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Chemical Kinetic Influences of Alkyl Chain Structure on the High Pressure and Temperature Oxidation of a Representative Unsaturated Biodiesel: Methyl Nonenoate Aleksandr Fridlyand,†,‡ S. Scott Goldsborough,†,‡ and Kenneth Brezinsky*,† †

Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor Street, Chicago, Illinois 60607, United States ‡ Energy Systems Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, United States S Supporting Information *

ABSTRACT: The high pressure and temperature oxidation of methyl trans-2-nonenoate, methyl trans-3-nonenoate, 1-octene, and trans-2-octene are investigated experimentally to probe the influence of the double bond position on the chemical kinetics of long esters and alkenes. Single pulse shock tube experiments are performed in the ranges p = 3.8−6.2 MPa and T = 850−1500 K, with an average reaction time of 2 ms. Gas chromatographic measurements indicate increased reactivity for trans-2-octene compared to 1-octene, whereas both methyl nonenoate isomers have reactivities similar to that of 1-octene. A difference in the yield of stable intermediates is observed for the octenes when compared to the methyl nonenoates. Chemical kinetic models are developed with the aid of the Reaction Mechanism Generator to interpret the experimental results. The models are created using two different base chemistry submodels to investigate the influence of the foundational chemistry (i.e., C0−C4), whereas Monte Carlo simulations are performed to examine the quality of agreement with the experimental results. Significant uncertainties are found in the chemistry of unsaturated esters with the double bonds located close to the ester groups. This work highlights the importance of the foundational chemistry in predictive chemical kinetics of biodiesel combustion at engine relevant conditions.

I. INTRODUCTION To understand and have the capability to reliably predict the combustion behavior of alternative, carbon-neutral fuels such as biodiesel, which consist primarily consist of fatty acid methyl esters (FAMEs), it is crucial to understand the chemical kinetics of their long hydrocarbon side chains. Examples of FAMEs are illustrated in Figure 1b. Because the alkyl side chains in FAMEs constitute the largest functional group within these molecules, it is expected that they control many important features, such as cetane number, sooting tendency, etc. Similarly sized alkanes and alkenes are expected to share many important chemical kinetic properties. For instance, in monounsaturated alkenes and FAMEs (those containing a single double bond), it has been observed that the position of the double bond and its configuration (cis or trans), influence the reactivity of the molecule.1−9 A double bond in a hydrocarbon side chain is shorter than a single bond and has higher dissociation energy. Adjacent allylic sites are where the weakest C−C and C−H bonds are located. The position of the allylic sites in alkenes and FAMEs is illustrated in Figure 1a,b, designated by α. The weakest C−C bonds in the chain are those between positions α and β. These allylic C−C and C−H bonds strongly influence how an unsaturated molecule will initially decompose.10,11 The position of the double bond in the chain dictates the number of allylic C−C and C−H bonds present in the molecule (illustrated in © XXXX American Chemical Society

Figure 1. (a) Molecules investigated experimentally and modeled in the present study. (b) Molecules investigated experimentally and modeled in the prior study.7 The position α signifies the position of the allylic hydrogens, and the bond between α and β is the weaker allylic C−C bond. The dashed box highlights the similar molecular structures between the methyl nonenoate and octene isomers. Special Issue: 100 Years of Combustion Kinetics at Argonne: A Festschrift for Lawrence B. Harding, Joe V. Michael, and Albert F. Wagner Received: January 28, 2015 Revised: February 20, 2015

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DOI: 10.1021/acs.jpca.5b00914 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

are illustrated in Figure 1b. These molecules were chosen because they allow the FAMEs to be directly compared to their side-chain analogs (octenes) and have all been previously shown to have differing reactivities in the low temperature regime. Zhang et al.1 studied the low temperature ignition behavior of MN2D, MN3D, and methyl nonanoate in a motored Cooperative Fuel Research Engine with gasoline direct injection in the intake runner, compression ratios in the 4.43−14 range, and φ ≈ 0.25. They observed the negligible two-stage ignition behavior from the unsaturated species compared to the case of the saturated one, and the reactivity was ranked as methyl nonanoate > methyl trans-2-nonenoate > methyl trans-3-nonenoate. Hellier et al.5 found a nonlinear relationship among octene isomers in a modern diesel engine and a strong influence from the cis−trans isomerism. In their study, trans-2-octene and trans/cis-3-octenes were less reactive than 1-octene. However, both 3-octene isomers were more reactive than trans-2-octene. The hypothesis for the present experiments is that any reactivity difference between MN2D and MN3D would be similar to the difference we expect between 1-octene and trans-2-octene. New chemical kinetic models are developed in the present study with the aid of the RMG to interpret the results of the shock tube experiments. In addition, simple Monte Carlo simulations are performed to investigate the uncertainty in the generated models to improve and understand the agreement between the models and the experimental results. A number of techniques have been applied in the literature toward determining uncertainty in chemical kinetic model predictions.13,14 Global sensitivity analysis can be used to identify important reactions that might otherwise be missed through local sensitivity analysis (e.g., ref 15). Evaluation of uncertainty across the entire model parameter space is feasible, but to achieve reasonable accuracy would require a probabilistic and correlated description of uncertainty in model parameters.16 In the absence of an accurate description of uncertainties in most chemical kinetic parameters, modest but reasonable estimates are used in the present study. The sensitivity of the model predictions to the uncertainties in the foundational model for the smallest molecules is also tested by building the models we two different submodels. The techniques employed here are aimed at developing straightforward methods to examine quantitative agreement between chemical kinetic models and experimental data. The purpose of this investigation is to gain new insight into the oxidative behavior of real biodiesel molecules as well as to identify the limitations of and opportunities for improvement in the predictive capabilities of chemical kinetic models for these molecules. The organization of the rest of this manuscript is as follows. In section II the high pressure, single pulse shock tube experiment is briefly described along with methodology specific to the present study. Section III presents the experimental results and important observations. Section IV discusses the modeling methodology employed in the present study and introduces the Monte Carlo uncertainty analysis performed in the present study. Section V presents the modeling and uncertainty analysis results for the octene isomers. Finally, section VI presents the simulation results and discussion of the important chemical kinetics for the methyl nonenoate isomers.

Figure 1a,b), as well as the types of radicals that initially form. It has been observed experimentally in the low temperature regime that more centrally located double bonds generally decrease the reactivity of the isomers when they are transconfigured.1−6,8,9 However, in the intermediate and high temperature regimes, an inversion of reactivity has been observed in trans-configured alkene isomers,6,8 but not long FAMEs.9 The authors of this paper have previously investigated the influence of the double bond position on the reactivity of four decene isomers, including 1-decene, cis-2-decene, cis-5-decene, and trans-5-decene, in the high pressure and the intermediate to high temperature regime using the single pulse shock tube experiment.7 This apparatus provides the capability to probe the stable intermediate reaction species over a wide range of temperature and pressure relevant to combustion engine conditions. These molecules are illustrated in Figure 1a. It was found that when the double bond is more centrally located, such as in the cases of cis-2-decene and 5-decenes, the molecules are more reactive. This was evident in the increased fuel consumption observed for 2- and 5-decenes, as well as for different yields of major stable intermediates. These same reactivity results were found to qualitatively agree with the observations of Mehl et al.6 and Battin-LeClerc et al.,8 who observed increased reactivity for the isomer with the more central double bond among the three hexene isomers (1, trans2-, and trans-3-) in the intermediate and high temperature regimes. However, a recent study on the autoignition behavior of long FAMEs by Wang et al.,9 where methyl 9-decenoate and methyl trans-5(6)-decenoate were investigated, found indistinguishable reactivity at intermediate temperatures. In our previous study,7 different yields of benzene were also observed. 5-Decenes generated the most benzene and 1-decene the least, suggesting a possible influence of the location of the double bond on the sooting characteristics of similar molecules. The cis and trans isomerism in the case of 5-decenes was also found to have no influence on the reactivity of the fuel molecules or the yields of major stable intermediates. The results for both 5-decene isomers were essentially identical at the experimental conditions of the HPST. Chemical kinetic models were also developed in the prior work with the aid of the Reaction Mechanism Generator (RMG),12 to elucidate the important chemical kinetic routes for the decene isomers. At the conditions of the UIC High Pressure Shock Tube facility, it was found that the fission of the allylic C−C bond was the single most important reaction for all decene isomers. 1-Decene was found to be unique in that this reaction led to the resonantly stabilized and unreactive allyl radical, whereas for other isomers this fission reaction led to resonantly stabilized radicals that decomposed more readily. Although the models generally captured the experimental fuel consumption behavior and the formation of major stable intermediates, further improvements could still be made to better the agreement between the experiments and the model predictions for a few of the smallest stable intermediates (C2H6 and C2H2), as well as the formation of final combustion products, CO and CO2.7 To extend our previous work to more diesel-like molecules, new HPST experiments are conducted with two commercially available FAME isomers and two comparable alkenes in the present study. The investigated molecules are methyl trans-2nonenoate (MN2D), methyl trans-3-nonenoate (MN3D), 1octene (C8H16-1), and trans-2-octene (t-C8H16-2), where these B


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II. EXPERIMENTAL METHODS The design and construction of the High Pressure Single Pulse Shock Tube (HPST) have been previously described in detail by Tranter et al.17,18 The methodology for simulating the HPST results has been discussed by Tang et al.19 The HPST setup used in the experiments for this work was most recently presented by Malewicki et al.20 and Comandini et al.21 The experiments conducted for this investigation are performed using identical setup and experimental conditions as in our previous study.7 A brief review is presented here. The HPST is constructed of machined and bolted sections of 17-4PH stainless steel, capable of reaching pressures of up to 100 MPa. The driver section is 1753 mm long, which is variable using a 50.8−1194 mm stainless steel plug, and has an inner diameter of 50.8 mm. The driven section used in the present experiments has an inner diameter of 25.4 mm with a 2997 mm length. The shock tube is uniformly heated to 100 °C using proportional-integral-derivative temperature controllers and heating tape. The single pulse operation is also facilitated by a dump tank connected by a 45° angle port near the diaphragm section. The diaphragms used are single thin metal discs with a cross-shaped score in the middle. This creates a petal-like opening pattern, which prevents pieces of the diaphragm from breaking off. The diaphragms used in current the experiments are 0.635 mm thick (3003 Al) with a 0.127 mm deep score, for nominal shock pressures of 0.5 MPa. The diaphragms are burst by allowing the driver section to continue filling up with helium until the pressure difference across the diaphragm naturally breaks it. This leads to some scatter in the experimental conditions, e.g., post shock pressure and temperature. The arrival of the incident shock wave near the endwall of the driven section is monitored by six PCB 113A22 (5000 psi) or 113A23 (10 000 psi) pressure transducers. The time of arrival is measured using two PCI-DAS4020/12 high speed data-acquisition cards, and the velocity is extrapolated to the endwall. The pressure at the endwall is monitored using an additional PCB 113B24 (1000 psi) pressure transducer, from which the average reaction pressure and reaction time are determined. The estimated uncertainty in reported pressure measurements is ±0.1 MPa and ±0.1 ms in reaction time. The reaction temperatures in the experiments are not measured directly but calibrated using the external chemical thermometer technique,18 with 1,1,1-trifluoroethane (TFE) and cyclopropanecarbonitrile (CPCN) employed as the calibration gases. CPCN is used to calibrate temperatures between 900 and 1100 K, whereas TFE was used to calibrate temperatures between 1200 and 1300 K. Between 1100 and 1200 K, the temperatures are interpolated. Above 1300 K, the temperature calibration is extrapolated. The estimated systematic uncertainties in the reported temperatures are ±15 K below 1300 K and increase to ±30 at 1500 K. Random error is represented as scatter in the experimental data. Test mixtures with oxygen (99.999% purity Airgas) and approximately 100 ppm of each fuel in argon (99.999% purity Airgas passed through an additional O2 trap) are prepared in a heated, 40 L, high pressure vessel. The purity of methyl nonenoate isomers is ≥97% (Sigma-Aldrich). 1-Octene and trans-2-octene had purities of 98% and 97%, respectively, from Sigma-Aldrich. The purity and identity of each isomer are confirmed with HP 5973 Mass Selective Detector (MSD) analysis. All species calibrations are prepared using standard gaseous calibration mixtures from Sigma-Aldrich and Restek,

with the exception of the parent fuels. Those calibration mixtures are prepared manometrically. The relative uncertainty in all species calibrations is estimated to be up to ±10%. The postshock gases are withdrawn using the online GC sampling technique21 and analyzed using flame ionization and thermal conductivity detectors. The product species were identified by a combination of MSD analysis and comparison to retention times of known species from commercially available calibration standards. The details of the GC methods are included in the Supporting Information. The experiments for each molecule were conducted by sweeping a temperature range of 850−1500 K, at an equivalence ratio of φ ≈ 1, while also covering a narrow range of pressures [(3.8−6.2) ± 0.1 MPa] and reaction times [(1.3−2.4) ± 0.1 ms].

III. EXPERIMENTAL RESULTS A total of 58 tests are conducted with methyl trans-2-nonenoate (MN2D) and methyl trans-3-nonenoate (MN3D). A total of 65 tests are conducted with 1-octene (C8H16-1) and trans-2-octene (t-C8H16-2). The major and minor stable intermediates detected are the same as those of the decene isomer study.7 The major stable intermediates observed included CO, CO2, methane (CH4), ethane (C2H6), ethylene (C2H4), acetylene (C2H2), propene (C3H6), 1-butene, and 1,3-butadiene. The minor stable intermediates positively identified are propane (C3H8), allene, propyne, 1-pentene, and benzene. The carbon recovery is greater than 90% at most temperatures, except within the vicinity of 1050 K, where it is greater than 80%, with this slight reduction due a large number of polyunsatured species that form. As discussed previously,7 the small abundance of these polyunsatured linear and cyclic species and their coelution make their positive identification and quantification difficult. All the experimental results are tabulated in the Supporting Information. The results are presented here as mole fractions as a function of reaction temperature. Figure 2 illustrates the overall reactivity of the fuels tested by plotting the fuel mole fraction where the small differences in

Figure 2. Normalized (by initial fuel mole fraction) postshock fuel mole fraction measurements from experiments with octene and methyl nonenoate isomers. C


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Figure 3. Normalized (by initial fuel mole fraction) mole fractions of major stable intermediates for octene isomer experiments.

In both sets of experiments, different yields of benzene are observed for isomers with the double bond in different positions. Both trans-2-octene and methyl trans-3-nonenoate had larger yields of benzene than their isomers. In our previous work,7 we discussed some possible pathways that can account for the different benzene yields. However, because benzene is only a minor product in all the experiments, examining the pathways to its formation is beyond the scope of the present work. Additionally, it can be seen in Figure 4 that both esters promote increased formation of CO2 at lower temperatures than the octene isomers. This is a common trait for all esters, which is due to the pyrolytic chemistry of the ester functional group.22 It was initially postulated that any difference in the reactivity of the FAMEs and their alkene analogs would be similar. The methyl nonenoate isomers have the same number of allylic hydrogen sites and the same number of weak allylic carbon− carbons as their alkenyl side-chain analogs. It was therefore hypothesized that the more centrally located double bond in MN3D and trans-2-octene, leading to two allylic C−H sites, would increase the reactivity of both molecules. Contrary to this hypothesis, the results for the FAMEs and the octenes show different trends in reactivity with changes to the double bond position. This observation of the different

preshock fuel concentration are taken into account via normalization. These data indicate that the observed trends for 1-octene and trans-2-octene results are essentially identical to those of 1-decene and cis-2-decene7 where trans-2-octene is more reactive than 1-octene. This difference in reactivity is illustrated in Figure 2 by the increased consumption of t-2C8H16 compared to 1-C8H16 at similar shock temperatures. Conversely, there is no difference in reactivity between the two FAME isomers as also seen in Figure 2. Here the two FAMEs are observed to have reactivities similar to that of 1-octene. The results for the major stable intermediates of the octene isomers are plotted in Figure 3 and match closely the results for 1-decene and cis-2-decene in our previous study.7 The increased reactivity of trans-2-octene can also be seen here where this is demonstrated by the larger yield of stable intermediates, CH4, C2H6, C2H2, CO, at lower shock temperatures. Significantly different yields for propene, C3H6, 1-butene, C4H8-1, and 1,3butadiene (1,3-C4H6) between the two octene isomers are observed as well. However, the results for the two FAMEs indicate no major difference in the rates of formation or maximum yields of major stable intermediates, containing one or two carbons. The only major differences in the yields are observed for propene, 1-butene, and 1,3-butadiene, as shown in Figure 4. D


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Figure 4. Normalized (by initial fuel mole fraction) mole fractions of major stable intermediates for methyl trans-2-nonenoate (MN2D) and methyl trans-3-nonenoate (MN3D) experiments.

ment. To adequately do this, we draw upon our experience with the decene models from ref 7, and some of these results are presented here for reference. IV.A. Model Development. Chemical kinetic models are developed to describe the intermediate to high temperature oxidation of the methyl nonenoates and the octenes using the same approach as employed previously.7 The Reaction Mechanism Generator (RMG)12 was used, which is a tool to systematically generate detailed chemical kinetic models from elementary reactions for any C−H−O−S containing molecules. Reactions belonging to 30+ different classes are considered during the model generation. To constrain the size of a particular model, a user-defined error tolerance is employed that controls the final size of the kinetic mechanism. RMG can reasonably estimate high pressure limit reaction rate constants for large molecules, whereas it relies on a “seed mechanism” to describe the oxidation of the smallest species (e.g., C0−C2 at least). RMG functionality is well documented, and only its implementation in the present study is described here. For each of the four fuel molecules investigated in this study, RMG was run at 5 MPa, 1100 K, 1400 K, with a fixed reaction time of 0.016 s, and an error tolerance of 0.01−0.02. Expected product species were added to the condition file to ensure

reactivity trends for the FAMEs is in agreement with the results of Wang et al.9 In their recent shock tube measurements of ignition delay times for methyl 9-decenoate and methyl trans5(6)-decenoate, the reactivity of both isomers was indistinguishable above 1000 K. These two sets of results lead to the hypothesis that the ester group in unsaturated FAMEs may have a dampening effect on reactivity where, as discussed, most all of the measured intermediates show lower extents of production with the FAMEs. This, and other chemical kinetic considerations unique to the FAMEs, are investigated and discussed in the subsequent modeling section VI where detailed models are used to explore and interpret the experimental findings.

IV. CHEMICAL KINETIC MODEL AND SIMULATIONS To understand the chemical kinetic influences of the alkyl side chain on the oxidation behavior of these unsaturated FAMEs, it is necessary to utilize an accurate chemical kinetic model. Because no validated ones exist in the literature for the species investigated, these are developed here. Furthermore, it is important to quantify the effects of model uncertainty on the predicted results, e.g., via Monte Carlo simulations, to ascertain where the discrepancies lie and to facilitate model improveE


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foundational models. The RMG models are generated here using seed mechanisms from USC Mech II29 and ARAMCO Mech 1.3.30 For the purpose of the comparison, these models are assumed to include a sufficient number of reactions to describe the chemistry for the C0−C4 species, and as such, reactions generated by RMG for the seed mechanism species are removed. Through this we are able to isolate the influence of the foundational model without added uncertainty from RMG-generated reactions. IV.B. Monte Carlo Uncertainty Analysis. In our previous investigation with decene isomers,7 some disagreement was observed between the chemical kinetic models developed with the aid of RMG and the experimental results. To sample and gauge the uncertainty in model predictions between the chemical kinetic models developed in the present study, as well as the previous decene one,7 simple Monte Carlo simulations are also performed. This facilitates the use of confidence bands on the simulation results and highlights features where the model uncertainty needs to be improved, or significantly altered to properly capture the experimental measurements. In this section the method is briefly described and results of its application to the 1-decene model from our previous study are presented. The method is further applied to the octene isomer results in the following section. The methodology is not applied to the FAMEs in this work, as will be discussed shortly. The simulations entail assigning an uncertainty probability distribution to each rate constant of the chemical kinetic models. An iteration of the model is generated by taking a random sample from within the uncertainty of each rate constant, and simulations of the experimental points performed using this perturbed model. This procedure is repeated for a large number of iterations. The final results are a distribution of predicted values. In the present case, the results represent only a limited section (a sample) of the total uncertainty in the model. Two simple cases are investigated, including uncertainty in all rate constants of ±30%, and an uncertainty factor of UF = 2. These uncertainties are applied only to the Arrhenius preexponential factor A with uniform probability. There are few reactions known to be uncertain to less than ±30%, and a uniformly distributed factor of 2 is a more reasonable estimate. No correlated uncertainties are considered here. In reality, the uncertainty of many individual rate constants is much higher, especially for those that are estimated from rate rules, e.g., UF ∼ 10−100. Using a different probability distribution, e.g., normal distribution, is only possible for rate constants with a statistically significant number of determinations, which is rare. However, even under that condition it has been shown by Sheen and Wang31 that using a normal distribution in place of uniform distribution leads to a slightly narrower standard deviation in the final results. To get an accurate probability distribution of the model output, the uncertainties in all of the Arrhenius parameters, as well as the thermochemistry and the pressure dependence would need to be considered. However, the purpose of the analysis presented here is to only examine the uncertainties in the chemical kinetic models using modest but reasonable uncertainty estimates. For the case of 1-decene discussed shortly, uncertainties across the entire model are investigated by first removing the pressure dependence from the nominal model. It is not straightforward to apply uncertainty factors to all pressure dependent rate constant expressions and pressure dependence

sufficient detail in describing their chemistry. In this work, pressure dependent reaction rate constants are only included for the smallest molecules in the seed mechanism, or foundational chemistry model. These conditions are found to generate models with sufficient detail in a reasonable amount of time to permit rapid iteration, which is necessary to achieve adequate fidelity in the simulation results. The expanded RMG reaction database used in our previous study with decene isomers was general enough to also be used to generate models for octene isomers and served as a base for expansion for methyl nonenoate isomers, using reaction rate rules specific to FAMEs that are based on a literature review. The RMG databases used in generating the present models are available elsewhere.23 The final models used to simulate the experiments with the FAMEs and octenes contained 200−400 species and 10 000− 20 000 reactions. All the simulations are performed using the closed, homogeneous batch reactor at a constant pressure as implemented in CHEMKIN.24 Preshock gas composition, reaction time, and the reaction pressure for each test are supplied as input. The final models used in the present study are available in the Supporting Information. In our previous study, a seed mechanism was assembled consisting of H2−O2 chemistry from Burke et al.,25 along with GRI-Mech3.0,26 and additional C3−C4 reactions from the literature, as described in ref 7. The final models reasonably predicted the fuel consumption and the formation of the most stable intermediates. However, it was not possible to reproduce the reactivity difference observed between 1-decene and the other isomers without adjusting the rate constant for the fission of the allylic C−C bond. 1-Decene was found to be uniquely sensitive to the oxidation chemistry of allyl radicals, which itself had high uncertainty. Additionally, the peak yields of ethane and acetylene were underpredicted, and at the highest temperatures the predicted rate of formation of final oxidation products (CO and CO2) was underpredicted. These discrepancies in yields of ethane and acetylene, in the case of the decenes, were attributed to the seed mechanism from GRI-Mech 3.0 being insufficient to describe C2 oxidation chemistry, based on sensitivity analysis. The slower formation of final oxidation products (CO and CO2) at the highest temperatures of the experiments was similar to the disagreement seen previously27 between single pulse shock tube data and various chemical kinetic models. In that study, different models from the literature demonstrated large variability in the predicted oxidation of ethylene at 0.4 MPa and 1000−1500 K. None were found to be in agreement with the experimental data. As observed previously by Chaoqi et al.,28 the uncertainty in chemical kinetic models for small molecules may be more than just due to reaction rate constants. In their analysis of various small molecule models for predicted combustion behavior of ethylene, they found that important reactions in some models were entirely absent in others. This type of uncertainty cannot be simply taken into account with techniques such as Monte Carlo simulations. RMG permits models to be built in a modular fashion. Accordingly, in the present study two different seed mechanisms for C0−C4, i.e., foundational chemistry, are utilized to investigate the sensitivity of the results to the choice of the initial seed mechanism. The purpose of using two seed mechanisms is to investigate the uncertainties that can be attributed to the foundational small molecule chemistry. This can provide insight into improvements necessary in the F


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Figure 5. (a) Example results of Monte Carlo (MC) simulation results for 1-decene. Histograms of predicted fuel mole fraction at (b) 1066 K and (c)1130 K showing the interquartile range (IQR) and interdecile range (IDR) of results.

Figure 6. Comparison of Monte Carlo (MC) simulation results at the ±30% uncertainty level (IQR and IDR) and the experimental results for some of the major stable intermediates. Nominal model results as well as the “best fit” model from the MC simulations are shown for comparison as well.

along with the spread from the uncertainty, with the experimental data included as well. Figure 5b,c highlights the distribution of fuel consumption predictions at two representative temperatures for the 1000 iterations conducted and indicates that the results have sufficiently converged on a central value. At T = 1066 K, the results are well approximated by a normal probability distribution. However, at T = 1130 K, where most of the fuel has been consumed during the test conditions, i.e., where the fuel mole fraction is close to zero, the distribution is skewed and is no longer well represented by a normal distribution. For this reason, mean and standard deviation was not used to present the data and the rest of the results of the MC simulations are presented as interquartile range (IQR) and interdecile range (IDR), representing the difference between the 75th and 25th percentile and 90th and 10th percentile of the simulation results, respectively. It is important to note that the convergence to a central value shown in Figure 5b,c, which occurs after only ∼1000 samples are conducted, is due to the fact that although there are thousands of uncertain parameters in the kinetic mechanism, only a handful have a strong influence on the predicted mole fractions of the fuel. This feature is frequently identified by local sensitivity analyses. Though not presented here, it should be noted that at UF = 2, simulations were also performed covering a total of 10 000 samples (100 000 individual CHEMKIN runs) to confirm the convergence. No significant reduction was observed in the distribution of the results. It is therefore

is unnecessary because the experiments are essentially isobaric. The pressure dependence is eliminated by simply evaluating all the rate constants at 0.5 MPa. The reactions are then written in the high-pressure limit CHEMKIN format. Those reactions that are near the low pressure limit at the experimental conditions are written strictly in the low pressure limit CHEMKIN format. Simulation results from both versions of the model (original, i.e., with pressure dependence, and simplified, i.e., without pressure dependence) were compared and showed identical results for the conditions of the experiments. The experimental data set for 1-decene includes 34 individual shocks. To demonstrate the methodology, 10 of the 34 experiments7 are selected for the Monte Carlo simulations such that the most important features of the experimental results are examined while spanning the full range of temperature. For each level of uncertainty (i.e., ±30%, UF = 2.0), the rate constant of each reaction is sampled randomly and independently (i.e., each rate constant is randomly varied within the defined probability distribution). All ten experiments are then simulated with the perturbed model using CHEMKIN.24 A total of ∼1000 samples are taken for each uncertainty level. Scripts automating these procedures are written in Python and are available elsewhere.23 An example of the raw Monte Carlo (MC) simulation results for fuel decomposition at the ±30% uncertainty level is shown in Figure 5a where the nominal model results are indicated, G


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Figure 7. Comparison of Monte Carlo (MC) simulation results at the ×2 uncertainty level (IQR and IDR) and the experimental results for some of the major stable intermediates. Nominal model results as well as the “best fit” model from the MC simulations are shown for comparison as well.

concluded that ∼1000 simulations are sufficient to sample the uncertainty in the model predictions. The MC simulation results are presented in Figures 6 and 7 for some of the major stable intermediates at both uncertainty levels. The error bars applied to the experimental data represent two of the biggest sources of systematic uncertainty in the experimental data. The uncertainty in temperature is due to the uncertainty in the decomposition rates of the chemical thermometers used. The uncertainties in the reported species measurements are primarily due to possible errors in species calibrations prepared for the gas chromatographic analysis. Random errors in the experiments are small compared to these systematic uncertainties and are indicated by the scatter in the experimental measurements. It can be seen in Figure 5 that for a fixed temperature a small perturbation in the rate constants of only ±30%, gives a large range of possible mole fraction results. However, the majority falls within a narrower band around a central value. This narrowing of the predictions is further illustrated in Figure 6 for 1-decene mole fractions, where the lower temperature experimental systematic uncertainties are greater than the large majority of the MC simulation results. Similar trends are observed in the formation some of the major stable intermediates (e.g., C3H6 and C2H4), which might be expected with such small perturbations to the model. However, at higher temperatures (>1100 K), the spread in the MC simulation results increases noticeably such that it exceeds the error bounds of the experimental measurements. As was discussed in the previous study,7 the nominal model, i.e., the one generated by RMG, was unable to reproduce the data for CO, CO2, C2H2, and C2H6 at the highest temperatures. With small perturbations to the model and the increased spread in simulations results, there is still a large disagreement with the aforementioned species, and this signifies a larger than superficial discrepancy. The results are also highlighted in Figure 6 for a “Best Fit” where these indicate a perturbed model from within the 1000 samples that has the smallest least squared error compared to those of the ten experimental points. This “Best Fit” designation is useful for checking how close a perturbed model can come compared to the experimental data. In most cases, the “Best Fit” results are almost identical to those of the nominal model, with only modest improvements in predicted

CO and CO2, whereas in all cases the “Best Fit” results are within the range of most frequent values from the MC simulations. With the uncertainty in rate constants raised to a more reasonable UF = 2 for all reactions, the trend in uncertainty bounds of the model remains similar, but it can be seen in Figure 7 that the overall uncertainty grows significantly larger. Particularly at higher temperatures, the spread in MC simulation results is much larger than the systematic uncertainty in the experiments. As can be seen for CO, CO2, C2H2, and C2H6 in Figure 7, however, even with a reasonable uncertainty estimate, it is still not possible to reproduce all the experimental observations. The “Best Fit” for this level of uncertainty is able to reproduce most of the experimental results much better than the nominal model, except in the case of C2H2 which still shows a very large discrepancy. For C2H6, though the model results are better, the “Best Fit” results fall significantly outside of the most frequently predicted values. This indicates an extreme and an unlikely case in terms of perturbations that would be necessary to the rate constants to bring the model into agreement with the experiments. The MC simulation results presented in this section highlight the confidence interval in the model, which is relatively large, even for the modest level of uncertainty explored here (UF = 2.0) and indicate that substantial changes to the model are required to bring the predictions into agreement with the data. Alternatively, errors in the experimental data that could account for the discrepancies do not seem to be possible due to experimental constraints such as the high carbon recovery rate, which indicate no large errors have occurred in the measurements. As was discussed in the previous study,7 it is believed that the disagreement between the 1-decene model predications and the experiments is due to uncertainties within the seed mechanism used (primarily associated with GRI Mech 3.0). It was hypothesized that a better seed mechanism might be able to reconcile the differences. This hypothesis is explored here using two updated foundational chemistry mechanisms, and the results are presented in the subsequent sections.

V. OCTENE ISOMERS MODELING RESULTS V.A. Sensitivity to Seed Mechanism Choice. As was suggested in the previous section, and by the local sensitivity H


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The Journal of Physical Chemistry A analysis conducted in our previous study,7 the uncertainties in the seed mechanism used by RMG, i.e., the foundational chemistry may have a strong influence on the final model predictions. To clarify this, models for the two octene isomers are generated with two published small molecule mechanisms. Additional MC simulations are performed on two of the new models with the intent to determine the contribution to uncertainty in the predictions from the RMG-generated portion. This is discussed in section V.B. The same set of reaction rate rules and RMG inputs used for generating the decene isomer models are used to generate models for 1-octene and trans-2-octene oxidation. In place of the seed mechanism used previously,7 USC Mech II29 (111 species and 784 reactions) and ARAMCO Mech 1.330 (253 species and 1542 reactions) are used here. The thermochemistry database included with each model is also used as the primary source for all species in RMG, whereas the same thermochemistry databases used in decene modeling are used for other species. The foundational chemistry models were developed by two independent groups and include a detailed description of C0−C4 chemistry. In addition, ARAMCO Mech 1.3 includes numerous reactions describing the chemistry of many small oxygenated species, and this makes it a good candidate as a seed mechanism for modeling FAMEs. USC Mech II is the foundation of the JetSurf 2.0 model,32 which was demonstrated in a previous single pulse shock tube study27 to capture the high pressure and temperature oxidation trends between ethylene and heptane, (though not the absolute results). To compare the sensitivity of the final simulation results to the choice of seed mechanism, any additional reactions (and possible uncertainty) of the species involved in the foundational model that are added by RMG are removed. This is equivalent to assuming that each seed mechanism describes the C0−C4 chemistry in sufficient detail. The RMG-generated reactions that are left are those that “feed” species into the seed mechanism. For additional comparison, the results for 1-octene are also simulated using the methyl 9-decenoate (MDE9D) model from Lawrence Livermore National Lab (LLNL), developed by Herbinet et al.33 Most of the reaction rate rules specific to alkenes in the present models were adapted from the work of Herbinet et al. and are essentially the same as those used by Mehl et al. to model high temperature hexene ignition behavior.6 The LLNL MDE9D model was developed hierarchically, using reaction rate rules to add chemistry for the oxidation of alkenes, alkanes, and FAMEs on top of a small molecule foundation. The simulation results for the predicted fuel mole fractions from both octene isomers are compared in Figure 8a,b. Here it can be seen that the predicted consumption of both octene isomers using the models built with both the USC and ARAMCO seed mechanisms is essentially the same. It is not surprising that the LLNL MDE9D model yields the same results as those generated by RMG because the same reaction rate rules are used in both models. The primary difference between the LLNL MDE9D model and the RMG-generated models presented here is the different foundational chemistry. In our previous study with decenes, the rate constant used for the primary initiation reaction (fission of allylic C−C bond) was a factor of 2−3 faster for 2- and 5-decenes compared to 1decene, in the temperature range of the HPST experiments. This was the only way that the complete reactivity trend could be recovered. A sensitivity analysis revealed a unique sensitivity

Figure 8. Comparison of octene isomer experiments and model simulations using two RMG-generated models with USC Mech II and ARAMCO Mech 1.3 as the seed mechanism. Simulations for (a) 1octene are compared using the two versions of the initiation reaction rate constant (nominal and adjusted from ref 7). Included are additional simulation results for 1-octene oxidation using LLNL methyl 9-decenoate model (LLNL MDE9D).33

of 1-decene to the oxidation of allyl radicals, as mentioned earlier. Using the same reaction rate constant for the 1-octene model as was done for 1-decene results in slight underpredictions of the fuel consumption, as noted in Figure 8a. To achieve better agreement, the rate constant for the fission of the allylic C−C bond is adjusted for both 1-octene and trans-2octene, and this can be seen in Figure 8b. New sensitivity analysis for the predicted mole fraction of 1-octene demonstrates how the local sensitivity has changed for the 1alkene isomers compared to results of our previous study, as shown in Figure 9. Although the 1-octene results are still sensitive to the reaction of allyl radicals with hydroperoxyl radicals (aC3H5 + HO2), the sensitivity is significantly reduced compared to that of the same analysis performed with the 1-decene model.7 The I


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Figure 9. Normalized sensitivity for fuel mole fraction from the 1-octene model using USCMechII as the seed mechanism at 1050 K, 2.1 ms reaction time, and 5 MPa reaction pressure.

Figure 10. Comparison of 1-octene simulation results for major intermediate species using ARAMCO Mech 1.3 and USC Mech II as the seed mechanisms in RMG. Included are additional simulation results for 1-octene oxidation using LLNL methyl 9-decenoate model (LLNL MDE9D).33

hypothesis from the previous section and from our previous study7 that a more robust foundational mechanism can resolve discrepancies seen for these species in the previous work. Remaining discrepancies between the model predictions and the experimental data for the smallest species at the highest temperatures can still be attributed to uncertainties in the small molecule chemistry, as will be shown in the next section. Systematic improvements to the foundational models are thus necessary to improve a mechanism’s predictive capability; however, these improvements are beyond the scope of this work. Both RMG models for 1-octene significantly overpredict the peak 1-butene (C4H8-1) formation and underpredict the peak 1,3-butadiene formation compared to the model developed for 1-decene.7 Using the previous seed mechanism and the same reaction rate rules, the agreement between the prediction of 1butene and 1,3-butadiene from 1-decene is better. The discrepancy between the experimental measurements and the

overall sensitivity graph more closely resembles those of 2- and 5-decenes seen previously. Using either the nominal or the adjusted rate constant yields simulation results within the combined random and systematic uncertainties of the 1-octene experimental results. For these reasons, only the adjusted rate constant for 1-octene results are used in the remainder of comparisons with 1-octene experiments. This unified set of reaction rate rules allows for better comparison of important reactions. The results for major intermediate species are presented in Figures 10 and 11 for 1-octene and trans-2octene, respectively. There are several important observations that can be made regarding the simulation results of the 1-octene experiments using the two RMG models and the LLNL MDE9D mechanism. Both RMG models yield very similar results that capture the order of magnitude of all stable intermediates, with only minor differences. The peak magnitudes of ethane (C2H6) and acetylene (C2H2) are captured well, confirming the J


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Figure 11. Comparison of trans-2-octene simulation results for major intermediate species using ARAMCO Mech 1.3 and USC Mech II as the seed mechanisms in RMG.

Figure 12. Flux diagrams showing major pathways consuming the parent fuel at 1050 K, 5 MPa, and 2.3 ms for (a) 1-octene and (b) trans-2-octene. The percentages are the absolute amount that each pathway consumed (∼54% total of initial fuel for 1-octene and ∼68% for 2-octene). The Habstraction reactions, indicated by dashed arrows, are those involving CH3, O, OH, H, and HO2 radicals. The dash-dot arrows indicate the H atom addition to the double bond reactions. Other reactions in each case indicate all other remaining H-abstraction and bond fission reactions.

underpredicted. In contrast, the 2-decene model had better agreement with peak propene, and about equal agreement with 1-butene and 1,3-butadiene.7 It is interesting to note that despite the disagreements, the two generated models, using two different foundational chemistry models, produce similar results for the octene isomers. This consistency is examined again in section VI where the methyl nonenoate isomer results are discussed. Using the consistent set of reaction rate rules, reaction flux diagrams are calculated for the two octene isomers using the ARAMCO Mech 1.3 based models, and these are shown in Figure 12a,b.

predicted 1-butene and 1,3-butadiene concentrations might suggest an unknown error in the data; however, the LLNL MDE9D model is able to much more adequately capture the experimental measurements, though it overpredicts 1,3butadiene. Again, the major difference between the RMG and the LLNL models is the small molecule chemistry. Contributions to the uncertainties in the model predictions from only the RMG-generated reactions are examined in the next section. Similar observations can be made from simulation results of trans-2-octene experiments, which are presented in Figure 11. Here it is apparent that 1-butene and 1,3-butadiene are better predicted, though peak ethane and propene (C3H6) are K


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Figure 13. Comparison of Monte Carlo (MC) for the 1-octene model using USCMechII as the seed mechanism. Only RMG-generated reactions were manipulated, and 1000 samples were taken.

Figure 14. Comparison of Monte Carlo (MC) for the trans-2-octene model using USCMechII as the seed mechanism. Only RMG-generated reactions were manipulated, and 1000 samples were taken.

The analysis of the flux diagrams in Figure 12a,b leads to many of the same conclusions that were made for the decene isomers.7 Despite the increased significance of the allylic C−C bond fission reaction for 1-octene, the total amount consumed of each isomer stayed similar (∼54% and ∼68%, respectively with ARAMCO Mech, compared to ∼48% and ∼71%, respectively, using the old seed mechanism for 1-octene/ decene and 2-octene/decene, respectively). With new rules, the allylic C−C bond fission reaction consumes 24% of 1-octene and approximately 20% of 2-octene. However, the difference in reactivity between the two isomers still appears to be due primarily to the increased importance of H atom abstraction reactions for 2-octene. Not only do the abstraction reactions of allylic H atoms consume twice as much of the initial 2-octene compared to 1-octene, but all the other abstraction reactions are more significant as well. The unique reactivity of the allyl and the but-1-en-3-yl radicals, formed from the primary dissociation of 1-octene and 2-octene respectively, likely plays

an important part in determining these trends. This is discussed further in section VI.B. V.B. RMG Reaction Uncertainty: Monte Carlo Simulations. In section IV.B, the uncertainty in the entire 1-decene model from our previous study7 was highlighted using simple Monte Carlo simulations. With a modest but reasonable estimate of uncertainty in all reactions (UF = 2), variations in the model predictions are shown to be significantly larger than experimental uncertainties. However, the MC simulations also reveal a deficiency in the original model’s ability to predict the oxidation of a few C2 species. Local sensitivity analysis in our previous study suggested that the discrepancy strongly depended on the reactions in the foundational chemistry model. This was tested by investigating the sensitivity of the predicted results for octene to two different seed mechanisms. Though predictions for the C2 species improved, there are still discrepancies between the simulation results and the experiments for C0−C2 species. As was done for the 1-decene model L


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VI. METHYL NONENOATE ISOMERS MODELING RESULTS VI.A. Methyl Nonenoate Isomer Model Development. The models used to interpret the methyl nonenoate isomers experimental results are developed following the same procedure discussed previously.7 The reaction rate rules specific to alkenes are used, along with new reaction rate rules specific to FAME oxidation that are added or updated (which includes 44 additional rules). Both USC Mech II29 and ARAMCO Mech 1.330 are investigated as foundational mechanisms for the models. Similar to the octene models presented already, the reactions generated by RMG for species within the seed mechanism are removed from the final models. There have been few modeling studies on the oxidation of large fatty acid esters, and even fewer of unsaturated FAMEs. Only four studies have modeled the oxidation of unsaturated FAMEs with the double bonds located close to the ester group. Gail̈ et al.35 conducted oxidation experiments using a Jet Stirred Reactor (JSR) in the 850−1400 K range, ∼0.1 MPa, and 0.07 s residence time with methyl trans-2-butenoate (MB2D). They developed a chemical kinetic model that was able to capture many of their observed results. Garner et al.36,37 conducted oxidation experiments with methyl trans-2-octenoate (MOCT2D) using the HPST in the 900−1450 K range, ∼2.7 MPa and ∼5.3 MPa pressures, and an average reaction time of 1.65 ms. They developed a chemical kinetic model to predict acetylene and NOx formation from the unsaturated ester. Recently, Zhang et al.38 conducted experiments with methyl trans-3-hexenoate (MHX3D) using a JSR in the 560−1200 K temperature range, ∼1 MPa, and a residence time of 0.7 s. They developed a chemical kinetic model capable of capturing the magnitudes of the major stable intermediates measured with gas chromatographic analysis. Most recently, Wagnon et al.,39 studied the autoignition behavior of methyl trans-3-hexeneoate along with gas sampling and speciation analysis using a rapid compression machine (RCM). They developed a chemical kinetic model based on the previous work of Herbinet et al.,33 where this model, and the models from Zhang et al., were used to interpret their results. The previously investigated molecules most closely resembling the isomers studied here are illustrated in Figure 15.

in section IV.B, additional MC simulations are performed here for the octene conditions to highlight the uncertainty in the kinetic models and the extent of agreement with the experimental data. These calculations are performed exactly as described in section VI.B. However, for these sets of runs, the uncertainties are only assigned to RMG-generated reactions. A UF = 2 was assigned to all “exact” rules used by RMG and UF = 5 for all “estimated” reactions by RMG. Uniform probability distributions are utilized as well. The purpose of these calculations is to investigate the extent to which the RMG-generated reactions, particular to the fuel-relevant chemistry, contribute to the overall uncertainty and the disagreement between the models and the experimental results. The simulations are performed for both octene isomers using only the USC Mech II based model, however, with a total of ∼1000 samples per isomer. Unfortunately, the ARAMCO Mech 1.3 model was found to be numerically unstable and prone to frequent failure during CHEMKIN simulations. The results presented in this paper with the ARAMCO Mech based models are performed by manually setting the maximum time step in CHEMKIN, which significantly increases the necessary time for each individual simulation. It is therefore unsuitable for the Monte Carlo simulations within the computational framework employed here. The results are presented in Figures 13 and 14 using the same manner as described in section IV.B (where IQR and IDR bands are shown). It is interesting to note that the MC simulation results illustrateed in Figures 13 and 14 indicate a pattern that is quite different from what is observed when the entire 1-decene model uncertainty is sampled, as presented in section IV.B, e.g., Figure 7. The greatest range of variability in the predicted results is primarily confined to the lowest and intermediate temperatures of the experiments, in contrast to the 1-decene results, which showed the most variability at high temperatures. In addition, the overall variability is significantly less than is observed for 1-decene at UF = 2. At the highest temperature, the variation in RMG-generated reactions had the smallest effect on the intermediate species for both octenes. The vast majority of the predicted values for O2, CO, CO2, and C2H4 fall within less than 20% of the median at the highest temperatures, which is why the uncertainty bands appear narrow. The “Best Fit” results in Figures 13 and 14 also show only modest improvement over the nominal models. This means that adjustments of greater than factors of 2−5 are needed to be made to some reaction rate rules to reconcile the remaining disagreement between the models and the experimental results. These results demonstrate that the model predictions and disagreements with the experimental data are dominated primarily by the chemistry of the smallest molecules that is described in the foundational model along with its associated uncertainties. These findings are similar to those recently presented by Hébrard et al.34 Using global sensitivity analysis of n-butane oxidation and speciation data, they showed that high temperature ignition behavior, as well as the species formation, are mainly determined by the base chemistry for C0−C2 species. Because the focus of this investigation is to study the chemistry specific to the parent molecule, and in the absence of an optimal foundational model, no further optimization of reaction rate rules for alkenes and FAMEs is undertaken here. Optimization and uncertainty reduction are left as subjects of future work.

Figure 15. Previously investigated unsaturated fatty acid methyl esters with the double bond positioned close to the ester group: (a) methyl trans-2-butenoate study of Gail et al.;35 (b) methyl trans-2-octenoate studied by Garner et al.;36 (b) methyl trans-3-hexenoate studied by Zhang et al.38 and Wagnon et al.39

The majority of the new reaction rules for the FAMEs come from ab initio studies of methyl butanoate decomposition from Huynh et al.40 and Ali et al.,41 the modeling study of Herbinet et al.,33 and the methyl butanoate model of Fisher et al.42 Additional reaction rate rules and individual reactions based on the results of the unsaturated species in Figure 15 are adapted where appropriate, and this is discussed later. The naming convention for FAMEs and their radicals utilized here was first proposed by Fisher et al.,42 and has been adapted in many other studies. In the shorthand notation of each M


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was described for decene7 and octene, the primary source of 1,3-butadiene for alkenes is the β-scission of alk-1-en-3-yl radicals. For 1-decene/octene these primarily form from the allylic H atom abstraction. For other alkene isomers studied, these radicals form in larger part from the primary dissociation (fission of allylic C−C bond) reactions. Given the close position of the double bond to the ester group, there is no direct pathway from either of the FAME molecules to form alk1-en-3-yl radicals. The flux diagram for MN2D and MN3D at 1050 K is shown in Figure 19. The primary dissociation reaction for MN2D leads to a MB2D4J radical, illustrated in Figure 19a, which is doubly stabilized by resonance. There is no direct way for this radical to form 1,3-butadiene. It will most readily undergo β-scission to form vinyl ketene (CH2CHCHCO). The abstraction of allylic H atom from MN2D leads to another radical that is doubly resonantly stabilized, MN2D4J, also illustrated in Figure 19a. This radical will preferentially undergo β-scission to form MPE24D (methyl penta-2,4-dienoate). Similarly for MN3D, as shown in Figure 19b, primary dissociation of the fuel leads to a MPE3D5J radical, which can form 1,3-butadiene via β-scission. However, this reaction is more restricted due to the presence of the carbonyl group compared to the alk-1-en-3-yl radicals from the alkenes. The abstraction of allylic H atoms from MN3D leads to the formation of MN3D2J and MN3D5J resonance stabilized radicals, illustrated in Figure 19a. The rate constants for the abstraction reactions leading to MN3D2J were increased by 50% to account for the weaker “doubly allylic” C−H bond,43 similar to the reaction rules used by Zhang et al. for methyl trans-3-hexenoate.38 MN3D2J will primarily β-scission into MPE24D, and MN3D5J will primarily β-scission into MHX35D (methyl hexa-3,5-dienoate). For all these radicals, there is either no easy pathway to 1,3butadiene or the reactions leading to it are more restricted than they would be for alkenes. Zhang et al.,38 to account for the measured 1,3-butadiene, increased the rate constant for H atom addition to MPE24D and subsequent β-scission to 1,3butadiene by a factor of ∼5 from analogous reactions for 1,3butadiene leading to ethylene and a vinyl radical.44 Their predicted mole fractions of 1,3-butadiene were still underpredicted and mole fractions of MPE24D overpredicted. Wagnon et al.39 did not measure 1,3-butadiene in their gas sampling of the RCM reaction chamber, neither was it predicted in significant quantities by their model. However, the amount of carbon recovered in their experiments was reported to be ∼6.1%. To justify this, they attributed the majority of the carbon to the parent fuel and polyunsaturated methyl esters, as was predicted by their model, and these could not be reliably measured or detected by their analytical techniques. Garner et al.45 included a pathway in their model from vinyl ketene to but-1-en-3-yl (C4H7) radicals, via CH2CHCHCO + CH3C4H7 + CO, from an analogous reaction for ketene (CH2CO + CH3C2H5 + CO). This reaction was the primary source of 1,3-butadiene in their model predictions, and no other unique pathways were considered. Gail̈ et al.,35 did not compare their model predictions to their 1,3-butadiene measurements. However, the rate of production analysis of methyl trans-2-butenoate oxidation at typical HPST conditions indicated that 1,3-butadiene in their model primarily formed from decomposition of various butene isomers (1-butene, trans2-butene, and cis-2-butene). All the butene isomers, as well 1,3butadiene, were only minor stable intermediates at their

species, the number followed by a D denotes the position of any double bonds, and a number followed by J is the position of any radical sites. For example, the shorthand notation for methyl trans-2-nonenoate is MN2D. This notation is illustrated for other species in Figures 1 and 15 and is used in discussion later. The normalized results for predicted MN2D and MN3D consumption are compared to experimental data in Figure 16.

Figure 16. Comparison of simulation results for the two FAME isomers using RMG-generated models with USC Mech II or ARAMCO Mech 1.3 as the seed mechanisms.

Here it can be seen that the reactivity of the two FAMEs follows that of 1-octene, as noted in Figure 2. Furthermore, it is apparent that the reactivity for MN2D and MN3D is not completely recovered by either model, though the closest predictions are achieved using the ARAMCO Mech 1.3 model as the seed mechanism. The discrepancies between the model predictions and the experimental data, in particular the reactivity differences between the isomers, appears to be within the combined random and systematic uncertainties of the experiments. Certainly, the difference in reactivity is smaller than seen with alkene isomers. However, the simulation results using USC Mech II as the seed model, not only have a larger absolute disagreement with the absolute measurements of the two FAME molecules but predict a more significant difference in reactivity trends. These features are discussed in the next section. VI.B. Methyl Nonenoate Isomer Reactivity. The predicted mole fractions for major stable intermediates from MN2D and MN3D using both versions of the models (ARAMCOMech1.3 and USCMechII based) are shown in Figures 17 and 18, respectively. Here it is evident that all of the generated models are able to capture the order of magnitude of the major intermediate species. The ARAMCO Mech based model provides the best agreement, not only with reactivity in Figure 16, but with the major stable intermediates for both FAME isomers studied. The remaining discrepancies are on par with those observed for octene isomer results discussed in section V. No further optimization was performed for the two FAME molecules. Of particular interest for the two FAME isomers are the reaction pathways leading to the formation of 1,3-butadiene. As N


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Figure 17. Comparison of simulation results for major stable intermediates from methyl trans-2-nonenoate, using two RMG-generated models with ARAMCOMech1.3 and USCMechII as seed mechanisms.

The observation that the resonantly stabilized radicals from the primary dissociation (fission of allylic C−C bond) of MN2D and MN3D are less reactive than the alk-1-en-3-yl radicals from alkenes leads to an important similarity that can be observed with 1-alkenes studied here and in our previous work. As described in Figure 12, the primary dissociation of 1octene leads to formation of very stable allyl radicals (aC3H5), whereas 2-octene leads to a far more unstable but-1-en-3-yl radical. In a previous single pulse shock tube study on the recombination of allyl radicals,48 it was shown that at the present experimental conditions allyl radicals do not readily dissociate below 1100 K, and preferentially recombined into 1,5-hexadiene. Only above 1100 K will allyl appreciably dissociation to form allene and an H atom. In the present study, the model for all the alkenes predict that at temperatures below 1100 K, the allyl radicals will preferentially recombine with themselves to form 1,5-hexadiene, methyl radicals to form 1-butene (C4H8-1), and H atoms to form propene (C3H6). This is supported by experimental results for 1-decene7 and 1-

experimental conditions. Only 1-butene was detected in appreciable amounts in the present study. Adjusting the rate constants in the reaction pathway leading from 1-butene to 1,3butadiene could not be done to account for the 1,3-butadiene concentrations seen experimentally while maintaining reasonable agreement with 1-butene measurements. This suggests that another pathway to 1,3-butadiene must exist. The best results for the predicted 1,3-butadiene shown in Figures 17 and 18 are achieved by using a combination of the pathways proposed by Zhang et al.38 and Garner et al.45 The rate constant used for the reaction of vinyl ketene with methyl radical is about a factor of ∼70 lower than that used by Garner et al., approximately a factor of ∼50 lower than estimates for the analogous reaction of ketene from Woods and Haynes,46 and an order of magnitude higher than proposed by Hidaka et al.47 It should be noted that these pathways are speculative. Neither MPE24D nor vinyl ketene could be positively identified and quantified in appreciable amounts. However, the high carbon recovery rate suggests that this specie (MPE24D) was either short-lived or accumulated in only minor amounts. O


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Figure 18. Comparison of simulation results for major stable intermediates from methyl trans-3-nonenoate, using two RMG-generated models with ARAMCOMech1.3 and USCMechII as seed mechanisms.

with the experimental observations of Wang et al.,9 who found indistinguishable reactivity between methyl 9-decenoate and methyl trans-5(6)-decenoates. Due to the remaining uncertainties in the fate of the primary radicals of MN2D and MN3D, explanations for the source of different reactivity trends cannot be definitively concluded at this time. Additional studies probing the chemistry of molecules such as MPE24D need to be conducted in the future.

octene (section V), for which the largest concentrations of 1butene and propene were observed. A hypothesis can then be made that the reason MN2D and MN3D follow the reactivity of 1-octene is because the radicals that form from the primary dissociation are less reactive at lower temperatures, similar to allyl radicals. If this is true, it is possible then that methyl 8-nonenoate (MN8D) and methyl trans-7-nonenoate (MN7D), which have double carbon bonds further from the ester moiety, as typically seen in fuel-relevant biodiesels, might have reactivity trends similar to those of 1octene and trans-2-octene. This hypothesis is tested here by generating two additional models for MN8D and MN7D. The experimental conditions are simulated and the results presented in Figure 20 where the fuel consumption trends are plotted. As can be seen here, for the same initial conditions, at approximately 1050 K, 50% of MN8D is predicted to be consumed compared to 67% of MN7D. For MN2D and MN3D, 63% and 73% of the initial fuel are consumed, respectively. Though the overall reactivity trends are not recovered, MN8D is predicted to be the least reactive of all the isomers. It should be noted, however, that these results conflict

VII. CONCLUDING REMARKS New experiments were conducted using the high pressure, single pulse shock tube experiment, probing the influence of the double bond position on the oxidation behavior of long fatty acid methyl esters (methyl trans-2-nonenaote and methyl trans3-nonenoate) and similarly sized alkenes (1-octene and trans-2octene). The experiments permitted the reactivity (as measured by increased fuel consumption at similar conditions) of the two fatty acid methyl ester isomers to be compared directly to their alkene side-chain analogs. It was hypothesized that any difference in reactivity between the ester isomers and the P


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Figure 19. Flux diagrams showing major pathways consuming the parent fuel at 1050 K, 5 MPa, and 2.3 ms for (a) methyl trans-2-nonenoate and (b) methyl trans-3-nonenoate. The percentages are the absolute amount that each pathway consumed (∼62% total of initial fuel for MN2D and ∼72% for MN3D). The H-abstraction reactions, indicated by dashed arrows, are those involving CH3, O, OH, H, and HO2 radicals. The dash-dot arrows indicate the H atom addition to the double bond reactions. Other reactions in each case indicate all other remaining H-abstraction, bond fission reactions.

Figure 20. Comparison of the four methyl nonenoate models. Initial conditions are 100 ppm of fuel at φ = 1, 5 MPa, 2 ms reaction time for all temperatures. Q


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The Journal of Physical Chemistry A Notes

octene isomers would be similar. However, it was found that although trans-2-octene was more reactive than 1-octene, the reactivity of the two methyl nonenoate isomers was indistinguishable at the conditions of these experiments. New chemical kinetic models were developed using the Reaction Mechanism Generator (RMG) based on the extended RMG database developed for the decene isomers. New reaction rate rules were updated specific to fatty acid methyl esters. The models were generated using two published literature models for C0−C4 species, USCMechII and ARAMCOMec1.3. The choice of the submodel was found to have a small influence on the predicted reactivity of the parent fuel, and a strong influence on the agreement between model predictions for major stable intermediates. Monte Carlo simulations were performed to probe the degree of uncertainty in the simulation results due to inherent uncertainty in the reaction rate constants as well as to evaluate the quality of agreement with the experimental results. Significant variability was found in the simulation results in the intermediate and high temperatures of the experiments when a factor of 2 uncertainty was considered in all reaction rate constants. However, it was determined that the majority of the variability at the highest temperatures of the experiments was dominated by the variability in the small molecule submodels. These results highlight the importance of a need for an accurate foundational model to have truly predictive chemical kinetics. An agreed upon small molecule, foundational model with constrained uncertainties would go a long way toward isolating and high-lighting the remaining uncertainties in models for large molecules and surrogates representing real fuels. The chemical kinetic models developed for the methyl nonenoate isomers indicate only a small difference in reactivity when ARAMCOMech1.3 was used as the base mechanism, which could not be resolved in the experiments due to the combined systematic and random errors. However, when the models were built using USCMechII, similar results could not be achieved, with the models predicting a larger than experimental error in reactivity. Additionally, significant uncertainties exist in the chemistry of unsaturated esters, with the double bond position close to the ester group, warranting further study. On the basis of simulations with the models developed for methyl 8-nonenoate and methyl trans-7-nonenoate using ARAMCOMech1.3, it is hypothesized that unsaturated esters, with the double bond position far from the ester group, the reactivity trends will be identical to those of alkenes.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Dr. Stephen Garner, Dr. Tomasz Malewicki, and Miroslaw Liszka for their help with the experiments. The authors also thank Professor William H. Green and Shamel Merchant from the Massachusetts Institute of Technology for their guidance on using RMG. This manuscript has been created in part by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357, with funding provided by the Office of Energy Efficiency and Renewable Energy, Office of Vehicle Technology.

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ASSOCIATED CONTENT

S Supporting Information *

The pressure, temperature, reaction time and the mole fractions (in ppm) of species detected for each shock is included with the Supporting Information. The gas chromatography methods used to collect the data summarized in the Supporting Information. Additionally, the final generated models used in the interpretation of the experimental results are included as well. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*K. Brezinsky. E-mail: [email protected]. Phone: 312-996-9430. R


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