Improved Shock Tube Measurement of the CH4 + Ar = CH3 + H + Ar

Jul 5, 2016 - The current data are in good consensus with various theoretical and review studies, but at the low temperature end they suggest a slight...
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Improved Shock Tube Measurement of the CH4 + Ar = CH3 + H + Ar Rate Constant using UV Cavity-Enhanced Absorption Spectroscopy of CH3 Shengkai Wang, David F. Davidson,* and Ronald K. Hanson High Temperature Gasdynamics Laboratory, Mechanical Engineering, Stanford University, California 94305, United States S Supporting Information *

ABSTRACT: We report an improved measurement for the rate constant of methane dissociation in argon (CH4 + Ar = CH3 + H + Ar) behind reflected shock waves. The experiment was conducted using a sub-parts per million sensitivity CH3 diagnostic recently developed in our laboratory based on ultraviolet cavity-enhanced absorption spectroscopy. The high sensitivity of this diagnostic allowed for measurements of quantitatively resolved CH3 time histories during the initial stage of CH4 pyrolysis, where the reaction system is clean and free from influences of secondary reactions and temperature change. This high sensitivity also allowed extension of our measurement range to much lower temperatures (99.97% purity, with the major impurity being N2 and other impurities such as O2 being less than 15 ppm) were used in the experiments and diluted in research-grade high-purity Ar (6.0 grade and 5.0 grade, with total hydrocarbons less than 0.1 and 0.5 ppm, respectively; all gases were supplied by Praxair. Some initial experiments were performed with commercial grade CH4 of >99% purity, with O2 less than 50 ppm.) The gas mixtures were prepared manometrically in a 40 L stainless steel mixing tank that was equipped with a magnetic stirrer to accelerate the mixing, and typical mixing times were at least 2 h to ensure the mixture homogeneity. For more accurate control of the mixture composition, low CH4 concentration (99% purity CH4 and 5.0 grade Ar.

data yields an Arrhenius expression for the title rate constant as k1 (1.7 atm) = 3.7 × 1016 exp(−42 200 K/T) cm3/mol·s, with an overall 2σ uncertainty factor of 1.25. The current data are compared with previous experimental results in the Arrhenius plot shown in Figure 4a. The hightemperature end of the current measurement is seen to be in excellent agreement with the study of Davidson et al.,6 which also utilized a UV laser absorption diagnostic for CH3 detection and hence is considered most relevant to the present study. Also evident from this comparison is that the improved CH3 detectivity of the current study has led to a significant reduction in the scatter of data. The earlier ARAS study by Roth,11 laser schlieren study by Tabayashi and Bauer,8 and IR emission/ absorption study by Heffington et al.3 also agree in trend with the current measurement. The most recent experimental measurement from Koike et al.,4 however, is seen to be higher than the current work by about a factor of 2 in the overlapping temperature region and appears to have lower activation energy, but this difference is probably due to the relatively large scatter of the Koike et al. data. At much higher temperatures, the laser schlieren data from Keifer and Kumaran9 also show lower activation energy than the current study, probably

Figure 4. Comparison of current and Davidson et al.6 k1 with various studies: (a) experiment; (b) theory and review. Note that in (a), results from Roth,11 Tabayashi and Bauer,8 and Heffington et al.3 are almost identical; and they all agree in trend with the current data. E

DOI: 10.1021/acs.jpca.6b02572 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Table 2. Rate Parameters for Falloff Curves of CH4 (+ Ar) = H + CH3 (+ Ar) from Recent Studies reaction direction association

association

dissociation

dissociation

a

falloff parameters

reference

k∞ = 2.01 × 1014(T/300 K)0.186 exp(−T/25 200 K) cm3 mol−1 s−1 valid over 130−3000 K k0 = 2.34 × 1021 exp[−(T/21.22 K)0.5] cm6 mol−2 s−1 over 100−5000K Fc = 0.262 + [(T − 2950 K)/6100 K]2 over 100 − 4000 K Kc = exp(52044 K/T) [1.35 × 10−1 (T/300 K)−1.76 + 2.51 × 10−3 (T/300 K)0.67] cm3 mol−1 over 300 − 5000 K k/k∞ = xF(x)/(1 + x) with x = k0[Ar]/k∞ F(x) = 1 − (1 − Fc) exp{−[log(1.5x)/N]2/Na} with N = 0.75−1.27 log Fc, Na = 2 for log(1.5x) > 0, and Na = 2[1− 0.15log(1.5x)] for log(1.5x) < 0 k∞ = 2.01 × 1014(T/300 K)0.186 exp(−T/25 200 K) cm3 mol−1 s−1 k0 = 2.34 × 1021 exp[−(T/21.22 K)0.5] cm6 mol−2 s−1 Fc = 0.63exp(−T/3315 K) + 0.37exp(−T/61 K) Kca = 6.25 × 10−3T0.06exp(52 900 K/T) cm3 mol−1 over 300−2500K k/k∞ = xF(x)/(1 + x) with x = k0[Ar]/k∞ log F(x) = log Fc/{1 + [(log x + C)/(N − 0.14{log x + C})]2} with N = 0.75−1.27 log Fc and C = −0.4 −0.67 log Fc k∞ = 2.4 × 1016 exp(−52 800 K/T) s−1 over 1000 − 3000 K k0 = 4.5 × 1017 exp(−45 700 K/T) cm3 mol−1 s−1 over 1000−1700 K k0 = 4.7 × 1047T−8.2 exp(−59 200 K/T) cm3 mol−1 s−1 over 1700−5000K Fc = exp(−T/1350 K) + exp(−7834 K/T) over 1000 − 5000 K Kc = 5.1 × 102 T−0.217 exp(−53 010 K/T) mol cm−3over 300 − 5000 K k/k∞ = xF(x)/(1 + x) with x = k0[Ar]/k∞ log F(x) = log Fc/{1 + [(log x + C)/(N − 0.14{log x + C})]2} with N = 0.75−1.27 log Fc and C = −0.4 −0.67 log Fc k∞ = 2.10 × 1016 exp(−52 800 K/T) s−1 over 1000 − 2500 K k0 = 3.91 × 1017exp(−45 200 K/T) cm3 mol−1 s−1 over 1000 − 2500 K Fc = exp(−T/1350 K) + exp(−7834 K/T) over 1000 − 5000 K Kca= 1.60 × 102 T−0.06 exp(−52 900 K/T) mol cm−3 over 300−2500K k/k∞ = xF(x)/(1 + x) with x = k0[Ar]/k∞ log F(x) = log Fc/{1 + [(log x + C)/(N − 0.14{log x + C})]2} with N = 0.75−1.27 log Fc and C = −0.4 −0.67 log Fc

Troe and Ushakov,19 2012

Golden,20 2013

Baulch et al.,35 2005

this evaluation

Kc calculated using Active Thermodynamics Tables.39

Figure 5. Comparison of various falloff fits with the previous experimental data. (a): High-temperature data from Davidson et al.6 Color coding is used to distinguish different temperatures, with the temperature data representing a binning of values at approximately the temperature indicated. Error bars correspond to 2σ-equivalent uncertainty limits of +70%/−50%. The solid lines are from the current evaluation. The dashed lines are from the Golden study in 2013.20 The dotted lines are from the Troe and Ushakov study in 201219 and are nearly identical to the current evaluation. The dash-dot lines are from the Baulch et al. review in 2005.35 (b) Low-temperature data from Barnes et al.17 Error bars correspond to 2σ-equivalent uncertainty limits of +45%/−35%. Same line styles as in the left panel are used to distinguish different sources.

below. However, we do not recommend the use of these new

three parameters in the low- and high-pressure limit rate constant expressions (namely, A0, E0, and A∞) via Bayesian analysis (for details please refer to the attached Supporting Information). The value of Fc remains unchanged, and the overall changes in both k0 and k∞ (see Table 2) are still within the uncertainty limits of Baulch et al.35 (a factor of 2), yet these new parameters provide better fit to the current data as well as the high-temperature data from Davidson et al.6 and the lowtemperature data from Barnes et al.,17 as illustrated in the Table of Contents image at the end of the manuscript and Figure 5

parameters beyond 1000−2500 K, where they are underconstrained and may deviate from theoretical norms. Care is also advised when applying these new rate constants to methane/air flame simulations, as adjustment for the collisional efficiency of N2 (which is ∼40% to ∼60% higher than that of Ar; see results from Jasper and Miller18 and Troe and Ushakov19) is generally required. F

DOI: 10.1021/acs.jpca.6b02572 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

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(5) Davidson, D. F.; Di Rosa, M. D.; Chang, A. Y.; Hanson, R. K.; Bowman, C. T. A Shock Tube Study of Methane Decomposition using Laser Absorption by CH3. Symp. Combust., [Proc.] 1992, 24, 589−596. (6) Davidson, D. F.; Hanson, R. K.; Bowman, C. T. Revised Values for the Rate Coefficients of Ethane and Methane Decomposition. Int. J. Chem. Kinet. 1995, 27, 305−308. (7) Vompe, G. A. Thermal Decomposition of Methane at Low Pressures and High Temperatures. Russ. J. Phys. Chem. 1973, 47, 1396−1399. (8) Tabayashi, K.; Bauer, S. H. The Early Stages of Pyrolysis and Oxidation of Methane. Combust. Flame 1979, 34, 63−83. (9) Kiefer, J. H.; Kumaran, S. S. Rate of Methane Dissociation over 2800−4300 K: the Low-Pressure-Limit Rate Constant. J. Phys. Chem. 1993, 97, 414−420. (10) Bowman, C. T. Non-Equilibrium Radical Concentrations in Shock-Initiated Methane Oxidation. Symp. Combust., [Proc.] 1975, 15, 869−882. (11) Roth, I. P. ARAS-Messungen an einigen HochtemperaturKohlenwasserstoff-Reaktionen. Forsch. Ingenieurwes. 1980, 46, 93−102. (12) Klemm, R. B.; Sutherland, J. W.; Rabinowitz, M. J.; Patterson, P. M.; Quartemont, J. M.; Tao, W. Shock Tube Kinetic Study of Methane Dissociation: 1726 K ≤ T ≤ 2134 K. J. Phys. Chem. 1992, 96, 1786− 1793. (13) Sutherland, J. W.; Su, M. C.; Michael, J. V. Rate Constants for H + CH4, CH3 + H2, and CH4 Dissociation at High Temperature. Int. J. Chem. Kinet. 2001, 33, 669−684. (14) Brouard, M.; Macpherson, M. T.; Pilling, M. J. Experimental and RRKM Modeling Study of the Methyl+ Hydrogen Atom and Deuterium Atom Reactions. J. Phys. Chem. 1989, 93, 4047−4059. (15) Cheng, J. T.; Yeh, C. T. Pressure Dependence of the Rate Constant of the Reaction Atomic Hydrogen + Methyl Radicals = Methane. J. Phys. Chem. 1977, 81, 1982−1984. (16) Chen, C. J.; Back, M. H.; Back, R. A. The Thermal Decomposition of Methane. I. Kinetics of the Primary Decompositionto C2H6 + H2; Rate Constant for the Homogeneous Unimolecular Dissociation of Methane and its Pressure Dependence. Can. J. Chem. 1975, 53, 3580−3590. (17) Barnes, R. W.; Pratt, G. L.; Wood, S. W. Pressure Dependence of Methane Dissociation. J. Chem. Soc., Faraday Trans. 2 1989, 85, 229−238. (18) Jasper, A. W.; Miller, J. A. Theoretical Unimolecular Kinetics for CH4 + M = CH3 + H + M in Eight Baths, M= He, Ne, Ar, Kr, H2, N2, CO, and CH4. J. Phys. Chem. A 2011, 115, 6438−6455. (19) Troe, J.; Ushakov, V. G. The Dissociation/Recombination Reaction CH4 (+ M) ⇔ CH3 + H (+ M): A Case Study for Unimolecular Rate Theory. J. Chem. Phys. 2012, 136, 214309. (20) Golden, D. M. What, Methane Again?! Int. J. Chem. Kinet. 2013, 45, 213−220. (21) Hanson, R. K.; Davidson, D. F. Recent Advances in Laser Absorption and Shock Tube Methods for Studies of Combustion Chemistry. Prog. Energy Combust. Sci. 2014, 44, 103−114. (22) Sun, K.; Wang, S.; Sur, R.; Chao, X.; Jeffries, J. B.; Hanson, R. K. Time-Resolved In Situ Detection of CO in a Shock Tube Using Cavity-Enhanced Absorption Spectroscopy with a Quantum-Cascade Laser near 4.6 μm. Opt. Express 2014, 22, 24559−24565. (23) Wang, S.; Sun, K.; Davidson, D. F.; Jeffries, J. B.; Hanson, R. K. Shock-Tube Measurement of Acetone Dissociation using CavityEnhanced Absorption Spectroscopy of CO. J. Phys. Chem. A 2015, 119, 7257−7262. (24) Sun, K.; Wang, S.; Sur, R.; Chao, X.; Jeffries, J. B.; Hanson, R. K. Sensitive and Rapid Laser Diagnostic for Shock Tube Kinetics Studies using Cavity-Enhanced Absorption Spectroscopy. Opt. Express 2014, 22, 9291−9300. (25) Nations, M.; Wang, S.; Goldenstein, C. S.; Sun, K.; Davidson, D. F.; Jeffries, J. B.; Hanson, R. K. Shock-Tube Measurements of Excited Oxygen Atoms using Cavity-Enhanced Absorption Spectroscopy. Appl. Opt. 2015, 54, 8766−8775. (26) Wang, S.; Sun, K.; Davidson, D. F.; Jeffries, J. B.; Hanson, R. K. Cavity-Enhanced Absorption Spectroscopy with a ps-Pulsed UV Laser

CONCLUSIONS The second-order methane dissociation rate constant k1 was accurately determined from microsecond-resolved CH3 time histories that were recorded behind reflected shock waves using a sub-parts per million sensitivity CH3 diagnostic. Conducted at temperatures between 1487 and 1866 K and pressures of ∼1.7 atm, the current study reported the first direct shock tube measurement for k1 at T < 1700 K: k1 = 3.7 × 10 16 exp(−42 200 K/T) cm3/mol·s, with a 2σ uncertainty factor of 1.25. Current data agreed well with most previous experimental results within the overlapping temperature range yet had much less scatter. Recent theoretical and review studies also recovered the current measurement within their uncertainty limits but exhibited increasing discrepancies from the current results at lower temperatures. A re-evaluation of the existing experimental results in the falloff region was then performed, yielding updated falloff expressions that resulted in improved agreement with most existing data: k∞ = 2.10 × 10 16 exp(−52 800 K/T) s−1, k0 = 3.91 × 1017 exp(−45 200 K/T) cm3 mol−1 s−1, and Fc = exp(−T/1350 K) + exp(−7834 K/T), all valid over 1000−2500 K. This new expression for k1 may provide improved combustion modeling when the title reaction is important.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b02572. • Details on the optimization of the k1 falloff rate expression • Table of the intermediate falloff data of k1 selected as optimization targets • Optimal solution of A0, E0, and A∞ and corresponding uncertainty analysis (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1-(650)-725-2072. Fax: +1-(650)-723-1748. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Air Force Office of Scientific Research through AFOSR Grant No. FA9550-12-1-0472, with Dr. C. Li as contract monitor. The authors would like to thank Dr. H. Wang and Dr. D. Golden for helpful discussions.

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REFERENCES

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DOI: 10.1021/acs.jpca.6b02572 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpca.6b02572 J. Phys. Chem. A XXXX, XXX, XXX−XXX