Kinetics of the Reactions of H and CH Radicals with n ...Generation of CH3 and H atoms. Methyl...

Paper # 070RK-0189-135164 Topic: Reaction Kinetics

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8th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute

and hosted by the University of Utah May 19-22, 2013

Kinetics of the Reactions of H and CH3 Radicals with n-Butane: Shock-Tube Experiments and the Establishment of Relative and

Absolute Rates through Reaction Network Analysis

Jeffrey A. Manion, David A. Sheen, and Iftikhar A. Awan

Chemical Sciences Division

National Institute of Standards and Technology Gaithersburg, MD, 20899-8320

Abstract

Methyl radicals and hydrogen atoms are important intermediates in the combustion of hydrocarbon fuels. Both species attack aliphatic fuels via abstraction of H to form unstable alkyl radicals and either CH4 or H2. The relative and absolute rates of these processes are important parameters in combustion and fuel pyrolysis models and can impact global phenomena of interest such as ignition delay times. A difficulty in studying these processes at high temperatures is that rapid decomposition of the intermediate alkyl radicals produced in the initial H abstraction reaction leads to formation of both additional H and additional CH3, making it difficult to separate the kinetic behavior of the two species under many conditions.

In the present work we have carried out shock-tube studies in which we have, in separate experiments, used the thermal decomposition of hexamethylethane or tert-butylperoxide to generate either H or CH3 in the presence of n-butane, a representative hydrocarbon fuel. A radical-chain inhibitor may or may not have been added to the mixture to be studied. An experimental design algorithm has been applied to select concentrations and conditions that allow the kinetic processes of interest to be disentangled. Experiments were conducted between 900 K and 1150 K and pressures of 150 to 300 kPa. Hydrogen atoms and CH3 radicals were generated at low concentrations [< 50 μL/L (ppm)] in the presence of 770 to 10 000 μL/L of n-butane. Toluene was added as a radical-chain inhibitor at levels of up to 30 000 μL/L. The mixture selections result in well-characterized systems in which the significant products are produced by a limited set of chemical reactions. In conjunction with post-shock product analyses, detailed chemical modeling, and the use of polynomial chaos expansion techniques, relative rate constants for attack of H and CH3 on the primary and secondary hydrogens of n-butane have been determined. Data on the main olefin products are found to constrain the relative rates, while data on secondary products establish reaction network relationships that limit and allow improved estimation of the absolute rate constants. The presently determined rate constants are compared with values used in current combustion models. Implications with respect to the modeling of n-butane ignition delay times are examined.

Key Words: shock tube, kinetics, methyl radicals, H atoms, butane, reaction networks. Corresponding author: [email protected] 1. INTRODUCTION

The present paper is concerned with the kinetics of the attack of methyl radicals and hydrogen atoms on n-butane, a

representative aliphatic fuel. The initial reaction in both cases is abstraction of H, forming alkyl radicals and either CH4 or H2. At high temperatures the alkyl radicals are unstable, leading to fuel breakdown and propagation of radical chain reactions. Attack of H or CH3 may occur at either primary or secondary hydrogen sites, leading to different subsequent


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products and chemistry. The relative and absolute rates of these processes are important parameters in combustion and fuel pyrolysis models and can impact global phenomena of interest such as ignition delay times.

There are relatively few kinetic data pertaining directly to these reactions at high temperatures, where rapid

decomposition of the intermediate alkyl radicals results in the regeneration of both additional H and additional CH3. Both species can propagate subsequent chains, making it difficult to separate the kinetic behavior under many conditions.

In the present work we seek to deconvolve the processes by carrying out a combined set of experiments wherein H

and CH3 are generated separately in shock-tube experiments in the presence of excess n-butane. An experimental design algorithm has been applied in conjunction with detailed chemical kinetic modeling to select concentrations and conditions that allow the kinetic processes of interest to be disentangled. The results are analyzed on the basis of a chemical kinetic model and polynomial chaos expansion techniques in order to obtain relative and absolute rate constants for attack of H and CH3 on the primary and secondary hydrogens of n-butane. Finally, we examine the effects of using the presently determined rate constants with respect to the modeling of n-butane ignition delay times. 2. EXPERIMENTAL METHODS

Shock Tube Methodology. Experiments are carried out in a heated single pulse shock tube configured so as to have

reaction times of (500 ± 50) μs, as determined by high speed pressure transducers. Details of the apparatus have been reported elsewhere.1 The present study involves the creation of small quantities [< 50 μL/L (ppm)] of the radicals of interest, either hydrogen atoms or methyl radicals, via the thermal decomposition of an appropriate precursor. The radicals are generated in the presence of much larger concentrations of n-butane, the substrate of interest. The radical chain inhibitor toluene has been added to some mixtures, but not all. Stable reaction products are determined from post-shock gas chromatographic (GC) analyses.

Shock temperatures in our experiments are determined by following a standard unimolecular reaction with well-defined rate parameters. Experimental rate constants are determined utilizing

kstd = τ -1 ln([std]i/[std]f)],

where τ is the residence time and the subscripts i and f refer to the initial and final concentrations, respectively. The rate expression for the standard, kstd = Aexp(-E/T), is easily rearranged to obtain the temperature of a particular experiment. The work reported herein uses the unimolecular decompositions of chlorocyclo-pentane, 4-vinylcyclohexene, and hexamethylethane as standard reactions, the selection based on the mixture and temperature range of interest. In all cases the monitored reaction products from the standards are expected to be stable and not formed by any other processes. The rate parameters, taken from previous work,2 including our recent examination of several temperature standards3 are: k(chlorocyclopentane → cyclopentene + HCl)/s-1 = 4.47×1013exp(-24570/T), k(4-vinylcyclohexene → 2butadiene)/s-1 = 2.51×1015exp(-31100/T) s-1, and k(hexamethylethane → 2 t-butyl)/s-1 = 2.51×1016exp(-34400/T) s-1. For mixtures containing HME, chlorocyclopentane was used as the temperature standard below 1030 K. At higher temperatures this standard is not reliable due to high conversions and attendant boundary effects.3 Under these conditions HME itself was used as the standard. For the above standards and temperature range, standard uncertainties (1σ) in the derived average shock temperatures are expected to be about 1%.2,3

Generation of CH3 and H atoms. Methyl radicals are generated from the thermal decomposition of tert-butylperoxide (tBPO):

(tert-C4H9O)2 → 2 (CH3)3CO (6)

(CH3)3CO → CH3 + (CH3)2C=O (7)

The kinetics of reaction (6) were determined by Raley et al.4 sixty years ago and the process has been extensively studied since. The available rate data5 are in good agreement. Lewis6 reported k /s-1 = 2.14x1015 exp(-18,300/T) from studies at (528 to 677) K and a linear extrapolation of these results indicates a half life of about 0.2 μs at 900 K. Decomposition of the tert-butoxy radical is several orders of magnitude faster,7-9 with the consequence that that under our conditions tert-butylperoxide can be considered to be a pulse source of acetone and methyl radicals. Acetone is stable and inert under our conditions.

A convenient source of hydrogen atoms is hexamethylethane (HME), which decomposes thermally via:

Hexamethylethane → 2 t-butyl (8)


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t-butyl → iso-butene + H (9)

This process has been used in this laboratory for many years. Reaction (8) is much slower than (6) and H atoms are not released as an initial pulse, but are rather generated over the full shock-heating time period. It is worth noting that isobutene formation provides a direct count of the number of H atoms released into the system by the precursor. When compared with total product formation this then provides an indication of the total chain length, and thus some experimental measure of the complexity of any secondary chemistry.

While HME decomposition represents a generally clean source of H atoms, Tsang has reported10 the formation of propene as a minor side process, corresponding to 3% of isobutene formation. This result was checked by us in separate experiments with mixtures containing only HME, inhibitor, and argon. We find propene/isobutene product ratios of (0.035 ± 0.007) under our conditions. In our studies with HME, the propene yield attributed to attack on n-butane was thus reduced by an amount equal to 0.035[isobutene]. This minor correction is about 3% at all temperatures.

Gas Chromatographic – Mass Spectral Analyses. Following the shock, samples are extracted via an automated valve

and loop system for analysis. The present analyses utilized a Hewlett Packard 6890N GC equipped with two columns and both flame ionization (FID) and mass spectral (MS) detectors. A Restek 30 m x 0.53 mm i.d. Rt-Alumina (aluminum oxide porous layer) capillary column was utilized for optimized detection of the lighter gases (smaller than ca. C4). Larger species were separated on a J & W Scientific 30m x 0.53 mm i.d. DB-1 (100% dimethypolysiloxane) capillary column. Effluent from the DB-1 column was quantitatively split with an Agilent Technologies Dean’s Switch and simultaneously sent to MS and FID detectors. The MS was used primarily to confirm product identities with concentrations based on the FID analyses. We utilized the cryogenic mode of the GC for analysis, with the oven temperature programmed from 213 K to 453 K (-60 oC to 180 oC) with constant carrier gas flow.

Molar FID responses of all product olefins were determined from standard samples. We estimate the standard analytical uncertainty (1σ) for the main ethene and propene products to be about 3%.

Chemicals. n-Butane (99+ %, Aldrich), tert-butyl-peroxide, (98%, Aldrich), hexamethylethane (98%, Aldrich),

chlorocyclopentane (99%, Aldrich), 4-vinylcyclohexene (98%, Aldrich), toluene (99%, Aldrich) and argon (Praxair, 99.999%), were the chemicals used in the kinetic studies. Except for toluene, which was redistilled, all chemicals were used without further purification, other than degassing during preparation of the mixtures. GC analyses of the resulting mixtures revealed only the usual traces of hydrocarbon impurities, none of which were present in quantities expected to impact the results. Product amounts were corrected for trace backgrounds, if present.

Selection of experimental conditions. The particular mixtures and sets of experimental conditions that are examined

herein are based on a mathematical design algorithm that we describe more fully elsewhere in these proceedings.11 In brief, the design algorithm considers a selected set of possible experiments covering a range of mixture compositions and pressure, temperature combinations that are accessible with our shock tube. This is the full dataset. An existing prior model of the expected chemistry, presently based on JetSurF 2.0,12 is then used to simulate the results and determine how well the full dataset constrains the model parameters of interest, in this case the rate parameters for attack of H and CH3 on n-butane. The algorithm is then applied to generate a minimal dataset that spans the rate parameter space as completely as possible while containing the fewest possible redundancies. The selected mixture compositions for the experiments are based on this minimal dataset and are given in Table 1.

3. RESULTS AND DISCUSSION Shock Tube Data. Products and Mechanism – Experiments with tBPO. Decomposition of t-butylperoxide (tBPO) produces methyl radicals and acetone, the latter of which is observed as a stable byproduct whose amount is invariant for each mixture. Also unrelated to the chemistry of interest are the decomposition products of our temperature standards, cyclopentene from chlorocyclopentane (Mixture A) and 1,3-butadiene from 4-vinylcyclohexene (Mixture B). Other products are attributed as direct or indirect products of the reaction of methyl radicals with the substrate and inhibitor.


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Table 1. Gas mixtures used in the present experiments. The remaining balance is argon.

Components in mixtures a (μL/L) Mix n-butane tBPO HME Toluene A b 8 075 19.8 - 30 376 B c 10 065 20.1 - 29 563 C d 770 - 43.2 - D e 775 - 44.8 7 706 E f 9 690 - 47.0 11 853

a tBPO = tert-butylperoxide, HME = hexamethylethane; b 40 μL/L chlorocylopentane (CCP) added as temperature standard; c 40 μL/L 4-vinylcyclohexene (4VCHE) added as temperature standard; d 26 μL/L CCP added as temperature standard; e 24 μL/L CCP added as temperature standard; HME used as temperature standard; f 31 μL/L CCP added as temperature standard; _____________________________

The four main products are methane, ethane, ethene, and propene. Several other species are observed at levels corresponding to typically a few percent of the main products, including benzene, ethylbenzene, propane, 1-butene, E-2-butene, Z-2-butene, and isopentane.

The main products are accounted for by the following set of reactions, for convenience numbered where possible as per JetSurF 2.0:12

CH3 + CH3 → C2H6 R108

CH3 + n-butane → 1-butyl + CH4 R643

CH3 + n-butane → 2-butyl + CH4 R644

1-butyl → C2H4 + C2H5 R582

C2H5 → C2H4 + H R252

2-butyl → C3H6 + CH3 R592

H + n-butane → 1-butyl + H2 R633

H + n-butane → 2-butyl + H2 R634

Consideration of the above reactions makes it apparent that methane to ethane product ratios are determined primarily by the competition between recombination of methyl radicals (R108) and abstraction of hydrogen from n-butane by CH3 (R643 and R644), while propene to ethene ratios reflect the relative rates of radical attack on the primary and secondary hydrogen of n-butane by both CH3 and H. As noted in the Introduction, the primary difficulty is in separation of the relative contributions of the reactions of H and CH3 in determining the final olefin product spectrum.

Experimentally, a clear indication of the presence of hydrogen atoms is the formation of benzene, the result of the displacement of methyl from the toluene inhibitor by H atoms:

H + toluene → C6H6 (benzene) + CH3 R674

H and CH3 also attack toluene via abstraction of the methyl hydrogens, leading to the resonance stabilized benzyl radical.

H + toluene → C7H7 (benzyl) + H2 R673

CH3 + toluene → C7H7 (benzyl) + CH4 R676

This is of course the mode of action of the inhibitor, replacing active radicals with a much more inert species. It also leads to the observed ethylbenzene via recombination with CH3.

CH3 + benzyl → ethylbenzene R805

Plausible routes to the minor C3 to C5 species are put forth below.


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CH3 + C2H5 → C3H8 (propane) R279

CH3 + 2-butyl → iC5H10 (isopentane) (8)

2-butyl → E-2-butene + H R565a

2-butyl → Z-2-butene + H R565b

2-butyl → 1-butene + H R554

1-butyl → 1-butene + H (9)

Most of these minor processes are present in the JetSurF reaction set. Ejection of H from butyl radicals is much less favored than the β C-C scissions R582 and R592. Experimentally, the ratios of butene to propene and ethene indicate branching fractions for C-H scission of 0.02 to 0.05, consistent with recent observations.13,14

Products and Mechanism – Experiments with HME. Isobutene and cyclopentene are the only measured products not attributed directly or indirectly to reaction of H with the substrate or inhibitor. The former is the olefin product of our H atom precursor and the latter is from our temperature standard. The product spectrum is qualitatively similar to that observed with tBPO. Ethene and propene remain the main olefin products, but the ratio of these two species is smaller in the HME system. When the inhibitor toluene is present, amounts of benzene are significantly increased relative to the tBPO results, an indication of much higher concentrations of H atoms in the HME case. Conversely, the methyl radical products methane and ethane, while still present, are formed in much smaller amounts.

Modeling Methods

Method Overview. The above discussion provides a qualitative description of the most important chemistry. Our

quantitative analysis makes use of a more detailed reaction model comprised of a larger reaction set, together with Monte Carlo techniques to analyze the data. The methodology entails the use of an initial reaction model (the Prior Model) in which the relevant parameters (rate constants) are each assigned a known or assumed uncertainty. The permissible solution space of the Prior Model can be defined by carrying out multiple trial runs in which rate parameters are randomly varied within their uncertainties. The present experimental observations, with assigned uncertainties, are then used as the basis for adjustment (conditioning) of the Prior Model using the subsequently described formalism. The result is a Posterior Model in which certain active rate constants are better determined. A particular advantage of the methodology is that it leads to a correlation matrix that succinctly describes the parameter interrelationships that are defined by the conditioning data. This correlation matrix may be retained for the subsequent analyses of later systems.

Details of the method are given below. Prior reaction model and active parameter determination. The Prior Model is the Jet Surrogate Fuel H2/CO/C1-C4

submodel, version 2.0 (JetSurF 2),12 augmented to include formation of ethylbenzene and thermal decomposition of HME and tBPO.15 It has 124 species and 819 reactions. The experimental measurements used to constrain the model are listed in Table 2. Uncertainty in the experimental measurements was estimated by fitting a modified Arrhenius equation to the experimental data and calculating the uncertainty in the regression. This gives a 1σ uncertainty of approximately (0.05 to 0.10), equivalent to a 2σ uncertainty of (10 to 20)%. Active parameters are selected by a one-at-a-time sensitivity analysis. For each experiment and reaction rate parameter (either an Arrhenius prefactor or activation energy), the uncertainty-weighted sensitivity coefficient , was computed, where is the simulation prediction, is a generalized rate parameter and is its uncertainty factor. The active rate parameters are those for which , / , 0.02.

, ln(1)

Uncertainty factors in the Arrhenius prefactors are taken from JetSurF 2.12 Uncertainty factors in activation energies were estimated using ln ⁄ , where Ek is the activation energy of Rk, with Tc = 1000 K. In simulations, the shock tube was treated as a homogeneous adiabatic reactor. Species concentrations following the shock


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Table 2. Mixture compositions and target measurements used for optimization.

Simulated composition (%) T (K) Target values, μL/L (ppm) C4H10 Toluene tBPO C2H4 C3H6 C2H6 CH4

Mixture A 0.8075 3.03761 0.0019800 850 1.44 0.87 20.0 7.53

1050 6.94 6.93 17.5 20.0 Mixture B 1.006499 2.956337 0.0020149 950 3.35 4.39 19.1 11.5

1150 205 81.4 22.5 112 Simulated composition (%) T (K) Target values (dimensionless)

C4H10 Toluene HME C2H4/C3H6 Mixture C 0.076962 0 0.0043207 900 0.85

1150 1.17 Mixture D 0.077522 0.77064 0.0044804 950 0.99

1150 1.52 Mixture E 0.968972 1.18533 0.0047035 950 0.87

1150 1.46 were determined using the VODE solver16 to integrate the chemical rate equations supplied by Sandia CHEMKIN 17 over a period of 500 µs.

Model Constraint and Uncertainty Minimization. Model constraint uses the method of uncertainty analysis using polynomial chaos expansions (MUM-PCE),18 which is summarized here. In this method, a Prior Model is defined, which in this case is JetSurF 2. This model is then conditioned on the set of experimental measurements to produce the best Posterior Model given the Prior Model and experimental data. MUM-PCE assumes that the uncertain parameters in the model can be expressed as a random vector , where is the factorial variable vector whose elements are

ln ,⁄ln

(2)

where fi is the uncertainty factor of the ith active parameter . ξ is a vector of independent, identically distributed normal random variables with mean 0 and variance 1, and is a transformation matrix, so that follows a multivariate normal distribution with mean and covariance matrix .

MUM-PCE applies Bayes’ Theorem to determine the joint probability density function (PDF) of the active parameters, which results in the following PDF for the rate parameters in the Posterior Model

ln ~ 4 (3)

where is the model prediction as a function of the factorial variables x, Ne is the number of experiments and Nr the number of active variables. This PDF can be approximated by a multivariate normal distribution, which will then have an that best reproduces the experimental measurements, and a that best reproduces their uncertainty. is found by finding the mode of the PDF in Eq. 3, equivalent to the least-squares optimization problem

argmax ln(4)


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which is solved using the LMDIF solver in the MINPACK library.19 is found by linearizing the model predictions in the vicinity of , which yields

4(5)

where Jr is the gradient of . To reduce the computational complexity of solving Eqs. 4 and 5, the method of solution mapping 20,21 is used, in which predicted values of experimental measurements are expressed as polynomials with respect to the reaction rate parameters, , where and are the first and second derivatives of . The derivatives are calculated using the sensitivity-analysis-based method (SAB).22 Then Jr in Eq. 5 is 2 .

Experimental Consistency Analysis. It is not always possible to generate a model that simultaneously reproduces all observations. This could be caused by inconsistency between measurements, meaning that the uncertainty on the measurements has been underestimated; it could also be caused by an underestimated uncertainty in the rate coefficients, or by a missing chemical pathway. A method of identifying inconsistent observations was proposed by Sheen and Wang.18 Inconsistent observations are then iteratively removed from the target set until a self-consistent set is generated. In this procedure, a consistency function is defined as

2(6)

If 0, then the rth experimental target is inconsistent. If there is only one such inconsistent observation, it is removed. If there is more than one, then a strength function is defined as

· (7)

which is the normalized scalar product between the Posterior Model vector and the model response gradient. This function was chosen because the optimized model vector will tend to move such that it is parallel to the response surface gradient of highly inconsistent targets. Inconsistent observations are ranked by the product , and the one with the largest such value is removed from the data set. The procedure is iterated until all targets are consistent with the Posterior Model. Model Results

General observations. Figure 1 shows the modeled species concentrations versus time for mixtures containing 50 μL/L of tBPO and 10 000 μL/L of n-butane. Figures 2 and 3 show similar plots for mixtures containing 50 μL/L of HME and 10 000 μL/L and 1 000 μL/L of n-butane, respectively.

For the tBPO system, Figure 1 shows that formation of the stable products methane, ethane, ethene, and propene is essentially complete well before the end of the 500 μs heating time. This is a result of the use of a pulse source of methyl radicals, the rapid recombination rate of CH3, and the limited ability of the system to propagate radical chains. Radical concentrations follow the order [CH3] >> [C2H5] >> [H].

The situation for the HME system is different. In this case, concentrations of the olefin products rise rapidly throughout the heating period, and then plateau immediately at the start of the post-shock quenching period. This is not true, however, for the saturated products, methane, ethane, and propane. Significant fractions of these species are formed in the quench. This difference between the tBPO and HME systems is largely due to much lower methyl radical concentrations in the latter case. The absolute concentration of H is perhaps unsurprisingly larger with the HME precursor, yet methyl radicals are present in much larger concentrations than H atoms in both systems. This reflects the much higher reactivity of H compared with CH3. The radical concentrations in the HME system follow [CH3] >> [H] > [C2H5].


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Figure 1. Modeled species concentrations versus time for mixtures containing 50 μL/L of tBPO and 10 000 μL/L of n-butane.

Figure 3. Modeled species concentrations versus time for mixtures containing 50 μL/L of HME and 1 000 μL/L of n-butane. Solid and dashed lines are referenced to the left and right vertical axes, respectively.

Figure 2. Modeled species concentrations versus time for mixtures containing 50 μL/L of HME and 10 000 μL/L of n-butane. Solid and dashed lines are referenced to the left and right vertical axes, respectively. _____________________________

Target measurements. Our MUM-PCE analysis requires the selection of appropriate measurement targets. Ethene and propene product amounts are a key measure of the relative rate of radical attack on the primary and secondary hydrogens of n-butane. For tBPO systems the absolute amounts of these olefins were targeted, as were the absolute amounts of CH4 and C2H6. Ethane and methane quantities were not targeted for the HME studies because of significant continued formation of these products in the post-shock quenching period (see Figures 2 and 3). Unlike the tBPO case, in systems utilizing HME the olefin product concentrations increase rapidly throughout the shock heating period, with the consequence that uncertainties in the reaction time could impact the results. The ratio of C2/C3 olefin products, however, is only weakly dependent on the reaction time and was selected for this system as a better target than the absolute product quantities. Despite this we note, vide infra, that the modeled absolute product amounts were in excellent agreement with experiment in the HME system.

To reduce the computational cost the present optimization considers only a representative selection of experiments covering the range of conditions examined. Specific targets have been given in Table 2.

Modeled species profiles. Selected experimental results are compared with the Prior and Posterior Models in Figures

4 – 6. All experimental data points are shown in these figures, with the targeted values of Table 2 enclosed by circles. The model results for all mixtures are in generally good agreement with experiment. In these plots the blue points pertain to the Prior Model and the red to the Posterior Model. The significantly reduced scatter in the Posterior Model results is indicative of marked improvement in the relevant rate parameters after conditioning with the present experiments.

1.E‐11

1.E‐10

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10,000 K / T Figure 4. Comparison of selected experimental and modeled results for Mixture A, tBPO precursor. Blue dots indicate the range of results based on the Prior Model, while red dots show results of the Posterior Model conditioned on the experimental results from all mixtures. Retained targets are indicated with heavy black circles, while lighter circles indicate non-retained targets.


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10,000 K / T Figure 5. Comparison of selected experimental and modeled results for Mixture B, tBPO precursor. Blue dots indicate the range of results based on the Prior Model, while red dots show results of the Posterior Model conditioned on experimental results from all mixtures. Retained targets are indicated with heavy black circles, while lighter circles indicate non-retained targets. Experimental values at higher temperatures, approximately 10,000 K/T < 9.5 are typically high (see text). The value used for the optimization is the fit, not the actual measurement.


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10,000 K / T Figure 6. Comparison of selected experimental and modeled results for Mixtures C, D, and E, HME precursor. Blue dots indicate the range of results based on the Prior Model, while red dots show results of the Posterior Model conditioned on experimental results from all mixtures. Retained targets are indicated with heavy black circles, while lighter circles indicate non-retained targets. _____________________________

Olefin ratios are well-predicted for all mixtures. Absolute product amounts are also in excellent agreement with

experiment for HME systems, whereas with tBPO the experimental product amounts are slightly higher than modeled. At present this is not fully understood, but could reflect either issues with the model chemistry, or systematic errors in the experiments. The largest discrepancies are seen with the results for Mixture B, wherein the model increasingly underpredicts the concentrations of the C1 to C3 species at temperatures above 1050 K. Examination of the model shows that unimolecular decomposition of n-butane begins to impact the results at higher temperatures, and is more significant for large n-butane/precursor ratios (e.g. Mixtures B and E). Since n-butane decomposition leads to the same olefin products as radical attack, and additionally increases the total radical pool, it is not surprising that these conditions are the most difficult to predict. For this reason the lower temperature conditions are expected to more cleanly define the rate parameters of interest.

Rate Constants for Abstraction of H from n-Butane

Figures 7 and 8 present plots of the derived relative and absolute rate constants for abstraction of the primary and

secondary hydrogens of n-butane by H atoms and methyl radicals. Blue and red dots pertain to the Prior and Posterior models as before. Also presented in these figures are lines that correspond to mean values of the rate constants in the Prior and Posterior models. The results are presented numerically in Table 3.

10-310-210-1100101102103

8 9 10 11

[C2H

4]

10,000 K / T

Mixture C Mixture C

Mixture E

Mixture D Mixture D

Mixture E


12

10-2

10-1

100

101

8 9 10 11 12

k p/ks

10,000 K / T

1011

1012

1013

8 9 10 11 12

k p / (c

m3 m

ole-1

s-1

)

10,000 K / T

10-2

10-1

100

101

8 9 10 11 12

k p/ks

10,000 K / T

1012

1013

8 9 10 11 12

k s / (c

m3 m

ole-1

s-1

)

10,000 K / T

Table 3. Optimized rate constants from the Posterior Model. and are the respective 2σ uncertainty factors for the Prior and Posterior Models. The recommended rate expressions are of the form k = ATbexp(-E*/T).

A E Posterior rate coefficientsa

n Reaction lnln

lnln

log10 A* b* E*/R (K)

R633 C4H10 + H ↔ pC4H9 + H2 3 2.1 0.66 1.2 1.16 0.83 5.92 ± 0.32 2.54 3045 ± 499 R634 C4H10 + H ↔sC4H9 + H2 3 1.9 0.58 1.2 1.18 0.91 6.44 ± 0.28 2.40 2458 ± 445 R643 C4H10 + CH3 ↔ pC4H9 + CH4 3 1.8 0.55 1.2 1.16 0.84 -0.14 ± 0.26 3.65 3332 ± 549 R644 C4H10 + CH3 ↔ sC4H9 + CH4 3 1.7 0.47 1.2 1.17 0.87 0.66 ± 0.22 3.46 2812 ± 483

a units: cm3 mol-1 s-1

Figure 7. Relative and absolute rate constants for abstraction of the primary and secondary hydrogens of n-butane by CH3 radicals. Note in particular that the ratio kp/ks is much better defined by the present data.

Figure 8. Relative and absolute rate constants for abstraction of the primary and secondary hydrogens of n-butane by H atoms. Note in particular that the ratio kp/ks is much better defined by the present data.

109

1010

8 9 10 11 12

k p / (c

m3 m

ole-1

s-1

)

10,000 K / T

108

109

1010

1011

8 9 10 11 12

k s / (c

m3 m

ole-1

s-1

)

10,000 K / T

Abstraction of H by CH3 radicals. Absolute values of the rate constants for abstraction of H by methyl radicals are changed by less than 40% by the present data and analysis. However the uncertainty is reduced by about a factor of two. Also, the relative rate constants for abstraction of primary and secondary hydrogens, kR643/kR644, (kp/ks) is shifted by about 40% and is much better defined. This is important because it is this ratio that determines the particular olefins that are produced in the initial breakdown of n-butane and hence is a key parameter controlling the subsequent chemistry of the system. Note in Figure 7 that there is almost no scatter in the rate constant ratio, kp/ks.

Abstraction of H by H atoms. The situation for H atoms is similar to that observed for methyl radicals. There are again relatively modest changes of up to about 40% in the absolute values of the H abstraction rate constants. Uncertainties in these values are again reduced by about half relative to the Prior Model. A major improvement is again in defining the precise branching ratio for abstraction of the secondary and primary hydrogens. This ratio is shifted by about 30% in the temperature range of our experiments. Ignition Delay Times

It is of interest to determine what impact, if any, the present results have on the prediction of measured global

properties such as ignition delay times. To that end, eleven measurements of n-butane ignition delay times from Horning et al.24 and two from Burcat et al.23 were modeled with the Prior and Posterior Models. The data cover n-butane compositions of (0.5 to 2.5)%, fuel equivalence ratios of 0.5 to 2, and pressures of 1.2 atm to 8.5 atm (122 kPa to 867 kPa).

Selected results are presented in Figures 9 and 10. To better visualize the impact of the present measurements, results are presented for two cases: (1) where all parameters other than the H/CH3 + n-butane rate constants are assumed to have no uncertainty, and (2) where the uncertainty in all JetSurF rate constants is considered. The results of these analyses are presented numerically in Table 4.

The Table 4 values show that the uncertainty in the ignition delay times due specifically to the H/CH3 + n-butane reactions is reduced by about 40% whereas the overall uncertainty is reduced by about 20%. A sensitivity analysis shows that largest uncertainties in the modeled ignition delays are from the H + n-butane and H + O2 reactions. Contributions to the overall uncertainty in the Prior Model were about equal for these two reactions.

The CH3 + n-butane rate constants do not play a strong role with respect to ignition delay times. Note, however, that the methyl radical reactions may well be important in other systems, particularly under more pyrolytic conditions.

Table 4. Ignition delay time predictions and uncertainties

Composition (%) P (atm) T (K) Prior prediction Posterior prediction Ref

C4H10 O2 Ln τ (µs) 2 a 2 b Ln τ (µs) 2 a 2 b / a / b

2.5 16.25 8.5 1230 5.77 0.96 0.56 6.11 0.92 0.4 0.96 0.71 23

2.5 16.25 8.5 1372 4.2 0.94 0.66 4.53 0.76 0.38 0.81 0.58 23

0.5 3.25 1.2 1560 4.82 0.6 0.34 4.92 0.52 0.2 0.87 0.59 24

0.5 3.25 1.2 1477 5.55 0.72 0.48 5.71 0.58 0.28 0.81 0.58 24 1 6.5 1.2 1558 4.37 0.66 0.42 4.52 0.56 0.26 0.85 0.62 24 1 6.5 1.2 1404 5.87 0.9 0.68 6.12 0.68 0.36 0.76 0.53 24 2 13 1.2 1435 5.05 0.9 0.68 5.31 0.7 0.38 0.78 0.56 24 1 6.5 2.6 1567 3.8 0.68 0.46 3.96 0.56 0.26 0.82 0.57 24 1 6.5 2.6 1453 4.87 0.84 0.62 5.09 0.64 0.34 0.76 0.55 24 1 6.5 5 1433 4.68 0.86 0.66 4.94 0.66 0.36 0.77 0.55 24 1 3.25 1.2 1733 4.23 0.46 0.26 4.31 0.4 0.16 0.87 0.62 24 1 13 1.2 1353 5.42 1.06 0.8 5.73 0.84 0.46 0.79 0.58 24 1 13 1.2 1453 4.33 0.84 0.58 4.54 0.7 0.36 0.83 0.62 24

a: Predicted ignition delay time uncertainty considering uncertainty in all JetSurF rate constants; b: considering uncertainty in R + C4H10 system only.


14

101

102

103

7.0 7.5 8.0

τ ign /

μs

10,000 K / T

2.5% n-C4H

10, φ = 1, p = 8.5 atm

101

102

103

7.0 7.5 8.0

τ ign /

μs

10,000 K / T

2.5% n-C4H

10, φ = 1, p = 8.5 atm

102

103

6.0 6.5 7.0

τ ign /

μs

10,000 K / T

0.5% n-C4H

10, φ = 1, p = 1.2 atm

102

103

6.0 6.5 7.0τ ig

n / μs

10,000 K / T

0.5% n-C4H

10, φ = 1, p = 1.2 atm

102

103

6.5 7.0

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 1, p = 1.2 atm

102

103

6.5 7.0

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 1, p = 1.2 atm

101

102

103

6.5 7.0

τ ign /

μs

10,000 K / T

2.0% n-C4H

10, φ = 1, p = 1.2 atm 101

102

103

6.5 7.0

τ ign /

μs

10,000 K / T

2.0% n-C4H

10, φ = 1, p = 1.2 atm

Figure 9. Comparison of selected experimental[refs] and modeled results for n-butane ignition delay times. Figures in the left hand column show results considering the uncertainty in the H/CH3 + n-butane reactions only, while those in the right hand column considers the uncertainty in a JetSurF rate constants.


15

102

103

6.5 7.0 7.5

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 1, p = 2.6 atm

102

103

6.5 7.0 7.5

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 1, p = 2.6 atm

101

102

103

6.5 7.0 7.5

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 1, p = 5.0 atm

101

102

103

6.5 7.0 7.5

τ ign /

μs10,000 K / T

1.0% n-C4H

10, φ = 1, p = 5.0 atm

101

102

5.5 6.0 6.5

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 2, p = 1.2 atm

101

102

5.5 6.0 6.5

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 2, p = 1.2 atm

101

102

103

6.5 7.0 7.5

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 0.5, p = 1.2 atm 101

102

103

6.5 7.0 7.5

τ ign /

μs

10,000 K / T

1.0% n-C4H

10, φ = 0.5, p = 1.2 atm

Figure 10. Comparison of selected experimental[refs] and modeled results for n-butane ignition delay times. Figures in the left hand column show results considering the uncertainty in the H/CH3 + n-butane reactions only, while those in the right hand column considers the uncertainty in a JetSurF rate constants.


16

4. Conclusions

The present work presents a combined experimental and modeling study of the kinetics of the reactions of H atoms

and CH3 radicals with n-butane. By generating the radicals of interest in separate experiments under well defined conditions we have been able to separate the kinetics of the two processes despite the fact that both radicals are present in both systems. A mathematical design algorithm has been applied to select the optimum conditions under which the processes can be disentangled. In conjunction with post-shock product analyses, detailed chemical modeling, and the use of polynomial chaos expansion techniques, significantly improved absolute and relative rate constants for attack of H and CH3 on the primary and secondary hydrogens of n-butane have been determined. The relative rate constants, the main determinant of the olefin product branching ratio, are defined in particular with great precision. The impact of these measurements on the modeling of n-butane ignition delay times has been examined. Modeled delay times are found to depend about equally on the rate constants for the H + n-butane and H + O2 reactions. The CH3 + n-butane reaction does not affect ignition delay but could play a role under more pyrolytic conditions. The present measurements reduce the uncertainty in the modeled ignition delay times due specifically to the H + n-butane reactions by about 40%, while the overall uncertainty due to all reactions is reduced by about 20%. References

(1) Awan, I. A.; McGivern, W. S.; Tsang, W.; Manion, J. A. Decomposition and Isomerization of 5-Methylhex-1-yl Radical.

J. Phys. Chem. A 2010, 114, 7832. (2) Tsang, W. Comparative-Rate Single-Pulse Shock Tube Studies on the Thermal Stability of Polyatomic Molecules In

Shock Waves in Chemistry; Lifshitz, A., Ed.; Marcel Decker: New York and Basel, 1981. (3) Awan, I. A.; Burgess, D. R., Jr.; Tsang, W.; Manion, J. A. Standard Reactions for Comparative Rate Studies:

Experiments on the Dehydrochlorination Reactions of 2-Chloropropane, Chlorocyclopentane and Chlorocyclohexane. Int. J. Chem. Kinet. 2012, 44, 351.

(4) Raley, J. H.; Rust, F. F.; Vaughan, W. E. Decompositions of Di-T-Alkyl Peroxides .1. Kinetics. J. Am. Chem. Soc. 1948, 70, 88.

(5) Manion, J. A.; Huie, R. E.; Levin, R. D.; Burgess Jr., D. R.; Orkin, V. L.; Tsang, W.; McGivern, W. S.; Hudgens, J. W.; Knyazev, V. D.; Atkinson, D. B.; Chai, E.; Tereza, A. M.; Lin, C.-Y.; Allison, T. C.; Mallard, W. G.; Westley, F.; Herron, J. T.; Hampson, R. F.; Frizzell, D. H. NIST Chemical Kinetics Database, NIST Standard Reference Database 17, Version 7.0 (Web Version), Release 1.4.3, Data version 2011.11, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899-8320. Web address: http://kinetics.nist.gov/ National Institute of Standards and Technology: Gaithersburg, Maryland, 20899-8320.

(6) Lewis, D. K. Di-Tert-Butyl Peroxide Decomposition Behind Shock-Waves. Can. J. Chem.-Rev. Can. Chim. 1976, 54, 581.

(7) Batt, L.; Hisham, M. W. M.; Mackay, M. Decomposition of the Tert-Butoxy Radical .2. Studies over the Temperature-Range 303-393-5. International Journal of Chemical Kinetics 1989, 21, 535.

(8) Batt, L.; Robinson, G. N. Decomposition of the Tert-Butoxy Radical .1. Studies over the Temperature-Range 402-443-K. International Journal of Chemical Kinetics 1987, 19, 391.

(9) Batt, L.; Robinson, G. N. Arrhenius Parameters for the Decomposition of the Tert-Butoxy Radical. Int. J. Chem. Kinet. 1982, 14, 1053.

(10) Tsang, W. Thermal Decomposition of Hexamethylethane 2,2,3-Trimethylbutane and Neopentane in a Single-Pulse Shock Tube. J. Chem. Phys. 1966, 44, 4283.

(11) Sheen, D. A.; Manion, J. A. “Kinetics of the Reactions of H and CH3 Radicals with n-Butane: An Experimental Design Study using Reaction Network Analysis ”; 8th U.S. National Combustion Meeting, 2013, Park City, Utah.

(12) Wang, H.; Dames, E.; Sirjean, B.; Sheen, D. A.; Tangko, R.; Violi, A.; Lai, J. Y. W.; Egolfopoulos, F. N.; Davidson, D. F.; Hanson, R. K.; Bowman, C. T.; Law, C. K.; Tsang, W.; Cernansky, N. P.; Miller, D. L.; Lindstedt, R. P. JetSurF, A high-temperature chemical kinetic model of n-alkane (up to n-dodecane), cyclohexane, and methyl-, ethyl-, n-propyl and n-butyl-cyclohexane oxidation at high temperatures, JetSurF version 2.0; (http://melchior.usc.edu/JetSurF/JetSurF2.0), 2010, September 19.

(13) Manion, J. A.; Awan, I. A. The Decomposition of 2-Pentyl and 3-Pentyl Radicals. Proc. Combust. Inst. 2013, 34, 537. (14) Awan, I. A.; Burgess, D. R., Jr.; Manion, J. A. Pressure Dependence and Branching Ratios in the Decomposition of 1-

Pentyl Radicals: Shock Tube Experiments and Master Equation Modeling. J. Phys. Chem. A 2012, 116, 2895.


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(15) Sheen, D. A.; Rosado-Reyes, C. M.; Tsang, W. Kinetics of H atom attack on unsaturated hydrocarbons using spectral uncertainty propagation and minimization techniques. Proc. Combust. Inst. 2013, 34, 527.

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