Inference and combination of missing data sets for the determination of [formula omitted] thermal decomposition rate uncertainty

Abstract

The thermal decomposition of H2O2 is an important process in hydrocarbon combustion, playing a particularly crucial role in providing a source of radicals at high pressure where it controls the 3rd explosion limit in the H2-O2 system, and also as a branching reaction in intermediate-temperature hydrocarbon oxidation. As such, estimating the Arrhenius parameters of the rate expression for this reaction and their joint uncertainty is crucial for performing meaningful predictive combustion computations. Raw experimental data is typically unavailable for most reported investigations of elementary reaction rates. Rather, what is typically available are summary statistics on measured quantities. The unavoidable loss of information in the use of summary statistics versus raw data for inference makes the direct computation of the necessary joint uncertainty structure of the parameters in rate expressions difficult. To overcome this situation we perform a statistical inference procedure relying on maximum entropy principles and approximate Bayesian computation methods, and employing a two-level nested Markov Chain Monte Carlo algorithm, to approximate the joint posterior density on the H2O2 decomposition rate parameters for a selected case of laser absorption measurements in a shock tube study, subject to the constraints imposed by the rate constant statistics and available information reported for this experiment. This procedure constructs a set of hypothetical H2O2 concentration decay profiles consistent with the reported statistics in the form of mean values and error bars of rate constants at the given experiment temperatures, and the data fitting model originally employed by the experimentalists - essentially reconstructing the missing experimental data in an approximate form. These consistent hypothetical data sets are then used to determine the joint Arrhenius parameter density through straightforward Bayesian inference within a pooling procedure. We apply the method in the context of combining the information within a single experimental setting (i.e. across a temperature range for fixed pressure) for the purposes of estimating Arrhenius parameters, and then extend the analysis to incorporate information from additional experiments (at a different target pressure) resulting in a decrease in the uncertainty of the parameter estimates as this new information is employed. We also highlight the flexibility of operating in this data-centric framework with a view to generating unbiased consensus rate expressions up to the full mechanism level when using multiple sources of experimental results in different forms.