re-evaluation of rate coefficients

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Formation of NO in high temperature N2/O2/ H2O mixtures - re-evaluation of rate coefficients Noémi A. Buczkó, Tamás Varga, Istvan Gyula Zsely, and Tamás Turanyi Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b00999 • Publication Date (Web): 01 Jun 2018 Downloaded from http://pubs.acs.org on June 1, 2018

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Formation of NO in high temperature N2/O2/H2O mixtures − re-evaluation of rate coefficients Noémi A. Buczkó, Tamás Varga, István Gy. Zsély*, Tamás Turányi Institute of Chemistry, Eötvös Loránd University (ELTE), Budapest, Hungary KEYWORDS: NO formation, thermal NO, mechanism optimization, uncertainty quantification

ABSTRACT

A re-evaluation of the flow reactor experiments of Abian et al. (Int. J. Chem. Kinet. 2015; 47: 518-532) is presented. In these experiments nitrogen oxide formation was measured at atmospheric pressure in temperature range 1700–1810 K, using several mixtures containing different ratios of oxygen, nitrogen and water vapor. Based on the mechanism of Abian et al., the two most important reaction steps for NO formation (R1: NO + N = N2 + O and R2: N2O + O = 2 NO) were identified by local sensitivity analysis. For the optimization of the Arrhenius parameters of these reaction steps, 25 datapoints measured by Abian et al., two direct rate coefficient measurements (73 data points) and one theoretical calculation were used. The obtained mechanism with the optimized Arrhenius parameters (R1: A = 1.176·1010 cm3mol–1s–1, n = 0.935, E/R = –693.68 K; R2: A = 1.748·1016 cm3mol–1s–1, n = –0.557, E/R = 14447 K) described the results of the flow reactor experiments, direct measurements and theoretical calculations much better compared to the Abian et al. mechanism, and also several recent NOx

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mechanisms. The rate coefficients of these elementary reactions were obtained with low uncertainty in the temperature range of 1600 K to 2200 K.

* E-mail address: [email protected] (I. Gy. Zsély).

1. Introduction Nitrogen oxides constitute an important category of atmospheric pollutants [1]. NO is mainly formed in combustion systems, including power station furnaces and internal combustion engines. In hydrocarbon combustion systems, NO can be formed in several chemically different routes from the N2 of air. At high temperature, NO is formed mainly in the thermal (Zeldovich) route. Although the thermal route was described first more than 70 years ago [2], the related rate coefficients are still not known accurately. This formation route was investigated experimentally by Bowman [3], Engleman et al. [4] and recently Abian et al. [5]. The rate determining reaction (R1) N + NO = N2 + O has been examined several times directly [6-14]. Its reverse reaction N2 + O = N + NO (R-1) is also an extensively studied reaction [15-39]. The thermodynamic data of the related species are known accurately ([40]); therefore, at a given temperature the forward rate coefficient can be calculated from the reverse one and the thermal equilibrium, without inducing further significant error. Using the calculation method of Nagy et al. [41], the estimated error of lnk is in the order of 10–5 due to the uncertainty of thermodynamic data. As Abian et al. [5] demonstrated, our knowledge on the rate coefficient of reaction R1 still has not reached the desired accuracy. Abian et al. also suggested a rate expression for reaction R1: N + NO = N2 + O based on their flow reactor experiments [5]. NO concentration was measured at the outlet of a tubular reactor heated to high temperature (in the range of 1700 K – 1810 K), while the inlet gases were various


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N2/O2/H2O mixtures at atmospheric pressure. The temperature range of the experiments was too narrow to determine the activation energy of reaction R-1 accurately. Therefore, the activation energy of this reaction was set to a literature value of Ea= 318.4 kJ mole-1 [42], the preexponential factor A was fitted at each experimental condition separately, and then averaged yielding A = 1.4 × 1014 cm3mol–1s–1. Abian et al. combined this information with the results of some direct rate determinations taken from the literature. They recommended new Arrhenius parameters for reaction R1: A = 9.4⋅1012 cm3mol–1s–1, n = 0.14 in the temperature range of 250 K − 3000 K. Our aim was to determine a rate expression for reaction R1 valid in the high temperature range of practical combustion systems, and also to characterize its uncertainty at these temperatures. The re-evaluation of the experimental results of Abian et al. revealed that these data carry information also on the Arrhenius parameters of reaction R2: N2O + O = 2 NO.

2. The parameter optimization method The global parameter optimization algorithm applied here has been described by Turányi et al. [43] and utilized for the investigation of several combustion systems [44-51]. According to this method, the optimal set of parameters is obtained by minimizing the following objective function:

1 E (p) = N

N

1 ∑ i =1 N i

2

 Yijmod (p) − Yijexp    , ∑ exp   ( ) σ Y j=1  ij  Ni

(1)

Here N is the number of data sets and Ni is the number of data points in the i-th data set. The exp

value yij

is the j-th measured data point in the i-th data set. For the indirect measurement data, mod

the modelled value is Yij , obtained from a simulation using an appropriate detailed mechanism,


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which belongs to a given set of rate parameters p, which are the ln A, n, and E/R Arrhenius parameters of the reactions. For the directly measured and theoretically determined rate mod

coefficients, Yij

corresponds to the calculated rate coefficient at a given temperature, pressure

and bath gas. During the global minimum search, multiple random parameter sets p are created within the uncertainty domain of the parameters, the corresponding E(p) values are evaluated and the minimum search is continued in the neighbourhood of the point having the lowest E(p) value [43]. The squared deviation of the simulation result from the experimental value is divided with the number of data points, therefore datasets with different number of datapoints have equal contribution to E if the average deviation is identical. The standard deviation of an experiment was determined for each data set separately. Constant absolute error ( σ ( yij ) is identical for all data j within data set i) was assumed for the measured exp

species concentrations, in this case Yij = yij applies. Constant relative error, implying identical

σ (ln yijexp ) values for all data j within data set i, was assumed for the directly measured and theoretically determined reaction rate coefficients; thus Yij = ln yij . Following the method described by Nagy et al. [41], uncertainty limits were calculated from direct rate coefficient measurements and theoretical studies of the rate coefficient. The prior uncertainty limits represent the range in which the rate coefficients can be considered as physically meaningful. Therefore, these uncertainty limits can be used as boundaries for the optimization method, ensuring that only physically feasible random parameter sets are tested. The posterior covariance matrix can be determined as a result of the parameter optimization procedure as described by Turányi et al. [43]. Covariance matrix of all Arrhenius parameters can be transformed to temperature-dependent posterior uncertainty limits of the rate coefficients.


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The evaluation of the error function (1) requires simulations of the experiments. The SENKIN code [52] of the CHEMKIN-II package [53] was used for the simulations, and in-house developed MATLAB code Optima was used for the optimization and uncertainty quantification calculations. This code was rewritten in C++ and published as code Optima++ [54]). The experimentally measured temperature−distance profiles in the tubular reactor were used in the simulations in such a way that these profiles were converted to temperature−time profiles knowing the flow rate, and plug flow conditions were assumed. All experimental data were encoded in ReSpecTh Kinetics Data Format [55].

3. Data used Abian et al. [5] discussed in details the experiments of Bowman (1971) [3] and Engleman et al. (1973) [4]. They concluded that these experimental data are not appropriate for the characterization of the rate coefficient of reaction R1. This was one of the motivations for the design of the tubular reactor experiments of Abian et al. Their analysis was confirmed by our calculation results. Therefore, we used only the data of Abian et al. [5] as indirect experimental data. We used all experimental data of Abian et al., while they processed the data related to three of the four mixtures investigated, and neglected the results related to initial O2 concentration of 0.45%. Abian et al. reported 8% scatter for their measurements, and it was used as 1σ uncertainty in our calculations. Abian et al. [5] applied the Klippenstein et al. [56] mechanism for the evaluation of their experimental data. They determined new Arrhenius parameters for reaction R1. We will refer to the Klippenstein mechanism with the new rate parameterization for R1 as the Abian et al. mechanism. In our simulations we used a base mechanism which was composed from two sources. The nitrogen chemistry reactions came from the Abian et al. mechanism. The hydrogen


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combustion chemistry block was taken from our recent optimized H2/CO reaction mechanism [47], which has been tested against large amount of hydrogen and syngas combustion experimental data. Table 1 shows that the original Klippenstein et al. mechanism very well reproduced the flow reactor data. Interestingly, the Abian et al. mechanism provided a worse result. The likely reason is that the new recommended rate parameters for R1 are representative in a very wide temperature range starting from 250 K. Our base mechanism provided almost identical results compared to those of the Abian et al. mechanism. Local sensitivity analysis was performed using the base mechanism at the condition of each Abian et al. experiment. Reaction 1: NO + N = N2 + O showed dominant sensitivity in each case, but reaction 2: N2O + O = 2 NO also had a non-negligible influence on the calculated NO concentration. All other rate coefficients had negligible sensitivity at any of the conditions. A typical sensitivity plot is shown in Fig. 1. Therefore, the Arrhenius parameters of both elementary reactions were selected for the optimization.

NO + N = N2 + O

N2O + O = 2 NO

HO2 + OH = H2O + O

1708 K 1758 K 1806 K

NH + NO = N2O + H

NO2 + O = NO + O2

0.0

0.2

0.4

0.6

0.8

Normalized local sensitivity coefficient

Fig. 1. The most sensitive reactions on the calculated NO concentration at three different temperatures. Mixture composition 20.9% O2, 78.6 % N2, 0.5 % H2O.


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A significant part of the direct experiments and theoretical results for these two reactions were related to low temperatures (48 K − 755 K) (R1: [15, 17-21, 23, 25-28, 31, 33, 35-38, 57]; R2: [58]). Since the aim of this work is to obtain accurate rate expressions valid at high temperatures, these results could not be used. Several rate parameters were determined using complex reaction mechanisms from shock tube, flame or static measurements (R1: [6-14] ; R-1: [16, 22, 24, 29, 34, 39] ; R2: [59-71] ; R-2 [12, 16, 72-76]). This kind of measurements usually have high and not controlled uncertainty. Excluding all these experiments, only the following few determinations remained: the shock tube measurements of Davidson and Hanson [30] and Michael and Lim [32] for R1, and the theoretical determination of Gonzalez et al. [77] for R2. The uncertainty of these data were assumed to be σ(ln k) = 0.16, 0.23 and 0.38, respectively. These uncertainties were based on the scatter of the experimental data and assuming uncertainty parameter f=0.5 (multiplication factor u=3) for the theoretical values. The number of data points used were 33, 40, and 9, respectively.

4. Determination of the prior uncertainty domains For the determination of the prior uncertainty domains we used programs u-Limits, UBAC and JPDAP [41, 78]. The 1500 K − 2700 K temperature interval was selected for the prior uncertainty calculations, which also determines the validity range of the optimized rate coefficients. The mean values were the rate coefficients used in the Abian et al. mechanism. Considering the results of all direct determinations in this temperature range, we chose temperature independent prior uncertainty parameter f=1.1 for reaction R1 NO + N = N2 + O, which assigns more than one magnitude uncertainty to the rate coefficient (see Fig. 2). For reaction R2 N2O + O = 2 NO the case is similar, and temperature independent uncertainty


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parameter f=1.0 is appropriate for the description of the uncertainty of the rate determination (see Fig. 3).

15.0 14.5 [6] 14.0

[12] [11]

[14]

[39]

13.5

[30]

[7]

3

-1 -1

lg(k / cm mol s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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13.0

[34]

[8] [9]

[22]

[29]

[32]

[16]

[24]

12.5 12.0 0.40

0.45

0.50

0.55

0.60

0.65

1000 K / T

Fig. 2. Determination of the prior uncertainty range for reaction R1: NO + N = N2 + O. Solid lines: direct rate determinations including those that were measured in the reverse direction and calculated using the thermodynamic equilibrium constant (citations in figure). Thick dashed red line: mean value (the rate coefficient of Abian et al.), thin dashed red lines: uncertainty limits. Temperature range: 1500-2700 K.


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13

12

[73] [62] [12]

[10] [74]

[66] 11

[76] [67]

[77]

[61]

[16]

[70]

3

-1 -1

lg(k / cm mol s )

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[72] [63] [69]

10

[23]

[64]

[77] [60]

9 0.40

0.45

0.50

0.55

0.60

0.65

1000 K / T

Fig. 3. Determination of the prior uncertainty range for reaction R2: N2O + O = 2 NO. Solid lines: direct rate determinations including those that were measured in the reverse direction and calculated using the thermodynamic equilibrium constant (citations in figure). Thick dashed red line: mean value (the rate coefficient of Abian et al.), thin dashed red lines: uncertainty limits. Temperature range: 1500-2700 K.

5. Results During the parameter optimization, all 6 Arrhenius parameters were fitted to the 25 indirect data points and 3 direct data series at the same time. The 8% experimental error was used as 1σ standard deviation in the objective function. This choice enlarges the deviations for the smaller measured values, therefore the reproduction of 0.45% O2 and 8.0% O2 experiments became better. As Table 1 shows, the optimization decreased the error function values from E=370 to E=186. We also tried the optimization without changing the rate parameters of reaction R2, but in this case the error function value was much higher (E=215). The final optimized mechanism


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(provided in the Supporting Information) described much better the flow reactor measurements, and the agreement with the indirect experimental results remained very good (E=8.89). The optimized Arrhenius parameters are R1: A = 1.176·1010 cm3mol–1s–1, n = 0.935, E/R = – 693.68 K; R2: A = 1.748·1016 cm3mol–1s–1, n = –0.557, E/R = 14447 K. The Abian et al. experimental data were also simulated with several recently published NOx mechanisms. The results are shown in Table 1 and in Fig. 4. Table 1 shows that the optimized mechanism provides the best overall reproduction of the experimental data Abian 2015

base mechanism

Indirect measurements

360.66

Direct measurements Total

optimized optimized GRI 3.0

Klippenstein

Konnov 2009

Mével 2009

Polimi 2014

San Diego 2014

(R1 only)

(final)

2011

365.89

210.14

177.10

288.56

1154.07

1126.23

215.03

1076.54

1035.08

3.97

3.97

(4.71)

8.89

9.18

8.14

5.57

5.69

10.68

11.74

364.63

369.86

(214.86)

185.99

297.74

1162.21

1131.80

222.72

1087.22

1046.83

Table 1 Error function values for the following mechanisms: Abian et al. 2015 [5], base mechanism (see text), optimized (R1 only), optimized (final), GRI 3.0 [79], Konnov 2009 [80], Mével et al. 2009 [81], Klippenstein et al. 2011 [56], Polimi 2014 [82], San Diego 2014 [83]. The direct measurement and total values are in parentheses in the column of “optimized (R1 only)”, indicating that in this case the values refer to the deviations of the rate coefficients of R1 only.


10

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30

20

15

10

5

0 1700

1720

1740

1760

exp. present work GRI 3.0 Konnov 2009 Mevel 2009 POLIMI 2014 SanDiego 2014 Abian 2015 Klippenstein 2011

60

0.45 % O2, 99.05 % N2, 0.5 % H2O

NO outlet concentration / ppm


25

1780

50

40

30

10

0 1700

1800

1.8 % O2, 97.7 % N2, 0.5 % H2O

20

1720

1740

1760

1780

1800

T/K

T/K

180

100

160

8.0 % O2, 91.5 % N2, 0.5 % H2O


120


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Energy & Fuels

80

60

40

20

0 1700

1720

1740

1760

1780

1800

140

20.9 % O2, 78.6 % N2, 0.5 % H2O

120 100 80 60 40 20 0 1700

1720

T/K

1740

1760

1780

1800

T/K

Fig. 4. Comparison of the measured (black squares, Abian et al. [5]) and the simulated NO concentration values (solid black line: optimized mechanism, solid red line: GRI 3.0 mechanism [79], solid green line: Konnov 2009 mechanism [80], dashed black line: Mével et al. 2009 [81], dashed red line: Klippenstein 2011 [56], dashed green line: POLIMI 2014 [82], dotted black line: San Diego 2014 [83], dotted red line: Abian et al. mechanism [5]. Initial mixture compositions are given in the panels.

The analysis provided not only optimized values, but uncertainty limits. Figs. 5 and 6 are the corresponding Arrhenius plots for reactions R1 and R2, respectively. These show the initial rate


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coefficients, their prior uncertainty limits, the utilized direct determinations and also the theoretical values of the rate coefficients as symbols. For reaction R1: NO + N = N2 + O the smallest uncertainty parameter is f= 0.175 at temperature T= 1630 K and it is below f=0.226 in the temperature range of 1600 K to 2200 K. For reaction R2: N2O + O = 2 NO the smallest uncertainty parameter is f= 0.144 at temperature T= 1885 K and it is below f=0.619 in the temperature range of 1600 K to 2200 K. This shows that the determined rate coefficients are known with low uncertainty in the temperature range important for practical combustion systems. The posterior covariance matrix is provided in the Supporting Information. This matrix contains the raw information of the uncertainty and can be transformed to temperature-dependent posterior uncertainty limits of the rate coefficients, as presented with black thin lines in Figs. 5 and 6.

14.5

14.0

-1

-1

lg( k / cm mol s )

13.5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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13.0

12.5

12.0 0.4

0.5

0.6

0.7 -1

0.8

0.9

1.0

-1

1000 T / K

Fig. 5. Arrhenius plot of reaction R1 NO + N = N2 + O. Black lines: optimized values (this work), [5] red lines: the prior rate expression. Solid lines: mean values, dashed lines: the


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respective 3σ uncertainties. Experimental data: green triangles, Davidson and Hanson [30]; green circles, Michael and Lim [32].

13.0 12.5 -1

12.0

-1

11.5

3

lg( k / cm mol s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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11.0 10.5 10.0 9.5 9.0 0.35

0.40

0.45

0.50 -1

0.55

0.60

0.65

-1

1000 T / K

Fig. 6. Arrhenius plot of reaction R2 N2O + O = 2 NO. Black lines: optimized values (this work), red lines: the prior rate expression. Solid lines: mean values, dashed lines: the respective 3σ uncertainties. Theoretical values: green triangles, Gonzalez et al. [77].

6. Summary Thermal NO-formation is the dominant route of nitrogen oxide generation from the N2 of the air in high temperature combustion systems. Abian et al. [5] recently published NO concentrations measured in a tubular reactor fed by N2/O2/H2O mixtures. At the conditions of these experiments, the produced NO depends mainly on the rate determining step R-1 N2 + O =


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NO + N of the thermal route. The kinetic analysis of the experimental conditions revealed that the simulated NO concentration also depends on the rate parameters of reaction R2 N2O + O = 2 NO. The nitrogen chemistry model of Klippenstein et al. [56] was updated and used for the parameter optimization studies. The Arrhenius parameters of both reactions were fitted to the experimental data of Abian et al. and also the results of selected direct measurements and theoretical determinations. The calculations took into account the experimental error of Abian et al. [5]. The obtained mechanism reproduces all experimental data of Abian et al. in a reasonable manner. Reaction mechanisms Klippenstein 2011 [56] showed almost as good results as the optimized one. GRI 3.0 [79] and Abian 2015 [5] provided acceptable results for experimental datasets 2-5, but failed for set 1. Mechanisms GRI 3.0 [79], Konnov 2009 [80], Mével 2009 [81], Polimi 2014 [82], and San Diego 2014 [83] mechanisms do not reproduce well datasets 1 and 4. The present work included the determination of the temperature dependent uncertainty limits for the rate coefficients. These posterior uncertainty limits are narrow in the temperature range of 1600 K to 2200 K, important for the accurate simulation of thermal NO formation in practical combustion systems.

Acknowledgement The authors thank Professors Peter Glarborg and Maria Alzueta for providing us the temperature−distance profiles measured in the tubular reactor and the helpful discussions related to these measurements. We also thank the help of Ms. Éva Valkó in the usage of code u-Limits. Author Contributions


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TT suggested the topic, NAB, TV and ZSIGY carried out the calculations, ZSIGY prepared the figures, TT and ZSIGY wrote the text of the manuscript. All authors have given approval to the final version of the manuscript. Funding Sources We acknowledge the support of the Hungarian National Research, Development and Innovation Office – NKFIH grant K116117 and COST Action CM1404 “SmartCats”. References


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[1] Jacobson, M. Z. Atmospheric pollution: History, science, and regulation; Cambridge University Press, 2002. [2] Zeldovich, Y. B. The oxidation of nitrogen in combustion and explosions. Acta Physicochim USSR 1946, 21, 577–628. [3] Bowman, C. T. Investigation of nitric oxide formation kinetics in combustion processes: The hydrogen-oxygen-nitrogen reaction. Combust Sci Technol 1971, 3, 37. [4] Engleman, V. S.; Bartok, W.; Longwell, J.; Edelman, R. B. Experimental and theoretical studies of NOx formation in a jet-stirred combustor. Symp (Int) Combust 1973, 14, 755–765. [5] Abián, M.; Alzueta, M. U.; Glarborg, P. Formation of NO from N2/O2 Mixtures in a Flow Reactor: Toward an Accurate Prediction of Thermal NO. Int J Chem Kinet 2015, 47, 518– 532. [6] Bachmaier, F.; Eberius, K. H.; Just, T. The Formation of Nitric Oxide and the Detection of HCN in Premixed Hydrocarbon-air Flames at 1 Atmosphere. Combust Sci Technol 1973, 7, 77. [7] Iverach, D.; Basden, K. S.; Kirov, N. Y. Formation of Nitric Oxide in Fuel-Lean and Fuel-Rich Flames. Symp (Int) Combust 1973, 14, 767. [8] Harris, R. J.; Nasralla, M.; Williams, A. The Formation of Oxides of Nitrogen in High Temperature CH4-O2-N2 Flames. Combust Sci Technol 1976, 14, 85. [9] Blauwens, J.; Smets, B.; Peeters, J. Mechanism of "Prompt" NO Formation in Hydrocarbon Flames. Symp (Int) Combust 1977, 16, 1055.


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re-evaluation of rate coefficients

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