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An optimized kinetic model of H2/CO combustion

Scott G. Davisa,*, Ameya V. Joshia, Hai Wanga, Fokion Egolfopoulosb

a Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USAb Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA

Abstract

We propose a H2CO kinetic model which incorporates the recent thermodynamic, kinetic, and speciestransport updates relevant to high-temperature H2 and CO oxidation. Attention has been placed onobtaining a comprehensive and kinetically accurate model able to predict a wide variety of H2CO com-bustion data. The model was subject to systematic optimization and validation tests against reliable H 2CO combustion data, from global combustion properties (shock-tube ignition delays, laminar flamespeeds, and extinction strain rates) to detailed species profiles during H2 and CO oxidation in flow reactorand in laminar premixed flames. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Kinetics; Detailed reaction model; Hydrogen; Carbon monoxide

1. Introduction

The most successful model of H2CO combus-tion has been that of Mueller et al. [1], developedon the basis of a careful evaluation of relevant ki-netic parameters and flow reactor experiments.The model is also able to predict a wide rangeof flame experiments. Over the last few years,

however, the rate parameters of the key reactionH + O2 + M = HO2 + M and its third-body effi-ciencies have been revised [2,3], giving an urgentreason for a re-examination of the H2CO com-bustion model. The downward revision of the en-thalpy of formation of OH [4] may also exert aninfluence on the overall reaction kinetics of H2combustion.

Several new studies [57] have been reported inrecent years. Two of these studies analyzed thehydrogen submodel [5,6], both being an extensionof the model of Mueller et al. The third analysis[7] considered both H2 and CO chemistry and isthe predecessor to the present study. The objec-tives of the present study are (1) to provide an up-date for the H2 CO combustion reaction model

on the basis of recent kinetic data, and (2) to opti-mize the H2CO model against available H2COcombustion data.

2. Reaction model

The unoptimized (trial) reaction model consistsof 14 species and 30 reactions as shown in Fig. 1.The model and its thermochemistry and transportproperty files can be found at the URL: http://ignis.me.udel.edu/h2co. The trial model was based

on a careful review of recent kinetics literature,considering both direct data and compilations. Alarge number of GRI 3.0 rate parameters [8] were

1540-7489/$ - see front matter 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.doi:10.1016/j.proci.2004.08.252

* Corresponding author. Present address: Exponent,21 Strathmore Road, Natick, MA 01760, USA. Fax: +1508 647 3619.

E-mail address: [email protected] (S.G. Davis).

Proceedings of the Combustion Institute 30 (2005) 12831292

www.elsevier.com/locate/proci

Proceedingsof the

CombustionInstitute
http://ignis.me.udel.edu/h2cohttp://ignis.me.udel.edu/h2cohttp://ignis.me.udel.edu/h2cohttp://ignis.me.udel.edu/h2co

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found to be appropriate and are used. The discus-sion below highlights the choice of key rateparameters.

The rate expression of H + O2 = O + OHwas taken from GRI 3.0 [8]. The rate coeffi-cient of H + O2(+M) = HO2(+M) was basedon Troe [2], who employed a high-pressurerate krec,1 (cm

3 mol1 s1) = 4.65 1012T0.44 anddeveloped the low-pressure and fall-off expres-sions for Ar and N2 as the bath gases. The broad-ening factor Fc was found to be 0.5 for both thirdbodies. Troes fall-off rate parameterization, how-ever, could not be directly used in CHEMKIN[19], because the low-pressure limit rate coefficientk0 does not share the same temperature depen-dence for different third bodies. We had to devel-

op parameterized rate expressions (see Fig. 1)based on the k0 expression of Ar and using thefall-off formula of Troe [20]. A collision efficiencyfactor b = 0.53 was used for Ar relative to N2.The collision efficiency of He was assumed to beequal to that of Ar. The study of Michael et al.[3] supports a collision efficiency of O2 smallerthan that of N2. We found that for O2, b = 0.75gives a good agreement with experiment [3] andtheory [2]. For H2O, Troe [2] suggested that thebroadening factor is close to the strong-collisionlimit. We chose a b value of 12 (relative to N2)

with the resulting rate in good agreement withthose of Troe and others [2,3,21].

The k0 expression of H + OH + M =H2O + M was taken from [8] with the b valuesequal to 0.38 and 6.3 for Ar and H2O, respectively[12]. The rate expression of Michael et al. [10] was

employed for H2 + O2 = H + HO2. ForOH + OH(+M) = H2O2(+M), the k0 expression,given in the reverse direction by Baulch et al.[12], was refitted based on the new heat of forma-tion of the OH radical along with the low temper-ature data of Zellner et al. [11]. The krec,1expression and the b value of H2O (6) were takenfrom [11] while the Troe fall-off parameters [22]were the same as those in GRI 3.0. The rateexpressions for H2O2 + OH = HO2 + H2O weretaken directly from [15], though the high-temper-ature expression was refitted using a modifiedArrhenius expression to avoid the rate constantvalues exceeding the collision limit when extrapo-lated to high temperatures.

For CO + O(+M) = CO2(+M), the k1 expres-

sion was taken from [13], and following Allenet al. [23], k0 was taken from the QRRK analysisof Westmoreland et al. [24] and fall-off was that ofLindemann. The collision efficiency of H2O wasassumed to be 12. The rate constant forCO + OH = CO2 + H was re-analyzed in thepresent study, and the experimental data wererefitted by the sum of two modified Arrheniusexpressions. The new expression resolves moreaccurately the high temperature data of Woold-ridge et al. [25] as well as the data found in [26].Without this revision, it was not possible to recon-

cile the high-temperature H2 ignition data withthe H2 CO laminar flame speeds. The knownpressure dependence of this reaction was not con-sidered as this dependence is quite unimportantfor the CO oxidation experiments consideredherein.

Fig. 1. Trial reaction model of H2CO oxidation, active parameters, and their spans employed in model optimization(see Refs. [9,14,1618]).

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3. Computational and optimization method

A comprehensive review was conducted for alarge number of H2 CO combustion data. Thir-ty-six experiments were chosen as optimizationtargets as shown in Table 1. They can be classified

into four categories: (1) laminar flame speeds ofH2air, H2O2He, and H2COair mixtures, (2)the peak mole fractions of H and O in a low-pres-sure burner-stabilized H2O2 Ar flame, (3) theconsumption rates of H2 and CO during the reac-tion of H2O2N2 and COO2H2ON2 mixturesin a turbulent flow reactor, and (4) ignition delaytimes of H2O2Ar and H2COO2Ar mixturesbehind reflected shock waves.

Ignition delay and flow reactor calculationswere conducted using a kinetic integrator inter-faced with CHEMKIN [19] by assuming adiabaticcondition. Ignition delays were modeled using theconstant-density model, whereas flow reactormodeling used the constant-pressure assumption.The numerical ignition delays were determinedfollowing the same ignition criteria as in therespective experiments. Laminar flame speedsand structure were calculated using Premix [40],employing thermal diffusion, and multicomponenttransport. Diffusion coefficients of several keypairs were updated [41].

Sensitivity analyses were conducted for igni-tion delay and consumption rates of the fuel inflow reactor with a brute force method. For lam-

inar flame speeds and H and O peak mole frac-tions in burner-stabilized flames, the localsensitivity methods were utilized. Based on thesensitivity information, active rate parameters(to be optimized) were chosen for each target.The entire set of active parameters consists of 28A-factors and third-body efficiency factors asshown in Figs. 1 and 2.

The optimization approach is similar to earlierstudies [8,43]. Briefly, the solution mapping tech-nique was employed to express a response by a sec-ond-order polynomial g2 a0

Pnj1aixi

Pni1P

njPibijxixj, where as and bs are the coefficients,xs are factorial active variables given byx = ln(a/atrial)/ln(f), where a is the active A factoror third-body efficiency factor, and f is its span oruncertainty factor. The uncertainty factor was esti-mated on the basis of kinetic uncertainty and is pro-vided in Fig. 1 for each active parameter. Thoughan optimization of the temperature dependence ofrate coefficients is possible, we chose not to varythe T-dependence because of the insufficient num-ber of systematic experimental targets [43].

For flow reactor targets, the response was

found to be highly non-linear with respect to xs.

These responses are expressed by adding a hyper-bolic tangent term to account for the S-shapeddependence of response with respect to xs,g g2 c tanha00

Pnj1 a

0ixi

Pni1

PnjPib

0ijxi

xj. The coefficients for the flow reactor and igni-

tion delay targets were calculated by a factorialdesign test [43]. The coefficients for flame targetswere obtained using the sensitivity analysis basedmethod [44].

Minimization was carried out on the objectivefunction L2 = Ri[(gi,expt gi,calc)/ri]

2 subject to

the constraint 1 < {x} < +1, where the subscriptidenotes the ith target. Each target was individuallyweighted by their uncertainty r

i. The target values

and their uncertainties are presented in Table 1.

4. Results and discussion

The trial kinetic model was tested against awide range of experimental data. The predictionsof the trial model for the 36 target values areshown in Table 1 (the trial column). Overallthe model performed well against these experi-

mental data. The exceptions are: it overpredictsH2O2He flame speeds, the H and O mole frac-tions in the burner-stabilized flame, and theconsumption rate of H2 for the 1.0% H21.5O2%N2 flowreactor mixture at 943 K and2.5 atm.

To reconcile these discrepancies, optimizationwas then carried out for 28 active parameters withrespect to 36 targets. All active parameters wereallowed to vary freely within their uncertaintyspans. The optimal parameter set was obtained

as the minimum ofL2, first from a random sampleof the multidimensional parameter space, fol-

lowed by a Newton search of the L2 minimumin the parameter space. The values of optimizedactive parameters are shown in the last columnof Fig. 2 (expressed as the optimized-to-trialparameter ratio). To obtain the optimized model,the active parameters (A-factors and third-bodyefficiency factors) shown in Fig. 1 should be mul-tiplied by their corresponding ratios.

Validation of the optimized model will be dis-cussed below. Figure 3 presents experimental[2731,45] and computed laminar flame speeds ofH2air and air-equivalent mixtures where N2 was

replaced by Ar or He. With trial model predictionsalready close to the experimental values, the opti-mization served only to fine-tune the model, result-ing in excellent agreement with the experiment ascan be seen in Fig. 3 and Table 1. The trial modeltends to overpredict the H2O2 He flame speedsat elevated pressures (Table 1). The discrepanciesare clearly caused by kinetics as a previous studyshowed that the uncertainty in the transport coeffi-cients cannot account for the observed differences[41]. Now the optimized model can successfully pre-dict these H2O2He flame speeds [27] as seen in

Fig. 4. This agreement was brought by loweringthe rate of OH + H2 = H + H2O, H + HO2 =OH + OH, and a small increase in the rate ofH + O2 + H2O = HO2 + H2O.

The dominant sensitivity of the laminar flamespeeds of H2 COair mixtures, especially the

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Table 1

Optimization targets

Target No. Composition (mol %) T0 (T5) (K) p0 (p5) (atm) Comments Target

H2 O2 CO H2O Diluent Value

Flame speed

fls 1a 29.6 14.8 N2 298.2 1 H2air, / = 1 204 2

fls 1b 55.8 9.3 N2 298.2 1 H2air, / = 3 217 2

fls 2a 20 10 He 298.2 1 / = 1 206 2

fls 2b 36 8 He 298.2 1 / = 2.25 249 2

fls 3a 13.8 6.9 He 298.2 15 / = 1 58 6fls 3b 21.9 6.3 He 298.2 15 / = 1.75 88 9

fls 4a 1.6 14.2 30.9 N2 298.2 1 / = 1.148 40 4

fls 4b 3 8 59 N2 298.2 1 / = 3.895 52.5 5

fls 5a 14.8 14.8 14.8 N2 298.2 1 / = 1 111.5 1

fls 5b 28.1 9.2 28.1 N2 298.2 1 / = 3.05 154.5 1

fls 6a 9.2 17.4 7.8 N2 298.2 1 CO/H2 = 0.84 10.3 2

fls 6b 2.9 17.4 14.1 N2 298.2 1 CO/H2 = 4.90 18.5 2

Flat flame

flf 1a 39.7 10.3 Ar 0.047 xH,max 0.067 0

flf 1b 39.7 10.3 Ar 0.047 xO,max 0.002 0

Flow reactor

flw 1a 1.18 0.61 N2 914 15.7 a 8.6 0

flw 2a 1.01 0.52 N2 935 6 a 13.0 0

flw 3a 1.0 1.5 N2 943 2.5 a 98 1

flw 4a 0.5 0.5 N2 880 0.3 a 261 2

flw 5a 0.517 1.014 0.65 N2 1038 1 b 354 4

flw 6a 0.494 0.988 0.65 N2 1038 3.46 b 140 2

flw 6b 0.494 0.988 0.65 N2 1038 3.46 c 229 2

flw 7a 0.482 1.002 0.65 N2 1068 6.5 d 14.1 0

flw 8a 0.95 0.49 N2 934 3.02 e 19.0 1

flw 8b 0.95 0.49 N2 934 3.02 f 70 5

Shock-tube ignition

ign 1a 6.67 3.33 Ar 1051 1.729 Onset of p rise 231 1

ign 1b 6.67 3.33 Ar 1312 2.008 50 2

ign 2a 20 10 Ar 1033 0.518 Maximum p 238 1

ign 2b 20 10 Ar 1510 0.493 29 2

ign 3a 0.5 0.25 Ar 1754 33 Maximum [OH] 10 3

ign 4a 2 1 Ar 1189 33 Maximum [OH] 293 1

ign 4b 2 1 Ar 1300 33 11 4

ign 5a 0.1 0.05 Ar 1524 64 Maximum [OH] 54 2

ign 6a 0.05 1 12.17 Ar 2160 1.492 Onset of CO2 rise 63 2

ign 6b 0.05 1 12.17 Ar 2160 1.492 [O] = 2.5 1014 cm3 47 2

ign 6c 0.05 1 12.17 Ar 2625 1.949 Onset of CO2 rise 23 1

ign 6d 0.05 1 12.17 Ar 2625 1.949 [O] = 2.5 1014 cm3 11 6

a The target value is DxH2 =Dtj0:6cH2 0:4

, where x is the mole fraction (ppm); c is the fractional conversion.b DxCO=Dtj

0:6cCO0:4

.c Dtj0:95cCO0:75.d DxCO=Dtj

0:6cCO0:4

.

e DxCO=Dtj0:95cH2 0:85

.f Dtj0:9cH2 0:4

.

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95% CO + 5% H2 mixtures, to CO + OH =CO2 + H has been observed elsewhere [32] andnecessitated a re-evaluation this reaction. It wasdetermined that the sum of two modified Arrhe-nius expressions was necessary to predict the lam-

inar flame speed data. Figures 5 and 6 show thatthe optimized model reproduces experimentalH2COair laminar flame speeds [32,33].

Figure 7 depicts species profiles for four se-lected H2 oxidation experiments in a turbulentflow reactor [13]. Time shift was necessary to

match the computed profiles with the experimen-tal counterparts. The amounts of time shift werefound to be similar with those used by Muelleret al. [13]. It is seen that the optimized model pre-dicts the experimental species profile accurately,and it also improved the prediction of the experi-ment as compared to the trial model (cf. Fig. 7B).Similarly, the results of Fig. 8 show that for COoxidation [35] the optimized model accurately pre-dicts the CO consumption rate over an extendedpressure range.

The trial model could accurately reconcilemost of the ignition delay data for H

2O

2diluent

mixtures, and optimization served only to im-prove these predictions as can be seen in Table1. In addition, Fig. 9 shows a plot of experimentaland computed ignition delay times for H2O2Armixtures [3638,46] behind reflected shock waves.Here, the experimental shock-tube ignition delay

data were fitted into s (ls) = [H2]0.154[O2]

0.693

[Ar]0.04 [6.77 108T0.252 e9234/T] for non-run-

Fig. 4. Experimental (symbols [27]) and computed(lines: the optimized model) H2O2He flame speeds.

Fig. 5. Experimental (symbols [32]) and computed(lines: the optimized model) H2 COair flame speeds

at a pressure of 1 atm.

Fig. 6. Experimental (symbols [33]) and computed(lines: the optimized model) H2 COair flame speedsat a pressure of 1 atm.

Fig. 2. Target-active parameter matrix.

Fig. 3. Experimental (symbols) and computed (lines: theoptimized model) H2 air and air equivalent (N2 isreplaced by Ar or He) flame speed at a pressure of 1 atm.


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away data, i.e., those fall on the nearly linearportion of the curves of Fig. 9, where [] denotesconcentration in mol/cm3. For mixtures of H2O2N2 [47,48], comparison was also made as seenin Fig. 10, where the result should only be consid-ered as a secondary validation because the vibra-tional relaxation of N2 was not accounted for in

modeling. The optimized model also predictsfairly well the ignition delay of CO-H2O2Armixtures [39] as seen in Fig. 11.

The optimized model resulted in improvedprediction of the species profiles measured in alow-pressure H2O2Ar flame, though the concen-

Fig. 7. Experimental (symbols [13]) and computed(lines) species mole fraction profiles during hydrogenoxidation in a flow reactor. Solid lines: optimized model;dashed lines: trial model.

Fig. 8. Experimental (symbols [35]) and computed(lines) [CO]/[CO]0 profiles during moist CO oxidationin a flow reactor. Cases (a): 1.014% CO + 0.517%

O2 + 0.65% H2O i n N2, p = 1 atm, T0 = 1038 K, (b)1.01% CO + 0.496% O2 + 0.65% H2O in N2,p = 2.44 atm, T0 = 1038 K, (c) 0.988% CO + 0.494%O2 + 0.65% H2O in N2, p = 3.46 atm, T0 = 1038 K, (d)0.984% CO + 0.497% O2 + 0.65% H2O in N2,

p = 6.5 atm, T0 = 1040 K, and (e) 0.994% CO + 1.47%O2 + 0.65% H2O in N2, p = 9.6 atm, T0 = 1039 K.

Fig. 9. Experimental (symbols) and computed (lines)ignition delay times of H2O2 Ar mixtures behindreflected shock waves. Symbols: (a) 6.67% H2 + 3.33%O2, p5 = 1.352.90 atm; (b) 5% H2 + 5% O2, p5 = 1.352.90 atm (onset of pressure rise [36]), (c) 0.5%H2 + 0.25% O2, p5 = 33 atm, (d) 2% H2 + 1% O2,

p5 = 33 atm, (e) 0.5% H2 + 0.25% O2, p5 = 57 atm, (f)

0.33% H2 + 0.17% O2, p5 = 64 atm, (g) 0.1%H2 + 0.05% O2, p5 = 64 atm, (h) 0.5% H2 + 0.25% O2,

p5 = 87 atm (maximum OH absorption rate [38]), (i) 8%H2 + 2% O2, p5 = 5 atm (maximum OH emission) [46],and (j) four H2 + O2 mixtures [37]. Lines: (1) 0.5%H2 + 0.25% O2, p5 = 87 atm (maximum [OH] rate), (2)2% H2 + 1% O2, p5 = 33 atm (maximum [OH] rate), (3)8% H2 + 2% O2, p5 = 5 atm (maximum [OH]), and (4)5% H2 + 5% O2, p5 = 2 atm (maximum pressuregradient).

Fig. 10. Experimental (symbols) and computed (lines)

ignition delay times behind reflected shock waves forH2O2N2 mixtures. Experimental data were determinedfrom onset of pressure rise [47] and maximum rate ofOH emission [48].


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trations of H and O are still overpredicted (see,Table 1). These discrepancies may well be causedby the experimental uncertainty due to flame per-turbation by the sample probe.

Finally, the trial model (dashed lines) and theoptimized model (solid lines) were comparedagainst extinction strain rates of ultra-lean H2

air mixtures [42]. These experiments were not usedas optimization targets because of large influencesfrom the uncertainties in the diffusion coefficients.The results of Fig. 12 indicate that both the trialand optimized model can accurately predict thedata for the leaner equivalence ratios, and beginto deviate as the equivalence ratio approaches0.5. Again, this deviation may be due to diffusioneffects and shows the need to include diffuse coef-ficients in the optimization space [42].

The optimization procedure also allows us toprobe the residual kinetic uncertainties. We found

that the rate coefficient of H + O2 = OH + O al-ways stayed within 5% of the trial value for alloptimization runs made, including the use of asmaller number of targets and/or a reduceddimensionality of active parameter space. The ratecoefficient is within 8% and 20% from the analysis

of Troe and Ushakov [49] for T> 1500 and1000 K, respectively. Again, our assignment ofrate constant uncertainties prior to optimizationis consistent with these differences. Of the remain-ing active parameters, the optimized k2, k3, and k4values are often within 20% of the trial values. For

H + O2(+M) = HO2(+M), optimization led to a10% increase in the rate coefficient of the basereaction (M = N2), which is acceptable. ForM = H2O, the optimized third-body efficiencywas a factor of 1.09 of the trial value. Coupledwith the change in the rate for base reaction(M = N2), the third-body efficiency of H2O rela-tive to N2 remains unchanged. Optimizationyielded a smaller efficiency factor for argon, dri-ven primarily by the ignition delay data (the trialmodel overpredicts ignition delays). The resultingefficiency factor is equal to 0.46 (relative to N2),and the corresponding rate coefficient forH + O2 + Ar = HO2 + Ar is within the experi-mental uncertainty given in [10]. The low-temper-ature rate coefficient of HO2 + OH = HO2 + OHand the high-temperature rate of HO2 +HO2 = O2 + H2O2 were lowered by 18% and13% upon optimization, respectively. Both give abetter agreement with the rates recommended byTroe and Ushakov [49].

Among the 28 active parameters, 12 hit theirrespective boundaries of uncertainty spans. Thefraction of these parameters is much smaller thanwhat is usually encountered in kinetic model opti-mization (see, for example [50]). Some of theseparameters are either inadequately constrainedbecause of a lack of relevant targets or becausethey are only marginally active for H2CO com-bustion (e.g., 9c, 9e, 23, 25, 29, and 29a). Othersmay be caused by target data inconsistency [51].These issues, while worthy to explore, are clearlyoutside of the scope of the present study.

5. Summary

A H2 CO kinetic model was proposed. Themodel was based on a comprehensive review of lit-erature kinetic data, considering the recent revi-sions in the rate coefficient of H + O2(+M) =HO2(+M), its third-body efficiencies, and the en-thalpy of formation of the OH radical. The trialmodel performed very well against most of theH2/CO combustion data. Discrepancies in the pre-dictions, however, existed for several data sets.These discrepancies were successfully resolved byoptimization within the uncertainty bounds of therelevant rate parameters with respect to 36 targets,

including the global combustion properties of igni-tion delays and laminar flame speeds, and the de-tailed species profiles during H2 and COoxidation in flames and flow reactors. It is shownthat this set of H2CO combustion targets can bereconciled within the underlying kinetic uncertain-

Fig. 11. Experimental (symbols [39]) and computed(lines) ignition delay times behind reflected shock waves.The experimental ignition delay was determined fromthe onset of infrared emission due to CO2; the compu-tational ignition delay determined from the maximumCO2 concentration gradient.

Fig. 12. Experimental (symbols [42]) and computed(lines) extinction strain rates as a function of theequivalence ratio for ultra-lean H2air mixtures.


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ties, and the optimized kinetic model is predictivefor all reliable H2CO combustion data consideredherein.

Acknowledgments

This work was supported by AFOSR (GrantNos. F49620011014 and F496200210002) underthe technical supervision of Dr. Julian M. Tishk-off. The work at UD was also supported byNSF (CTS-9874768).

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Comments

J. Troe, University of Gottingen, Germany. I see prob-lems with this type of optimization of elementary reac-tion rate coefficients on the basis of macroscopicreaction systems. The conditions of the macroscopicexperiments just do not correspond to those of separatestudies of the elementary reactions. In particular, pres-sure-dependent reactions like H + O2 + M or HO +CO + M depend strongly on the third bodies M. In mac-roscopic reaction systems, these M may also be H2O,

reactive atoms, or reactive radicals. For the latter, colli-sion efficiencies may differ markedly from the values de-rived for third bodies like N2. The optimization of thispaper may mix this all up. I would recommend leavingthe results, from separate elementary reaction rate stud-ies untouched and only optimize those collision efficien-cies (or rate coefficients) that are otherwise inaccessibleor unknown.

Reply. We agree that optimization of reaction ratecoefficients on the basis of macroscopic reaction systemscannot provide rate values more accurate than isolatedmicroscopic experiments or ab initio theoreticalstudies. The purpose of optimization is to examine theability of up-to-date rate coefficients for predicting theresponses of macroscopic reaction systems. This is, afterall, the practical purpose of fundamental reaction kinet-ics. In our optimization procedure, we ask two basicquestions. First, do the latest developments in reactionkinetics, i.e., better and more accurate rate coefficients,predict or give rise to better predictions for the macro-scopic reaction systems? Second, given the uncertaintyin each and every rate parameter, can the responses ofmacroscopic reaction systems be better predicted by sys-tematic optimization within the uncertainty bounds of

each rate parameter? We maintain that the ultimate goalof kinetics studies can only be achieved by fundamentaltheoretical and experimental studies supplemented fre-quently by studies such as the one reported here.

The collision efficiencies of different species are in-deed markedly different, and it is precisely this reasonwhy we chose to optimize the key, individual collisionefficiencies for key pressure-dependent reactions. Uncer-tainty bounds intrinsically limit to which extent each effi-ciency factor can be varied, thus maintaining theirphysical nature, for example, H2O is a more efficientthird body. For this reason, we do not see any funda-

mental reason why optimization would mix this up. Asa practical measure we note that for H + O2 + M =HO2 + M the un-optimized third body efficiencies are0.53, 0.53, 0.75, 12, and 1 for Ar, He, O2, H2O, andH2, respectively, relative to that of N2, and the optimizedefficiency factors are 0.4, 0.46, 0.85, 11.9, and 0.75. These

optimized factors are well within their respective rangeof uncertainties.

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Juan Li, Princeton University, USA. The rate con-stant of CO + OH () CO2 + H is pressure-depen-dent. The authors provide a new expression of the rateconstant by fitting the literature experimental results.However, most of the experimental results were mea-sured at low pressures. Is it proper to use the rate con-stant expression for high-pressure cases?

Reply. A recent theoretical study [1] showed that therate coefficient for CO + OH = CO2 + H starts to devi-ate from the low pressure limit (by more than 2%) whenpressure becomes greater than ca. 20, 80, 700, 3600 and13000 bar for T= 800, 1000, 1500, 2000, and 2500 K,respectively. This suggests that the reaction would in-deed be at or nearly at its low-pressure limit under theconditions of all experimental data considered herein.Furthermore, the optimized rate expression agrees towithin 5% of the theoretical result of [1] in the tempera-ture range of 8002500 K.

Reference

[1] A. Joshi, H. Wang, Int. J. Chem. Kinet. (2004)submitted for publication.

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S.S. Kumaran, Cabot Corporation, USA. Howdoesthebath gas bc impart the flame speed map (uncertainties)?What is therelativebc of various bath gases towards otherreactions (title reaction) CO + OH fi CO2 + H?

Reply. The influence of third body efficiencies of cer-tain pressure-dependent reactions on flame speed hasbeen known for quite a while (Ref. [43] in paper). Activeefficiency factors were considered in model optimization.

Based on recent theoretical studies, e.g. [1], theCO + OH reaction would indeed be very close to itslow-pressure limit under conditions of all experimentsconsidered herein. For this chemical activation process,the impact of various bath gases would therefore be vir-

tually unimportant for the present study.

Reference

[1] A. Joshi, H. Wang, Int. J. Chem. Kinet. (2004)submitted.


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David Smith, University of Leeds, UK. For part oftheir optimization, the authors use the burning velocitydata of McLean (Ref. [32] in paper). The experiments,particularly those with 25% CO/5% H2 fuel were care-fully chosen to have high sensitivity to the CO + OHreaction. Two comments on these data:

1. All expanding spherical flame methods for burningvelocity measurements have hot burnt gas inside theflame; thereby prone to radiative heat loss. For theseflames (relatively show burning and high CO2 con-tent), measured burning velocities may be low by upto 45%.

2. As reported in the paper, the authors found that com-puted burning velocities were sensitive to CO + OHrate only at temperatures around 1160 K. Compari-son with these experimental data says essentially noth-ing about CO + OH at other temperatures.

Reply. Radiative heat loss would have little influenceon measured flame speeds, as long as you are not near theflammability limits [1,2]. The 95% CO + 5% H2 in airflame data measured by the expanding spherical flamemethods and used as model optimization and validationtargets were far from the flammability limits and thusthey should be affected minimally by radiative heat loss.

The fact that the CO + OH reaction is influential in afairly narrow temperature range for the 95% CO + 5%H2 flames is a very important result. Although compari-

son with these flame speed data says very little aboutCO + OH at other temperature, it does point out the sub-tle fact that a single modified Arrehnius expression can-not reconcile available flame speed and shock tube dataof CO. Specifically, a proper prediction for the 95%CO + 5% H2 flames requires a smaller rate coefficient attemperatures around 1160 K, yet a single modifiedArrehnius expression would not be able to reconcileflame speed and shock tube data that are sensitive tothe rate coefficient of the CO + OH reaction at highertemperatures.

References

[1] C.K. Law, F.N. Egolfopoulos, Proc. Combust. Inst.24 (1992) 137144.

[2] G. Rozenchan, D.L. Zhu, C.K. Law, S.D. Tse, Proc.Combust. Inst. 29 (2002) 14611469.

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Frederick L. Dryer, Princeton University, USA. Yourmethod of optimization appears to involve adjustments

only in the pre-exponent in rate correlations, which re-sults in rate changes at all temperatures. We have shown[1] that there are temperature windows for each inputparameter (rate constant, diffusion coefficient) where

laminar flame speed is most sensitive to the specificparameter. These windows are small in comparison tothe total temperature range of the particular flame. Thusin optimizing against all of the different types of experi-mental targets that were utilized, your method simulta-neously adjusts each rate constant at all temperatures

while optimizing against a particular target that coversa particular temperature range. Would it not be moreappropriate to optimize both the pre-exponent and tem-perature dependence (functional shape) of each rate cor-relation? Essentially you forced such a result here forone rate by proposing a different correlation ofCO + OH than appears in the published literature. Wehave shown the importance of adjusting both pre-expo-nent and temperature dependence of rate correlationsfor several elementary reactions involved in the H2/CO/O2 oxidation mechanism, including this one [2].

References

[1] Work in Progress Poster 1F2-13, Int. J. Chem. Kin.(2004) submitted.

[2] Work in Progress Poster 1F1-04, Int. J. Chem. Kin.(2004) submitted.

Reply. We agree with the fact that each target (flamespeed, ignition delay, and flow reactor) is sensitive to agiven input parameter (i.e., reaction rate, diffusion coef-ficient) at a specific temperature or over a given temper-ature range, depending on the experimental conditions,

including pressure. This is precisely the reason why wechose targets that covered an extensive temperature(8802625 K) and pressure (0.333 atm) range in orderto ensure accurate optimization of the input parameterover an extended temperature and pressure range. Whilewe agree that a simultaneous optimization of the pre-ex-ponential and temperature dependence would be morerigorous, this level of optimization was not needed ascan be seen by the excellent agreement between modelpredictions of the optimized model and experimentaldata over extensive temperature and pressure ranges.

A theoretical analysis by Troe [1] has shown that due

to the complexity of the CO + OH reaction, there is noinherentreason to believe that a singlemodified Arrehniusexpression can adequately describe the rate of this reac-tion over an extended temperature range. We proposedto refit the experimental data for the CO + OH reactionusinga summationof two modified Arrehniusexpressionsto more accurately reconcile the experimental data forhigh, intermediate and low temperatures. This expressionalso agrees very well will our recent theoretical result [2].

References

[1] J. Troe, Proc. Combust. Inst. 27 (1998) 167175.[2] A. Joshi, H. Wang, Int. J. Chem. Kinet. (2004)

submitted.


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