Determining predictive uncertainties and global sensitivities for large parameter systems: A case study for n-butane oxidation

A global sampling approach based on low discrepancy sequences has been applied in order to propose error bars on simulations performed using a detailed kinetic model for the oxidation of n-butane (including 1111 reactions). A two parameter uncertainty factor has been assigned to each considered rate constant. The cases of ignition and oxidation in a jet-stirred reactor (JSR) have both been considered. For the JSR, not only the reactant mole fraction has been considered, but also that of some representative products. A temperature range from 500 to 1250 K has been studied, including the negative temperature coefficient (NTC) region where the predictive error bars have been found to be the largest. It is this temperature region where the highest number of reactions play a role in contributing to the overall output errors. A global sensitivity approach based on high dimensional model representations (HDMR) has then been applied in order to identify those reactions which make the largest contributions to the overall uncertainty of the simulated results. The HDMR analysis has been restricted to the most important reactions based on a non-linear screening method, using Spearman Rank Correlation Coefficients at all studied temperatures. The final global sensitivity analysis for predicted ignition delays illustrates that the key reactions are mainly included in the primary mechanism, for temperatures from 700 to 900 K, and in the C0C2 reaction base at higher temperatures. Interestingly, for predicted butane mole fractions in the JSR, the key reactions are almost exclusively from the reaction base, whatever the temperature. The individual contribution of some key reactions is also discussed.