- Email: [email protected]
Kinetic modeling of the oxidation of large aliphatic hydrocarbons
Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 773–780
KINETIC MODELING OF THE OXIDATION OF LARGE ALIPHATIC HYDROCARBONS ¨ RGEN WARNATZ MARIA NEHSE and JU Interdisziplina¨res Zentrum fu¨r Wissenschaftliches Rechnen (IWR) Universita¨t Heidelberg Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany CHRISTOPHE CHEVALIER Institut fu¨r Technische Verbrennung (ITV) Universita¨t Stuttgart Pfaffenwaldring 12, D-70569 Stuttgart, Germany
Because of the complexity of low-temperature oxidation, a detailed reaction scheme of higher hydrocarbons (which are components of practical fuels) typically involves several hundred chemical species taking part in thousands of elementary reactions. Nevertheless, only a very limited number of different reaction types is appearing, for example, alkane thermal decomposition, H-atom abstraction to form an alkyl radical, alkyl radical isomerization, and b decomposition of the alkyl radical for the high-temperature range and a few additional reaction types at low temperature. A LISP program developed for the automatic generation of reaction mechanisms is able to produce mechanisms for the oxidation of aliphatic hydrocarbons. In contrast to earlier attempts described in the literature, a rather complete description of the reaction paths for the decomposition of the intermediate dihydroperoxyalkyl radicals and a description of the aldehyde oxidation is included. The transition between low- and high-temperature range with a negative temperature dependence is well reproduced. With the help of newly available experiments for n-decane, the reaction mechanisms for n-heptane and n-decane are validated for a wide range of pressures, temperatures, and equivalence ratios, covering conditions dictated by potential applications. This is a severe test case, because calculated ignition-delay times are very sensitive with respect to the quality of the reaction mechanism used. Additional sensitivity analysis based on the OH concentration shows the principal rate-determining reactions. However, more kinetic data for high hydrocarbons and oxygenated species are necessary to validate the reaction mechanism, especially with respect to chain-length dependencies of rate coefficients and the behavior of fuels with multiple C–C bonds. Furthermore, some results on flame velocity are given for n-heptane.
Introduction The oxidation of hydrocarbon fuels is an important element in modeling combustion in automobile engines, including autoignition, flame propagation, and pollutant emissions. Detailed kinetic data are necessary to describe these combustion phenomena and to develop simplified reaction schemes needed for such things as three-dimensional calculations of autoignition and turbulent flame propagation [1–3]. Because of the complexity of low-temperature oxidation, a detailed reaction scheme of higher hydrocarbons (which are components of practical fuels) typically involves several hundred chemical species taking part in thousands of elementary reactions. Nevertheless, only a very limited number of different reaction types appears (e.g., alkane thermal decomposition, H-atom abstraction to form an alkyl radical, alkyl radical isomerization, and b decompo-
sition of the alkyl radical for high temperatures and a few additional reaction types at low temperatures [3–5]). Therefore, it is possible to formulate these reactions and their rate expressions using simple rules. These rules are executed with the aid of a computer code described in detail in previous papers [5,6]. LISP is used as a support system, since the best flexibility with regard to the data structures, the algorithm development, and the user interface design is available in this programming language. The code considers only the decomposition of carbon chains larger than C4, because the high-temperature oxidation mechanism for C1 through C4 hydrocarbons already exists [1,7,8] and the rate coefficients of the small species strongly depend on the chain length. The high-temperature oxidation up to C4 species used earlier [4–8] did not consider the decomposition of aldehydes or the aldehyde radicals of C3 and C4 hydrocarbons. Thus, there was a miss-
773
774
KINETIC MECHANISMS—MODELS AND EXPERIMENTS TABLE 1 Rate coefficients for high-temperature reactions [3,7,8]; k 4 A • Tb • exp(1Ea/RT) Primary
Secondary
Tertiary
(a) H-atom abstraction (per C-H bond, A in cm3 • mol • s/b/Ea in kJ/mol) RH ` H 9.38 • 1006/2.0/32.2 4.50 • 1006/2.0/20.9 RH ` O 1.67 • 1013/0.0/32.9 1.30 • 1013/0.0/21.8 09 6.50 • 1008/1.25/2.94 RH ` OH 1.43 • 10 /1.05/7.58 RH ` HO2 1.87 • 1012/0.0/81.2 1.68 • 1012/0.0/71.2 11 RH ` CH3 2.20 • 10 /0.0/48.6 2.00 • 1011/0.0/39.8 4.20 • 1012/0.0/85.7 1.50 • 1012/0.0/71.2 RH ` CH3O2 12 RH ` O2 4.20 • 10 /0.0/205. 1.00 • 1013/0.0/199.
1.26 • 1014/0.0/30.6 1.00 • 1013/0.0/13.7 4.00 • 1012/0.0/1.85 1.00 • 1012/0.0/60.3 1.00 • 1011/0.0/33.1 3.00 • 1012/0.0/62.8 2.00 • 1012/0.0/193.
(b) Alkyl radical isomerization (A in s11/b/Ea in kJ/mol) (1,4) ring 1.00 • 1011/0.0/88.3 (1,5) ring 1.00 • 1011/0.0/59.0 (1,6) ring 1.00 • 1011/0.0/88.3
1.00 • 1011/0.0/67.4 — —
1.00 • 1011/0.0/75.8 1.00 • 1011/0.0/46.5 1.00 • 1011/0.0/75.8
(d) b decomposition of alkyl radical (A in s11/b/Ea in kJ/mol) R → RS ` Olefin
2.50 • 1013/0.0/120.
(d) Alkane decomposition (A in s11/b/Ea in kJ/mol) RH → RS8 ` RS9
3.20 • 1016/0.0/339.
ing link between the oxygenated species formed in the initial O2 attack and formation of the final products. The additional reaction paths are more important for the n-decane oxidation than for the n-heptane oxidation. The missing reactions are generated once by the automatic program and added to the C1– C4 handwritten mechanism. Afterwards, this modified C1–C4 mechanism is added to the computergenerated one for the C5–CFuel system. The mechanism generation has been performed for nheptane and n-decane and then validated by comparing computed autoignition delay times with results from shock tube experiments available in the literature [10,26]. Additionally, some results on flame velocity are given. n-Heptane is one of the primary reference fuels used to determine the octane number and also as diesel fuel model, because its cetane number is typical of a good diesel fuel. The n-decane and mixtures of n-decane and aromatic species such as toluene [9] or methylnaphthalene [10] may be used to model kerosenes. For n-heptane/air mixtures, the initial pressure has been varied between p 4 3.2 bar and 40 bar and the initial temperature between T 4 660 K and 1400 K, while the equivalence ratio covers the range between f 4 0.5 and 2.0. For n-decane/air mixtures, the calculations were made for p 4 13 bar and for initial temperatures between T 4 660 K and 1400 K and equivalence ratio f 4 1.0 and 2.0. Sensitivity analysis based on the OH concentration during the induction phase shows the principal rate-limiting reactions in the high-temperature and the low-temperature regimes.
High-Temperature Reaction Mechanism The high-temperature mechanism [3,8,11] consists of attack of radicals on the parent aliphatic hydrocarbon RH, isomerization of the alkyl radicals R• formed, b decomposition of the alkyl radicals R•, and thermal decomposition of the parent aliphatic hydrocarbon RH to form two (about equally heavy) smaller radicals RS•, RH ` X• → R• ` XH (X 4 H, O, OH, O2, HO2, CH3 O2 , CH3 ) R• → R8• R• → RS• ` OlefinS RH → RS8• ` RS9• Together with the C1–C4 mechanism [8], this gives a complete mechanism for the high-temperature oxidation of aliphatic hydrocarbons; rate coefficients are given in Table 1. For demonstration, this mechanism is used for the simulation of flame velocities in n-heptane/air mixtures; the result is compared with experiments [12,13] in Fig. 1. A sensitivity analysis (Fig. 2) with respect to the flame velocity delivers results very similar to those for other aliphatic hydrocarbons [11,14]: The ratedetermining steps are, as usual, reactions of small molecules unspecific to the hydrocarbon considered and mainly governed by the H2-O2-CO chemistry. Low-Temperature Reaction Mechanism According to the pioneering work of Halstead et al. [15], the low-temperature oxidation of the ali-
KINETIC MODELING OF LARGE ALIPHATIC HYDROCARBONS
775
atom abstraction (external H-atom abstraction is relatively slow [4,5]): RO2• → QOOH• (internal abstraction) where QOOH• is a corresponding alkylhydroperoxy radical with fuel structure. These alkylhydroperoxy radicals (QOOH•) then can eliminate OH and produce a cyclic ether (QO) by concerted ring closure, decompose to a fuel olefin and HO2• [16], or react with a second O2 [21]: QOOH• → QO ` OH• (chain propagation) QOOH• → OlefinF ` HO2• (chain propagation) QOOH• ` O2 i O2QO2H• (second O2 addition)
Fig. 1. Laminar flame velocity in n-heptane–air mixtures (Tu 4 298 K, p 4 1 bar); lines, simulation; points, experiments by v Gibbs and Calcote [12] and m Gerstein et al. [13].
phatic fuel RH is initiated by the reaction with O2 to produce the corresponding alkyl radicals R• and HO2•, which in turn react with the fuel. The alkyl radicals formed can be decomposed by b scission of a C–C bond to produce an olefin and a smaller alkyl radical RS•, isomerize to an isomeric alkyl radical R8• (the four steps to this point are already treated as part of the high-temperature mechanism), react with O2 to produce a alkylperoxy radical (RO2•), and react with O2 by H-atom abstraction to an olefin with fuel structure (OlefinF) and HO2• (rate coefficients for low-temperature reactions are found in Table 2), R• ` O2 i RO2• (first O2 addition) R• ` O2 → OlefinF ` HO2• (H-atom abstraction) If the temperature increases, RO2• radical will decompose back to the reactants. This leads to an inverse temperature dependence of the reaction (the so-called degenerate chain branching [1,15]). The RO2• radicals then will undergo internal H-
The second O2-addition reaction path (rate coefficient as for the first O2 addition) is the only one leading to chain branching (see later). Again, the O2QO2H• radical formed in the last reaction can undergo external or internal H-atom abstraction with minor importance for the external one. Thus, only the internal H-atom abstraction (rate coefficient as for RO2• internal abstraction) is used in the following: O2QO2H• → HO2Q8O2H• (internal abstraction) HO2Q8O2H• → HO2Q8O ` OH• (chain propagation) HO2Q8O → OQ8O• ` OH• (chain branching) The OQ8O• indicated in the last reaction can decompose (via b decomposition) into two other oxygenated species, often aldehydes. It is worth noting that the internal H-atom abstraction in O2QO2H• leads to chain branching. Thus, a distinct acceleration of the ignition process should be expected as a result of the second O2 attack on the QOOH• radical. This effect (together with the degenerate branching behavior) can explain the experimentally observed temperature dependence of the ignition-delay times (see Fig. 3). Finally, the reaction paths of the aldehydes formed have been described (see Kaiser et al. [23]); rate co-
Fig. 2. Sensitivity analysis for the laminar flame velocity in an n-heptane–air mixture at p 4 1 bar, Tu 4 298 K for rich (black) and lean (white) conditions.
776
KINETIC MECHANISMS—MODELS AND EXPERIMENTS TABLE 2 Rate coefficients for low-temperature reactions; k 4 A • Tb • exp(1Ea/RT)
(a) Reactions of alkyl radicals with O2 (A in cm-mol-s units/b/Ea in kJ/mol) [17,18] R ` O2 → RO2 RO2 → R ` O2 R ` O2 → Olefin ` HO2 Olefin ` HO2 → R ` O2
2.00 • 1012/0.0/0.0 4.00 • 1015/0.0/117. 1.00 • 1012/0.0/8.4 1.70 • 1012/0.0/57.6
(b) RO2 → QO2H, O2QO2H → HO2Q8O2H (per C–H bond, A in s11/b/Ea in kJ/mol) [19] primary secondary (1,4) ring 1.00 • 1011/0.0/85.8 1.00 • 1011/0.0/71.2 (1,5) ring 1.00 • 1011/0.0/61.1 1.00 • 1011/0.0/46.5 1.00 • 1011/0.0/50.2 (1,6) ring 1.00 • 1011/0.0/62.8 (1,7) ring 1.00 • 1011/0.0/100. 1.00 • 1011/0.0/85.8
tertiary 1.00 • 1011/0.0/56.5 — 1.00 • 1011/0.0/37.7 —
(c) QO2H → RO2, HO2Q8O2H → O2QO2H (per C–H bond, A in s11/b/Ea in kJ/mol) [19,20] (1,4) ring 1.00 • 1011/0.0/52.3 1.00 • 1011/0.0/52.3 1.00 • 1011/0.0/27.6 (1,5) ring 1.00 • 1011/0.0/27.6 (1,6) ring 1.00 • 1011/0.0/29.3 1.00 • 1011/0.0/31.4 (1,7) ring 1.00 • 1011/0.0/66.9 1.00 • 1011/0.0/67.0
1.00 • 1011/0.0/43.4 — 1.00 • 1011/0.0/30.6 —
(d) QO2H → Q ` HO2 and QO2H → QO ` OH (A in s11/b/Ea in kJ/mol) [7] QO2H → Q ` HO2 QO2H → Oxirane ` OH QO2H → Oxetane ` OH QO2H → Tetrahydrofurane ` OH
3.00 • 1011/0.0/83.8 3.00 • 1011/0.0/58.6 3.00 • 1011/0.0/54.4 3.00 • 1011/0.0/12.6
(e) HO2Q8O2H decomposition (A in s11/b/Ea in kJ/mol) [7,21] HO2Q8O2H → HO2Q8O ` OH HO2Q8O → OQ8O ` OH
1.00 • 1009/0.0/31.4 8.40 • 1014/0.0/180.
(f) H-atom abstraction from aldehyde (A in cm3 • mol • s/b/Ea in kJ/mol) [24] RCHO ` OH → RCO ` H2O RCHO ` O2 → RCO ` HO2 RCHO ` HO2 → RCO ` H2O2 RCHO ` CH3O2 → RCO ` CH2O2H
1.75 • 1013/0.0/0.00 2.00 • 1013/0.5/175. 1.00 • 1012/0.0/42.0 1.00 • 1012/0.0/42.0
(g) Decomposition of aldehyde radicals (A in s11/b/Ea in kJ/mol) [24] RCO → R ` CO
1.58 • 1013/0.0/72.0
efficients are given by Kojima [24]. The aldehyde (RCHO) formed in the OQ8O• decomposition can easily form aldehyde radicals (RCO•), which at low temperatures produce peracyl radicals via a second O2 addition RCHO ` X → RCO• ` XH (X 4 OH, O2, HO2, CH3O2) RCO• ` O2 → RCOO2H• The peracyl radicals can undergo external H-atom abstraction and produce CO2 by the decomposition reaction RCOO2H → R• ` CO2 ` OH• With increasing reaction temperature, another path is favored for the aldehyde radicals that produces CO and an alkyl radical because the acetyl radicals
decompose directly into a smaller alkyl radical and CO, RCO• → R• ` CO Because of the lack of kinetic data for the route via RCOO2H•, only the decomposition path is implemented.
Comparisons with Experimental Results To verify the implemented rules, the low-temperature mechanisms for n-heptane and n-decane oxidation have been computer generated. The resulting mechanism for n-heptane consists of about 1200 reactions and 200 species and for n-decane about 1650 reactions and 350 species. With the use of a spatially homogeneous instationary program [25], ignition-
KINETIC MODELING OF LARGE ALIPHATIC HYDROCARBONS
Fig. 3. Ignition-delay times s in stoichiometric n-heptane–air mixtures as a function of the initial temperature T for different pressures p; lines, simulations (this work); symbols, experiments [26].
Fig. 4. Ignition-delay times s in n-heptane–air mixtures as a function of the initial temperature T at different equivalence ratios f at p 4 40 bar; lines, simulations (this work); symbols, experiments [26].
delay times are calculated at various conditions and compared to corresponding experiments [10,26]. Figure 3 presents ignition-delay times s of a stoichiometric n-heptane–air mixture plotted versus the inverse of the initial temperature T behind the reflected shock wave. The calculated values (lines) and the experimental points (symbols) [26] show good agreement at various pressures. It should be noticed that the pressure dependence is shifted to higher temperatures for increasing pressure. The influence of the pressure on the ignition-delay time is distinct
777
Fig. 5. Ignition-delay times s in n-heptane–air mixtures as a function of the initial temperature T for different equivalence ratios f at a pressure p 4 13.5 bar; lines, simulations (this work); symbols, experiments [26].
in the transition region and smallest for low temperatures. The negative temperature dependence that occurs in the transition between the high- and low-temperature regimes is reproduced quite well by the mechanisms. The dependence of the ignition-delay times of nheptane–air mixtures on the equivalence ratio f is shown in Figs. 4 and 5. In Fig. 4, the pressure is about p 4 40 bar in all experiments, whereas the equivalence ratio has been varied between f 4 0.5 and 2.0. In Fig. 5, the pressure is kept constant at p 4 13.5 bar and the equivalence ratio f is changed. The calculated values can describe the measured ones quite well. The dependence of s on f in the high-temperature region is small, increases toward lower temperatures, and is largest in the transition region. Here, the fuel-rich mixtures show the smallest ignition delays. For lower pressure (p 4 13.5 bar), the agreement between the computed ignitiondelay times and the experimental values is better than for the higher pressure (p 4 40 bar). Calculated ignition-delay times of n-decane–air mixtures at p 4 13 bar for the two equivalence ratios f 4 2.0 and 1.0 and constant volume are plotted in Fig. 6. They are compared with new results reported by Adomeit and co-workers [10]. The agreement of experimental and calculated induction times are better for n-heptane, but the behavioral tendency of the ignition delays can be described. The ignition-delay times are also smallest for fuel-rich mixtures. In the high-temperature region, the influence of the equivalence ratio is smaller than that for n-heptane. The transition region of the calculated values is shifted toward high temperatures. If the rate coefficient of the reverse of the first O2 addition were changed for
778
KINETIC MECHANISMS—MODELS AND EXPERIMENTS
Fig. 6. Ignition-delay times s in n-decane–air mixtures as a function of the initial temperature T for different equivalence ratios f at a pressure p 4 13 5 1.5 bar; lines, simulations (this work); symbols, experiments [10].
Fig. 8. Sensitivity analysis for the OH concentration in an n-decane–air mixture during ignition delay at p 4 13 bar, T 4 1400 K; only relative sensitivities larger than 0.3 are listed.
n-decane are slightly shorter than for n-heptane. This behavior can be explained by the longer carbon chain of n-decane. The difference at high temperatures is in agreement with the usual picture of the dependence of ignition delay on molecular size [3]. Sensitivity and Path Analyses
Fig. 7. Comparison of ignition-delay times s in stoichiometric n-heptane–air mixtures at p 4 13.5 bar and a stoichiometric n-decane–air mixture at p 4 13 bar as a function of the initial temperature T; lines, simulations (this work); symbols, experiments [10,26].
n-decane, the agreement between experimental and calculated data would be better. Thus, rate coefficients for this reaction type should be made dependent on the carbon chain length. It would be interesting to have kinetic data for this reaction for higher hydrocarbons to validate the values assumed. In Fig. 7, the induction times in stoichiometric nheptane–air mixtures and n-decane–air mixtures have been compared at p 4 13 bar. In the transition and low-temperature regions, the induction times of
At high temperatures, the ignition of aliphatic hydrocarbons is governed mainly by chain-branching processes that are rather unspecific for the fuel considered. However, they are fuel specific at low temperatures, leading to very complex reaction systems if the numerous isomeric structures are taken into consideration [2]. A detailed sensitivity analysis based on the OH concentration was carried out, revealing the principal rate-limiting reactions. Figure 8 shows the results for a stoichiometric n-decane–air mixture in which the pressure is p 4 13 bar and the initial temperature T 4 1400 K. As usual, at high temperatures [7,8], there is sensitivity to reactions of fuelunspecific small molecules with even smaller contributions from C3- and C4-species. Furthermore, alkyl-radical b decomposition and isomerization and the H-atom abstraction of the fuel and its initial thermal decomposition are rate limiting because all of these reactions are fuel specific. In the transition region (Fig. 9), the picture is totally different: All contributions stem from fuel-specific reactions. However, because of the complex mechanism, a detailed explanation of the sensitivities listed seems difficult (e.g., negative sensitivities for OH-forming reactions caused by the negative temperature dependence). It is worth mentioning that
KINETIC MODELING OF LARGE ALIPHATIC HYDROCARBONS
779
REFERENCES
Fig. 9. Sensitivity analysis for the OH concentration in an n-decane–air mixture during ignition delay at p 4 13 bar, T 4 800 K; only relative sensitivities larger than 0.3 are listed; no details on the isomer structures of the lowtemperature species in reactions (6)–(23) is given because of the complexity of nomenclature.
the initial attack of the n-decane or its thermal decomposition does not show considerable sensitivity. Similar results have been obtained for mixtures of nheptane and n-cetane with air at low temperatures [3,5–7]. Conclusions A LISP program for the automatic generation of reaction mechanisms is able to produce reaction mechanisms for the oxidation of aliphatic hydrocarbons; these describe the experiments well. The transition between the low- and high-temperature regimes with a negative temperature dependence is reproduced. The reaction mechanisms of n-heptane and n-decane are validated for a wide range of conditions of pressure, temperature, and equivalence ratios, covering the low- and high-temperature oxidation regimes and conditions dictated by potential applications. Yet more kinetic data for high hydrocarbons and oxygenated species are necessary to validate the reaction mechanism, especially with respect to chain-length dependencies of rate coefficients (first and second O2 addition) and the behavior of fuels with multiple C–C bonds. Acknowledgments This work was supported by the DFG (SFB 259, SFB 359, LEIBNIZ Program), the BMBF (TECFLAM Project), and the EC/Daimler-Benz (JOULE Program). We thank Drs. P. Deuflhard and H. Melenk (Konrad-ZuseZentrum, Berlin) for fruitful cooperation.
1. Warnatz, J., Maas, U., and Dibble, R. W., Combustion, Springer, Heidelberg/Berlin, 1996. 2. Maas, U. and Pope, S. B., Combust. Flame 88:239–264 (1992). 3. Warnatz, J., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 553–579. 4. Westbrook, C. K., Warnatz, J., and Pitz, W. J., TwentySecond Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 893–901. 5. Chevalier, C., Pitz, W. J., Warnatz, J., Westbrook, C. K., and Melenk, H., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 93–101. 6. Chevalier, C., Warnatz, J., and Melenk, H., Ber. Bunsenges. Phys. Chem. 94:1362–1367 (1990). 7. Chevalier, C., Dissertation, Institut fu¨r Technische Verbrennung, Universita¨t Stuttgart 1993. 8. Chevalier, C. and Warnatz, J., “Survey of Reactions in the C/H/O System,” in Combustion Chemistry (Gardiner, W. C. Jr., Ed.), Springer Verlag, New York, 1996. 9. Doute´, C., Delfau, J. L., Akrich, R., and Vovelle, C., Combust. Sci. Technol. 106:327–344 (1995). 10. Fieweger, K., Pfahl, U., Blumental, R., and Adomeit, G., Kolloquium des Sonderforschungsbereich 224, “Motorische Verbrennung,” (Pischings, F., Ed.), March 19–20, 1996, RWTH Aachen, 1996. 11. Warnatz, J., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 369–384. 12. Gibbs, C. J. and Calcote, H. C., J. Chem. Eng. Data 4:226–241 (1959). 13. Gerstein, M., Levine, O., and Wong, E. L., J. Am. Chem. Soc. 73:418–422 (1951). 14. Warnatz, J., Combust. Sci. Technol. 34:177–200 (1983). 15. Halstead, M. P., Prothero, A., and Quinn, C. P., Proc. R. Soc. London, Ser. A 322:377–403 (1971). 16. Barbieri, G., Di Maio, F. P., and Lignola, P. G., Combust. Sci. Technol. 98:95–122 (1994). 17. Benson, S. W., Prog. Energy Combust. Sci. 7:125–134 (1981). 18. Morgan, C. A., Pilling, M. J., Tulloch, J. M., Ruiz, R. P., and Bayes, K. D., J. Chem. Soc. Faraday Trans. 78:1323– 1330 (1982). 19. Fish, A., in Organic Peroxides (Swern, D., Ed.), Wiley, New York, 1970. 20. Baldwin, R. R. and Walker, R. W., Fourteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1973, pp. 241–257. 21. Pollard, R. T., in Comprehensive Chemical Kinetics Vol. 17 Gas-Phase Combustion (Bamford, C. H. and Tipper, C. F. H., Eds.), Elsevier, New York, 1977, pp. 249–367. 22. Walsh, A. D., Ninth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1963, pp. 1046–1055. 23. Kaiser, E. W., Westbrook, C. K., and Pitz, W. J., Int. J. Chem. Kinet. 18:655–688 (1986). 24. Kojima, S., Combust. Flame 99:87–136 (1994). 25. Maas, U. and Warnatz, J., Combust. Flame 74:53–69 (1988). 26. Ciezki, H. K. and Adomeit, G., Combust. Flame 93:421– 433 (1993).
780
KINETIC MECHANISMS—MODELS AND EXPERIMENTS
COMMENTS Anthony Marchese, Princeton University, USA. It is common practice to extrapolate elementary rate constants obtained for the H-atom abstraction from smaller alkanes (e.g., N-C4H10) for larger alkanes, based only on the number of abstraction sites. Is there experimental evidence to support this practice for much larger alkanes (e.g., N– C10H22, n-C16H34, and above)? Author’s Reply. We are not aware of experimental evidence to support this practice for n-C10H22 or above in the literature, but transition-state theory can be used to extrapolate rate coefficients for such reactions [1,2].
REFERENCES 1. Cohen, N. and Westberg, K. R., Int. J. Chem. Kinet. 18:99 (1986). 2. Cohen, N., Int. J. Chem. Kinet. 23:397–417 (1991). ● Dr. Henry J. Curran, Lawrence Livermore National Laboratory, USA. In your low-temperature oxidation scheme, do you include b-scission of the hydroperoxy-alkyl (QOOH) radical? This is important in predicting both the reactivity of the system and product species formation. Author’s Reply. In this oxidation scheme we do not include b-scission of the hydroperoxy-alkyl (QOOH) radical. We consider that the hydroperoxy-alkyl radical can eliminate OH to produce cyclic ether (QO), decompose to a fuel olefin and HO2, or react with a second O2. We think that these three reaction paths are the important ones. ● J. F. Griffiths, University of Leeds, UK. It worries me to see that a complex kinetic model is validated only against overall ignition delays. There is a considerable body of experimental chemical information over a wide range of temperature (especially for n-Heptane) against which the predicted chemistry can be tested. Much of this has been obtained in spatially uniform reactors (e.g., CSTR) so a quantitative match can be expected. Author’s Reply. The ignition delay time and laminar flame velocity are global values, but the calculated ignition delay times are very sensitive with respect to the quality of the reaction mechanism used. Auto-ignition of hydrocarbons is of enormous importance in piston engine combustion. Thus, we first validate the mechanism for these global values as shown in this paper. In a further study, the vali-
dation of the mechanism against experimental results obtained in spatially uniform reactors (e.g., CSTR) is planned. ● William J. Pitz, Lawrence Livermore Laboratory, USA. You showed some sensitivity results where the low-temperature degenerative branching steps (the reaction of the hydroperoxy alky peroxy) to give a ketohydroperoxide and OH) exhibited a sensitivity indicating that these reactions retards the overall oxidation rate. In an earlier talk [1], we showed that this generic-step was one of the most accelerating steps for the propane system. Do you have any explanation for this unexpected result?
REFERENCE 1. Koert, D. N., Pitz, W. J., Bozzelli, J. W., and Cernansky, N. P., Chemical Kinetic Modeling of High Pressure Propane Oxidation & Comparison to Experimental Results, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 633–640. Author’s Reply. This is a global sensitivity analysis. We consider the time until the temperature rises (the time where the radical pool is built). If you consider a shorter time the sensitivity coefficients of the reactions mentioned by you are positive making the accelerating reaction steps. ● Ray W. Walker, Hull University, UK. I am concerned about the conclusions drawn from this type of study. It is clear that experimental data can be interpreted within certain conditions, by the mechanism proposed. However, the agreement in itself does not validate the mechanism. In particular, the experimental data have to cover a much wider variation of mixture composition, particularly the [fuel]/[O2] ratio, ideally by at least a 20–30 factor. For this reason sensitivity analyses should be carried over very wide ranges of conditions. Author’s Reply. Those experimental data for ignition delay times available in the literature cover the range presented in the paper. For n-Heptane-air mixtures the initial pressure has been varied between p 4 3.2 bar and 40 bar and the initial temperature between T 4 660 K and 1400 K, while the equivalence ratio covers f 4 0.5, 1, 2. The pressures and temperatures considered cover the parameter range most important for engine combustion. Because of lack of space only the sensitivity analyses for stoichiometric n-Decane-air mixtures are shown.
KINETIC MODELING OF THE OXIDATION OF LARGE ALIPHATIC HYDROCARBONS ¨ RGEN WARNATZ MARIA NEHSE and JU Interdisziplina¨res Zentrum fu¨r Wissenschaftliches Rechnen (IWR) Universita¨t Heidelberg Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany CHRISTOPHE CHEVALIER Institut fu¨r Technische Verbrennung (ITV) Universita¨t Stuttgart Pfaffenwaldring 12, D-70569 Stuttgart, Germany
Because of the complexity of low-temperature oxidation, a detailed reaction scheme of higher hydrocarbons (which are components of practical fuels) typically involves several hundred chemical species taking part in thousands of elementary reactions. Nevertheless, only a very limited number of different reaction types is appearing, for example, alkane thermal decomposition, H-atom abstraction to form an alkyl radical, alkyl radical isomerization, and b decomposition of the alkyl radical for the high-temperature range and a few additional reaction types at low temperature. A LISP program developed for the automatic generation of reaction mechanisms is able to produce mechanisms for the oxidation of aliphatic hydrocarbons. In contrast to earlier attempts described in the literature, a rather complete description of the reaction paths for the decomposition of the intermediate dihydroperoxyalkyl radicals and a description of the aldehyde oxidation is included. The transition between low- and high-temperature range with a negative temperature dependence is well reproduced. With the help of newly available experiments for n-decane, the reaction mechanisms for n-heptane and n-decane are validated for a wide range of pressures, temperatures, and equivalence ratios, covering conditions dictated by potential applications. This is a severe test case, because calculated ignition-delay times are very sensitive with respect to the quality of the reaction mechanism used. Additional sensitivity analysis based on the OH concentration shows the principal rate-determining reactions. However, more kinetic data for high hydrocarbons and oxygenated species are necessary to validate the reaction mechanism, especially with respect to chain-length dependencies of rate coefficients and the behavior of fuels with multiple C–C bonds. Furthermore, some results on flame velocity are given for n-heptane.
Introduction The oxidation of hydrocarbon fuels is an important element in modeling combustion in automobile engines, including autoignition, flame propagation, and pollutant emissions. Detailed kinetic data are necessary to describe these combustion phenomena and to develop simplified reaction schemes needed for such things as three-dimensional calculations of autoignition and turbulent flame propagation [1–3]. Because of the complexity of low-temperature oxidation, a detailed reaction scheme of higher hydrocarbons (which are components of practical fuels) typically involves several hundred chemical species taking part in thousands of elementary reactions. Nevertheless, only a very limited number of different reaction types appears (e.g., alkane thermal decomposition, H-atom abstraction to form an alkyl radical, alkyl radical isomerization, and b decompo-
sition of the alkyl radical for high temperatures and a few additional reaction types at low temperatures [3–5]). Therefore, it is possible to formulate these reactions and their rate expressions using simple rules. These rules are executed with the aid of a computer code described in detail in previous papers [5,6]. LISP is used as a support system, since the best flexibility with regard to the data structures, the algorithm development, and the user interface design is available in this programming language. The code considers only the decomposition of carbon chains larger than C4, because the high-temperature oxidation mechanism for C1 through C4 hydrocarbons already exists [1,7,8] and the rate coefficients of the small species strongly depend on the chain length. The high-temperature oxidation up to C4 species used earlier [4–8] did not consider the decomposition of aldehydes or the aldehyde radicals of C3 and C4 hydrocarbons. Thus, there was a miss-
773
774
KINETIC MECHANISMS—MODELS AND EXPERIMENTS TABLE 1 Rate coefficients for high-temperature reactions [3,7,8]; k 4 A • Tb • exp(1Ea/RT) Primary
Secondary
Tertiary
(a) H-atom abstraction (per C-H bond, A in cm3 • mol • s/b/Ea in kJ/mol) RH ` H 9.38 • 1006/2.0/32.2 4.50 • 1006/2.0/20.9 RH ` O 1.67 • 1013/0.0/32.9 1.30 • 1013/0.0/21.8 09 6.50 • 1008/1.25/2.94 RH ` OH 1.43 • 10 /1.05/7.58 RH ` HO2 1.87 • 1012/0.0/81.2 1.68 • 1012/0.0/71.2 11 RH ` CH3 2.20 • 10 /0.0/48.6 2.00 • 1011/0.0/39.8 4.20 • 1012/0.0/85.7 1.50 • 1012/0.0/71.2 RH ` CH3O2 12 RH ` O2 4.20 • 10 /0.0/205. 1.00 • 1013/0.0/199.
1.26 • 1014/0.0/30.6 1.00 • 1013/0.0/13.7 4.00 • 1012/0.0/1.85 1.00 • 1012/0.0/60.3 1.00 • 1011/0.0/33.1 3.00 • 1012/0.0/62.8 2.00 • 1012/0.0/193.
(b) Alkyl radical isomerization (A in s11/b/Ea in kJ/mol) (1,4) ring 1.00 • 1011/0.0/88.3 (1,5) ring 1.00 • 1011/0.0/59.0 (1,6) ring 1.00 • 1011/0.0/88.3
1.00 • 1011/0.0/67.4 — —
1.00 • 1011/0.0/75.8 1.00 • 1011/0.0/46.5 1.00 • 1011/0.0/75.8
(d) b decomposition of alkyl radical (A in s11/b/Ea in kJ/mol) R → RS ` Olefin
2.50 • 1013/0.0/120.
(d) Alkane decomposition (A in s11/b/Ea in kJ/mol) RH → RS8 ` RS9
3.20 • 1016/0.0/339.
ing link between the oxygenated species formed in the initial O2 attack and formation of the final products. The additional reaction paths are more important for the n-decane oxidation than for the n-heptane oxidation. The missing reactions are generated once by the automatic program and added to the C1– C4 handwritten mechanism. Afterwards, this modified C1–C4 mechanism is added to the computergenerated one for the C5–CFuel system. The mechanism generation has been performed for nheptane and n-decane and then validated by comparing computed autoignition delay times with results from shock tube experiments available in the literature [10,26]. Additionally, some results on flame velocity are given. n-Heptane is one of the primary reference fuels used to determine the octane number and also as diesel fuel model, because its cetane number is typical of a good diesel fuel. The n-decane and mixtures of n-decane and aromatic species such as toluene [9] or methylnaphthalene [10] may be used to model kerosenes. For n-heptane/air mixtures, the initial pressure has been varied between p 4 3.2 bar and 40 bar and the initial temperature between T 4 660 K and 1400 K, while the equivalence ratio covers the range between f 4 0.5 and 2.0. For n-decane/air mixtures, the calculations were made for p 4 13 bar and for initial temperatures between T 4 660 K and 1400 K and equivalence ratio f 4 1.0 and 2.0. Sensitivity analysis based on the OH concentration during the induction phase shows the principal rate-limiting reactions in the high-temperature and the low-temperature regimes.
High-Temperature Reaction Mechanism The high-temperature mechanism [3,8,11] consists of attack of radicals on the parent aliphatic hydrocarbon RH, isomerization of the alkyl radicals R• formed, b decomposition of the alkyl radicals R•, and thermal decomposition of the parent aliphatic hydrocarbon RH to form two (about equally heavy) smaller radicals RS•, RH ` X• → R• ` XH (X 4 H, O, OH, O2, HO2, CH3 O2 , CH3 ) R• → R8• R• → RS• ` OlefinS RH → RS8• ` RS9• Together with the C1–C4 mechanism [8], this gives a complete mechanism for the high-temperature oxidation of aliphatic hydrocarbons; rate coefficients are given in Table 1. For demonstration, this mechanism is used for the simulation of flame velocities in n-heptane/air mixtures; the result is compared with experiments [12,13] in Fig. 1. A sensitivity analysis (Fig. 2) with respect to the flame velocity delivers results very similar to those for other aliphatic hydrocarbons [11,14]: The ratedetermining steps are, as usual, reactions of small molecules unspecific to the hydrocarbon considered and mainly governed by the H2-O2-CO chemistry. Low-Temperature Reaction Mechanism According to the pioneering work of Halstead et al. [15], the low-temperature oxidation of the ali-
KINETIC MODELING OF LARGE ALIPHATIC HYDROCARBONS
775
atom abstraction (external H-atom abstraction is relatively slow [4,5]): RO2• → QOOH• (internal abstraction) where QOOH• is a corresponding alkylhydroperoxy radical with fuel structure. These alkylhydroperoxy radicals (QOOH•) then can eliminate OH and produce a cyclic ether (QO) by concerted ring closure, decompose to a fuel olefin and HO2• [16], or react with a second O2 [21]: QOOH• → QO ` OH• (chain propagation) QOOH• → OlefinF ` HO2• (chain propagation) QOOH• ` O2 i O2QO2H• (second O2 addition)
Fig. 1. Laminar flame velocity in n-heptane–air mixtures (Tu 4 298 K, p 4 1 bar); lines, simulation; points, experiments by v Gibbs and Calcote [12] and m Gerstein et al. [13].
phatic fuel RH is initiated by the reaction with O2 to produce the corresponding alkyl radicals R• and HO2•, which in turn react with the fuel. The alkyl radicals formed can be decomposed by b scission of a C–C bond to produce an olefin and a smaller alkyl radical RS•, isomerize to an isomeric alkyl radical R8• (the four steps to this point are already treated as part of the high-temperature mechanism), react with O2 to produce a alkylperoxy radical (RO2•), and react with O2 by H-atom abstraction to an olefin with fuel structure (OlefinF) and HO2• (rate coefficients for low-temperature reactions are found in Table 2), R• ` O2 i RO2• (first O2 addition) R• ` O2 → OlefinF ` HO2• (H-atom abstraction) If the temperature increases, RO2• radical will decompose back to the reactants. This leads to an inverse temperature dependence of the reaction (the so-called degenerate chain branching [1,15]). The RO2• radicals then will undergo internal H-
The second O2-addition reaction path (rate coefficient as for the first O2 addition) is the only one leading to chain branching (see later). Again, the O2QO2H• radical formed in the last reaction can undergo external or internal H-atom abstraction with minor importance for the external one. Thus, only the internal H-atom abstraction (rate coefficient as for RO2• internal abstraction) is used in the following: O2QO2H• → HO2Q8O2H• (internal abstraction) HO2Q8O2H• → HO2Q8O ` OH• (chain propagation) HO2Q8O → OQ8O• ` OH• (chain branching) The OQ8O• indicated in the last reaction can decompose (via b decomposition) into two other oxygenated species, often aldehydes. It is worth noting that the internal H-atom abstraction in O2QO2H• leads to chain branching. Thus, a distinct acceleration of the ignition process should be expected as a result of the second O2 attack on the QOOH• radical. This effect (together with the degenerate branching behavior) can explain the experimentally observed temperature dependence of the ignition-delay times (see Fig. 3). Finally, the reaction paths of the aldehydes formed have been described (see Kaiser et al. [23]); rate co-
Fig. 2. Sensitivity analysis for the laminar flame velocity in an n-heptane–air mixture at p 4 1 bar, Tu 4 298 K for rich (black) and lean (white) conditions.
776
KINETIC MECHANISMS—MODELS AND EXPERIMENTS TABLE 2 Rate coefficients for low-temperature reactions; k 4 A • Tb • exp(1Ea/RT)
(a) Reactions of alkyl radicals with O2 (A in cm-mol-s units/b/Ea in kJ/mol) [17,18] R ` O2 → RO2 RO2 → R ` O2 R ` O2 → Olefin ` HO2 Olefin ` HO2 → R ` O2
2.00 • 1012/0.0/0.0 4.00 • 1015/0.0/117. 1.00 • 1012/0.0/8.4 1.70 • 1012/0.0/57.6
(b) RO2 → QO2H, O2QO2H → HO2Q8O2H (per C–H bond, A in s11/b/Ea in kJ/mol) [19] primary secondary (1,4) ring 1.00 • 1011/0.0/85.8 1.00 • 1011/0.0/71.2 (1,5) ring 1.00 • 1011/0.0/61.1 1.00 • 1011/0.0/46.5 1.00 • 1011/0.0/50.2 (1,6) ring 1.00 • 1011/0.0/62.8 (1,7) ring 1.00 • 1011/0.0/100. 1.00 • 1011/0.0/85.8
tertiary 1.00 • 1011/0.0/56.5 — 1.00 • 1011/0.0/37.7 —
(c) QO2H → RO2, HO2Q8O2H → O2QO2H (per C–H bond, A in s11/b/Ea in kJ/mol) [19,20] (1,4) ring 1.00 • 1011/0.0/52.3 1.00 • 1011/0.0/52.3 1.00 • 1011/0.0/27.6 (1,5) ring 1.00 • 1011/0.0/27.6 (1,6) ring 1.00 • 1011/0.0/29.3 1.00 • 1011/0.0/31.4 (1,7) ring 1.00 • 1011/0.0/66.9 1.00 • 1011/0.0/67.0
1.00 • 1011/0.0/43.4 — 1.00 • 1011/0.0/30.6 —
(d) QO2H → Q ` HO2 and QO2H → QO ` OH (A in s11/b/Ea in kJ/mol) [7] QO2H → Q ` HO2 QO2H → Oxirane ` OH QO2H → Oxetane ` OH QO2H → Tetrahydrofurane ` OH
3.00 • 1011/0.0/83.8 3.00 • 1011/0.0/58.6 3.00 • 1011/0.0/54.4 3.00 • 1011/0.0/12.6
(e) HO2Q8O2H decomposition (A in s11/b/Ea in kJ/mol) [7,21] HO2Q8O2H → HO2Q8O ` OH HO2Q8O → OQ8O ` OH
1.00 • 1009/0.0/31.4 8.40 • 1014/0.0/180.
(f) H-atom abstraction from aldehyde (A in cm3 • mol • s/b/Ea in kJ/mol) [24] RCHO ` OH → RCO ` H2O RCHO ` O2 → RCO ` HO2 RCHO ` HO2 → RCO ` H2O2 RCHO ` CH3O2 → RCO ` CH2O2H
1.75 • 1013/0.0/0.00 2.00 • 1013/0.5/175. 1.00 • 1012/0.0/42.0 1.00 • 1012/0.0/42.0
(g) Decomposition of aldehyde radicals (A in s11/b/Ea in kJ/mol) [24] RCO → R ` CO
1.58 • 1013/0.0/72.0
efficients are given by Kojima [24]. The aldehyde (RCHO) formed in the OQ8O• decomposition can easily form aldehyde radicals (RCO•), which at low temperatures produce peracyl radicals via a second O2 addition RCHO ` X → RCO• ` XH (X 4 OH, O2, HO2, CH3O2) RCO• ` O2 → RCOO2H• The peracyl radicals can undergo external H-atom abstraction and produce CO2 by the decomposition reaction RCOO2H → R• ` CO2 ` OH• With increasing reaction temperature, another path is favored for the aldehyde radicals that produces CO and an alkyl radical because the acetyl radicals
decompose directly into a smaller alkyl radical and CO, RCO• → R• ` CO Because of the lack of kinetic data for the route via RCOO2H•, only the decomposition path is implemented.
Comparisons with Experimental Results To verify the implemented rules, the low-temperature mechanisms for n-heptane and n-decane oxidation have been computer generated. The resulting mechanism for n-heptane consists of about 1200 reactions and 200 species and for n-decane about 1650 reactions and 350 species. With the use of a spatially homogeneous instationary program [25], ignition-
KINETIC MODELING OF LARGE ALIPHATIC HYDROCARBONS
Fig. 3. Ignition-delay times s in stoichiometric n-heptane–air mixtures as a function of the initial temperature T for different pressures p; lines, simulations (this work); symbols, experiments [26].
Fig. 4. Ignition-delay times s in n-heptane–air mixtures as a function of the initial temperature T at different equivalence ratios f at p 4 40 bar; lines, simulations (this work); symbols, experiments [26].
delay times are calculated at various conditions and compared to corresponding experiments [10,26]. Figure 3 presents ignition-delay times s of a stoichiometric n-heptane–air mixture plotted versus the inverse of the initial temperature T behind the reflected shock wave. The calculated values (lines) and the experimental points (symbols) [26] show good agreement at various pressures. It should be noticed that the pressure dependence is shifted to higher temperatures for increasing pressure. The influence of the pressure on the ignition-delay time is distinct
777
Fig. 5. Ignition-delay times s in n-heptane–air mixtures as a function of the initial temperature T for different equivalence ratios f at a pressure p 4 13.5 bar; lines, simulations (this work); symbols, experiments [26].
in the transition region and smallest for low temperatures. The negative temperature dependence that occurs in the transition between the high- and low-temperature regimes is reproduced quite well by the mechanisms. The dependence of the ignition-delay times of nheptane–air mixtures on the equivalence ratio f is shown in Figs. 4 and 5. In Fig. 4, the pressure is about p 4 40 bar in all experiments, whereas the equivalence ratio has been varied between f 4 0.5 and 2.0. In Fig. 5, the pressure is kept constant at p 4 13.5 bar and the equivalence ratio f is changed. The calculated values can describe the measured ones quite well. The dependence of s on f in the high-temperature region is small, increases toward lower temperatures, and is largest in the transition region. Here, the fuel-rich mixtures show the smallest ignition delays. For lower pressure (p 4 13.5 bar), the agreement between the computed ignitiondelay times and the experimental values is better than for the higher pressure (p 4 40 bar). Calculated ignition-delay times of n-decane–air mixtures at p 4 13 bar for the two equivalence ratios f 4 2.0 and 1.0 and constant volume are plotted in Fig. 6. They are compared with new results reported by Adomeit and co-workers [10]. The agreement of experimental and calculated induction times are better for n-heptane, but the behavioral tendency of the ignition delays can be described. The ignition-delay times are also smallest for fuel-rich mixtures. In the high-temperature region, the influence of the equivalence ratio is smaller than that for n-heptane. The transition region of the calculated values is shifted toward high temperatures. If the rate coefficient of the reverse of the first O2 addition were changed for
778
KINETIC MECHANISMS—MODELS AND EXPERIMENTS
Fig. 6. Ignition-delay times s in n-decane–air mixtures as a function of the initial temperature T for different equivalence ratios f at a pressure p 4 13 5 1.5 bar; lines, simulations (this work); symbols, experiments [10].
Fig. 8. Sensitivity analysis for the OH concentration in an n-decane–air mixture during ignition delay at p 4 13 bar, T 4 1400 K; only relative sensitivities larger than 0.3 are listed.
n-decane are slightly shorter than for n-heptane. This behavior can be explained by the longer carbon chain of n-decane. The difference at high temperatures is in agreement with the usual picture of the dependence of ignition delay on molecular size [3]. Sensitivity and Path Analyses
Fig. 7. Comparison of ignition-delay times s in stoichiometric n-heptane–air mixtures at p 4 13.5 bar and a stoichiometric n-decane–air mixture at p 4 13 bar as a function of the initial temperature T; lines, simulations (this work); symbols, experiments [10,26].
n-decane, the agreement between experimental and calculated data would be better. Thus, rate coefficients for this reaction type should be made dependent on the carbon chain length. It would be interesting to have kinetic data for this reaction for higher hydrocarbons to validate the values assumed. In Fig. 7, the induction times in stoichiometric nheptane–air mixtures and n-decane–air mixtures have been compared at p 4 13 bar. In the transition and low-temperature regions, the induction times of
At high temperatures, the ignition of aliphatic hydrocarbons is governed mainly by chain-branching processes that are rather unspecific for the fuel considered. However, they are fuel specific at low temperatures, leading to very complex reaction systems if the numerous isomeric structures are taken into consideration [2]. A detailed sensitivity analysis based on the OH concentration was carried out, revealing the principal rate-limiting reactions. Figure 8 shows the results for a stoichiometric n-decane–air mixture in which the pressure is p 4 13 bar and the initial temperature T 4 1400 K. As usual, at high temperatures [7,8], there is sensitivity to reactions of fuelunspecific small molecules with even smaller contributions from C3- and C4-species. Furthermore, alkyl-radical b decomposition and isomerization and the H-atom abstraction of the fuel and its initial thermal decomposition are rate limiting because all of these reactions are fuel specific. In the transition region (Fig. 9), the picture is totally different: All contributions stem from fuel-specific reactions. However, because of the complex mechanism, a detailed explanation of the sensitivities listed seems difficult (e.g., negative sensitivities for OH-forming reactions caused by the negative temperature dependence). It is worth mentioning that
KINETIC MODELING OF LARGE ALIPHATIC HYDROCARBONS
779
REFERENCES
Fig. 9. Sensitivity analysis for the OH concentration in an n-decane–air mixture during ignition delay at p 4 13 bar, T 4 800 K; only relative sensitivities larger than 0.3 are listed; no details on the isomer structures of the lowtemperature species in reactions (6)–(23) is given because of the complexity of nomenclature.
the initial attack of the n-decane or its thermal decomposition does not show considerable sensitivity. Similar results have been obtained for mixtures of nheptane and n-cetane with air at low temperatures [3,5–7]. Conclusions A LISP program for the automatic generation of reaction mechanisms is able to produce reaction mechanisms for the oxidation of aliphatic hydrocarbons; these describe the experiments well. The transition between the low- and high-temperature regimes with a negative temperature dependence is reproduced. The reaction mechanisms of n-heptane and n-decane are validated for a wide range of conditions of pressure, temperature, and equivalence ratios, covering the low- and high-temperature oxidation regimes and conditions dictated by potential applications. Yet more kinetic data for high hydrocarbons and oxygenated species are necessary to validate the reaction mechanism, especially with respect to chain-length dependencies of rate coefficients (first and second O2 addition) and the behavior of fuels with multiple C–C bonds. Acknowledgments This work was supported by the DFG (SFB 259, SFB 359, LEIBNIZ Program), the BMBF (TECFLAM Project), and the EC/Daimler-Benz (JOULE Program). We thank Drs. P. Deuflhard and H. Melenk (Konrad-ZuseZentrum, Berlin) for fruitful cooperation.
1. Warnatz, J., Maas, U., and Dibble, R. W., Combustion, Springer, Heidelberg/Berlin, 1996. 2. Maas, U. and Pope, S. B., Combust. Flame 88:239–264 (1992). 3. Warnatz, J., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 553–579. 4. Westbrook, C. K., Warnatz, J., and Pitz, W. J., TwentySecond Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 893–901. 5. Chevalier, C., Pitz, W. J., Warnatz, J., Westbrook, C. K., and Melenk, H., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 93–101. 6. Chevalier, C., Warnatz, J., and Melenk, H., Ber. Bunsenges. Phys. Chem. 94:1362–1367 (1990). 7. Chevalier, C., Dissertation, Institut fu¨r Technische Verbrennung, Universita¨t Stuttgart 1993. 8. Chevalier, C. and Warnatz, J., “Survey of Reactions in the C/H/O System,” in Combustion Chemistry (Gardiner, W. C. Jr., Ed.), Springer Verlag, New York, 1996. 9. Doute´, C., Delfau, J. L., Akrich, R., and Vovelle, C., Combust. Sci. Technol. 106:327–344 (1995). 10. Fieweger, K., Pfahl, U., Blumental, R., and Adomeit, G., Kolloquium des Sonderforschungsbereich 224, “Motorische Verbrennung,” (Pischings, F., Ed.), March 19–20, 1996, RWTH Aachen, 1996. 11. Warnatz, J., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 369–384. 12. Gibbs, C. J. and Calcote, H. C., J. Chem. Eng. Data 4:226–241 (1959). 13. Gerstein, M., Levine, O., and Wong, E. L., J. Am. Chem. Soc. 73:418–422 (1951). 14. Warnatz, J., Combust. Sci. Technol. 34:177–200 (1983). 15. Halstead, M. P., Prothero, A., and Quinn, C. P., Proc. R. Soc. London, Ser. A 322:377–403 (1971). 16. Barbieri, G., Di Maio, F. P., and Lignola, P. G., Combust. Sci. Technol. 98:95–122 (1994). 17. Benson, S. W., Prog. Energy Combust. Sci. 7:125–134 (1981). 18. Morgan, C. A., Pilling, M. J., Tulloch, J. M., Ruiz, R. P., and Bayes, K. D., J. Chem. Soc. Faraday Trans. 78:1323– 1330 (1982). 19. Fish, A., in Organic Peroxides (Swern, D., Ed.), Wiley, New York, 1970. 20. Baldwin, R. R. and Walker, R. W., Fourteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1973, pp. 241–257. 21. Pollard, R. T., in Comprehensive Chemical Kinetics Vol. 17 Gas-Phase Combustion (Bamford, C. H. and Tipper, C. F. H., Eds.), Elsevier, New York, 1977, pp. 249–367. 22. Walsh, A. D., Ninth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1963, pp. 1046–1055. 23. Kaiser, E. W., Westbrook, C. K., and Pitz, W. J., Int. J. Chem. Kinet. 18:655–688 (1986). 24. Kojima, S., Combust. Flame 99:87–136 (1994). 25. Maas, U. and Warnatz, J., Combust. Flame 74:53–69 (1988). 26. Ciezki, H. K. and Adomeit, G., Combust. Flame 93:421– 433 (1993).
780
KINETIC MECHANISMS—MODELS AND EXPERIMENTS
COMMENTS Anthony Marchese, Princeton University, USA. It is common practice to extrapolate elementary rate constants obtained for the H-atom abstraction from smaller alkanes (e.g., N-C4H10) for larger alkanes, based only on the number of abstraction sites. Is there experimental evidence to support this practice for much larger alkanes (e.g., N– C10H22, n-C16H34, and above)? Author’s Reply. We are not aware of experimental evidence to support this practice for n-C10H22 or above in the literature, but transition-state theory can be used to extrapolate rate coefficients for such reactions [1,2].
REFERENCES 1. Cohen, N. and Westberg, K. R., Int. J. Chem. Kinet. 18:99 (1986). 2. Cohen, N., Int. J. Chem. Kinet. 23:397–417 (1991). ● Dr. Henry J. Curran, Lawrence Livermore National Laboratory, USA. In your low-temperature oxidation scheme, do you include b-scission of the hydroperoxy-alkyl (QOOH) radical? This is important in predicting both the reactivity of the system and product species formation. Author’s Reply. In this oxidation scheme we do not include b-scission of the hydroperoxy-alkyl (QOOH) radical. We consider that the hydroperoxy-alkyl radical can eliminate OH to produce cyclic ether (QO), decompose to a fuel olefin and HO2, or react with a second O2. We think that these three reaction paths are the important ones. ● J. F. Griffiths, University of Leeds, UK. It worries me to see that a complex kinetic model is validated only against overall ignition delays. There is a considerable body of experimental chemical information over a wide range of temperature (especially for n-Heptane) against which the predicted chemistry can be tested. Much of this has been obtained in spatially uniform reactors (e.g., CSTR) so a quantitative match can be expected. Author’s Reply. The ignition delay time and laminar flame velocity are global values, but the calculated ignition delay times are very sensitive with respect to the quality of the reaction mechanism used. Auto-ignition of hydrocarbons is of enormous importance in piston engine combustion. Thus, we first validate the mechanism for these global values as shown in this paper. In a further study, the vali-
dation of the mechanism against experimental results obtained in spatially uniform reactors (e.g., CSTR) is planned. ● William J. Pitz, Lawrence Livermore Laboratory, USA. You showed some sensitivity results where the low-temperature degenerative branching steps (the reaction of the hydroperoxy alky peroxy) to give a ketohydroperoxide and OH) exhibited a sensitivity indicating that these reactions retards the overall oxidation rate. In an earlier talk [1], we showed that this generic-step was one of the most accelerating steps for the propane system. Do you have any explanation for this unexpected result?
REFERENCE 1. Koert, D. N., Pitz, W. J., Bozzelli, J. W., and Cernansky, N. P., Chemical Kinetic Modeling of High Pressure Propane Oxidation & Comparison to Experimental Results, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 633–640. Author’s Reply. This is a global sensitivity analysis. We consider the time until the temperature rises (the time where the radical pool is built). If you consider a shorter time the sensitivity coefficients of the reactions mentioned by you are positive making the accelerating reaction steps. ● Ray W. Walker, Hull University, UK. I am concerned about the conclusions drawn from this type of study. It is clear that experimental data can be interpreted within certain conditions, by the mechanism proposed. However, the agreement in itself does not validate the mechanism. In particular, the experimental data have to cover a much wider variation of mixture composition, particularly the [fuel]/[O2] ratio, ideally by at least a 20–30 factor. For this reason sensitivity analyses should be carried over very wide ranges of conditions. Author’s Reply. Those experimental data for ignition delay times available in the literature cover the range presented in the paper. For n-Heptane-air mixtures the initial pressure has been varied between p 4 3.2 bar and 40 bar and the initial temperature between T 4 660 K and 1400 K, while the equivalence ratio covers f 4 0.5, 1, 2. The pressures and temperatures considered cover the parameter range most important for engine combustion. Because of lack of space only the sensitivity analyses for stoichiometric n-Decane-air mixtures are shown.