represents the connection of a reactant species and a reaction or a reaction and a product species. The length (weight) of an edge is a function of the mass flow (flux) through the reaction. The total length of a pathway from a reactant to a product species is the sum over all edges from the source vertex to the destination vertex. The question of identifying the most important reactions is equivalent to finding the shortest path from a reactant species to a product species. Typically, changes of parameters in the kinetic system, e.g. temperature, pressure, initial concentrations and reaction time may result in different best paths or shortest path solutions. These changes can be monitored with our tool. An example of an application treating the decomposition of methane in a dielectric-barrier discharge is presented in this paper.