Energy &Fuels 1987,1, 405-411 for 12 h, washed with H 2 0 and then aqueous NaHC03, and dried with MgS04. It was distilled through a 12-in. Heli-pak column, and the fraction boiling 35-36 "C was collected and stored over 4-A molecular sieves. Ethyl diazoacetate was prepared from ethyl glycinate hydrochloride and distilled; bp 24-26 "C (1.5 Torr).20 Methanol was distilled through a 12-in. Heli-pak column and the fraction boiling a t 64.0-64.5 "C was collected and stored over 4-A molecular sieves. Toluene was distilled through a 12 in. Heli-pak column and the fraction boiling a t 110-110.5 "C was collected and stored over 4-A molecular sieves. Reaction of Coal with Ethyl Diazoacetate. The Illinois No. 6 coal was crushed under argon to pass through a 100-meshscreen and dried a t 120-125 "C for 3 h under Nz. After the coal was cooled for 30 min, 1-g portions were put into 100-mL roundbottomed flasks into which was put 10 mL of pentane and the ethyl diazoacetate (none for coal 0 and 1 , 2 , and 3 g for coals 1, 2, and 3, respectively). The mixtures were stirred under Nz overnight, and the pentane was removed under vacuum over ca. 30-40 min. The flasks were heated slowly to 100 "C until the N2 evolution ceased (20-30 min; monitored with a bubbler), and then the temperature was raised to 120 "C for an additional 30 min. After they were weighed, the samples were stored under N2. Approximately 0.4 g of each sample was extracted with 9:l tol(20)Searle, N.E. Org. Syn. Coll. Vol. 4 1963, 424.
405
uene:methanol in a Soxhlet extractor for 24 h, and the extract was concentrated to about 1.5 mL by distillation through a 12-in. Vigreux column. Aconitic Acid T r i e t h y l E s t e r (7). Compound 7 was made by Fischer esterification of 17.2 g of aconitic acid (Pfizer, cis and trans) in 50 mL of absolute ethanol, 50 mL of benzene, and 1 mL of concentrated H2S04.21 The solvents were flash distilled; the residue was taken up in 100 mL of ether, which was washed with three 5-mL portions of 0.5 N NaOH and three 100-mL portions of water and dried over MgS04. Yield: 15 g (61%). NMR and GC indicate the product to be a mixture of cis and trans aconitic acid triethyl ester. NMR (60 MHz; CDC1,): 6 1.1-1.6 (m, 9 H, C H J , 3.4-4.7 (m, 8 H, CH,), 6.47 and 7.0 (s and m, respectively, 1 H, C=CH). TGA analyses were performed on 10-20-mg samples in an Ar or N2 atmosphere. The temperature was programmed from 85 to 1050 "C a t a rate of 20 "C/min. In general five runs were performed on each sample.
Acknowledgment. We thank the Department of Energy Pittsburgh Energy Technology Center (Grant No. DE-FG22-86PC90532)and the National Science Foundation (Grant No. CDP-8007514) for support of this work. (21)Ingold, C. K.J. Chem. SOC.1921, 119, 350.
Quasi-Global Model for Benzene Oxidation in a Flat H z / O ~ / C ~ H ~Flame /N~ Mark C. Jackson and Normand M. Laurendeau* Flame Diagnostics Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907 Received November 10, 1986. Revised Manuscript Received June 1, 1987
We have investigated the oxidation of benzene in a lean (4 = 0.6), flat, premixed H2/Oz/C6H6/Nz flame by employing a novel sampling system consisting of a quartz probe, two Teflon-lined diaphragm pumps and two gas chromatographs. With this system, quantitative species concentration profiles were obtained for C6H6and C2H2at a pressure of 76 Torr. Spatial profiles for these compounds were also obtained by solving the relevant one-dimensional species conservation equations. A five-step quasi-global model for benzene oxidation was developed by matching the predicted profiles for C6H6 and C2H2to those obtained experimentally. The most important reactions are the pyrolysis of benzene, C6H6s C6H5 H, and the global oxidation of the phenyl radical C6H5+ O2 2CO + C2H2+ C2H,. Arrhenius parameters determined for the global reaction are A = 1.1f 0.2 X 1015cm3/(mo14 and E = 24 f 1 kcal/mol.
+
1. Introduction In this investigation, we develop a quasi-global model for benzene oxidation under flame conditions by measuring C6H6 and CzHz profiles in a lean (4 = 0.6), premixed, Hz/02/C6H6/Nzflame at 76 Torr with a novel sampling system. The sampling system consists of a quartz probe, two in-line vacuum pumps, and associated gas chromatois used with an appropriate set of graphs. A flame elementary and global chemical reactions to solve the conservation equations for the one-dimensional, steady(1) Smooke, M. D. J. Comput. Phys. 1982, 48, 72. (2)Bero, C. S. Users Manual for Sandia Flame Code at Purdue; Flame Diagnostics Laboratory, School of Mechanical Engineering,Purdue University: West Lafayette, IN, 1986.
0887-0624/87/2501-0405$01.50/0
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state Hz/02/C6H6/N2flame. The kinetic parameters for the quasi-globalmodel me obtained from the literature and from comparisons between the predicted species profiles and those obtained from the experimental data. 1.1. Benzene Oxidation in Flame Environments. Bittner and Howard3p4 used a molecular beam/mass spectrometer system to obtain detailed species profiles for a near sooting (4 = 1.8),premixed C6H6/02/Nzflame at a pressure of 20 Torr and a cold gas velocity of 0.5 m/s. (3) Bittner, J. D.; Howard, J. B. Eighteenth Symposium (Znternationul) on Combustion;The Combustion Institute: Pittsburgh, PA, 1981; p 1105. (4)Bittner, J. D.;Howard, J. B. Nineteenth Symposium (Znternational) on Combustion;The Combustion Institute: Pittsburgh, PA, 1982; p 211.
0 1987 American Chemical Society
406 Energy & Fuels, Vol. 1, No. 5, 1987
Jackson and Laurendeau
Table I. Experimental Conditions for Previous Investigations of Benzene Kinetics experiment pyrol/oxidn temp; press. 1400-1900 K; 2-8 atm shock tube Asaba and Fujii12 (1971) single pulse absorption spectroscopy 1300-1700 K; 2-8 atm shock tube Fujii and Asaba13 (1973) single pulse absorption spectroscopy IR emission gas chromatography 1090-1615 K; 1-80 atm shock tube Fujii et aLB(1974) IR spectroscopy 1700-2800 K; 1.1-1.7 atm shock tube McLain et al.s (1979) IR and UV spectroscopy 213-1150 K; 20-200 Torr flow reactor Tully et al.lS (1981) resonance fluorescence 350-1500 K; 18-76 Torr shock tube Miller et al." (1982) flat flame burner mass spectroscopy gas chromatography UV spectroscopy 298-950 K; 100 Torr reaction cell Nicovich et al.14 (1982) flash photolysis resonance fluorescence 298-1000 K; 10-200 Torr reaction cell Nicovich and Ra~ishankara'~ flash photolysis (1984) resonance fluorescence 1515-2500 K; 0.2-3.0 atm shock tube Kern et al.I0 (1984) time-of-flight mass spectroscopy atomic resonance absorption spectroscopy laser-schlieren density gradients 1600-2300 K; 1.9-2.7 atm shock tube Hsu et al.19 (1984) CW CO laser 790-1400 K; 86-140 Torr flow reactor Madronich and Felder17 (1985) fluorescence spectroscopy 1200-2400 K shock tube Colket16(1986) single pulse gas chromatography ref
The stable species profiles imply that acetylene (C2H2)may be an important intermediate in the conversion of C6H6 to CO. Bittner and Howard3 suggested attack by oxygen atoms as the major path for benzene consumption due to the early appearance of large mole fractions of C6H60 and C5H6. Hydrogen abstraction by H or OH was not considered to be a major route for C6H6destruction due to the low concentration of phenyl radicals (C6H5). Howard and McKinnon5 later found that H and OH attack on benzene under rich conditions occurred at a rate comparable to that of 0-atom attack. Howard and McKinnon also observed that the rates of benzene decay from 0, OH, and H attack were not sufficient by themselves to explain the rapid decay of benzene in rich flames. Venkat et al.6used a turbulent flow reactor at 1atm to obtain profiles of 11 stable species for C6H6/OZ/Armixtures with equivalence ratios ranging from 0.39 to 1.50. In a recent review of the oxidation of aromatics at high temperature, Brezinsky' reassessed and further interpreted the data of Venkat et al. On the basis of the order of appearance of the species maxima, an involved but qualitative benzene oxidation mechanism was proposed in which the benzene molecule is oxidized to the phenyl radical, forms phenoxy (C6H50)by addition of an 0-atom from 02,0, or H02,and subsequently decomposes to the cyclopentadienyl (C5H5)radical via CO expulsion. The C5H5radical then breaks down to the open-chain buta-
dienyl radical (C4H5)via attack by 0, OH and H02,and the C4H5radical finally decomposes to vinylacetylene, acetylene, and ethylene. Large concentrations of phenol were found by Venkat et a1.: which suggests that phenyl radicals are formed via H-abstraction by OH, H, and 0 atoms. This chemistry is quite complex, and rate coefficients for each reaction are unavailable at the present time. Venkat et al. observed, however, that if the butadienyl radical quickly falls apart to form acetylene and the vinyl radical (C2H3),then the phenyl oxidation mechanism can be summarized by CsH5+ O2 2CO + CzH2+ C2H3,as proposed by McLain et a1.8 In this study, we seek a quasi-global model of benzene oxidation for flame conditions; moreover, we assume that the major intermediate is the phenyl (C6H5)radical. By making this assumption, we are able to investigate which reactions are paramount in benzene oxidation and which reactions need further investigation. Although the proposed model is incomplete, we anticipate that it will guide further investigations that will more fully unravel the complex chemistry of benzene oxidation. 1.2. Preliminary Benzene Oxidation Model. A set of elementary and global reactions has been assembled from the literature to describe the oxidation and pyrolysis of benzene. All rate coefficients are given by the Arrhenius equation in its modified form
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k f = AT* exp( (5) Howard, J. B.; McKinnon, J. T. "Aromatics Oxidation and Soot Formation in Flames"; Presented at the DOE/BES Contractors Meeting, Argonne National Laboratory, Argonne, IL, 1985. (6) Venkat, C.; Brezinsky, K.; Glassman, I. Nineteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1982; p 143. (7) Brezinsky, K. Prog. Energy Combust. Sci. 1986, 17, 1.
$)
where k f is the forward rate coefficient, A is the pre-exponential factor, a is the temperature exponent, E is the (8) McL& A. G.;Jachimowski, C. J.; Wilson, C. H. NASA Technical Paper 1472; Langley Research Center: Hampton, VA, 1979.
Quasi-Global Model for Benzene Oxidation
Energy & Fuels, Vol. I, No. 5, 1987 407
Table 11. Preliminary Model for Benzene Oxidation (a = 0) no.
A, E, mol cma s cal/mol ref
reacn
1 2 3 4 5 6 7 8 9 10 11
Pyrolysis C& s? C6H5 + H C6H6 G C4H4 + CzHz C&3 + H ?i C&* C& C&7 C & 3+ H C&3 + H it CsH5 + H2 CeH.5 Ft C4H3 + CzHz C4H4F? C4H3+ H C4H4 s C4H2 + HZ C4H4 F? 2C2Hz C4H3 + H F! C4Hz + HZ C4H4+ H F! C4H3+ H2
5.OE+15 1.3E+14 4.OE+13 1.3E+16 3.OE+12 1.2E+15 7.1E+ll 1.OE+13 1.OE+13 2.OE+14 3.OE+14
108000 88000 4310 32200 8100 82000 65000 73000 80000 14500 14500
a b c
12 13 14 15 16
Oxidation C & 3 + 02 S C6H5+ HOz C& + 0 it C6H5 + OH C& + OH F? CBH5 + H20 C & 3+ HOz S CsH5 + HzOz C6H5 0 2 2CO + C2H2 + CzH3
6.3E+10 2.83+13 2.1E+13 l.OE+ll 7.53+13
60000 4910 4570 18200 15000
d
-+
-P
-+
c c
b b b b b b
e
f d g
'Hsu et al.19 *Kern et al.1° cNicovich and Ra~ishankara.'~ dFujii et aL9 e Nicovich et al." 'Madronich and Felder17 McLain et al.' 'Rate parameters of unimolecular reactions not corrected for pressure dependence.
activation energy (cal/mol), and R is the universal gas constant (1.9872 cal/(mol.K)). Units for lzf and A are s-l for unimolecular reactions and cm3/(moles) for bimolecular reactions. Table I summarizes the major experimental investigations used to develop the preliminary benzene oxidation model given in Table 11. All of the kinetic results were obtained in shock tubes, flow reactors, reaction cells, or flat flame burner systems. In 1974, Fujii et al.9 presented a 25-step mechanism to describe the ignition of lean mixtures of benzene in oxygen. Our work takes the basic structure developed by Fujii et al. and incorporates elementary and quasi-global reactions from more recent investigations to assemble an initial kinetic model. Pyrolysis reactions from Kern et al.l0are included for completeness. The oxidation of C1-C4 hydrocarbons, including H2 and CO kinetics, is considered by using the comprehensive 100-step acetylene mechanism of Miller et al." McLain et a1.8 have presented an oxidation model for benzene that is based largely on the work of Asaba and Fujii12and Fujii and Asaba.13 We incorporate their global route C6H5+ Oz 2C0 + C2H2+ C2H3for oxidation of phenyl in the preliminary kinetic model. This overall step bypasses the phenoxy (C6H50) cyclopentadienyl (C5H5) butadienyl (C4H5)route proposed by Venkat et al.6and Bre~insky.~ Nicovich et a l . I 4 have measured rate parameters for the C6H6+ 0 reaction using the pulsed photolysis/resonance fluorescence method. The products are assumed here to be those given by Fujii and Asaba13 (C6H5 OH). As there is no data for higher temperatures, we use the Arrhenius parameters given by Nicovich et al.14for the temperature range 298 < T < 867 K.
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(9) Fujii, N.; Asaba, T.; Miyama, T. Acta Astronaut. 1974, 1 , 417. (IO) Kern, R. D.; Wu, C. H.; Skinner, G. B.; Rao, V.S.; Kiefer, J. H.; Towers, J. A.; Mizerka, L. J. Twentieth Symposium (International)on Combustion; The Combustion Institute Pittsburgh, PA, 1984; p 789. (11) Miller, J. A.; Mitchell, R. E.; Smooke, M. D.; Kee, R. J. Nineteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1982; p 181. (12) Asaba, T.; Fujii, N. Thirteenth Symposium (International) on Combustion; The Combustion Institute Pittsburgh, PA, 1971; p 155. (13) Fujii, N.; Asaba, T. Fourteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1973; p 433. (14) Nicovich, J. M.; Gump, C. A.; Ravishanha, A. R. J.Phys. Chem. 1982, 86, 1684.
Nicovich and Ra~ishankara'~ studied the reaction of hydrogen atoms with benzene using pulsed photolysis/ resonance fluorescence over the temperature range 298-1000 K. Three elementary reactions were proposed: C6H6 + H F! C&* C6H7 C6H7 C& + H C6H6 H C&5 H2 +
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+
+
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Nicovich and Ravishankara observed that at temperatures greater than 600 K, the rate of the reverse reaction, C6H7 C6H6 H,is so large that the addition reaction is insignificant. Colket16also shows that the C6H7sequence is important only at low temperatures and that it has a negligible impact on benzene pyrolysis. Nevertheless, all three elementary reactions are included in the initial benzene model. The reaction C6H6+ H C6H5+ Hz is generally unimportant below loo0 K but may be significant at flame temperatures.15 Madronich and Felder17have determined that the reaction of hydroxyl radical with benzene procedes by two routes: C6H6 + OH e C6H5 H2O H C6H6 OH F? C&@H The mechanistic studies performed by Madronich and Felder at 1300 K show that the nonabstraction channel contributes less than 20% to the overall reaction rate. Tully et a1.18 also found that the abstraction route dominates at elevated temperatures. As reaction rate coefficients and detailed kinetics for phenol are not available, the nonabstraction channel is not included in the preliminary benzene model. Hsu et al.19 used a 25-step oxidation mechanism to fit rate coefficients for the unimolecular pyrolysis of benzene, C6H6F? C6H5+ H. These investigators based their study on reactions taken from Fujii and Asabamwithout utilizing the more recent data of Nicovich et al.,14 Nicovich and Ravishankara,15 and Madronich and F e l d e P for the reactions of benzene with 0, H, and OH, respectively. Hsu et al. also determined the CO sensitivity (% [CO] change) for the major benzene reactions under fuel-lean conditions. The order of importance of the reactions was found to be C6H6 F! C6H5 + H, C6H5 + 0 2 , C&6 + OH, and C6H6 + 0. As expected, the % [CO] change was quite insensitive to benzene attack by atomic hydrogen. 1.3. Flame Code. Predicted species profiles for onedimensional, premixed laminar flames can be obtained by solving the appropriate flame equations. Equations for continuity, conservation of species, and conservation of energy, an equation of state, and appropriate boundary conditions can be handled by a variety of numerical techniques. Warnatz21assessed the numerical methods used by eight groups that have developed laminar flame codes by comparing solutions for a standard hydrogen/oxygen flame.
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+
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(15) Nicovich, J. M.; Ravishankara, A. R. J. Phys. Chem. 1984, 88, 2534. (16) Colket, M. B., III. Prepr. Pap-Am. Chem. Soc., Diu. Fuel Chem. 1986, 31(2),98. (17) Madronich, S.; Felder, W. J. Phys. Chem. 1986, 89, 3556. (18) Tully, F. P.; Ravishanha, A. R.; Thompson, R. L.; Nicovich, J. M.; Shah, R. C.; Kreutter, N. M.; Wine, P. H. J. Phys. Chem. 1981,85, 2262. (19) Hsu, D. S. Y.; Lin, C. Y.; Lin, M. C. Twentieth Symposium (International) on Combustion;The Combustion Institute: Pittsburgh, PA, 1984; p 623. (20) Fujii, N.; Asaba, T. J. J. Fac. Eng., Uniu. Tokyo, Ser. B 1977, 34(1), 189. (21) Wamatz, J. In Numerical Methods in Laminar Flame Propagation; Peters, N., Warnatz, J., Eds.;Vieweg: Wiesbaden, FRG, 1982.
408 Energy & Fuels, Vol. 1, No. 5, 1987
The procedure developed by Smooke,' which employs a damped-modified/Newton method, correlated well with the results of the other methods and provided the second fastest code surveyed by Warnatz. A revised version of the code with full documentation is now available from Sandia National Laboratories.22 The same flame code has previously been applied to acetylenell and H2/Oz/ HCN/Ar23 flames. Smooke et al.24described the use of adaptive gridding to significantly reduce the number of subintervals needed in flame codes compared with codes that use equispaced meshes. Smooke26has supplied us with an updated version of the flame code that includes variable time stepping, which allows the step size to increase as needed for faster convergence. These two flame codes have been integrated and adapted for use on Purdue's CDC Cyber 205 by Bero2 of the Flame Diagnostics Laboratory. To compare predicted profiles from the flame code with the experimental results, it is preferable to replace the conservation of energy equation with an experimental temperature profile. The measured temperature profile leads to a more accurate solution of the species conservation equations and takes into account the actual distributed heat losses present in the flame. For these reasons, the measured temperature profile is employed in this investigation. 2. Experimental Apparatus and Procedures The trace-additive approach developed by Peterson and LaurendeauZ6is used in this investigation. A trace amount of benzene is added to an H 2 / 0 2 / N 2flame, which is characterized by relatively large concentrations of the primary OH, 0, and H radicals. Under such conditions, the concentrations of carboncontaining species such as CO, COz, and various hydrocarbons provide a direct link to the oxidizing additive; moreover, profiles of these additive-derived species are easily measured because of their absence in the undoped hydrogen-oxygen flame. This method allows study of a wide variety of hydrocarbon oxidation reactions with the help of calculated OH, 0, and H profiles by using the well-known hydrogen-oxygen kinetics. A lean (4 = 0.6) H2/02/C&/Nz flame is employed in this investigation, with a burner pressure of 76 Torr and a cold (298 K) gas velocity of 30 cm/s. Initial mole fractions of H2, 02,N2, and C6H6are 0.174, 0.173, 0.651, and 0.0022, respectively. The burner facility consists of a flat-flame burner, associated gas-mixing and liquid-injection systems, and a pressure vessel. The burner is a 6-cm porous-plug, flat-flame burner supplied by McKenna Products, Pittsburg, CA. The porous plug is internally cooled, and a guard ring supplied with inert gas is used to minimize entrainment of surrounding gases. The water used to cool the burner is maintained a t a constant temperature of 70 "C by a Lauda (Model RM6) constant temperature bath. The burner is also encased in a low-pressure aluminum vessel capable of containing flames from 10 to 760 Torr. Liquid injection is accomplished by using a Sage Instruments syringe pump (Model 352) supplied by Orion Research, Cambridge, MA. The gas-mixing facility and liquid-injection system have been described elsewhere.% Flow rates from the gas-mixing (22)Kee, R. J.; Grcar, J. F.; Smooke, M. D.; Miller, J. A. "A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames"; Sandia National Laboratories Report SAND85-8240;Sandia National Laboratories: Livermore, CA, 1985. (23)Miller, J. A.; Branch, M. C.; McLean, W. J.; Chandler, D. W.; Smooke, M. D.; Kee, R. J. Twentieth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1984;p 673. (24)Smooke, M. D.;Miller, J. A.; Kee, R. J. In Numerical Methods in Laminar Flame Propagation, Peters, N., Warnatz, J., Eds.; Vieweg: Wiesbaden, FRG, 1982. (25)Smooke, M.D.,Department of Mechanical Engineering, Yale University, New Haven, CT, personal communication, 1985. (26)Peterson, R. C.; Laurendeau, N. M. "A Kinetic Mechanism for Fuel-Nitrogen Conversion in Lean to Rich Flames"; Presented at the Spring Meeting, Central States Section, The Combustion Institute, Columbus, OH, 1982.
Jackson a n d Laurendeau Probe
Burner Frit
Singe Diaphrogm Pumps
Guard Ring
Temp
Figure 1. Schematic of sampling system. panel are monitored by using calibrated rotometers and are accurate to approximately &4% for all gases; the liquid-injection syringe pump is precalibrated to *0.5%. However, this error does not take into account any evaporative losses that might occur in the vaporization system or at the connection of the syringe to the gas panel. All gases and liquids have purities of a t least 99.9% except oxygen, which has a purity of 99.5%. Although the surface of the burner remains clean when pure Hz/O2/N2flames are used, a tar-like depcsit forms when these flames are doped with benzene and cold (16 "C) tap water is used to cool the burner. The burner deposits are avoided by using water a t 70 OC. This indicates that the deposits arise from condensation of species produced by pyrolysis/oxidation of benzene. The sampling system is shown in Figure 1. A quartz probe with a 100-pm sampling hole is used to obtain samples of combustion products from the low-pressure flame. Species profiles are obtained by moving the burner surface relative to the stationary quartz probe. The probe tip is cooled by cold tap water (-16 "C). To prevent condensation, heating tape is used to maintain the sample line a t 100 OC. The sample line includes two dual-chamber, Teflon-lined, diaphragm vacuum pumps manufactured by Thomas Industries, Sheboygan, WI (Model 2737VM390). The vacuum pumps are placed directly behind the quartz probe and are connected in series to give a sample-line pressure of 8 Torr. This system is required to provide a pressure ratio of 1 0 1 across the probe as recommended by Fristrom and Westenberg.n Gas samples are collected in 10-mL stainless-steel sample loops within a small oven prior to injection into the gas chromatographs. All tubing and connections are Teflon-lined stainless steel to reduce adsorption onto the walls of the tubing. Two separate gas chromatographs are used to analyze stable gaseous species via Supelco columns: MS-5A and Chromosorb 102 for fixed gases and 23% SP-1700 for c6 hydrocarbons and below. A Carle hydrogen-transfer tube is used for separation of hydrogen. The fixed gases (02, Hz, CO, COP)are monitored with two thermal conductivity detectors, while the hydrocarbons (CHI, CZH6, CsHs, C2H2,C6H6)are monitored with a flame-ionization detector. Each cycle of sample collection, injection into the gas chromatographs, and analysis takes over 2 h. A Varian controller/data recorder is used to control all switching, temperature programming, and data collection from the detectors. Standard gas samples are used to calibrate the experimental results for benzene and acetylene. Approximate errors based on repetitive calibrations with two standard gas samples are found to be *4% for benzene and *l%for acetylene. The concentration range is 20-1080 ppm for C6H6 and 15-45 ppm for C2H2. Details of the experimental setup and calibration can be found in ref 28.
3. Results and Discussion The temperature profile was determined by using a radiation-corrected BeO/Yz03-coated,75-pm Pt/Pt-10% Rh t h e r m o c ~ u p l e . ~The ~ temperature and species profiles (27)Fristrom, R. M.; Westenberg, A. A. Flame Structure; McGrawHill: New York, 1965,p. 181. (28)Jackson, M. C. M.S. Thesis, School of Mechanical Engineering, Purdue University, West Lafayette, IN, 1986. (29)Harris, M. M. M.S. Thesis, School of Mechanical Engineering, Purdue University, West Lafayette, IN, 1985.
Energy & Fuels, Vol. 1, No. 5, 1987 409
Quasi-Global Model for Benzene Oxidation
750
500
250
Distance above Burner ( c m )
0
0. 2
0. 4
0.6
0. E
1. 0
Distance above Burner (cm)
Figure 2. Experimental temperature profde for Hz/0z/C6H6/Nz flame, 4 = 0.6, P = 76 Torr.
Figure 3. Comparison of experimental benzene (0) and acetylene (0) profiles to predicted profiles for best-fit (-) and RRKM (- -) models. The nonzero CzHzconcentration predicted at the burner surface arises from multicomponent diffusion.
Table 111. Best-Fit Model for Benzene Oxidation (a = 0) A, E, no. reacn mol cm3 s cal/mol ref R1 C6H6 S CsH5 H 5.OE+15 108000 a 8100 b R2 C & 3+ H F? CsH5 + Hz 3.OE+12 4910 c R3 C & 3+ O F? CBH5 + OH 2.83+13 4570 d R4 C6H6 + OH F? C&5 + HzO 2.1E+13 24000 e R5 C6H5+ Oz 2 c 0 + CzH2+ C2H3f l.lE+15
~~
-*
'HSU et al.19 Nicovich and Ra~ishankara'~ Nicovich et al." dMadrovich and FeldeP e present study 'Plus 100-step acetylene mechanism of Miller et al."
were aligned by making all position measurements with respect to the burner surface. The experimental and smoothed temperature profiles are shown in Figure 2. The temperature at the surface of the burner was assumed to be 400 K. The smoothed temperatures were used as input to the flame code. Calibrated species profiles were obtained for C6H6and C2H2,the two species most directly affected by changes in the rate parameters of Table 11. Of the remaining measured species, only H2,C02,CO, and O2were both (1) incorporated in the preliminary benzene model and (2) available in sufficient quantity to obtain reliable concentration profiles. (We note, however, that the CHI and C21& peaks occurred at approximately 0.20 cm above the burner surface.) A calibrated profile for H2 concentration and relative profiles for the C02, CO, and O2 concentrations showed good agreement with predictions made with the final kinetic model. Especially good results were obtained for the H2 data; in particular, the peak experimental and calculated mole fractions agreed within 1% . Since these profiles were influenced significantly by the acetylene mechanism, only the C6H6and C2H2profiles were employed to evaluate the preliminary benzene oxidation model. 3.1. Best-Fit Benzene Oxidation Model. The H2/ 02/C6H6/N2flame at @I = 0.6 and P = 76 Torr was modeled by using the Sandia flame code. The benzene reactions in Table I1 were combined with the acetylene mechanism of Miller et al.llto form a quasi-global benzene oxidation model. The transport and thermodynamic properties for C6H5and C6H7were assumed to be the same as those for C6H,. After many computer runs, reactions 1,5,13,14, and 16 of Table I1 were found to give essentially the same C6H6and C2H2profiles as all 16 reactions. The best fits to the experimental profiles for benzene and acetylene were obtained by using the rate coefficients given in Table 111,as demonstrated by the solid curves of Figure 3. As might be expected, replication of the data
Distance above Burner (crn)
Figure 4. Benzene production rate by various elementary reactions (Rl-R4; see Table 111) as a function of distance above the burner.
at 0.10 cm above the burner gave experimental deviations within the 4% and 1% calibration errors found for C6H6 and C2H2,respectively. All rate coefficients in Table I11 were taken from the literature, except that of the global reaction for phenyl oxidation, C6H6+ O2 2C0 + C2H2 C2H,. The rate coefficient for this reaction was found by varying the activation energy and the preexponential factor to match the location and amplitude, respectively, of the C2H2peak. The best-fit model determined in this investigation is similar to that proposed by Hsu et al.19 to explain benzene ignition under lean conditions in a shock tube. When the two benzyl (C6H7)reactions (Table 11)were added to the best-fit model, the only change was a slight dip in the benzene concentration in the first 0.05 cm above the burner. This region, with a temperature below 730 K, contains no experimental data; hence, the effect of the C6H, reactions cannot be verified. Our results, however, are clearly in agreement with those of Nicovich and Ravishankara,ls who indicate that the C6H7reactions are unimportant above 600 K. The CBH7reactions also have essentially no effect on the acetylene profile. If the remaining reactions in Table I1 are added to the best-fit model, virtually no change occurs in either the benzene or the acetylene profiles. Therefore, only the five reactions given in Table I11 are necessary to the best-fit model. 3.2. Relative Importance of Benzene Oxidation Reactions. Of the five reactions that make up the best-fit benzene model (Table 111), reaction R1 has the largest single impact on the benzene profile, as shown by the
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Jackson and Laurendeau
410 Energy &Fuels, Vol. 1, No. 5, 1987
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Distance above Burner (cm)
Figure 5. Phenyl production rate by various elementary reactions (Rl-R5; see Table 111) as a function of distance above the burner. production rate of C6H6 in Figure 4. This result follows from the large reverse rate of the decomposition reaction, C6H6e C6H5 H. In the early, low-temperature portion of the flame, benzene is produced from R1 almost as fast as it is destroyed by reactions R3 and R4. This behavior is similar to that found by Baldwin et for benzene oxidation at 500 "C, where about 10-20% of the phenyl radicals reacted with Hz to regenerate benzene. The order of importance of the reactions controlling benzene decay is R3 > R4 > R2, except at very early times where R4 > R3. This is the same order found by Hsu et al.19 for ignition of lean mixtures. The order will clearly change under richer conditions. Reaction R5 affects the benzene profile in a secondary manner through the rate of oxidation of phenyl radicals. Since phenyl produces benzene via the reverse of R1, the slower the forward rate of R5, the longer benzene remains in the flame. The molar production rate of phenyl (C6H5) by all five reactions is shown in Figure 5. Note that R5 consumes C6H5much more slowly than R1. The normalized sensitivity is defined as21 A y k m a = aAi
0
0.4
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Distance obove Burner (cm)
Figure 6. Normalized sensitivity of benzene concentration to rate coefficients for reactions Rl-R5 (see Table 111).
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where Ykmmis the maximum mass fraction of the kth species in the flame and Ai is the preexponential factor of the ith reaction. The sensitivities are calculated by employing the Jacobian matrix used to determine the predicted species profiles for the best-fit benzene Using a normalized sensitivity prevents anomalous values in the post flame zone due to the very low species concentrations in this region. Figure 6 shows the normalized sensitivity of benzene concentration to changes in the forward rate coefficient of reactions Rl-R5. The benzene concentration is most sensitive to changes in the rate coefficient of R1 and least sensitive to R2. An increase in the forward rate coefficient of R1 causes a large increase in the concentration of C6H6due to its extremely large reverse reaction rate (e.g., at 0.2 cm, T = 1050 K, k f = 1.5 X ~O-'S-~, and k, = 9.5 X lo1' cm3/(mo1.s). The reverse reaction rate increases faster than the forward rate at all temperatures. As anticipated, consumption of C6H6by H is unimportant under fuel lean conditions compared to oxidation by 0 and OH. The relative importance of the remaining reactions R3-R5 varies. At low temperatures, R4 > R3 > R5; near the middle of the flame zone, R3 > R4 > R5; and a t high temperatures, R5 > R3 > R4. (30)Baldwin, R. R.; Scott, M.; Walker, R. W. Twenty-First Symposium (International) on Combustion; The Combustion Institute: Pittaburgh, PA, 1986, in press.
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Figure 7. Forward rate Coefficients for various rate parameters of the elementary reaction CsHs F! CsH5+ H: (A) Hsu et (B)Kern et al.;l0 (C) Fujii et al.;9(D)Colket;16 (RRKM data) Kiefer and Shah.32
3.3. Rate Coefficient for C6H6e C6H5+ H. The rate coefficient determined by Hsu et al.19for the unimolecular reaction C6H6 2 C6H5+ H gives the best fit to the experimental benzene decay data. Hsu et al. fit their kinetic data at 1.9-2.7 atm and 1600-2300 K. They also found high-pressure rate parameters of A = 5.75 X 10l6s-l and E = 116000 cal/mol. Kiefer et al.,31 in their study of benzene pyrolysis, used RRKM theory to model the effect of pressure on this reaction at 140-740 Torr and temperatures from 1900 to 2400 K. Good agreement was found between the rate coefficient measured by Hsu et al.19 and that predicted by using the RRKM model at 2.3 atm and between 1600 and 2400 K. At our request, Kiefer and,Shah32extended their RRKM calculations to a pressure of 76 Torr and a temperature range of 400-1400 K. An Arrhenius fit gives log A = 15.2 f 7.9, CY = 0.44 f 2.37, and E = 114 200 f 3500 cal/mol, where the errors represent 2 standard deviations. Figure 7 shows a comparison of Kiefer and Shah's forward rate coefficient and those obtained by extrapolating Hsu et al.'s rate coefficient to a temperature range of 400-1400 K. The rate coefficients of Kern et al.,l0 Fujii et a1.: and ColkeP are included for comparison. As shown in Figure 3, the RRKM results strongly overpredict the benzene decay rate. In contrast, the rate coefficients of Kern et a1.,I0 Fujii et al.,9 and Colket16underpredict the benzene decay rate. Compared to the CzHz (31) Kiefer, J. H.; Wei, H. C.; Kern, R. D.; Wu, C. H. Znt. J. Chem. Kinet. 1985, 17, 225.
(32) Kiefer, J. H.;Shah, J. N., personal communication, 1986.
Energy &Fuels, Vol. 1, No. 5, 1987 411
Quasi-Global Model for Benzene Oxidation
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