Uncertainty propagation in the derivation of phenomenological rate coefficients from theory: A case study of n-propyl radical oxidation

Abstract Global uncertainty and sensitivity analysis is used to study the propagation of uncertainties in fundamental theoretical parameters through to uncertainties in the predicted temperature and pressure dependent phenomenological rate coefficients. Predictions are obtained from ab initio transition state theory based master equation calculations. The fundamental parameters for these rate predictions include barrier heights, well depths, vibrational frequencies, collision frequency, and energy transfer parameters. A random sampling high-dimensional model representation (HDMR) approach is used to perform the global sensitivity analysis. This approach determines the predicted distributions of the phenomenological rate coefficients based on a quasi-random sample of the fundamental parameters within their uncertainty range. Sensitivity analysis then identifies the main parameters which contribute to variance in the predicted distributions. Here the approach is applied to a study of the oxidation of the propyl radical, employing the parameters derived in our recent theoretical study. We find rates at 3σ variances that typically differ from the most frequent values by factors of 4–6, with the uncertainties decreasing with increasing temperature. For the well skipping reactions there are more parameters that contribute significantly to the variance, the second-order sensitivities are greater, and the uncertainties increased with increasing pressure. For the other reactions, the uncertainties tend to decrease with increasing pressure.

[1]  Tamás Turányi,et al.  Effect of the uncertainty of kinetic and thermodynamic data on methane flame simulation results , 2002 .

[2]  James A. Miller,et al.  Master equation methods in gas phase chemical kinetics. , 2006, The journal of physical chemistry. A.

[3]  J. F. Griffiths,et al.  A global sensitivity study of cyclohexane oxidation under low temperature fuel-rich conditions using HDMR methods , 2009 .

[4]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[5]  Tamás Turányi,et al.  Local and global uncertainty analysis of complex chemical kinetic systems , 2006, Reliab. Eng. Syst. Saf..

[6]  J. Zádor,et al.  Kinetics of elementary reactions in low-temperature autoignition chemistry , 2011 .

[7]  Chih-Jen Sung,et al.  Autoignition of methanol: Experiments and computations , 2011 .

[8]  J. Zádor,et al.  New experiments and validated master-equation modeling for OH production in propyl + O2 reactions , 2011 .

[9]  Michael Frenklach,et al.  Optimization of combustion kinetic models on a feasible set , 2011 .

[10]  Michael J Davis,et al.  Theoretical validation of chemical kinetic mechanisms: combustion of methanol. , 2010, The journal of physical chemistry. A.

[11]  W. Green,et al.  Role of O2 + QOOH in low-temperature ignition of propane. 1. Temperature and pressure dependent rate coefficients. , 2012, The journal of physical chemistry. A.

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

[13]  Tamás Turányi,et al.  Uncertainty analysis of NO production during methane combustion , 2008 .

[14]  T. Ziehn,et al.  A global sensitivity study of sulfur chemistry in a premixed methane flame model using HDMR , 2008 .

[15]  Lawrence B. Harding,et al.  Uncertainty driven theoretical kinetics studies for CH3OH ignition: HO2 + CH3OH and O2 + CH3OH , 2011 .

[16]  Chih-Jen Sung,et al.  Reaction kinetics of CO + HO(2) --> products: ab initio transition state theory study with master equation modeling. , 2007, The journal of physical chemistry. A.

[17]  Alison S. Tomlin,et al.  GUI-HDMR - A software tool for global sensitivity analysis of complex models , 2009, Environ. Model. Softw..

[18]  Herschel Rabitz,et al.  Global uncertainty assessments by high dimensional model representations (HDMR) , 2002 .

[19]  S. Klippenstein,et al.  Experimental and theoretical investigation of the self-reaction of phenyl radicals. , 2010, The journal of physical chemistry. A.

[20]  Tamás Turányi,et al.  Numerical investigation of the uncertainty of Arrhenius parameters , 2011 .

[21]  Michael Frenklach,et al.  OH(OD) + CO: Measurements and an Optimized RRKM Fit , 1998 .

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

[23]  L. Curtiss,et al.  Assessment of Gaussian-4 theory for energy barriers , 2010 .

[24]  H. Rabitz,et al.  Efficient input-output model representations , 1999 .

[25]  Alison S. Tomlin,et al.  The Use of Global Sensitivity Methods for the Analysis, Evaluation and Improvement of Complex Modelling Systems , 2011 .

[26]  Michael Fairweather,et al.  Evaluation of models for the low temperature combustion of alkanes through interpretation of pressure-temperature ignition diagrams. , 2006, Physical chemistry chemical physics : PCCP.

[27]  Stephen J. Klippenstein,et al.  Measurements, theory, and modeling of OH formation in ethyl + O2 and propyl + O2 reactions , 2003 .