UNCERTAINTY ANALYSIS OF NITROGEN OXIDE FORMATION
IN METHANE COMBUSTION

I. Gy. Zsély, J. Zádor, T. Turányi
Eötvös University (ELTE), Hungary
zsigy@chem.elte.hu

The combustion of methane is one of the most frequently modelled chemical reactions due to its high academic and industrial importance. Methane is the main component of natural gas, which is widely used for power generation and heating. NO is the major pollutant formed during natural gas combustion. Methane combustion mechanisms are widely used for the prediction of the NO production and can be used for the design of low-NOx burners. No quantitative investigation of the uncertainty of the NO production has been published. Also, the uncertainty of the ratios of the various NO formation routes is not known.
In this study, the Leeds Methane Oxidation Mechanism [1], extended with an NO-formation mechanism [2] was used. This joint mechanism is capable of simulating the formation of NO during methane combustion at a wide range of conditions. The mechanism contains 340 irreversible reactions of 56 species. The kinetic data were updated based on a literature search and the thermodynamic data were revised using Burcat’s recent thermodynamic database [3]. 
The NO formation kinetics was investigated at the conditions of the experiments of Bartok et al. [4]. This set of experiments is a frequently used benchmark of NO formation during methane combustion. The experiments were carried out in a perfectly stirred reactor at atmospheric pressure. The residence time was 3 ms and the equivalence ratio was changed between 0.67 and 1.75. The simulations were carried out with the PSR code [5] of the CHEMKIN-II package. This program was modified for calculating the local enthalpy-of-formation sensitivity coefficients and carrying out sequential calculations with several different parameter sets as required by the global uncertainty analysis methods. Local uncertainties were calculated by program KINALC [3].
	Combustion models include thousands of parameters, like kinetic parameters, thermodynamic data, diffusion coefficients etc. In this study, the uncertainty of rate coefficients and enthalpy-of-formation data were considered. For the rate coefficients, lognormal distribution was assumed; the variance was determined [6] from the uncertainty factor f, which was available from several kinetic databases. Normal distribution was assumed for the enthalpies-of-formation of each species; the expected values and the variances were determined from thermodynamic databases. The uncertainties of all kinetic and thermodynamic parameters were assumed to be independent.
	Based on local sensitivity coefficients and the variance of parameters, and using the rules of error propagation [6] uncertainty of the calculated NO concentration was determined. This local uncertainty analysis allows computationally cheap investigation of the contribution of parameters to the uncertainty of results and the determination of the ratio of the kinetic and thermodynamic uncertainties.
Monte Carlo Analysis with Latin Hypercube Sampling (LHS MC) [7] was carried out; 1000 parameter sets were generated and used in the simulations in each case. Processing the results, the probability density function of the calculated NO concentration was determined. Also, this analysis shows [7], which are the possible maximum and minimum NO concentrations that can be achieved by tuning all parameters simultaneously within their physically realistic limits.
	At lean conditions, the measured data are well within the uncertainty limits of simulations. At fuel rich conditions, the uncertainty limits are lower and the experimental data are outside the uncertainty limits, showing a major applicability problem of the mechanism at these circumstances. There was good agreement at all conditions between the variance of NO concentrations calculated by local and global (Monte Carlo) methods.
	We have determined that at stoichiometric conditions the uncertainty of the calculated NO concentration is mainly due to the uncertainty of kinetic parameters. Changing the equivalence ratio to lean and especially to rich conditions, the contribution of the thermodynamic data to the uncertainty significantly increased. The lists of reactions and species were determined, belonging to the kinetic parameters and enthalpies-of-formation that cause high uncertainty of NO production. These parameters included the enthalpy-of-formation of NNH at lean conditions; kinetic parameters of reactions NO+NH=N2O+H, O+NNH=NH+NO, H+CH2=CH+H and H2O+CH=CH2O+H near stoichiometric conditions; and H2O+CH=CH2O+H at fuel rich conditions. 
In combustion systems, NO can be formed in four parallel pathways; these are the thermal, prompt, via N2O and via NNH formation routes. The relative contribution of these formation pathways and their uncertainty was investigated as a function of equivalence ratio. Based on the Monte Carlo analysis results at three equivalence ratios, NO-formation histograms for each route were generated. 

Figure 1: Comparison of the experimental data of Bartok et al [4] (squares), the simulation results (line) and the 1 uncertainty of the simulation results.

Acknowledgement: Support of OTKA fund T043770 is greatly acknowledged.

References

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[2]	Hughes KJ, Tomlin AS, Hampartsoumian E, Nimmo W, Zsély IG, Ujvári M, Turányi T, Clague AR, Pilling MJ: An investigation of important gas-phase reactions of nitrogenous species from the simulation of experimental measurements in combustion systems, Combust. Flame 124, 573-589(2001)
[3]	http://garfield.chem.elte.hu/Combustion/Combustion.html
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