Sensitivity Analysis of a Mechanism for Methane Oxidation Kinetics

Abstract - A sensitivity test procedure developed by Shuler and co-workers for obtaining systematic estimates of the sensitivity of the solution of coupled sets of non-linear differential equations to variations in parameters is applied to a 23-equation methane oxidation mechanism. The sensitivity method is based on varying each rate constant sinusoidally with a specific frequency assigned to each rate constant over an arbitrary range. The results are Fourier analyzed to determine quantities which measure the uncertainty in the solution as well as the individual contributions from each rate constant. By application of this procedure, we obtain estimates for the sensitivity of species concentrations of reactants, products and free radicals which occur in the CH 4 -0 2 -Ar system subject to a simultaneous variation of all rate coefficients over a ± 50 percent uncertainty range. We present results for a stoichiometric reaction of the CH 4 -0 2 -Ar system at 2000° K for a time corresponding to ignition. Jt is found that of the 23 reactions (plus their reverse) included in the mechanism, only about 5-7 reactions (depending on the species in question) strongly affect the concentration of that species. For the specific case of the Ο-atom concentration, we find that our six most sensitive reactions include the five reported previously by Bowman in the Fifteenth Symposium (International) on Combustion. For the ±50 percent variation in rate constants, we find deviations from the mean concentration ranging from ∼3 to ∼71 percent, depending on species.