CO、甲醛及甲醇燃烧综合动力学机理研究

N10-CO、甲醛及甲醇燃烧综合动力学机理研究（A Comprehensive Kinetic Mechanis m for CO,CH2O,andCH3OH Combustion）

摘要：

本文构建了适用于 CO、甲醛、甲醇燃烧的C₁氧化详细动力学机理，包含 18 种组分、84 步可逆反应，基于层级式方法更新 H₂/O₂子机理与热力学参数。通过 850–950 K、1.5–6.0 atm 下甲醛氧化实验与文献数据验证，拟合优化 CO+OH、HCO 分解等关键反应速率常数。模型经激波管、层流火焰、流动反应器多工况校验，温度 300–3000 K、压力 0.03–20 atm，可精准预测点火延迟、火焰速度与组分浓度。揭示 HO₂/H₂O₂化学在高压工况的关键作用，为含氧燃料燃烧模拟提供标准化基础机理。

ABSTRACT:  New  experimental  profiles  of  stable  species  concentrations  are  reported  for formaldehyde oxidation in a variable pressure flow reactor at initial temperatures of 850–950 K and at constant pressures ranging from 1.5 to 6.0 atm. These data, along with other data pub- lished in the literature and a previous comprehensive chemical kinetic model for methanol oxi- dation, are used to hierarchically develop an updated mechanis m for CO/H2O/H2/O2, CH2O, and CH3OH oxidation  Important modifications include recent revisions for the hydrogen–oxygen submechanis m (Li et al., Int JChem Kinet 2004, 36, 565), an updated submechanis m for methanol reactions, and kinetic and thermochemical parameter modifications based upon recently pub- lished information. New rate constant correlations are recommended for CO+ OH = CO2 + H (R23) and HCO + M = H + CO + M (R24), motivated by a new identification of the tempera- tures over which these rate constants most affect laminar flame speed predictions (Zhao et al., Int J Chem Kinet 2005, 37, 282). The new weighted least-squares fit of literature experimental data for (R23) yields k23 = 2.23 × 105 T1.89 exp(583/T )cm3/mol/s and reflects significantly lower rate constant values at low and intermediate temperatures in comparison to another recently recommended correlation and theoretical predictions. The weighted least-squares fit of lit- erature results for (R24) yields k24 = 4.75 × 1011 T0.66 exp(_7485/T ) cm3/mol/s, which predicts values within uncertainties of both prior and new (Friedrichs et al., Phys Chem Chem Phys 2002, 4, 5778; DeSain et al., Chem Phys Lett 2001, 347, 79) measurements. Use of either of the data correlations reported in Friedrichs et al. (2002) and DeSain et al. (2001) for this reaction sig- nificantly degrades laminar flame speed predictions for oxygenated fuels as well as for other hydrocarbons. The present C1/O2  mechanis m compares favorably against a wide range of ex- perimental conditions for laminar premixed flame speed, shock tube ignition delay, and flow reactor species time history data at each level of hierarchical development. Very good agree- ment of the model predictions with all of the experimental measurements is demonstrated.

OC   2007 Wiley Periodicals, Inc. Int J Chem Kinet 39:  109–136, 2007

INTRODUCTION

The  hierarchical  nature  of  hydrocarbon   oxidation kinetics  and the  importance  of s mall molecule  and radical kinetics in controlling the oxidation of larger carbon number  species  are well-established notions [ 1,2].  The  hydrogen–oxygen  kinetic  submechanis m [2] controls the most reactive radical pool composition of H, OH, O, and HO2  that attack the primary fuel. Carbon monoxide is a major intermediate species, and its conversion to CO2  is responsible for a significant fraction  of the  exothermicity  accompanying  hydro- carbon oxidation. It has been shown (e.g., [2,3]) that nearly all carbon atoms bonded to one another, to hy- drogen atoms, or hydroxyl groups are converted to CO through formaldehyde (CH2 O) and/or formyl radicals (HCO). Formyl radicals are a major source of H atoms and HO2 radicals in larger carbon nu  mber hydrocarbon combustion.

 Methanol (CH3 OH), the simplest alcohol, converts to  CO  through  CH2 O  reactions  and  introduces  ad- ditional species, particularly CH2 , CH3 , CH3 O, and CH2 OH [4]. Over almost all conditions of practical in- terest, methanol combustion produces CH3 in such mi- nor concentrations that no C2  hydrocarbon species are formed and, hence, no sooting occurs. The collection of kinetic phenomena involved in hydrogen/oxygen, car- bon monoxide, formaldehyde, and methanol is there- fore a representative of the s mall radical pool interac- tions that couple with methyl radical and higher carbon number species and radicals in hydrocarbon combus- tion systems.

Detailed  mechanis ms  for  H2 ,  CO,  CH2 O,  and CH3 OH combustion  are also individually of practi- cal importance. Hydrogen kinetic properties have long been of interest in terms of safety, given the major use of hydrogen in chemical synthesis and fuel refining. The proposed transition to a hydrogen energy economy further emphasizes the need to understand hydrogen safety issues [e.g., 5,6] as well as hydrogen co  mbus- tion under mild combustion conditions and with very high-exhaust gas recirculation. Carbon monoxide and formaldehyde  are primary pollutant  species emitted from many combustion systems and are i  mportant in reforming chemistry to produce hydrogen from hydro- carbons, as well as in atmospheric chemistry, toxicity, and carcinogen assess ments and an alyses. Methanol is used as an oxygenate additive in gasoline and is also an attractive alternative to traditional transportation fu- els because of its nonsooting characteristics, its facile synthesis from a wide variety of feedstocks, and its possible interim role as a hydrogen carrier for fuel cell applications.

The  combustion  chemistry  of each  of the  above species has been extensively studied previously. Ex- perimental  data exist in the literature from laminar flame, shock tube, flow reactor, and static reactor ex- periments, collectively covering a wide range of ini- tial temperature, pressure, and equivalence ratio. Our group has had a long involvement in studying these s mall molecule kinetics in flow reactors (Yetter et al. [7,8]; Hochgreb and Dryer [9]; Kim et al. [ 10], Nor- ton and Dryer [ 11], Held and Dryer [4, 12], Mueller et al. [ 13– 17]). We have previously developed com- prehensive mechanis ms for CO  [8],  CH2 O  [9],  and CH3 OH [4], and our recent work on updating and de- veloping a comprehensive mechanis m for hydrogen– oxygen [ 18] that includes advances in chemical kinetic rate and thermochemical information as well as val- idation data  sources points to the need to  similarly revisit and update our prior work on carbon monox- ide, formaldehyde, and methanol kinetics. While the flow reactor data we have previously published for hy- drogen, carbon monoxide, and methanol systems, each covering a very wide range of pressures, our prior work on formaldehyde oxidation was limited to atmospheric pressure studies [9]. In that work, chemical an alyses were conducted using offline gas chromatography, an a nalytical method with potentially higher uncertainties than can be achieved using the Fourier transform in- frared (FTIR) online an alytical   methods available to- day. Formaldehyde oxidation obtained in a variable pressure flow reactor (VPFR) at initial temperatures of 850–950 K and constant pressures ranging from 1.5 to 6.0 atm to expand the range of validation con- ditions. Moreover, new experiments in other venues, especially for CH2 O oxidation, have appeared in the literature using shock tubes [ 19–22] and laminar pre- mixed flames [23]. In addition, there have been some elementary kinetic publications further addressing the important reactions involved in the C1 oxidation system (e.g., [ 19,24,25]).

Utilizing our recent work on hydrogen/oxygen ki- netics [ 18], and updating the CO/O2 , CH2 O/O2 , and CH3 OH/O2 mechanis ms with more recent kinetic and thermochemical information, a comprehensive mecha- nis m has been hierarchically developed [26] that satis- factorily reproduces new experimental targets as well as those utilized in the original mechanis m studies ap- pearing in [4,8,9]. This paper reports the key features of the updated mechanis m,  summarizes the comparisons of predictions with experimental targets as performed in [26], and augments these earlier comparisons using the results with some additional, recently published, kinetic  measurements  and  experimental  validation data.

EXPERIMENTAL METHODS

The new experiments on formaldehyde oxidation re- ported here were conducted in the Princeton variable pressure flow reactor [27]. Detailed information on the VPFR instrumentation and experimental methodology can be found in other publications [28], and only a brief description is given here.

Carrier gas (N2  in this study) is heated by a pair of electrical resistance heaters and directed into a reactor duct. Oxygen is also introduced at the duct entrance. The carrier gas/oxygen mixture flows around a baffle plate into a gap serving asthe entrance toa diffuser. The vaporized fuel (trioxane with water in this study) flows into the center tube of a fuel injector and injects radi- ally outward into the gap where it rapidly    mixes with the carrier gas and oxygen. The reacting mixture exits the diffuser into a constant area test section. Near the exit of the test section, a sampling probe is positioned on the reactor centerline to continuously extract and convectively quench a s mall percentage of the flow. At the same axial location, the local reaction gas temper- ature is measured with a type R thermocouple accurate to ±3 K.

The sample gas flows via heated Teflon lines to an- alytical equipment including a FTIR spectrometer, an electrochemical O2  a nalyzer, and a pair of nondisper- sive infrared an alyzers for CO and CO2. Other sta- ble  species of interest  (e.g., CH2 O, H2 O)  are mea- sured continuously online using FTIR spectrometry. The measurement uncertainties for the data reported here are O2 :±2%, CO:±2%, CO2 :±2%, CH2 O:±3%, and H2 O:±6% of reading.

The distance between the point of fuel injection and the sampling position is varied by moving the fuel vapor injector probe (with attached mixer/diffuser as- sembly) relative to the fixed sampling location. Mean axial velocity measurements along the centerline of the reactor are used to correlate distance with residence time. By these means, profiles of stable species versus residence time can be determined experimentally. The uncertainty in the residence time is approximately 5%.

In the present experiments, formaldehyde monomer was  generated through the  decomposition  of  1,3,5- trioxane. Hochgreb and Dryer [9] also employed this technique  in  their  atmospheric  pressure  flow  reac- tor (APFR) experiments. Trioxane decomposition pro- ceeds by the concerted rupture of the three C   O bonds to form three formaldehyde molecules [9,29]. Using gas chromatography, it was experimentally verified that CH2 O is the only product of trioxane decomposition, and trioxane decomposition is much faster than the subsequent reaction of formaldehyde at flow reactor conditions. For modeling purposes,  1    mol  of triox-ane reactant could therefore be replaced by 3 mol of formaldehyde.

In earlier work, [9,29], trioxane was melted and de- livered as a liquid to the evaporator of a prior APFR. A similar methodology would have required a complex modification of the present reactor, and a different ap- proach to deliver trioxaneto thereactor was utilized. At 18◦ C, the solubility of trioxane in water is 17.2 g/100 mL [30]. Trioxane was dissolved in distilled water, and the unheated solution was volumetrically metered to a liquid vaporizer system located within the VPFR pres- sure shell and at the immediate entrance to the fuel vapor injector probe. The metered liquid flow was gas- blast atomized using heated nitrogen, and the nitrogen, water vapor, and trioxane vapor mixture was then in- jected into the reactor at the mixing location with hot carrier gas. It was verified that the decomposition rate of trioxane at the conditions of the reported experi- ments led to immediate formation of monomer during the injection and mixing process, well upstream of the radially uniform reaction region where the reported data were obtained. Due to heat addition limitations for the hot nitrogen used to vaporize the liquid reactant flow and the solubility limit of trioxane in water, the maximum initial CH2 O mole fraction investigated was limited to 500 ppm. Other than this limitation, the use of water to deliver the trioxane did not significantly affect the experiments, as the amount of water added was included in the kinetic modeling comparisons.

A series of moist formaldehyde oxidation experi- ments were conducted in the VPFR at initial tempera- tures of 850–950 K and in the pressure range of 1.5–6.0 atm. For all of the experiments, the total carbon and oxygen balances experimentally determined at each residence time were within 4% of the specified input. The nearly identical total carbon and oxygen concen- trations at each  sampling location not only provide verification of the experimental measurements but also imply that any other carbon- or oxygen-containing sta- ble species present were only in negligible quantities. Although formic acid has been observed using these same diagnostics in VPFR experiments on methanol [4] and dimethyl ether [31] oxidation, none was de- tected in the present experiments on formaldehyde ox- idation. This is most likely the result of the very low fuel concentrations studied here, and that formic acid would be expected to be below detection limits.

UPDATED KINETIC MECHANIS MS FOR CO, CH2 O, AND CH3 OH COMBUSTION

We used a slightly modified version of the methanol mechanis m  published  by  Held  and  Dryer  [4]  as  a starting point in developing the present mechanis m.* In the course of the present work, a number of ther- mochemical parameters and rate constant correlations were modified to reflect more recent kinetic informa- tion. The revised H2/O2   submechanis m is discussed in detail and validated against a large set of hydro- gen/oxygen targets in a separate publication [ 18], and this submechanis m is absorbed without further mod- ifications in the present work. Revisions included the use of the heat of formation of OH reco   mmended by Ruscicetal. [33], which isin very good agreement with recent experimental results [34]. For the current work, we utilized 3.0 kcal/mol as the standard heat of for- mation of HO2 at 298.15 K [35]. Very recently, Ruscic et al. [36] have updated this heat of formation to 2.94 ± 0.06 kcal/mol. This change makes no significant differ- ence in the level of comparison of computations with the targets utilized in the present work.

In addition to revising the components associated with the hydrogen–oxygen submechanis m, the follow- ing revisions were also adopted over the course of this work.

Thermochemical Data for CH2 OH

The thermochemical properties of CH2 OH, including enthalpy of formation, standard entropy, and heat ca- pacity at different temperatures, were updated to those reported by Johnson and Hudgens [37]. The data of Johnson and Hudgens also agree well with another re- cent IUPAC evaluation by Ruscicetal. [38]. These ther- modynamic properties were fitted with a 14-coefficient polynomial [39].

CO+ OH= CO2 + H (R23)

This well-studied reaction is of critical importance to combustion modeling because it is the main pathway to convert CO to CO2 , the oxidation of CO is responsi- ble for a major fraction of the energy release derived in oxidation of hydrocarbons, and CO2  dissociation im- portant in determining adiabatic flame temperatures as a function of pressure. The reaction proceeds through the formation of HOCO adducts and thus is pressure dependent, particularly at low temperatures  [25,40]. Under most practical combustion conditions, however, the reaction can be treated as pressure-independent.

*In verifying the published mechanis m, we found that the model reported in [4] resulted in calculated fla   me speeds that were much higher than those shown in the publication. Dr. Held [32] concurs that the fla   me speed calculations reported in the paper resulted from the slightly modified version of the reported mechanis m, used as a basis in the current work.

The rate of oxidation of H2/CO/O2  and moist CO mixtures is very sensitive to reaction (R23) [8]. More- over, laminar flame speed predictions of hydrocarbons are strongly influenced by this reaction [41,42]. It is not surprising that targets such as shock tube ignition delay data or flow reactor data would constrain model parameters only over the particular range of temper- ature covered by the work. However, the temperature range over which laminar flame speed predictions are most sensitive to a particular elementary reaction has typically not been considered.

Recently, Zhao et al. [43] introduced a methodology to  determine  the  temperature-dependent  sensitivity of premixed laminar flame speeds to elementary rate constant   and  transport  properties.  A nalyses  were conducted by locally perturbing the parameter with a Gaussian function profile. The center of the Gaussian profile was moved with an assigned temperature mean, and the sensitivity of the predicted flame speed was determined as a function of the perturbation-assigned mean temperature.  The  ana lysis  leads to the  deter- mination  of  a  “temperature  window”  in  which  the predicted  laminar  flame  speed  is found to be most sensitive to perturbations in the particular parameter. The  temperature  sensitivity  of  laminar  flames  for hydrogen/carbon  monoxide  mixtures  with  respect to (R23) was used as an application demonstration. The predicted laminar flame speed was shown to be most  sensitive  to  the  specific  rate  of  (R23)  in  the temperature range 300–1900 K (Fig. 1).

Recently,  Yu   [44],  Troe   [45],  Zhu   et  al.  [46], and  Senosiain  et  al.  [25]  performed  detailed  Rice– Ramsperger–Kassel–Marcus (RRKM) calculations to model the temperature and pressure dependence of this reaction. Most of these correlations were primarily cal- ibrated against high-temperature shock tube data and predict higher rates than experimental measurements at low to intermediate temperatures, as shown in Fig. 2 (the only exception being the results of Zhu et al. [46] which underpredict the majority of experimental data at the temperatures of interest). These temperatures include  the temperature  sensitivity  window  for  CO laminar flame speed to this reaction. If one assumes that the theoretical fits misrepresent the specific rate of this reaction by comparison with the (presumably) more accurate experimental data at these temperatures, one would expect CO/H2  flame speeds to be overpre- dicted with the reaction models based on these rate parameters. Indeed, as shown in Fig. 3, GRI-Mech 3.0 [47], which uses the values of Yu [44], overpredicts the experimentally measured CO/H2/air laminar flame speeds of McLean et al. [48].

On the basis of the above considerations, we fit the entire body of experimentally measured rate constants

Figure   1    Sensitivity   spectrum    of   reactions   CO+ OH = CO2+ H,    (R23),   HCO+ M = H+ CO+ M,   (R24),    and HCO+ O2 = HO2+ CO, (R25), for a range of equivalence ratio predicted by the present C1/O2  kinetic  mechanis m . The figures are taken from Zhao et al. [43]. Figure (a) is the sensitivity spectrum of (R23) for ambient CO/H2/air flames of two initial fuel compositions (95% CO+ 5% H2  and 50% CO+ 50% H2); (b) is that of (R24) and (R25) for ambient CH3OH/air flames. Bars indicate the temperature range where the sensitivity is more than 10% of the maximum value, and lines represent the temperature span for the specific flame.

available in the literature [44,49–54] by the method of weighted least squares to obtain a more representative correlation of the experimental measurements of this rate constant. The sum of weighted squared errors

is minimized by taking the rate constant, k, as

In Eq. (1), kexp  is the rate constant measured experi- mentally at temperature Ti , and σi  is the absolute error of log kexp at Ti . Equation (2) was used as the rate con- stant of reaction (R23) in this study. The values shown in parentheses in Eq. (2) are the 95% confidence inter- vals of the fitted parameters.

Figure 2 shows the comparison of this expression with literature results, including those of Lissianski et al.  [54] which in the current study were recalcu- lated based on the present thermochemical data and the rate constant of the reverse reaction of (R23) provided in the original paper  [54]. The new correlation pre- dicts specific rate constant values in close agreement with those obtained from the correlation of Yu et al.

[55]  (within  6%  at  800–3500 K) derived by  fitting their high-temperature experimental measurements in a  shock  tube.  In  the  temperature  window  of  800– 2000 K, predictions from the new expression agree well (within 10%) with those of Troe [45] at 1 atm, while they are about 20% lower than the theoretical predictions of Yu [44] and Senosiain et al. [25] at1atm.

Very recently, and since the thesis research on this work  [26], another theoretical treatment of reaction

Figure 2    Rate constant of reaction CO+ OH → CO2 + H (R23).  Symbols  are  experimental  data  (except  for  atmo- spheric pressure theoretical results of Zhu et al. [46]). Lines are the recommendations of Yu [44], Troe [45], Yu et al. [55] at 1 atm, Senosiain et al. [25] at 1 atm, Joshi and Wang [56] at the low-pressure limit, and that used in the present C1 mechanis m (Eq. (2)).

(R23) has appeared in the literature  [56]. Joshi and Wang [56] have pointed out that consideration of both cis- and trans-isomeric forms of HOCO adduct as well as hindered rotation connecting the two (ignored in prior theoretical studies) leads to significant changes in  the predicted thermal rate constant for reaction (R23). The resulting expression recommended by these au- thors is also plotted in Fig. 2. As can be seen, their re- sult is significantly lower at the intermediate tempera- tures of interest than the earlier theoretical predictions. Joshi and Wang have also indicated that “the treatment of the title reaction (R23) remains semi-empirical as more than one different model can satisfactory repro- duce a wide range of data.” The present empirical fit (Eq. (2)) is approximately half-way between the the- oretical results of Senosiain et al.  [25] and the new results of Joshi and Wang [56].

Figure 3    Laminar flame speed of CO/H2/air mixtures at 298 K and  1  atm. The fuel composition is 95% CO and 5% H2 . Symbols—experimental data of McLean et al. [48]; dotted line—predictions of GRI-Mech 3.0 [47]; solid line— predictions of GRI-Mech 3.0 modified by replacing the rate coefficients of reactions (R24) and (R25) with the recom- mendations of Friedrichs et al. [ 19] and DeSain et al. [24], respectively.

HCO+ M= H+ CO+ M (R24) and HCO+ O2 = HO2 + CO (R25)

Both the unimolecular decomposition and abstraction reactions of formyl radicals are the main pathways to generate CO during the high-temperature combustion of hydrocarbons. Because the H atom in HCO is very weakly bound, the dissociation reaction (R24) com- petes strongly with the H-abstraction reactions from HCO by H, OH, and O2. Timonen et al. [57,58] di- rectly measured the rate constant of reactions (R24) and (R25) in a heated tubular reactor below 832 and 713 K, respectively. More recently, Friedrichs et al.

[ 19] detected HCO in a shock tube for the first time by using frequency-modulated spectroscopy. Based on a reaction mechanis m primarily derived from GRI-Mech 3.0 [47], the rate constant of reaction (R24) was esti- mated by fitting the experimental HCO profiles at 835– 1230 K [ 19]. The work of Friedrichs et al. [ 19] infers that the rate of (R24) is about two times lower than the measurements of Timonen et al. [57]. DeSain et al.

[24] also studied reaction (R25) at 296–673 K experi- mentally and reported a temperature-independent rate constant, which is about two times lower than that of Timonen et al. [58] at 1000 K.

In a flow reactor study of CH2 O/NO/O2 , Glarborg et al. [59] adopted the expressions of Friedrichs et al.

[ 19] and DeSain et al.  [24] for reactions (R24) and (R25), respectively, in a revised kinetic mechanis m, which predicted their flow reactor measurements rea- sonably well. Incorporating these expressions within the present mechanis m also results in as good agree- ment  with  the  flow  reactor  experiments  of  [9]  as achieved using the recommendations of Timonen et al. [57,58]. Closer inspection, however, reveals that the ratio  k24/k25   for the  new  correlations  is  almost the same as that used previously, and that the CH2 O/O2 system predictions under flow reactor conditions are sensitive to this ratio, rather than to the absolute mag- nitudes of the individual specific rate constants  [9]. On the other hand, premixed laminar flame speeds of  hydrocarbons, particularly those of simple oxygenates such as formaldehyde and methanol, are very sensitive to the absolute rates of (R24) and (R25) (e.g.,  [4]). Using the recommendations of [ 19,24] yields substan- tially different flame speed predictions from those ob- tained with the correlations of Timonen et al. [57,58]. Attempting to compensate for these discrepancies by combinatorial modifications of other elementary rate constants degrades the quality of predictions against other experimental targets.

Figure 3 compares the experimental flame speeds of CO/H2/air mixtures  [48]  with model predictions of GRI-Mech-3.0 [47] and with the predictions of a “modified”  GRI-Mech-3.0 in which the rate coeffi- cient correlations for reactions (R24) and (R25) are replaced by the recommendations of Friedrichs et al. [ 19] and DeSain et al. [24], respectively. The overall uncertainty of the experimental flame speeds was re- ported to be ±3% [48]. Obviously, the predictions of the modified mechanis m are significantly degraded in co  mparison to those using the original mechanis m and depart substantially from the experiments, particularly at fuel rich equivalence ratios. Similar behavior was observed for the laminar flame speeds of other hydro- carbon/air mixtures, particularly those for CH3 OH/air and C2H5 OH/air mixtures. In further demonstration of the novel method of temperature-dependent sensitivity ana lysis, Zhao et al. [43] showed that 1300–2000 and 1200–1900 K are the temperature windows where hy- drocarbon laminar flame speed predictions are most sensitive  to  reaction  (R24)  and  (R25),  respectively (Fig. 1). These temperature ranges are well above the range of conditions of both the recent measurements of [ 19,24], and the earlier measurements of Timonen et al. [57,58]. Extrapolation of the rate constant cor- relations recommended in [ 19,24] yields substantially lower values for the rate constants within these temper- ature ranges than extrapolation of those recommended in [57,58]. As a result of these an alyses, the correla- tions recommended previously by Timonen et al. [57] and those in [ 19,24] were not adopted in this study even though the reported rate measurements [ 19,24] appear to have s maller estimated uncertainties than the previ- ous measurements [57,58]. Instead, we again applied a weighted least-squares fitting to all experimental data available in the literature for k24  [ 19,20,57,60–73] to  yield a new rate correlation,

Figure 4 compares this new correlation with the litera- ture data and the previous correlations. In the range of  1500–2000 K, the prediction of Eq. (3) agrees with the data correlation of Timonen et al. [57] within 30% and is about 2–3 times higher than the correlation recom- mended by Friedrichs et al. [ 19]. Over 500–1300 K, where the rate coefficient of (R24) was measured by Friedrichs et al. [ 19], Timonen et al. [57], Krasnoperov et al.  [72], and Hippler et al.  [73], the  current cor- relation predicts values  almost equidistant from the measurements reported by Timonen  et  al.  [57]  and Friedrichs et al. [ 19].

Figure   4    Rate   constant   of   reaction   HCO+ M    →

H+ CO+ M  (R24). Symbols and lines with  symbols are literature results: 田 Friedrichs et al. [ 19];   Hidaka et al.

[20]:  o Timonen  et  al.  [57];   Pearson  et  al.  [60];  -8- Schecker et al. [61]; 8- Browne et al. [62]; Bowman

[63]; ▲ Ahumada et al. [64];     Baldwin et al. [65];   Wang et al. [66]; v Westbrook et al. [67];  Campbell et al. [68]; v Hochnadel et al [69];  Cherian et al. [70];  Cribb et al.

[71];   Krasnoperov et al. [72];   Hippler et al. [73]. The dotted line is the recommendation of Timonen et al. [57], the dashed line is the recommendation of Friedrichs et al. [ 19], and the solid line represents the values used in the present model (Eq. (3)).

It  should be noted that the correlation  shown in Eq. (3) was obtained by fitting low-pressure limit data. Timonen et al. [57] concluded, based on resonance the- ory, that significant deviations from the low-pressure limit would occur at (high) pressures beyond the scope of practical combustion processes, and reaction (R24) may be regarded as being in the low-pressure limit for most combustion applications. Recently, the pressure dependence of the rate constant of reaction (R24) has been measured by Krasnoperov et al. [72] and Hip- pler et al. [73], and the data show a somewhat unusual pressure falloff behavior. Based on their measurements and an isolated resonance model with variable reso- nance lifetimes, Hippler et al. [73] challenged the con- clusions drawn by Timonen et al. [57] and indicated that deviations from the low-pressure limit may occur even below atmospheric pressure; Krasnoperov [74], however, has questioned the experimental method and an alyses performed by Hippler et al.  [73] when ob- taining low-pressure data (see [74,75] for full details). Figure5plots the pressure-dependent measurements of Krasnoperov et al. [72] and Hippler et al. [73] and com- pares them against the low-pressure data of Friedrichs et al. [ 19] and Ti   monen et al. [57] as well as Eq. (3). It is clearly seen that, even though falloff behavior is ob- served, the deviation from the low-pressure limit data is only significant at temperatures below 580 K; the calculated values (using Eq. (3)) are within a factor of 2–3 of the measured high-pressure data below this temperature. At lower temperatures and in any applica- tions related to combustion, the reaction of HCO with HO2 will be far more important than (R24). Therefore for combustion modeling, the use of a low-pressure limit rate constant for reaction (R24) causes no signif- icant differences in model predictions. Regardless of this result, more studies of the falloff behavior of (R24) are warranted.

Figure 5 Pressure dependence of the rate constant of reaction (R24) as measured by Krasnoperov et al. [72] ( : 1bar; : 10 bar; : 30 bar; : 100 bar) and Hippler et al.[73] ( : 1 bar; : 10 bar; : 30 bar; : 100 bar), the rateexpression used in the present model (solid line) as well asthe low pressure measurements of Friedrichs et al. [19] andTimonen et al. [57] ( and , respectively) are also shownfor comparison.

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