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

Abstract

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 t h e 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 t h e n then b e e n applied in order to identify those reactions which make the largest contributions toTo whom correspondence should be addressed. E-mail : Frederique.Battin-Leclerc@univ-lorraine.fr. 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 s t u d i e d temperatures. The final global sensitivity analysis for p r ed ict ed ignition delays illustrates that the key reactions are mainly included in the primary mechanism, for temperatures from 700 to 900 K, and in the C 0 -C 2 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.

The influence of n -butanol blending on the ignition delay times of gasoline and its surrogate at high pressures

“…Here, the reaction of formaldehyde + OH is important across the whole temperature range, but particularly so at the highest temperature. The sensitivity analysis also shows that the reactions of HO 2 dominate above 780 K. Nagy et al [42] highlighted uncertainties of a factor of 2.5 in the reaction rate for HO 2 The isomerisation reactions from RO 2 to QOOH are of lower importance here than fuel + OH which contrasts with the behaviour of smaller molecules [43]. However, they do feature for both iso-octane and n-heptane channels across the range of temperatures studied, and thus uncertainties in the temperature dependence of these reactions could affect the prediction of NTC behaviour.…”

“…Although it is well known [43] that isomerisation reactions of RO 2 dominate auto-ignition chemistry in general low-temperature mechanisms for smaller fuels, the dominance of the main fuel hydrogen abstraction reactions in the blended TRF-butanol scheme may be due to its key role in determining the amount of n-butanol that goes to termination steps compared with how much is available for chain branching and propagation. The ability of the reaction mechanism to correctly predict the low temperature delays for both n-butanol and the blend requires that the balance between the two dominant abstraction channels for n-butanol + OH is known for a wide range of temperatures and significant uncertainty still exists requiring further study.…”

Chemical model reduction under uncertainty

“…We next describe the utilization of the above construction for simplification of a 176-species, 1111-reaction, uncertain n-butane-air mechanism with published uncertainty for Arrhenius rate parameters [23], based on constant pressure homogeneous ignition. We explore convergence of the results as a function of the number of random samples, and examine errors in ignition delay time and uncertain trajectories with respect to the detailed mechanism.…”

“…The specification of uncertain parameters in [23] for each reaction [27]. However, it may be argued that the correlation struc- .…”

Uncertainty of the rate parameters of several important elementary reactions of the H2 and syngas combustion systems

“…In most of these studies (see e.g. [25][26][27][28][29][30][31][32][33]) only the uncertainty of the Arrhenius parameter A was considered, and it was assumed to be equal to the temperature-independent uncertainty of the rate coefficient, characterized by the uncertainty parameter f. Maybe the only exception is the recent article of Hébrard et al [34], where the uncertainty of the rate coefficient k at 300 K and the uncertainty of the temperature dependence of k were considered separately at the uncertainty analysis of an n-butane oxidation mechanism. However, Hébrard et al did not consider the joint uncertainty of the Arrhenius parameters.…”