Global Uncertainty Propagation and Sensitivity Analysis in the CH₃OCH₂ + O₂ System: Combining Experiment and Theory To Constrain Key Rate Coefficients in DME Combustion

Abstract

Statistical rate theory calculations, in particular formulations of the chemical master equation, are widely used in order to calculate rate coefficients of interest in combustion environments as a function of temperature and pressure. However despite the increasing accuracy of electronic structure calculations, small uncertainties in the input parameters for these master equation models can lead to relatively large uncertainties in the calculated rate coefficients. Master equation input parameters may be constrained further using experimental data and the relationship between experiment and theory warrants further investigation. In this work the CH 3 OCH 2 + O 2 system, of relevance to the combustion of dimethyl ether (DME), is used as an example and the input parameters for master equation calculations on this system are refined through fitting to experimental data. Complementing these fitting calculations, global sensitivity analysis is used to explore which input parameters are constrained by which experimental conditions, and which parameters need to be further constrained in order to accurately predict key elementary rate coefficients. Finally, uncertainties in the calculated rate coefficients are obtained using both correlated and uncorrelated distributions of input parameters.

Harnessing the Combined Power of Theoretical and Experimental Data through Multiscale Informatics

“…A number of recent studies have explored the impact of various uncertainties in ab initio transition‐state‐theory‐based calculations of elementary reaction rate constants using typical model components. Generally speaking, the sources of uncertainty can be qualitatively grouped into four categories.…”

“…Generally speaking, the sources of uncertainty can be qualitatively grouped into four categories. First, there are uncertainties in the evaluation of the energetics of stationary points, which are often represented as uncertainties in barrier heights and intermediate well depths . Second, there are uncertainties in the evaluation of the partition function, which can be represented as uncertainties in all harmonic frequencies or groups of harmonic frequencies and/or hindered rotor potentials (within the context of a rigid‐rotor‐harmonic‐oscillator model with 1‐D hindered rotors for the torsional modes).…”

“…Third, there are uncertainties in the evaluation of the tunneling transmission coefficient, which are often represented as uncertainties in the imaginary frequency , well depth from reactants to the entrance well , and well depth from products to the exit well (within the context of an Eckart tunneling model). Fourth, there are uncertainties in collisional energy transfer, which is usually represented as uncertainties in the magnitude and temperature dependence of the average energy transferred per down collision (within the context of a strong‐collision‐in‐ J exponential down model) and Lennard–Jones parameters (within the context of the Lennard–Jones collision frequency model).…”

“…As concluded elsewhere and demonstrated in Figs. , uncertainties in model parameters from each of those four groups can contribute substantially to predictions of rate constants and experimental observables . For example, Fig.…”

“…In forward and inverse uncertainty quantification involving theoretical kinetics calculations, uncertainties in the theoretical parameters are usually assigned estimated uncertainty factors and are usually assumed to be uncorrelated (as a result of minimal information about their probability density functions). More accurate representations of the uncertainties in theoretical calculations would benefit from improved understanding of both the magnitude of typical uncertainties in the calculated values as well as cross‐correlations among them .…”