Model Development and Reduction PrincetonUniversity Methods for High-temperature Large Alkane Molecule Kinetics 31st International Symposium on Marcos Chaos, Andrei Kazakov, Zhenwei Zhao, Frederick L. Dryer Combustion [email protected] August 6-11, 2006 Mechanical & Aerospace http://www.princeton.edu/~combust Engineering Department University of Heidelberg, Germany

Introduction Model Development There is continued interest in developing a better understanding of the pyrolysis and oxidation of large hydrocarbons which are The current mechanism was built in a hierarchal manner. A high temperature hexadecane representative of real fuels over a wide range of operating conditions. This is motivated by the need to improve the efficiency and emission submechanism was combined with our recent update of the H2/O2 kinetic model [3] along with C1-C4 of pollutant species from existing combustion systems as well as new engine/propulsion designs that may use new fuels/surrogates (to kinetics including the modifications listed in [4]. In the hexadecane submechanism, five classes of represent more complex full-blended gasolines). To this end, robust chemical kinetics models and more accurate numerical tools are needed reactions are treated: to improve our understanding of the complex physical and chemical processes taking place in combustion systems. Recognizing the problem ™ C-C, C-H bond homolysis: Rate constants for these unimolecular fuel decomposition reactions were of mechanistic complexity versus predictive robustness, this study aims to develop a partially reduced skeletal mechanism for large alkane Table 1. H-atom abstraction rates. calculated from the recombination reactions of two molecules and the methodology is applied to n-hexadecane. Hexadecane is a primary reference fuel for cetane rating of diesel fuels and is a (cm3-mol-s-cal) radical species to form the stable parent molecule major component in simple mixtures used to emulate the autoignition and combustion behavior of distillate-type fuels utilized in advanced Radical Log (A)/H bE a using thermochemistry. For reactions leading to Primary sites engine designs (e.g. direct injection and homogeneous charge compression ignition diesel engines). Models of this molecule [1, 2] are scarce hexadecyl + H, a recombination rate constant of H 6.97 2.00 7,700 and involve a large number of reactions and species which make them not readily applicable to the simulation of multi-dimensional fluid 1x1014 cm3/(mol s) was assumed [5]. For reactions flow problems. O 5.62 2.40 5,500 involving CH3 the recombination rate was assumed OH 6.37 1.80 974 to be 2x1013 cm3/(mol s) whereas for decompositions HO2 3.90 2.55 16,500 where the smallest product is ethyl or larger, the 10-2 CH3 11.34 0.00 11,600 12 3 CO CO CO recombination rate was set to 7x10 cm /(mol s) [5].

CO2 CO CO O2 12.82 0.00 50,900 2 2 ™ H-atom abstraction: Abstraction by H, O, OH, CH2O -3 CH2O -3 CH2O 10 10 C2H5 10.72 0.00 12,300 -3 H H H 10 2 2 2 HO , CH , O , C H , C H , and aC H is considered. C H 11.22 0.00 18,000 2 3 2 2 3 2 5 3 5 2 3 Rates are as listed in Table 1. aC3H5 11.12 0.00 20,500

-4 -4 ™ Isomerization: 1,4/1,5/1,6 internal hydrogen 10-4 10 10 Secondary sites H 6.64 2.00 5,000 transfers were considered. Rates follow the rules of O 4.76 2.60 1,769 Westbrook and Pitz [6]. -5 10 -5 -5 OH (C-C-C-) 5.70 2.00 -596 ™ 10 10 β-scission: The alkyl radicals formed are assumed to CH 4 10-3 (-C-C-C-) 5.47 2.00 -1,391 decompose through β-scission into a 1-olefin and a C2H6 HO 3.68 2.60 13,900 1,3-C4H6 2 smaller alkyl radical which, in turn, also decomposes C H / 2 -4 2 4 10 CH 11.3 0.00 9,500 -4 -4 3 following this β-scission pattern. The decomposition 10 C3H6 10 O 13.3 0.00 47,590 aC3H4 2 of all radicals larger than ethyl is treated in this

C2H5 10.10 0.00 10,400 manner. Rate constant were calculated from the -5 10 -5 Mole Fraction Mole

Mole Fraction 10 Mole Fraction C2H3 11.30 0.00 16,800 reverse reaction, that is, the addition of an alkyl -5 10 aC H 10.70 0.00 16,100 CH4 C2H4 / 2 CH4 C2H4 / 2 3 5 radical across the double bond of an alkene (Log A =

C2H6 C3H6 C2H6 C3H6 10-6 -6 11, Ea = 7,200 cal/mol [5]). 1,3-C4H6 aC3H4 10 1,3-C4H6 aC3H4

™ Olefin reactions: Olefins larger than C4 follow unimolecular decomposition pathways as well as H 1-C4H8 / 5 1-C4H8 / 5 1-C H / 5 4 8 1-C5H10 abstraction (by H, O, OH, and CH ) from primary, secondary and vynilic sites with subsequent 1-C5H10 3 1-C5H10 1-C6H12 1-C6H12 1-C H -5 rapid decomposition. Rates listed in [7] and [8] were used. 6 12 1-C7H14 10 -5 1-C7H14 10 1-C H -5 7 14 10 1-C8H16 1-C8H16 1-C H 8 16 1-C9H18 1-C9H18 1-C10H20 Model Reduction 10-6

-6 An approach similar to that previously applied in our laboratory for n-decane [9] is extended here for 10 -6 ABC10 n-hexadecane. The originally developed detailed mechanism (above) included detailed treatment of

1000 1040 1080 1120 1160 1200 1000 1040 1080 1120 1160 1200 1000 1050 1100 1150 1200 1250 the alkyl radicals formed, incorporating both internal hydrogen isomerization and β-scission reactions T (K) T (K) T (K) and consisted of 151 species undergoing 1,155 reactions. In order to reduce the number of required 2.5x10-4 -2 species and simultaneously maintain the desired mechanistic detail, it was assumed that each of the φ = 0.5 1.6x10 φ = 0.5 -4 2.0x10 φ = 1.0 φ = 1.0 alkyl radicals in the system exists in isomeric partial equilibrium above the C4 level. Using the φ = 1.5 φ = 1.5 1.2x10-2 corresponding isomerization rates, the relative concentrations of each isomer within a given radical 1.5x10-4 group were calculated as a function of temperature and an Arrhenius-type expression (i.e. k = ATb exp -3 -4 8.0x10 1.0x10 (Ea/RT)) was fitted to the results. The calculated Arrhenius parameters were used to modify the rates Mole Fraction Mole Fraction associated with the decomposition of each isomer radical. As a result, only a single radical species was -3 5.0x10-5 4.0x10 DE needed to represent all the isomers associated with it and the respective reaction channels associated with each isomer. Using this approach, the resulting reduced model consisted of 98 species and 944 0.0 0.0 1000 1040 1080 1120 1160 1200 1000 1040 1080 1120 1160 1200 reactions. T (K) T (K) Figure 1. Comparison of experimental [2] and computed species profiles for the oxidation of hexadecane at atmospheric pressure in a Jet Stirred Reactor (JSR) with a mean residence time of 70 ms. (A) φ = 0.5, 0.03% C H / 1.47% O / 98.5% N ; (B) φ = 1.0, 0.03% C H / 16 34 2 2 16 34 Further Validation 0.735% O2 / 99.235% N2; (C) φ = 1.5, 0.03% C16H34 / 0.49% O2 / 99.48% N2; (D) hexadecane consumption; (E) oxygen consumption. 45 (Similarity to other Alkanes) 40 s) Despite the lack of experimental data (aside from the early / 120 work of Wagner and Dugger [12]), the current model was 35 0.30 H 2 C H Closed Symbols - Mixture I - C16/C7 (1:1 wt) CH 2 6 Validation 4 Open Symbols - Mixture II - C16/C7 (1:3 wt) used to calculate laminar flame speeds of hexadecane/air 30 C3H6 0.25 C2H4 / 2 80 ™ Oxidation: To date, the only detailed mixtures at atmospheric pressure as this parameter is 25 n-C16H34 [12] 0.20 n-C H [13] experimental study on the oxidation of commonly used to partially validate kinetic models. It is 5 12 Flame Speed (cm Speed Flame n-C H [14] 0.15 20 7 16 hexadecane is that of Ristori et al. [2]. They expected, however, that hexadecane flame speeds will be n-C16H34, model 40 0.10 studied the gas–phase oxidation of C16H34 in a very close to those of other linear alkanes since they share 15 0.60.811.21.4 0.05 Jet Stirred Reactor (JSR) at atmospheric similar structures and flame temperatures (see Ref. 12) and, Equivalence Ratio 0 pressure over 1000-1250K temperature range in fact, the current model shows this (Figure 4). The ability 0 Figure 4. Calculated hexadecane laminar C H flame speed compared with experimental 3 8 1-C H and for equivalence ratios spanning from 0.5 of the mechanism to accurately predict these flame speeds 1,3-C H 5 10 4 6 120 data [12] for other large alkanes. 0.08 n-C16H34 1-C4H8 through 1.5. Concentration profiles were depends on the small-molecule kinetics as discussed in [4]. obtained for major and minor species (up to 0.06 On the other hand, Horning et al. [14] reported that ignition times of n-alkanes (from C3 up to C10) mol / (100 mol reacted mixture) reacted mol / (100 mol 80 decene). Figure 1 shows the results obtained exhibit similar pressure and oxygen concentration as well as activation energies. For qualitative 0.04 from the current model compared against the purposes, the ignition delay of a stoichiometric mixture of C H /O /Ar was calculated at atmospheric

Mole Fraction Mole 16 34 2 40 experimental data [2]. As can be seen, the 0.02 pressure over 1,300 < T < 1,500K. The apparent activation energy obtained from the calculation was model successfully captures reactivity trends approximately 44,000 cal/mol. This value compares well with the value reported by Horning et al. of 0 0 as the equivalence ratio is varied. The model 46,550 cal/mol. 0.010 1-C6H12 0.005 0.01 0.015 0.02 0.025 1-C H 1-C H 14 28 Time (s) also predicts well the formation of alkenes. 8 16 Benzene 1-C9H18 C H /2 1-C H 0.008 2 4 5 10 Some disparities exist in the prediction of CO CH 3 x Σ(1-C H - 1-C H ) 4 6 12 15 30 Summary C3H6/2 Mixture I, model and 1,3-butadiene. Such discrepancies have 0.006 1-C H Mixture II, model 4 8 previously been reported [4, 9]; our laboratory A partially reduced skeletal reaction mechanism for the high temperature oxidation and pyrolysis of n- 0.004 Figure 3. Measured [11] and predicted is currently further refining the mechanism hexadecane has been developed consisting of 98 species and 944 reactions. By assuming that the alkyl species profiles during the steam radicals formed during these processes are in isomeric partial equilibrium, a considerable reduction in 0.002 copyrolysis of hexadecane/heptane below the C3 level in order to improve these mixtures in a flow reactor at 1033 K and results. The model, however, yields results the required number of species was achieved while still maintaining the desired level of detail. The 0 atmospheric pressure. 65 70 75 80 85 90 comparable to the values obtained using the mechanism has been shown to reproduce the limited available experimental data and its performance is Fuel Conversion (%) mechanism developed in [2] which consists of nearly 300 species and 1,800 reactions. comparable to that of other much larger mechanisms available in the literature; furthermore, the model Figure 2. Experimental [10] and shows encouraging trends when considering other high temperature processes. The method described calculated species profiles during the ™ Pyrolysis: In industrial applications, alkenes are usually “manufactured” by pyrolysis of here can, thus, be successfully applied to the generation of compact mechanisms for other large alkanes steam pyrolysis of hexadecane at a temperature of 973 K and atmospheric raw materials such as LPG and naphtas. In recent years, however, the use of higher- found in modern fuels. pressure. Dashed lines are predictions boiling materials has increased, especially gas-oil. Hexadecane kinetics studies are, thus, References using the model of Ristori et al. [2] 1. C. Chevalier, W. J. Pitz, J. Warnatz, C. K. Westbook, and H. Melenk, Proc. Combust. Inst. 24, 93-101 (1992). beneficial for these applications as the carbon content of gas-oil is similar to that of C16H34 2. A. Ristori, P. Dagaut, and M. Cathonnet, Combust. Flame 125, 1128-1137 (2001). 3. J. Li, Z. Zhao, A. Kazakov, and F. L. Dryer, Int. J. Chem. Kinet. 36, 566-575 (2004). (it is noted, however, that gas-oil is a complex mixture of a large number of paraffins, aromatics, and naphtas). Figures 2 and 3 compare 4. Z. Zhao, J. Li, A. Kazakov, F. L. Dryer, and S. P. Zeppieri, Combust. Sci. Tech. 177, 89-106 (2005). computed species profiles against available data [10, 11] obtained during the thermal (steam) cracking of hexadecane and 5. D. L. Allara and R. Shaw, J. Phys. Chem. Ref. Data 3, 523-559 (1980). 6. C. K. Westbrook and W. J. Pitz, pp.39-54 in Complex Chemical Reaction Systems: Mathematical Modeling and Simulation (1987). hexadecane/heptane mixtures at atmospheric pressure in quartz and stainless steel reactors, respectively. Reasonable agreement is observed 7. W. Tsang, J. Phys. Chem. Ref. Data, 17, 887-952 (1988). 8. W. Tsang, J. Phys. Chem. Ref. Data, 20, 221-273 (1991). for major species. Trends for large alkenes are also reproduced although it is noted that considerable experimental uncertainty exists for 9. S. P. Zeppieri, S. D. Klotz, and F. L. Dryer, Proc. Combust. Inst. 28, 1587-1595 (2000). 10. D. Depeyre, C. Flicoteaux, and C. Chardaire, Ind. Eng. Chem. Proc. Dev. 24, 1251-1258 (1985). these measurements since the concentration of species larger than 1-pentene was very low. Of special importance are the alkane mixture 11. E. Barketová and M. Bajus, Petroleum and Coal 41, 48-56 (1999). results shown in Fig. 3 as only one extra species was added to the model (along with abstraction reactions following the rules in Table 1). 12. P. Wagner and G.L.Dugger, J. Am. Chem. Soc. 77, 227-231. 13. S. G. Davis and C. K. Law, Combust. Sci. Tech. 140, 427-449 (1998). 14. D. C Horning, D. F. Davidson, and R. K. Hanson, J. Propul. Power 18, 363-371 (2002).