Rate constant evaluation & choices

In selecting the species and reactions for the C₀-C₂ portion of the foundational fuel chemistry model, we have tried to assemble a comprehensive list applicable to temperatures above 1000 K and up to high pressures.  Some highly oxygenated or weakly bound species are omitted, and some reactions of negligible consequence are included (subject to possible mechanism reduction).  We have not at this time included mechanisms for alternate C₂ fuels such as DME, ethanol, and methyl acetate, which might be added and separately optimized, but likely have negligible effect on the hydrocarbon oxidation.  The GRI Mech species HCCOH is assumed to isomerize (by H) to CH₂CO.  During the course of our initial work, we have identified CH₃O₂, CH₃OOH, C₂H₅O₂, C₂H₅OOH, C₂H₂OH, and the isomers vinyl alcohol (C₂H₃OH) and ethylene oxide (oxirane, cyC₂H₄O) as species whose kinetics should be included in future versions.  Addition of HOCO, C₂H₅O, and C₂H₄OH may however not be required, based on our initial evaluation.  Reliable self-consistent thermodynamics for computing (and evaluating) reverse rate constants are taken from the available Third Millennium Active Thermochemical Tables (ATcT) [1,2].

Choices for rate constants and product branching involve subjective judgment, and often several functionally equivalent expressions are available.  Since critical values will be optimized, exact best selections are not required.  Individual sources are given in the mechanism table, without detailed discussion.  We have relied on previous evaluations for many values, notably the recent hydrogen models from Princeton [3] and Stanford [4], and the IUPAC combustion kinetics evaluations of Baulch et al. [5].  This latter reference is also a prominent source for the needed uncertainty limits employed in the optimization. Liberal values were typically selected for uncertainty ranges.   Note that deviations from the recommended values are included in the optimization’s objective (error) function, so there is a penalty for large kinetics changes.  Direct experimental rate constant measurements are the preferred source for our rate constant values.  Theoretical calculations of potential surfaces and rate constants play a large role too in providing final expressions.  This is necessary to give proper extrapolation outside of limited measurement conditions, and theory expressions are adjusted to agree with the data when required.  Reliance on theoretical values for product branching ratios is often needed.  In some cases, only theoretical values or estimates made from similar reactions are available. 

For the mechanism to be valid and consistent over a wide temperature and pressure range (to high values), a proper parameterization of recombination, decomposition, and chemical activation rate constants is vital.  We select available Master Equation calculations with appropriate pressure falloff parameterization that best match experimental data; inputs are transition state and energy transfer parameters.  Relative efficiencies for different collider gases are often unmeasured for many systems.  We used data where available and consistent (without any temperature dependence), and otherwise employ generic relative values chosen for GRI Mech [6].  When different collider efficiencies or low-pressure limit rate constants are separately optimized, we have placed appropriate bounds on the ranges of relative efficiencies.  Multichannel chemical activation reactions have a negative pressure dependence, due to collisional stabilization of the bound intermediate at high pressures.  The current model does not account for this effect, and uses the low-pressure limit rate constant values.  This may result in some high-pressure inaccuracy, will be more of a problem for larger species, and needs to be remedied in future versions.  The reactions most affected are

CH₃ + CH₃ ⟷ H + C₂H₅
OH + CH₃ ⟷ ¹CH₂(S) + H₂O.

We encountered particular difficulty in evaluating rate expressions for ethylene decomposition.  Recent data from Stanford [7] shows little pressure dependence, for the main H₂CC+H₂ channel.  Accommodating these rates theoretically requires a loose transition state (plausible for the carbene insertion), and a fast low-pressure rate with sharp falloff.  We used a Lindemann parameterization (F_c = 1) and the experimental rate expression to set the low pressure limit rate k(0), and this is hard to justify theoretically. Since ethylene is the most important large fuel pyrolysis product, good ethylene kinetics and targets will be of particular importance.  Rates and products for

C₂H₃ + OH ⟷ products
C₂H₃ + O₂ ⟷ products

also merit reevaluation. 

Newer theory results [8] also suggest a faster rate for the spin forbidden decomposition of CO₂, but our optimization was able to accommodate this and in fact forces the adoption of such higher values.  There are also some difficulties and uncertainties in evaluating some of the reaction product yields, which is particularly important when one channel yields extra radicals or more reactive species, and can vary with temperature and pressure.  HCO product for example can often be formed with more than enough internal energy to decompose.

 

Uncertainty evaluation

A key element of the rate evaluation is an assessment of the uncertainty factor of the reaction rate constants. These limits are used later in the selection and allowed ranges of the optimization parameters. These values are necessarily subjective estimates. When multiple reliable determinations of a rate constant are available, an uncertainty limit encompassing their range is typically selected (excluding outliers). We generally avoided the sometimes over-optimistic values given for individual measurements. For reactions covered by the Baulch et al. reviews, we have typically chosen to use their uncertainties. In cases where we adopted values based on the compilations of Tsang [9,10], often estimates, his estimated uncertainties were used. Our ranges are intended to allow what we consider all possibly reasonable values to the optimization. Bear in mind that the objective function of the optimization includes terms for rate constant deviations from the evaluated values, so choices near these estimated uncertainty limits are disfavored.

References

[1]  Ruscic B, Pinzon RE, vonLaszewski G, Kodeboyina D, Burcat A, Leahy D, Montoya D, Wagner AF. Active Thermochemical Tables: Thermochemistry for the 21st Century. J Phys Conf Ser. 2005;16:561-70.

[2]  Goos E, Burcat A, Ruscic B. New NASA Thermodynamic Polynomials Database With Active Thermochemical Tables updates. Report ANL 05/20 TAE 960; Extended Third Millennium Thermodynamic Database of New NASA Polynomials with Active Thermochemical Tables update, Available from: http://garfield.chem.elte.hu/Burcat/NEWNASA.TXT.

[3]  Li J, Zhao Z, Kazakov A, Dryer FL. An updated comprehensive kinetic model of hydrogen combustion. Int J Chem Kinet. 2004;36:566-75.

[4]  Hong Z, Davidson DF, Hanson RK. An improved H2/O2 mechanism based on recent shock tube/laser absorption measurements. Combust Flame. 2011;158:633-44.

[5]  Baulch DL, Bowman CT, Cobos CJ, Cox RA, Just T, Kerr JA, Pilling MJ, Stocker D, Troe J, Tsang W. Evaluated kinetic data for combustion modeling: supplement II. J Phys Chem Ref Data. 2005;34:757-1397.

[6]  Smith GP, Golden DM, Frenklach M, Moriarty NW, Eiteneer B, Goldenberg M, Bowman CT, Hanson RK, Song S, Gardiner Jr WC, Lissianski VV, Qin Z. GRI-Mech 3.0; 1999. Available from: http://www.me.berkeley.edu/gri_mech/.

[7]  Ren W, Davidson DF, Hanson RK, Int J Chem Kinet 2012;44:423-432; private communication.

[8]  Jasper AW, Dawes R, J Chem Phys. 2013;139:154313

[9]  Tsang W, Hampson R. Chemical kinetic data base for combustion chemistry. Part I. Methane and related compounds. Journal of Physical and Chemical Reference Data. 1986;15:1087-279.

[10]  Tsang W. Chemical kinetic data base for combustion chemistry. Part 2. Methanol. Journal of Physical and Chemical Reference Data. 1987;16:471-508.