Energy Fuels 2010, 24, 2439–2448 Published on Web 03/10/2010
: DOI:10.1021/ef901489k
Comparative Study of Methyl Butanoate and n-Heptane High Temperature Autoignition Benjamin Akih-Kumgeh and Jeffrey M. Bergthorson* Department of Mechanical Engineering, McGill University, Montreal, Quebec Received December 4, 2009. Revised Manuscript Received February 15, 2010
A comparative study of the high-temperature autoignition of methyl butanoate and n-heptane is carried out behind reflected shock waves. The ignition delay times of both fuels are compared at constant argon-to-oxygen ratios, equivalence ratios, and pressures. It is found that both hydrocarbons have comparable high-temperature ignition behavior under stoichiometric conditions in line with recent observations for longer chain alkanes and modeling results for methyl esters. However, differences are observed in the effect of equivalence ratio. Whereas the effect of equivalence ratio at constant argon/oxygen ratio on n-heptane ignition delay times is weak, its effect on methyl butanoate ignition is more appreciable. Representative experimental results from this study are compared with simulations using the most recent chemical kinetic mechanisms for the oxidation of methyl butanoate and the n-heptane mechanism by Curran et al. (Curran, H.; Gaffuri, P.; Pitz, W.; Westbrook, C. Combust. Flame 1998, 114, 149-177) While there is good agreement at stoichiometric conditions, the models deviate from experiment under rich conditions. Correlations are obtained by linear regression of the data from this study. The correlation format is also applied to numerical simulation results, thereby providing an alternative method for assessing the relative performance of chemical kinetic models.
widely studied hydrocarbons, such as n-heptane, has not been addressed in detail. HadjAli et al.10 investigated the lowtemperature ignition of C4-C8 methyl esters in a rapid compression machine. They compared the first stage ignition of methyl hexanoate at low temperatures to C4-C7 n-alkanes and found that the first stage ignition delay times of methyl hexanoate were comparable with those of n-heptane, while the onset of the negative temperature coefficient for methyl hexanoate occurred at a lower temperature. However, experimental data of high-temperature ignition for methyl esters have not yet been compared to those of higher alkanes. Recently, Akih-Kumgeh and Bergthorson11 carried out a shock tube ignition study of the simplest alkanoic acid methyl ester, methyl formate. They compared ignition delay times calculated using their proposed methyl formate ignition correlation to methane and ethane data at the same pressure, argon/oxygen ratio, and equivalence ratio. It was observed that methyl formate ignites more readily than methane but less readily than ethane. Efforts in modeling conventional hydrocarbon oxidation are being directed toward developing chemical kinetic models applicable to a wide range of hydrocarbons.12-14 The goal is
Introduction There is continued interest in understanding the combustion properties of biodiesel. Modeling the detailed combustion chemistry of practical biodiesel fuel is challenging and thus necessitates the choice of shorter chain methyl esters as surrogate fuels for combustion property studies. Methyl butanoate is one of many shorter chain methyl esters proposed as surrogates for biodiesel. A detailed chemical kinetic mechanism for its combustion was first proposed by Fisher et al.2 Through experimental studies3-6 and theoretical investigations,7,8 modifications have been suggested to enhance its applicability to a wider range of combustion conditions. Dooley et al.5 used ignition data from a rapid compression machine and a shock tube study by Metcalfe et al.,4 as well as species concentration profiles from flow and jet-stirred reactors, to test their modified version of the original mechanism by Fisher et al.2 Although there was good agreement in most cases, discrepancies were observed especially in the high-pressure rapid compression machine data. Recently, another chemical kinetic model for methyl butanoate and ethyl butanoate has been proposed by Hakka et al.9 The mechanism is validated against ignition delay times and jet-stirred reactor data. Although the understanding of methyl ester combustion is advancing, comparison of methyl ester oxidation to more
(9) Hakka, M.; Bennadji, H.; Biet, J.; Yahyaoui, M.; Sirjean, B.; Warth, V.; Coniglio, L.; Herbinet, O.; Glaude, P.; Billaud, F.; Battin-LeClerc, F. Int. J. Chem. Kinet. 2009, in press. (10) HadjAli, K.; Crochet, M.; Vanhove, G.; Ribaucour, M.; Minetti, R. Proc. Combust. Inst. 2009, 32, 239–246. (11) Akih-Kumgeh, B.; Bergthorson, J. Energy Fuels 2010, 24, 396–403. (12) Buda, F.; Bounaceur, R.; Warth, V.; Glaude, P.; Fournet, R.; Battin-Leclerc, F. Combust. Flame 2005, 142, 170–186. (13) Westbrook, C. K.; Pitz, W. J.; Herbinet, O.; Curran, H. J.; Silke, E. J. Combust. Flame 2009, 156, 181–199. (14) Sirjean, B.; Dames, E.; Sheen, D. A.; You, X.-Q.; Sung, C; Holley, A. T.; Egolfopoulos, F. N.; Wang, H.; Vasu, S. S.; Davidson, D. F.; Hanson, R. K.; Pitsch, H.; Bowman, C. T.; Kelley, A.; Law, C. K.; Tsang, W.; Cernansky, N. P.; Miller, D. L.; Violi, A. Lindstedt, R. P. A high-temperature chemical kinetic model of n-alkane oxidation, JetSurF version 0.2, September 08, 2008; Accessed October 4, 2009.
*To whom correspondence should be addressed. E-mail: jeff.bergthorson@ mcgill.ca. (1) Curran, H.; Gaffuri, P.; Pitz, W.; Westbrook, C. Combust. Flame 1998, 114, 149–177. (2) Fisher, E.; Pitz, W.; Curran, H.; Westbrook, C. Proc. Combust. Inst. 2000, 28, 1579–1586. (3) Gaı¨ l, S.; Thomson, M. J.; Sarathy, S. M.; Syed, S. A.; Dagaut, P.; Dievart, P.; Marchese, A. J.; Dryer, F. L. Proc. Combust. Inst. 2007, 31, 305–311. (4) Metcalfe, W.; Dooley, S.; Curran, H.; Simmie, J.; El-Nahas, A.; Navarro, M. J. Phys. Chem. A 2007, 111, 4001–4014. (5) Dooley, S.; Curran, H.; Simmie, J. Combust. Flame 2008, 153, 2–32. (6) Walton, S.; Wooldridge, M.; Westbrook, C. Proc. Combust. Inst. 2009, 32, 255–262. (7) Huynh, L.; Lin, K.; Violi, A. J. Phys. Chem. A 2008, 112, 13470–13480. (8) Hayes, C.; Burgess, D. Proc. Combust. Inst. 2009, 32, 263–270. r 2010 American Chemical Society
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: DOI:10.1021/ef901489k
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to establish kinetic models for the pyrolysis and oxidation of practical fuels such as diesel and jet fuel, which usually comprise a variety of hydrocarbons. Westbrook et al.13 proposed a mechanism for the oxidation of higher n-alkanes from n-heptane to n-hexadecane. From the simulated fuel/air ignition delay times for these alkanes, they observed that higher alkanes starting from n-heptane have comparable ignition delays in the high-temperature region with some deviations in the negative temperature coefficient (NTC) region. This behavior has also been observed in experiments.15,16 Shen et al.16 reported the first high-temperature ignition data for tetradecane/air and concluded, by comparing with n-heptane, n-decane, and n-dodecane, that any differences in the reactivity of n-alkanes above C7 are slight and are within experimental uncertainty. Although these studies involve fuel/air mixtures, similar conclusions are expected for fuel/oxygen/argon mixtures with constant argon/oxygen ratios. These observations suggest the existence of common features in the oxidation of hydrocarbons that can be very useful in the process of developing and optimizing chemical kinetic models for compounds with limited experimental data. The similarity can then be extended to other oxygenated hydrocarbons after careful studies. Dagaut et al.17 studied the kinetics of rapeseed methyl ester oxidation and found a strong similarity with the combustion of n-hexadecane. Herbinet et al.18 developed a chemical kinetic model for methyl decanoate: a moderately long chain methyl ester that has been suggested as a better surrogate for biodiesel than shorter chain methyl esters. Although ignition delay times were not available for methyl decanoate, Herbinet et al.18 used available shock tube ignition data for n-decane to test their mechanism and found that the new mechanism reproduced the ignition behavior over both the low- and high-temperature regions. In the process of optimizing a model to account for other combustion properties, such as flame speed or CO2 and NOx formation, this similarity of ignition behavior can be useful in constraining the model in the absence of extensive ignition data for the fuel being modeled. An instance of this is accounting for the early formation of CO2 during the oxidation of methyl esters as investigated by Farooq et al.19 (methyl-acetate, -propanoate, and -butanoate) and Herbinet et al.18 (methyl decanoate), the latter observing that methyl decanoate ignition is similar to n-decane ignition despite the different CO2 formation pathway. Furthermore, in practical systems where combustion is coupled with fluid dynamics, numerical simulations rely on reduced chemical kinetic schemes. The development of such reduced models is challenging and can be guided by an understanding of the similarities and differences in combustion properties between more extensively studied and less studied fuels. This work investigates the high-temperature ignition behavior of methyl butanaote (MB) and n-heptane over a pressure range of 1-10 atm and a temperature range of 1024-1715 K. The relative ignition behavior at temperatures less than 1000 K is not the subject of this study; however, it is known that these two fuels have marked differences in their low-temperature
Figure 1. End wall pressure and chemilumescence of the CH radical (at 430 nm) measurements with corresponding ignition delay time, τ, for an MB/O2/Ar mixture of type A at 4.9 atm and 1274 K. The average rate of normalized pressure rise in the shock tube is 6%/ms.
chemistry, with MB not exhibiting the NTC behavior characteristic of n-heptane.5 Experimental conditions from selected studies in the literature are chosen for each of the fuels in order to validate the experiments and to compare the relative ignition behavior of these two fuels. The mixtures are prepared in accordance with the expression: φF þ νðO2 þ DArÞ
ð1Þ
where φ is the equivalence ratio, F is the fuel, ν is the stoichiometric coefficient of the fuel (ν = 6.5 for MB and ν = 11 for n-heptane), and D is the argon/oxygen ratio of the mixture. In this study, comparison is made over a range of temperatures for mixtures with the same equivalence ratio and argon/oxygen ratio at constant average pressures. Correlations are proposed for the experimental data for each of the fuels. The same correlation method is applied to ignition delay times predicted by detailed chemical kinetic mechanisms. Comparison of correlations provides a convenient means of deducing the important high-level similarities and differences between detailed chemistry models and experiments. Experimental Technique Experiments are carried out in a 5.0 cm inner diameter stainless steel shock tube. Details of this shock tube facility are given elsewhere,11 and only the essential details specific to this study are mentioned here. The vapor pressures of methyl butanaote and n-heptane at 20 °C are 30 and 40 torr respectively. During the mixture preparation process, fuel is injected such that the resulting pressure is less than 60% of its vapor pressure. Oxygen and argon are added very slowly to avoid compressing the fuel to the point of local condensation. The methyl butanoate is of 99% purity, n-heptane is of 98% purity, and the gases employed in this study are oxygen (99.995%) and argon (99.995%), with helium (99.995%) used as a driver gas. The ignition delay time is obtained from light emission at the endwall with the shock arrival time determined from the endwall pressure trace (see Figure 1). The ignition delay is obtained by the intersection of the line of maximum slope of the CH signal with the average photodiode signal prior to ignition onset. The postreflected shock temperature is calculated from the one-dimensional shock equations with frozen chemistry using the GasEq equilibrium software.20 The thermodynamic data for methyl butanoate are taken from Dooley et al.,5 while those for the bath gases, n-heptane, and oxygen are taken from the thermodynamic
(15) Fieweger, K.; Blumenthal, R.; Adomeit, G. Combust. Flame 1997, 109, 599–619. (16) Shen, H.-P.; Steinberg, J.; Vanderover, J.; Oehlschlaeger, M. Energy Fuels 2009, 23, 2482–2489. (17) Dagaut, P.; Gaı¨ l, S.; Sahasrabudhe, M. Proc. Combust. Inst. 2007, 31, 2955–2961. (18) Herbinet, O.; Pitz, W.; Westbrook, C. Combust. Flame 2008, 154, 507–528. (19) Farooq, A.; Davidson, D.; Hanson, R.; Huynh, L.; Violi, A. Proc. Combust. Inst. 2009, 32, 247–253.
(20) Morley, C. A Chemical Equilibrium Program for Windows; 2009; Accessed June 22, 2009.
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Table 1. List of Gas Mixtures Employed in This Study mixture
φ
Ar/O2 ratio, D
fuel
% fuel
% O2
A
1.0
14.2
MB n-heptane
0.99 0.58
6.50 6.53
B
1.0
21.6
MB n-heptane
0.67 0.40
4.38 4.40
C
1.0
8.00
MB n-heptane
1.69 1.00
10.9 11.0
D
0.5
8.05
MB n-heptane
0.85 0.50
11.0 11.0
E
2.0
7.93
MB n-heptane
3.32 2.01
10.8 11.0
F
1.0
3.76
MB n-heptane
3.10 1.88
20.3 20.6
G
2.0
34.5
MB n-heptane MB/n-heptane
0.84 0.50 0.64
2.79 2.80 2.80
Figure 2. Effect of presssure on ignition using A mixtures (φ = 1.0, D = 14.2) for MB and n-heptane. 1 atm: MB (b), MB data by Metcalfe et al.4 (O), n-heptane (9); 10 atm: MB ((), MB data by Hakka et al.9 ()), n-heptane ().
database in GasEq. Uncertainty in the calculated temperatures result from the uncertainties in the shock velocity and composition of the combustible gas. It is estimated that the average temperature uncertainty in this work is between 10 and 25 K. Nonideal effects in the shock tube lead to a rise in the postreflected shock pressure prior to ignition. The current shock tube was characterized using nonreactive oxygen/argon mixtures (8.5% O2 and 91.5% Ar) and the pressure rise was found to be, on average, 6%/ms, comparable with findings by Petersen and Hanson21 for a high-pressure shock tube of the same diameter. The rise in pressure for reactive shots is a combination of preignition chemistry and nonideal gas-dynamic effects as observed by Davidson et al.22 This is evidenced by the rise in pressure prior to ignition observed in simulations using a constant volume reactor. Assuming the pressure rise is isentropic, the associated temperature rise is about 2%/ms, which causes an 8% reduction in an ignition delay time of 500 μs. Delay times shorter than 100 μs are unaffected by the small pressure rise. These relatively small uncertainties do not compromise the findings discussed in this paper. For the purpose of comparison with simulations, the shock tube ignition process is modeled as a constant volume adiabatic reactor using the CANTERA software package.23 The ignition delay is obtained as the time from the beginning of the simulation to the time of peak CH concentration. Because of the very rapid rise in CH concentration, the ignition delay thus obtained is practically the same as would be obtained by extrapolating the line of maximum slope to the preignition CH concentration level. In the shock tube experiment, the CH signal is broader because observation through the endwall captures chemiluminescence for successive ignition processes down the shock tube. Table 1 lists the different compositions of mixtures employed in this study. The last mixture of type G is a blend of 56% MB and 44% n-heptane. From the equivalence ratio, φ, and Ar/O2 ratio, D, in Table 1, together with the stoichiometric air/fuel ratio, ν, for each of the fuels, the mixture mole fractions can be recovered using the equations: φ Xfuel ¼ ð2Þ φ þ νð1 þ DÞ XO2 ¼
ν φ þ νð1 þ DÞ
ð3Þ
XAr ¼
νD φ þ νð1 þ DÞ
ð4Þ
The effect of pressure on ignition of MB and n-heptane is studied at average pressures of 1, 4, and 10 atm. The effects of equivalence ratio and dilution are also investigated. The conditions of mixture G (φ = 2.0 and D = 34.5), a blend of 56% MB and 44% n-heptane, is also investigated at 4 atm. The conditions are chosen to compare with previously published ignition data for one of the fuels studied.
Results and Discussion Comparison of Ignition Delay Time Measurements. Ignition delay times, τ, of MB and n-heptane are compared as a function of temperature, T, at pressures, p, of 1 and 10 atm in Figure 2. An argon/oxygen ratio of D = 14.2 (corresponding to type A mixtures in Table 1) is chosen to match conditions in the study by Metcalfe et al.4 and Hakka et al.9 (1.0% MB, 6.5% O2, and 92.5% Ar). In the experiments, postreflected shock pressures vary from the nominal pressure, thus the ignition delay times shown in the figures in this study are scaled to the average pressure using a power law: ð5Þ τ µ pγ whose exponent, γ, for each fuel is determined by linear regression of the experimental data as presented later in eqs 7 and 8. The MB data at 1 atm are compared to previously published data by Metcalfe et al.,4 showing good agreement. Recent MB data by Hakka et al.9 at an average pressure of 8.4 atm have been scaled to 10 atm for comparison with the current data. As shown in Figure 2, the agreement is good, especially at higher temperatures. However, the measurements of Hakka et al.9 show a higher apparent activation energy than observed in this study. It is observed that at both pressures, the temperature sensitivities or apparent activation energies and the ignition delay times of both MB and n-heptane are comparable. This is an important observation regarding the high-temperature ignition behavior of methyl esters and n-alkanes. By fixing the ratio of argon/oxygen, D, at stoichiometric conditions, the same relative ignition behavior is observed as in the fuel/air study of alkanes by Westbrook et al.13 To further investigate this observation, comparison is carried out at other pressures and dilution levels. The conditions in Figure 3 are taken from a previous study of n-heptane
with ν = 6.5 for MB and ν = 11 for n-heptane. (21) Petersen, E. L.; Hanson, R. K. Shock Waves 2001, 10, 405–420. (22) Davidson, D. F.; Gauthier, B. M.; Hanson, R. K. Proc. Combust. Inst. 2005, 30, 1175–1182. (23) Goodwin, D. Proceedings of CVD XVI and Euro CVD 14, Electrochemical Society 2003, 14, 155–162.
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Figure 3. Effect of pressure on ignition using B mixtures (φ = 1.0, D = 21.6). 1 atm: MB (b), n-heptane (9), n-heptane by Horning et al.24 (0); 4 atm: MB (), n-heptane ((), n-heptane by Horning et al.24 ()).
Figure 5. Comparison at rich conditions for G mixtures, p = 4 atm, φ = 1.9-2.0 and average D = 34.5. MB (b), n-heptane (9), n-heptane by Burcat et al.25 (0), blend of 56% MB and 44% n-heptane ().
Figure 4. Comparison of ignition delay times for lean (D mixtures) and rich (E mixtures) equivalence ratios at p = 4 atm and D = 8.0. φ = 0.5: MB (b), n-heptane (9), n-heptane by Burcat et al.25 (0); φ = 2.0: MB (Δ), n-heptane ().
Figure 6. Effect of Ar/O2 ratio, D, on ignition delay times for stoichiometric A and F mixtures at p = 10 atm. A mixtures (D = 14.2): MB (b), n-heptane (9); F mixtures (D = 3.7): MB (), n-heptane (().
by Horning et al.24 (0.4% n-C7H16, 4.4% O2, and 95.2% Ar, or φ = 1.0 and D = 21.6 as in mixture type B). The present n-heptane data show fairly good agreement with data by Horning et al.,24 and again the ignition delay times of MB and n-heptane are equivalent under the same φ and D conditions. The data by Horning et al.24 show a stronger temperature sensitivity than measured n-heptane ignition data. The relative ignition behavior is also compared at lean and rich conditions to establish the effect of equivalence ratio at nearly constant argon/oxygen ratios and pressures. Figure 4 shows that, for lean mixtures, MB has observably longer ignition delay times than n-heptane, whereas for rich mixtures, MB has shorter ignition delay times than n-heptane. n-Heptane shows no distinct effect of φ on ignition, whereas MB shows an inverse relation between ignition delay time and equivalence ratio under these conditions. As observed by Saxena et al.,26 at low pressure ignition delay times tend to
increase with increasing equivalence ratio, but this trend can reverse as the pressure increases. In Figure 5, ignition delay times of MB, n-heptane, and mixtures of both fuels (56% MB and 44% n-heptane) are compared at compositions given by G mixtures. MB shows shorter ignition delay times than n-heptane, as observed in Figure 4, while those of the blend, 56% MB and 44% n-heptane, are intermediate between the two fuels. Figure 6 shows the effect of argon/oxygen ratio, D, on the relative ignition delay times of both fuels. It is observed that at both lower and higher argon dilution, MB and n-heptane have comparable ignition delay times. In Figure 7, MB, n-heptane and iso-octane ignition delay times are compared at 10 atm using data for iso-octane in oxygen/argon mixtures from Shen et al.27 It is found that n-heptane and iso-octane have similar high-temperature ignition delay times, as previously observed in a fuel/air study at 13 atm by Fieweger et al.28 It is further observed that under these conditions the ignition delay times of MB
(24) Horning, D. C.; Davidson, D. F.; Hanson, R. K. J. Prop. Power 2002, 18, 363–371. (25) Burcat, R.; Farmer, A.; Matula, R. 13th Int. Symp. Shock Tubes Waves 1981, 826–833. (26) Saxena, P.; Peters, N.; Williams, F. A. Combust. Flame 2007, 149, 79–90.
(27) Shen, H.-P.; Vanderover, J.; Oehlschlaeger, M. Combust. Flame 2008, 155, 739–755. (28) Fieweger, K.; Blumenthal, R.; Adomeit, G. Proc. Combust. Inst. 1994, 25, 1579–1585.
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Figure 7. Comparison of MB and n-heptane ignition delay times with published data for iso-octane at 10 atm with compositions according to mixture F: MB (b), n-heptane (2), iso-octane - Shen et al.27 (0), iso-octane - Akih-Kumgeh and Bergthorson11 (9).
Figure 9. Comparison of experiments at 10 atm with simulations for stochiometric compositions according to mixture A. Data: n-heptane (9), MB (b), MB - Hakka et al.9 (O), sim: n-heptane Curran et al.1 (solid line), MB - Dooley et al.5 (dash line), MB Hakka et al.9 (dash-dot line).
Figure 8. Comparison of experiments at 1 atm with simulations for stoichiometric compositions according to mixture A. Data: n-heptane (9), MB (b), MB - Metcalfe et al.4 (O), sim.: n-heptane Curran et al.1(solid line), MB - Dooley et al.5 (dash line), MB Hakka et al.9 (dash-dot line).
Figure 10. Comparison of experiments with simulations at 4 atm with stoichiometric compositions according to mixture B. Data: n-heptane (9), MB (b), n-heptane - Horning et al.24 (0), sim.: n-heptane - Curran et al.1 (solid line), MB - Dooley et al.5 (dash line), MB - Hakka et al.9 (dash-dot line).
Deviations are observed between model and experiment for nonstoichiometric mixtures. Figure 11 shows that the experimental ignition delay times are shorter than model predictions at an equivalence ratio of φ = 2.0 and an Ar/O2 ratio of D = 7.93, which corresponds to approximately 11% O2 in the mixture. This deviation could stem from mechanism optimization based on experimental data obtained mainly at stoichiometric conditions for mixtures with high argon content. Since the effect of equivalence ratio on ignition delay time can vary from positive to negative depending on the pressure and temperature region, it would appear that such influences result from competing reactions with fuel-derived radicals and radicals involved in fuelspecific reactions. The MB models predict shorter ignition delays than the n-heptane model as observed in experiment. Correlations. Ignition delay correlations are obtained by linear regression of the experimental data. The correlations are developed in the form:
are comparable to those of both n-heptane and iso-octane at the same φ and D. Comparison with Chemical Kinetic Models. Selected conditions from the results presented above are compared to simulations using the n-heptane mechanism by Curran et al.,1 as well as the MB mechanisms by Dooley et al.5 and Hakka et al.9 In Figure 8 it is observed that the methyl butanaote mechanism by Dooley et al.5 predicts longer ignition delay times than both the MB mechanism by Hakka et al.9 and the n-heptane mechanism by Curran et al.1 at a pressure of 1 atm. Good agreement is observed with the previous data by Metcalfe et al.4 for the MB mechanism by Dooley et al.5 The other two mechanisms predict shorter ignition delay times than the experimental data; however, the predictions are within the scatter of the experimental data. Figure 9 shows that MB and n-heptane ignition delay times are comparable and in closer agreement with the n-heptane and Hakka et al.9 mechanisms at 10 atm. In Figure 10, results obtained with the stoichiometric mixture B are compared to simulations at 4 atm and the data is found to be in close agreement with the model predictions.
τ ¼ CφR Dβ pγ expðEa =RTÞ
ð6Þ
where τ is the ignition delay time in microseconds, C is a constant, φ is the equivalence ratio, D is the ratio of the argon 2443
Energy Fuels 2010, 24, 2439–2448
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Figure 12. MB ignition data scaled to 10 atm, φ = 1.0 and D = 14.2 using the correlation parameters of eq 8. Scaled data (), correlation (solid line), and 95% confidence interval prediction bounds for new measurements (dash lines).
Figure 11. Comparison of experiments with simulations for type E (rich) mixtures (φ = 2.0) at 4 atm. Data: n-heptane (9), MB (b), sim.: n-heptane - Curran et al.1 (solid line), MB - Dooley et al.5 (dash line), MB - Hakka et al.9 (dash-dot line).
concentration to the oxygen concentration, p is the pressure in atm, Ea is the global activation energy in kcal/mol, and R = 1.986 10-3 kcal/(mol K) is the universal gas constant. The format of eq 6 is well suited for comparison purposes in which the diluent/oxygen ratio, D, is maintained constant, as in air. Another feature of the correlation is that it uses parameters such as equivalence ratio, diluent/oxygen ratio, pressure, and temperature, which are easier to compare than correlations based on concentrations. Linear regression of the n-heptane and MB data after taking the logarithm of eq 6 results in the following correlations: n-heptane : τ ¼ ð3:26 10 -5 Þφ -0:02 D1:22 p -0:89 expð36:7=RTÞ ð7Þ MB : Figure 13. n-Heptane ignition data scaled to 4 atm, φ = 0.5, and D = 8.0 using the correlations parameters of eq 7. Scaled data (), correlation (solid line), and 95% confidence interval prediction bounds for new measurements (dash lines).
τ ¼ ð2:46 10 -5 Þφ -0:48 D1:04 p -0:80 expð38:1=RTÞ ð8Þ In Figure 12, the ignition delay times for MB are scaled to a φ value of 1.0, D of 14.2, and a pressure of 10 atm using eq 8. Also plotted are 95% confidence interval prediction bounds for new measurements. Figure 13 shows a similar scaling and prediction bounds for n-heptane with a φ value of 0.5, D of 8.0, and a pressure of 4 atm. The normalized root-meansquare deviation, σNRMSD, is 37% for MB and 29% for n-heptane. A major source of uncertainty in the measurement of shock tube ignition delay times is the temperature. An estimated uncertainty of 10-25 K results from the uncertainty in shock speed. For small variations in temperature the percentage deviation in ignition delay time, στ, associated with an uncertainty in temperature, ΔT, is found to be " # τ0 - τ Ea ΔT 100 ð9Þ 100 ¼ 1 -exp στ ¼ τ0 RT0 2
should be noted, however, that temperature uncertainties resulting from uncertainties in the shock velocity are higher at higher postreflected shock temperatures. The uncertainty in the correlation parameters is much smaller than the standard deviation of the measured data plotted in Figures 12 and Figure 13. The same correlation format in eq 6 has been adopted to correlate ignition delay times obtained from simulations using detailed kinetic mechanisms. This is done by defining a range of values for φ, D, p, and T in the high-temperature region where Arrhenius behavior is observed. Fuel, oxygen, and argon compositions are related to φ and D in accordance with eqs 2-4. Using a random number generator, the conditions for each simulation are chosen such that the equivalence ratio is in the range of φ = 0.2-2.2, the pressure is in the range of 1-20 atm, and argon/oxygen ratios, D, range from 3.7 to 25 (corresponding to 21% O2:79% Ar to 3.8% O2:96.2% Ar). Ignition delay times are simulated for 250 combinations of φ, D, p, and T for each fuel and kinetic mechanism. The correlation parameters are determined by linear regression. For the MB mechanism by Dooley et al.,5 the correlation obtained by simulating 500 combinations of the correlation parameters was very close to that found using 250 simulations, indicating that the model correlation is converged.
where T0 is the temperature at which the uncertainty is evaluated and τ0 is the corresponding ignition delay time. At 1024 K, the lowest temperature in this study, assuming a global activation energy of 38 kcal/mol, a temperature uncertainty of 15 K results in an uncertainty in τ of -31% to þ23%. At the highest temperature, 1654 K, the same considerations lead to uncertainty in τ of -11% to þ10%. It 2444
Energy Fuels 2010, 24, 2439–2448
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Table 2. Correlation Parameters for Various Kinetic Mechanisms and Experiments C
R
β
γ
Ea
MB by Hakka et al.9 MB by Dooley et al.5 n-heptane by Curran et al.1 n-heptane by Sirjean et al.14
Mechanisms 1.1 10-6 7.3 10-6 2.7 10-5 7.0 10-5
0.19 0.09 0.38 0.64
0.85 0.77 0.60 0.72
-0.57 -0.68 -0.64 -0.67
47.5 44.4 41.2 38.3
n-heptane MB
Experiments 3.3 10-5 -0.02 2.5 10-5 -0.48
1.22 1.04
-0.89 -0.80
36.7 38.1
Figure 15. Simulations using detailed chemical kinetic mechanisms compared to their respective correlations. MB mechanism by Dooley et al.5 at φ = 2.0, D = 34, and p = 4 atm: sim. (thin solid line), correlation (dash-dot line); n-heptane mechanism by Curran et al.1 at φ = 0.5, D = 8, and p = 4 atm: sim. (thick solid line), correlation (dash line).
Figure 14. Simulated ignition delay times for MB using the mechanism by Dooley et al.5 scaled to p = 10 atm, φ = 1.0, and D = 14.2. Scaled data (), correlation (solid line), and 95% confidence interval prediction bounds for new simulations (dash lines).
The correlation parameters for the different mechanisms considered here are given in Table 2 together with the experimental correlations presented previously. Although the global activation energies of all models are higher than those of the experimental correlations, the n-heptane correlation based on the mechanism by Sirjean et al.14 has comparable activation energy with the experimental correlations. The exponents for the pressure and argon/oxygen ratio terms are lower in all model correlations than those experimentally determined. In this case optimizing the models at low pressure and high argon dilution may be responsible for the deviations observed at higher pressures and lower argon dilution. Interestingly, there is an opposite equivalence ratio dependence predicted by the mechanisms than observed in experiments, which is likely responsible for the deviations between the models and experiment seen at rich conditions in Figure 11. The mechanism by Sirjean et al.14 shows a stronger positive equivalence ratio exponent than the other mechanisms. However, given that the equivalence ratio varies in the range 0.5-2.0, its effect on ignition delay time is not very pronounced. Furthermore, the limited variation of equivalence ratios in available experiments may have contributed to an insufficient resolution of this effect. Under stoichiometric conditions, the correlations are expected to perform very satisfactorily since the equivalence ratio exponent, R, has no effect on the calculated ignition delay times. Figure 14 shows the simulated ignition delay times for MB using the mechanism by Dooley et al.5 scaled to the conditions of φ = 1.0, D = 3.7, and p = 10 atm, with σNRMSD of 14%. It is observed that the present correlation format is well suited for scaling ignition delay times over this range of
Figure 16. Assessment of deviations of experimental and mechanism correlations from MB experimental correlation. Composition based on A mixtures at a pressure of 10 atm. Mechanism correlations: n-heptane - Curran et al.1 (thin line), MB - Dooley et al. (thick line), MB - Hakka et al. (dash dot line); n-heptane experimental correlation (dash line).
parameters. The correlation shows more deviation at lower temperatures, corresponding to the curvature in the logarithmic plot of ignition delay times observed in simulation results. In Figure 15, ignition delay times simulated using detailed chemical kinetic mechanisms for MB and n-heptane are compared to the those calculated using the simplified correlation. The overall agreement is within a factor of 1.5, illustrating that the correlation can capture the performance of the model over this range of parameters. With this general method, the ratio of ignition delay times can be defined, facilitating the comparison of a model with experiment or with a different model: τ C R -Rref β -βref γ -γref ¼ φ D p exp½ðEa -Ea, ref Þ=RT ð10Þ τref Cref
In Figure 16, the ratio of ignition delay times from correlations of experimental data and kinetic mechanisms are compared to the reference correlation obtained from the MB experiments using eq 10. It is observed that the n-heptane experimental correlation is closest to the reference MB correlation as previously discussed. The MB mechanism by Dooley et al.5 predicts consistently higher ignition delay 2445
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where the rate constants are those of the three key reactions in eqs 11-13, [M] is the concentration of the collision partners weighted by their chaperon efficiencies, and [CmHn]0 is the initial fuel concentration, which takes the form [CmHnOp]0 for oxygentated fuels. For a given fuel, if all the rate constants are cast into the Arrhenius form, one can obtain the global activation energy from eq 16 as: 1 ð17Þ Ea ¼ ð -Ea, 7 þ 2Ea, 6 þ 2Ea, 3 Þ 3
times than both experimental correlations and the other two mechanisms. Both the n-heptane1 and MB9 mechanisms are closest to the data at higher temperatures but deviate significantly at lower temperatures. This difference arises because of the higher global activation energies of the models compared to the experiments. In the process of kinetic model improvement, numerical values of τ/τref at given conditions can be used as targets for model optimization. Oxidation Chemistry and Sensitivity Analysis. The experimental results presented in this study show that the hightemperature ignition delay times of MB and n-heptane are comparable, which suggests that the collapse of ignition delay times observed for higher n-alkanes by Fieweger et al.15 and Shen et al.16 is not limited to n-alkanes. These results also support the suggestion by Herbinet et al.18 that the ignition delay times of methyl decanoate should be similar to those of n-decane. Although each of the fuels studied here undergoes oxidation through a series of chain reactions, the similarity in their high-temperature ignition delay times points to the fact that the complex mechanisms can result in simplified global reactions that are similar in behavior. These observations can be traced back to the early work of Rice29 and Rice and Herzfeld,30 where they noted that the decomposition of organic compounds into smaller compounds can result in simple overall reaction orders. The resulting global activation energies can be interpreted in terms of some key elementary reactions in the mechanism. For hydrocarbons, Varatharajan et al.31 and Saxena et al.26 have developed simplified approximations for the high-temperature ignition delay time, based on analyses of detailed chemical kinetic mechanisms. Saxena et al.26 have proposed that for propane and higher alkanes, as well as for a number of other fuels, ignition delay times above 1000 K can be calculated by employing rate parameters of three types of elementary steps, namely: k3
Cm Hn þ HO2 sf Cm Hn -1 þ H2 O2
ð11Þ
k6
ð12Þ
2HO2 sf H2 O2 þ O2
ð13Þ
H2 O2 þ M sf 2OH þ M k7
Using rate constants employed in Saxena et al.26 for n-heptane, eq 17 leads to an activation energy of 41.2 kcal/ mol assuming that the third body reaction in eq 12 is in the high-pressure limit and 39.4 kcal/mol when in the lowpressure limit. Similarly, for MB the activation energy is 38.9 and 37.1 kcal/mol at the high- and low-pressure limits, respectively. These global activation energies are in good agreement with the present data and are comparable with the range of values reported in the literature. On the basis of elementary reaction time scale analysis, Peters32 suggests that the main ignition delay time is of the same order as the time scale of the nonfuel specific reaction 12. The rate of this reaction depends on the pressure and the relative concentrations of hydrogen peroxide and the collision partners. The fuel concentration and its chaperon efficiency could become influential as the equivalence ratio is increased. However, as observed in this study, the effect of equivalence ratio may vary for different fuels, suggesting differences in reaction pathways. Analyses of the reaction pathways using the two MB mechanisms and the n-heptane mechanism at 4 atm and 1300 K for A mixtures are performed. Figure 17 shows the fuel consumption pathway at 200 μs for n-heptane using the mechanism by Curran et al.1 and for MB using the mechanism by Hakka et al.9 The predicted ignition delay times in this case are 434 μs for n-heptane and 451 μs for MB by Hakka et al.9 Prior to ignition, fuel is consumed mainly through H abstraction reactions with H and OH radicals. The MB mechanism by Hakka et al.9 indicates that unimolecular decomposition is more important than it is in the other two mechanisms. The MB mechanism by Dooley et al.5 shows similar trends as observed with n-heptane, however the predicted ignition delay time is longer (654 μs). The difference in the ignition delay time may be partially explained by the difference in the subsequent decomposition pathways of the primary radicals from the fuel. The sensitivities of ignition delay times to rate constants of elementary reactions for both fuels have been analyzed using the n-heptane mechanism by Curran et al.1 and the two MB mechanisms by Dooley et al.5 and Hakka et al.9 These analyses are performed at a pressure of 10 atm and a temperature of 1250 K for mixtures with type F composition. The 16 most important reactions in each case are presented in Figures 18-20. As would be expected, enhancing the rate of the reaction between atomic hydrogen and molecular oxygen leads to shorter ignition delay times of the system in all three cases. Also important are reactions between small olefins and radicals such as CH3 with O2 and HO2. In the case of the MB mechanisms, some reactions involving formaldehyde, CH2O, also lead to increased reactivity when their rates are increased. Among the 16 reactions in all cases, several similar
Only the first reaction is fuel specific, whereas the other two are well-known reactions of the hydrogen/oxygen system. For n-heptane, eq 11 is: k3
n-C7 H16 þ HO2 sf n-C7 H15 þ H2 O2
ð14Þ
while for MB it takes the form k3
C5 H10 O2 þ HO2 sf C5 H9 O2 þ H2 O2
ð15Þ
These reactions are obtained after rigorous analysis of a skeletal mechanism and a reduced mechanism of seven reactions. They proposed the following ignition delay time approximation ( )1=3 k7 ð16Þ τ ¼ 8:27 2 k6 k3 2 ½M2 ½Cm Hn 0 (29) Rice, F. O. J. Am. Chem. Soc. 1931, 53, 1959–1972. (30) Rice, F. O.; Herzfeld, K. F. J. Am. Chem. Soc. 1934, 56, 284–289. (31) Varatharajan, B.; Petrova, M.; Williams, F.; Tangirala, V. Proc. Combust. Inst. 2005, 30, 1869–1877.
(32) Peters, N. Proc. Combust. Inst. 2009, 32, 1–25.
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Figure 17. Consumption pathway at 1300 K and 4 atm with compositions according to Mixture A (φ = 1.0 and D = 14.2) at 200 μs after reaction onset. At this time 81.0% and 60.3% of the initial n-heptane and MB, respectively, have reacted. Left: n-heptane - Curran et al.,1 Right: MB - Hakka et al.9
Figure 18. Sensitivity of ignition delay time, τ, to rate constants of elementary reactions during n-heptane ignition with composition according to mixture F (φ = 1.0 and D = 3.76) at 10 atm and 1250 K. The ignition delay time, τ, is 217 μs, and the mechanism is by Curran et al.1
Figure 19. Sensitivity of ignition delay time, τ, to rate constants of elementary reactions during MB ignition with composition according to mixture F (φ = 1.0 and D = 3.76) at 10 atm and 1250 K. The ignition delay time, τ, is 209 μs, and the mechanism is by Hakka et al.9 Species names have been modified from those in the original publication for clarity.
reactions lead to longer ignition delay times. These are: recombination of methyl radicals to form ethane; reaction between two hydroperoxy, HO2, radicals to yield hydrogen peroxide; as well as formation of less-reactive methane and oxygen from methyl and hydroperoxy radicals. For the MB mechanism by Hakka et al.,9 H-abstraction from MB by atomic hydrogen leads to longer ignition delay times. This reaction has the same effect in the mechanism by Dooley et al.5 but appears as the 19th most sensitive reaction under these conditions. It is interesting to note that for the fuel specific reactions among these 16, n-heptane shows two unimolecular decomposition reactions to C2-C5 radicals (ethyl, propyl, butyl, and pentyl radicals). These alkyl radicals then undergo reactions with other smaller radicals, to yield the simpler oxygenated radicals discussed above. The MB mechanisms, on the other hand, show that in addition to unimolecular decompositions of the ester, the fuel also undergoes important H-abstraction reactions, yielding primary radicals. These primary radicals need to react further before the
simpler aldehydes, olefins, and alkyl radicals, etc., are formed. This has implications for the development of mechanisms for higher alkanes and oxygenates. Whereas higher alkane oxidation is strongly dependent on C0-C5 chemistry that has relatively more reliable kinetic and thermochemical data, the rate parameters for the additional oxygenatespecific reactions in higher methyl ester combustion may prove to be more difficult to accurately estimate. The similarity in the role of C0-C5 chemistry in both MB and n-heptane could be exploited in the process of mechanism development and kinetic data estimation for other methyl esters. These results also show that sensitivity and reaction pathway analyses are complementary; reactions such as the unimolecular decomposition of fuel into primary radicals are not the most important fuel consumption channels but do appear, as in the case of n-heptane, among the most sensitive reactions to ignition delay times when their rate parameters are perturbed. These observations could be useful in the process of mechanism reduction. 2447
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The similarity is attributed to similar controlling elementary reactions as discussed by Saxena et al.26 and Peters.32 Under nonstoichiometric conditions, there are observable differences in ignition behavior that may arise from different reaction pathways and their corresponding rates. It is also observed that the kinetic models used in this study do not agree with experiment at rich conditions. Ignition delay time correlations for the high-temperature region are proposed based on the data from the present study. The same correlation format is applied to simulated ignition delay times using recent chemical kinetic mechanisms. This constitutes an important means of comparing models to correlated experimental data as well as to other chemical kinetic models. It is found that deviations occur because of differences in the apparent activation energies, pressure, and dilution effects. The two models for methyl butanoate studied here differ from each other in predicting ignition delay times. Generally, the mechanism by Dooley et al.5 predicts longer ignition delays and results in a lower apparent activation energy than the mechanism by Hakka et al.9 This leads to good agreement between the models at low temperatures and more pronounced deviations at higher temperatures. There is good agreement in most cases between the data in this study and published data, and there is fairly good agreement with the models for n-heptane and MB. This study provides further insight on the similarities and differences in combustion properties of methyl esters such as methyl butanoate and n-alkanes such as n-heptane.
Figure 20. Sensitivity of ignition delay time, τ, to rate constants of elementary reactions during MB ignition with composition according to mixture F (φ = 1.0 and D = 3.76) at 10 atm and 1250 K. The ignition delay time, τ, is 269 μs, and the mechanism is by Dooley et al.5
Conclusion A comparative study of the high temperature autoignition of methyl butanoate and n-heptane in oxygen/argon mixtures has been carried out. It is observed that when the argon/ oxygen ratio, D, is fixed to simulate different “synthetic air” compositions, both compounds have comparable ignition delay times at the same pressure and temperature under stoichiometric conditions. This similarity has important implications for the further modeling and optimization of chemical kinetic mechanisms for methyl butanaote and higher methyl esters, as well as for other higher alkanes. These observations are in line with recent observations on the ignition of long chain n-alkanes by Westbrook et al.13
Acknowledgment. Acknowledgment is made to the donors of the American Chemical Society Petroleum Research Fund for partial support of this research. Further support by the National Science and Engineering Research Council of Canada is gratefully acknowledged. The authors thank Professor Andrew Higgins and other members of our Shock Wave Physics Group at McGill University for helpful discussions.
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