Semidetailed Kinetic Model for Gasoline Surrogate Fuel Interactions

Article pubs.acs.org/EF

Semidetailed Kinetic Model for Gasoline Surrogate Fuel Interactions with the Ignition Enhancer 2‑Ethylhexyl Nitrate J. C. G. Andrae* J A Reaction Engineering, SE-183 32 Täby, Sweden ABSTRACT: A semidetailed chemical kinetic model has been developed describing the interaction of gasoline surrogate fuels with the ignition enhancer 2-ethylhexyl nitrate (2EHN). The model, which consists of 788 reactions among 157 species, has been checked for validity using ignition delay data obtained in a shock tube for the fuel n-heptane and rapid compression machine for primary and toluene reference fuels. The validation showed that the model can predict the reactivity trends in the measured data including differences observed between different fuels and operating conditions, which is an improvement compared to previous models for this system in the literature. The kinetic model has been used to study the effect of fuel sensitivity on the ignition delay when 2EHN is added to a gasoline surrogate fuel with a constant research octane number of 95. The efficiency of 2EHN is a nonlinear function of temperature that increases with fuel sensitivity and doping level. This is interpreted by results from a kinetic analysis which shows that, as fuel sensitivity increases, key chain branching reactions become more important. At lower temperatures (2. Results from a brute force sensitivity analysis on the kinetics indicate that this can be related to a lower value of the inverse pressure exponent for the ignition delay time with increasing fuel sensitivity. Moreover, the kinetic analysis shows that reactions involving the 3-heptyl radical become inhibitory or less promoting while increasing the fuel sensitivity. The results presented in this work provide important information for development of advanced combustion engines such as homogeneous charge compression ignition (HCCI).

1. INTRODUCTION Homogeneous charge compression ignition (HCCI) combustion has been drawing considerable attention due to high efficiency and lower nitrogen oxide (NOx) and particulate matter (PM) emissions.1 Two important problems prohibiting market penetration are inability to extend the operating range to high load and difficulty in controlling combustion phasing. Recent research has significantly mitigated these challenges, and thus, HCCI has a promising future for automotive and power generation applications.2 An important feature of the HCCI concept is that combustion phasing and operation range can be controlled by the modification of fuel characteristics. In this context, fuel additives may be used to dynamically control fuel reactivity during engine operation.3−8 2-Ethylhexyl nitrate (2EHN), which is a conventional ignition improver used to better the cetane number (CN) of diesel fuels, has become of interest to enhance the autoignition of regular gasoline. Ji et al.9 studied the use of 2EHN and ditert-butyl peroxide (DTBP) to enhance the autoignition of the regular gasoline in an HCCI engine at naturally aspirated and moderately boosted conditions (up to 1.8 bar absolute) with a constant engine speed of 1200 rpm. The ignition improvers could effectively enhance the HCCI autoignition reactivity of conventional gasoline, offering significant benefits for HCCI engines. In the case of 2EHN, NOx emissions increased with increased 2EHN concentration but were still acceptable and below the US-2010 standard at boosted conditions. While 2EHN has been widely shown to not affect the emissions of conventional diesel combustion, the effect of using a fuel doped with 2EHN in direct-injection, premixed low-temperature © 2015 American Chemical Society

diesel combustion (LTC) was an increase in the engine-out NOx emissions at the tested operational condition.10 The use of 2EHN can be combined with reactivity controlled compression ignition (RCCI), which is an autoignition combustion strategy that operates through in-cylinder blending of diesel-like and gasoline-like fuels.11,12 Splitter and Reitz13 showed that, through proper optimization of engine conditions and fuels, engine efficiency may be increased by using RCCI. As a result of its importance, 2EHN has been investigated in fundamental experiments while detailed theoretical and modeling studies have also been undertaken.14−21 Goldsborough et al.21 recently conducted experiments and modeling to investigate the autoignition behavior of two gasoline surrogates doped with 2EHN to better understand dopant interactions with nonaromatic and aromatic fuels, including accelerating kinetic pathways and enhanced exothermicity. They used diluted reaction conditions in their study and two fuel sensitivities (S = 0 and S ≈ 4). The results indicated that the doping effectiveness of 2EHN was fairly similar between the two simple surrogates studied, where minor influences were observed at the lowest temperatures, while at higher temperatures the influence was large and very nonlinear with doping level. The detailed kinetic model was able to capture some of the reactivity trends. However, the extents of predicted cetane enhancement were too large, while the differences in fuel interactions between the two fuels gave an excessive stimulation of the nonaromatic blend. Received: March 19, 2015 Revised: May 6, 2015 Published: May 7, 2015 3944

DOI: 10.1021/acs.energyfuels.5b00589 Energy Fuels 2015, 29, 3944−3952

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Energy & Fuels

have some exothermicity and thus can provide a thermal stimulant to supplement the accelerating kinetic pathways.21 Table 1 shows the added reactions with associated rate constants for the 2EHN subset where reaction steps involving 3-heptyl radicals have been added. The subsequent reactions of NO2 and CH2O are already contained in the TRF base mechanism. The overall model consists of 157 species and 788 reactions. The results from the validation of the mechanism are described in Section 4.

This indicates that improvements could be made in the kinetic modeling of the interaction between 2EHN and surrogate fuels. Moreover, the effect of fuel sensitivity (S = RON − MON) is important when using gasoline as fuel but has not been examined much before. The objective of this study is to develop a semidetailed chemical kinetic model for the interaction of 2EHN with gasoline surrogate fuels and provide more insight into the effect of fuel sensitivity on the ignition delay. Reactions describing 2EHN decomposition are added to a validated model for toluene reference fuel including sensitization effect of NO. After validation against ignition delay data measured in a shock tube and rapid compression machine, the new model is being used to study the effect of increased fuel sensitivity on the ignition delay when 2EHN is added to a gasoline surrogate fuel with constant RON. Sensitivity analysis is conducted, and the results are discussed in terms of reactions kinetics. The results presented provide important information for the development work on, for example, advanced combustion engines such as HCCI and RCCI.

3. NUMERICAL SOLUTION METHOD All simulations were performed with the CANTERA software package.24 Ignition delay under adiabatic conditions (Section 4.1.1 and 4.2 below) assumed a homogeneous reactor with a constant internal energy, constant volume constraint. Ignition was assumed to be accomplished at the moment of maximum pressure rise rate. A similar ignition delay time (for high-temperature ignition) is achieved when having an ignition criterion as the time when the temperature has increased 400 K from the initial temperature. For simulations of ignition delay in a RCM (Section 4.1.2 and 4.1.3 below), the rate of change of volume was introduced on the basis of the specific machine geometry and compression ratio and to account for heat losses.

4. RESULTS AND DISCUSSION 4.1. Model Validation. 4.1.1. Neat n-Heptane in a Shock Tube. To check the validity of the kinetic model for the n-

2. CHEMICAL KINETIC MODEL The base mechanism for model development was a semidetailed chemical kinetic model for toluene reference fuels with added reactions describing the sensitization effect of NO.5,22 This mechanism could successfully predict the influence of NO on the combustion phasing of gasoline surrogate fuels in a HCCI engine. In this work, the mechanism has been extended to include reactions for 2EHN decomposition. 2EHN (see Figure 1) decomposes forming form-

Figure 1. Chemical structure of 2-ethylhexyl nitrate. aldehyde, nitrogen dioxide, and specifically 3-heptyl radicals which are active chemical species.16,17,20 Hartmann et al.,20 who studied the fuel n-heptane, argued that generating new predictive models for EHN/fuel mixtures from the pure-fuel mechanisms of these fuels is straightforward as the reaction-accelerating effect of the heptyl radicals that originate from EHN decomposition is most likely also found for hydrocarbons other than n-heptane. Therefore, a similar ignitionenhancing effect of 2EHN is also expected for other fuels. The products from 2EHN decomposition interact with the fuel and other gases to accelerate the ignition process, and the early reactions often

Figure 2. Comparison of measured and simulated ignition delay times for n-heptane with 0.1 and 1.0% (by weight) 2EHN and pure nheptane (0.0%) in air. p5 = 4.0 MPa, λ = 1.0. Symbols: Experiments by Hartmann et al.20

Table 1. Reactions and Rate Constants for 2-Ethylhexyl Nitrate (2EHN) and Decomposition Products number

reaction

Aa

778 779 780 781 782 783 784 785 786 787 788

2EHN → C7H15-3 + CH2O + NO2 C7H16 + NO2 ↔ C7H15-3 + HONO C7H15-3 + NO2 → C5H11 + CH3HCO + NO C7H16 + C7H15-1 → C7H15-3 + C7H16 C7H16 + C7H15-3 → C7H15-1 + C7H16 C7H15-1 → C7H15-3 C7H15-3 → C7H15-1 C7H16 + C7H15-2 → C7H15-3 + C7H16 C7H16 + C7H15-3 → C7H15-2 + C7H16 C7H15-2 → C7H15-3 C7H15-3 → C7H15-2

1.00 × 10 5.80 × 1013 1.20 × 1014 6.00 × 1011 9.00 × 1011 8.32 × 109 2.65 × 108 6.00 × 1011 6.00 × 1011 5.75 × 109 5.75 × 109 16

na

Eaa

ref

0.00 0.00 0.00 0.00 0.00 0.98 1.38 0.00 0.00 1.39 1.39

167.36 117.57 62.76 43.51 51.46 141.25 151.80 43.51 43.51 166.10 166.10

14, 17, 20 5b 5c 23c 23c 23c 23c 23c 23c 23c 23c

kf = ATn exp (−Ea/RT). A units: mol, cm, s. Ea units: kJ/mol. b↔ Rate constant for reversed reaction calculated with the equilibrium constant and thermochemical data. cThe original rate constant has been multiplied by a factor of 6.

a

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Figure 3. Comparison of measured and simulated ignition delay times for n-heptane with 0.1% (by weight) 2EHN and pure n-heptane (0.0%) in air. p5 = 4.0 MPa, λ = 2.0. Symbols: Experiments by Hartmann et al.20

Figure 6. Ignition delay in a RCM. To = 318 K, po = 0.1 MPa, λ = 2.5, and CR = 16. Experiment by Tanaka et al.18

Figure 4. Pressure as a function of time in a RCM. CO2/air, CR = 16, To = 318 K, and po = 0.1 MPa. Experiment by Tanaka et al.18

Figure 7. Ignition delay in a RCM. λ = 1.0, [O2] = 11.4 mol %, CR = 10.2. TRF91 = 20 vol % toluene, 12.8 vol % n-heptane, and 67.2 vol % iso-octane. t1 = cool flame ignition delay. Experiments by Goldsborough et al.21

Figure 5. Pressure as a function of time in a RCM. To = 318 K, po = 0.1 MPa, λ = 2.5, and CR = 16. Experiment by Tanaka et al.18

Figure 8. Ignition delay in a RCM using different doping levels of 2EHN. λ = 1.0, [O2] = 11.4 mol %, and CR = 10.2. Symbols are experiments by Goldsborough et al.21

heptane fuel component, the shock tube experiments by Hartmann et al.20 were used. They measured ignition delay times (τ) for a temperature range of 690 K ≤ T5 ≤ 1275 K at a pressure of 40 ± 2 bar for stoichiometric and lean mixtures

under engine relevant conditions. Figures 2 and 3 show the results from the simulations. The model can predict the effect on the ignition delay by adding 2EHN to n-heptane for a large range of temperatures 3946


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Figure 9. Ignition delay in a RCM using different doping levels of 2EHN. λ = 1.0, [O2] = 11.4 mol %, CR = 10.2. TRF91 = 20 vol % toluene, 12.8 vol % n-heptane, 67.2 vol % iso-octane. Symbols are experiments by Goldsborough et al.21

Figure 12. Relative efficiency of TRF91 compared to PRF91 for different doping levels of 2EHN. λ = 1.0, [O2] = 11.4 mol %, CR = 10.2. TRF91 = 20 vol % toluene, 12.8 vol % n-heptane, and 67.2 vol % iso-octane. Symbols are experiments by Goldsborough et al.21

Figure 10. Relative efficiency of PRF91 when using different doping levels of 2EHN. λ = 1.0, [O2] = 11.4 mol %, and CR = 10.2. Symbols are experiments by Goldsborough et al.21

Figure 13. Calculated ignition delay (τ) for an undoped gasoline surrogate fuel. λ = 1.0.

for the RCM in Table 1 of Tanaka et al.25 was used to set up the RCM simulations. The compression stage in the RCM is taken into account, and to model heat losses in the RCM, the heat transfer model by Tanaka et al.25 was used:

Figure 11. Relative efficiency of TRF91 when using different doping levels of 2EHN. λ = 1.0, [O2] = 11.4 mol %, CR = 10.2. TRF91 = 20 vol % toluene, 12.8 vol % n-heptane, and 67.2 vol % iso-octane. Symbols are experiments by Goldsborough et al.21

V (t ) = π (r + δ)2 × (h + 2δ)

(1)

⎧ h2 + d − u pt , t ≤ 0 ⎪ ⎪ h = ⎨ h2 + d(1 − u pt /2d)2 , 0 < t ≤ 2d /u p ⎪ ⎪ h2 , t > 2d /u p ⎩

(2)

d = u pts/2

(3) 0.5

δ = (α u × t ) ,

t>0

(4)

In this case, d in eq 3 was calculated to be 0.0024 m on the basis of a piston speed of 10 m/s and a time between the inflection point and peak compression pressure of 0.48 ms. The thermal boundary layer was assumed to be laminar, and the thermal diffusivity used to calculate the thickness of the thermal boundary layer in eq 4 was set to 15 × 10−6 m2/s on the basis of the best fit to an inert gas/air mixture (see Figure 4). To simplify the analysis, a second inflection point that occurs during the major pressure rise due to combustion was not considered in the calculations.

and is also sensitive to changes in equivalence ratio and doping level. The influence of 2EHN on the ignition delay is the largest in the low-temperature regime (770−1000 K). 4.1.2. PRF in a RCM. Tanaka et al.18 measured ignition delay times in a RCM at fuel-lean conditions (λ = 2.5) for PRFs doped with different amounts of 2EHN. To check the validity of the kinetic model, these data were simulated. The data given 3947


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Energy & Fuels Table 2. Parameters Used to Fit Eq 8 for Two Gasoline Surrogate Fuelsa

a

fuel

ln (A1)

n1

B1

ln (A2)

n2

B2

ln (A3)

n3

B3

S=0 S=8

−18.90 −17.90

0.06 0.25

15 300 15 500

23.75 22.00

2.87 2.43

−10 100 −10 000

−10.20 −10.20

1.00 0.92

13 900 13 450

A unit: ms; B unit: K; Values of n to be used with pressure in bar.

Figure 17. Calculated relative efficiency for a gasoline surrogate fuel doped with 1.0% 2EHN. (a) po = 2.0 MPa and (b) po = 4.0 MPa. Figure 14. Comparison between a three-part exponential model and a semidetailed kinetic model. RON = 95, S = 0, and λ = 1.0.

Figure 18. Calculated relative efficiency for a gasoline surrogate fuel doped with 3.0% 2EHN. (a) po = 2.0 MPa and (b) po = 4.0 MPa. Figure 15. Comparison between a three-part exponential model and a semidetailed kinetic model. RON = 95, S = 8, λ = 1.0.

4.1.3. PRF and Toluene + PRF Mixture in a RCM. Goldsborough et al. investigated the effect of 2EHN on the ignition delay for gasoline surrogate fuels in a RCM.21 The compressed pressure was 21 bar, covering compressed temperatures from 675 to 1025 K with stoichiometric fuel− oxygen ratios at O2 = 11.4%. The fuels were a PRF and a toluene reference fuel (TRF) blend of n-heptane/iso-octane/ toluene where the aromatic fraction of the latter was set to 20% (liquid volume). The content of n-heptane was adjusted so that the overall reactivity of the undoped fuels was similar and had a Anti-Knock Index (AKI) of approximately 91 and a cetane number of approximately 25. Doping levels of 0.1, 1.0, and 3.0% (liquid volume basis) were used. To simulate the experiments above, in addition to the data given on the RCM in the article, the supplementary data given in ref 21 was used to set up the RCM simulations. The same RCM model to simulate the experiments was used as in Section 4.1.2. However, no stopping distance was included, and the thermal diffusivity was set to 7.5 × 10−6 m/s for best fit with inert gas/air mixtures. Figure 7 shows the results for simulations of undoped mixtures. The general trends in the data are well predicted by the model. However, the delay times are significantly under-

Figure 16. Calculated relative efficiency for a gasoline surrogate fuel doped with 0.1% 2EHN. (a) po = 2.0 MPa and (b) po = 4.0 MPa.

The simulations show very good agreement for the fuel PRF90 (see Figures 5 and 6). However, the model somewhat under-predicts the delay times for iso-octane (PRF100, see Figure 6). 3948


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Energy & Fuels Table 3. Brute Force Sensitivity Analysisa

a

number

reaction

Sign 2.0 MPa

Sign 4.0 MPa

622 625 755 756 778 780 782 784 786 788

HO2 + NO ↔ NO2 + OH NO2 + H ↔ NO + OH O2C7H14O2H + NO → OH +2CH2O + CH2CHCH3 + C2H4 + NO2 AC8H16OOH-BO2 + NO → OH + 2CH2O + IC4H8 + C2H4 + NO2 2EHN → C7H15-3 + CH2O + NO2 C7H15-3 + NO2 → C5H11 + CH3HCO + NO C7H16 + C7H15-3 → C7H15-1 + C7H16 C7H15-3 → C7H15-1 C7H16 + C7H15-3 → C7H15-2 + C7H16 C7H15-3 → C7H15-2

−0.010 −0.004 0.001 0.010 −0.032 −0.032 −0.025 −0.004 −0.058 −0.007

−0.014 −0.001 0.002 0.015 −0.046 −0.027 −0.028 −0.002 −0.065 −0.004

To = 675 K, λ = 1.0, S = 0, 1% 2EHN.

Table 4. Brute Force Sensitivity Analysisa

a

number

reaction

Sign 2.0 MPa

Sign 4.0 MPa

622 625 729 755 756 766 769 770 778 780 782 786 788

HO2 + NO ↔ NO2 + OH NO2 + H ↔ NO + OH NO + OH(+M) ↔ HONO(+M) O2C7H14O2H + NO → OH + 2CH2O + CH2CHCH3 + C2H4 + NO2 AC8H16OOH-BO2 + NO → OH + 2CH2O + IC4H8 + C2H4 + NO2 C6H5CH2 + HONO ↔ C6H5CH3 + NO2 C6H5CH2 + NO2 ↔ C6H5CH2O + NO C6H5CH2OO + NO ↔ NO2 + C6H5CH2O 2EHN → C7H15-3 + CH2O + NO2 C7H15-3 + NO2 → C5H11 + CH3HCO + NO C7H16 + C7H15-3 → C7H15-1 + C7H16 C7H16 + C7H15-3 → C7H15-2 + C7H16 C7H15-3 → C7H15-2

−0.137 −0.055 −0.004 0.006 0.020 −0.040 −0.009 0.149 −0.012 0.013 −0.017 −0.036 −0.002

−0.146 −0.023 −0.002 0.006 0.018 −0.074 0.031 0.148 −0.010 0.019 −0.014 −0.030 −0.001

To = 675 K, λ = 1.0, S = 8, 1% 2EHN.

Figure 12 shows Reff for TRF91 divided by Reff for PRF91 (i.e., combining the data in Figures 10 and 11). A value higher than 1 means that that PRF91 is more efficient than TRF91 when doped with 2EHN. Although the measured data (taken directly from the Supporting Information in ref 21) when presented in this way are very scattered, the trend is that TRF91 is more efficient than PRF91 for higher concentrations of 2EHN and with increasing temperature. The model can also predict this trend. Overall, the validation of the semidetailed kinetic model presented in this section has showed that the model can predict the reactivity trends in measured data including differences observed between different fuels and operating conditions. The model is therefore suitable for use in further simulation studies of this system. 4.2. Influence of Fuel Sensitivity on the Relative Efficiency of 2EHN. In this section, the validated kinetic model is further used to examine the effect of fuel sensitivity and 2EHN for undiluted mixtures at different pressures and temperatures. 4.2.1. Undoped Fuel. Kalghatgi et al.27 has developed a correlation to determine the volume fractions of n-heptane, isooctane, and toluene in a gasoline surrogate fuel that matches a real gasoline for both RON and MON.

predicted especially in the negative temperature coefficient (NTC) region. This observed deviation may not necessarily mean that the kinetic model is too reactive. It can also be explained by physical−chemical couplings that occur in RCMs due to reaction chamber−crevice interactions during multistage ignition events that are not accounted for by the RCM model.26 A more physically realistic RCM model to account for fluid dynamic effects during compression and postcompression charge inhomogeneity is beyond the scope for this study. The model was further used to simulate different doping levels of 2EHN. Figures 8 and 9 show the results of the simulations together with the measured data for the overall ignition delay. Although the model under-predicts the measured delay times, especially for the undoped fuel mixture, the overall trends in the measured data can be captured by the model. Figures 10 and 11 show the results in Figures 8 and 9 presented as a relative efficiency (Reff) where the ignition delay time for the doped mixture is divided with the ignition delay time for the undoped mixture. The reactivity trends in the measured data can be predicted by the model including the differences observed between the two fuels; for example, for PRF91, the relative efficiency of 2EHN decreases (Reff increases) at the highest compressed temperatures and the lowest doping level (see Figure 10). However, there is an overestimation of the enhancement by 2EHN at temperatures below around 770 K and an underestimation at higher temperatures (see Figures 10 and 11).

RON = (1.0023 − 1.0355 PRF)TMF + 118.09 TMF − 1.777 (5)

S = 14.07 TMF

(6)

In eqs 5 and 6, TMF is the mole fraction of toluene in the fuel blend, and in eq 6, S is the fuel sensitivity (RON-MON). This 3949


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The effect of pressure on the ignition delay is also important. Figure 13 shows that in addition to lowering the ignition delay time, the NTC behavior is shifted toward higher temperatures with increased pressure. Increasing the initial pressure for a given temperature alters the equilibrium of the reactions that initiate alkylperoxy radical isomerization (R· + O2 ↔ RO2·) with the equilibrium favoring RO2· as pressure increases. For the global pressure dependence on the ignition delay, a PRF (S = 0) exhibits a higher value of the inverse pressure exponent for the delay time than a non-PRF (S > 0), resulting in τ for a non-PRF that could be higher than that for it’s associated RON. This tendency increases with pressure and decreases with temperature and is mostly marked with olefenic and toluenic fuels.29−31 To estimate the value of the inverse pressure exponent, it is usually assumed that the ignition delay can be described by a simple Arrhenius type equation with a pressure correction of the form shown in eq 7. τ = Ap−n e(B / T )

(7)

Then, a linear model is fitted by multiple regression, with 1/ T and ln (p) as independent variables and ln (τ) as the dependent variable.27,30 However, since eq 7 is a single-step correlation that attempts to represent the ignition delay of distinct temperature regimes, the NTC behavior that is important for PRF and fuels with a low value of S cannot be described properly. To account for NTC behavior for those fuels, Yates et al. proposed a correlation where the overall ignition delay is described by a three-part exponential model32 τoverall = {(τ1 + τ2)−1 + (τ3)−1}−1

(8)

This model involves two distinct regimes, a two-stage low temperature regime and a single-stage high temperature regime. In eq 8, each ignition delay is described by eq 7. The stages of low-temperature regime are sequential and expressed as an arithmetic sum of individual ignition delays τ1 and τ2. The hightemperature regime represents an alternative competing pathway with ignition delay τ3. Equation 8 was used to estimate the pressure dependence for gasoline surrogate fuels with different fuel sensitivity. Table 2 shows the parameters used in eq 8 for the best fit to kinetic modeling results for RON = 95 and two different values of S. Figures 14 and 15 show a comparison of predictions of the three-part exponential model and the semidetailed kinetic model for TRF used in this work. Good agreement is found, and as would be expected, the overall pressure dependence is more pronounced for the PRF fuel (S = 0, Table 2). 4.2.2. Fuel Doped with 2EHN. The gasoline surrogate fuel (RON = 95) was doped with different levels of 2EHN (0.1, 1.0, and 3.0 vol %), and the same simulations were conducted for the undoped fuel. Figures 16−18 show the results as a relative efficiency. Overall, the efficiency increases (lower value of Reff) with S and doping level, but it is highly nonlinear. At temperatures below around 750 K, the efficiency actually decreases as S is increased. The effect of pressure on the results is also evident. At the higher pressure (4.0 MPa), Reff is somewhat higher compared to the lower pressure (2.0 MPa), and at temperatures below around 750 K, the efficiency actually decreases (higher value of Reff) even more for po = 4.0 MPa as S is increased (see Figures 16b−18b). This is a fuel effect that can be related to the

Figure 19. Calculated sensitivity coefficients as a function of initial temperature. po = 4.0 MPa, λ = 1.0, and 1% EHN.

correlation was used to determine fuel compositions of a gasoline surrogate fuel with a constant RON of 95 and varying fuel sensitivity. Figure 13a,b shows calculated ignition delay times as a function of temperature for two different pressures. It is wellknown that the ignition delay is highly correlated to fuel composition.28 As the fuel sensitivity changes, the ignition delay also changes. At lower temperatures, fuels with higher S exhibit longer τ, and for higher temperatures, the negative temperature coefficient (NTC) behavior is less pronounced and τ becomes shorter with increased S. 3950


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→ C5H11 + CH3HCO + NO) becomes inhibitory with decreasing temperature (see Figure 19e). Figure 19g shows that for fuels with a high fuel sensitivity R786 (C7H16 + C7H15-3 → C7H15-2 + C7H16) becomes less promoting below around 740 K. This has a strong influence on the relative efficiency as indicated in Figure 17b, where the shapes of the curves are similar at lower temperatures to the ones in Figure 19g.

differences in inverse pressure exponent for the delay time as shown in the previous section. 4.2.3. Sensitivity Analysis. The results were further analyzed where a brute force sensitivity analysis on the kinetic mechanism was conducted. In such an analysis, the forward rate constants are doubled one at a time for each reaction, and the sensitivity for the main ignition delay is then defined as Sign =

τ(2A) − τ(A) τ (A )

5. CONCLUSIONS A semidetailed chemical kinetic model has been developed describing the interaction of gasoline surrogate fuels with the ignition enhancer 2-ethylhexyl nitrate (2EHN). The model, which consists of 788 reactions among 157 species, has been checked for validity using ignition delay data obtained in a shock tube for the fuel n-heptane and rapid compression machine for primary and toluene reference fuels. The validation showed that the kinetic model can predict the reactivity trends in the measured data including differences observed between different fuels and operating conditions, which is an improvement compared to previous models for this system in the literature. The model is therefore suitable for use in further simulation studies. The validated kinetic model has been used to study the effect of fuel sensitivity on the ignition delay when 2EHN is added to a gasoline surrogate fuel with a constant research octane number of 95. Generally, the efficiency of 2EHN becomes a nonlinear function of temperature that increases with fuel sensitivity and doping level. Results from a kinetic analysis show that, as S increases, the more important the chain branching reactions HO2 + NO → NO2 + OH, NO2 + H → NO + OH, and HONO(+M) → OH + NO(+M) become. This helps to explain why the efficiency of 2EHN increases with S and doping level. At lower temperatures (2. Results from a brute force sensitivity analysis on the kinetics indicate that this can be related to a lower value of the inverse pressure exponent for the ignition delay time with increasing S. Moreover, the kinetic analysis shows that reaction C7H15-3 + NO2 → C5H11 + CH3HCO + NO becomes inhibitory with decreasing temperature and increasing S while reaction C7H16 + C7H15-3 → C7H15-2 + C7H16 becomes less promoting. Calculated brute force sensitivity coefficients as a function of temperature for selected reactions show that there is a stronger variation in the sensitivity coefficients for temperatures below around 830 K, indicating a more significant effect on the lower temperature chemistry by adding 2EHN. The results presented in this work provide important information for development of advanced combustion engines such as homogeneous charge compression ignition (HCCI).

(9)

In eq 9, A is the pre-exponential factor in the rate expression for a reaction. A negative value of Sign means that an increased rate for the reaction leads to a shorter ignition delay. In the analysis, sensitive reactions in the 2EHN decomposition/NOx chemistry have been sought which are able to explain the observed behavior shown in Figures 16−18. Tables 3 and 4 show the results at a low initial temperature, 1% 2EHN doping, and two values of S. By inspecting Figure 17a,b at To = 675 K, Reff decreases from ∼0.32 to ∼0.29 for S = 0. Table 3 shows that, for S = 0, there is overall increased sensitivity toward enhancement by 2EHN as the initial pressure is doubled. Especially, reactions in which formed 3-heptyl radicals from 2EHN decomposition react with n-heptane (R782 and R786) show increased sensitivity with pressure. Figure 17a,b also shows that, at To = 675 K, Reff increases from ∼0.4 to ∼0.52 for S = 8. Table 4 shows that, for S = 8, there is an overall decreased sensitivity for reactions toward enhancement by 2EHN as pressure is doubled. Although some reactions show a large negative sensitivity (R622 and R766), at the same time, other reactions with competing pathways for NO and NO2 consumption show an even larger positive sensitivity (R769 and R770), the net effect being a decreased sensitivity toward enhancement by 2EHN. It can be noted that reactions 769 and 770 are not sensitive for S = 0. For selected reactions, sensitivity coefficients were also calculated as a function of temperature at po = 4.0 MPa (see Figure 19a−h). As expected, the sensitivity coefficients for the reactions change with temperature and fuel composition. By analyzing the effect of temperature, there is a stronger variation in the sensitivity coefficients for temperatures below around 830 K, indicating a more significant effect on the lower temperature chemistry by adding 2EHN. This was also suggested by Goldsborough et al. using a detailed kinetic model.21 When the fuel sensitivity increases, the sensitivity coefficients for chain branching reactions decrease in value. Figure 19a,b,h shows that, the higher the value of S, the more sensitive the fuel becomes to R622 (HO2 + NO → NO2 + OH), R625 (NO2 + H → NO + OH), and R729 (HONO(+M) → OH + NO(+M)). This can be compared with Figures 16−18 which show that this leads to an efficiency of 2EHN that increases with fuel sensitivity and doping level. Nevertheless, Figure 19c,d shows that the sensitivity of R769 (C6H5CH2 + NO2 → C6H5CH2O + NO) and R770 (C6H5CH2OO + NO → NO2 + C6H5CH2O) increases below 830 K. This is important as R770 competes with the chain branching reaction R622 for NO and R769 competes with R625 and R766 (C6H5CH3 + NO2 → C6H5CH2 + HONO) for NO2 when S > 2 (see Figure 19f). It can also be noted that for the highest fuel sensitivity R780 (C7H15-3 + NO2

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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NOMENCLATURE CR = compression ratio, − d = stopping distance during compression in RCM, m h = actual cylinder height, m DOI: 10.1021/acs.energyfuels.5b00589 Energy Fuels 2015, 29, 3944−3952

Article

Energy & Fuels

(17) Bornemann, H.; Scheidt, F.; Sander, W. Int. J. Chem. Kinet. 2002, 34, 34−38. (18) Tanaka, S.; Ayala, F.; Keck, J. C.; Heywood, J. B. Combust. Flame 2003, 132, 219−239. (19) Lee, K.; Lee, C.; Ryu, J.; Kim, H. Energy Fuels 2005, 19, 393− 402. (20) Hartmann, M.; Tian, K.; Hofrath, C.; Fikri, M.; Schubert, A.; Schießl, R.; Starke, R.; Atakan, B.; Schulz, C.; Maas, U.; Kleine Jäger, F.; Kühling, K. Proc. Combust. Inst. 2009, 32, 197−204. (21) Goldsborough, S. S.; Johnson, M. V.; Banyon, C.; Pitz, W. J.; McNenly, M. J. Proc. Combust. Inst. 2015, 35, 571−579. (22) Andrae, J. C. G. Fuel 2013, 107, 740−48. (23) Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K. Combust. Flame 1998, 129, 253−280. (24) CANTERA 1.7, http://sourceforge.net/projects/cantera, Accessed: June 1, 2010. (25) Tanaka, S.; Ayala, F.; Keck, J. C. Combust. Flame 2003, 133, 467−481. (26) Goldsborough, S. S.; Mittal, G.; Banyon, C. Proc. Combust. Inst. 2013, 34, 685−693. (27) Kalghatgi, G.; Babiker, H.; Badra, J. SAE Int. J. Engines 2015, 8 (2), 505−519 DOI: 10.4271/2015-01-0757. (28) Perez, P. L.; Boehman, A. L. Energy Fuels 2012, 26, 6106−6117. (29) Bradley, D.; Head, R. A. Combust. Flame 2007, 147, 171−184. (30) Fikri, M.; Herzler, J.; Starke, R.; Schulz, C.; Roth, P.; Kalghatgi, G. T. Combust. Flame 2008, 152, 276−281. (31) Andrae, J. C. G.; Head, R. A. Combust. Flame 2009, 156, 842− 851. (32) Yates, A.; Swarts, A.; Viljoen, C. SAE Tech. Pap. Ser. 2005, DOI: 10.4271/2005-01-2083.

h2 = clearance height between piston and cylinder head, m HCCI = homogeneous charge compression ignition 2EHN = 2-ethylhexyl nitrate RON = research octane number, − MON = motor octane number, − PRF = primary reference fuel RCCI = reactivity controlled compression ignition RCM = rapid compression machine S = fuel sensitivity, − Sign = sensitivity coefficient, − p = pressure, Pa po = initial pressure, Pa pc = pressure at end of compression, Pa p5 = compressed pressure in shock tube, Pa r = cylinder bore radius, m t = time, s ts = time between inflection point and maximum compressed pressure, s up = piston speed in RCM, m/s T = temperature, K To = initial temperature, K Tc = temperature at end of compression, K T5 = compressed temperature in shock tube, K TMF = toluene mole fraction, − TRF = toluene reference fuel, − V = volume, m3 Greek Letters

αu = thermal diffusivity, m2/s δ = thickness of thermal boundary layer, m λ = air/fuel equivalence ratio, − τ = ignitition delay, ms

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REFERENCES

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Semidetailed Kinetic Model for Gasoline Surrogate Fuel Interactions

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