Article pubs.acs.org/EF
Large Scale Chemical Kinetic Models of Fossil Fuel Combustion: Adequate as Engineering ModelsNo More, No Less Keith Schofield* Materials Research Laboratory, University of California, Santa Barbara, California 93106, United States ChemData Research, Inc., P.O. Box 40481, Santa Barbara 93140 ABSTRACT: Computers and integration codes now provide for mega-size modeling of chemical kinetics. Although complex and often speculative, this can be surprisingly successful in approximately reproducing experimental data for fossil fuel combustion. How such agreements can occur generally remains neither questioned nor discussed in spite of the now large number of differing fuels and blends that are being investigated. On the contrary, the conclusion invariably is that such models are indeed valid. In reality, this is impossible simply due to the complex nature of the differing chemistries involved for which kinetic information remains sparse. The present analysis and assessment discusses the reasons for their apparent success, the overlooked guidance that has always been available, and their ultimate limitations. A suggestion is that they be referred to as engineering chemical simulations and be tailored toward reduced schemes. They should not become regarded as a basis for specific chemical insights for which there can be no foundation now or in the foreseeable future.
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INTRODUCTION Combustion is a major component of our modern day energy needs and is likely to remain so throughout this century. Although predominantly based on carbon fuels, there could be a modification over time away from current “old-carbon” sources such as oil, natural gas, and coal. The past decade has seen the beginnings of this, with engineering modifications toward biofuels, with ethanol being the current major commercially produced alternate. The fact that such bioproducts are seen as a zero-carbon addition to the environment is a strong motivator, but even this factor is debatable and has to be carefully assessed for correctness in each case.1,2 This is especially important as many newly suggested biofuels already are being considered and modeled, although their commercial viability remains unanalyzed. Generally, these fuels can all be categorized as partially oxygenated organic compounds. Those familiar with the literature will be well aware of this extensive interest in alternate oxygenated fuels and how it has escalated the field of chemical kinetic modeling. Previously concerned mainly with pollutants, such as NOx, this explosive interest in oxygenated fuels and their individual ignition/combustion parameters and potential emissions is such that well over one hundred relevant major kinetic modeling papers have appeared in the last two years and now are emerging at an ever increasing pace. Each of these studies of a wide range of oxygenated fuels and blends presents very large chemical mechanisms aimed at reproducing experimental data to an acceptable approximation. In each case a statement of validation of the specific chemical mechanism is evident even though these models can differ very significantly from fuel to fuel. This is a remarkable occurrence, and its casual acceptance is incredible. After analyzing this entire literature, one is left with the affirmation that any fuel can be readily modeled to reproduce data acquired from any of the myriad of differing analytical methods. The fact that this is never generally commented upon, especially when it is clearly apparent that many of these models are chemically flawed, forms the basis of © 2012 American Chemical Society
this paper. The issue is not raised even in the latest review of combustion kinetic modeling.3 As a result, a further aspect addressed herein concerns the nature of the potential value of these models. Are they already more than adequate as engineering tools, and can they convey any insight into the chemistry of combustion, which seems to be a growing interpretive temptation? Consequently, with an emphasis on the last two years of research, the experiences with modeling have been carefully assessed and the reason for their apparent success modeling the combustion of fossil fuels is analyzed. Also, there is a consideration of whether there should be concerns that this is being misconstrued and taken as a basis for stating specific chemical conclusions.
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LARGE CHEMICAL KINETIC MODELS The availability of ChemKin4 and other integration codes coupled to ever larger computers now has facilitated analyses of extensive chemical reaction schemes. Early modeling of methane flames had found this to be adequately achievable. However, a decade ago it was noted for methane that four different models could reproduce the same experimental measurements with a similar level of accuracy.5 This was in spite of the fact that of the 44 most sensitive chemical reactions, the various models utilized significantly different rate constants for 14 of these reactions. What soon became apparent was an insensitivity of the models to exactness. This appeared to be a common aspect of organic combustion chemistry as it became extended to other hydrocarbons. It generalized further into a similar adequacy for low carbon content alcohols and ethers. As a result, in the past decade with a major justification being the predictability of potential emission problems and usage of more environmentally sensitive fuels, kinetic modeling has embraced Received: May 18, 2012 Revised: August 5, 2012 Published: August 7, 2012 5468
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depend on these compilations. Otherwise, estimates are used. Consequently, it is beyond question that a reasonable fraction of the rate constants in all current models are not accurate. Also, cursory examinations show that in many cases, due to a lack of data, some species generally are never included. Two examples would be C2O and C2. Interest is now turning to the former of these as being a possible major player in combustion, and it was always felt in early measurements on C2 that a good fraction of the combustion carbon preceded through this species.45 Consequently, it was intriguing when there was a rush to add organic−enol intermediates to models the moment they were observed in molecular beam mass spectrometric (MBMS) monitoring.46,47 The apparent success of chemical kinetic modeling has to be intriguing to chemists especially when compared to other computerized large modeling concepts in chemistry that were never equally successful. One example would be models such as those describing chemical thermodynamic equilibrium distributions. A decade ago, an ambitious program to model coal combustion and its trace impurities was attempted.48 It was a significant endeavor to predict the potential interactions between all the active ingredients in coal, but met with limited success. This stemmed from the fact that condensed phases of some species are involved for which the thermodynamic data remain nonexistent. This is still the case for many inorganic compounds, particularly mixed metallic materials. However, in this case, the required values can not be readily calculated theoretically or reliably estimated. As a result, the output from such calculations becomes controlled by a necessarily incomplete database and can be questionable. Because of this, thermodynamic equilibrium programs although in general use and of value, do operate at times under this sometimes overlooked limitation.
the oxygenated fuels in general. This has blossomed not only in the number of publications but also disturbingly into the size of the chemical models. For example, for methyl stearate combustion, the latest model now contains 6203 species and 43 444 reactions,6 or for a 2-methyl, C20 alkane hydrocarbon flame 7200 species and 31 400 reactions.7 Both models were “validated” against experimental data. Table 1, which is a random sample of a few of the most recent publications, clearly illustrates this point. This table shows the very diverse range of organics currently being examined many of which severely lack kinetic reaction rate data from direct measurements. In addition the table lists the various types of experimental data against which these models are compared. Whether the experimental data is based on highly sophisticated sampling and real-time analysis or uses other methods of collecting flame samples with subsequent analysis does not appear critical. The fact that the chemistry, occurring on nanosecond time scales, can be meaningfully sampled at all and give reasonable values is noteworthy. This in itself has to imply that there is an underlying buffering of the species relative distribution that is modifying at a much slower rate. The level of chemical complexity in any one of these models is hard to mentally conceive without actually examining their full list of reactions. Figure 1, for ethyl butanoate, and Figure 2, for n-butylbenzene oxidations, portray a small fraction of this by illustrating parts of the initial primary breakdown channels in their large networks of reactions. Numerous other studies now have extended even further by modeling fuel blends such as one mixture of methyl octanoate, n-decane, and 1-methyl naphthalene that considered 1964 species connected by 7748 reactions at a pressure of 6−10 atm in a stirred reactor.36 Other examples include the modeling of ethanol/n-heptane (1758 species, 3153 reactions),37 ethanol/ methyl octanoate (1087 species, 4592 reactions),38 propene with either ethanol or dimethyl ether,39 n-decane/n-dodecane/isooctane,40 toluene/1-hexene, n-heptane or iso-octane mixtures, 1-hexene/iso-octane with 1550 species and 6000 reactions,41 and methyl palmitate/n-decane or methyl decanoate/methyl 9-decenoate/n-heptane.42 All such studies conclude that these can likewise be modeled with adequate accuracies. Whenever such extreme complexity is encountered, it necessarily raises questions. It seems that the computer has brought us to a point when such efforts are so large that they can no longer be adequately published or reviewed. The model and its conclusions have to be accepted somewhat on faith. As discussed below, questions of accuracy are very difficult to assess, as also are any type of error limits. More importantly, model restrictions generally are vague with little indication of the consequences of operating at other than the tested condition. Moreover, the question of whether a larger model is better has to be addressed especially when errors necessarily exist in the model and also to some degree in the validating experimental data. There have been only a few papers published attempting to discuss such aspects, mainly in the area of sensitivity analyses, and even fewer that try to explain why it is that such modeling manages to give reasonable answers. It is to be remembered that in most of these models only a small fraction of the required reaction rate constant data have been experimentally measured. Moreover, any required reaction branching ratio values are almost nonexistent. It is now apparent that although valuable at the time, compilations of rate data such as GRI-Mech 3.043 were quite deficient and incorrect in many ways. Even the more recent tabulations by Baulch et al.44 now require updating. Nevertheless, many models still
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WHY ARE MOST CHEMICAL KINETIC MODELS ADEQUATE FOR ORGANIC FUELS? On ignition, combustion reactions differ from other chemistries in that the kinetic propagation rates are large. They generally approximate to the actual molecular collision frequency and have rates further accelerated by chain branching. As a result, species are formed and destroyed in times measured on nanosecond scales at atmospheric pressure. Creighton49 was among the first to realize not only that methane combustion could be modeled by a limited number of about 30 reactions, but more importantly that soon after ignition certain “chemical balances” between species were apparent. The consequence of this was to introduce an insensitivity to the required exactness in values for the individual rate constants. Since then, he has further developed these ideas theoretically showing that steady-state concentrations of radicals and ″the time constants for achieving steady-states are an inherent feature of any reaction mechanism″.50,51 The concept of the rapid formation of a radical pool in acetylene combustion was proven by measurements of the C2 and CH radical concentrations in the burned gases of a series of fuel-rich flames.52 These are two chemically very different intermediate species. CH is the more reactive and in the flames studied had a half-life of about 50−120 ns. On the other hand that for C2 was about 150−560 ns. As a result, it was unexpected that the relative concentrations of the two species when measured over a 0.5 ms burned gases decay region clearly indicated that they were tracking one another. No direct chemical connection between the species was possible. On assessing many of the potentially important fast chemical reactions in these 5469
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1-C3H7OH (CH3)2CHOH 1-C4H9OH
1-propanol 2-propanol 1-butanol
5470
HCHO CH3CHO
formaldehyde
acetaldehyde
aldehyde
CH3COC2H5
2-butanone
ketone
(CH3O)2CH2 (C2H5O)2CH2
dimethoxymethane diethoxymethane
double ether
ring ether
ether
1-C4H9OH C2H5CH(OH)CH3 (CH3)3COH 1-C4H9OH C2H5CH(OH)CH3 (CH3)2CHCH2OH (CH3)3COH CH3OC2H5 C2H5OC2H5 t-C4H9OCH3 t-C4H9OC2H5 c-C4H4O
C2H5OH
ethanol
alcohol
1-butanol sec-butanol t-butanol 1-butanol sec-butanol iso-butanol t-butanol methyl ethyl ethyl ethyl t-butyl methyl t-butyl ethyl furan
i-C4H8
iso-butene
alkene
56 50
107
234
107
206
351 178
568
1369
546
1368
1051
7000
300
215
3608
large
large 281
7000
252
520
300
36
99
2800 complex
C16H34 C7H14
c-alkane
11000 model
11000
2800
alkane 31400 3401
no. species/reactions 7200 714
structure C7H16−C20H42 n-C8H18 C8H18 C8H18 C8H18 C8H18 C16H34
fuel
2-methyl alkanes n-octane 2-methyl heptane 3-methyl heptane 2,5-dimethyl hexane 2,2,4-trimethyl pentane 2,2,4,4,6,8,8heptamethylnonane n-hexadecane methyl cyclohexane
category
Table 1. Recent Examples of Chemical Kinetic Models for Various Organic Fuels
model fit to data from three premixed, 50 mbar, Φ = 1.4, 1.8, 2.2 flames; MBMS analysis of 40 species; complex reaction network; reasonable agreement in spite of uncertainties Three doped, Φ = 2.5, C2H4/O2/Ar 50 mbar flames, MBMS analysis of 22 hydrocarbon and 5 noncarbon intermediates; 72 reaction sub-mechanism listed: model validated. model fit to atm. pressure shock tube ignition delay data, Φ = 0.5−2; model correct in suggesting importance of CO structural bond fit to data of two premixed 30 mbar, Φ = 0.22, 1.09, flames; MBMS monitoring of CH2O, HCO, CO, CO2, and 7 noncarbon species: model validated. data from three flat premixed flames, 50 mbar, Φ = 0.75, 1, 1.25; MBMS analysis of 11 stable species and CH3; two models compared and significant differences reported
model fit to pyrolysis shock tube data of major stable species analyzed by gas chromatography; model inconsistent with FID observationsb
model fit to counterflow flame and previous data; limited stable species monitored by gas chromatography; too complex and speculative a breakdown networkb
fit to MBMS data, 3-premixed low pressure flames; not consistent with FID 0.5C atom pool lossb fit to ignition delays and doped CH4 diffusion flame data; stable species monitored by gas chromatography; deficiencies in modeling discussed
fit to data of 3 low-pressure Φ = 1.0, 1.75, 1.9, 20−40 mbar premixed flames; TOF mass spectral analysis of 40 species, masses 1−98 fit to MBMSa data from one lean premixed Φ = 0.225 flame with added H2, 40 mbar, 21 species monitored: model validated fit to data from three 50 mbar premixed flames, Φ = 0.75, 1.0, 1.25, 15 species monitored by MBMS; also, atm. pressure stirred flow reactor data at Φ = 0.25− 2.0, 890−1250 K; model branching to C2H4 and C2H5O as suggested by FID observations fit to counterflow flames and other available data; probe sampling of stable species with delayed gas chromatography: model validation 900−2000 K
model compared to limited shock tube ignition and jet stirred reactor data; adequate agreement for several stable species
model validated by flame, stirred reactor, and shock tube data model fit to laminar speed data of atm. pressure counterflow flames; minimal differences noted.
comment
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22
21
20
19
18
17
16
15
14
13
12
10,11
9
7 8
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a
5471
C5H11COOCH3 C6H13COOCH3 C9H19COOCH3 C9H19COOCH3 C11H23COOCH3 C13H27COOCH3 C15H31COOCH3 C17H35COOCH3
methyl stearate ethyl propanoate methyl butanoate methyl i-butanoate methyl butanoate ethyl butanoate
methyl methyl methyl methyl methyl methyl methyl methyl
hexanoate heptanoate decanoate decanoate dodecanoate tetradecanoate palmitate stearate
methyl linolenate
401 531 1251 1247 2012 3061 4442 6203
203 115
large
119 128 103 111 3500
large
2440 3236 7171 7775 13004 20412 30425 43444
1317 1011
large
885 954 826 885 17000
large
2210
8086
MBMS: molecular beam mass spectrometry. bInconsistency with FID expectations explained later.
saturated ester
methyl crotonate ethyl crotonate methyl acrylate ethyl acrylate methyl oleate methyl linoleate
unsaturated ester
HCOOCH3 CH3CHCHCOOCH3 CH3CHCHCOOC2H5 CH2CHCOOCH3 CH2CHCOOC2H5 C9H18C8H15COOCH3 C6H12C3H4 C8H15COOCH3 C3H6(C3H4)2 C8H15COOCH3 C17H35COOCH3 C2H5COOC2H5 C3H7COOCH3 i-C3H7COOCH3 C3H7COOCH3 C3H7COOC2H5
methyl formate
formate ester
C6H5C4H9
n-butyl benzene 404
335
C6H5C2H5
268
no. species/reactions
ethyl benzene
aromatic
structure 45
fuel CH3COOH
acetic
acid
category
Table 1. continued
models fit to jet stirred reactor data of stable intermediates; reaction mechanism generation software; inconsistent agreement with some data
fit to shock tube ignition, Φ = 0.25−2.0, and jet stirred reactor data, Φ = 0.5−1.0; analysis of stable products by gas chromatography; complex models and inadequacies indicated data from a jet stirred reactor, 500−1100 K, Φ = 1.0; analysis of 30 stable products by gas chromatography; reaction software generator, complex models inconsistent with FID expectationsb
complex models fit to data of a low pressure Φ = 1.56 flame; photoionization MBMS analysis of numerous carbon intermediates; factors of 2−3 or more uncertainty and unique pathways contrary to FID expectationsb
models fit to previous shock tube ignition and jet stirred reactor data; illustrates the chemical reaction complexity involved: models validated
24
model fit to data from three flat premixed, 50 mbar, Φ = 0.77, 0.9, 1.05, flames; MBMS analysis of 7 hydrocarbon and 7 other flame species; C2H4 and C2H2 species underestimated; no direct initial CO2 formation invoked blended into ethanol, 5 atm. pressure premixed flames, Φ = 1.7−2.2, probe sampler, stable product gas chromatographic/mass analysis; ambitious model including soot formation model fit to oxidation studies, jet-stirred reactor, 10 atm. pressure, Φ = 0.25−2.5; analysis of stable species by gas chromatography/mass analysis. five low-pressure laminar flames, Φ = 1−1.8, MBMS analysis, 4 noncarbon and 8 carbon species; primary channels inconsistent with FID observationsb models fit to shock tube ignition delay data Φ = 0.25, 1, 2; initiation reactions inconsistent with FID with too many primary CO, CO2 product channelsb
6
33
32
31
29,30
28
27
26
25
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Figure 1. Primary channels and reaction flux analysis for the oxidation of ethyl butanoate (C3H7COOC2H5) in a plug flow reactor. Reproduced with permission from ref 34. Copyright 2011 Elsevier.
Figure 2. Primary channels and reaction flux analysis for the low temperature oxidation of n-butyl benzene. Reproduced with permission from ref 35. Copyright 2012 Elsevier.
flames, it was found possible to assemble a network of reactions to illustrate species interconnectivity. This is reproduced in Figure 3, which clearly shows the chemical separation of CH from C2 and the large number of intermediates required to connect them. From this study, it became obvious that Creighton’s conclusions were correct. If there are a very large number of reactions that all rapidly interconnect the various
intermediates one to another, then the obvious consequence has to be the establishment of a steady state distribution. This general distribution then will gradually change and adjust in unison as various species are removed. Organic chemistry is so rich in energetic kinetic channels that there will invariably be multiple ways to produce or convert any one species into another. Any initial organic molecular structure 5472
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and probably best source for experimental data at present utilizes molecular beam mass spectrometry (MBMS).53,54 Such measurements assume the concept of minimal perturbation, which has to remain a questionable issue for some chemistries. However, to hopefully alleviate any such problem in the present situation, it has become standard to burn flames at reduced pressures. Ironically, whereas the existence of a steady-state distribution at atmospheric pressure can be rapidly achieved, as the pressure is lowered a point will be reached when it may become kinetically constrained and the benefits of buffering within the pool lost. As a result, the dilemma then can become that not only are the MBMS flame measurements corrupted, but the kinetic model itself loses its insensitivity to the rate constants and the mechanism. However, evidence seems to be that dropping to one-tenth of atmospheric pressure in the flames remains acceptable. In reality, for fossil fueled flames, MBMS data from atmospheric pressure flames with valid steady state distributions might in fact be quite adequate for testing engineering models. For other chemistries such as NOx modeling, sampling may be more critical and extensive developments have recently led to a quick-quench probe for sampling aircraft emissions.55
Figure 3. Rapid reactions of hydrocarbon and flame species that produce a steady-state pool of hydrocarbon radicals in acetylene flames.52
has to be broken down to the point that smaller carbon fragments can finally be converted to CO and CO2. Until then the carbon remains in the form of organic radicals that are rapidly interconnecting one to another. Occasionally, as already illustrated in Figures 1 and 2, kinetic models will produce reactive flowcharts showing a flux analysis of the individual reactions. These highlight the potentially major routes but unfortunately do not convey the interrelationships that exist between the species and fail to illustrate the fact that they have formed a pool of carbon species with its consequential significant implications.
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KINETIC MODELS AND THEIR COMPATIBILITY WITH FLAME IONIZATION DETECTOR DATA It would seem strange to couple the flame ionization detector (FID) to fossil fuel combustion modeling but they are in fact intimately connected, and unfortunately, this either has never been realized or accepted. It still remains totally ignored by the kinetic modeling community. This is especially disappointing because there is a specific need for any form of guidance when designing the basic architecture of kinetic models. To have ignored such a valuable source has been unfortunate. It could have and still can aid many researchers, but now being over fifty years old, the behavior of the FID is mainly lost in the archival literature and given little credence. However, the instrument remains and always has been an invaluable tool for chromatography. Fifty-four years ago, the FID was invented by chance.56,57 Trace samples of gaseous hydrocarbons were blended with pure H2 and burned as a small diffusion flame in air. It was noted that the measured level of chemi-ionization in the flame was linearly proportional to the amount of carbon in each sample. It in essence was acting as a very good carbon atom counter. If the same molecular amounts of CH4, C3H8, c-C6H12, C6H6, or 1,3C4H6 were added then the levels of recorded ionization approximated very closely to ratios in the proportions of 1, 3, 6, 6, and 4, respectively. This has been a very useful commercial analyzer and, for example, can integrate surprisingly well the carbon content of the complex mix of the hundreds of unburned hydrocarbons in automobile exhaust.58 It also proved useful to quantitatively measure the effluents in chromatographic separations. It was soon determined that the reaction producing the ionization was that between the CH radicals produced in the flame and atomic oxygen. However, as to how such a diverse array of hydrocarbons could each proportionally produce the corresponding equivalent amount of CH remained unresolved until quite recently.59 The answer, as outlined above, lay in the formation of a carbon steady-state radical pool. All hydrocarbons on combustion follow very fast stages of oxidation. While oxygen concentrations remain large, the chemical reactions proceed almost instantly to CO, CO2, and H2O with the subsequent almost quantum jump in temperature through the brief reaction-zone flame region. Depending on the
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CONSEQUENCES OF STEADY-STATES AND RADICAL POOLS The fact that steady-state distributions and radical pools exist in flames is the fundamental reason that has enabled oxygenated fuels and large chain hydrocarbons to be adequately modeled. It is the underlying simplicity necessary to overcome the deficiencies in the kinetic descriptions. All the radicals that can form will do so and have relative concentrations that persist in spite of their individual short lifetime. As mentioned above, this was why CH and C2 concentrations could be measured in the burned gases of some flames for periods more on millisecond time-scales. This resulted from the buffering effect produced by the existence of a total radical pool. Variations in one radical concentration will instantly be averaged over all. Due to this, models in fact do not have to be complete nor contain all the species to retain their approximate nature. A possible role for any one missing is lessened by the pool averaging. Additionally, errors in specific rate constants also are averaged and the overall degree of required exactness lessened. This is the basic reason why reduced mechanisms can be constructed and still remain adequate. In addition, because of this networking, no single rate constant can really be isolated in such a scheme and identified as either being correct or in error. Moreover, any alteration of its magnitude to better fit the data is not chemically valid unless that new value has been determined by other measurements unconnected with the system. Random modifications to rate constant values constitute empirical parametric changes that cannot relate to the true chemistry. Normally, due to the limitations of all these models, the radical concentrations and their ratios that emerge are values that result from the averaging by the pool buffering of the model’s total errors. An intriguing aspect of these kinetic modeling studies is their necessary dependence on being tested against experimental measurements. This carries the implicit assumption that such experimental data are valid and reflect reality in the flame. With kinetic rates that occur on nanosecond time scales, depending on the sampling system, a species concentration would normally change within the time frame of any measurement. The current 5473
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necessarily will contain an unrecognized bias. In other words if the initial reaction architecture of the predominant reactions is not consistent with FID predictions, it becomes questionable that it is chemically rigorous yet still may appear to be adequate. For example, in the combustion of an ether such as CH3OCH3 this has to predominantly form essentially CH3 and CH2O in its initial breakdown to reflect one carbon (CO) that will not produce carbon radicals. It is inconsistent if producing CH3OH and CH3 or CH2 type structures. The case of diethyl ether, C2H5OC2H5, similarly has to lose one carbon due to preoxidation. This means it has to produce a CO product in its primary reactions. In other words it has to produce the equivalent of C2H5 and CH3CHO. On examining some of the many kinetic models, their primary reactive breakdown of the fuel splinters into so many channels that the exactness required by the FID becomes rather difficult to assess. However, even the most cursory look at the network illustrated in Figure 1 indicates a dominant initial reaction producing the acid and ethylene which implies a loss to preoxidation of only one carbon and not the expected loss of 1.5 carbons. Consequently, without an initial foundational chemical correctness, the concept of improving such a model or adjusting it in any way would seem to be chemically meaningless.
equivalence ratio, it is only when the concentration of oxygen falls to sufficiently low levels that sustainable carbon radical concentrations can become established. These then rapidly form a pool of unburned carbon radicals that apportions the remaining total available carbon according to their interconnecting kinetic network. Because the FID flame conditions always remain invariant, the fractional share defining the CH concentration of the total unburned pool remains the same. Its concentration is a direct reflection of the quantity of unburned carbon in the pool, which is directly proportional to the total carbon input. The fact that benzene, C6H6, with its aromatic structure gave a measure 6-fold larger than the simple alkane, CH4, indicated that there necessarily had to be such an underlying simplification occurring in the combustion. Soon after its initial development, researchers started measuring the FID ionization responses of organic molecules other than for the individual hydrocarbons. They had noted few if any anomalies with any hydrocarbon type be it saturated, unsaturated, cyclic, branched chain, or even aromatic. Only acetylene behaved slightly anomalously,59 and this only for acetylene itself and not for its larger derivatives such as methyl or ethyl acetylene.60 However, it was immediately apparent that the FID did show a precise sensitivity to the presence of oxygen in an organic structure. Any containing a CO bonding structure such as ketones, aldehydes, or organic acids essentially counted all the carbons except that one. The combustion treated the CO structure as an already internally oxidized carbon that could not participate in any radical pool. Ethers were found to react similarly and not respond to one carbon in the structure even if in a ring structure such as with furan, c-C4H4O. However, seemingly bizarre, primary alcohols counted all the carbons except for one-half of a carbon. Secondary alcohols could lose the effect of about three-quarters of a carbon atom but tertiary alcohols only about one-quarter. Methyl and ethyl esters such as acetates or as large as butyrates consistently had 1.5 carbons not counted, behaving as a molecule with both a CO and a COH type structure. Double esters such as oxalates, malonates, succinates, glutarates, or adipates all tended to behave similarly as expected indicating that values closer to three carbons in the structure were already oxidized.61 A partial list of such FID responses available in the literature for these and other oxygenated organic structures was recently tabulated.59 This consistent structural behavior was more general than being solely a feature of the FID and was later reproduced in low-pressure premixed flame studies examining the ionization levels with 29 different organic fuels.60 The results implied that organic structures did not burn in a chemically independent or unique manner but favored specific breakdown channels that led to similar pools of unburned carbon and hence similar CH concentrations. Consequently, the FID behavior clearly prescribes guidelines for the necessary predominant breakdown channels for correctness. A kinetic model is required to be consistent with this structural behavior to be chemically valid. The models that have been published are complex partly due to the multitude of potential major reactions with H, O, OH, and O2 besides other species that are included in the total model. Moreover, many of these reactions have a variety of branching; also organic molecules have carbon chain structures that can be attacked at numerous sites. Consequently, with little guidance, some models often invoke channels that are not consistent with FID expectations. In spite of such errors, a model still will produce a pool of radicals over which the carbon is distributed. Due to the error averaging, it can still look reasonable and be assumed to be acceptable but
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SENSITIVITY AND ERROR ANALYSES Many excellent papers have analyzed and suggested methods to resolve the question of a model’s adequacy. The major problem, as in most models is that it can only be judged on its contents. No program can indicate what may be missing or what is in error. The assumption made is that the model is complete but may have deficiencies only in the values of some of its rate constants. Sensitivity analysis methods are based on accepting such limitations. These were developed soon after ChemKin.62 Their purpose is to examine flux rates in the model and establish the critical reactions. As illustrated in more detail,63 such analyses become highly mathematical. Their results are only as meaningful as is the model. In other words if the model contains fundamental errors, these percolate through the analysis and can give erroneous biases. Examples have been noted that, even when differing parameter sets exist, identical concentration profiles still can be produced by a model.63 One further technique recently developed outlines a theoretical validation of a suggested mechanism.64 This is an ambitious approach that tries to ensure all the chemical reaction steps are included and theoretically then individually calculates those uncertain rate constants and enthalpies. The model is updated as it is screened through this adding of refined values. Methanol, already quite extensively studied, was chosen as the example case with 18 species and 93 reactions. Such a method may be of value to fine-tune well-established simple models with small molecular sizes, but the theoretical calculation of rate constants for larger molecules is still a very demanding task even if possible and also with uncertain errors.65 To calculate even a single rate constant generally constitutes a scientific paper. Recent examples have calculated the rate constants for OH with n-butanol, C4H9OH,66 H, and CH3 with i-C5H1267 and OH, and O2 with phenoxy (C6H5O).68 These illustrate the level of effort and complexity. It seems very ambitious to now suggest the calculation of hundreds or thousands! Moreover, even then such efforts ultimately still require experimental validation, another very demanding task that requires expertise.69 The most recent suggestion is to have a global data collection effort. This conceives of refining a model by utilizing large data banks of experimental measurements 5474
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gathered from around the world using a wide range of techniques.70 Although initially aimed at refining models for hydrogen combustion, this will encounter the above-mentioned dilemmas for precisely modeling fossil fuels. It has to be assumed that the fundamental reaction architecture is correct. However, the reaction complexity is such that there are always numerous adequate models that can fit any data. Alternate channels can invariably be invoked to be equivalent such that no sufficiently accurate experimental data can distinguish them from the chemically rigorously correct singular solution. There are simply too many variables. No method, other than through chemical experience or new insights or information from further experimentation enables errors to be corrected in a model. However, as already pointed out, the chemistry can even be largely insensitive even to changes of adding species, activation energies, or a further mechanism. Mathematical techniques now are available to discriminate between models,71 but are especially intriguing when we know that all the models are necessarily flawed. Nevertheless, it is this rich chemical nature discussed above with carbon-based fuels that makes these models so alluring that they can remain somewhat adequate. This is the true discovery that is their value. Consequently, it is easy to see how a false illusion of correctness has infiltrated such a discipline. There can be no justification for fitting a model to experimental data by randomly modifying individual rate constants other than for converting the model into an empirical fit. Due to such uncertainties it seems hard to even justify enlarging or “improving” models solely on a basis of better experimental data fits.
The example of soot formation or more importantly its inhibition has emerged as one major justification for the use and modeling of oxygenated fuels. However, it is a little disconcerting again that the input from archival research and related FID data have been ignored or are being gradually rediscovered. For example, Schmieder in 198482 using C14 studies traced the structural source of the carbon in soot. In this sublime paper, it was shown then that the CO carbon in benzoic acid was absent in combustion generated soot, as was only one-half of the COH carbons in 1-butanol combustion. The labeled methyl carbon in toluene was only slightly different from any of the six ring carbons. It is quite remarkable that even then and not until recently was it noted that such structural behavior for soot formation mimicked exactly that seen in FID relative ionization responses. A more recent study by Buchholz et al.83,84 repeated this C14 labeling method but for dibutyl maleate (CHCOOC4H9)2 combustion. This unsaturated double-ester again clearly confirmed that the chain carbons and butyl carbons, saturated or unsaturated, were all randomly present in the soot. The two CO carbons played no role. Although the oxygen was not measured it was speculated therein that some CO2 might be formed directly from the COO groups. This is a very important statement, because the question of what happens to the oxygen in oxygenated fuels is pivotal to their fundamental ability to reduce soot formation and does need to be considered correctly. Single esters were examined extensively in the FID and shown to always break down to show a CO radical and an RO oxy-radical. These would consistently result in reducing the radical pool by about 1.5 carbons (depending slightly on the structure of the RO radical) and never indicated any suggestion of a one carbon/ two oxygen atom loss.59 Coupled to earlier studies,59 a significant paper in the chromatographic literature measuring the FID sensitivities of double esters does in fact imply the answer to this speculation of direct CO2 formation.61 Such sensitivities are the calibration factors used in chromatography for quantifying effluents from separation columns that utilize FID detection. However, due to the difficulty of injecting known quantities of trace levels of such organic materials into an FID they have never been particularly easy to measure with great precision. Nevertheless, with care they can be obtained with reasonable accuracy that is confirmed by several independent studies. In the present case, the question to be answered concerning the behavior of double esters is relatively simple: are two carbons removed from the radical pool as CO2 from their two COO groups, or is the initial breakdown similar to that of the single esters and in essence two CO and two RO radicals produced. The latter would imply an approximate three or slightly more carbons being removed depending on the nature of the R group. In a most extensive study, Morvai et al. measured the sensitivity responses to the ethyl, iso-propyl, n-propyl, iso-butyl, and n-butyl esters of oxalic, malonic, succinic, glutaric, and adipic as well as even larger double acids.61 Their values are very uniform over these five acid structures but do vary slightly due to the specific ester grouping. However, coupled to other earlier values it is very clear for any double ester that more than 2.5 and less than 3.9 carbons have been indicated as not being involved in the radical pool that can lead to soot formation. An average value of all the data would imply slightly above three. Although not as precise as one might like, this does at least strongly confirm that it is unlikely for CO2 to be a primary product in both single and double ester combustion.
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VALUE OF SUCH MODELING Models are developed for a specific purpose, and this generally will set their guidelines and boundaries. However, in the field of combustion, the two rather differing disciplines of chemistry and engineering overlap which can complicate their individual goals. Practical engineering combustion systems invariably are complex with many adjustable parameters. Flowfields are involved that themselves require demanding descriptions. As a result, from early chemical kinetic modeling efforts when their relative insensitivity to an exact chemistry became noted, the computational fluid dynamic (CFD) modelers rapidly embraced the possibility of incorporating reduced chemical combustion models into their full-scale combustion simulations.72 The addition of even simplified models does appear to have value and although of a qualitative nature has aided theoretical development.73 This need has generated innumerable kinetic mechanism reduction methods that drastically reduce the size of the models without compromising their usefulness.74−80 Moreover, when three differing reduced chemical models of differing sizes from three different groups were recently incorporated into a CFD model and compared, all predicted flame structures with the same level of accuracy.81 This re-emphasizes the problem or shows the irrelevance of trying to sort out what might be the most chemically correct version. As a result, this raises the important question of whether more refined models really are needed at all. To be rigorously exact is not possible in the foreseeable future, and some level of error has to remain that can never be corrected. Their qualitative accuracy remains of some value and can indicate potential environmental issues although these of course will always be apparent from experiment. 5475
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of its carbon atoms. If that is included, data points are moved to lower equivalence ratios but by no more than about 5% and so do not change the implications of the plot. This said, what can be concluded about the known soot inhibiting qualities of oxygenates and is a model really needed to answer the question? Soot forms when the ratio of radical carbon to remaining reactive oxygen exceeds a certain critical value. At this point,, too little oxygen exists and the radicals engage in a thermodynamically driven reverse pyrolysis striving toward the formation of carbon as soot and also hydrogen. The input C/O ratio that can be calculated from a flame equivalence ratio has always been noted as an important indicator for soot formation thresholds. What it indirectly conveys is the role also being played by the hydrogen in the fuel. As a result, in comparing structural sensitivities the C, H, and O ratios introduce their own contributions. With oxygenated fuels, they inhibit soot partly from their hydrogen content and also from the structural consequences of the oxygen. For example, eqs 1 and 2 imply that for stoichiometric mixtures, CH4 and CH3OH have the same C/O and C/H algebraic ratios, yet methane can produce soot while methanol can not.
These fuel structural effects have been noted as being an important consideration in several fuel sooting tendency studies.85,86 By statistical analyses, these have again re-established the relative functionalities of the bonding in oxygenates as noted above. However, there seems yet to be no realization that the occurrence of these structurally preoxidized carbons will also modify the effective equivalence ratio, and the C/O and C/H ratios of the free carbon in any potential soot-producing radical pool. One of these recent studies examined the relative sooting tendencies of 186 oxygenated, 89 hydrocarbons, and 72 aromatic fuels.86 Quantitative measurements of sooting tendencies have been and still are an experimental dilemma for soot formation research. This recent study introduced a new method of utilizing a slightly sooting methane diffusion flame and adding 1000 ppmv (equal molecular quantities: parts per million by volume) of each test compound into the fuel flow. The resulting maximum mass concentration of soot was monitored by laserinduced incandescence. However, even this method introduces its own complexities. The resulting data are necessarily affected by the different equivalence ratio that each fuel additive experiences. As molecular weight of the additive increases, sooting will necessarily increase due to increased carbon loading. Nevertheless, such studies are very valuable in again confirming the consequences of aromatic, cyclic structures and chain branching but actually convey little information concerning oxygenate behavior with respect to soot formation. For example, if these data for the oxygenated fuels are taken and replotted together with that for the alkanes, it is seen to be quite normal. This is illustrated in Figure 4 by showing the
CH4 + 2O2 = CO2 + 2H 2O C/O = 0.25, C/H = 0.25 (FID radical pool values unchanged) (1)
CH3OH + 1.5 O2 = CO2 + 2H 2O C/O = 0.25, C/H = 0.25 (FID values C/O = 0.14, C/H = 0.125) (2)
If blended together though, methane’s soot can be inhibited. This is because the C−OH bond removes the equivalence of one-half a carbon and one-half an oxygen atom from the radical pool. Correspondingly, the C/H ratio is also reduced. Another way of conceiving this is that the true equivalence ratio in the radical pool is reduced. The radical pool C/O ratio is 0.14 for methanol. A 50/50 mixture of eqs 1 and 2 is not a true stoichiometric mixture in the radical pool from the point of view of the FID or soot formation but rather Φ = 0.929, with a C/O ratio of 0.214 and C/H = 0.188. This is the reason for the inhibition. As mentioned, inhibition has always been possible by blending one fuel with a high H/C ratio into one that is smaller. Adding CH4 (C/O = 0.25) into C2H2 (C/O = 0.4) would inhibit the sooting of the latter but oxygenates with their even lower C/O values have more commercial appeal. Consequently, by such blending manipulations, it is easy to modify the critical soot C/O level, the pool equivalence ratio, and the C/H ratio. As examples, Table 2 lists seven studies concerning soot suppression where sufficient data were published to permit calculation of the true consequences of the blending effects. By examining this in detail, three aspects become obvious. Not only is the radical pool equivalence ratio lower than the molecular proportions suggest, but the C/O and the C/H ratios are lowered especially when the added effect of the structural oxygen is included. Inal and Senkan87 compared the effects of three oxygenates on blends with heptanes. For the blends studied they noted the three to be comparable in reducing soot levels, which is clearly seen by the equal equivalence, C/O and C/H ratios predicted from the structural expectations. A similar study examined four blends with differing oxygenates.89 The main point of all these studies was to confirm the soot inhibition of such blending. This was clearly evident in the pronounced effects that can result with
Figure 4. The relative sooting indices for numerous oxygenate fuels and alkanes as a function of the equivalence ratio they experience, relative to hexane taken as 1.0. Calculated from the experimental results in the supplemental data of McEnally and Pfefferle.86
scaled sooting tendencies against their effective equivalence ratios relative to the behavior of n-hexane which was taken as having a zero sooting tendency in that study. In fact, the figure is seen to be hardly affected whether the structural nature of the oxygen in the oxygenate fuels is considered or not. Generally, its sooting tendency is approximately similar to the corresponding alkane with one carbon less in its structure. The figure solely emphasizes the expected fact that low carbon content and reduced low equivalence ratios will not produce soot. As a result, oxygenates do not predominantly inhibit soot because they are partially oxidized but also because they are in fact like saturated hydrocarbons and have difficulty producing soot precursor radicals in a low carbon radical pool. Figure 4 is actually plotted not considering the preoxidized nature of some 5476
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Table 2. Oxygenate Blending Modification of the Effective Equivalence, C/O, and C/H Ratios C/O
main fuel n-C7H16
C2H4
Φ, formula equivalence ratio
Φ, effective radical pool ratio
2.10
2.10 2.08 2.09 2.09 2.34 2.32 2.31 2.64 2.61 2.60 5.00 4.89 4.94 4.92 4.92 1.66 1.76 1.81 1.93 2.05 2.48 2.37 2.42 1.36 1.48 1.46 2.00 1.99 1.97 1.96 1.94 1.92
2.34
2.64
n-C7H16
C6H5C2H5
C2H4
C3H7COOCH3
C6H6
5.00
1.66 1.79 1.87 2.04 2.21 2.48
1.54 1.68 1.67 2.00
oxygenate and % total fuel mole fraction t-C4H9OCH3 CH3OH C2H5OH
18 17 18
C2H5OH C2H5OH
9.1 20
C2H5OH C2H5OH
9.0 20
CH3OCH3 C3H7CHO CH3COCH3 C2H5COC2H5
33 20 25 27
C2H5OH C2H5OH C2H5OH C2H5OH
44 70 87 95
(CH3O)2CH2 (C2H5O)2CH2
14 8.4
CH3OH
48
C2H5OH C2H5OH C2H5OH C2H5OH C2H5OH
18 34 47 59 70
dimethoxy methane, (CH3O)2CH 2,20 and the effect of methanol on another oxygenate, methyl butanoate. The structural oxygen-induced changes that can occur for individual oxygenated fuels have been summarized more clearly in detail in Table 3. This shows the relative potential of differing oxygenate structures. If it is required to exploit the blending potential, it is obvious that low molecular weight oxygenates (low carbon content) should be used otherwise the oxygen structural benefits will be minimized. Blending is seen to be little more than an exercise of diluting the amount of carbon that becomes available to the radical pool and the resulting modification of the C/O and C/H values. The magnitude for differing oxygenates can be readily calculated. The major point of this discourse is not to delve into understanding the detailed chemistry of soot formation but to partly illustrate that exercises such as soot suppression do not even need a model and an adequate chemical understanding exists. Moreover, the mechanisms of soot formation still are ill-defined. Any realistic model will be chemically even more complex as it reduces to pure organic chemistry with no underlying simplifications. At present, FID relative structural responses and an approximate indication of oxygenate sooting tendencies would appear more than adequate to resolve engineering fuel blending applications.
fuel/oxygenate/O2 mole fractions
atomic ratio
FID predicted pool ratio
5.50/0.00/28.79 4.70/1.02/28.28 5.20/1.07/28.03 5.07/1.08/28.07 3.81/0.00/4.88 3.46/0.35/4.88 3.07/0.76/4.88 3.39/0.00/3.84 3.07/0.30/3.84 2.71/0.67/3.84 0.31/0.00/0.69 0.27/0.14/0.68 0.27/0.07/0.68 0.27/0.09/0.68 0.25/0.09/0.67 0.04/0.00/0.25 0.04/0.03/0.25 0.03/0.06/0.26 0.02/0.12/0.26 0.01/0.16/0.26 0.33/0.00/0.40 0.27/0.04/0.40 0.27/0.03/0.40 0.12/0.00/0.49 0.12/0.00/0.48 0.09/0.08/0.43 0.12/0.00/0.44 0.11/0.02/0.43 0.09/0.05/0.42 0.08/0.07/0.41 0.07/0.10/0.40 0.05/0.12/0.38
0.669 0.660 0.656 0.658 0.781 0.753 0.727 0.882 0.844 0.810 1.592 1.452 1.535 1.516 1.522 0.632 0.631 0.605 0.581 0.571 0.825 0.762 0.787 0.479 0.513 0.478 0.818 0.768 0.736 0.703 0.670 0.635
0.669 0.654 0.653 0.655 0.781 0.748 0.717 0.882 0.841 0.802 1.592 1.497 1.562 1.550 1.557 0.632 0.622 0.582 0.539 0.513 0.825 0.736 0.774 0.392 0.424 0.380 0.818 0.765 0.729 0.691 0.651 0.608
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C/H atomic ratio
FID predicted pool ratio
0.438 0.435 0.428 0.430 0.500 0.478 0.455 0.500 0.478 0.455 0.438 0.421 0.444 0.444 0.449 0.800 0.652 0.530 0.424 0.368 0.500 0.470 0.482 0.500 0.500 0.432 1.000 0.879 0.776 0.686 0.606 0.536
0.438 0.423 0.422 0.424 0.500 0.467 0.432 0.500 0.468 0.432 0.438 0.395 0.431 0.426 0.430 0.800 0.626 0.482 0.356 0.291 0.500 0.410 0.446 0.350 0.350 0.289 1.000 0.864 0.748 0.646 0.557 0.478
ref 87
88
89
25
20
90
91
CONCLUSIONS A chemical understanding has been presented that explains the present adequacy of numerous chemical kinetic models of fossil fuel combustion in spite of their approximate nature or in some cases errors. It is argued that there is little justification in endeavoring to elevate them to being chemically more rigorously correct. The fact that this would require a greater knowledge of chemistry, reaction branching, and the validation of such a large amount of fundamental data tends to suggest this is neither feasible nor worthwhile. It seems that this realization may now be entering into these endeavors. The most recent suggestions are to develop reduced piecemeal components that represent specific structural fuel components that can be added together to produce reduced models that are sufficiently adequate descriptions for practical engineering applications.92 This level of apparent success has arisen from the unique richness of organic oxidation chemistry that can provide multichannel connections between all the potential carbon radicals and generate an underlying commonality and simplification. It is remarkable that a model can have a foundational architecture that is not correct yet still be labeled ″adequate″. However, it is this lack of model sensitivity that also removes any method for identifying fundamental errors. Moreover, it also emphasizes that such models should not be used to resolve the chemistry. 5477
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Table 3. Structural Oxygen-Induced Percent Decreases in the Formula Equivalence Ratio of ϕ = 1 and the C/O and C/H Ratios between the Formula and the Actual Radical Pool Compositions for Individual Oxygenated Fuels structure alcohol
double alcohol ether
double ether
ketone
aldehyde acid ester
oxygenate methanol ethanol 1-pentanol ethylene glycol dimethyl methyl ethyl t-butyl methyl dimethoxymethane diethoxymethane cyclo-1,3-dioxolane 2-methoxytetrahydropyran acetone 2-hexanone c-hexanone acetaldehyde hexanal acetic butyric methyl acetate butyl acetate methyl butanoate butyl butanoate methyl stearate
CH3OH C2H5OH C5H11OH (−CH2OH)2 (CH3)2O CH3OC2H5 CH3OC4H9 (CH3O)2CH2 (C2H5O)2CH2 c-C3H6O2 c-C5H9O(OCH3)
CH4O C2H6O C5H12O C2H6O2 C2H6O C3H8O C5H12O C3H8O2 C5H12O2 C3H6O2 C6H12O2
(CH3)2CO C4H9COCH3 c-C6H10O CH3CHO C5H11CHO CH3COOH C3H7COOH CH3COOCH3 CH3COOC4H9 C3H7COOCH3 C3H7COOC4H9 C17H35COOCH3
C3H6O C6H12O C6H10O C2H4O C6H12O C2H4O2 C4H8O2 C3H6O2 C6H12O2 C5H10O2 C8H16O2 C19H38O2
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: 805-966-6589. Fax: 805-965-9953. Notes
The author declares no competing financial interest.
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C/O decrease
C/H decrease
17% 8 3 20 17 11 7 25 14 29 13
33% 13 4 30 30 17 9 44 20 40 14
50% 25 10 50 50 33 20 67 40 67 33
13 6 6 20 6 25 10 21 9 12 7 3
14 6 6 25 6 25 10 25 10 12 7 3
33 17 17 50 17 50 25 50 25 30 19 8
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A model arises from our understanding of chemistry and our understanding can not be advanced by the model. Due to the complexity and flexibility of such models any interpretation of the chemistry from a model does risk being potentially flawed. As a result, any such predictions or interpretations necessitate confirmation by further experiment to have acceptance. For true exactness, models require accurate rate constants but the loss of identity in a radical pool introduces the predicament that this is not critical and modification of any such values by experimental data fitting reduces a model to being an empirical one. Consequently, any present attempt to suggest that the chemistry in these models is valid and verified has to remain unacceptable.
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radical pool ϕ decrease
REFERENCES
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