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Energy & Fuels 2008, 22, 1610–1619
Detailed Kinetic Modeling of Particulate Formation in Rich Premixed Flames of Ethylene Andrea D’Anna* Dipartimento di Ingegneria Chimica, UniVersità di Napoli “Federico II”, Piazzale V. Tecchio, 80-80125 Napoli, Italy ReceiVed October 30, 2007. ReVised Manuscript ReceiVed January 18, 2008
A detailed kinetic mechanism of aromatic growth and particulate formation is presented, and it is tested over a range of different operating conditions in rich premixed laminar flames of ethylene. The model includes reaction pathways leading to the formation of molecular particles and their coagulation to soot by using a discrete-sectional approach for the gas-to-particle process. Good predictions are obtained of major oxidation and pyrolysis products, as well as of trace species, particulate concentrations, and particle size distributions. At low flame heights and in nonsooting conditions, the model predicts particle size distribution functions with a single mode centered at about 2 nm, in good agreement with experimental data. At increasing flame heights in sooting flames, the particle size distribution function develops toward a bimodal shape. Modeled data shows the formation of a large number concentration of particle smaller than 3 nm, which are not currently detected by standard techniques based on the measurement of particle mobility. Sensitivity of the predictions to the particulate-phase reaction rates is performed. Model analysis shows the importance of the mechanism of aromatic-molecule addition to aromatic radicals in the formation of nanosized particle and the importance of acetylene addition in soot loading.
Introduction The formation of combustion-generated particles is a central topic of research activities in the field of combustion of fossil fuels. It is driven by the concern about the adverse effects that combustion-formed particulate have on human health and on climate.1,2 In recent years, much progress has been made in the understanding of particulate formation in combustion. The current picture of particulate formation in flame environments considers acetylene and aromatic compounds the main precursors of particles.3–5 Benzene and polycyclic aromatic hydrocarbons (PAHs) are formed close to the flame front of aliphatic fuel flames; thereafter, they grow in the postflame regions reaching the molecular masses of the incipient soot particles (103–104 Da which correspond to equivalent spherical sizes of a few nanometers). Aromatic and acetylene addition through surface reactions on the incipient particles and structural rearrangements contribute to soot particle loading and mature soot particle formation. The formation of aromatics in laminar premixed flames has been followed by probe sampling and chemical analysis of * Corresponding author. Tel.: +30 081 768 2240. Fax: +39 081 593 6936. E-mail:
[email protected]. (1) Lighty, J.; Veranth, J. M.; Sarofim, A. F. J. Air Waste Manage. Assoc. 2000, 50, 1565–1618. (2) Kennedy, I. M. Proc. Combust. Inst. 2007, 31, 2757–2770. (3) Haynes, B. S.; Wagner, H. Gg. Prog. Energy Combust. Sci. 1981, 7, 229–273. (4) Bockhorn, H., Ed. Soot Formation in Combustion: Mechanisms and Models; Springer-Verlag: Heidelberg, 1994. (5) Abstracts of the International Workshop on Combustion Generated Fine Carbon Particles, Villa Orlandi, Italy, May 13–16, 2007; available online at http://www.irc.cnr.it/gif-jpg/DANNA/DANNA-SERVER/workshopcompleto2.pdf or http://primekinetics.org.
reaction products6–13 and by the spectroscopic characterization of the flames.14–16 The growth process has been followed in situ by the measurement of the scattering in excess to that of gaseous compounds,17,18 by time-of-flight mass spectrometry,19–21 and by probe sampling followed by detailed particle size distribution (PSD) measurements with differential mobility (6) Bockhorn, H.; Fetting, F.; Heddrich, A. Proc. Combust. Inst. 1986, 21, 1001–1012. (7) Bockhorn, H.; Fetting, F.; Heddrich, A.; Wannemacher, G. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 819–825. (8) Ciajolo, A.; D’Anna, A.; Barbella, R.; Tregrossi, A.; Violi, A. Proc. Combust. Inst. 1996, 26 (2), 2327–2333. (9) Ciajolo, A.; D’Anna, A.; Barbella, R.; Tregrossi, A. The formation of volatile hydrocarbons, benzene and polycyclic aromatic hydrocarbons in the fuel-rich combustion of ethylene. First European Congress on Chemical Engineering, ECCE1, Florence, Italy, May 4–7, 1997. (10) Ciajolo, A.; D’Anna, A.; Barbella, R. Combust. Sci. Technol. 1994, 100, 271–281. (11) Lam, F. W.; Howard, J. B.; Longwell, J. P. Proc. Combust Inst. 1989, 22, 323–332. (12) Marinov, N. M.; Pitz, W. J.; Westbrook, C. K.; Castaldi, M. J.; Senkan, S. M. Combust. Sci. Technol. 1996, 116-117, 211–226. (13) Castaldi, M. J.; Marinov, N. M.; Melius, C. F.; Huang, J.; Senkan, S. M.; Pitz, W. J.; Westbrook, C. K. Proc. Combust. Inst. 1996, 26, 693. (14) Harris, S. J. In Soot Formation in Combustion. An International Round Table Discussion; Vandenhoeck & Ruprecht: Gottingen, 1990; p 101. (15) Minutolo, P.; Gambi, G.; D’Alessio, A.; D’Anna, A. Combust. Sci. Technol. 1994, 101 (1/6), 309–325. (16) D’Alessio, A.; D’Anna, A.; D’Orsi, A.; Minutolo, P.; Barbella, R.; Ciajolo, A. Proc. Combust. Inst. 1992, 24, 973–980. (17) D’Alessio, A.; D’Anna, A.; Gambi, G.; Minutolo, P. J. Aerosol Sci. 1998, 29 (4), 397–409. (18) Minutolo, P.; Gambi, G.; D’Alessio, A.; Carlucci, S. Atmos. EnViron. 1999, 33 (17), 2725–2732. (19) Bachmann, M.; Wiese, W.; Homann, K.-H. Proc. Combust. Inst. 1996, 26, 2259. (20) Thierley, M.; Grotheer, H.-H.; Aigner, M.; Yang, Z.; Abid, A.; Zhao, B.; Wang, H. Proc. Combust. Inst. 2007, 31, 639–647. (21) Apicella, B.; Carpentieri, A.; Alfè, M.; Barbella, R.; Tregrossi, A.; Pucci, P.; Ciajolo, A. Proc. Combust. Inst. 2007, 31, 547–553.
10.1021/ef700641u CCC: $40.75 2008 American Chemical Society Published on Web 04/01/2008
Particulate Formation in Ethylene Premixed Flames
analysis (DMA),22–24 atomic force microscopy (AFM),25 and size exclusion chromatography (SEC).26 The formed molecular particles coalesce forming larger particles; the resulting size distribution functions of the particles show a bimodal shape in the initial stages of soot formation with a the first mode due to particles with sizes of the order of 1–5 nm and a second mode constituted by primary soot particles with sizes of the order of 20–30 nm.22–25 The particle coalescence regime is followed by particle agglomeration into chainlike structures as shown by electron microscopy measurements.27 The new data has stimulated modeling activity.28–36 Most of the modeling work has focused on the prediction of the flame structure, in terms of concentration profiles of pyrolysis and oxidation products.28Several works have focused on the predictions of the mean properties of particulate, including volume fractions, and mean particle sizes,29–32 whereas just few works have focused on the prediction of PSD and on the testing of the sensitivity of PSDs with respect to operating parameters.33–36 Models focused on PSD predictions neglect to simultaneously compare gas-phase flame products although the correctness of the particle predictions relies on the accuracy of the species profiles supplied by the gas-phase. Moreover, particle dynamics affect the correctness of species profiles of intermediates compounds, particularly benzene and PAHs. This paper presents a detailed kinetic model of particulate formation able to describe the current picture of soot formation in premixed flames of ethylene with the aim of predicting both the concentration profiles of trace pyrolysis products involved in the process of particulate formation and the details of PSDs. Comparison of model predictions with experimental data have assisted the model development. The actual kinetic model is a development of a previous PAH formation model37 which now includes also reaction pathways responsible for molecular particle nucleation, i.e. the transition from gas-phase species to nascent particles, and their coagulation to larger soot particles. (22) Zhao, B.; Yang, Z.; Johnston, M. V.; Wang, H.; Wexler, A. S.; Balthasar, M.; Kraft, M. Combust. Flame 2003, 133, 173–188. (23) Sgro, L. A.; De Filippo, A.; Lanzuolo, G.; D’Alessio, A. Proc. Combust. Inst. 2007, 31, 631–638. (24) Zhao, B.; Yang, Z.; Li, Z.; Johnston, M. V.; Wang, H. Proc. Combust. Inst. 2005, 30, 1441–1448. (25) Barone, A. C.; D’Alessio, A.; D’Anna, A. Combust. Flame 2003, 132 (1/2), 181–187. (26) Alfè, M.; Apicella, B.; Barbella, R.; Tregrossi, A.; Ciajolo, A. Energy Fuels 2007, 21 (1), 136–140. (27) Lahaye, J.; Prado, G. In Particulate Carbon: Formation during Combustion; Siegl, D. C., Smith, G. W., Eds.; Plenum: New York, 1981, pp 33–35. (28) Frenklach, M. Phys. Chem. Chem. Phys. 2002, 4, 2028–2037. (29) Frenklach, M.; Wang, H. In Soot Formation in Combustion: Mechanisms and Models; Bockhorn, H., Ed.; Springer-Verlag: Heidelberg, 1994; pp 165–192. (30) Frenklach, M.; Wang, H. Proc. Combust. Inst. 1990, 23, 1559. (31) Wang, H.; Frenklach, M. Combust. Flame 1997, 110, 173. (32) Appel, J.; Bockhorn, H.; Wulkow, M. Chemosphere 2001, 42, 635– 645. (33) Singh, J.; Patterson, R. I. A.; Kraft, M.; Wang, H. Combust. Flame 2006, 145 (1–2), 117–127. (34) Marchal, C.; Moréac, G.; Netzell, K.; Kasper, M.; Mauss, F. The Pressure Dependence of Soot Particle Size Distribution Functions. Third European Combustion Meeting ECM, Crete, Greece, April 1–13 2007; paper 4.7. (35) Blanquart, G.; Pitch, H. A Joint Volume-Surface-Hydrogen MultiVariate Model for Soot Formation. In International Workshop on Combustion Generated Fine Carbon Particles, Villa Orlandi, Italy, May 13–16, 2007. (36) D’Anna, A.; Alfè, M.; Apicella, B.; Tregrossi, A.; Ciajolo, A. Energy Fuels 2007, 21 (5), 2655–2662. (37) D’Anna, A.; Violi, A. Energy Fuels 2005, 19 (1), 79–86.
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A discrete-sectional approach38,39 is used for the modeling of the gas-to-particle process; the ensemble of aromatic compounds with molecular mass higher than the largest aromatic compounds in the gas-phase (pyrene) is divided into classes of different molecular mass and all reactions are treated in the form of gas-phase chemistry using compound properties such as mass, numbers of carbon and hydrogen atoms averaged within each section. With the sectional method approach, the molecular mass distribution of the species is obtained from the calculation and not hypothesized a priori. The model has been tested in different flame conditions in order to verify its capability to match the main experimental evidence and to test the sensitivity of particulate concentration and PSDs with respect to the kinetic rates used. Model Development Particulate formation in flames of aliphatic hydrocarbons has been schematized in partially parallel processes. In the following a description of the main reaction steps is presented whereas the detailed reaction mechanism is available in the Supporting Information. Formation of Gas-Phase Aromatics. The formation and growth of aromatic compounds bridges the main oxidation chemistry and particulate formation. During oxidation hydrocarbon fuel generates small radicals which react to form the first aromatic ring. The gasphase kinetic mechanism to model hydrocarbon oxidation and pyrolysis is built on the GRI mechanism for C1 and C2 species.40 Reactions are added to extend the mechanism to higher hydrocarbons and to account for the formation of benzene.41,42 The formation of phenyl radical and benzene is considered to occur through two reaction pathways: the addition of n-C4H3 and n-C4H5 to C2H2, leading to phenyl and benzene + H, respectively, and the self-combination of propargyl radicals. Details of the reaction pathways leading to benzene and the reaction constants used is reported elsewhere.37 The formation of naphthalene, the first compound in the PAH series, is modeled through two routes: the first is the sequential addition of C2H2 to phenyl radical; the second is the combination of resonantly stabilized radicals. The first mechanism is usually known as the HACA mechanism (H-abstraction-C2H2-addition).29 It occurs by way of a two-step process involving hydrogen abstraction to activate aromatics, followed by subsequent acetylene addition. This process is also used here to model the formation of multiring structures such as phenanthrene and pyrene (the largest compounds modeled explicitly). By-products of the HACA process are ethynyl-substituted PAH and five-membered aromatics such as acenaphthylene. Two different reaction sequences of resonantly stabilized radicals are included for the formation of naphthalene: the combination of two cyclopentadienyl radicals12,13 and the combination of benzyl and propargyl radicals.43 In rich ethylene flames the combination of benzyl and propargyl radicals is the dominant source of naphthalene, although this reaction have a high activation energy. Reaction rates for the resonantly stabilized radical combination pathways are evaluated by assuming activation energy equal to the heat of reaction.37 The pathway involving the combination of (38) Pope, C. J.; Howard, J. B. Aerosol Sci. Technol. 1997, 27, 73–94. (39) Richter, H.; Granata, S.; Green, W. H.; Howard, J. B. Proc. Combust. Inst. 2005, 30, 1397–1405; http://web.mit.edu/anish/www/ MITcomb.html. (40) Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty, N. W.; Eiteneer, B.; Goldenberg, M.; Bowman, C. T.; Hanson, R. K.; Song, S.; Gardiner, W. C., Jr.; Lissianski, V. V.; Qin, Z. http://www.me.berkeley.edu/ gri_mech/index.html. (41) Musick, M.; Van Tiggelen, P. J.; Vandooren, J. Bull. Soc. Chim. Belg. 1996, 105 (9), 555–574. (42) Miller, J. A.; Melius, C. F. Combust. Flame 1992, 91, 21–39. (43) Colket, M. B.; Seery, D. J. Proc. Combust. Inst. 1994, 25, 883.
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resonantly stabilized radicals is also used for the modeling of phenanthrene through the cyclopentadienyl and indenyl radical combination. Growth of Aromatics and Particle Inception. Acetylene and aromatics, from benzene to pyrene, are the building blocks for the growth process which leads to the formation of high-molecularmass, molecular particles. The mechanism consists in the sequential addition both of acetylene and aromatic molecules to aromatic radicals. Acetylene addition is the extension of the HACA mechanism to larger compounds with the assumption that, due to the high number of sites where acetylene can be attached, it is possible to hypothesize that each acetylene addition sequence forms a closed aromatic ring and hence it leads to the formation of fully condensed aromatic structures. This is possible in view of the fast migration of radical sites on aromatic molecules as molecular mass increases.44 Aromatic molecule addition to aromatic radicals leads to the formation of aromatic-aliphatic linked, biphenyl-like, compounds. This reaction sequence is favored by the presence of a non negligible concentration of five-member ring PAHs in the PAH inventory. These compounds grow rapidly forming resonantly stabilized radical intermediates.45,46 Acetylene and the aromatic addition sequences begin with the H-loss of an aromatic compound to produce the corresponding PAH radical either through decomposition reactions of aromatics or H-abstraction by H and OH radicals. Aromatic radicals can react with other aromatic radicals or with H atoms ending the growth sequence. Iteration of these pathways leads to the formation of a large number of high-molecular-mass compounds and of its structural isomers. The increasing number of species formed with increasing molecular mass makes impossible to follow the evolution of single compounds. Instead, starting from pyrene, classes of compounds, each covering a mass range, have been utilized. Classes are characterized by their average molecular mass and by the number of carbon and hydrogen atoms. Reactions are treated in the same way as for gas-phase chemistry. The aromatic growth and oxidation mechanism is schematized as follows: Ai ⇒ Ri + H
(Rx1)
Ai + H ⇒ Ri + H2
(Rx2)
Ai + OH ⇒ Ri + H2O
(Rx3)
Ri + H2 ⇒ Ai + H
(Rx4)
Ri + H2O ⇒ Ai + OH
(Rx5)
Ri + C2H2 ⇒ Ai + H
(Rx6)
Ri + Aj ⇒ Ai+j + H
(Rx7)
Ri + Rj ⇒ Ai+j
(Rx8)
Ri + H ⇒ Ai
(Rx9)
Ai + OH ⇒ Ak + HCO
(Rx10)
Ri + O2 ⇒ Ak + 2CO
(Rx11)
The sectional size dependence in reactions Rx1 and Rx6 are obtained by interpolating the kinetic data of the MIT kinetic scheme.39 For all other reactions size dependence is obtained from gas-kinetic theory with an exponent of 2/3 for a gaseous species colliding with a particle (surface area to volume ratio) and with 1/6 for a particle to particle collision based on the average size of the two particles.47 Rate constants for the aromatic growth mechanism are evaluated on the basis of structural similarities with the reaction rates of PAHs. The rate of hydrogen loss via the unimolecular reaction (Rx1) is evaluated using as reference the rate of benzene decomposition. Initiation reactions (Rx2 and Rx3) are reversible, and the forward reaction rates are assumed to be equal to H atom abstraction from naphthalene molecules. The reaction rate is scaled by the variation in collision efficiencies to take into account the increase of reactivity. Equilibrium of the initiation reactions (Rx4 and Rx5) is strongly affected by the number of C atoms in the molecule. Radical compounds composed of a large number of C atoms are stable enough to survive in their radical form, because of the delocalization of the unpaired electron resulting in a lower rate of the reverse reactions.48 At present, reverse reaction rates (Rx4 and Rx5) for the lumped species belonging to the first three classes of compounds (300–1200 Da) are here evaluated from equilibrium constant of coronene. For larger molecular masses, thermodynamic properties are not known; in these cases, reactions Rx4 and Rx5 are considered irreversible. The rate constant for acetylene addition to aromatic radicals (Rx6) is based on the reaction rate of naphthyl + acetylene scaled by increasing collision efficiencies. On the basis of structural similarity, the rate constant for phenyl + benzene is used as the reference for the corresponding aromatic radical + aromatic molecule reaction (Rx7) which is scaled for variation in collision efficiencies. Termination reactions of aromatic radicals with other aromatic radicals (Rx8) or with H atoms (Rx9) ending the growth sequence have rate constants evaluated from the collision efficiencies of the reacting species. Hydroxyl radical [OH] was identified by Neoh et al.49 to be the dominant oxidizing species of soot in flames. The activation energy for Rx10 is estimated from similar reactions for benzene and PAH’s, and the collision frequency accounts for the size of the oxidized particles from Neoh et al. data. Oxidation by O2 molecules (Rx11) uses the rate constant of naphthyl + O2 accounting for the increase of the collision efficiency of large species.50 Coagulation. The aromatics growth process can occur also by formation of molecular clusters after the collision of molecular compounds. Ai + Aj ⇒ Ai+j
(Rx12)
Here, Ai is an aromatic compound having a molecular mass corresponding to the ith class of compounds and Ri is its radical. The first lumped species (Ai and Ri with i ) 1) have 24 C-atoms and are formed by the self-combination of gas-phase aromatic radicals and reactions between gas-phase aromatic radicals and gasphase aromatic molecules, similar to reactionsRx8 and Rx7 in the growth mechanism.
Colliding molecular particles coalesce completely yielding new spherical structures, whereas larger particles may agglomerate into chainlike structures. At present, the model does not account for the formation of chainlike structure, and each collision is considered coalescent; this hypothesis can be accepted considering that the flames studied are not fully sooting and the agglomeration process of soot is not so active. The interaction energy in this case is due to van der Waals forces. Small molecular mass aromatics may exhibit low interaction energy to form a stable three-dimensional structure at flame temperatures. As the molecular mass of the aromatic compounds increases, because of the aromatic growth pathways, the van der Waals interaction energy between high molecular mass aromatic molecules increases and the coagulation efficiency becomes more effective.
(44) Moriarty, N. W.; Frenklach, M. Proc. Combust. Inst. 2000, 28, 2563–2573. (45) D’Anna, A.; Violi, A.; D’Alessio, A.; Sarofim, A. F. Combust. Flame 2001, 127 (1/2), 1995–2003. (46) Violi, A.; Sarofim, A. F.; Truong, T. N. Combust. Flame 2001, 126, 1506–1515.
(47) D’Anna, A.; Kent, J. Combust. Flame, 2008, 152, 573-587. (48) Howard, J. B. Proc. Combust. Inst. 1990, 23, 1107–1127. (49) Neoh, K. G.; Howard, J. B.; Sarofim, A. F. Proc. Combust. Inst. 1985, 20, 951–957. (50) Xu, F.; El-Leathy, A. M.; Kim, C. H.; Faeth, G. M. Combust. Flame 2003, 132, 43–57.
Particulate Formation in Ethylene Premixed Flames This simple consideration has been used by D’Alessio et al.51 to explain the low coagulation efficiency measured in premixed flames of ethylene. In their approximation coagulation is considered to depend on two phenomena: the collision rate, determined from gaskinetic theory applied to large molecules and the pairwise interaction between particles according to a Lennard-Jones attractive and repulsive potential. The energy of interaction between two particles is given by the sum of all the interactions between molecules which constitute the particles. Thus the energy of interaction is a function of both the geometry of the interacting particles and of their physicochemical characteristics through the Hamaker constant.52 In this formulation, energy redistribution inside the forming clusters is completely neglected. Although this is an approximation the simple model reproduces the experimentally observed low coagulation efficiency of small particles in premixed flames well.18,51 The low coagulation efficiency is in agreement with the results obtained by Wong et al.53 on the lifetimes of dimers of aromatics having aromatic-aliphatic-linked structures. These compounds show a lower lifetime, i.e. lower coagulation efficiency, with respect to pericondensed aromatics having the same molecular weight. It is beyond the purpose of this paper to go deeply into the details of the coagulation mechanism which requires a molecular dynamic approach. Here, the simple model proposed by D’Alessio et al.51 is applied. Particle collision efficiency has been evaluated for a Hamaker constant 5 × 10-20 J. This value of the Hamaker constant is typical of benzenic rings (3 × 10-20 J) more than of graphite (5 × 10-19 J). A variation of the Hamaker constant as a function of the change of the chemical structure of the particles toward mature soot should be considered. Computations. Premixed flame modeling is performed by solving species mass fraction balance. Experimental temperature profiles are used as input to the model in order to reduce the uncertainties in the heat loss through the cooling system of the burner and the radiative heat loss due to particles. An accurate temperature profile is needed since temperature strongly affects the concentration profiles particularly of trace compounds. The equations are solved in elliptic form. In the present work, species include the gas-phase molecules and the particulate sections, the particle size classes, as described by Pope and Howard38 and Richter et al.39 Particle size distribution is defined by a range of sections, each containing a nominal hydrocarbon species in order of increasing atomic mass. The carbon number of each section ranges from 24-4 × 108, a particle size range of 1–250 nm if a density varying from 1.2 to 1.8 is considered. Twenty six sections are used in a geometric series with a carbon number ratio of two between sections. This distribution is considered to give adequate resolution of particle size distribution and the range is large enough not to constrict the scheme. The decrease of the H/C ratio with increasing particle size is fixed by definition of the number of carbon and hydrogen atoms in each section; it ranges from 0.5 in the first section down to 0.08 in the last section. Characteristics of the sections are given elsewhere.54 Transport and thermodynamic properties for the gas-phase species are from Chemkin55 database. Diffusivities of the large sectional species are obtained from Stokes friction with Cunningham (51) D’Alessio, A.; Barone, A. C.; Cau, R.; D’Anna, A.; Minutolo, P. Proc. Combust Inst. 2005, 30 (2), 2595–2603. (52) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: London, UK, 1991. (53) Wong, D.; Schuetz, C. A.; Frenklach, M. Molecular Dynamics Simulations of PAH Dimerization. In International Workshop on Combustion Generated Fine Carbon Particles, Villa Orlandi, Italy, May 13–16, 2007. (54) D’Anna, A.; Kent, J. Combust. Flame 2006, 144 (1–2), 249–260. (55) Kee, R. J.; Rupley, F. M.; Miller, J. A.; Coltrin, M. E.; Grcar, J. F.; Meeks, E.; Moffat, H. K.; Lutz, A. E.; Dixon-Lewis, G.; Smooke, M. D.; Warnatz, J.; Evans, G. H.; Larson, R. S.; Mitchell, R. E.; Petzold, L. R.; Reynolds, W. C.; Caracotsios, M.; Stewart, W. E.; Glarborg, P. CHEMKIN Collection, release 3.5; Reaction Design, Inc.: San Diego, CA, 1999. (56) Friedlander, S. K. Smoke, dust and haze: fundamentals of aerosol behaViour; John Wiley & Sons: New York, USA, 1977.
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Figure 1. Comparison between experimental data and model results for acetylene (C2H2), allene (CH2CCH2), and propyne (CH3CCH) in an ethylene/O2 flame with C/O ) 0.80 and a cold gas velocity of 4 cm/s. Data are from refs 8 and 9.
correction factors based on the Knudsen number.56 Thermophoretic flux is applied to sections.
Results and Discussion The kinetic mechanism is used to model particulate formation in different atmospheric pressure premixed ethylene flames operating in slightly sooting and sooting conditions. The flames have been characterized by using different experimental approaches and techniques obtaining experimental data which cover the main flame structures, the aromatic formation and growth, and the particle dynamic. The first set of experimental data used is a sooting premixed flame of ethylene/oxygen at C/O ) 0.80 with a cold gas velocity of 4 cm/s.8,9 The model well reproduces the main flame structure: maximum reactant consumption occurs at about 1.5 mm above the burner in correspondence to the maximum flame temperature, thereafter oxidation products, CO and CO2, and pyrolysis products, methane, acetylene, propene, allene, butadiene, and benzene are the dominant species in the postoxidation zone of this flame. Figures 1 and 2 report the comparison between experimental and modeled concentration profiles of acetylene, allene, propyne, butadiene, and benzene.
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Figure 2. Comparison between experimental data and model results for 1,3-butadiene (CH2CHCHCH2) and benzene (C6H6) in an ethylene/ O2 flame with C/O ) 0.80 and a cold gas velocity of 4 cm/s: (- - -) model results obtained by removing the particulate mechanism from the kinetic scheme. Data are from refs 8 and 9.
Acetylene and C3 hydrocarbons (Figure 1) show typical profiles of stable pyrolysis products since they maximize downstream of the flame front and thereafter their concentrations reach a constant value in the post flame region. 1,3-Butadiene (Figure 2) shows a similar profile but it reaches negligible values in the post flame region indicating its role as intermediate specie. Benzene (Figure 2) shows a rise-decay profile and a slight increase in the postflame region in this flame condition. The decrease of benzene concentration at the flame front is due both to the high temperature in this flame region which causes benzene decomposition and to molecular growth leading to higher molecular mass aromatics. Model predictions are in good agreement with experimental data for both major compounds and trace species. Modeled concentration profiles of gas-phase PAHs are reported in Figure 3 compared with the experimental data.8,9 Naphthalene and acenaphthylene are the most abundant PAHs. They are formed just downstream of the maximum concentration of benzene. The model well reproduces both the concentration profiles of each PAHs (comparison is made on a linear scale) and also the decrease of PAH concentration moving from naphthalene to pyrene. It is interesting to note that the amount of either benzene and PAHs is reasonably well reproduced if the gas-phase submechanism is coupled with the particulate submechanism. If the particulate submechanism is removed from the kinetic scheme the amount of aromatics predicted by the model is much higher. Indeed, aromatics are building bricks of the molecular growth process and of particulate formation and hence are continuously consumed by particle nucleation and surface reactions. Figures 2 (lower part) and 3 show as dashed lines the concentration profiles of benzene and aromatics predicted in this latter case (particulate mechanism removed from the
Figure 3. Comparison of modeled concentration profiles naphthalene, acenaphthylene, phenenthrene, and pyrene with experimental data in an ethylene/O2 flame with C/O ) 0.80 and a cold gas velocity of 4 cm/s: (- - -) model results obtained by removing the particulate mechanism from the kinetic scheme. Data are from refs 8 and 9.
kinetic scheme). About 70% of the carbon in benzene and PAHs formed when particle formation is removed ends up in particulate matter. Particulate concentration profile is reported in Figure 4 and compared with the experimental data.8 The model predicts a monotonic increase of the concentration of particulate which starts with a high formation rate just downstream of the flame front and levels-off in the postflame region.
Particulate Formation in Ethylene Premixed Flames
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Figure 4. Particulate concentration profile along the axis of an ethylene/ O2 flame with C/O ) 0.80 and a cold gas velocity of 4 cm/s. Data are from ref 8.
Figure 6. Comparison of experimental condensed species and soot concentration profiles with modeled data in an ethylene/O2 flame with C/O ) 0.80 and a cold gas velocity of 4 cm/s. Modelled CS comprises particles with sizes up to 7 nm whereas soot comprises particles with sizes larger than 7 nm. Data are from ref 8. Figure 5. Predicted molecular mass distribution of particulate at 10 mm from the burner exit in the C/O ) 0.80 ethylene/O2 flame. The vertical line distinguishes regions between CS and soot.
Modeled particulate is defined as the sum of all gas-phase PAHs and all sectional species from 24 C-atoms upward whereas experimental particulate includes PAHs and highmolecular-mass compounds, both constituting the so-called condensed species (CS), and soot. The condensed species and soot are operationally defined classes of compounds separated from each other on the basis of their solubility/insolubility in dichloromethane. Recently, Ciajolo et al.26 have shown that the different solubility of CS and soot reflects the different molecular mass distributions of these two classes of compounds: CS comprise both PAH with molecular masses in the range 200 and 1000 Da and species with molecular masses up to 100 000 Da whereas soot is composed of species with molecular masses higher than 100 000 Da. The use of the sectional method allows the molecular mass distribution of combustion-formed particles to be numerically obtained and to distinguish three fundamental types of particles by size: PAHs with molecular size between 128 and 300 Da, (particles with equivalent sizes lower than 1 nm), molecular particles with masses between 300 and 100 000 Da (particles with equivalent sizes from 1 to 7 nm) and soot particles with masses higher than 100 000 Da (particles with equivalent sizes from 7 to 250 nm). Figure 5 reports the computed molecular mass distribution of the particulate formed in the ethylene/oxygen flame at 10 mm from the burner exit. The molecular mass distribution is similar to that experimentally found26 and allows to calculate the concentrations of CS (particles with sizes lower than 7 nm) and soot (particles with sizes larger than 7 nm) along the flame. Figure 6 reports the comparison between model prediction and experimental concentration values of CS and soot. The
concentration profiles of CS is reasonably well predicted whereas the concentration of soot is underestimated by 30%. It has been established that benzene and particulate concentration profiles, CS and soot, are strongly affected by flame temperature.8 Figure 7 (upper part) reports the comparison of the model results with benzene concentration profiles measured keeping constant the C/O ratio at 0.80 and changing the cold gas flow velocity from 2 to 6 cm/s, which correspond to different maximum temperatures.8 As already shown, benzene shows a rise-decay profile and a gentle increase in the postflame region in the intermediate temperature flame (cold gas flow velocity V ) 4 cm/s, Tmax ) 1650 K). In the highest temperature flame (cold gas flow velocity V ) 6 cm/s), about 1750 K at the peak value, benzene concentration increases to a maximum value downstream of the flame front and decreases to very low values in the postoxidation zone of the flame (dashed-point line), due to decomposition more than to oxidation or molecular growth. In the lowest temperature flame (cold gas flow velocity V ) 2 cm/s), about 1550 K at the peak value, benzene profile shows a continuous rise downstream of the flame front and a level-off in the postflame region (dashed line). The model reproduces reasonably well, in comparison with experimental data, the three concentration profiles of benzene in the ethylene flames showing the importance of flame temperature in determining the behavior of benzene concentration profiles. The model is also able to reproduce the variation of particulate concentrations by changing the maximum flame temperatures from 1550 and 1750 K as shown in Figure 7 (intermediate part). The increase of the temperature causes a reduction of the concentration of particulate. The increase of the temperature in the range examined determines a first increase of the soot concentration and a decrease in the highest temperature flame. The model is able to
1616 Energy & Fuels, Vol. 22, No. 3, 2008
D’Anna
Figure 7. Concentration profiles of benzene, particulate, and soot along the axes of three ethylene flames with C/O ) 0.80 and different cold gas velocities: (b, - - -) V ) 2 cm/s (Tmax ) 1550 K); (0 —) V ) 4 cm/s (Tmax ) 1650 K); (2 - - - -) V ) 6 cm/s (Tmax ) 1750 K). Data are from ref 8.
reproduce the bell-shaped behavior of soot concentration as a function of the temperature as shown in Figure 7 (lower part) where experimental and modeled soot concentration profiles in the three flames are reported. Model predictions indicate that temperature affects also the size distribution functions of the particulate. Figure 8 reports the predicted size distribution functions along the axis of the three ethylene flames. The lowest temperature flame is characterized by the formation of particles with fully developed bimodal size distribution functions with the first mode in the 1–2 nm range and a second mode with particles between 20 and 200 nm (Figure 8a). As temperature is increased from 1550 to 1650 K, the first mode remains unchanged whereas particles belonging to the second mode have lower sizes (from 10 to 200 nm Figure 8b). In the higher temperature conditions (1750 K), the second mode is less evident than before (Figure 8c). These results can be explained with a continuous nucleation of nanosized particles in the lower temperature flames due to the formation of benzene and gas-phase aromatics also in the postoxidation region of the flames. Newly nucleated particles react with already-formed soot particles increasing their sizes.
Figure 8. Predicted size distribution functions in the particle range between 1 and 200 nm along the flame axes of three ethylene flames with C/O ) 0.80 and different cold gas velocities: (a) V ) 2 cm/s (Tmax ) 1550 K); (b) V ) 4 cm/s (Tmax ) 1650 K); (c) V ) 6 cm/s (Tmax ) 1750 K).
In the highest temperature flame, both benzene and gas-phase aromatics are almost completely decomposed downstream of the flame front and cannot contribute to the growth of aromatics and nucleation of new particles. As a consequence the increase of soot particle size is reduced. Comparison of model results with the probe data8,9 has allowed us to show that the developed kinetic mechanism is able to reproduce the main flame structure and the formation of soot, PAHs and condensed species quite well but do not allow us to verify the aromatic growth model, due to the lack of experimental data on the details of particle dynamic in these flames. In the last years, D’Alessio and co-workers17,18 have reported a series of experimental data on the dynamic of the particles formed in slightly sooting ethylene flames. Through
Particulate Formation in Ethylene Premixed Flames
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Figure 9. Concentration profiles of soot (b) and molecular particles ()) and mean particle sizes (0) along the axis of a C/O ) 0.77 ethylene/ air flame. Experimental data are from ref 17. The dashed line represents the modeled concentration profile of PAHs.
in situ optical measurements they were able to follow the concentration profiles and the mean sizes of two classes of particles: visible-transparent nanoparticles and soot particles. Figure 9 (upper part) reports the comparison between predicted and measured concentration profiles of both classes of particles measured in a C/O ) 0.77 ethylene/air flame. Model predictions agree well with experimental data. The experimental concentration profile of visible transparent nanoparticles shows a fast increase in the main oxidation zone of the flame up to 2 mm and a decrease after 4 mm in correspondence of soot inception. Soot concentration starts after 4 mm and increases in the postflame region. The model is able to correctly reproduce the formation of high-molecular mass compounds which precedes soot inception, the soot inception delay and the soot concentration profile. Modeled high-molecular mass compounds formed before soot are mainly composed of PAHs (dashed line in Figure 9) and molecular particles with sizes between 1 and 7 nm. The mean sizes of the formed particulate have been experimentally determined by using scattering and extinction measurements. Figure 9 (lower part) reports the comparison between measured D63 (mean size derived by scattering/extinction measurements) and predicted ones. The model is able to reproduce the formation of small-size particles in the region of the flame where soot is not formed yet, below 4 mm, and the fast increase of particle sizes at the soot inception. The good agreement of model predictions with the experimental results indicates that the proposed kinetic model is able to predict not only the total amount of particulate matter but also its molecular growth. To better check the capability of the model to reproduce the concentration profiles and the sizes of soot and molecular particles, a laminar premixed flame of ethylene studied by Wang and co-workers22 has been modeled. These authors have used a nanoscanning mobility particle sizer to measure the size distribution functions of the particles formed at different heights
Figure 10. Size distribution functions of the particles along the axis of a C/O ) 0.69 ethylene/air flame. From bottom to top size distributions at 15, 7, and 6 mm height Experimental data are from ref 22.
along a C/O ) 0.69 ethylene/air flame. The adopted measuring technique was able to detect particles in the range 3–80 nm. Figure 10 shows the comparison of the modeled size distribution functions with experimental data at three heights along the flame axis, namely 6, 7, and 15 mm. In agreement with experimental results, the model reproduces a unimodal size distribution function at lower heights in the flame (6 mm) and the development toward a bimodal size distribution function at higher flame heights (7 and 15 mm). Modeled data cover a size range wider than the experimental one, between 1 and 250 nm and clearly shows the presence of a large number concentration of particle smaller than 3 nm, with a peak at about 1.5–2 nm. Modeled data however are not able to reproduce the clear dip experimentally found crossing from the first to the second mode of the particle size distribution function. The model predicts the number concentration profile of particles with sizes larger than 3 nm within an order of magnitude (full line) and a large number concentration of small particles (size
