Article pubs.acs.org/JPCA
High-Temperature Rate Constant Determination for the Reaction of OH with iso-Butanol Genny A. Pang,* Ronald K. Hanson, David M. Golden, and Craig T. Bowman Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States ABSTRACT: This work presents the first direct experimental study of the rate constant for the reaction of OH with iso-butanol (2-methyl-1-propanol) at temperatures from 907 to 1147 K at near-atmospheric pressures. OH time-histories were measured behind reflected shock waves using a narrow-linewidth laser absorption method during reactions of dilute mixtures of tert-butylhydroperoxide (as a fast source of OH) with iso-butanol in excess. The title reaction’s overall rate koverall
constant (OH + iso-butanol ⎯⎯⎯⎯→ all products) minus the rate constant for the kβ
β-radical-producing channel (OH + iso-butanol → 1-hydroxy-2-methyl-prop-2-yl radical + H2O) was determined from the pseudo-first-order rate of OH decay. A two-parameter Arrhenius fit of the experimentally determined rate constant in the current temperature range yields the expression (koverall − kβ) = 1.84 × 10−10 exp(−2350/T[K]) cm3 molecule−1 s−1. A recommendation for the overall rate constant, including kβ, is made, and comparisons of the results to rate constant recommendations from the literature are discussed.
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INTRODUCTION Biobutanol is as an attractive bioderived fuel for transportation applications because of its many advantages over bioderived ethanol, including a higher energy density, a lower propensity to attract water (thus it can be easily transported and stored in the current gasoline infrastructure), and properties suitable for operation in unmodified gasoline engines.1 While the traditional structure of butanol present in biobutanol is the 1-butanol isomer, recent technologies have been developed to economically synthesize the iso-butanol isomer (2-methyl-1propanol) from biomass sources. For example, the strategy developed by Atsumi et al.2 demonstrates high-yield, highspecificity production of iso-butanol from glucose using native organisms. Because iso-butanol is becoming an important butanol isomer present in economically produced biobutanol, developing accurate detailed kinetic mechanisms describing the high-temperature oxidation of iso-butanol is of importance for optimizing the design of practical transportation engines powered by combustion of biobutanol. The hydrogen-atom abstraction by a hydroxyl radical (OH) from iso-butanol is an important elementary reaction in a hightemperature iso-butanol oxidation mechanism because this reaction describes a dominant fuel consumption pathway during the combustion process. This reaction can occur via four reaction channels to produce water and a radical with the chemical formula C4H9O in one of the following radical structures: isobutoxy or one of four isomers of a hydroxyalkyl radical (α, β, γ, distinguished by the radical position with respect to the oxygen atom). The radical products are expected to react through rapid isomerization and beta-scission decomposition. Figure 1 illustrates the four reaction pathways of the title reaction and the major subsequent reaction pathways. © 2012 American Chemical Society
Figure 1. Dominant reaction pathways of iso-butanol after reaction with OH.
Shock tube experiments with tert-butylhydroperoxide (TBHP) as a fast source of OH have become a common technique for measuring rate constants for reactions of OH with combustion-relevant organic compounds. A pseudo-first-order reaction technique is commonly employed, using test mixtures of TBHP with the organic compound of interest in excess, and the resulting OH time-history is monitored by absorption from a microwave discharge,3 resonance lamp,4 or narrow-linewidth laser.5 Our previous work6 on the rate constant determination Received: March 21, 2012 Revised: April 18, 2012 Published: April 19, 2012 4720
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for the reaction of OH with 1-butanol elucidated the importance of accounting for subsequent OH-producing reactions in the study of pseudo-first-order reactions in the family of butanol + OH. For the reaction of OH with iso-butanol, the only critical secondary OH-producing reaction is the betascission decomposition of the β-radical (1-hydroxy-2-methylprop-2-yl), which has no significant competing secondary reaction pathways. Thus, this reaction channel has a net-zero contribution to the OH consumption. This paper presents the results of OH time-history measurements in reflected shock experiments of TBHP with iso-butanol in excess. The overall rate constant of the title reaction minus the rate constant for the β-radical-producing
Table 1. Rate Constants for the Reactions of Significance in the OH Sensitivity That Were Added to the Base Mechanisma k = A·Tb exp(−E/T) reaction title reaction OH + iso-butanol → iso-butoxy + H2O OH + iso-butanol → α-radical + H2O OH + iso-butanol → β-radical + H2O OH + iso-butanol → γ-radical + H2O reaction with H H + iso-butanol → iso-butoxy + H2 H + iso-butanol → α-radical + H2 H + iso-butanol → β-radical + H2 H + iso-butanol → γ-radical + H2
k non ‐ β
channel (OH + iso-butanol ⎯⎯⎯⎯→ non-β-radical products) is determined from the measured pseudo-first-order OH decays, and a temperature-dependent expression is determined for knon‑β. An overall rate constant for the title reaction (OH + isokoverall
butanol ⎯⎯⎯⎯→ all products) is suggested based on the rate constant for the β-radical-producing reaction channel (OH + kβ
iso-butanol → β-radical + H2O) of Merchant and Green.7 Comparisons to rate constants for the title reaction from the literature are made.
A
b
E
reference current work current work
2.56 × 10−24
3.70
−2.49 × 103
Merchant and Green7 current work
1.57 × 10−21
3.14
+4.38 × 103
Sarathy et al.9
1.46 × 10−19
2.68
+1.47 × 103
Sarathy et al.9
1.08 × 10−18
2.40
+2.25 × 103
Sarathy et al.9
2.21 × 10−18
2.54
+3.40 × 103
Sarathy et al.9
All reactions are reversible. The units of A are [cm3 molecule−1 s−1], and the units of E are [K]. The sum of the three absent rate constants is determined in the current work.
a
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EXPERIMENTAL SECTION The experimental details are identical to those described in our previous work,6 thus only a brief description will be given. All experiments were performed in the Stanford Kinetics Shock Tube facility. The test mixtures were prepared manometrically in a 12 L stainless-steel mixing tank using anhydrous 99.5% 2-methyl-1-propanol (iso-butanol) and TBHP solution 70% by weight in water, each from Sigma Aldrich, and 99.998% purity argon gas from Praxair as the mixture diluent. A Coherent Verdi 532 nm solid state laser was used to pump a Spectra Physics 380 ring-dye cavity with an intracavity frequency doubling crystal to produce laser light at 306.7 nm, specifically tuned to the peak of the R1(5) absorption line in the OH A-X(0,0) band. The OH time-history was monitored in the reflected-shock experiments using this setup at a sample rate of 1 MHz, with an estimated measurement accuracy of ±3% in OH mole fraction.
section that the OH time-history is insensitive to rate constants for these reactions, as long as a reasonable estimate was used (k ≥ 105 s−1). We note that beta-scission reactions eliminating a hydrogen radical are also possible; however, these reactions are expected to occur at a much slower rate than the beta-scission reactions that break a C−C or C−O bond, due to bond energy arguments. The relative rate constants for these beta-scission reactions in the Sarathy et al. mechanism9 further confirm that the beta-scission reactions breaking a C−H bond are negligible. Therefore, hydrogen-eliminating beta-scission reactions are not included in the current mechanism; however, the influence of up to 10% of the β-radical reacting through such a channel (instead of regenerating OH) is considered in the uncertainty analysis for our rate constant determination. Reactions describing the unimolecular decomposition of iso-butanol also were not included in the current mechanism because these reactions are not expected to be important at temperatures less than 1200 K. The addition of the unimolecular decomposition reactions of iso-butanol and the corresponding rate constants (and perturbations of those rate constants by up to a factor of 2) from the Sarathy et al. mechanism9 to the current mechanism was examined, and these changes introduced negligible change (less than a 2% change in the rate of OH decay) in the simulated OH time-histories at 1200 K. Furthermore, the absence of iso-butanol decomposition was verified experimentally by using the OH absorption diagnostic in shock-heated mixtures of dilute iso-butanol in argon (without TBHP); no OH formation was observed in these experiments, further supporting our assumption of the absence of iso-butanol decomposition in the current experimental temperature range. The current kinetic mechanism thus contains all the reactions expected to occur under the experimental conditions of the current work; however, this mechanism will not fully describe experiments outside of our current temperature range or iso-butanol oxidation. The CHEMKIN-PRO suite of programs
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KINETIC MODELING AND ANALYSIS Model Description. A kinetic mechanism was constructed to describe the time evolution of the reaction process with our test mixture of dilute TBHP and iso-butanol in excess. In addition to the four channels of the title reaction, this mechanism consists of a base mechanism that includes secondary reactions due to the presence of TBHP as the OH precursor, as well as the subsequent reactions that are expected to occur following the title reaction as illustrated in Figure 1. The base mechanism used is the 1-butanol mechanism described in a previous work,6 which contains alkane reactions from the JetSurF 1.0 mechanism,8 reactions and rate constants for the TBHP-related reactions from another previous work,5 and updated rate constants for small alkyl and hydroxyalkyl radical reactions relevant to butanol chemistry. The rate constants describing important secondary reactions of iso-butanol are taken from Merchant and Green7 and Sarathy et al.,9 and are listed in Table 1. The isomerization and beta-scission reactions shown in Figure 1 involving iso-butoxy and the iso-C4H8OH radicals were considered in the current analysis; we will show in the following 4721
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analysis, and therefore these rate constants have negligible influence on the OH time-history, and estimates for the rate constants for these reactions are sufficient.
by Reaction Design was used to perform all mechanism simulations in this study, and constant internal energy and constant volume constraints were assumed. OH Sensitivity Analysis. The results of an OH sensitivity analysis at 1079 K and 1.1 atm with a representative test mixture are shown in Figure 2. The OH sensitivity is defined as
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RESULTS AND DISCUSSION Rate Constant Measurements. OH time-histories were measured in reflected-shock experiments of mixtures of TBHP with iso-butanol in excess, diluted in argon. Two test mixtures were prepared, with initial iso-butanol-to-TBHP concentration ratios of 10 and 15. The reflected shock conditions were nominally 1 atm, with temperatures ranging from 907 to 1147 K. Sample measured OH time-histories are shown in Figure 3
Figure 2. OH sensitivity calculation using the current kinetic mechanism at 1079 K, 1.1 atm, with 220 ppm iso-butanol and 15 ppm TBHP.
∂[ln(xOH)]/∂[ln(ki)], where xOH is the OH mole fraction and ki is the rate constant for reaction i. The OH sensitivity to knon‑β is dominant, and the magnitudes of the OH sensitivity to the individual channels will follow the order of the branching ratio of the channels, which have not been previously studied in this temperature range. The early time (first 40 μs) total OH sensitivity to knon‑β does not depend on the non-β branching ratios (i.e., koh/knon‑β, kα/knon‑β, kγ/knon‑β); therefore, we will make no assumptions about these branching ratios in this work. While the OH sensitivity to knon‑β is dominant, the OH sensitivity to kβ is negligible, regardless of the branching ratio of this channel. This is expected because the β-radical will rapidly decompose to produce an OH radical via a beta-scission decomposition mechanism ,and there are no competing non− OH-producing consumption reaction pathways for the βradical. Hence, the kβ reaction channel results in a net-zero rate of OH concentration change. Therefore, simulated OH timehistories are insensitive to kβ, and the simulated rate of OH decay is sensitive to only knon‑β. Minor OH sensitivity to secondary reactions is present from a reaction of iso-butanol with a hydrogen atom and reactions related to the TBHP as the OH precursor. The reaction of isobutanol with hydrogen to produce a β-radical product (H + isobutanol → β-radical + H2) will lead to subsequent OH production via decomposition of the β-radical. While the rate constant for this reaction is not well-known, the OH concentration is only sensitive to this reaction at later times (after the H atom pool has had time to build up), and thus the early time OH time-history can be assumed to be insensitive to the rate constant for this reaction. Rate constants for the reactions important in the OH sensitivity analysis that are related to TBHP as the OH precursor (TBHP → tert-butoxy + OH and OH + CH3 → CH2(s) + H2O) have been previously measured5 with uncertainties of ±30%. The rate constants for the isomerization and beta-scission decomposition of the isobutanol radicals are not significant in the OH sensitivity
Figure 3. Sample OH time-history measurements at temperatures of 1134 K, 1079 K, 1047 K, and 937 K. Left figures are mixture of 150 ppm iso-butanol and 15 ppm TBHP, right figures are 220 ppm iso-butanol and 15 ppm TBHP. Also shown are simulated OH concentration time-histories using the current kinetic mechanism with the best-fit rate for knon‑β and with the best-fit rate perturbed by ±30%.
at representative temperatures over our experimental conditions. The OH time-histories all follow a near-exponential decay at all temperatures after the initial TBHP decomposition to OH, which occurs over a finite time at temperatures under 1000 K. The OH time-histories for the two different mixtures can be compared in Figure 3, illustrating a faster OH decay rate in the mixture with a larger initial iso-butanol-to-TBHP concentration ratio. The non-β rate constant for the reaction of OH with isobutanol, defined as knon‑β = koh + kα + kγ, was determined by matching a simulated OH time-history from the kinetic mechanism with each measured OH time-history, using knon‑β as the free parameter. The OH simulations from the kinetic mechanism with the best-fit to the data are shown in Figure 3, along with the OH simulations with the best-fit value of knon‑β perturbed by ±30% to illustrate the sensitivity of the OH decay rate to knon‑β. Table 2 lists the values for knon‑β determined from our measured OH time-histories for each of our experimental temperatures. 4722
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Table 2. Rate Constants knon‑β and koverall for Each Experimental Data Point, and the Resulting Branching Ratio for the β-Channel mixture 150 ppm iso-butanol, 15 ppm TBHP
220 ppm iso-butanol, 15 ppm TBHP
T [K]
P [atm]
1147 1134 1047 1011 1079 974 937 925 907
1.0 1.0 1.1 1.1 1.1 1.2 1.2 1.2 1.2
kβ (Merchant and Green7) [cm3molecule−1s−1]
knon‑β (from data) [cm3molecule−1s−1] 2.37 2.31 1.96 1.74 2.13 1.62 1.49 1.49 1.37
× × × × × × × × ×
10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11
4.68 4.60 4.11 3.93 4.28 3.76 3.60 3.55 3.48
× × × × × × × × ×
10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12 10−12
koverall [cm3molecule−1s−1] 2.84 2.77 2.37 2.14 2.55 1.99 1.85 1.85 1.72
× × × × × × × × ×
10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11
kβ/koverall [%] 16 17 17 18 17 19 19 19 20
determined using an uncertainty of ±30% for the rate constants for the reactions TBHP → tert-butoxy + OH and OH + CH3 → CH2(s) + H2O, and an uncertainty factor of 2 for the reaction H + iso-butanol → β-radical + H2. While the large uncertainty of the rate constant for the latter reaction can have a significant effect on the late-time OH mole fraction (at times >40 μs), there is only minimal effect on the early time OH decay rate that was used for the rate constant determination. For temperatures below 1000 K, the uncertainty of the rate constant for the TBHP decomposition reaction becomes more significant as the temperature decreases, and the largest overall uncertainty for knon‑β is ±21% at 907 K. These uncertainty limits are illustrated in Figure 4. Comparison to Rate Constant Recommendations. Several detailed kinetic mechanisms for iso-butanol oxidation have been developed in recent years.7,9−12 Each of these mechanisms includes four site-specific rate constants (i.e., koh,kα,kβ,kγ) for the title reaction, estimated by examination of the rate constants for analogous reactions. Comparison of the current data for knon‑β with the corresponding rate constant sum from three of the most recent mechanisms7,9,12 is shown in Figure 4. The rate constants used by Merchant and Green7 show the best agreement with our current work. The rate constants used in the Sarathy et al. mechanism9 are 15−25% slower than the current measurements, and the rate constants used in the Grana et al. mechanism12 are 25−40% slower than the current measurements. The rate constants used in the Sarathy et al. and Grana et al. mechanisms show agreement within the uncertainty limits of the current work only at the lowest temperatures studied. Atkinson13,14 developed an empirical structure−activity relationship (SAR) to estimate the rate constants for reactions of OH with organic compounds, including alcohols, at temperatures from 250 to 1000 K. The parameters in their SAR include a rate constant term for each H-atom abstraction site (primary, secondary, and tertiary carbons and hydroxyl group) in the organic compound, and substituent factors that influence the rate constant term at each reaction site based on the identity of the neighboring substituent groups. The parameters in the SAR were determined from data for rate constants of OH with alkanes, alcohols, and diols at near-atmospheric temperatures. Kwok and Atkinson15 and Bethel et al.16 have published updated substituent factors at 298 K that can be extrapolated to higher temperatures using the exponential relationship Fx(T) = exp(Ex/T), where Fx is the substituent factor. We computed knon‑β using the method of Atkinson, with updated substituent factors from Kwok and Atkinson and Bethel et al., by omitting the rate constant term and substituent
Figure 4. Rate constant measurements for knon‑β. The error bars represent the results of a detailed uncertainty analysis. Also shown are comparisons to the corresponding rate constants used in recently developed iso-butanol oxidation mechanisms7,9,12 and using the SAR of Atkinson13,14 with updated substituent factors.15,16
Figure 4 presents an Arrhenius plot of knon‑β for all of our experiments. The data can be described in Arrhenius form by the expression ⎛ 2350 ⎞ k non ‐ β = 1.84 × 10−10exp⎜ − ⎟ ⎝ T[K] ⎠
in units of cm3 molecule−1 s−1, valid over the temperature range 907 to 1147 K. To our knowledge, these are the first experimental rate constants associated with the title reaction in this temperature range. A detailed uncertainty analysis was performed to examine the total uncertainty in the determination of knon‑β based on uncertainties in temperature, pressure, initial TBHP and isobutanol concentrations, laser intensity and wavelength, OH absorption coefficient, data fitting, impurities, branching ratios of the non-β reactions, the rate constants of the three most important secondary reactions in the mechanism, and the possible influence of unimolecular iso-butanol decomposition reactions and hydrogen-producing beta-scission reactions of the β-radical that were omitted from the mechanism. The influence of these uncertainties on the total uncertainty on knon‑β is estimated to be ±12% at temperatures above 1000 K, with signal noise and the initial iso-butanol concentration as the dominant factors contributing to the total uncertainty. Uncertainty in the rate constants for the three most important secondary reactions have only a small (
