Forward and reverse uncertainty analyses for RRKM/master equation based kinetic predictions: A case study of ethyl with oxygen

Abstract

In the realm of combustion kinetic modeling, the norm involves employing thousands of reactions to delineate the chemical conversion of hundreds of species. Notably, theoretically predicted rate coefficients and branching ratios, derived through the RRKM/master equation (ME) model, play an increasing role in kinetic modeling. Thus minimizing the uncertainty of theoretical prediction across wide working conditions is crucial to refine a kinetic model. The present study takes ethyl (C₂H₅) + oxygen (O₂) reaction system to show that combined forward and reverse uncertainty analysis can be used to further constrain calculated rate coefficients and branching ratios, which were already calculated by high-level quantum chemistry methods. Forward global uncertainty analysis with the artificial neural network-high dimensional model representation (ANN-HDMR) method is employed to select key parameters affecting total rate coefficients of C₂H₅ + O₂ and branching ratios of C₂H₅ + O₂ = C₂H₄ + HO₂ (C1). Reverse uncertainty analysis with Bayesian method was then applied to refine the key input parameters based on experimental data at working conditions selected by sensitivity entropy. Although the target RRKM/ME model system was built on high level theoretical calculations, the combined forward and reverse uncertainty analyses are still able to reduce uncertainties of predicted total rate coefficients of C₂H₅ + O₂ and branching ratios for C1 across a wide range of working conditions. Specifically, the uncertainties of total rate coefficient and C1 branching ratio have been reduced from 1.46 and 1.52 to 1.30 and 1.36 at 298 K and 1 Torr. The analysis process proposed in the present work effectively extrapolates the constraint ability of accurate measured data at one condition to wide working conditions based on the RRKM/ME model.