Using Bayesian analysis to quantify uncertainties in the H + O2 → OH + O reaction

Abstract A stochastic Bayesian approach is applied to investigate the uncertainty in the rate coefficient of H + O 2  → OH + O ( k 1 ) using the latest shock-tube experimental data. We simultaneously calibrate all random variables using a recently developed stochastic simulation algorithm which allows for efficient sampling in the high-dimensional parameter space. We introduce the idea of “irreducible” uncertainty when considering other parameters in the system. Nine stochastic models are constructed depending on the choice of uncertainties, hydrogen concentration, gas temperature, pressure, and rate coefficients of other reactions. The sensitivity analysis of uncertainty in k 1 on these uncertainty parameters is performed. It is shown that the introduction of “irreducible” uncertainty does not always increase the uncertainty of k 1 . In addition, we observe the high sensitivity of uncertainty in k 1 to the uncertainty in the measured time-shift. Our results show the strong temperature dependence of the uncertainty in the rate coefficient.

[1]  Serge Prudhomme,et al.  Probabilistic models and uncertainty quantification for the ionization reaction rate of atomic Nitrogen , 2011, J. Comput. Phys..

[2]  Serge Prudhomme,et al.  On the assessment of a Bayesian validation methodology for data reduction models relevant to shock tube experiments , 2012 .

[3]  Andrew Packard,et al.  Sensitivity analysis of uncertainty in model prediction. , 2008, The journal of physical chemistry. A.

[4]  J. Beck,et al.  Updating Models and Their Uncertainties. I: Bayesian Statistical Framework , 1998 .

[5]  Tamás Varga,et al.  Determination of rate parameters based on both direct and indirect measurements , 2012 .

[6]  Raymond W. Walker,et al.  Evaluated kinetic data for combustion modelling supplement I , 1994 .

[7]  Aamir Farooq,et al.  Hydrogen peroxide decomposition rate: a shock tube study using tunable laser absorption of H(2)O near 2.5 microm. , 2009, The journal of physical chemistry. A.

[8]  Ronald K. Hanson,et al.  A new shock tube study of the H + O2 → OH + O reaction rate using tunable diode laser absorption of H2O near 2.5 μm , 2011 .

[9]  David A. Sheen,et al.  The method of uncertainty quantification and minimization using polynomial chaos expansions , 2011 .

[10]  Ronald K. Hanson,et al.  Shock tube study of the reaction hydrogen atom + oxygen .fwdarw. hydroxyl + oxygen atom using hydroxyl laser absorption , 1990 .

[11]  Pascal Pernot,et al.  Statistical approaches to forcefield calibration and prediction uncertainty in molecular simulation. , 2011, The Journal of chemical physics.

[12]  Terese Løvås,et al.  Spectral uncertainty quantification, propagation and optimization of a detailed kinetic model for ethylene combustion , 2009 .

[13]  Kenji Miki,et al.  Uncertainty quantification of a graphite nitridation experiment using a Bayesian approach , 2011 .

[14]  Peter J Seiler,et al.  Prediction uncertainty from models and data , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[15]  Lambros S. Katafygiotis,et al.  Updating of a Model and its Uncertainties Utilizing Dynamic Test Data , 1991 .

[16]  Sai Hung Cheung,et al.  Bayesian uncertainty analysis with applications to turbulence modeling , 2011, Reliab. Eng. Syst. Saf..

[17]  Tamás Turányi,et al.  Uncertainty of Arrhenius parameters , 2011 .

[18]  T. Germann,et al.  Quantum Mechanical Pressure-Dependent Reaction and Recombination Rates for O + OH → H + O2, HO2 , 1997 .

[19]  H. Bässler,et al.  Hole transport in bis(4‐N,N‐diethylamino‐2‐methylphenyl)‐4‐methylphenylmethane , 1991 .

[20]  B. C. Garrett,et al.  Quantifying the non-RRKM effect in the H + O2 ⇄ OH + O reaction , 1997 .

[21]  P. Frank,et al.  High temperature reaction rate for H+O2=OH+O and OH+H2=H2O+H , 1985 .

[22]  Sai Hung Cheung,et al.  Calculation of Posterior Probabilities for Bayesian Model Class Assessment and Averaging from Posterior Samples Based on Dynamic System Data , 2010, Comput. Aided Civ. Infrastructure Eng..

[23]  M. Frenklach,et al.  Determination of the rate coefficient for the reaction hydrogen atom + oxygen .fwdarw. hydrogen + oxygen atom by a shock tube/laser absorption/detailed modeling study , 1991 .

[24]  Serge Prudhomme,et al.  Estimation of the nitrogen ionization reaction rate using electric arc shock tube data and Bayesian model analysis , 2012 .

[25]  S. Cheung,et al.  Bayesian uncertainty quantification of recent shock tube determinations of the rate coefficient of reaction H + O2 OH + O , 2012 .

[26]  C. Westbrook,et al.  A comprehensive modeling study of hydrogen oxidation , 2004 .