SHOCK TUBE STUDIES OF BIOFUEL KINETICS · Units: s-1 3(unimolecular), cm mol-1s-1(bimolecular) Table A-1: Summary of measured ignition delay times for 1-butanol diluted in argon

i

SHOCK TUBE STUDIES OF BIOFUEL KINETICS

A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MECHANICAL

ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD

UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE

OF DOCTOR OF PHOLOSOPHY

Ivo Stranic

March 2014

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/fn462rq9726

© 2014 by Ivo Stranic. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/fn462rq9726

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Ronald Hanson, Primary Adviser


Craig Bowman


David Davidson

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

v

Abstract

The harmful emissions associated with the combustion of fossil fuels combined with the

rapidly increasing global demand for energy present serious challenges to the long term

sustainability of life on this planet. Fossil fuels currently account for approximately 81% of

worldwide energy usage, and approximately 22% of global energy consumption occurs in the

transportation sector.

One approach for addressing the world’s energy challenges is to reduce the consumption

of fossil fuels by improving the numerical simulation capabilities of combustion systems, thus

enabling engineers to design more efficient combustion devices. A prerequisite for this design

capability is the understanding of chemical kinetics of the fuels that are being utilized. An

alternative approach for reducing the consumption of fossil fuels is developing renewable energy

alternatives that eliminate the need for fossil fuels altogether. Biofuels are of particular interest as

an alternative fuel in the transportation sector because their net CO2 footprints can be

significantly lower compared to those of traditional fossil fuels.

The goal of this dissertation is to study the chemical kinetics of biofuels, which would

ultimately allow them to be used more efficiently in the combustion devices of the future. This

work is primarily experimental, and it can be divided into three parts:

First, the chemical kinetics of butanol, a promising second generation biofuel, were

investigated extensively. A variety of kinetic targets such as ignition delay times and species

time-histories were measured accurately over a wide range of conditions. These high-accuracy

data have been used by research groups around the world in order to validate and improve

chemical kinetic models.

Second, rate constants for reactions of ethanol and tert-butanol with OH radicals were

investigated. These reactions are one of the primary removal pathways of fuels during

combustion, and they significantly affect the combustion properties of these fuels. Measurements

vi

were performed using isotopic labeling of 18

O in the alcohol group in order to eliminate the

recycling of OH radicals following H-atom abstraction at β-sites, which commonly perturbs

measurements of rate constants for reactions of alcohols with OH radicals.

Third, various experimental techniques were developed and improved while performing

these measurements. This work presents the first application of isotopic labeling and laser

absorption in shock tubes, which shows significant promise for future chemical kinetic studies.

Furthermore, the rate constant for cyclohexene decomposition was determined with the highest

accuracy to date. These measurements are likely to improve a myriad of comparative rate and

chemical thermometry studies that use cyclohexene decomposition as a reference reaction.

Finally, a high-temperature laser absorption diagnostic for measuring acetylene concentration was

developed. Time-resolved shock tube measurements of this critical combustion intermediate

should significantly improve the experimental capabilities for performing chemical kinetic

studies.

vii

Acknowledgements

I would like to thank my advisor, Prof. Ronald Hanson, for guiding me throughout my

research. He was an invaluable source of wisdom and inspiration throughout my work, and his

relentless pursuit of excellence in research will continue to guide me in my future work. I would

also like to thank Prof. David Golden and Prof. Thomas Bowman, who in addition to being co-

authors on several of my publications, provided valuable insights through many of my research

projects. I must also thank Dr. David Davidson, who essentially ensures that our research group

maintains its ability to run top-quality experiments. His advice on numerous practical problems

helped me quickly overcome experimental obstacles. My primary source of wisdom about

spectroscopy came from Dr. Jay Jeffries. I thank him for the numerous helpful discussions we’ve

had about lasers, optics, and absorption spectra.

I would also like to thank my family, especially my parents, for their support during my

studies. Their encouragement for pursuing a PhD at Stanford University was critical for the

completion of this work. I must also thank all of my colleagues at the Hanson Research Group

who were always willing to provide me with valuable research advice. Notably, I would like to

thank Prof. Subith Vasu, who helped me understand and operate shock tubes, and Dr. Genny

Pang, who was an invaluable co-author and advisor on several publications. I would also like to

thank Deanna Chase, Joseph Harmon, and Sheng Yang, whom I had the pleasure of advising

during their summers at our lab. Finally, I would like to thank all of my friends for being an

excellent source of support, relaxation, and fun over the years.

Work presented here was supported by the Combustion Energy Frontier Research Center

(funded by the Department of Energy) and the Air Force Office of Scientific Research.

viii

Table of Contents

Abstract.……………………………………………………………………………………..….....v

Acknowledgements …………………………………………………………………………......vii

List of Tables………………………………………………………………………………….…xii

List of Figures…………………………………………………………………………………...xiv

1 CHAPTER 1: Introduction ................................................................................................... 1

1.1 Motivation ........................................................................................................................ 1

1.2 Chemical Kinetic Mechanisms ........................................................................................ 2

1.3 Butanol ............................................................................................................................. 4

2 CHAPTER 2: Experimental Methods .................................................................................. 6

2.1 Introduction ...................................................................................................................... 6

2.2 Shock Tube Facility ......................................................................................................... 6

2.2.1 Overview .................................................................................................................. 6

2.2.2 Temperature and Pressure Measurements .............................................................. 10

2.2.3 Experimental Modeling .......................................................................................... 11

2.3 Emission Diagnostics ..................................................................................................... 13

2.4 Laser Diagnostics ........................................................................................................... 15

2.4.1 Overview ................................................................................................................ 15

2.4.2 Diagnostic Details .................................................................................................. 18

2.4.3 Cross-section Measurements .................................................................................. 20

2.5 Fuel + OH Reaction Rate Constant Measurements........................................................ 22

2.5.1 Overview ................................................................................................................ 22

ix

2.5.2 Secondary Reactions .............................................................................................. 23

3 CHAPTER 3: Kinetic Studies of the Butanol Isomers ..................................................... 26

3.1 Introduction .................................................................................................................... 26

3.2 Ignition Delay Time Measurements ............................................................................... 27

3.2.1 Overview ................................................................................................................ 27

3.2.2 Results .................................................................................................................... 30

3.3 Multi-Species Time-History Measurements .................................................................. 40

3.3.1 Overview ................................................................................................................ 40

3.3.2 Modeling Shock Tube Experiments of Endothermic Reacting Systems ............... 41

3.3.3 Results .................................................................................................................... 44

3.4 Conclusions .................................................................................................................... 59

4 CHAPTER 4: Isotopic Labeling ......................................................................................... 60

4.1 Introduction .................................................................................................................... 60

4.2 16OH vs

18OH Spectra .................................................................................................... 61

4.3 Ethanol + OH ................................................................................................................. 64

4.3.1 Overview ................................................................................................................ 64

4.3.2 Ethanol + OH Kinetics ........................................................................................... 65

4.3.3 Results .................................................................................................................... 71

4.4 tert-Butanol + OH .......................................................................................................... 76

4.4.1 Introduction ............................................................................................................ 76

4.4.2 tert-Butanol + OH Kinetics .................................................................................... 77

x

4.4.3 Results .................................................................................................................... 83

4.5 Conclusions .................................................................................................................... 90

5 CHAPTER 5: Cyclohexene Decomposition Rate Constant Measurements ................... 92

5.1 Introduction .................................................................................................................... 92

5.2 Experimental Setup ........................................................................................................ 93

5.3 Kinetic Modeling ........................................................................................................... 94

5.4 Results .......................................................................................................................... 100

5.5 Conclusions .................................................................................................................. 107

6 CHAPTER 6: High-Temperature Acetylene Diagnostic ................................................ 108

6.1 Introduction .................................................................................................................. 108

6.2 Experimental Methods ................................................................................................. 109

6.3 Interference Absorption ............................................................................................... 112

6.4 Results .......................................................................................................................... 113

6.5 Diagnostic Application ................................................................................................ 121

6.6 Conclusions .................................................................................................................. 126

7 CHAPTER 7: Summary and Future Work ..................................................................... 127

7.1 Summary ...................................................................................................................... 127

7.2 Future Work ................................................................................................................. 128

7.3 Publications .................................................................................................................. 130

APPENDICES……………………………………………………………………………….....132

APPENDIX A: TABLES OF RAW DATA ............................................................................ 132

xi

A.1 Ignition delay times for the butanol isomers ............................................................ 132

A.2 Ethanol + OH Rate Constant Measurements ........................................................... 138

A.3 tert-Butanol + OH Rate Constant Measurements .................................................... 140

A.4 Cyclohexene Decomposition Rate Constant Measurements .................................... 142

APPENDIX B: ADDITIONAL DATA ON THE PYROLYSIS AND OXIDATION OF THE

BUTANOL ISOMERS ............................................................................................................ 143

B.1 Ignition Delay Times of 2-Butanol and tert-Butanol ............................................... 143

B.2 Ignition Delay Times of 1-Butanol in Air ................................................................ 144

B.2 Multi-Species Time-histories for 2-Butanol Pyrolysis ............................................ 150

APPENDIX C: UNCERTAINTY ANALYSIS OF ALCOHOL + OH REACTION RATE

CONSTANT MEASUREMENTS ........................................................................................... 159

Bibliography…………………………………………………………………………………....163

xii

List of Tables

Table 2.1: Dimensions of the shock tubes utilized in this work. Diameter refers to the driven

section.

Table 2.2: Comparison of the measured room-temperature cross-sections in the current work

with data from the PNNL database56

. Units are m2mol

-1. Uncertainty in the current study is ± 3%.

Table 5.1: Rate constants for reactions modified and added to the Silke at al.121

mechanism.

Units: s-1

(unimolecular), cm3mol

-1s

-1(bimolecular)

Table A-1: Summary of measured ignition delay times for 1-butanol diluted in argon. T and P

values correspond to the initial post-shock conditions.



Table A-3: Summary of measured ignition delay times for iso-butanol diluted in argon. T and P


Table A-4: Summary of measured ignition delay times for tert-butanol diluted in argon. T and P


Table A-5: Summary of measured ignition delay times for 1-butanol in stoichiometric air.

Mixtures made with N2 and O2 only. T and P values correspond to the initial post-shock

conditions.

Table A-6: Summary of the measurements of the overall rate constant for the ethanol + OH

reaction. Mixtures are balanced in argon.

Table A-7: Summary of the measurements of the non-β rate constant for the ethanol + OH


Table A-8: Summary of the measured 16

k’. Mixtures are balanced in argon.



xiii

Table A-10: Summary of the rate constant measurements for cyclohexene decomposition. All

mixtures are balanced in argon.

xiv

List of Figures

Figure 1.1: Molecular structure of the four butanol isomers. Greek letters represent the notation

for the various molecular sites.

Figure 2.1: Schematic of the shock tube. a-d show the different stages of a shock tube experiment.

a.) at vacuum. b.) filled with driver and driven gas. c.) post diaphragm burst. d.) post incident-

shock reflection

Figure 2.2: Representative pressure for an argon shock using helium driver gas. Post-reflected-

shock conditions: T = 1512 K, P = 1.35 atm.

Figure 2.3: Representative pressure trace for an argon shock using a driver insert and a tailored

60/40 He/N2 driver gas. Post-reflected-shock conditions: T = 965 K, P = 2.25 atm.

Figure 2.4: Experimental apparatus for emission measurements. Further details on the optical

arrangement for emission measurements can be found in previous work49

. BP = Bandpass.

Figure 2.5: Experimental apparatus for direct laser absorption measurements using common

mode rejection. BP = Bandpass. I and Iref represent the transmitted and reference light

intensities, respectively.

Figure 2.6: Measured Absorption cross-sections of cyclohexene, 1,3-butadiene, and 1,3-

cyclohexadiene from 1.5-3.8 atm. Data exhibited no pressure dependence.

Figure 2.7: OH time-histories during the pyrolysis of 15.5 ppm TBHP/H2O/Argon. Solid lines

represent measurements, dashed lines represent simulations using the Leplat et al.58

mechanism

(see Section 4.3) to which the TBHP sub-mechanism from Pang et al.57

was appended.

Figure 3.1: Ignition delay time measurement of 2-Butanol in 4% O2 diluted in Ar, = 1. Initial

post-reflected-shock conditions: T = 1176 K, P = 40.5 atm.

Figure 3.2: Measured ignition delay times for 1-butanol. P = 1.2 atm, ϕ = 1, xO2 = 0.03, diluted

in argon. Data by Moss et al.41

are not scaled to a common pressure (P ≈ 1.10-1.35 atm).

xv


in argon.


in argon.







Figure 3.7: Measured ignition delay times for iso-butanol. P = 1.2 atm, ϕ = 1, xO2 = 0.03,

diluted in argon. Data by Moss et al.41


Figure 3.8: Measured ignition delay times for tert-butanol, P = 1.2 atm, ϕ = 1, xO2 = 0.03,



Figure 3.9: Measured ignition delay times for 1-butanol, xO2 = 0.04, diluted in argon. Pressure in

atmospheres. The Sarathy et al. mechanism8,9

was modified to include rate constants for the

unimolecular decomposition of 1-butanol from work by Rosado-Reyes and Tsang61

. Uncertainties

are approximately equal to twice the height of the data points.

Figure 3.10: Measured ignition delay times for iso-butanol, xO2 = 0.04, diluted in argon.

Pressure in atmospheres. Uncertainties are approximately equal to twice the height of the data

points.

Figure 3.11: Measured ignition delay times for the butanol isomers at 43 atm, xO2 = 0.04, diluted

in argon. Uncertainties are approximately equal to twice the height of the data points.

Figure 3.12: Measured and simulated pressure for 1% 1-butanol pyrolysis. Initial post-reflected-


Figure 3.13: Simulated temperature for 1% 1-butanol pyrolysis. Initial conditions: T = 1477 K, P

= 1.52 atm.

xvi

Figure 3.14: Simulated CO mole fraction for 1% 1-butanol pyrolysis. Initial conditions: T =

1477 K, P = 1.52 atm. CV simulations performed using the Sarathy et al.8,9

mechanism.

Figure 3.15: Measured OH mole fraction for 1% 1-butanol pyrolysis.

Figure 3.16: Measured H2O mole fraction for 1% 1-butanol pyrolysis.

Figure 3.17: Simulated OH mole fraction for 1% 1-butanol pyrolysis. CV simulations performed

using the Cook et al.64

mechanism. Temperature and pressure indicate initial post-reflected-shock

conditions.

Figure 3.18: Measured H2O mole fraction for 1% 1-butanol pyrolysis. Solid lines represent

measurements, dotted lines represent CV simulations performed using the simulations performed

using the Sarathy et al.8,9

mechanism.

Figure 3.19: Measured OH mole fraction for 1% 1-butanol pyrolysis. Solid lines represent

measurements, dotted lines represent CV simulations performed using the Sarathy et al.8,9

mechanism.

Figure 3.20: H2O sensitivity analysis for 1% 1-butanol pyrolysis. Initial conditions: T = 1348 K,

P = 1.83 atm. CV simulations performed using the Sarathy et al.8,9

mechanism.

Figure 3.21: Measured CO mole fraction for 1% 1-butanol pyrolysis. Solid lines represent


mechanism.

Figure 3.22: CO sensitivity for 1% 1-butanol pyrolysis. Post-reflected-shock conditions: Initial

Conditions: T = 1603 K, P = 1.36 atm. CV simulations performed using the Sarathy et al.8,9

mechanism.

Figure 3.23: Measured CO mole fraction for 1% 1-butanol pyrolysis. Initial post-reflected-shock

conditions: T = 1477 K, P = 1.52 atm.

Figure 3.24: C2H4 mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements,

dotted lines represent CV simulations using the Sarathy et al.8,9

mechanism.

xvii

Figure 3.25: C2H4 sensitivity analysis for 1% 1-butanol pyrolysis. Initial conditions: T = 1348 K,


mechanism.

Figure 3.26: Measured OH mole fraction for 1% iso-butanol pyrolysis. Solid lines represent


mechanism.

Figure 3.27: Measured H2O mole fraction for 1% iso-butanol pyrolysis. Solid lines represent


mechanism.

Figure 3.28: OH sensitivity for 1% iso-butanol pyrolysis. Initial Conditions: T = 1440 K, P = 1.73

atm. CV simulations performed using the Sarathy et al.8,9

mechanism.

Figure 3.29: Measured CO mole fraction for 1% iso-butanol pyrolysis. Solid lines represent


mechanism.

Figure 3.30: CO sensitivity for 1% iso-butanol pyrolysis. Post-reflected-shock conditions: Initial


mechanism.

Figure 4.1: 16

OH and 18

OH spectra of the R22(5.5) transition in the A-X(0,0) band at 1000 K, 1

atm. 18

OH lineshape assumed to be the same as that of 16

OH as determined by Herbon et al.51

.

18OH linecenter taken from Cheung et al.

68.

Figure 4.2: Peak absorbance near the R22(5.5) transition of 16

OH at the time of peak OH mole

fraction during 0.1% tert-butanol/argon pyrolysis. 16

OH R22(5.5) transition linecenter at

32558.72 cm-1

. Sub-plot shows absorbance time-history and indicates the time of peak

absorbance. Post-reflected shock conditions: T ≈ 1515 K, P ≈ 1 atm.

Figure 4.3: Measured 16

OH time-histories during neat TBHP pyrolysis, acquired at the

linecenter of the R11(5.5) and R22(5.5) transitions in the A-X(0,0) band. 50 ppm TBHP, diluted in

argon. Post-reflected shock conditions: T = 1108 K, P = 1.2 atm.

xviii

Figure 4.4: Dominant reaction pathways related to ethanol + OH reactions.

Figure 4.5: Sensitivity analysis of 16

OH in a labeled experiment. T = 1032 K, P = 1.08 atm, 349

ppm ethan18

ol, 28 ppm TBHP, 80 ppm H2O, diluted in argon.


OH in an unlabeled experiment. T = 1029 K, P = 1.03 atm,

354 ppm ethan16


Figure 4.7: Representative 16

OH time-histories for ethan16

ol/TBHP/argon mixtures (knon-β in units

of cm3mol

-1s

-1). Post-reflected shock conditions: T = 1023 K, P = 1.03 atm. Discrepancy in the

rise of 16

OH is caused by the limited time resolution of the diagnostic (~5µs).

Figure 4.8: Comparison of the measured overall and non-β rate constants for the title reaction

with previous theoretical and experimental work at high temperatures. Curves by Zheng and

Truhlar79

represent calculations using the M08-SO/6-31+G(d,p) method. Curve labeled “Fit”

was generated based on all experimental data shown in Figure 4.10.

Figure 4.9: Comparison of the measured branching ratio BRβ with previous theoretical work.

Figure 4.10: Comparison of the measured overall rate constant for the title reaction with

previous theoretical and experimental work. Data from past studies are excluded if they were

performed at conditions that are not sensitive to reactivity at the β-site. Data are best fit by the

expression: koverall = 5.07 x 105 T

2.31 exp(608/T) cm

3mol

-1s

-1

Figure 4.11: Dominant reaction pathways related to tert-butanol + OH reactions.



ppm tert-butan18




500 ppm tert-butan16



OH time-histories for tert-butanol/TBHP/argon mixtures (k’ in

units of cm3 molecule

-1 s

-1). Initial post-reflected shock conditions: T = 1020 K, P = 1.2 atm.

Figure 4.15: Arrhenius plot of measured 16

k’ and 18

k’. Solid lines show Arrhenius fits.

xix

Figure 4.16: Comparison of the measured overall tert-butanol + OH reaction rate constant (k4.3

= 18

k’) with values used in mechanisms from the literature.

Figure 4.17: Comparison of the measured branching ratio product BR1BR2 near 1.1 atm with

values used in mechanisms from the literature.

Figure 4.18: Comparison of the estimated branching ratio BR1 with values used in mechanisms

from the literature.

Figure 4.19: Comparison of the inferred branching ratio BR2 near 1.1 atm with values used in

mechanisms from the literature.

Figure 5.1: Representative measurement and simulation of ethylene mole fraction time-histories.

Reaction rate constant for simulations specified at the post-reflected-shock temperature. Note

that the rate constant changes slightly throughout the measurement time due to a small decrease

in temperature. 1% cyclohexene diluted in argon. Post-reflected-shock conditions: T = 1192 K, P

= 3.52 atm.

Figure 5.2: Measurements of the rate constant for cyclohexene decomposition in the current

study, as well as a comparison with measurements from the literature. Pressure range in the

current study is 0.8-3.7 atm. Pressure in past studies is indicated if measurements were

performed at multiple pressures. Uncertainties in the current study are approximately equal to

the height of the data points.

Figure 5.3: Subset of measurements of the rate constant for cyclohexene decomposition in the

current study, as well as comparisons with measurements from the literature, in the temperature

range where cyclohexene is commonly used as a reference. Pressure range in the current study is

0.8-3.7 atm.

Figure 5.4: Difference in the inferred temperature using chemical thermometry. ΔT = Tprevious work

- Tcurrent work, where Tcurrent work is the inferred temperature using the rate constant expression for

Reaction 1 from the current study, and Tprevious work is the inferred temperature using the rate

constant for Reaction 5.1 from previous work.

xx

Figure 6.1: Absorption spectrum of acetylene at 1400 K, 1 atm calculated using HITRAN

2012138

. Primary plot shows the entire spectrum from 500-3500 cm-1

, subplot shows spectrum in

the 3300 cm-1

band.

Figure 6.2: Schematic of the proposed acetylene diagnostic for kinetic studies in shock tubes (BP

= Bandpass)

Figure 6.3: Comparison of the measured absorption spectrum of acetylene with previous work

near 3335.55 cm-1

at 297 K, 1 atm. Brackets indicate the diluent. Measurements were performed

using a 0.0804% mixture in a 79.9 cm static cell.

Figure 6.4: Comparison of the measured high-temperature absorption spectrum of acetylene

near 3335.55 cm-1

with HITRAN 2012138

simulations. Measurements were performed with

acetylene diluted in argon, simulations assume dilution in air.

Figure 6.5: Measured high-temperature absorption coefficient of acetylene at three different

wavelengths near 3335.55 cm-1

, scaled to 1 atm using Equations 6.1-6.4. Data were acquired

from 0.8-4.0 atm. Lines represent the fits using Equations 6.1-6.4. % Errors indicate deviations

of the fits from the measurements. Standard deviations of errors at linecenter, 3335.20 cm-1

, and

3335.82 cm-1

are 1.7%, 4.6%, and 3.7%, respectively.

Figure 6.6: Measured shift of the absorption peak relative to that at room temperature and

pressure (νShift = νHi-temp– νRTP). Errors indicate the deviation of the fit using Equation 6.2 relative

to the experimental data (νError = νFit – νMeasured).Uncertainty in the measurement is approximately

± 0.002 cm-1

.

Figure 6.7: Measured high-temperature absorption coefficient of propyne and 1-butyne at three

different wavelengths near 3335.55 cm-1

. Propyne data at the wavelength of the acetylene

absorption peak are fit using the expression: kν, [cm-1

atm-1

]= 0.675 – 3.44x10-4

T[K]. Pressures

are indicated in selected propyne measurements in order to demonstrate that its absorption

coefficient becomes increasingly wavelength independent at higher pressures.

xxi

Figure 6.8: Acetylene time histories during the pyrolysis of 0.75% propene/argon. Solid lines

represent measurements, dashed lines represent CV simulations using the USC Mech. V2.0

kinetic mechanism. Legend indicates initial post-reflected shock conditions. Measurements and

error bars do not account for the increase in the acetylene absorption coefficient caused by the

reduction in temperature associated with the endothermic pyrolysis of propene. A representative

temperature time-history is shown in Figure 6.10.

Figure 6.9: Acetylene time histories during the pyrolysis of 0.75% 1-butene/argon. Solid lines




reduction in temperature associated with the endothermic pyrolysis of 1-butene.

Figure 6.10: Representative acetylene time-history during the pyrolysis of 0.75% propene/argon.

T and P indicate initial post-reflected-shock conditions. Variable T data was calculated based on

the simulated temperature time-history using the USC Mech V2.0 kinetic mechanism.

Uncertainties in the Variable T data were estimated based on a 30 K uncertainty in the

temperature profile from the kinetic simulation.

Figure 6.11: Estimated detection limit (SNR = 1) of the proposed acetylene diagnostic as a

function of temperature and pressure assuming an absorbance noise of 0.002 and pathlength of

14.13 cm.

Figure B-1: Measured ignition delay times for 2-butanol, xO2 = 0.04, diluted in argon. Pressure

in atmospheres. Uncertainties are approximately equal to twice the height of the data points.

Figure B-2: Measured ignition delay times for tert-butanol, xO2 = 0.04, diluted in argon.


points.

Figure B-3:Measured ignition delay times for 1-butanol, P = 20 bar, ϕ = 1, in air. Heufer et

al.34

data is subject to non-reactive, facility-dependent, pre-ignition pressure increases.

xxii

Figure B-4: Ignition delay time measurement of 1-butanol in stoichiometric air. Initial reflected




Figure B-6: Pressure traces from CV autoignition simulations of 1-butanol in stoichiometric air

using the Vranckx et al.33

mechanism. Pinitial = 20 atm. Temperature refers to Tinitial.

Figure B-7: Measured OH mole fraction for 1% 2-butanol pyrolysis. Solid lines represent


mechanism.

Figure B-8: Measured H2O mole fraction for 1% 2-butanol pyrolysis. Solid lines represent


mechanism.

Figure B-9: OH sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1449 K, P = 1.8


mechanism.

Figure B-10: Measured OH mole fraction for 1% 2-butanol pyrolysis. Initial post-reflected-shock

conditions: T = 1449 K, P = 1.8 atm Solid lines represent measurements, dotted lines represent

CV simulations performed using the Sarathy et al.8,9

mechanism.

Figure B-11: Measured H2O mole fraction for 1% 2-butanol pyrolysis. Initial post-reflected-

shock conditions: T = 1449 K, P = 1.8 atm Solid lines represent measurements, dotted lines

represent CV simulations performed using the Sarathy et al.8,9

mechanism

Figure B-12: Measured C2H4 mole fraction for 1% 2-butanol pyrolysis. Solid lines represent


mechanism.

Figure B-13: C2H4 sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1449 K, P =

1.8 atm. CV simulations performed using the Sarathy et al.8,9

mechanism.

xxiii

Figure B-14: Measured CO mole fraction for 1% 2-butanol pyrolysis. Solid lines represent


mechanism.

Figure B-15: CO sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1603 K, P = 1.36


mechanism.

Figure C-1: Magnitude of the uncertainty in the measured overall rate constant for the reaction

ethanol + OH associated with each factor considered in the analysis. Random uncertainty factors

are indicated by *, the rest are systematic. Uncertainties are ±, unless specified otherwise. 205

ppm ethan18

ol, 12 ppm TBHP, 35 ppm H2O, diluted in argon. T = 914 K, P = 1.09 atm.


tert-butanol + OH associated with each factor considered in the uncertainty analysis. Random

uncertainty factors are indicated by *, the rest are systematic. Uncertainties are ±, unless

specified otherwise. 500 ppm tert-butan18

ol, 28 ppm TBHP, 81 ppm H2O, diluted in argon. T =

1167 K, P = 1.20 atm.

xxiv

1

1 CHAPTER 1: Introduction

1.1 Motivation

One of the primary challenges facing society today is the need for environmentally

friendly sources of energy. Fossil fuels, which currently account for 81% of worldwide energy

usage1, are responsible for 66% of the global greenhouse gas emissions

2. Global climate change

such as rising temperatures and sea levels caused by increased greenhouse gas emission could

potentially have a devastating effect on the sustainability of life on this planet3. Furthermore, the

combustion of fossil fuels in the transportation sector is a primary cause of urban pollution4.

One approach to solving these energy challenges is to convert fossil fuels to energy more

efficiently. This approach has two specific goals: improving the energy efficiency of combustion

devices in order to maximize the energy output per unit of consumed fossil fuels, and reducing

pollutant emissions by designing combustion systems that combust fossil fuels more effectively.

Though significant progress has been made in achieving these goals, improvements in efficiency

cannot sufficiently reduce the consumption of fossil fuels in order to solve the energy challenges

outlined above. Nonetheless, improvements in the design of combustion devices will continue to

significantly mitigate the overall consumption of fossil fuels.

A more long-term approach to solving the world’s energy challenges is to develop

affordable and clean energy sources that can replace fossil fuels altogether. Biofuels, which are

any organic fuel derived from plants or animals on a renewable basis, are a promising alternative

energy source that can be used as a substitute for fossil fuels without major modifications to the

energy infrastructure. Due to their similar physical properties, biofuels are a likely candidate for

replacing traditional fuels in the transportation sector, which accounts for approximately 21% of

energy used worldwide1. Though the combustion of biofuels has similar pollutant characteristics

as the combustion of fossil fuels, biofuels have significantly lower life-cycle-greenhouse-gas-

2

emissions due to the removal of greenhouse gasses during the production process. Biofuel

production has increased fivefold from 2000 to 20105, and the share of biofuels in the

transportation sector is expected to increase from 3% today6 to 27% in 2050

5. Therefore,

advancing the knowledge of both the production and combustion of biofuels is of significant

scientific interest.

1.2 Chemical Kinetic Mechanisms

The combustion of virtually all fuels proceeds via a series of chemical reactions between

the fuel, oxidizer, and their fragments. In order to accurately simulate a chemically reacting

system, a series of differential rate equations for each species identified in the reacting system

must be solved using the known temperature- and pressure-dependent rate constants for each

specified reaction. In addition, the temperature-dependent enthalpy and entropy for each of the

species must be known in order to predict the thermodynamic properties of the reacting system.

The chemical kinetic mechanism for a particular fuel simply refers to the collection of these

kinetic and thermodynamic parameters, that when combined with appropriate gas-dynamic

models, are a powerful tool for predicting the performance of combustion devices. The utility of

chemical kinetic mechanism has increased significantly with the advent of powerful computing

tools. Though past numerical studies of combustion devices required the use of highly simplified

kinetic mechanisms in order to reduce computing times to a manageable duration, the continuing

increase in computing power will enable engineers to use more complete chemical kinetic

mechanisms to simulate their combustion designs.

The complexity of chemical kinetic mechanism varies greatly depending on the

molecular size of the fuels they describe. For example, the combustion of small molecules such as

hydrogen can be accurately modeled using 10 species and 20 reactions7. However, combustion

simulations of the C4 alcohol butanol may require 284 species and 1892 reactions8,9

. The

3

significance of chemical reactions to the performance of chemical kinetic mechanisms is often

hierarchical in nature, because certain chemical reactions affect the performance of a kinetic

mechanism much more than others. For instance, the reaction H + O2 → OH + O is commonly

regarded as the most important reaction in combustion because it affects the rate of combustion

more than any other reaction for virtually any hydrocarbon. Therefore, the performance of

chemical kinetic mechanisms can be improved significantly by studying the subset of chemical

reactions that significantly affect its predictive capabilities.

The development of chemical kinetic mechanisms is a highly iterative process.

Researchers typically postulate the set of chemical reactions and corresponding temperature-

dependent reaction rate constants that may occur during the combustion of a particular fuel. Rate

constants for particular reactions can be measured, calculated, or estimated using a variety of

theoretical and experimental methods. The kinetic mechanism is then tested against a variety of

experimental targets such as ignition delay times, species time-histories, spatial concentration

profiles, flame speeds, etc. If possible, discrepancies between the experimental measurements and

mechanism predictions are then attributed to a subset of chemical reactions in the kinetic

mechanism, and rate constants for these reactions are studied in greater detail. The mechanisms

are then updated using more accurate reaction rate constants, typically resulting in better

agreement with the experimental data. Due to the limited accuracy of theoretical methods for

calculating reaction rate constants, experimental measurements of global kinetic targets are

invaluable for validating and improving chemical kinetic mechanisms.

The purpose of this thesis is to present novel experimental data and techniques that will

advance the study of chemical kinetics and ultimately enable significant improvements to

chemical kinetic mechanisms. Measurements of butanol ignition delay times and species time-

histories presented in this work provide a wide array of kinetic targets for testing and refining

chemical kinetic mechanisms. Several of these data have already been used for this purpose since

publication. Furthermore, measurements of the rate constants for reactions of ethanol and tert-

4

butanol with OH radicals represent a highly accurate determination of critical reaction rate

constants for these fuels. In order to perform these rate constant measurements, a novel technique

that combines isotopic labeling and laser absorption in shock tubes was developed, and it will

serve as a powerful tool of future kinetic studies. Measurements of the rate constant for

cyclohexene decomposition will also significantly improve the accuracy of kinetic studies that

utilize chemical thermometry or comparative rate techniques. Finally, the development of a laser

absorption diagnostic for acetylene provides yet another target species that experiments can use to

validate the performance of kinetic mechanism.

1.3 Butanol

A primary focus of this thesis is the study of butanol kinetics. As shown in Figure 1.1,

butanol is a C4 alcohol with four isomers, and it is a strong biofuel candidate because of its

significant advantages compared to the current most abundantly used biofuel, ethanol. It has a

larger energy density, it is less hygroscopic, which means it can be transported in gasoline

pipelines, it can be blended with gasoline in higher concentrations, and it is less volatile10,11

. The

synthesis of butanol has been of significant scientific interest, and a number of private companies

have sought to commercialize the production process. The private sector has primarily focused on

the commercialization of 1-butanol and iso-butanol due to their relatively low production

costs12,13

.

Butanol kinetics has been the subject of several recent scientific studies. Though past

work has primarily focused on the kinetics of 1-butanol, several of the most recent studies have

focused on the other isomers. Past experimental work has been performed in rapid compression

machines14,15

, flames16–22

, flow reactors17,22,23

, static reactors24

, and internal combustion engines25–

30. Shock tubes, in particular, have provided a wide array of kinetic targets including ignition

delay times, species time-histories, and elementary reaction rate constant31–39

. Several kinetic

5

mechanisms for the high-temperature oxidation of butanol have also been proposed, with limited

success in matching the experimental targets generated in the above studies8,9,31,40–43

.

In this study, a wide variety of chemical kinetic targets and reaction rate constants for

butanol have been measured. These data have been used by scientists around the world to develop

and improve their kinetic mechanisms. The details and implications of the various data types that

were acquired are presented in their respective chapters.

Figure 1.1: Molecular structure of the four butanol isomers. Greek letters represent the notation

for the various molecular sites.

6

2 CHAPTER 2: Experimental Methods

2.1 Introduction

Chemical kinetics can be studied using a variety of tools, though experiments typically

contain two key elements. The first is a chemical reactor, which in this work is a shock tube. The

second is a variety of diagnostics that are used to measured parameters of interest that are relevant

to combustion inside the chemical reactor. In this work, laser absorption is used to measure the

concentrations of various species in the shock tube, and light emission is utilized to accurately

characterize the time of ignition. The main advantage of these diagnostics is that they operate

with high-temporal resolutions necessary for monitoring kinetic processes in real time, and they

are also in-situ, which means that they do not interfere with the chemical processes that occur in

the shock tube.

2.2 Shock Tube Facility

2.2.1 Overview

A shock tube is an ideal reactor for studying chemical kinetics due to its gas-dynamic

simplicity. Shock tubes create a high-temperature and high-pressure environment that ideally

exhibits homogeneous, adiabatic, constant-volume (CV), stagnant gas conditions for the reacting

mixture. Therefore, since virtually all non-kinetic processes such as fluid flow, transport,

turbulence, and heat transfer are negligible, a shock tube can be modeled as a simple

homogeneous, CV, adiabatic reactor. Using this model, the primary computational task of

numerical solvers is to solve the differential rate equations for the reactions specified in the

kinetic mechanism, which is a relatively simple computational task. It is noted that shock tubes

do not exhibit ideal behavior under all conditions, and experiments must be carefully designed if

the ideal model is expected to accurately simulate the experimental environment.

7

As shown in Figure 2.1a, a shock tube is simply a tube, typically stainless steel and

round, divided into two sections separated by a diaphragm. To operate the shock tube, the test

mixture is placed into the driven section, and the driver section is filled to a higher pressure, often

with an inert gas (Figure 2.1b). When the pressure difference across the diaphragm exceeds the

breaking pressure, the diaphragm bursts and an incident shock wave travels toward the endwall of

the shock tube, thus increasing the temperature and pressure of the mixture behind it (Figure

2.1c). Once the incident shock wave reaches the endwall, it reflects, and the reflected shock wave

further increases the temperature and pressure of the test gas (Figure 2.1d). The gas behind the

reflected shock wave exhibits the ideal conditions for studying chemical kinetics that are

described above. Measurements are typically performed at an axial location close to the endwall

of the shock tube, for example 1-2 cm from the endwall in the Stanford shock tubes, because that

is where the performance of the shock tube is most ideal. The dimensions and characteristics of

the three Stanford shock tubes used in this study are shown in Table 2.1.

Figure 2.1: Schematic of the shock tube. a-d show the different stages of a shock tube experiment.

a.) at vacuum. b.) filled with driver and driven gas. c.) post diaphragm burst. d.) post incident-

shock reflection

8

Shock

Tube

Diameter

[cm]

Driver

Length [m]

Driven

Length [m]

NASA 15.24 3.7 10.0

KST 14.13 3.4 8.5

HPST 5.00 3.0 5.0

Table 2.1: Dimensions of the shock tubes utilized in this work. Diameter refers to the driven

section.

A representative pressure time-history for a shock tube experiment in an inert gas on the

KST facility is shown in Figure 2.2. The step changes in pressure at points A and B represent the

arrival of the incident and reflected shock wave at the measurement location, respectively. The

arrival time of the reflected shock wave at the measurement location is defined as time zero, i.e.

the time at which chemical reactions begin to occur at this location. In most experiments, this

definition of time zero is adequate because the heating of the test mixture in the time interval

between the incident and reflected shocks is typically negligible, since the temperature behind the

incident shock is much lower than that behind the reflected shock. At times after point C, the

pressure and temperature begin to increase slightly due to non-idealities in the shock tube, thus

limiting the ideal test time for experiments at the conditions in Figure 2.2 to approximately 1000

µs. Point D represents the termination of the overall test time shock tube due to the arrival of the

expansion fans at the measurement location, thus causing a rapid drop in the temperature and

pressure.

9

0 500 1000 1500 2000 2500 30000.0

0.4

0.8

1.2

1.6

P [

atm

]

time [s]

A

B

CD

Figure 2.2: Representative pressure for an argon shock using helium driver gas. Post-reflected-


Although the ideal test time at the representative conditions shown in Figure 2.2 is 1000

µs, various methods are utilized in this work in order to extend the ideal test time. Driver inserts

are used in order to eliminate the facility dependent increase in pressure and temperature after

point C in Figure 2.244

. Furthermore, driver gas tailoring is used to eliminate the increase in

pressure associated with the reflection of the reflected shock wave from the contact surface

between the driver and driven gasses, as well as to extend the overall test time by reducing the

speed of sound in the driver section in order to delay the arrival of the expansion fans at the

endwall of the shock tube45

. A representative pressure trace of experiments conducted using

driver inserts and driver gas tailoring in order to extend the test time to 8000 µs is shown in

Figure 2.3.

10

0 2000 4000 6000 8000 100000.0

0.5

1.0

1.5

2.0

2.5

3.0

P [

atm

]

time [s]

Figure 2.3: Representative pressure trace for an argon shock using a driver insert and a tailored

60/40 He/N2 driver gas. Post-reflected-shock conditions: T = 965 K, P = 2.25 atm.

Mixtures used to perform shock tube experiments are typically generated in a

magnetically-stirred stainless steel mixing tank and are typically stirred for at least 30 minutes.

Relative molar fractions of the mixture components are calculated manometrically. In order to

ensure that the vapors inside the mixing tank do not condense, the partial pressure of each

component in the mixture is typically lower than its vapor pressure by at least a factor of three.

2.2.2 Temperature and Pressure Measurements

Due to the sensitivity of chemical kinetic processes to temperature and pressure, accurate

knowledge of these parameters in the reflected shock region of the shock tube is critical.

Temperature and pressure behind the reflected shock wave were calculated using the normal

shock relations with known initial temperature, pressure, mixture composition, and incident shock

speed at the endwall. Calculations are performed using an in-house code that is able to account

for the temperature-dependent thermodynamic properties of the gas mixtures employed.

11

Incident shock speeds are determined from shock arrival times at a series of five (NASA

and KST shock tubes) or six (HPST shock tube) pressure sensors distributed over the last 1.5 m

of the shock tube. The time interval between the arrival of the incident shock wave at two

consecutive transducers is used to calculate the average velocity of the incident shock wave

across the known distance between the transducers. It is observed that the incident shock speed

attenuates linearly as the shock wave approaches the endwall. Therefore, a linear extrapolation of

the incident shock speed is used to calculate the incident shock speed at the endwall.

The primary source of the uncertainty in the temperature and pressure behind the

reflected shock wave is the determination of incident shock speed at the endwall of the shock

tube. In the shock tubes used in this study, the incident shock speed at the endwall is known to

within ± 0.13%, and the final uncertainty in the calculated temperature and pressure is known to

within ± 0.35% and ± 0.7%, respectively, for dilute mixtures. Mixtures containing high fuel

concentrations exhibit greater uncertainties, because the uncertainty in the fuel concentration

itself affects the calculation of the post-reflected-shock temperature. A more detailed discussion

of the uncertainties in the temperature and pressure behind the reflected shock wave is provided

in Section 5.3.

2.2.3 Experimental Modeling

Virtually all experiments performed in this work require numerical modelling in order to

advance the knowledge of chemical kinetics. Modeling shock tube experiments requires a

chemical kinetic mechanism as well as an appropriate gas-dynamic model of the chemical

reactor. Generally, parameters of the chemical kinetic mechanism are treated as variables that

may be adjusted to achieve better agreement between the experiments and the simulations.

However, the choice of an appropriate gas-dynamic model is critical for ensuring that any

discrepancies between the experimental data and the simulations are attributed to flaws in the

kinetic mechanism.

12

In this work, all shock tube experiments are modelled using a homogeneous, constant-

volume (CV), constant internal energy (adiabatic) model. This model is a close representation of

the performance of the shock tube, as both the temperature and pressure behind the reflected

shock wave remain constant in experiments containing unreactive mixtures46

. Furthermore,

numerical simulations in previous work indicate that heat transfer from the reacting mixture

behind the reflected shock wave to the walls of the shock tube is negligible at the time scales of

the current experiments47

. It is noted that significant heat release of the reacting mixture inside the

shock tube, such as that caused by ignition, causes the ideal model of the shock tube to break

down. Therefore, ignition experiments in this work are not modelled beyond the time of ignition.

The shock tube model described above is executed using the CHEMKIN-PRO48

software

suite. A key function of this software program that is used continuously in this work is the ability

to perform sensitivity analysis of species concentrations to rate constants in the chemical kinetic

mechanism. The normalized sensitivity for the concentration of species i ([C]i) at a given time to

the rate constant for reaction j (kj) is defined in Equation 2.1:

Equation 2.1

Though a given species concentration is typically sensitive to a variety of reaction rate constants,

sensitivity analysis is a valuable tool for designing experiments where the measured species time-

histories are sensitive to a small subset of chemical reactions. In some experiments where a

particular species exhibits sensitivity to a single chemical reaction, the rate constant for that

reaction may be inferred directly by adjusting the rate constants in the kinetic mechanism until

good agreement is achieved between the experimental data and the simulations. However, the

accuracy of the rate constants of secondary reactions in the chemical kinetic mechanism must be

13

given careful consideration before any rate constants can be modified in order to achieve

agreement with the experimental data.

2.3 Emission Diagnostics

Ignition delay time in a shock tube is defined as the time interval between shock heating

due to the reflected shock wave and the primary ignition event. A comparison of measured and

simulated ignition delay times in shock tubes and rapid compression machines is one of the most

common methods for evaluating the accuracy of chemical kinetic mechanisms.

During the ignition process, a significant increase in the concentration of radical species

occurs. Therefore, one of the methods for identifying the time of ignition in a chemical reactor is

to identify the sudden growth in radical species concentrations. This can be achieved by

measuring the emission of light from excited OH radicals (OH*) at 307 nm from the A2Σ

+→X

2Π

band. Emission signals from other sources are rejected using a narrow bandpass UG-5 filter.

As shown in Figure 2.4, emission of light can be measured at both the sidewall and

endwall locations in the shock tube. The simplest measurements are performed at the endwall of

the shock tube, where the detector simply collects light emitted at any location in the shock tube.

In both endwall and sidewall diagnostics, it is critical that the emission signal can be attributed to

a particular axial location in the shock tube, because time zero varies along the axis of the shock

tube depending on the arrival time of the reflected shock wave. By assuming that ignition occurs

near the endwall of the shock tube before at any other location, the initial rise in the emission

signal can be attributed to ignition near the endwall. Therefore, since the arrival time of the

reflected shock at the endwall is known, the time interval between shock heating and ignition can

be inferred.

Emission measurements can also be performed in the direction perpendicular to the axis

of the shock tube. In these measurements, the optical setup shown in Figure 2.4 is used to

14

constrain the axial length (i.e. spatial resolution Δ) of the shock tube from which light can reach

the measurement detector. By minimizing the spatial resolution, the variations in time zero for the

gasses whose emission is recorded by the detector are also minimized. The time resolution of the

emission diagnostic (assuming it is not limited by the detector bandwidth) is equal to the

interaction time of the reflected shock wave with the gasses within the slab of the shock tube of

thickness equal to the spatial resolution. This interaction time is calculated by simply dividing the

spatial resolution by the speed of the reflected shock wave, and it approximately 10 µs in this

work. Further details on the optical arrangement and determination of spatial resolution are

described in the discussion of the “Type II” optical setup in previous work49

.

Figure 2.4: Experimental apparatus for emission measurements. Further details on the optical

arrangement for emission measurements can be found in previous work49

. BP = Bandpass.

15

2.4 Laser Diagnostics

2.4.1 Overview

Laser diagnostics are a powerful tool for studying chemical kinetics in shock tubes. The

primary laser diagnostic technique utilized in this work is fixed-wavelength direct absorption

(scanned-wavelength direct absorption is discussed separately in Chapter 6). A significant

advantage of this measurement technique compared to traditional gas sampling methods is that it

enables rapid measurements at MHz rates that can be used to determine the time evolution of

various kinetic targets in chemical reactors. A further advantage of laser diagnostic techniques is

that the measurements are performed in-situ, and they do not perturb kinetic processes in the

chemical reactor in any way. These rapid in-situ measurements can be used to measure

concentrations of radical species with short lifetimes, which serves as an invaluable kinetic target

for assessing the performance of chemical kinetic mechanisms. In this work, fixed-wavelength

direct absorption was used to measure the time evolution of species mole fractions (species time-

histories) for a variety of reacting mixtures in shock tubes.

Species mole fractions are inferred from laser intensity measurement via the Beer-

Lambert relation shown in Equations 2.2 and 2.3:

T = Equation 2.2

∑ Equation 2.3

where T is the transmission, I is the transmitted laser intensity through the shock tube in the

presence of absorbing species, I0 is the transmitted laser intensity through the shock tube without

the presence of the absorbing species, α is the absorbance, P is the pressure, ki is the absorption

coefficient of species i, and xi is the mole fraction of species i. The absorbance α in the Beer-

Lambert relation is also occasionally described using a slightly different parameter convention:

16

∑

where n is the overall number density and σi is the absorption cross-section of species i.

Typically, the absorption coefficient is commonly used to describe the absorption spectrum of

molecule with narrow absorption features, whereas the absorption cross-section is often used to

describe spectra of molecules with broad absorption features. The two conventions are

completely equivalent.

A schematic for a typical laser absorption experimental setup is shown in Figure 2.5. In

most experiments, the transmitted light intensity is normalized by the light intensity (Iref)

measured by a reference detector that collects light that does not pass through the shock tube.

This common-mode-rejection scheme is utilized in order to eliminate laser power fluctuations in

the measurements of the transmitted laser intensities.

Figure 2.5: Experimental apparatus for direct laser absorption measurements using common

mode rejection. BP = Bandpass. I and Iref represent the transmitted and reference light

intensities, respectively.

If measurements are performed in the presence of only one absorbing species i, the Beer-

Lambert relation can be rearranged to calculate its mole fraction using the following relation:

17

However, several of the measurements in this work are performed in the presence of multiple

absorbing species at the target wavelength, though the target species is typically the strongest

absorber. Nonetheless, absorption due to the other interfering species must be taken into account

in order to correctly infer the mole fraction of the target species from laser absorption

measurements.

In the presence of interfering species, the mole fraction of a target species can be inferred

by performing measurements at multiple wavelengths. Typically, the primary wavelength (on-

line) is selected to overlap with a strong absorption feature of the target species, while the

secondary wavelength (off-line) is selected to be near the target wavelength but at spectral

location where the target species has a low absorption coefficient. With knowledge of the

absorption coefficients of the target species i and interfering species int at both the on-line and

off-line wavelengths, the mole fraction of the target species can be inferred directly using

Equation 2.4:

( )

Equation 2.4

When the absorption feature of the target species is very narrow and the absorption spectrum of

the interfering species is broadband, the on-line and off-line wavelengths can be chosen such that

the absorption coefficient of the interfering species is constant at both wavelengths (R = 1), and

the absorption coefficient of the target species is negligible at the off-line wavelength. In this

case, the mole fraction of the target species can be inferred using a simplified version of Equation

2.4, as shown in Equation 2.5:

18

( ) Equation 2.5

2.4.2 Diagnostic Details

In this work, six different species were measured at a variety of wavelength using several

different lasers. Below are the details of each laser diagnostic that was used to perform

measurements.

16OH species time-histories were measured using direct absorption of light in the A-

X(0,0) band near 307 nm. Measurements of 16

OH in experiments without the presence of 18

O

isotopes were performed at the R11(5.5) transition because it has a strong absorption coefficient

that has been studied in greatest detail50,51

. Measurements in the presence of 18

O were performed

at the R22(5.5) in order to avoid spectral overlap between 16

OH and 18

OH at the target wavelength,

thus resulting in a 16

OH concentration measurement that is independent of the presence of 18

OH

(See Section 4.2). 16

OH species time-history measurements during butanol pyrolysis required

characterization of interference absorption due to formaldehyde and acetaldehyde. In these

experiments, 16

OH mole fractions were calculated using the two line technique described by

Equation 2.5, assuming that the interfering species exhibit broadband absorption near the target

wavelengths and that 16

OH does not absorb at the off-line wavelength (32611 cm-1

). The target

wavelengths were accessed by frequency-doubling the visible output of a narrow-linewidth ring

dye laser. Visible light near 614 nm was produced by pumping Rhodamine 6G dye in a Spectra

Physics 380A laser cavity using a Coherent Verdi 5W continuous wave laser at 532 nm. A

temperature-tuned AD*A non-linear crystal was used for intracavity frequency-doubling. Further

details on the 16

OH detection system as well as the 16

OH spectrum can be found elsewhere50,51

.

C2H4 species time-histories were measured using laser absorption at 10.532 µm near the

peak of a strong absorption feature of C2H4. In some experiments, interference absorption was

19

taken into account by performing off-line measurements at 10.675 µm away from the peak of the

absorption feature. Since the separation of the two wavelengths is relatively large and the

absorption of C2H4 is non-negligible at the off-line wavelength, it was necessary to explicitly

account for absorption of both C2H4 and the interfering species at each wavelength, as described

by Equation 2.4.

A tunable CO2 gas laser was used to access both wavelengths for measuring C2H4

concentrations, and a common-mode-rejection scheme was used to significantly reduce laser

noise. The major source of error associated with two-line C2H4 measurements stems from data

processing during manipulation of on-line and off-line measurements. Since on-line and off-line

experiments are not performed simultaneously, shock-to-shock variations may become significant

due to the relatively low differences between off-line and on-line absorbance in some

experiments. These effects are minimized by ensuring that the post-reflected-shock temperature

difference between on-line and off-line experiments did not exceed 15K. Further details about the

C2H4 detection scheme and detailed characterization of C2H4 absorption coefficient are available

elsewhere52,53

.

H2O species time-histories were determined by measuring absorption of 2551 nm light at

the peak of an absorption feature in the ν3 fundamental vibrational band of H2O. A continuous-

wave, distributed feedback (DFB) diode laser near 2.5 µm was used to generate the required

wavelength. A nitrogen purge system was implemented on the laser path in order to eliminate

signal loss due to absorption by atmospheric water. Due to the stability of the DFB laser,

common-mode-rejection was not required, and a measured H2O uncertainty of ± 6 % was

achieved at long times. This uncertainty was largely caused by a temperature uncertainty

throughout the test time which propagates into an uncertainty in the absorption coefficient (See

Section 3.3.2). Further details on the H2O detection system as well as H2O line characterization

can be found in previous work54

.

20

CO time-histories were determined by measuring direct absorption of 4.56 µm light at the

peak of the R(13) transition in the fundamental ro-vibrational band of CO. A quantum cascade

(QC) laser operating in continuous mode was used to generate the required wavelength. A

common-mode-rejection scheme was used which resulted in an uncertainty of approximately ± 6

% in the measurement, largely caused by a temperature uncertainty throughout the test time (See

Section 3.3.2). Further details regarding the CO diagnostic setup are described elsewhere55

.

The pre-shock fuel mole fraction inside the shock tube was verified by measuring the

absorption of 3.39 µm HeNe laser light across the diameter of the shock tube. This technique

takes advantage of broadband absorption exhibited by most hydrocarbons at 3.39 µm due to the

presence of C-H bonds. In some experiments, the sensitivity of this detection scheme was

increased by sampling gasses from the shock tube into a 29.9 m multi-pass optical cell. A detailed

description of the fuel detection diagnostic is described in previous work55

.

2.4.3 Cross-section Measurements

Though the temperature and pressure dependence of the absorption coefficient for many

of the species measured in this study has already been characterized in previous work, a variety of

absorption coefficients for new species have been measured here. Absorption coefficient

measurements were performed in this work for two distinct reasons. The first was to infer the

initial concentration of the fuels being studied in the shock tube before performing experiments,

thus requiring knowledge of their absorption coefficient at room temperature. The second was to

measure the formation or removal of particular species behind the reflected shock wave, thus

requiring knowledge of the absorption coefficient at high temperatures and pressures.

In several of experiments performed in this work, the vapor pressure of the fuels was of a

similar order of magnitude as the partial pressure of fuel in the mixing tank. A further reduction

of the partial pressure of the fuel in the mixing tank was not possible because it would result in an

insufficient total mixing tank pressure for the mixture to be used in multiple shock tube

21

experiments. Furthermore, some fuels may be “sticky”, which means that they may absorb onto

various surfaces. In experiments where absorption and/or adsorption were considered a

possibility, the concentration of the fuel in the shock tube was measured using direct laser

absorption at 3.39 µm in order to confirm that its concentration in the shock tube was equal to the

manometric calculation. Absorption cross-sections of these fuels were measured using pure fuel

mixtures in order to guarantee accurate knowledge of the partial pressure of the fuel in the shock

tube. The shock tube was typically filled to a pressure of 2-100 torr, which was typically limited

by the vapor pressure of the fuel. It was observed that the measured cross-sections exhibited no

pressure dependence, which is expected for broadband absorbers that were used as fuels in this

study. A comparison of the measured absorption cross-sections in this study with data from the

PNNL database56

is shown in Table 2.2.

Molecule Current

Study

PNNL

Database

1-Butanol 24.2 25.2

2-Butanol 15.5 15.3

iso-Butanol 19.4 19.6

tert-Butanol 11.9 11.6

Ethanol 7.9 7.6

Cyclohexene 33.9 33.0

Table 2.2: Comparison of the measured room-temperature cross-sections in the current work

with data from the PNNL database56

. Units are m2mol

-1. Uncertainty in the current study is ± 3%.

Cross-section measurements at high-temperatures were primarily performed for species

relevant to inferring the rate constant for cyclohexene decomposition, which is discussed in

Chapter 5. This work required measurements of the 10.532 µm absorption cross-section of 1,3-

butadiene, cyclohexene, and 1,3-cyclohexadiene. Experimental measurements as well as fits to

22

the data are shown in Figure 2.6, and the measurements exhibited no pressure dependence from

1.5-3.8 atm.

900 1000 1100 1200 1300 14000

2

4

6

8

10

[m2mol

-1] = 4.02 - 0.0049 T[K]

[m2mol

-1] = 0.40

Cyclohexene

1,3-Butadiene

1,3-CyclohexadieneA

bs

orp

tio

n C

ros

se

cti

on

[m

2m

ol-1

]

T [K]

[m2mol

-1] = 6.98 - 0.00131 T[K]

Figure 2.6: Measured Absorption cross-sections of cyclohexene, 1,3-butadiene, and 1,3-

cyclohexadiene from 1.5-3.8 atm. Data exhibited no pressure dependence.

2.5 Fuel + OH Reaction Rate Constant Measurements

2.5.1 Overview

Rate constant measurements for the reactions fuel + OH → products were performed by

creating a pseudo-first order reaction environment for the removal of OH radicals. Experiments

exhibiting pseudo-first order kinetics are designed by creating mixtures between two reactants

where the concentration of one of the reactants is approximately constant. In experiments where

OH radicals react with fuel, this can be achieved if the fuel is in excess in the chemical reactor,

thus preventing the reaction of OH radicals with the fuel from significantly reducing its absolute

concentration. This is quantified mathematically using the rate equation of OH radicals for the

reaction fuel + OH → products:

23

(

)

If the concentration of fuel is approximately constant, the above equation can be integrated

explicitly and the concentration time-history of OH can be inferred analytically:

Since the concentration of OH exhibits an exponential decay, kreaction can be determined from

measurements of the time constant of OH decay, assuming that that fuel concentration is known.

Though the above analysis illustrates the utility of pseudo-first order experiments, it does

not account for secondary reactions or slight changes in the fuel concentration that may affect the

decay rate of OH. In order to account for these phenomena, the rate constant for a target reaction

is inferred by fitting the simulated OH time-histories from the kinetic model to the experimental

data using the fuel + OH reaction rate constant as a free parameter that affects the pseudo-first-

order decay rate of OH. In this work, the rate constants for relevant secondary reactions are well-

characterized, thus yielding highly-accurate measurements of the rate constants for fuel + OH

reactions (see Section 2.5.2). As shown in Figure 4.7, the representative OH time-history during

measurements of the rate constant for the reaction of ethanol + OH → products exhibits pseudo-

first order decay. In addition, simulations of the measured pseudo-first order decay rate exhibit

high sensitivity to the target reaction rate constants.

2.5.2 Secondary Reactions

The accuracy of rate constant measurements for reactions of fuel with OH radicals using

kinetic simulations of pseudo-first-order experiments are somewhat dependent on accurate

knowledge of the rate constants for secondary reactions. In the current work, since tert-

24

butylhydroperoxide (TBHP) is used as a fast source of OH, the rate of TBHP decomposition (OH

generation) can affect the simulations of the measured OH time-histories. Measurements of the

rate constants for the target fuel + OH reaction are particularly sensitive to the TBHP

decomposition rates at temperatures between 900-1000 K, because the timescale of TBHP

decomposition is on the same order-of-magnitude as that of OH removal by the fuel. At

temperatures above 1000 K, TBHP decomposition becomes so fast that TBHP is fully

decomposed by the time that kinetic simulations are fit to the exponential decay of OH, thus

resulting in a measurement that is insensitive to the TBHP decomposition rate. At temperatures

below 900K, the decomposition of TBHP is too slow for the OH generation and removal process

to occur independently, thus constraining the minimum temperature at which experiments can be

conducted.

Further decomposition of the fragments of TBHP produces CH3 radicals in similar

concentrations as OH radicals. Since the reaction of OH radicals with CH3 radicals is very fast, it

can significantly contribute to the removal of OH in pseudo-first-order experiments. Therefore, it

is critical that kinetic simulations in these experiments contain accurate rate constants for these

reactions. In the current work, the sub-mechanism for critical reactions in involving TBHP and

CH3 radicals was taken from previous work by Pang et al.57

. As discussed by Pang et al.57

the

accuracy of the TBHP sub mechanism can be validated by measuring concentration time-histories

during neat TBHP decomposition. If simulations accurately model the rise in OH radicals during

TBHP decomposition as well as the decay in OH due to reactions with CH3 radicals, it can be

concluded that he kinetic mechanism accurately describes the abovementioned reactions. As

shown in Figure 2.7, experiments of neat TBHP decomposition in this work indicate that the rise

in OH near 900 K, and the decay of OH at near both 900 K and 1200 K is accurate (rise of OH

cannot at be resolved at high temperatures). Therefore, it is concluded that the TBHP sub-

mechanism developed by Pang et al.57

is accurate.

25

0 20 40 60 80 100 120 1400

4

8

12

16

OH

Mo

le F

rac

tio

n

time [s]

925 K, 1.13 atm

1162 K, 1.00 atm

Figure 2.7: OH time-histories during the pyrolysis of 15.5 ppm TBHP/H2O/Argon. Solid lines

represent measurements, dashed lines represent simulations using the Leplat et al.58

mechanism

(see Section 4.3) to which the TBHP sub-mechanism from Pang et al.57

was appended.

26

3 CHAPTER 3: Kinetic Studies of the

Butanol Isomers

3.1 Introduction

As discussed in Section 1.3, butanol is a promising biofuel candidate with potential

applications in the transportation sector. Therefore, kinetic studies of the isomers of butanol are of

significant interest to the scientific community. In this work, ignition delay times for the four

butanol isomers were measured behind reflected shock waves across a variety of conditions. In

addition, multi-species time-histories during the pyrolysis of 1-,2-, and iso-butanol were

measured using direct laser absorption. These data have been used extensively by several research

groups in order to validate and improve the performance of chemical kinetic mechanisms.

Though a variety of chemical kinetic mechanisms have been developed for the butanol

isomers8,9,31,40–43

, the mechanism by Sarathy et al.8,9

is typically regarded as the most accurate for

describing the overall kinetics of the butanol isomers. The accuracy of the mechanism is

attributed to the extensive set of experimental and theoretical data against which it was validated,

partially because it is the most recent of the comprehensive kinetic mechanisms for butanol. Due

to the extensive set of experimental data presented here, not all of the data can be modeled with

every available kinetic mechanism. Indeed, an assessment and comparison of the various

chemical kinetic mechanisms with the aim of selecting a series of optimal rate constants

expressions for reactions relevant to butanol kinetics could span an entire PhD thesis. The

purpose of the analysis presented here is to demonstrate how the data acquired in this study can

be used to optimize chemical kinetic mechanisms, but the optimization itself is not performed

here. As a result, the kinetic mechanism by Sarathy et al. 8,9

is primarily used for comparing

experimental data with kinetic simulations, though other mechanisms may also be discussed in

27

cases where they offer superior performance to the Sarathy et al. 8,9

mechanism. In addition, due

to the overall complexity of the combustion of butanol, a detailed analysis of the oxidation

pathways for butanol is not presented here. Finally, the primary focus of the discussion in this

work will be on 1-butanol and iso-butanol, because as discussed in Section 1.3, these isomers are

the primary biofuel candidates. The majority of data acquired during the pyrolysis and oxidation

of 2-butanol and tert-butanol are presented in APPENDIX B, and all ignition delay time

measurements are tabulated in APPENDIX A.

3.2 Ignition Delay Time Measurements

3.2.1 Overview

One of the simplest methods for evaluating the global accuracy of chemical kinetic

mechanisms is by comparing the predicted and measured ignition delay time of a fuel behind

reflected shock waves in a shock tube. Although shock tube studies of various butanol isomers

have been performed in previous studies31–35,39,41

, no single study has measured ignition delay

times for all four isomers over a wide range of pressures. In addition, there exists a significant

discrepancy between certain previous measurements, especially for isomers other than 1-butanol.

Measurements in this work are performed in order to expand the range of conditions available for

comparisons of numerical simulations, and to achieve closure on the discrepancies in the

experimental data available in the literature.

In this study, ignition delay times were measured for all four isomers of butanol.

Conditions studied include temperatures from 800-1750 K, pressures from 1.5-50 atm, and

equivalence ratios of 1.0 and 0.5 in mixtures containing 4% O2 dilute in argon. Several additional

data sets were collected at 1.0-1.5 atm in order to replicate conditions used by previous

researchers. Additional data were also collected at 20 atm for stoichiometric 1-butanol mixtures

in air at temperatures as low as 800 K. Low-temperature/high-pressure measurements were

28

performed using driver inserts and driver gas tailoring to insure near-constant-volume test

conditions at long test times. Measurements at pressures below 4 atm were performed on the KST

shock tube and endwall emission data was used to infer the ignition delay time. Measurements at

pressures above 10 atm were performed on the HPST shock tube, and sidewall emission data was

used to infer the ignition delay time (endwall data is not available on this shock tube). In both sets

of experiments, ignition delay time was defined as the time between the arrival of the reflected

shock wave at the observation port and the extrapolation of the maximum slope of the emission

signal to the baseline. Representative data are shown in Figure 3.1. The primary uncertainty in

the ignition delay time measurements presented here is caused by the uncertainty in the

temperature behind the reflected shock wave (See Sections 2.2.2 and 5.3). Ignition delay times of

the butanol isomers are not highly sensitive to equivalence ratio, pressure, and impurities (at the

levels present in the shock tubes utilized in this work).

-100 0 100 200 300 400 500 600 700

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Photodetector - Sidewall

Pressure - Reactive Shock

Pressure - Non-Reactive Shock

Rela

tive S

ign

al

[V]

time [s]

ign

Figure 3.1: Ignition delay time measurement of 2-Butanol in 4% O2 diluted in Ar, = 1. Initial

post-reflected-shock conditions: T = 1176 K, P = 40.5 atm.

It is important to note the role of pre-ignition heat release when modeling shock tube

experiments containing butanol mixtures. It was observed in experiments that there exists a slight

29

pre-ignition pressure increase even in dilute combustion experiments for all four isomers of

butanol. Experiments in unreactive mixtures indicate that these effects are not caused by typical

pressure increases that result from shock wave-boundary layer interactions. Figure 3.1 clearly

shows that the measured pressure traces exhibit slight pre-ignition pressure increases compared to

the pressure trace for an experiment containing pure argon. Such pressure increases are caused by

pre-ignition heat release which increases the temperature and pressure in the constant-volume

(CV) model calculation. These effects are also present in shock tube experiments, although in this

case, the reflected shock adjusts its speed in a way that partially offsets the CV constraint. Pre-

ignition pressure increases cause gases inside the measurement volume of a shock tube to expand

slightly through perturbations in the reflected shock speed, whereas this effect would be absent in

a CV reactor. It is expected that shock tube experiments containing significant pre-ignition

pressure rises caused by heat release would thus have longer ignition times than would be found

in a true CV experiment, because the temperature increase associated with pre-ignition energy

release would be lower in the shock tube than in the CV apparatus.

Although pre-ignition pressure increases were observed in this study, their effect was

minimized by using dilute mixtures. In the discussion of experiments in stoichiometric air (See

APPENDIX B), it is evident that using non-dilute mixtures has significant implications on

experimental modeling. Finally, it is noteworthy that pre-ignition pressure increases in 1-butanol

experiments have also been observed in rapid compression machine ignition delay time

measurements by Weber et al.14

and in shock tube ignition delay time measurements by Heufer et

al.34

.

30

3.2.2 Results

Mixtures diluted in argon

Figures 3.2 and 3.3 show an attempt to repeat 1-butanol ignition delay time experiments

at conditions in studies by Moss. et al.41

and Black et al.31

, respectively. Fairly good agreement is

found with these past experiments for 1-butanol, although ignition delay time measurements in

this work are shorter by up to 20% compared to those of the other experimenters. In addition,

Figures 3.2 and 3.3 show comparisons with an ignition delay time correlation for 1-butanol

developed by Noorani et al.32

based on their shock tube ignition delay time measurements.

Although no attempts were made to replicate experiments at the exact conditions used by Noorani

et al.32

, their correlation agrees well with our experimental data for 1-butanol at conditions used

by Moss et al.41

and Black et al.31

. It should be noted that the conditions used by Moss et al.41

and

Black et al.31

are slightly outside of the range of conditions for which the Noorani et al.32

correlation was developed. Finally, as shown in Figure 3.4, Zhang et al39

were successfully able

to replicate measurement of ignition delay times for 1-butanol from the current work. Overall,

there exists reasonable agreement among the experimental data sets for shock-tube ignition delay

time measurements for 1-butanol.

31

0.55 0.60 0.65 0.70 0.75 0.80

100

1000

= 1, XO

2

= 0.03

Current Study

Moss et al.

1333 K1538 K 1429 K

t ign [s]

1000/T [K-1]

1667 K

Noorani et al. - Correlation




0.60 0.65 0.70 0.75 0.80 0.85

100

1000

1667 K

= 1, XO

2

= 0.045

Current Study

Black et al.

1250 K1429 K

t ign [s]

1000/T [K-1]

Noorani et al. - Correlation


in argon.

32

0.70 0.75 0.80 0.85100

1000

1250 K1333 K1429 K

= 1, XO

2

= 0.04

t ign [

s]

1000/T [K-1]

Current Study

Zhang et al.


in argon.

Despite the agreement between measurements of ignition delay times for 1-butanol,

significant disagreement was observed with measurements by Moss et al.41

for 2-butanol, shown

in Figures 3.5 and 3.6, iso-butanol, shown in Figure 3.7, and tert-butanol, shown in Figure 3.8.

Although the measured ignition delay times are similar at lower temperatures, divergence is

evident at higher temperatures. Several possible causes for this disagreement were proposed and

investigated, and it was concluded that the only plausible explanation for the significant

disagreement between the experimental data is a significant impurity in the mixing tank and/or

shock tube, or accidental confusion of fuel sources and/or oxidizing gases.

33

0.60 0.65 0.70 0.75 0.80

100

1000

1667 K 1333 K1429 K1538 K

Current Study

Moss et al.

t ign [s]

1000/T [K-1]

= 1, XO

2

= 0.06




0.55 0.60 0.65 0.70 0.75 0.80

100

1000

1667 K 1333 K1429 K1538 K

Current Study

Moss et al.

t ign [s]

1000/T [K-1]

= 1, XO

2

= 0.03




34

0.60 0.62 0.64 0.66 0.68 0.70 0.72

100

200

300

400

500

600

700800

1613 K 1429 K1515 K

Current Study

Moss et al.

t ign [s]

1000/T [K-1]

= 1, XO

2

= 0.03

Figure 3.7: Measured ignition delay times for iso-butanol. P = 1.2 atm, ϕ = 1, xO2 = 0.03,



0.55 0.60 0.65 0.70

100

1000

1818 K 1667 K 1429 K1538 K

Current Study

Moss et al.

t ign [s]

1000/T [K-1]

= 1, XO

2

= 0.03

Figure 3.8: Measured ignition delay times for tert-butanol, P = 1.2 atm, ϕ = 1, xO2 = 0.03,



35

From Figures 3.5-3.8, it is evident that faulty post-reflected shock temperature

measurements of about 5-8% below the actual post-reflected shock temperature in this study

would explain the disagreement with Moss et al.41

for isomers other than 1-butanol. Such a large

temperature error would require a significant measurement error of the incident shock speed, or a

significant error in the thermodynamic properties of the driven gas mixture. The shock velocity

measurement system used in this study was carefully evaluated and it was found to be working

correctly. Furthermore, the thermodynamic properties of the driven gases were verified. Errors in

temperature measurements in this study are unlikely because they would manifest themselves

systematically, in which case our measurements would differ significantly with the 1-butanol data

by Black et al.31

, Moss et al.41

, and Noorani et al.32

, and Zhang et al.39

, as well as n-heptane data

by Horning et al.59

and Smith et al.60

(n-heptane data were acquired in order to verify the proper

functioning of the experimental apparatus). Uncertainties in temperature due to facility dependent

pressure rises are not observed in either study, and they would not explain the large discrepancy

observed here.

The role of impurities in the mixing tank and/or shock tube was assessed by repeating

experiments after cleaning the mixing tank, mixing manifold, and shock tube with acetone, as

well as by replacing the 1-butanol, 2-butanol, O2, and argon sources. Glassware used to supply

the mixing tank with the fuel vapor was also replaced. None of the above changes modified the

ignition delay time measurements. Simulations performed using 200 ppm of H and OH radicals

initially present in the fuel mixture showed only minor variations in the ignition delay time

compared to pure mixtures. The author does not wish to speculate on potential errors in the study

by Moss et al.41

, and the cause of the discrepancy between the two studies remains unknown.

Figure 3.9 shows the variation of ignition delay time as a function of pressure for 1-

butanol. As expected, ignition time decreases as a function of pressure, τign P-β

, with β ≈ 0.5-

0.8, though the exact dependence on pressure varies depending on the conditions. Global

correlations of ignition delay times for individual isomers were not developed because the wide

36

range of conditions does not merit such simplified analysis. Figure 3.9 clearly indicates that there

exists relatively good agreement between the experimental data and simulations using the Sarathy

et al. 8,9

mechanism for ignition delay times of 1-butanol. However, simulations overpredict the

measured ignition delay times by up to 50% at low pressures and high temperatures. This

discrepancy is likely explained by inaccuracies in the rate constants for the unimolecular

decomposition of butanol in the falloff region in the Sarathy et al.8,9

mechanism (Similar

conclusions are drawn from species time-histories discussed in Section 3.3.3.1). The rate

constants for the high-pressure-limit of the various 1-butanol unimolecular decomposition

channels in the Sarathy et al.8,9

mechanism are in excellent agreement with recent measurements

by Rosado-Reyes and Tsang61

. However, the values of k/k∞ in the Sarathy et al.8,9

mechanism

near 1400 K and 1.5 atm are approximately equal to 0.15, whereas measurements by Rosado-

Reyes and Tsang61

indicate that the rate constants for the unimolecular decomposition of 1-

butanol are pressure-independent above 1 atm. Therefore, the rate constants for the unimolecular

decomposition of 1-butanol in the Sarathy et al.8,9

mechanism near 1400 K and 1.5 atm may be

too low by an approximate factor of 6. As indicated in Figure 3.9, simulations using a modified

version of the Sarathy et al.8,9

that contains rate constant expressions for the unimolecular

decomposition channels of 1-butanol from work by Rosado-Reyes and Tsang61

show outstanding

agreement with the experimental data at all conditions. This improvement occurs because the

proposed modifications significantly increase the rate constant for the unimolecular

decomposition of 1-butanol at low pressures only, thus maintaining the good agreement with the

experimental data at high pressures.

As indicated in Figure 3.9, some ignition delay time measurements at high pressures

were performed without precise knowledge of the equivalence ratio in individual experiments.

This was caused by the tendency of some butanol isomers to adsorb onto the shock tube walls,

even at partial pressures lower than the vapor pressure at the wall temperature. These losses can

be significant in some experiments, and several of the initial data were acquired without the

37

verification of fuel concentration using direct absorption, which subsequently revealed that these

experiments had leaner than assumed fuel mixtures by up to 40%. To overcome this problem, a

passivation technique was developed where the shock tube was overfilled beyond the desired

initial driven pressure. The excess gas was then evacuated from the shock tube until the desired

driven pressure was achieved. This method allowed the initial overfilling of the shock tube to

saturate the adsorption sites of the shock tube so that once the excess gas was evacuated, the test

gas had the desired mole fraction of fuel. By overfilling the shock tube, the adsorbed butanol had

a negligible effect on reducing the fuel mole fraction inside the shock tube simply because the

amount of fuel placed in the shock tube was large. This method was validated by direct laser

absorption measurements of the test gases in the shock tube.

0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

100

1000

10000 = 1 = 0.60 - 0.75 = 0.75 - 1.0

Lines - Sarathy et al. = 1

Solid - Original

Dashed - Modified

1111 K1250 K1429 K

P = 43

P = 19P = 3.0

P = 1.5

t ign [s]

1000/T [K-1]

Figure 3.9: Measured ignition delay times for 1-butanol, xO2 = 0.04, diluted in argon. Pressure in

atmospheres. The Sarathy et al. mechanism8,9

was modified to include rate constants for the

unimolecular decomposition of 1-butanol from work by Rosado-Reyes and Tsang61

. Uncertainties

are approximately equal to twice the height of the data points.

38

Figure 3.10 shows a comparison of the measured ignition delay times of iso-butanol with

simulations using the Sarathy et al.8,9

and Merchant et al.42

mechanisms. The Merchant et al.42

mechanism was developed recently for modeling the combustion kinetics of iso-butanol, due to

the importance of this particular isomer as biofuel candidate. Since the authors of both

mechanisms used the data presented here for guidance and mechanism validation, it is

unsurprising that the mechanisms show agreement with the experimental data to within 50%.

Reasonable agreement between the mechanisms is encouraging given that they were generated

using completely different approaches. The Sarathy et al.8,9

mechanism was primarily developed

by examining previously inferred rate constant measurements for analogous reactions, whereas

the Merchant et al.42

mechanism was generated by calculating rate constants for most reactions

using the open-source software RMG62

. Though a detailed comparison between the mechanisms

is not discussed here, it is noted that the rate constants for the unimolecular decomposition

channels of iso-butanol in the Merchant et al.42

mechanism are likely more accurate than those in

the Sarathy et al.8,9

mechanism because they were taken from high-level quantum calculations by

Zhou et al63

.

39

0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

100

1000

= 1 = 0.65-0.90 = 0.90-1.05

Lines - = 1

Solid - Sarathy et al.

Dashed - Merchant et al.

P = 43

P = 19P = 3.0

1053 K1176 K1333 K

t ign [s]

1000/T [K-1]

1538 K

P = 1.5

XO

2

= 0.04

Figure 3.10: Measured ignition delay times for iso-butanol, xO2 = 0.04, diluted in argon.


points.

Figure 3.11 shows a comparison of ignition delay time measurements for the four

isomers of butanol at 43 atm, as well as a comparison with kinetic simulations using the Sarathy

et al.8,9

mechanism. The ignition times are shortest for 1-butanol and longest for tert-butanol. iso-

Butanol exhibits ignition delay times that are comparable to those of 1-buatnol, whereas and 2-

butanol exhibits ignition delay times that are slightly longer than those of iso- and 1-butanol. tert-

Butanol appears to have a slightly higher global activation energy compared to the other isomers,

as indicated by a steeper slope in the data on an Arrhenius plot. Kinetic simulations using the

Sarathy et al.8,9

mechanism show excellent agreement with the measured ignition delay times for

1-, 2-, and tert-butanol. The mechanism overpredicts the ignition delay times for iso-butanol by

up to 50%.

40

0.70 0.75 0.80 0.85 0.90 0.95 1.00

100

1000

1-butanol, = 0.75-1.00

2-butanol, = 0.80-1.05

iso-butanol, = 0.90-1.05

tert-butanol, = 0.95-1.05

Lines - = 1

Sarathy et al.

1111 K1250 K

t ign [s]

1000/T [K-1]

1429 K

XO

2

= 0.04

i-but

1-but

2-butt-but

Figure 3.11: Measured ignition delay times for the butanol isomers at 43 atm, xO2 = 0.04, diluted

in argon. Uncertainties are approximately equal to twice the height of the data points.

3.3 Multi-Species Time-History Measurements

3.3.1 Overview

Multi-species time-history measurements during the pyrolysis of hydrocarbon fuels can

provide valuable insights into the kinetics of fuel decomposition. However, due to the complexity

of high-temperature butanol pyrolysis kinetics, it is difficult to design butanol experiments where

species-time-histories are sensitive to only a few reaction rates. Similar observations were made

by Cook et al.64

. Therefore, the general approach in this work is not to modify specific reaction

rates in order to achieve best fits to multi-species measurements, but instead to provide an

extensive database of kinetic targets for use by modelers. Analysis is performed in order to

determine which reaction classes must be better understood in order to improve agreement

between simulations and experiments, and in some cases, reaction rates are modified at specific

conditions in order to demonstrate the effect of faster or slower rate coefficients. Several of the

41

reaction paths critical to the pyrolysis of butanol are discussed, and the convention used for

describing the various molecular sites of the butanol isomers is shown in Figure 1.1.

In this work, species time-histories of OH, H2O, CO were measured during the pyrolysis

of 1-butanol, 2-butanol (data in APPENDIX B), and iso-butanol. C2H4 species time-histories were

also measured during the pyrolysis of 1-butanol, and 2-butanol, though measurements were not

performed during the pyrolysis of iso-butanol due to the presence of interference from both iso-

butanol and propene.

3.3.2 Modeling Shock Tube Experiments of Endothermic Reacting Systems

Although dilute fuel mixtures were used throughout this study, the pyrolysis of large fuel

molecules is endothermic, thus causing a temperature and pressure drop after shock heating.

Accounting for temperature change in species time-history experiments can be critical due to the

sensitivity of some spectroscopic parameters to temperature. In addition, the choice of gas-

dynamic model becomes relevant because endothermicity causes shock tubes to deviate from the

ideal constant-volume (CV) behavior often assumed in kinetic simulations.

CV and constant-pressure (CP) assumptions are effectively limiting cases for modeling

the shock tube during pyrolysis experiments. The CV model represents the most constrained

shock tube, while the CP model represents an unconstrained shock tube where pressure variations

are fully negated by the expansion or contraction of the test gas. Figure 3.12 shows representative

pressure trace data from experiments in this work, which indicate that the measured pressure drop

is approximately half of that predicted using CV simulations. This is consistent with the

conclusion that the shock tube exhibits gas-dynamic behavior where the pressure trace lies

between the CP assumption and CV prediction. Note also that CV simulations using three

different mechanisms yield negligible differences in pressure. For non-reacting mixtures, our

shock tubes produce near-constant-pressure traces with pressure variations less than 2%.

Although shock tubes do not exhibit pure CV or CP behavior in the current experiments,

42

predictions of temperature and species time-history are relatively insensitive to the choice

between these two gas-dynamic models for dilute experiments, as discussed below.

0 200 400 600 800 10000.0

0.4

0.8

1.2

1.4

1.5

1.6

1.7

Measurement

CV Simulations

Sarathy et al.

Black et al.

Hansen et al.

P [

atm

]

time [s]

Constant Pressure

Figure 3.12: Measured and simulated pressure for 1% 1-butanol pyrolysis. Initial post-reflected-


Since temperature time-histories were not measured in this study, they are estimated

using kinetic simulations. Although it is preferred that shock tube measurements be conducted

with mixtures and at conditions that are expected to show little change in test conditions with

time, it was confirmed that simulated temperature time-histories in the current pyrolysis

experiments are fairly insensitive to kinetic mechanism or gas-dynamic model. As shown in

Figure 3.13, temperature time-history simulations using CP and CV gas-dynamic models using

three different chemical kinetic mechanism predict temperature reductions of 95 ± 17 K at long

times. Similar uncertainties in temperature are observed in all experiments in this study. As

expected, the magnitude of temperature reduction is largest using CV simulations and smallest

using CP simulations. Though neglecting such drops in temperature could cause a significant

error in some species time-history measurements (i.e. when the absorption coefficient is strongly

temperature dependent), a ± 17 K uncertainty observed by the locus of points encompassed by all

43

simulations shown in Figure 3.13 contributes to an error of no more than ± 8% for any of the

current species monitored.

0 200 400 600 800 1000

1360

1380

1400

1420

1440

1460

1480

T [

K]

time [s]

Sarathy et al.

Black et al.

Hansen et al.

Constant Pressure

Constant Volume

Figure 3.13: Simulated temperature for 1% 1-butanol pyrolysis. Initial conditions: T = 1477 K, P

= 1.52 atm.

Although temperature time-history simulations enable accurate data processing in this

study, it is equally important that future modelers have clear instructions on which gas-dynamic

models to use when simulating species time-histories in shock tube experiments. As demonstrated

in temperature time-history simulations, both CV and CP simulations provide reasonable

estimates for species mole fraction histories at conditions in this study. As shown in Figure 3.14,

CV and CP simulations predict CO mole fractions within 10% of each other. For other species

measured in this study, lower uncertainties are observed. The discrepancy between CV and CP

simulations is caused by temperature time-history variations for different gas-dynamic models,

shown in Figure 3.13. CV simulations will typically predict slightly slower formation of stable

species compared to CP simulations due to lower predicted temperatures throughout the

simulation. It is the opinion of the author that CV simulations provide a realistic representation of

44

the current shock tube study, and hence the CV model is used to simulate temperature and species

time-histories, as well as to perform sensitivity analysis. Nonetheless, it is worth noting that

further improvements in shock tube experiments could be achieved by employing even higher

dilution of reaction mixtures and also by incorporating temperature time-history measurements.

0 200 400 600 800 10000.000

0.002

0.004

0.006

CO

Mo

le F

racti

on

time [s]

CV

CP

Figure 3.14: Simulated CO mole fraction for 1% 1-butanol pyrolysis. Initial conditions: T =

1477 K, P = 1.52 atm. CV simulations performed using the Sarathy et al.8,9

mechanism.

3.3.3 Results

3.3.3.1 1-Butanol

OH and H2O Measurements

Figures 3.15 and 3.16 show a comparison of the measured OH and H2O species time-

histories during the pyrolysis of 1-butanol between this work and the study by Cook et al.64

. Good

agreement is observed between the two data sets, though the data in the current work is regarded

as more accurate due to the included treatment of temperature variations throughout the test time.

It is noted that the slight pressure difference in this study and the study by Cook et al.64

has a

negligible effect on the OH and H2O time-histories. When analyzing measured OH species time-

45

histories, it is important to understand how the uncertainty in post-reflected-shock temperature

affects the peak of the OH mole fraction. Figure 3.17 shows the locus of time-history data that

are expected within a 0.5% uncertainty in temperature. It is evident that the resulting uncertainty

in the peak OH mole fraction is approximately 13%. Therefore, the uncertainty in temperature

ultimately limits the resolution with which experimental OH time-history data can be compared

with other experimental or numeric data.

0 20 40 60 80 100 120 140 1600

2

4

6

8

10

1% 1-Butanol/Ar

OH

Mo

le F

racti

on

[p

pm

]

time [s]

Current study - 1348 K, 1.83 atm

Cook et al. (2011) - 1342 K, 1.51 atm

Figure 3.15: Measured OH mole fraction for 1% 1-butanol pyrolysis.

0 200 400 600 800 10000.000

0.001

0.002

0.003

0.004

0.005

H2O

Mo

le F

racti

on

time [s]

Current Study - 1348 K, 1.83 atm

Cook et al. - 1342 K, 1.51 atm

Figure 3.16: Measured H2O mole fraction for 1% 1-butanol pyrolysis.

46

0 25 50 75 100 125 1500

2

4

6

8

10

OH

Mo

le F

racti

on

[p

pm

]

time [s]

1348 K

1352 K

1344 K

P = 1.8 atm

Figure 3.17: Simulated OH mole fraction for 1% 1-butanol pyrolysis. CV simulations performed

using the Cook et al.64

mechanism. Temperature and pressure indicate initial post-reflected-shock

conditions.

Figures 3.18 and 3.19 show measurements of H2O and OH time-histories, respectively, at

a variety of temperatures, as well as a comparison with simulations using the Sarathy et al.8,9

mechanism. The model significantly underpredicts H2O and OH mole fractions at all times and

temperatures. Kinetic analysis indicates that simultaneous OH and H2O species time-history data

are very useful for the refinement of chemical kinetic mechanisms of 1-butanol because the

majority of water production at lower temperatures occurs due to H atom abstraction from 1-

butanol by OH. Therefore, as shown in Figure 3.20, H2O mole fraction time-histories are

sensitive to the above-mentioned abstraction rates, as well as to reactions that affect the OH

radical pool. For instance, the H2O mole fraction shows positive sensitivity to 1-butanol + H/OH

channels that produce C4H8OH-δ radicals due to their eventual β-scission into OH. This is not the

case for channels producing C4H8OH-γ, resulting in negative sensitivity of H2O to these channels.

Cook et al.64

demonstrated that the 1-butanol + H and 1-butanol + OH reaction sets are critical to

47

modeling 1-butanol pyrolysis, and that additional studies are necessary to determine branching

ratios of the above reaction sets. This is confirmed by simulations using the Sarathy et al.8,9

mechanism, which fails to accurately predict OH and H2O time-histories although the total 1-

butanol + OH reaction rate is in good agreement with experimental measurements35,37

. In

addition, at high temperatures, certain 1-butanol unimolecular decomposition reactions also

significantly affect the OH radical pool. Therefore, understanding all of the abovementioned

reaction classes is critical for improving agreement between simulations and measured OH and

H2O species time-histories.

0 200 400 600 800 10000.000

0.001

0.002

0.003

0.004

H2O

Mo

le F

racti

on

time [s]

1348 K, 1.83 atm

1385 K, 1.89 atm

1467 K, 1.73 atm

Figure 3.18: Measured H2O mole fraction for 1% 1-butanol pyrolysis. Solid lines represent

measurements, dotted lines represent CV simulations performed using the simulations performed

using the Sarathy et al.8,9

mechanism.

48

0 10 20 30 40 500

5

10

15

20

25

30

35

40

45

OH

Mo

le F

racti

on

time [s]

1348 K, 1.83 atm

1385 K, 1.89 atm

1467 K, 1.73 atm

Figure 3.19: Measured OH mole fraction for 1% 1-butanol pyrolysis. Solid lines represent


mechanism.

0 50 100 150 200 250

-0.2

0.0

0.2

0.4

0.6 pC

2H

4OH = C

2H

4+OH

1-C4H

9OH = CH

3+C

3H

6OH

1-C4H

9OH = C

4H

8-+H

2O

1-C4H

9OH+H = C

4H

8OH-+H

2

C4H

8OH- = C

3H

5OH+CH

3

H2O

Sen

sit

ivit

y

time [s]

Figure 3.20: H2O sensitivity analysis for 1% 1-butanol pyrolysis. Initial conditions: T = 1348 K,


mechanism.

49

CO Measurements

Figure 3.21 shows measured CO time-histories for 1% 1-butanol pyrolysis at a variety of

temperatures as well as comparisons with modeling using the Sarathy et al.8,9

mechanism.

Simulations slightly overpredict the measured CO mole fractions at long times, but greatly

underpredict the measured CO mole fractions at early times. Rate of production (ROP) analysis

indicates that CO is largely produced by the unimolecular decomposition of HCO, which is in

turn is generated from the decomposition of CH2OH. Therefore, as shown in Figure 3.22, the CO

mole fraction during the pyrolysis of 1-butanol is most sensitive to the 1-butanol unimolecular

decomposition channel that produces CH2OH:

1-C4H9OH ⟶ 1-C3H7 + CH2OH Reaction 3.1

0 10 20 30 40 400 8000.000

0.002

0.004

0.006

CO

Mo

le F

racti

on

time [s]

T = 1327 K, P = 1.50 atm

T = 1477 K, P = 1.52 atm

T = 1603 K, P = 1.36 atm

Figure 3.21: Measured CO mole fraction for 1% 1-butanol pyrolysis. Solid lines represent


mechanism.

50

0 100 200 300 400 500-0.2

0.0

0.2

0.4

0.6

CO

Sen

sit

ivit

y

time [s]

1-C4H

9OH = 1-C

3H

7+CH

2OH

1-C4H

9OH = CH

3+C

3H

6OH

1-C4H

9OH = C

2H

5+pC

2H

4OH

1-C4H

9OH+H = C

4H

8OH-+H

2

C2H

3OH = CH

3CHO

Figure 3.22: CO sensitivity for 1% 1-butanol pyrolysis. Post-reflected-shock conditions: Initial


mechanism.

At high temperatures, CO exhibits the largest sensitivity to Reaction 3.1 due to the

increased reaction rate of unimolecular decomposition reactions compared to abstraction

reactions by radicals. In addition, CO sensitivity to Reaction 3.1 is largest at early times where

the CO mole fraction is underpredicted most significantly. These observations are consistent with

measurements by Cook et al.64

, who concluded that several existing kinetic mechanisms

underpredict the early formation rate of CH2O, which is a precursor to CO. As discussed in

Section 3.2, rate constants for the unimolecular decomposition channels of 1-butanol in the

Sarathy et al.8,9

mechanism display significant falloff near 1 atm, which is in direct conflict with

experimental data by Rosado-Reyes and Tsang61

that indicate that these rate constants are

pressure independent near 1 atm. Therefore, as shown in Figure 3.23, kinetic simulations using

the Sarathy et al.8,9

mechanism using updated rate constants by Rosado-Reyes and Tsang61

significantly increase the early formation rate of CO near 1 atm, thus significantly improving the

agreement between measurements and simulations at early times. It is noted that sensitivity

51

analysis performed using the Sarathy et al.8,9

mechanism with the modification described above

demonstrates an even higher sensitivity of CO species time-histories to the rate constant of

Reaction 3.1 at early times.

0 10 20 30 40 400 8000.000

0.001

0.002

0.003

0.004

0.005

C

O M

ole

Fra

cti

on

time [us]

Measurement

CV Simulations

Sarathy et al.

Sarathy et al.

Modified

Figure 3.23: Measured CO mole fraction for 1% 1-butanol pyrolysis. Initial post-reflected-shock

conditions: T = 1477 K, P = 1.52 atm.

C2H4 Measurements

Figure 3.24 shows measured C2H4 time-histories at a variety of temperatures as well as

comparisons with simulations using the Sarathy et al.8,9

mechanism. At all temperatures, C2H4 is

slightly underpredicted, even considering the ± 10% uncertainty in the measurement. ROP

analysis shows that C2H4 is produced through a variety of pathways. These include C2H5

decomposition, C3H7 decomposition, β-scission of the C2H4OH-β radical, and β-scission of the

C4H8OH-δ radical. Therefore, as shown in Figure 3.25, C2H4 is sensitive to Reaction 3.1

discussed previously, as well as Reactions 3.2 and 3.3 shown below:

52

1-C4H9OH ⟶ C2H5 + C2H4OH-β Reaction 3.2

1-C4H9OH + H ⟶ C4H8OH-δ + H2 Reaction 3.3

At high temperatures, sensitivity to the unimolecular decomposition reaction dominates, thus

providing further evidence that the rate constants for the unimolecular decomposition channels of

1-butanol in the Sarathy et al.8,9

mechanism are too slow.

0 200 400 600 8000.000

0.002

0.004

0.006

0.008

0.010

C2H

4 M

ole

Fra

cti

on

time [s]

T = 1348 K, P = 1.83 atm

T = 1385 K, P = 1.89 atm

T = 1467 K, P = 1.73 atm

Figure 3.24: C2H4 mole fraction for 1% 1-butanol pyrolysis. Solid lines represent measurements,

dotted lines represent CV simulations using the Sarathy et al.8,9

mechanism.

53

0 50 100 150 200 2500.0

0.1

0.2

0.3

0.4

0.5 C

2H

5 = C

2H

4+H

1-C4H

9OH = C

2H

5+pC

2H

4OH

1-C4H

9OH = nC

3H

7+CH

2OH

1-C4H

9OH + H= C

4H

8OH-+H

2

C2H

4 S

en

sit

ivit

y

time [s]

Figure 3.25: C2H4 sensitivity analysis for 1% 1-butanol pyrolysis. Initial conditions: T = 1348 K,


mechanism.

3.3.3.2 iso-Butanol

OH and H2O Measurements:

As shown in Figures 3.26 and 3.27, kinetic simulations using the Sarathy et al.8,9

mechanism underpredict the measured OH and H2O mole fractions during iso-butanol pyrolysis,

respectively. It is noted that as during 1-butanol pyrolysis, the mole fractions of these two species

are highly interdependent because H-abstraction from iso-butanol by OH is a major production

pathway of H2O. OH radical branching is relatively simple in iso-butanol because only one iso-

butanol radical, iC4H8OH-β, produces OH radicals through a single β-scission pathway.

Therefore, as shown in Figure 3.28, OH (and H2O) mole fractions are highly sensitive to

branching of iso-butanol + H/OH reaction that favor the iC4H8OH-β radical. Most species also

exhibit sensitivity to Reaction 3.4, because it is the primary radical initiation reaction where

CH2OH and iC3H7 undergo unimolecular decomposition to produce H radicals.

54

iC4H9OH + M → iC3H7+CH2OH + M Reaction 3.4

iC4H9OH + M → iC4H8+H2O + M Reaction 3.5

Reaction 3.4 is also an important CO producing pathway because CH2OH falls apart to form

CH2O and then CO. As discussed in the subsequent CO measurements section, CO is

overpredicted at long times, and its early formation rate is in good agreement with measurements.

Therefore, the rate of Reaction 3.4 cannot be increased in order to improve agreement of OH

time-histories. In principle, increasing the rate of Reaction 3.5 could improve agreement between

experimental data and simulations using the Sarathy et al.8,9

mechanism for CO and H2O time-

histories at long times. However, this modification would not improve agreement for OH time-

histories, which are greatly underpredicted. Since OH and H2O time-histories are closely related,

the proposed modifications improve agreement between simulations and measurements for both

species. As a result, the remaining candidates for improving agreement between measurements

and simulations are H-abstraction reactions.

Though reactions of H and OH radicals with iso-butanol are both significant H-

abstraction pathways, it is likely that abstraction reactions by H radicals are largely responsible

for the discrepancies described above. The possibility of modifying H-abstraction rates by OH

radicals is eliminated because in the Sarathy et al.8,9

mechanism, these reactions are

approximately 20% slower, which is considered good agreement, with experimental

measurements provided by Pang et al.38

. Furthermore, increasing OH concentrations by

modifying individual iso-butanol + OH-abstraction rates without further decreasing the overall

iso-butanol + OH rate constant would require unrealistic modifications to the iso-butanol + OH

branching ratios. Therefore, it is postulated that inaccurate rate constants for iso-butanol + H

reactions are responsible for the underprediction of OH and H2O mole fractions. One clear path to

improving agreement between mechanisms and simulations is to adjust the rate constant of H-

abstraction reactions by H radicals to favor the iC4H8OH-β pathway, though the data presented

55

here do not exhibit sufficient specificity to justify quantitative modification of these reaction rate

constants.

0 10 20 30 40 500

20

40

60

80

OH

Mo

le F

racti

on

[p

pm

]

time [s]

1399 K, 1.75 atm

1440 K, 1.73 atm

1477 K, 1.77 atm

1518 K, 1.72 atm

Figure 3.26: Measured OH mole fraction for 1% iso-butanol pyrolysis. Solid lines represent


mechanism.

56

0 200 400 6000.000

0.001

0.002

0.003

0.004

0.005

H2O

Mo

le F

racti

on

time [s]

1399 K, 1.75 atm

1440 K, 1.73 atm

1477 K, 1.77 atm

1518 K, 1.72 atm

Figure 3.27: Measured H2O mole fraction for 1% iso-butanol pyrolysis. Solid lines represent


mechanism.

0 10 20 30 40 50

-0.4

0.0

0.4

0.8

1.2

OH

Sen

sit

ivit

y

time [s]

iC4H

9OH = iC

3H

7+CH

2OH

iC4H

9OH+H = iC

4H

8OH-+H

2

iC4H

9OH+H = iC

4H

8OH-+H

2

iC4H

9OH+OH = iC

4H

8OH-+H

2O

iC4H

9OH+OH = iC

4H

8OH-+H

2O

Figure 3.28: OH sensitivity for 1% iso-butanol pyrolysis. Initial Conditions: T = 1440 K, P = 1.73


mechanism.

57

CO Measurements

Figure 3.29 shows the measured CO mole fractions for iso-butanol pyrolysis, as well as

comparisons with simulations using the Sarathy et al.8,9

mechanism. There exists fair agreement

overall, though CO time-histories are overpredicted at high temperatures and long times, once

oxygenated intermediate species such as formaldehyde and acetaldehyde have largely

decomposed into CO. This is expected due to the underprediction of H2O described previously,

since H2O and CO measurements at high temperatures and long times account for over 90% of

the O atoms in the system. As shown in sensitivity analysis in Figure 3.30, CO is sensitive to

Reaction 3.4, especially at early times, to Reaction 3.5, as well as to the CH2O + H reaction

which has been studied in detail. CO also shows positive long-time sensitivity to H-abstraction

reactions which result in less OH, because their faster rates reduce H2O production, thus

increasing the CO yield. Therefore, the proposed modification to the H-atom abstraction rates by

H radicals from iso-butanol discussed in the previous section would improve the agreement

between measurements and simulation of CO time-histories, because they would partially replace

CO production for the production of H2O.

58

0 20 40 60 80 200 400 600 800 10000.000

0.002

0.004

0.006

CO

Mo

le F

racti

on

time [s]

1346 K, 1.50 atm

1485 K, 1.46 atm

1622 K, 1.36 atm

Figure 3.29: Measured CO mole fraction for 1% iso-butanol pyrolysis. Solid lines represent


mechanism.

0 200 400 600 800 1000-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

CO

Sen

sit

ivit

y

time [s]

iC4H

9OH = iC

3H

7+CH

2OH

CH2O+H = HCO+H

2

iC4H

9OH = H

2O+iC

4H

8

iC4H

9OH+H = iC

4H

8OH-+H

2

iC4H

9OH+H = iC

4H

8OH-+H

2

Figure 3.30: CO sensitivity for 1% iso-butanol pyrolysis. Post-reflected-shock conditions: Initial


mechanism.

59

3.4 Conclusions

In this work, a substantial amount of chemical kinetic data during the pyrolysis and

oxidation of the four isomers of butanol was generated for the purposes of validating and

improving chemical kinetic mechanisms. Ignition delay times for the four butanol isomers were

measured behind reflected shock waves across a variety of conditions from 800-1750 K, 1-50

atm. In addition, multi species time-histories during the pyrolysis of 1-,2-, and iso-butanol were

measured using direct laser absorption from 1300-1650 K near 1.5 atm. The utility of this data for

improving chemical kinetic mechanisms was demonstrated, though a complete optimization of

the mechanisms against the experimental data is reserved for future work. Several of the latest

chemical kinetic mechanism that have utilized the data presented here for mechanism

development show good agreement with a numerous chemical kinetic targets generated in a

variety of reactive environments.

60

4 CHAPTER 4: Isotopic Labeling

4.1 Introduction

H-atom abstraction of alcohols by OH radicals from β-sites produces hydroxyalkyl

intermediates that may rapidly dissociate to OH + alkenes at elevated temperatures (above

approximately 500 K). Therefore, psudo-first-order reaction rate constant measurements at high

temperatures performed by monitoring the rate of OH decay (See Section 2.5) typically exclude

reactivity at the β-site. In this work, isotopic labeling of 18

O in alcohols was used to distinguish

the 16

OH radicals that are generated by the OH-precursor and react with alcohols from the 18

OH

radicals that are recycled via the reaction pathways discussed above, thus enabling measurements

of the overall rate constant for the reactions tert-butanol + OH and ethanol + OH. Hess and

Tully65

and Dunlop and Tully66

have demonstrated this method in measuring the overall reaction

rate constant for ethanol + OH and propanol + OH using laser photolysis of H218

O as an OH

precursor. In order to spectrally distinguish 16

OH and 18

OH radicals in laser absorption

measurements, the 16

OH measurements were performed at the R22(5.5) transition, which does not

exhibit significant spectral overlap with 18

OH.

Isotopic substitution of 18

O is preferred to isotopic substitution of deuterium in this work

due to the lower expected kinetic isotope effect. Furthermore, Carr et al.67

have demonstrated that

in alcohols with a deuterium-labeled alcohol group, proton exchange may occur with trace

amounts of water present in the experiments, thus reducing the deuterium enrichment of the

alcohol mixture.

61

4.2 16OH vs

18OH Spectra

In order to correctly infer the 16

OH mole fractions in the presence of 18

OH, it is necessary

to perform measurements at a 16

OH transition that that does not exhibit overlap with the 18

OH

spectrum. Transition selection was performed by comparing the well-characterized51

UV

spectrum of 16

OH with measured transition linecenters68

of 18

OH. Though spectral parameters of

18OH transitions such as line broadening and line strength have not been measured, it was

assumed that for a given transition, the line strength and linewidth of the 18

OH transitions were

equal to those of 16

OH. Thus, as demonstrated in Figure 4.1, there is negligible spectral overlap

for the R22(5.5) transition between the peak of the 16

OH transition and the 18

OH spectrum.

32558.0 32558.5 32559.00

50

100

150

200

250

300

350

Ab

so

rpti

on

Co

eff

icie

nt

[cm

-1atm

-1]

Wavenumber [cm-1]

16

OH

18

OH R22

(5.5)

Figure 4.1: 16

OH and 18

OH spectra of the R22(5.5) transition in the A-X(0,0) band at 1000 K, 1

atm. 18

OH lineshape assumed to be the same as that of 16

OH as determined by Herbon et al.51

.

18OH linecenter taken from Cheung et al.

68.

The absence of spectral overlap between 16

OH and 18

OH at the selected 16

OH transition

was confirmed experimentally by monitoring absorbance at the peak of the R22(5.5) transition of

16OH during the shock heating of separate 0.1% mixtures of tert-butan

16ol and tert-butan

18ol

62

diluted in argon. By assuming that the OH formation kinetics during tert-butanol pyrolysis are the

same for the two isotopes, the pyrolysis of the above-mentioned mixtures at similar post-reflected

shock conditions should produce nearly-identical 16

OH and 18

OH concentration time-histories. As

a result, differences in measured absorbance during the pyrolysis of mixtures of the different

isotopically-labeled tert-butanol species can be directly attributed to variations in the absorption

coefficient of 16

OH and 18

OH at the measurement wavelength, which is that at the peak of the

R22(5.5) transition of 16

OH (32558.72 cm-1

).

During the pyrolysis of 0.1% mixtures of the tert-butanol, low concentrations of

formaldehyde and acetaldehyde are produced in addition to OH, which exhibit broadband

absorption near the wavelength used to probe 16

OH. Since the absorption of these species is

broadband, their absorption coefficient is expected to remain constant around a narrow

wavelength range near the R22(5.5) transition of 16

OH. Therefore, interference absorption of

acetaldehyde and formaldehyde can be characterized by measuring absorbance at a wavelength a

short distance away from the R22(5.5) transition of 16

OH.

The subplot in Figure 4.2 shows measured absorbance time-histories at the linecenter of

the R22(5.5) transition of 16

OH during the pyrolysis of tert-butan16

ol and tert-butan18

ol, as well as

off-line absorbance time-histories due to formaldehyde and acetaldehyde absorption measured

away from this transition using tert-butan16

ol. By comparing the absorbances at the time of peak

absorbance (tpeak), it is immediately evident that 16

OH, which is produced during tert-butan16

ol

pyrolysis, results in a significantly larger absorbance than 18

OH, which is produced during tert-

butan18

ol pyrolysis. The ratio of the absorption coefficients can be quantified as:

[

]

22

63

Therefore, it is concluded that since the absorption coefficient of 16

OH at the linecenter of the


OH is over 20 times greater than that of 18

OH, the presence 18

OH will not

interfere with measurements of 16

OH time-histories. This is consistent with what is expected from

the 16

OH lineshape from Herbon et al.51

and the 18

OH linecenter from Cheung et al.68

, as shown in

Figure 4.1.

0.00

0.01

0.02

0.03

0.04

0 20 40 600.00

0.01

0.02

0.03

0.04

0.05

Absorb

ance

time [s]

tert-butan16

ol - linecenter

tert-butan18

ol - linecenter

tert-butan16

ol - offline

32557 cm-1

tpeak

tert-butan16

ol

(offline - 32557 cm-1)

tert-butan18

ol

(linecenter)

Pea

k A

bso

rban

ce

tert-butan16

ol

(linecenter)

Figure 4.2: Peak absorbance near the R22(5.5) transition of 16

OH at the time of peak OH mole

fraction during 0.1% tert-butanol/argon pyrolysis. 16

OH R22(5.5) transition linecenter at

32558.72 cm-1

. Sub-plot shows absorbance time-history and indicates the time of peak

absorbance. Post-reflected shock conditions: T ≈ 1515 K, P ≈ 1 atm.

In addition to confirming the absence of spectral interference between 16

OH and 18

OH,

the accuracy of the absorption coefficient at the linecenter of the R22(5.5) transition of 16

OH was

verified. This was done by comparing measurements of 16

OH time-histories during neat TBHP

pyrolysis at nearly identical conditions, acquired separately at the linecenters of the R11(5.5) and

R22(5.5) transitions. Since the spectral properties of the R11(5.5) transition, which is commonly

used to probe 16

OH in this laboratory, have been characterized in great detail50,51

, measurements

64

of 16

OH using this transition are assumed to be accurate. As shown in Figure 4.3, 16

OH time-

histories measured using the two transitions are nearly identical in experiments with identical

initial conditions. Therefore, it is concluded that the absorption coefficient at the linecenter of the


OH is known accurately.

0 20 40 60 80 100

10

100

OH

Mo

le F

racti

on

[p

pm

]

time [s]

R22

(5.5)

R11

(5.5)

Figure 4.3: Measured 16

OH time-histories during neat TBHP pyrolysis, acquired at the

linecenter of the R11(5.5) and R22(5.5) transitions in the A-X(0,0) band. 50 ppm TBHP, diluted in

argon. Post-reflected shock conditions: T = 1108 K, P = 1.2 atm.

4.3 Ethanol + OH

4.3.1 Overview

Biofuels, primarily ethanol, currently account for approximately 3% of overall road-

transport fuel use globally6. The share of biofuels in road-transport fuel is expected to increase to

27% worldwide by 2050, with ethanol accounting for approximately 40% of the total biofuel

quantity5. Due to the increasing demand for ethanol, there is significant interest in developing

accurate combustion models for this fuel.

65

Rate constants for reactions of ethanol with OH radicals are critical for accurately

modeling ethanol combustion. In this study, the overall high-temperature rate constant for the

reaction ethanol + OH → products was measured using isotopic labeling of 18

O in the alcohol

group of ethanol. Isotopic labeling was utilized in order to eliminate the interference of OH-

producing reaction pathways that typically perturb rate constant measurements for reactions of

alcohols with OH radicals at high temperatures. Experiments using unlabeled ethanol were also

performed in order to determine the rate constant for the title reaction that excludes reactivity at

the β-site (non-β). By combining measurements of the overall and non-β reaction rate constants,

the branching ratio of the ethanol + OH reaction at the β-site (BRβ) was inferred.

4.3.2 Ethanol + OH Kinetics

The reaction ethanol + OH proceeds via three possible reaction sites, α, β, and o, defined

by reaction rate constants k4.1a, k4.1b, and k4.1c, respectively. The reaction pathways for these

reactions as well as structural formulas of relevant species are illustrated in Figure 4.4.

C2H5OH + OH → CH3CHOH + H2O Reaction 4.1a

→ CH2CH2OH + H2O Reaction 4.1b

→ CH3CH2O + H2O Reaction 4.1c

Reaction of ethanol with OH radicals at the β-site (Reaction 4.1b) produces CH2CH2OH radicals

that rapidly decompose at temperatures above 500 K via Reaction 4.2 to form ethylene and OH,

thus resulting in zero net OH consumption65,69

.

CH2CH2OH → C2H4 + OH Reaction 4.2

66

Therefore, high-temperature rate constant measurements for the reaction ethanol + OH performed

by monitoring the rate of removal of OH radicals typically exclude the contribution from the β-

site. A branching ratio for the reaction at the β-site is defined as:

Figure 4.4: Dominant reaction pathways related to ethanol + OH reactions.

The rate constant for the reaction of ethanol with OH radicals has been studied

extensively in previous work. Measurements were performed near atmospheric temperatures by

Wallington and Kurylo70

, Jiménez et al.71

, Greenhill and O’Grady72

, Dillon et al.73

, and Orkin et

al.74

, at intermediate temperatures by Carr et al.67

, Hess and Tully65

, and Meier et al.75

, and at

combustion temperatures by Sivaramakrishnan et al.76

and Bott and Cohen77

. Theoretical studies

have also been performed Xu and Lin78

, Zheng and Truhlar79

, and Galano et al.80

, and chemical

kinetic mechanisms for ethanol combustion have been developed by Marinov81

, Leplat et al.58

,

Natarajan and Baskharan82

, Norton and Dryer23

, and Dunphy and Simmie83

. Notably, experiments

by Hess and Tully65

at 295 K and 599 K utilized isotopically labeled H218

O as the 18

OH precursor,

67

thus overcoming the recycling of OH described previously. A comparison of their measurements

using unlabeled and labeled OH radicals clearly indicate that the rate of removal of OH in

unlabeled experiments begins to lose sensitivity to H-abstraction at the β-site near 500 K, with a

complete loss of sensitivity above 650 K. Therefore, high-temperature measurements performed

using unlabeled ethanol by Carr et al.67

, Sivaramakrishnan et al.76

and Bott and Cohen77

do not

account for reactivity at the β-site.

The rate constants for the title reaction were determined by fitting the simulated 16

OH

time-histories from the kinetic model to the experimental data using the ethanol + OH reaction

rate constants as free parameters that affect the pseudo-first-order decay rate of 16

OH. As

discussed in the introduction and demonstrated in Figure 4.5, the concentration of 16

OH in the

presence of excess ethan18

ol exhibits sensitivity to all three ethanol + OH reaction sites. However,

as shown in Figure 4.6, the concentration of 16

OH in the presence of excess ethan16

ol is not

sensitive to reaction at the β-site due the fast decomposition of the CH2CH2OH radical via

Reaction 4.1b. Therefore, experimental data in the labeled and unlabeled experiments may be

used to infer the overall and non-β rate constants for the ethanol + OH reaction, respectively. It is

noted that the relative branching of the reaction ethanol + OH at the α- and o- sites, with rate

constants k4.1a and k4.1c, respectively, remains an undetermined free parameter in the kinetic

simulations. However, brute force sensitivity analysis indicates that variations in the ratio

k4.1c/k4.1a from 0 to 1, which is a reasonable range based on theoretical calculations78,79

, do not

perturb the measurements of the overall or non-β rate constants for the title reaction by more than

4%.

68

0 20 40 60 80-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

No

rmalized

16O

H S

en

sit

ivit

y

time [s]

Primary Reactions

C2H

5OH + OH -> CH

3CHOH + H

2O

C2H

5OH + OH -> CH

3CH

2O + H

2O

C2H

5OH + OH -> CH

2CH

2OH + H

2O

Secondary Reactions

tert-C4H

9OOH -> tert-C

4H

8O + OH

CH3 + OH ->

1CH

2+H

2O

CH3 + OH -> CH

3OH

C2H

5OH + H -> CH

3CHOH + H

2



ppm ethan18


69

0 20 40 60 80-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

No

rmalized

16O

H S

en

sit

ivit

y

time [s]

Primary Reactions

C2H

5OH + OH -> CH

3CHOH + H

2O

C2H

5OH + OH -> CH

3CH

2O + H

2O

Secondary Reactions

tert-C4H

9OOH -> tert-C

4H

8O + OH

CH3 + OH ->

1CH

2 + H

2O

CH3 + OH -> CH

3OH

C2H

5OH + H -> C

2H

4OH + H

2



354 ppm ethan16


Simulations were performed using a modified version of the ethanol mechanism

proposed by Leplat et al.58

. The primary modifications to the mechanism were the addition of

reactions necessary for modeling TBHP decomposition, as well updates to the rate constants for

reactions of OH radicals with CH3 radicals, which are the principal source for secondary OH

removal. Rate constants for both of these reaction sets were taken from work by Pang et al57

. The

kinetic mechanism was also updated to include duplicate reactions for ethan18

ol and its labeled

fragments that are assumed to have equivalent reaction rate constants as their unlabeled

counterparts.

An examination of the literature revealed that the decomposition timescale of the

CH3CHOH radical at experimental temperatures near 900 K is similar to the ~100µs timescale of

70

16OH decay. This slow decomposition rate is a consequence of the geometry of CH3CHOH

radical, which only contains β-scission pathways that require the rupture of C-H bonds. Similar

radicals with different structures such as CH2CH2OH or CH3CH2O decompose much more

rapidly at similar conditions because β-scission pathways are available that rupture the weaker C-

C or C-O bonds, respectively69,84

. Since the decomposition rate of the CH3CHOH is relatively

slow, its concentration may reach levels similar to those of CH3 radicals, and thus its potential to

consume a non-negligible amount of 16

OH radicals must be considered. Critically, an accurate

kinetic model must contain reasonable rate constant estimates for both the decomposition of

CH3CHOH, which primarily affects its absolute concentration, as well as for the reaction

CH3CHOH + OH, which affects the rate of removal 16

OH radicals. It is concluded that the Leplat

et al.58

mechanism does not contain accurate rate constants for either reaction. The decomposition

reaction for the CH3CHOH radical was described by a bimolecular rate constant expression that

was estimated in previous work82

on ethanol ignition in shock tubes. A comparison with more

recent work described in the following paragraph indicates that this rate constant estimate is too

low at the conditions in this study. The reaction CH3CHOH + OH was described in the Leplat et

al.58

mechanism using a temperature-independent rate constant of 5 x 1012

cm3mol

-1s

-1, which is

also significantly too low because it is 30% slower than the measured rate constant in this work

for the reaction ethanol + OH. It is expected that the rate constant for this reaction would be

comparable to that of other hydrocarbon radical + OH reactions, whose rate constants are

typically on the order of 2 x 1013

cm3mol

-1s

-1.

In the current mechanism, the rate constant for the decomposition of the CH3CHOH

radical was taken from recent theoretical calculations by Dames69

. That work utilizes the

RRKM/Master Equation approach with electronic energies, molecular geometries, and force

constant from computations by Senosian et al.84

. The rate constant calculations by Dames69

are

preferred to similar calculations by Xu et al.85

, though the latter are slower by approximately a

factor of four at the conditions of the current experiments. The rate constants for the reaction

71

channels CH3CHOH + OH → CH2CHOH + H2O and CH3CHOH + OH → CH3CHO + H2O

were assumed to be equal to the rate constant for the reaction C2H5 + OH → C2H4 + H2O

estimated by Tsang and Hampson86

. The effect of the uncertainties in the above rate constants on

the inferred rate constant for the reaction ethanol + OH is discussed in the uncertainty analysis.

Notably, data reduction preformed using the Leplat et al.58

and Marinov81

mechanisms with

updated rate constants for the reactions discussed above resulted in nearly identical inferred

values of the title reaction rate constant.

4.3.3 Results

Measurements were acquired between 910 and 1274 K near 1.1 atm for a variety of

mixture compositions. The non-β rate constant was measured in 31 unlabeled experiments, and

the concentrations of ethan16

ol and TBHP were varied from 205-885 ppm and 10-38 ppm,

respectively. Rate constant measurements show excellent repeatability for a variety of mixture

compositions, which suggests that secondary reactions are accurately described in the kinetic

mechanism. Due to the high cost of ethan18

ol, the overall rate constant was measured in only 15

labeled experiments, and the concentrations of ethano18

ol and TBHP were varied from 285-349

ppm and 16-23 ppm, respectively. All overall and non-β rate constant measurements are tabulated

in APPENDIX A. Measured 16

OH time-histories exhibit a high signal-to-noise ratio, and

simulations indicate excellent sensitivity to the title reaction rate constants, as shown in Figure

4.7.

72

0 20 40 60 801

10

16O

H M

ole

Fra

cti

on

[p

pm

]

time [s]

Measurement

knon-

= 6.03 x 1012

1.2knon-

0.8knon-

354 ppm ethan16

ol

14 ppm TBHP

Diluted in argon


OH time-histories for ethan16

ol/TBHP/argon mixtures (knon-β in units

of cm3mol

-1s

-1). Post-reflected shock conditions: T = 1023 K, P = 1.03 atm. Discrepancy in the

rise of 16

OH is caused by the limited time resolution of the diagnostic (~5µs).

As shown in Figure 4.8, measurements of the non-β rate constant for the title reaction

agree within the uncertainty limits with previous studies by Sivaramakrishnan et al.76

(absorption,

TBHP precursor) and Carr et al.67

(flash photolysis/laser-induced fluorescence). The single

measurement from the study by Bott and Cohen87

(absorption, TBHP precursor) is 35% lower and

lies outside of the uncertainty bounds of the current data. A comparison of the overall and non-β

rate constant measurements, which differ by approximately 20%, can be used to infer the

temperature-dependent branching ratio of reaction at the β-site (BRβ), which is shown in Figure

4.9. Since labeled and unlabeled experiments were not carried out at identical temperatures, it is

not possible to calculate point values for BRβ. Instead, for the purposes of determining BRβ,

separate best fits to the current data valid from 900-1270 K were generated, yielding 8.14 x 10-6

T[K]5.39

exp(4162/T[K]) for the overall rate constant and 1.57 x 10-8

T[K]6.11

exp(5194/T[K]) for

the non-β rate constant (units of cm3mol

-1s

-1). These expressions are then used to compute a curve

for BRβ using the following expression:

73

BRβ = (Fit overall – Fit non-β) / Fit overall

The result is plotted in Figure 4.9.

0.8 0.9 1.0 1.1 1.2

4E12

6E12

8E12

1E13

1.2E13

833 K1250 K 1000 K

Ra

te C

on

sta

nt

[cm

3m

ol-1

s-1]

1000/T [K-1]

Overall

Current Study Fit

Xu and Lin Zheng and Truhlar

Non-

This work Carr et al.

Sivaramakrishnan et al. Bott and Cohen

Xu and Lin Zheng and Truhlar

Figure 4.8: Comparison of the measured overall and non-β rate constants for the title reaction

with previous theoretical and experimental work at high temperatures. Curves by Zheng and

Truhlar79

represent calculations using the M08-SO/6-31+G(d,p) method. Curve labeled “Fit”

was generated based on all experimental data shown in Figure 4.10.

74

900 1000 1100 1200

0.08

0.16

0.24

0.32

0.40

0.48

BR

T [K]

Current Study

Xu and Lin

Zheng and Truhlar

M08-SO/6-31+G(d,p)

Sivaramakrishnan et al.

Figure 4.9: Comparison of the measured branching ratio BRβ with previous theoretical work.

A comparison of the measurement for the overall rate constant with previous

measurements at lower temperatures is shown in Figure 4.10. Generally, there is good agreement

among the 9 experimental data sets that are presented, and the data are well fit using the

following expression valid from 250-1300 K:

koverall = 5.07 x 105 T[K]

2.31 exp(608/T[K]) cm

3mol

-1s

-1

It is observed that measurements of both the overall and non-β rate constants for the title reaction

exhibit a slight reduction in temperature dependence from 900-1000 K. This is evident in Figures

4.8 and 4.10, where the slopes of the experimental data from the current study between 900-1000

K (Figure 4.8) are lower than those of the fit to the aggregated experimental data across the full

temperature range (Figure 4.10). The author believes that the apparent reduction in the

temperature dependence in the current study may be caused by inaccuracies of the CH3CHOH

radical chemistry in the kinetic mechanism, which are discussed in detail in the uncertainty

analysis section (See APPENDIX C). Adjustments of the rate constant for relevant CH3CHOH

75

radical chemistry reactions within their uncertainties can reduce the measured title reaction rate

constant by up to 7% at 900 K. Nonetheless, the author does not believe that rate constants for

these reactions should be adjusted based only on the measurements of the overall and non-β rate

constant for the ethanol + OH reaction in this study.

1.0 1.5 2.0 2.5 3.0 3.5 4.01E12

1E13

250 K333 K500 K

Current Study Hess and Tully

Jimenez et al. Dillon et al.

Wallington and Kurylo Carr et al.

Greenhill and O'Grady Meier et al.

Orkin et al.

Fit Xu and Lin Galano et al.

Zheng and Truhlar (M08-SO/6-31+G(d,p))

Sivaramakhrishnan et al.

ko

vera

ll [

cm

3m

ol-1

s-1]

1000/T [K-1]

1000 K

Figure 4.10: Comparison of the measured overall rate constant for the title reaction with

previous theoretical and experimental work. Data from past studies are excluded if they were

performed at conditions that are not sensitive to reactivity at the β-site. Data are best fit by the

expression: koverall = 5.07 x 105 T

2.31 exp(608/T) cm

3mol

-1s

-1

Theoretical calculations show good agreement with the experimental data across a variety

of temperatures, as shown in Figures 4.8-4.10. Quantum chemistry calculations by Xu and Lin78

,

Zheng and Truhlar79

, and Sivaramakhrishnan et al.76

, which were performed using variational

transition state theory (VTST), muti-structural VTST, and variable reaction coordinate TST,

respectively, are in excellent agreement with the experimental data for the overall reaction rate

constant. However, Xu and Lin78

predict a branching ratio for the β-site that is below the current

measurement at temperatures above 1100K and is essentially at the limit of our experimental

76

uncertainty. The discrepancy between the theoretical calculations by Sivaramakhrishnan et al.76

and the experimental data for the branching ratio of the β-site could be explained by the fact that

their calculations for abstraction at the OH- and β-sites were performed at a lower level of theory

compared to calculations for abstraction at the α-site, which is the primary abstraction channel.

Nonetheless, fair agreement between the three studies is encouraging given that critical

parameters such as molecular geometries and potential energies were calculated using different

theoretical methods, the details of which can be found in the respective publications. It should be

noted that Zheng and Truhlar79

compute rate constants for the various pathways of the title

reaction using several density functionals that produce results that differ by up to a factor of four

at room temperatures. However, all of their calculations predict a branching ratio for the β-site

that is between 0.15 and 0.3 from 900-1200 K. In this study, the results using the M08-SO/6-

31+G(d,p) method are presented because they show superior agreement with the experimental

data. It may also be noted that calculations by Galano et al.80

, which were performed using

conventional TST, significantly underpredict the measured data at intermediate temperatures

where the calculations were performed.

4.4 tert-Butanol + OH

4.4.1 Introduction

tert-Butanol is a common fuel additive used as an octane booster to prevent knock in

spark-ignition engines. Several experimental studies22,41,88–94

, many of which were performed in

the last decade, have explored the combustion kinetics of tert-butanol. In addition, several

detailed kinetic mechanisms have been developed8,9,40,41,95

with varying success in matching the

kinetic targets produced in these experimental studies. Discrepancies in mechanism performance

are ultimately explained by order-of-magnitude differences in rate constants for several reactions

77

important to combustion, including for those of the H-atom abstraction of tert-butanol by OH and

the β-scission decomposition of the tert-C4H8OH radical.

4.4.2 tert-Butanol + OH Kinetics

The reaction tert-butanol + OH proceeds via H-atom abstraction from the methyl (CH3)

and alcohol (OH) groups in tert-butanol, as specified by Reactions 4.3a and 4.3b, respectively.

Figure 4.11 illustrates the network of chemical reactions relevant to the production and

consumption of OH as a result of these reactions, as well as the structural formulas of relevant

chemical species.

tert-C4H9OH + OH → tert-C4H8OH + H2O Reaction 4.3a

→ tert-C4H9O + H2O Reaction 4.3b

Figure 4.11: Dominant reaction pathways related to tert-butanol + OH reactions.

78

The overall rate constant for the reaction tert-butanol + OH, defined as

k4.3= k4.3a+k4.3b

was previously measured using relative rate methods by Cox and Goldstone96

, and Wu et al.97

,

and absolute measurement methods by Wallington et al98

, Teton et al.99

, Saunders et al.100

, and

McGillen at al.101

, all near room temperature. However, these measured values cannot be

accurately extrapolated to combustion temperatures. Measurements of the overall rate constant

for the reaction tert-butanol + OH at high temperatures are complicated by the existence of an

OH-producing pathway that effectively reduces the apparent OH consumption rate. This OH

regeneration occurs at the β-sites occurs via the tert-C4H8OH radical produced by Reaction 4.3a,

which as described by Reaction 4.4a and depicted in Figure 4.11, can undergo β-scission to

produce OH radicals. It can also undergo β-scission via an alternative major pathway that does

not produce OH, described by Reaction 4.4b.

tert-C4H8OH → OH + iso-C4H8 Reaction 4.4a

→ CH3 + iso-C3H5OH Reaction 4.4b

It follows that consecutive reaction of OH with tert-butanol via Reactions 4.3a and 4.4a leads to

the production of OH, and the relative production of the different products via Reactions (4.3a/b)

and (4.4a/b), which can be defined through the branching ratios:

BR1 = k4.3a/(k4.3a+k4.3b)

BR2 = k4.4a/(k4.4a+k4.4b)

79

are critical kinetic parameters which significantly affect simulations of tert-butanol oxidation. It

is noted that Reaction 4.5, which represents the decomposition of the tert-C4H9O radical

(produced by Reaction 4.3b), is not expected to form OH. Therefore, this reaction channel does

not significantly affect the OH concentration in this study.

tert-C4H9O → C3H6O + CH3 Reaction 4.5

The overall rate constant for the reaction tert-butanol + OH (k4.3) can be determined from

experiments with tert-butan18

ol by fitting the simulated 16

OH time-history from the kinetic

mechanism to the experimental data using the overall rate constant as the free parameter. Since

there are no secondary 16

OH generation pathways in these experiments, the decay rate of 16

OH is

not affected by the existence of OH regenerating pathways. The kinetic mechanism used in this

work was developed Sarathy et al.8,9

, and it was modified with well-characterized rate constants

for TBHP decomposition chemistry and secondary OH-consuming chemistry from Pang et al.57

.

Rate of production analyses using this kinetic mechanism indicate that 75-90% of the 16

OH-

consumption results from reactions with tert-butanol at the conditions in the current experiments,

though secondary reactions that consume OH exist and the Sarathy et al.8,9

mechanism was

modified with well-characterized rate constants for these reactions.

The overall rate constant for the reaction tert-butanol + OH needed to best fit the

measured data is independent of BR1 for experiments with tert-butan18

ol. The high sensitivity of

this measurement of k4.3 is demonstrated by the OH sensitivity analysis shown in Figure 4.12,

which reveals that the OH concentration is overwhelmingly sensitive to the tert-butanol + OH

reaction rate constant. Secondary reactions that consume OH exist and appear in the OH

sensitivity analysis shown in Figure 4.12, though the rate constants for these reactions are well-

characterized, and the kinetic model was modified to account for secondary OH-consuming

80

reactions (See Section 2.5). The experiments are pseudo-first-order, so the first-order decay

constant due to reactions of 16

OH with tert-butan18

ol can be defined by

18

k’= k4.3 = (k4.3a + k4.3b)

This value can be combined with the experimental data with tert-butan16

ol to provide information

about the branching ratio BR2.

0 20 40 60 80-4

-3

-2

-1

0

1

No

rmali

zed

16O

H S

en

sit

ivit

y

time [s]

Primary Reactions

tert-C4H

9OH + OH tert-C

4H

8OH + H

2O

tert-C4H

9OH + OH tert-C

4H

9O + H

2O

Secondary Reactions

CH3 + OH CH

3OH

CH3 + OH

1CH

2 + H

2O

iso-C4H

8 + OH iso-C

4H

7 + H

2O

tert-C4H

9OOH tert-C

4H

9O + OH



ppm tert-butan18


The measured 16

OH removal rate in experiments with tert-butan16

ol also demonstrates a

pseudo-first-order decay. However, as shown in Figure 4.13, sensitivity analysis for a

81

representative experiment in tert-butan16

ol shows that after initial TBHP decomposition, 16

OH

time-histories are most sensitive to multiple rate constants including k4.3a, k4.3b, k4.4a, and k4.4b. This

is expected considering that in experiments containing tert-butan16

ol, 16

OH is expected to be

consumed by Reactions 4.3a and 4.3b, and is produced by Reaction 4.4a. This complex OH

sensitivity behavior makes it difficult to measure any single rate constant from these experiments.

However, since the tert-C4H8OH radical decomposes rapidly, a quasi-steady state assumption can

be invoked (d[tert-C4H8OH]/dt = 0), and the rate law describing the disappearance of 16

OH due to

the reaction with tert-butan16

ol simplifies to:

( [ ]

)

[ ]

The component of the first-order decay rate due to reactions with tert-butan16

ol is thus:

16k’= (k4.3a + k4.3b) (1 - BR1BR2) =

18k’ (1 - BR1BR2)

While the first-order rate constant is a function of more than one kinetic parameter, the

overall value of 16

k’ needed to simulate the experimental data is unique. Therefore, 16

k’ was

inferred by best-fitting kinetic simulations of OH time-histories to the experimental

measurements of 16

OH decay in the experiments with excess tert-butan16

ol. Given the measured

18k’, it was verified the value of

16k’ required to best fit the experimental data is independent of

the value of the free parameters BR1 and BR2. It is observed that measurements cannot be fit using

kinetic simulations if either BR1 or BR2 are below 0.72. A brute force analysis indicates that

within the span of BR1:BR2 combinations examined, using possible values of BR1 and BR2

ranging from 0.72 to 1.0, the value of 16

k’ that fits the experimental data can be determined to

82

within 3%. It is noted that the inferred values of 16

k’ are independent of the chosen value for k4.3,

though the measured value of k4.3 = 18

k’ is preferred.

After determining 18

k’ and 16

k’ from the experimental data, the ratio of these two values

leads to the value of the product BR1BR2. As discussed in the Section 4.4.3, estimates of BR1 can

then be used to infer BR2.

0 20 40 60 80-1.0

-0.5

0.0

0.5

1.0

No

rmalized

16O

H S

en

sit

ivit

y

time [s]

Primary Reactions

tert-C4H

9OH + OH tert-C

4H

8OH + H

2O

tert-C4H

9OH + OH tert-C

4H

9O + H

2O

tert-C4H

8OH OH + iso-C

4H

8]

tert-C4H

8OH CH

3 + iso-C

3H

5OH

Secondary Reactions

CH3 + OH

1CH

2 + H

2O

CH3 + OH CH

3OH

iso-C4H

8 + OH iso-C

4H

7 + H

2O

tert-C4H

9OOH tert-C

4H

9O + OH





83

4.4.3 Results

Measurements of 18

k’ were acquired from 896 to 1208 K for a variety of mixtures, with

tert-butan18

ol concentrations near 500 ppm, and TBHP concentrations varying from 14 ppm to 29

ppm. Measurements of 16

k’ were performed from 896 to 1204 K for a variety of mixtures, with

tert-butan16

ol concentrations varying from 307 to 2080 ppm, and TBHP concentrations varying

from 9 ppm to 26 ppm. Measurements of 18

k’ were generally performed at lower tert-butanol

concentrations compared to measurements of 16

k’, because, as the data will demonstrate, the

decay rate of 16

OH in tert-butan18

ol is much faster compared to that in equal amounts of tert-

butan16

ol. All experiments were performed near 1.1 atm.

Figure 4.14 shows representative measurements and kinetic simulations of 16

OH time-

histories in the presence of excess tert-butan18

ol and tert-butan16

ol. Measured 16

OH time-histories

exhibit low noise, and kinetic simulations of the pseudo-first-order decay rate of 16

OH

demonstrate excellent sensitivity to 18

k’ and 16

k’, as shown in Figure 4.14 by simulations with 18

k’

and 16

k’ adjusted by ± 20%. It is estimated that the fitting uncertainty of 18

k’ and 16

k’ is ± 3%.

84

5

10

15

202530


ol

29 ppm tbhp

Measurement

18

k' = 1.06x10-11

1.218

k'

0.818

k'

16O

H M

ole

Fra

cti

on

[p

pm

]

0 20 40 60 80

5

10

15

202530


ol

17 ppm tbhp

Measurement

16

k' = 2.12x10-12

1.216

k'

0.816

k'

time [s]


OH time-histories for tert-butanol/TBHP/argon mixtures (k’ in

units of cm3 molecule

-1 s

-1). Initial post-reflected shock conditions: T = 1020 K, P = 1.2 atm.

Measurements of 18

k’ and 16

k’ exhibit Arrhenius behavior with low scatter and

uncertainty over the temperature range studied, as shown in Figure 4.15 (tabulated data are

presented in APPENDIX A). Arrhenius fits for these parameters are:

18k’ = (k4.3a + k4.3b) = 1.24 x 10

-10 exp(-2501/T [K]) cm

3 molecule

-1 s

-1

16k’ = (k4.3a + k4.3b) (1-BR1BR2) = 3.87 x 10

-11 exp(-2935/T [K]) cm

3 molecule

-1 s

-1

85

0.8 0.9 1.0 1.1

10-12

10-11

18k

' = k

4.3a+k

4.3b

16k

' = (k

4.3a+k

4.3b) (1-BR

1BR

2)

Net

OH

decay r

ate

du

e t

o r

eacti

on

wit

h t

ert

-bu

tan

ol

[cm

3 m

ole

cu

le-1 s

-1]

1000/T [K-1]

1111 K1250 K 909 K1000 K

Figure 4.15: Arrhenius plot of measured 16

k’ and 18

k’. Solid lines show Arrhenius fits.

As demonstrated in Figure 4.16, kinetic mechanisms offer a wide variety of values for

the overall rate constant for the reaction tert-butanol + OH. Notably, good agreement is shown

with the Moss et al.41

mechanism, which agrees with the current measurements within the

estimated uncertainties. The Moss et al.41

mechanism estimates the rate of Reaction 4.3a using an

Evans-Polanyi type correlations based on H-atom abstraction rates from ethane102

. The

mechanism also assumes that the rate of Reaction 4.3a is greater than that of Reaction 4.3b by

exactly a factor of nine, which is a reasonable estimate that is discussed in detail later in this

section. The rate constant estimate for the overall reaction tert-butanol + OH in the Sarathy et al.

8,9 mechanism, obtained from a combination of theory and experimental data, is 50% lower than

the current measurement. The Grana et al.40

mechanism suggests a rate constant for the overall

reaction tert-butanol + OH which is also 50% lower than the current measurement; their rate

constants were derived from previous work on predicting kinetic parameters for H-atom

abstraction reactions, validated against a wide array of experimental data103

. The Grana et al.40

mechanism also assumes that the rate of Reaction 4.3a is greater than that of Reaction 4.3b by

exactly a factor of nine. The Van Geem et al.95

mechanism estimates the rates for Reactions 4.3a

86

and 4.3b using the open source software package Reaction Mechanism Generator (RMG)62

, and

these rate constants yield a value for the rate constant for the reaction tert-butanol + OH which is

80% slower than the current measurement.

0.8 0.9 1.0 1.1

10-12

10-11

1111 K1250 K 909 K

Measurement

Sarathy et al.

Grana et al.

Van Geem et al.

Moss et al.

k4

.3 [

cm

3 m

ole

cu

le-1 s

-1]

1000/T [K-1]

1000 K

Figure 4.16: Comparison of the measured overall tert-butanol + OH reaction rate constant (k4.3

= 18

k’) with values used in mechanisms from the literature.

The ratio of 18

k’ and 16

k’ enables an experimentally-determined value for BR1BR2

approximately equal to 0.8 over the entire temperature range studied, as shown in Figure 4.17.

This indicates that for every OH molecule that reacts with tert-butanol, there is an 80%

probability that another OH molecule will be produced through the β-scission of the resulting

tert-C4H8OH radical. This provides further evidence that a rate constant measurement for the

reaction tert-butanol + OH is difficult without the use of isotopic substitution, because the net OH

decay rate in a mixture of tert-butan16

ol is strongly reduced by the regeneration of OH radicals.

Since neither BR1 nor BR2 can be greater than unity, the measurement of BR1BR2 places an upper

limit on both BR1 and BR2. The comparison of the measured BR1BR2 product with the values of

BR1BR2 obtained using the rate constants in the different mechanisms studied is shown in Figure

4.17.

87

0.8 0.9 1.0 1.10.0

0.2

0.4

0.6

0.8

1.0

Measurement

Sarathy et al.

Grana et al.

Van Geem et al.

Moss et al.BR

1B

R2

1000/T [K-1]

1111 K 909 K1000 K

Figure 4.17: Comparison of the measured branching ratio product BR1BR2 near 1.1 atm with

values used in mechanisms from the literature.

An estimation of BR1 can be used to infer BR2. To first order, BR1 can be estimated to be

between 0.9 and 1.0 based on the number of H atoms that are available for abstraction at the

methyl and alcohol sites (i.e. Reaction 4.3a can proceed via nine different H atoms in the methyl

groups of tert-butanol, whereas Reaction 4.3b can only proceed via a single H atom in the alcohol

group), and with the assumption that C-H bonds are generally weaker than O-H bonds. As shown

in Figure 4.18, the Sarathy et al.8,9

, Grana et al.40

, and Moss et al.41

mechanisms indicate that BR1

lies within this range, though the Van Geem et al.95

mechanism does not. The Sarathy et al.8,9

mechanism value of BR1 is a consequence of separate reaction rate estimates of Reactions 4.3a

and 4.3b described previously, whereas the Grana et al.40

and Moss et al.41

mechanism values of

BR1 are equal to 0.9 based solely on the degeneracy of reaction sites. The Van Geem et al.95

mechanism, which uses RMG to estimate the rate constants for Reactions 4.3a and 4.3b, does not

provide a reasonable estimate for BR1,

88

0.8 0.9 1.0 1.10.5

0.6

0.7

0.8

0.9

1.0

Measurement

Sarathy et al.

Grana et al.

Van Geem et al.

Moss et al.

BR

1

1000/T [K-1]

1111 K 909 K1000 K

Figure 4.18: Comparison of the estimated branching ratio BR1 with values used in mechanisms

from the literature.

In the current analysis, BR1 will be estimated more accurately than in the mechanisms

discussed previously through the use of quantum calculations for H-atom abstraction reactions by

OH radicals from the alcohol group and the measurements of the overall tert-butanol + OH

reaction rate from this study. Similar O-H bond dissociation energies in the alcohol group104

for

methanol, ethanol, and 1-butanol lead to calculated rate constants for the H-atom abstraction in

the alcohol group by OH in these alcohols that agree within 40% of one another78,105

. Because the

O-H bond dissociation energy in tert-butanol is also expected to be similar, quantum calculations

for the rate of H-atom abstraction by OH from the alcohol group of 1-butanol provide a

reasonable estimate for the rate constant of Reaction 4.3b. Using this estimate for Reaction 4.3b,

the rate constant for Reaction 4.3a was calculated under the constraint that the sum of the two

reaction rates, the overall tert-butanol + OH reaction rate, must lie within the uncertainty of the

measurement in this study. Using this method, an estimate of BR1 equal to 0.96 is calculated with

an overall uncertainty (peak-to-peak) of 6%, as shown in Figure 4.18. Despite an uncertainty

estimate of a factor of four on in the rate of Reaction 4.3b, BR1 is calculated accurately because

89

the relatively large measured value of the overall tert-butanol + OH reaction rate requires that the

vast majority of H-atom abstraction by OH in tert-butanol proceeds via Reaction 4.3a.

Using the above estimate of BR1, BR2 is calculated from the measurement of BR1BR2 with

overall uncertainties (peak-to-peak) of approximately 17% and 12% near 900 K and 1200 K,

respectively. As shown in Figure 4.19, the probability of the tert-C4H8OH radical undergoing β-

scission through Reaction 4.4a is greater than 80% at the conditions studied. These results are

significant because high-accuracy measurements of the branching of radicals produced during

decomposition of organic compounds are rare, though accurate knowledge of these kinetic

parameters can be important in developing kinetic mechanisms. Because of the previous lack of

knowledge surrounding these kinetic parameters, kinetic mechanisms provide a wide range of

estimates for BR2 ranging from 0.09 to 0.98, as shown in Figure 4.19.

0.8 0.9 1.0 1.10.0

0.2

0.4

0.6

0.8

1.0

Measurement

Sarathy et al.

Grana et al.

Van Geem et al.

Moss et al.

BR

2

1000/T [K-1]

1111 K 909 K1000 K

Figure 4.19: Comparison of the inferred branching ratio BR2 near 1.1 atm with values used in

mechanisms from the literature.

The Moss et al.41

and Sarathy et al.8,9

mechanisms provide reasonable estimates of BR2,

compared to the inferred value. It should be noted that these mechanisms present rate constant

90

expressions for Reactions 4.4a and 4.4b that were estimated at the high-pressure-limit, and

depending on the relative falloff behavior of these reactions, BR2 may exhibit some pressure

dependence. Rate constants for Reactions 4.4a and 4.4b in the Moss et al.41

mechanism were

derived from estimates of β-scission reaction rate constants in alkanes and ethers. Evans-Polanyi

type correlations using enthalpies obtained from THERGAS106

software are used to adjust the rate

constant for Reaction 4.4b, due to the effect of the alcohol group on the strength of the C-C bond.

The rates of Reactions 4.4a and 4.4b in the Sarathy et al.8,9

mechanism were determined from rate

constants for similar reverse reactions. Because the estimated rate constants from the Sarathy et

al.8,9

mechanism for the β-scission directions of these reactions are sensitive to thermodynamic

properties used in the estimation process, the uncertainty limits of the BR2 suggested by the

Satathy et al.8,9

mechanism are likely to overlap with the inferred value of BR2 from the current

experimental data.

As shown in Figure 4.19, calculations of BR2 using the Van Geem et al.62

mechanism,

which are based on RMG estimates, predict a value of BR2 which is significantly below the lower

bound imposed by measurements of BR1BR2. Calculations of BR2 using the Grana et al.40

mechanism exhibit the same problem.

4.5 Conclusions

The overall rate constants for the reactions tert-butanol + OH and ethanol + OH were

measured behind reflected shock waves in a shock tube. In addition, the branching ratio for the β-

scission pathways of the tert-C4H8OH radical as well as the branching ratio for the ethanol + OH

reaction at the β-site were determined. Isotopic labeling of 18

O in tert-butan18

ol and ethan18

ol was

used as a critical tool for overcoming the recycling of OH radicals that typically occurs when

measuring the overall rate constants for reactions of alcohols with OH radicals at high

temperatures. By spectrally distinguishing the recycled 18

OH radicals from the consumed 16

OH

91

radicals, the decay rates of 16

OH in the labeled experiments were sensitive to reactivity of OH at

all reaction sites of the alcohols. To the author’s knowledge, this is the first instance that isotopic

substitution and narrow-linewidth laser absorption have been used for high-temperature reaction

rate constant measurements behind reflected shock waves.

92

5 CHAPTER 5: Cyclohexene

Decomposition Rate Constant

Measurements

5.1 Introduction

A common experimental technique deployed to measure rates of reaction in shock tubes,

especially in single pulse facilities, is the comparative rate method 107

, where the rate constant of

a test reaction is measured relative to that of a reference reaction. If the rate constant for the

reference reaction is well-known, the absolute rate constant for the test reaction can be inferred.

The reference reaction can also be used as a chemical thermometer to explicitly determine the

experimental temperature, which is critical in experiments where the rate constants of the

reference and test reactions have different temperature dependences. Both comparative rate and

chemical thermometry methods require accurate knowledge of the rate constant for the reference

reaction as a function of temperature and pressure.

A common reaction used as reference near 1000 K is the decomposition of cyclohexene

via the pathway shown in Reaction 5.1.

cyclohexene → ethylene + 1,3-butadiene Reaction 5.1

The rate constant for Reaction 5.1 has been studied extensively using a variety of experimental

methods108–120

. Based on the detected species during the decomposition of cyclohexene, all-but-

one of these past studies concluded that Reaction 5.1 is the major decomposition pathway at

temperatures between 700-1200 K. However, a single study119

measured the rate constant for

93

alternative decomposition pathways and found that decomposition to 1,3-cyclohexadiene and H2

accounts for approximately 40% of cyclohexene decomposition at temperatures near 500 K.

Nonetheless, the scientific community generally agrees that Reaction 5.1 is the major

cyclohexene decomposition pathway in the temperature range where cyclohexene decomposition

is typically used as a reference reaction, between 950-1100 K. In this work, the rate constant for

Reaction 5.1 was determined by observing the rate of formation of ethylene using direct laser

absorption during the decomposition of cyclohexene behind reflected shock waves. These appear

to be the most accurate measurements of the rate constant for Reaction 5.1 thus far at elevated

temperatures, and the results are in fair agreement with past studies.

5.2 Experimental Setup

Experiments were performed behind reflected shock waves in the KST shock tube, and

direct laser absorption at 3.39 µm was used to confirm that the initial cyclohexene mole fraction

inside the shock tube was equal to the manometrically calculated value inside the mixing tank.

The ethylene mole fraction was measured using direct laser absorption at 10.532 µm. In this

study, it was necessary to consider absorption of cyclohexene and 1,3-butadiene at 10.532 µm

when calculating the mole fraction of ethylene. Since ethylene and butadiene are stable species at

the conditions in this study, their concentrations are equal in these experiments because they are

produced in a one-to-one ratio via Reaction 5.1. Furthermore, assuming that Reaction 5.1 is the

dominant cyclohexene decomposition pathway, the mole fraction of cyclohexene is related to that

of ethylene by the simple relation:

xethylene= xcyclohexene,initial – xcyclohexene Equation 5.1

94

Therefore, since the mole fractions of cyclohexene, butadiene, and ethylene are directly related,

the ethylene mole fraction can be explicitly calculated from the measured absorbance using the

following equation:

The absorption cross-section of ethylene at 10.532 µm was taken from previous work52

,

and the absorption cross-section of cyclohexene, 1,3-butadiene, and 1,3-cyclohexadiene at 10.532

µm were measured behind reflected shock waves in this study (See Section 2.4.3). Since the

absorption cross-section of cyclohexene is over an order of magnitude lower than that of ethylene

and 1,3-butadiene, the above analysis which accounts for the variations in absorbance caused by

the reduction in the cyclohexene mole fraction results in only a minor perturbation on the

measurement of the ethylene mole fraction. In addition, since the absorption cross-section of 1,3-

cyclohexadiene is low compared to that of ethylene and 1,3-butadiene, and since the alternative

cyclohexene decomposition pathway to 1,3-cyclohexadiene and H2 (which does not absorb

10.532 µm light) is at least an order of magnitude lower than the primary decomposition pathway

shown in Reaction 5.1 (see Section 5.3), decomposition of cyclohexene via this alternative

pathway would not perturb the measured ethylene mole fraction by more than 2.5%.

5.3 Kinetic Modeling

Simulations were performed using ideal shock tube model discussed in Section 2.2.3. A

comprehensive cyclohexane mechanism by Silke et al.121

was used as a basis for secondary

reactions that may occur in the shock tube. However, since this mechanism was not validated for

cyclohexene decomposition, the rate constants of several potential secondary reactions were

95

added and modified based on the latest values suggested in the literature, as summarized in Table

5.1. Though the rate constants for H-atom abstraction reactions from cyclohexene by H-radicals

were not modified, it was verified that these reactions had reasonable rate estimates in the Silke et

al.121

mechanism. The mechanism also indicates that H-radical generation is negligible at the

conditions in this study, because kinetic pathways that lead to H-radicals are at least two orders of

magnitude slower compared to decomposition of cyclohexene via Reaction 5.1. Therefore, since

H-radical generating pathways are very slow at the conditions in this study, simulations are not

affected by these reaction pathways and high-accuracy rate constant estimates for cyclohexene +

H reactions are not necessary.

Reaction k Ref.

Cyclohexene ↔ 2-Cyclohexenyl + H 5.01x1015

exp(-41140/T[K]) 122

1,3-butadiene ↔ C2H2+C2H4 7.00x1012

exp(-33790/T[K]) 123

1,3-butadiene ↔ C4H4+H2 2.50x1015

exp(-47680/T[K]) 124

1,3-butadiene ↔ i-C4H5+H 5.70x1036

T[K]-6.27

exp(-56570/T[K]) 125

1,3-butadiene ↔ n-C4H5+H 5.30x1044

T[K]-8.62

exp(-62240/T[K]) 125

C2H4+Ar ↔ C2H2+H2+Ar 2.61x1016

exp(-34130/T[K]) 52

C2H4+Ar ↔ C2H3+H+Ar 2.59x1017

exp(-48590/T[K]) 126

Table 5.1: Rate constants for reactions modified and added to the Silke at al.121

mechanism.

Units: s-1

(unimolecular), cm3mol

-1s

-1(bimolecular)

As expected, rate-of-production analysis indicates that virtually all chemical processes

occur via Reaction 5.1 at the conditions studied. The mechanism also confirms that 1,3-butadiene

and ethylene are equimolar at low conversion rates of cyclohexene because their overall

unimolecular decomposition rate constants are slower than that of Reaction 5.1 by a factor of 300

at the conditions in this study. This is explicitly confirmed in past studies by Tsang109

and Heyne

et al.127

, the latter of which indicates that ethylene and 1,3-butadiene are equimolar even at 60%

conversion rates of cyclohexene.

96

Simulations were performed with a rate constant estimate for the reaction cyclohexene →

1,3-cyclohexadiene + H2 nominally equal to zero. Though the rate constant for this reaction was

measured previously to be approximately one third of that for Reaction 5.1 near 500 K119

, several

subsequent studies have concluded that this pathway must be negligible at temperatures below

1200 K, based on the observed pyrolysis products of cyclohexene decomposition109,111–113

.

Therefore, past work suggests that this pathway is approximately one to two orders of magnitude

slower compared to that of Reaction 5.1 below 1200 K, though an agreed upon reaction rate

constant in the literature does not exist. Brute force analysis using an assumed rate constant for

the reaction cyclohexene → 1,3-cyclohexadiene + H2 that is up to 10% of the value for Reaction

1 does not perturb the experimentally inferred rate constant for Reaction 5.1 by more than 2%.

This is expected because the decomposition of cyclohexene via alternative pathways does not

significantly perturb the absolute cyclohexene mole fraction at low conversion rates where

simulations were fit to experimental data. Therefore, since the rate of ethylene formation via

Reaction 1 is proportional to the concentration of cyclohexene, it remains unperturbed by

alternative cyclohexene decomposition pathways at low conversion.

At a given post-reflected-shock condition, the rate constant for Reaction 5.1 was inferred

by adjusting its Arrhenius A-factor to achieve a best-fit between simulations and measurements

of ethylene formation. Simulations were performed using a temperature-dependent rate constant

for the Reaction 5.1 in order to account for small temperature changes which may occur

throughout the measurement time at high post-reflected-shock temperatures, due to the

endothermic decomposition of cyclohexene (details are provided in following paragraphs). Data

presented in this study are the values of the rate constant for Reaction 5.1 at the initial post-

reflected-shock temperature, calculated using the fitted Arrhenius A-factor and the Arrhenius

activation energy from the simulation. As a starting point, data were analyzed using a value of the

activation energy for Reaction 5.1 suggested by Tsang (1973)110

. Measurements of the rate

constant as a function of temperature were then used to calculate a new activation energy, and the

97

above data analysis procedure was repeated. Values of the measured reaction rate constant

converged after a single iteration, indicating that a point measurement behind a given reflected

shock wave is insensitive to the activation energy of the rate constant for Reaction 5.1 used to fit

the measured ethylene mole fraction time-history.

Since the rate of ethylene decomposition spans four orders of magnitude across the

temperature range in this study, various strategies were deployed to optimize measurements at

different temperatures. At low temperatures, due to the slow decomposition of ethylene, driver

inserts and driver gas tailoring were used in order to extend the measurement test time to 4 ms

and to eliminate non-ideal effects typically present in shock tubes at long test times. In addition,

the laser beam was passed twice through the diameter of the shock tube at the measurement

location in order to double the sensitivity of the ethylene diagnostic. Finally, an initial

concentration of cyclohexene of 3% was used in order to generate measurable concentrations of

ethylene throughout the test time. At low post-reflected-shock temperatures, temperature remains

constant throughout the test time due to the low conversion of cyclohexene. Based on the

accuracy of the shock speed measurement system, which is discussed at the end of this section,

and the uniformity in pressure observed throughout the test time, it is estimated that temperature

uncertainty throughout the test time in low post-reflected-shock temperature experiments is ±

0.8%.

At high temperatures, endothermic decomposition of cyclohexene causes a slight

temperature drop as a function of time behind the reflected shock wave. This affects

measurements of ethylene mole fraction due to the temperature dependence of the absorption

cross-sections. Furthermore, temperature variations as low as 5 K behind the reflected shock

wave must be taken into account while modeling the ethylene time-histories in order to account

for the time-evolution of the rate constant for Reaction 5.1, which is highly temperature

dependent. In order to minimize the uncertainty in the measured rate constant associated with

temperature changes behind the reflected shock wave, dilute 0.333% mixtures of cyclohexene

98

were used in high post-shock-temperature experiments. Furthermore, rate constants were inferred

by examining ethylene formation at early times when cyclohexene conversation was below 30%

and significant temperature change did not occur. On timescales where data were fitted to

simulations, temperature dropped by no more than 15 K, and absorption cross-sections were

corrected using simulated temperature time-histories, as described in previous work128

. At the

conditions studied, the magnitude of the temperature correction on ethylene mole fraction

measurements was less than 5%. Furthermore, by fitting the rate of ethylene formation using

simulations with a temperature-dependent rate constant for Reaction 5.1, simulations provide

good estimates for the time-evolution of the rate constant for Reaction 5.1 throughout the fitting

time. Since virtually all kinetic reactions in this study occur via Reaction 5.1, the fractional

conversion of cyclohexene to ethylene is directly related to temperature variations via the

adiabatic constraint, an appropriate gas-dynamic model of the shock tube, and accurate

knowledge of the thermodynamic properties of the three major species present in the shock tube.

Therefore kinetic simulations that are constrained to fit the measured ethylene time-histories

accurately predict the corresponding temperature changes inside the shock tube. The uncertainty

in the measured rate constant at high temperatures associated with the choice of gas-dynamic

model was considered in detail, based on the discussion in Section 3.3.2 on simulation of

temperature changes behind reflected shock waves due to endothermic reactions. This uncertainty

can be quantified by fitting the measured ethylene time-histories using both constant-pressure and

constant-volume gas-dynamic models, which result in measured values of the rate constant for

Reaction 5.1 that differ by no more than 2%.

The uncertainty in the initial temperature behind the reflected shock wave, which is

discussed in the following paragraph, for dilute experiments performed at high post-reflected-

shock temperatures is ± 0.35%. Measurements were not performed at temperatures above 1300 K

because the rapid formation of ethylene could not be measured accurately due the limited time

resolution of the ethylene diagnostic, which is approximately 7 µs.

99

The uncertainty of the initial post-reflected-shock temperature is primarily dependent on

the uncertainty in the extrapolated incident shock speed at the endwall of the shock tube. Incident

shock speeds are calculated by monitoring the arrival times of the incident shock wave at a series

of five pressure transducers near the endwall of the shock tube, which produce four

measurements of the average incident shock speed between adjacent pairs of fast-response

pressure transducers. Measured incident shock speeds show a linear attenuation rate of no more

than 0.8 %/m. Incident shock speed measurements between a given pair of pressure transducers

do not deviate from the linear fit used to extrapolate the measured incident shock speeds to the

endwall by more than 0.17%. Therefore it is estimated that the incident shock speed at the

endwall is known to within ± 0.13%, which contributes to an uncertainty in temperature behind

the reflected shock wave of ± 0.26%. These estimates are consistent with the absolute measured

timing error of the incident shock speed measurement system, which was characterized by

mounting all five pressure transducers at the same axial location in the shock tube and monitoring

the time response of the signal rise caused by the incident shock wave. It was observed that the

signals in all five pressure transducers reached the trigger level of the shock speed counters

within 1.1 µs of each other. Given that the typical time interval for an incident shock speed

measurement between a pair pressure transducers at the conditions in this study is 500 µs, a 1.1

µs timing error corresponds to an overall 0.22% uncertainty in the incident shock velocity. This

analysis is consistent with analysis of the uncertainty in the post-reflected-shock temperature

performed by Herbon50

. Furthermore, it is consistent with laser-absorption measurements of

temperature behind reflected shock waves performed in our laboratory by Farooq et al.46

, which

indicate that the mean deviation between the measured and calculated temperature was less than

0.11%. It is noted that the uncertainties in the post-reflected-shock temperature reported here are

primarily systematic and are significantly greater than those suggested by the scatter in the

experimental data. The mean deviation in the rate constant measurements from the Arrhenius fit

100

in this study is 4.3%, which based on the temperature sensitivity of the measured rate constant

suggests that the random uncertainty in the temperature is on the order of 0.15%.

Due to the large number of vibration modes in cyclohexene, the post-reflected-shock

temperature is also sensitive to the cyclohexene concentration in the shock tube, which is known

to within ± 1.5% of the manometrically calculated value. In dilute experiments using 0.333%

cyclohexene, the uncertainty in the initial cyclohexene mole fraction has a negligible effect on the

uncertainty in the post-reflected-shock temperature. However, in experiments using 3%

cyclohexene, the uncertainty in the cyclohexene concentration as well as its thermodynamic

properties contributes approximately ± 0.2% to the uncertainty in the post-reflected-shock

temperature.

5.4 Results

A representative measurement and simulation of the ethylene mole fraction time-history

is shown in Figure 5.1. The data exhibit low noise and simulations show excellent sensitivity to

the target rate constant. The characteristic shape of ethylene formation as a function of time is in

excellent agreement between measurements and simulations even at high temperatures, which

indicates that simulations provide good estimates for the temperature time-history behind the

reflected shock wave throughout the fitting time.

101

0 20 40 60 80 1000.00

0.02

0.04

0.06

0.08

0.10

0.12

Eth

yle

ne

Mo

le F

rac

tio

n [

%]

time [s]

Measurement

kt = 0

= 1226 s-1

1.1kt = 0

0.9kt = 0

Figure 5.1: Representative measurement and simulation of ethylene mole fraction time-histories.

Reaction rate constant for simulations specified at the post-reflected-shock temperature. Note

that the rate constant changes slightly throughout the measurement time due to a small decrease

in temperature. 1% cyclohexene diluted in argon. Post-reflected-shock conditions: T = 1192 K, P

= 3.52 atm.

Measurements of the rate constant for Reaction 5.1 at various temperatures are plotted in

Figure 5.2, and tabulated in APPENDIX A. Data in the current study were acquired from 0.8-3.7

atm and show no pressure dependence across the temperature range studied. Measurements are

best-fit by the Arrhenius expression:

k5.1 = 4.84 x 1014

exp(-31900[K]/T) s-1

The maximum uncertainty in the rate constant measurements in the current work is approximately

± 36% at temperatures below 1000 K, ± 21% at temperatures from 1000-1200 K, and ± 19% at

temperatures above 1200 K. Due to the large temperature sensitivity of the rate constant for

Reaction 5.1, the dominant contributor to the uncertainty in the measured rate constants is the

102

uncertainty in the post-reflected-shock temperature described in detail in the Section 5.3. Overall

uncertainties were calculated by linearly adding the uncertainties due to the following factors

(brackets indicate the contribution to the overall uncertainty in the rate constant for Reaction 5.1):

temperature (± 26% low T, ± 9% high T), pressure (± 1.5% low T, ± 0.7% high T), initial

cyclohexene mole fraction (± 1.5%), absorption cross-section of ethylene and 1,3-butadiene (±

2%), gas-dynamic model in simulations (± 1.5%, high T only), fitting uncertainty (± 2.0%

nominally, ± 5% low T), effect of secondary reactions on kinetic modeling (+ 2.0%, high T only),

effect of secondary reactions on measurement of ethylene (- 2.5%, high T only).

103

0.7 0.8 0.9 1.00.1

1

10

100

1000

10000

1000001250 K 1111 K

Current Study Arrhenius Fit

Previous Work

Lewis et al. Hidaka et al. Barnard et al.

Kiefer et al. (0.48-0.71 atm)

Tsang (1965) Tsang (1970)

Tsang (1973) Newman et al.

Skinner et al. (3 atm) Kraus et al.

k [

s-1]

1000/T [K-1]

kcurrent study

=

4.84 x 1014

exp(-31900 [K]/T) [s-1]

1000 K

Figure 5.2: Measurements of the rate constant for cyclohexene decomposition in the current

study, as well as a comparison with measurements from the literature. Pressure range in the

current study is 0.8-3.7 atm. Pressure in past studies is indicated if measurements were

performed at multiple pressures. Uncertainties in the current study are approximately equal to

the height of the data points.

Measurements in the current work exhibit lower scatter and uncertainty compared to

previous studies. Uncertainties in the reaction rate constant measurements from past studies are

generally on the order of ± a factor of 1.5-3.0. Previous studies show good agreement with the

current work at temperatures below 1250 K, and there exist greater discrepancies between studies

at higher temperatures. Though past studies offer a variety of explanations for the observed

discrepancies at high temperatures, they are not discussed in detail here because the focus of

104

discussion in the current work is at temperatures from 950-1100 K where Reaction 5.1 is typically

used as a reference. In this temperature range, there is variable agreement between studies for this

measured rate constant, as shown in Figure 5.3. It is noted that the Arrhenius rate constant

expressions for some previous studies shown in Figure 5.3 have been extrapolated beyond the

temperature range where measurements were performed. Figure 5.3 demonstrates that

measurements by Barnard et al.112

and Lewis et al. 91

are in good agreement with the current

study. Lewis et al. 113

do not propose a new reaction rate constant expression for Reaction 5.1 and

so it is not presented here. However, rate constant expressions for Reaction 5.1 by Tsang

(1965)108

and Tsang (1970)109

are up to 38% and 64% lower, respectively, compared to

measurements in the current study. Furthermore, rate constant expressions by Tsang (1973)110

,

which are referred to as the “best” estimate among the studies by Tsang108–110

and are also the

most commonly used in chemical thermometry and comparative rate studies129,130

, are up to 45%

lower than the measurements in the current work. Nonetheless, it is noted that rate constant

expressions from the current study and from the studies by Tsang108–110

likely lie within each

other’s combined uncertainties. Finally, measurements by Kraus et al.118

are up to an order of

magnitude lower compared to those in the current and other studies. It is noted that the lack of an

observed pressure dependence of the rate constant for Reaction 5.1 between 0.8-3.7 atm in the

current work indicates that the discrepancies between the past studies discussed here are not

caused by variations in experimental pressure. Analysis of the pressure dependence of Reaction

5.1 in previous work112,114

confirms that all studies discussed above should not exhibit any

significant pressure dependence at temperatures below 1200 K.

105

0.90 0.95 1.00 1.050.1

1

10

100

952 K1111 K 1053 K

k [

s-1]

1000/T [K-1]

Current Study Arrhenius Fit

Previous Work

Tsang (1965) Tsang (1970)

Tsang (1973) Kraus et al.

Barnard et al. Arrhenius Fit

Lewis et al.

1000 K

Figure 5.3: Subset of measurements of the rate constant for cyclohexene decomposition in the

current study, as well as comparisons with measurements from the literature, in the temperature

range where cyclohexene is commonly used as a reference. Pressure range in the current study is

0.8-3.7 atm.

The significance of the discrepancies in the recommended rate constant expressions for

Reaction 5.1 can be quantified by examining the corresponding variations in the inferred

temperature using the chemical thermometry method. As shown in Figure 5.4, the inferred

temperature using the rate constant expression from the current work compared to using the rate

constant expressions from studies by Tsang108–110

is up to 30 K lower at temperatures from 950-

1100 K. Although these modest temperature discrepancies are not unexpected given the

uncertainties in the individual rate constant measurements for cyclohexene decomposition, they

106

may have significant implications for other chemical kinetic studies. The temperature

discrepancies reported here are in excellent agreement with a recent study by Heyne et al.127

,

which indicates that temperature measurements from 950-1000 K in a flow reactor using a

thermocouple are 17K lower compared to calculated values using cyclohexene as a chemical

thermometer, when based on the rate constant for cyclohexene decomposition from Tsang

(1973)110

. It is noted that errors in chemical thermometry or comparative rate methods associated

with variations in the rate constant for Reaction 5.1 are primarily systematic. Therefore, rate

constant measurements from previous studies can be corrected retroactively using the updated

rate constant expression, if desired.

950 1000 1050 1100-20

0

20

40

60

80

100

120

T

[K

]

Tcurrent study

[K]

Tsang (1965)

Tsang (1970)

Tsang (1973)

Barnard et al.

Kraus et al.

Figure 5.4: Difference in the inferred temperature using chemical thermometry. ΔT = Tprevious work

- Tcurrent work, where Tcurrent work is the inferred temperature using the rate constant expression for

Reaction 1 from the current study, and Tprevious work is the inferred temperature using the rate

constant for Reaction 5.1 from previous work.

107

5.5 Conclusions

The rate constant for the reaction cyclohexene → ethylene + 1,3-butadiene was measured

between 950-1300 K and 0.8-3.7 atm. No pressure dependence was observed at these conditions.

Though measurements show fair agreement with previous studies, we believe this is the most

accurate determination of the rate constant for the target reaction to date. Discrepancies with

previous work in the measured rate constant for the target reaction correspond to variations in the

inferred temperature using the chemical thermometry method of approximately 30 K.

108

6 CHAPTER 6: High-Temperature

Acetylene Diagnostic

6.1 Introduction

Acetylene is an important intermediate or product species during the combustion of many

hydrocarbon fuels. It is also one of the primary precursors to soot131

. Improving the experimental

tools available for performing kinetic studies of reacting systems involving acetylene is thus of

significant interest to the combustion community. Due to their MHz time response and in-situ

measurement capabilities, continuous wave (CW) laser absorption diagnostics have become an

invaluable tool for studying chemical kinetics in shock tubes132–134

. Though measurements of the

acetylene mole fraction using scanned wavelength laser absorption, gas chromatography, and

time-of-flight mass spectrometry have already been performed in kinetic studies135–137

, laser

absorption diagnostics optimized for high-temperature, high-temporal resolution studies have not

yet been demonstrated. In this work, a fixed wavelength direct absorption laser diagnostic for

measurements of acetylene concentrations in shock tubes was developed. In addition, the utility

of the proposed diagnostic for performing chemical kinetic studies was demonstrated by

measuring acetylene species time-histories during the pyrolysis of propene and 1-butene.

The IR spectrum of acetylene has been studied in great detail both theoretically and

experimentally. Several of these studies have been used to develop the HITRAN 2012

spectroscopic database138

, which contains a comprehensive description of the acetylene spectrum

in the 3300 cm-1

band that is of primary interest in this work. The acetylene spectrum near this

wavelength is primarily composed of two cold bands, the ν3 band and the ν2 + (ν4+ ν5)0

combination band, as well as at least 18 hot bands 139

. Line positions and intensities for the two

cold bands in the HITRAN 2012 database138

were taken from work by Auwera et al.140

, and air-

109

and self-broadening coefficients were taken from work by Devi et al.141

and Varanasi et al.142

.

Details on the spectral parameters for the hot bands are described by Jacquemart et al.139

. Though

significant effort has been made to include hot transitions in the HITRAN 2012 database138

,

recently measured emission spectra by Moudens et al.143

demonstrate that the database does not

account for several hot-band transitions involving highly excited vibrational levels. Indeed, this is

confirmed experimentally in this work and is discussed in the Section 6.4.

6.2 Experimental Methods

The spectral location of the proposed acetylene diagnostic lies at the peak of the 3300 cm-

1 absorption band, as shown in Figure 1. Though acetylene exhibits stronger absorption near 700

cm-1

, this wavelength is not easily accessible using current lasers. Furthermore, the 3300 cm-1

band offers stronger absorption compared to the 1300 cm-1

and 6500 cm-1

bands which were used

to perform laser absorption measurements of acetylene in previous studies136,137

. Although

simulations using the HITRAN 2012 database138

do not fully agree with experimental

measurements (see Section 6.4), the authors believe that the database is sufficiently accurate for

selecting the optimal wavelength for the proposed diagnostic.

110

1000 2000 30000

1

2

3

4

Ab

so

rpti

on

Co

eff

icie

nt

[cm

-1atm

-1]

Wavenumber [cm-1]

3100 3200 3300 34000.0

0.2

0.4

0.6

0.8

1.0

Proposed Diagnostic

Figure 6.1: Absorption spectrum of acetylene at 1400 K, 1 atm calculated using HITRAN

2012138

. Primary plot shows the entire spectrum from 500-3500 cm-1

, subplot shows spectrum in

the 3300 cm-1

band.

The absorption spectrum of acetylene was measured using scanned-wavelength direct

absorption (DA)144

at room temperature in a 79.9 cm pathlength cell, and at high temperatures

behind reflected shock waves in the Stanford Kinetic Shock Tube. Measurements at room

temperature and pressure were performed in order to characterize the performance of the laser

(Nanoplus DFB laser, λ = 2998 nm @ 30 ºC) and detector systems (Vigo Systems PVI-3TE-4),

and to validate simulations using the HITRAN 2012 database138

at these conditions. Scanned-

wavelength DA measurements were performed from 3335.1 cm-1

to 3335.9 cm-1

using a sawtooth

signal scanned at 1 and 2.5 kHz in the static cell and shock tube, respectively, with a peak-to-peak

modulation current ranging from 200-350 mA (dI/dυ = -38 mA/cm-1

). The ideal constant-volume

(CV) test time in the shock tube was 1 ms, which allowed for at least 2 full scans of the acetylene

spectrum per experiment. All shock tube measurements were performed using 2%

acetylene/argon mixtures purchased from Praxxair (acetone free).

111

The absolute wavelength of the peak of the acetylene absorption feature at room

temperature and pressure was measured using a Bristol 721 wavelength meter (νuncertainty = ±

0.0035 cm-1

). The relative wavelength in scanned-wavelength experiments was determined by

measuring the transmission peak spacing of a solid germanium Fabry-Perot etalon (FSR = 0.0162

cm-1

). The wavelength shift of the peak of the acetylene absorption feature relative to that at room

temperature and pressure was determined by simultaneously measuring the laser intensity of a

secondary beam that was pitched through a 2.5 cm reference cell filled with a 0.2%

acetylene/argon mixture. Since knowledge of the absolute wavelength is not critical during the

implementation of the diagnostic in kinetic studies, the authors recommend centering the laser at

the peak of the acetylene absorption feature at the experimental conditions by adjusting the laser

injection current/wavelength relative to the absorption peak of acetylene in the reference cell.

This laser centering method requires accurate knowledge of the wavelength shift of the peak

absorption coefficient at the experimental conditions relative to that at room temperature and

pressure, as well a precise determination of the injection current-to-wavelength relationship for

the laser device, both of which were measured accurately in this work. The uncertainty in the

relative wavelength using this method is no greater than ± 0.002 cm-1

, which is significantly more

accurate than absolute wavelength measurements using most commercial wavelength meters.

The schematic for the proposed acetylene diagnostic for use in kinetic studies is shown in

Figure 6.2. Due to the sub-0.15% low- and high-frequency noise of the laser/detector system,

normalizing the measured transmitted laser intensity through the shock tube by the measured

laser intensity at a reference detector upstream of the shock tube (common-mode-rejection) was

not necessary. However, due to the relatively low power (~3mW) of the laser used in this work,

measurements indicated that light emission due to acetylene or other hydrocarbons may affect

laser absorption measurements. Therefore, as shown in Figure 6.2, an aperture and a narrow

bandpass filter (CWL = 3332 cm-1

, FWHM = 35 cm-1

) were added downstream of the shock tube

in order to eliminate this potential problem.

112

Figure 6.2: Schematic of the proposed acetylene diagnostic for kinetic studies in shock tubes (BP

= Bandpass)

6.3 Interference Absorption

Simulations using the HITRAN 2012 database138

reveal that interference absorption due

to the major combustion species such as CO, CO2, C2H2, CH4, and H2O (below 4 atm) is

negligible at the target wavelength for measuring acetylene concentrations. In addition, a broad

survey of the absorption spectra of a variety of hydrocarbons using the HITRAN 2012138

and

PNNL56

databases reveals that non-alkyne hydrocarbon species generally do not absorb light at

the target wavelength, because their primary mid-IR absorption band occurs at lower

wavenumbers near 3100 cm-1

.

However, the acetylene diagnostic proposed here will likely be deployed in reacting

systems that contain larger alkynes that also absorb light at the target wavelength. In such

experiments, interference absorption can be eliminated using a two-color technique described in

Section 2.4.1. It is important to note that although this method does not require accurate

knowledge of the absolute absorption coefficient of the interfering species, it does assume that

their absorption coefficients are wavelength independent at the two selected values.

113

Measurements discussed below demonstrate that the absorption coefficients of propyne and 1-

butyne, which are the most likely interfering species56

, are wavelength independent for the

wavelength pairs proposed in this diagnostic. Furthermore, larger alkynes that may interfere with

the proposed acetylene diagnostic are also likely to exhibit broadband absorption near the target

wavelength range.

6.4 Results

As shown in Figure 6.3, the measured acetylene spectrum in air at room temperature and

pressure is in excellent overall agreement with data from the PNNL database and with

simulations using the HITRAN 2012 database138

. However, the wavelength of the measured

absorption peak (3335.545 cm-1

) occurs at 0.0045 cm-1

lower wavenumber compared to

calculations using HITRAN 2012138

(3335.5505 cm-1

). Measurements of the spectral location of

the absorption peak were performed using two separate wavelength meters (Bristol Instruments

Model 721B, MIR and XIR) that yielded the same results, though the discrepancy observed in

this work is barely outside of the combined uncertainties of either wavelength meter and the

HITRAN 2012 database138,145

. However, since the author proposes adjusting the laser wavelength

to the absorption peak of acetylene at the experimental conditions relative to the absorption peak

of acetylene in a reference cell at room temperature and pressure, the discrepancy in the absolute

wavelength described above is not critical to the successful implementation of this diagnostic.

The author notes that as shown in Figure 6.3, the acetylene absorption spectrum in air is

significantly broader compared to that in argon. It is also noteworthy that the absorption feature

shown here is a blend of two comparably strong transitions at 3335.545 cm-1

and 3335.562 cm-1

.

114

3335.2 3335.4 3335.6 3335.80

5

10

15

20

25

30

Ab

so

rpti

on

Co

eff

icie

nt

[cm

-1a

tm-1]

Wavenumber [cm-1]

Measurement (Air)

Measurement (Ar)

HITRAN

2012 (Air)

PNNL (Air)

Figure 6.3: Comparison of the measured absorption spectrum of acetylene with previous work

near 3335.55 cm-1

at 297 K, 1 atm. Brackets indicate the diluent. Measurements were performed

using a 0.0804% mixture in a 79.9 cm static cell.

Though excellent agreement exists between the measurements and simulations at room

temperature and pressure, significant disagreement is evident at elevated temperatures. As shown

in Figure 6.4, simulations using the HITRAN 2012 database138

underpredict the measured

absorption coefficient by up to an order of magnitude at wavelengths away from the primary

absorption features. This is increasingly evident at high temperatures, which suggests that the

HITRAN 2012 database138

does not include all high-temperature transitions necessary for

simulating the absorption spectrum at these conditions143

. Since the HITRAN 2012 database138

was intended for simulating absorption spectra at terrestrial atmospheric temperatures, the

disagreement observed in this work is not unusual. It is noted that the discrepancy described

above cannot be explained by variations in the broadening coefficient of acetylene in air

compared to in argon, because the measurements performed in argon exhibit lower broadening

compared to simulations performed in air (See Figure 6.3). Furthermore, potential absorption due

115

to cold acetylene in the thermal boundary layer of the shock tube cannot explain the observed

discrepancy because the absorption spectrum of acetylene at low temperatures (300-1000 K) is

too narrow.

0

1

2

3

43335.2 3335.4 3335.6 3335.8

Measurement

HITRAN 2012929 K

1.42 atm

0.0

0.5

1.0

1.5

2.0

1226 K

1.45 atm

Ab

so

rpti

on

Co

eff

icie

nt

[cm

-1atm

-1]

3335.2 3335.4 3335.6 3335.80.0

0.2

0.4

0.6

Wavenumber [cm-1]

1586 K

1.66 atm

Wavenumber [cm-1]

Figure 6.4: Comparison of the measured high-temperature absorption spectrum of acetylene

near 3335.55 cm-1

with HITRAN 2012138

simulations. Measurements were performed with

acetylene diluted in argon, simulations assume dilution in air.

Due to the complexity of the acetylene spectrum in the target wavelength range at high

temperatures, spectral fitting using individual lineshape functions was not preferred. Instead,

critical parameters for performing fixed-wavelength DA measurements were extracted and fit

from the measured spectra. The parameters of interest are the peak absorption coefficient, the

wavelength shift of the absorption peak relative to that at room temperature and pressure, and the

116

absorption coefficient at two candidate wavelengths for performing off-line measurements for

characterizing interference. The relevant absorption coefficient measurements are shown in

Figure 6.5, and the least-squares fits for the above parameters are indicated in Equations 6.1-6.4

(T[K], P[atm]):

kν,peak [cm-1

atm-1

]= 2.31x1012

T-3.915

P(-1.013+0.000262 T)

Equation 6.1

λshift [cm-1

] = 0.0071 + 3.75x10-6

T – 0.00291P Equation 6.2

kν,3335.20 [cm-1

atm-1

] = 30200 T-1.711

P(0.928-0.000452 T)

Equation 6.3

kν,3335.82 [cm-1

atm-1

] = 355 T-1.081

P(1.135-0.000726 T)

Equation 6.4

The analytical expressions used to perform the fits of the absorption coefficient data were

selected based on the expected temperature and pressure dependences of the absorption

coefficient at high temperatures. The authors observed that the pressure dependence of the

measurements exhibited a slight dependence on temperature, thus requiring the addition of a

temperature cross term in order to empirically account for this effect. The percentage deviations

of the fits to the measured absorption coefficient data are normally distributed with standard

deviations of 1.7%, 4.6%, and 3.7%, at the peak, 3335.20 cm-1

, and 3335.82 cm-1

, respectively,

which indicates that appropriate functions were chosen to fit the experimental data. As expected,

the fitting errors are greater for non-absorption peak data because the data themselves exhibit

greater uncertainties due to the lower absorbances corresponding to those absorption coefficient

measurements. Off-line wavelengths were chosen based on the local minima in the absorption

coefficient in close proximity to the absorption peak. In order to reduce the effects of emission

using the laser system in this work, the 3335.20 cm-1

wavelength is preferred for off-line

measurements because it is generated at higher laser power.

117

0.1

1

1000 1200 1400 1600 1800

Peak

3335.20 cm-1

3335.82 cm-1

Ab

so

rpti

on

Co

eff

icie

nt

[cm

-1 a

tm-1]

1000 1200 1400 1600 1800

-10

0

10

T [K]

% E

rro

r

T [K]

Figure 6.5: Measured high-temperature absorption coefficient of acetylene at three different

wavelengths near 3335.55 cm-1

, scaled to 1 atm using Equations 6.1-6.4. Data were acquired

from 0.8-4.0 atm. Lines represent the fits using Equations 6.1-6.4. % Errors indicate deviations

of the fits from the measurements. Standard deviations of errors at linecenter, 3335.20 cm-1

, and

3335.82 cm-1

are 1.7%, 4.6%, and 3.7%, respectively.

Equations for fitting the absorption coefficient data were derived based on the expected

pressure and temperature dependence of the peak absorption coefficient at the experimental

conditions. However, it was not possible to apply such an intuitive approach for fitting the

measurement of the shift in the absorption peak because several factors contribute to this

phenomenon. As discussed previously, two strong absorption transitions (ν = 3335.545 cm-1

E” =

359.9 cm-1

, and ν = 3335.562 cm-1

E” = 649.0 cm-1

) contribute to most of the absorption at the

peak. Since the higher-wavenumber transition has a greater lower-state energy, it becomes

118

stronger relative to the lower-wavenumber transition at higher temperatures138

. Therefore, if only

linestrength is considered, the absorption peak shifts to higher wavenumbers at higher

temperatures. On the other hand, as shown in Figure 6.6, the experimental data indicates that at

higher pressures, the sum total of the broadening and shifting of each of the contributing

transitions causes the peak absorption coefficient to shift to lower wavenumbers. It was observed

that a simple linear fit in both temperature and pressure shown in Equation 3 agrees with

experimental measurements to within 0.002 cm-1

, which corresponds to a peak absorption

coefficient uncertainty of only 0.25%.

Uncertainties in the measured spectral parameters were estimated based on the

uncertainties for a variety of experimental factors that may perturb these measurements such as:

post-reflected-shock temperature and pressure, acetylene concentration, beam steering, baseline

drift, and laser noise. The estimated uncertainty of the peak absorption confident measurements

ranges from ± 3 % near 1100 K to ± 5 % near 1700 K. Uncertainties in the absorption coefficient

measurements at the two offline wavelengths are slightly greater due to the lower absorbances

corresponding to these measurements, and they are estimated to be ± 8 %. The uncertainty in the

measured spectral shift of the peak absorption coefficient is approximately ± 0.002 cm-1

.

119

0.000

0.002

0.004

0.006

0.008

0.010

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

P [atm]

1050-1200 K

1200-1400 K

1400-1600 K

1600-1720 K

Fit - 1100 K

Fit - 1700 K

Sh

ift

[cm

-1]

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

-0.002

0.000

0.002

Err

or

[cm

-1]

P [atm]

Figure 6.6: Measured shift of the absorption peak relative to that at room temperature and

pressure (νShift = νHi-temp– νRTP). Errors indicate the deviation of the fit using Equation 6.2 relative

to the experimental data (νError = νFit – νMeasured).Uncertainty in the measurement is approximately

± 0.002 cm-1

.

The primary absorption interference candidates for combustion chemistry studies are

alkyne species such as propyne and 1-butyne. As discussed in the Section 2.4.1, the two-color

technique for inferring the mole fraction of acetylene requires that the absorption coefficient of

the interfering species remains constant at the on-line and off-line wavelengths. This was

confirmed using measurements of the absorption coefficient of propyne and 1-butyne, as shown

in Figure 6.7. Measurements below approximately 1200 K were acquired using scanned-

wavelength DA because these species are relatively stable at lower temperatures. At higher

120

temperatures, separate measurements using fixed-wavelength DA were performed at each

wavelength of interest.

As shown in Figure 6.7, the absorption coefficient of propyne and 1-butyne is

approximately an order of magnitude lower than that of acetylene. Furthermore, it is relatively

pressure independent and constant in the wavelength range of interest. Though measurements

were sufficiently accurate to resolve a slight wavelength dependence of the absorption coefficient

of propyne near 1 atm, the variations are not severe enough to perturb the inferred values of the

acetylene mole fraction. Since the absorption spectra of propyne and 1-butyne are sufficiently

broad in the wavelength range of interest, the author concludes that the absorption spectra of

larger alkynes would exhibit similar wavelength dependence, thus enabling the deployment of the

proposed diagnostic in the presence of these species.

1000 1200 1400 1600 1800

0.10

0.15

0.20

0.25

0.30

0.35

Propyne

Acetylene peak

3335.20 cm-1

3335.82 cm-1

Acetylene peak

1-Butyne

Acetylene peak

3335.20 cm-1

3335.82 cm-1

Ab

so

rpti

on

Co

eff

icie

nt

[cm

-1 a

tm-1]

T [K]

1.3 atm

2.3 atm

1.0 atm

Figure 6.7: Measured high-temperature absorption coefficient of propyne and 1-butyne at three

different wavelengths near 3335.55 cm-1

. Propyne data at the wavelength of the acetylene

absorption peak are fit using the expression: kν, [cm-1

atm-1

]= 0.675 – 3.44x10-4

T[K]. Pressures

are indicated in selected propyne measurements in order to demonstrate that its absorption

coefficient becomes increasingly wavelength independent at higher pressures.

121

6.5 Diagnostic Application

The utility of the acetylene diagnostic proposed here is demonstrated by measuring

acetylene species time-histories during the pyrolysis of 0.75% mixtures of propene and 1-butene

diluted in argon, as shown in Figures 6.8 and 6.9, respectively. Measurements were performed

using the two-color technique described in the Section 2.4.1, and it was observed that

consideration of interference absorption reduced the inferred acetylene mole fraction by

approximately 15% compared to calculations that neglect interference.

0 500 1000 1500 2000 25000.000

0.002

0.004

0.006

0.008

Ac

ety

len

e M

ole

Fra

cti

on

time [s]

1469 K, 1.08 atm 1501 K, 1.07 atm

1528 K, 1.02 atm 1560 K, 1.03 atm

1590 K, 1.01 atm 1628 K, 1.00 atm

Figure 6.8: Acetylene time histories during the pyrolysis of 0.75% propene/argon. Solid lines




reduction in temperature associated with the endothermic pyrolysis of propene. A representative

temperature time-history is shown in Figure 6.10.

122

0 500 1000 1500 2000 25000.000

0.001

0.002

0.003

0.004

0.005

Ac

ety

len

e M

ole

Fra

cti

on

time [s]

1322 K, 1.17 atm 1398 K, 1.13 atm

1443 K, 1.09 atm 1481 K, 1.08 atm

1500 K, 1.07 atm

Figure 6.9: Acetylene time histories during the pyrolysis of 0.75% 1-butene/argon. Solid lines




reduction in temperature associated with the endothermic pyrolysis of 1-butene.

Constant-volume, constant-internal energy (CV) simulations of the acetylene time-

histories using the USC Mech. V2.0 chemical kinetic mechanism 146

demonstrate the utility of the

proposed diagnostic for full chemistry studies at combustion temperatures. As shown in Figure

6.8, the kinetic mechanism agrees reasonably well with measured acetylene time-histories during

the pyrolysis of propene, with the simulations slightly overpredicting the formation rate of

acetylene at early times. However, as shown in Figure 6.9, the mechanism underpredicts the early

formation rate of acetylene during the pyrolysis of 1-butene by at least a factor of three. Though

the discrepancy between the measurements and simulations for 1-butene pyrolysis is of

significant interest to the combustion community, the author wishes to defer rigorous discussions

of the chemical kinetics of 1-butene pyrolysis to future work.

123

It is important to note that the data presented in Figures 6.8 and 6.9 do not account for

variations in the absorption coefficient through the measurement time associated with the

endothermic pyrolysis of propene and 1-butene. Though the initial fuel concentrations in the

current experiments were optimized to produce measurable concentrations of acetylene while

mitigating the temperature drop associated with fuel decomposition, CV simulations indicate that

the temperature may drop by up to 75 K in the current experiments. Indeed, as discussed in

previous work Section 3.3.2, CV simulations of temperature time-histories can be used to

calculate the time evolution of the absorption coefficient with reasonable accuracy in pyrolysis

experiments in shock tubes. Though these simulations are ultimately limited by the accuracy of

the kinetic mechanism, they provide reasonable estimates of temperature time-histories that can

be used to significantly improve the quality of the measured acetylene mole fractions. It is noted

that the measured acetylene time-histories are insensitive to small variations in pressure, because

the change in absorbance caused by a greater number density of molecules (higher pressure) is

largely canceled out by the approximate inverse dependence of the absorption coefficient on

pressure (See Equation 6.1).

As shown in Figure 6.10, the inferred acetylene mole fractions based on CV simulations

of temperature time-histories are up to 25% lower compared to calculations that neglect

reductions in temperature. However, since the goal of current study is primarily to introduce a

new acetylene diagnostic for future use in kinetic research, the author does not wish to present

data that is affected by the choice of kinetic mechanism in this study. Instead, the author proposes

that users of the data presented here correct the measured acetylene time-histories themselves,

based on temperature time-histories generated by the kinetic mechanism of their choice. The

correction can be performed using the Equation 6.5:

( )

( )

Equation 6.5

124

where xcorrected is the inferred acetylene mole fraction, xnominal is the acetylene mole fraction

assuming a constant absorption coefficient (shown in Figures 6.8 and 6.9), kpeak is the peak

acetylene absorption coefficient calculated using Equation 6.1, k3335.20 is the acetylene absorption

coefficient at 3335.20 cm-1

calculated using Equation 6.3. The numerator is calculated at the post

reflected shock conditions indicated in the measurements, and the denominator is calculated at the

post-reflected-shock pressure combined with the estimated temperature time-history from kinetic

simulations. The initial temperature in the kinetic simulations is the initial post-reflected-shock

temperature.

0.000

0.002

0.004

0.006

0 500 1000 1500 2000 2500

Acety

len

e M

ole

Fra

cti

on

Constant T

Variable T

CV Simulation

USC Mech V2.0

T = 1590 K, P = 1.01 atm

0 500 1000 1500 2000 25001500

1550

1600

time [s]

T [

K]

time [s]

Figure 6.10: Representative acetylene time-history during the pyrolysis of 0.75% propene/argon.

T and P indicate initial post-reflected-shock conditions. Variable T data was calculated based on

the simulated temperature time-history using the USC Mech V2.0 kinetic mechanism.

Uncertainties in the Variable T data were estimated based on a 30 K uncertainty in the

temperature profile from the kinetic simulation.

125

The detection limit for the proposed acetylene diagnostic is constrained by the noise in

the measured laser intensity signal, which is primarily caused by steering of the laser beam due to

density gradients behind the reflected shock wave. The overall signal noise in this work

corresponds to an absorbance of approximately 0.002, though lower noise levels may be

attainable with improvements in the optical setup. Assuming an absorbance noise of 0.002 and a

pathlength through the shock tube of 14.13 cm, the detection limit (SNR = 1) of the acetylene

diagnostic at a variety of conditions is shown in Figure 6.11. The author notes that the detection

limit is highly temperature dependent, ranging from 50 ppm at 1100 K to 270 ppm at 1700 K (at 1

atm). In addition, higher pressures offer only modest improvements to the detection limit due to

the reduction in the absorption coefficient caused by pressure broadening.

1000 1200 1400 1600 18000

100

200

300

De

tec

tio

n L

imit

[p

pm

]

T [K]

1 atm

4 atm

Figure 6.11: Estimated detection limit (SNR = 1) of the proposed acetylene diagnostic as a

function of temperature and pressure assuming an absorbance noise of 0.002 and pathlength of

14.13 cm.

126

6.6 Conclusions

A fixed-wavelength direct absorption laser diagnostic for shock tube measurements of

acetylene concentrations was developed. The wavelength for the diagnostic was chosen at the

peak of the 3300 cm-1

band of acetylene at high temperatures. Diagnostic development involved

measurements of the peak absorption coefficient and its spectral location, as well as

measurements of the absorption coefficient away from the absorption peak for the purposes of

interference correction. Empirical fits for all of these parameters valid from 1070-1720 K and 0.8-

4.0 atm were developed. Absorption coefficient measurements for two potential interfering

species, propyne and 1-butyne, were also acquired. Data indicate that their absorption coefficients

are significantly broader compared to that of acetylene, which enables elimination of interference

using simple two-color techniques. The utility of the proposed diagnostic was demonstrated by

measuring acetylene species time-histories during the pyrolysis of propene and 1-butene.

127

7 CHAPTER 7: Summary and Future

Work

7.1 Summary

This work presents a series of experimental studies that were performed in order to

improve the understanding of the chemical kinetics of biofuels. Butanol, which is a promising

alternative fuel with applications in the transportation sector, received considerable attention. In

addition to studying the chemical kinetics of biofuels directly, several experimental techniques

were also developed in order to improve future studies of chemical kinetics.

First, a variety of kinetic targets such as ignition delay times and species time-histories

were measured with high-accuracy during the pyrolysis and oxidation of the four butanol isomers.

These novel data were acquired across a wide range of conditions that span different chemical

kinetic regimes. The data presented here have been used by research groups around the world in

order to validate and improve chemical kinetic models, several of which are now successful in

predicting numerous chemical kinetic targets acquired in a variety of reacting environments.

Second, rate constants for reactions of ethanol and tert-butanol with OH radicals were

measured using direct laser absorption and pseudo-first order techniques. These reactions are one

of the primary removal pathways of fuel during combustion, and they significantly affect the

combustion properties of these fuels. Isotopic labeling of 18

O in the alcohol group was used as a

key tool for overcoming the recycling of OH radicals following H-atom abstraction at β-sites,

which commonly perturbs measurements of rate constants for reactions of alcohols with OH

radicals. This study represents the first application of laser absorption combined with isotopic

labeling to make highly accurate chemical kinetic measurements behind reflected shock waves.

128

Finally, various experimental techniques were developed and improved while performing

these measurements. In addition to the development of isotopic labeling techniques discussed

above, the rate constant for cyclohexene decomposition was determined with the highest accuracy

to date. These measurements are likely to improve a myriad of comparative rate or chemical

thermometry studies that use cyclohexene decomposition as a reference reaction. Critically, the

rate constant measurements acquired here can be used to retroactively correct potential errors in

previous comparative rate studies, in addition to improving future work. Finally, a high-

temperature laser absorption diagnostic for acetylene was developed. Time-resolved shock tube

measurements of this critical combustion intermediate should significantly increase the tools

available for performing chemical kinetic studies. The utility of the diagnostic is evident from the

data presented in this work, because there still exist significant discrepancies in kinetic

mechanisms for describing the kinetics of C1-C4 hydrocarbons.

7.2 Future Work

A primary recommendation for future work in improving the understanding of butanol

kinetics is to consolidate the knowledge acquired during the development of a variety of chemical

kinetic mechanisms for butanol. Currently, a variety of high-quality chemical kinetic targets exist

for validating mechanisms, and several critical reaction rate constants relevant to the pyrolysis

and oxidation of butanol have already been measured and/or calculated using high-level quantum

calculations. However, no single kinetic mechanism has been optimized based on a set of all the

available data. This work is critical for developing a robust chemical kinetic mechanism that can

be used by engineers for designing combustion systems that utilize butanol, and to the author’s

knowledge, several researchers that are a part of the Combustion Energy Frontier Research

Center (the funders of this work) have begun to develop a final chemical kinetic mechanisms that

consolidates all of the currently available knowledge on butanol kinetics.

129

It is evident throughout this work that the branching of various reaction pathways

critically affects the combustion properties of large fuels. As demonstrated in the study of ethanol

+ OH and tert-butanol + OH reactions in this work, isotopic labeling can be used as a key tool for

studying the branching of various chemical reactions. For instance, a simple next step for use of

this technique could be to perform identical experiments performed here to infer the overall and

non-β rate constants for the reaction iso-butanol + OH (iso-butanol is the most promising biofuel

candidate of the four butanol isomers). In addition, in pyrolysis experiments of fuel molecules

that contain multiple oxygen atoms (i.e. methyl esters), selective isotopic labeling of 18

O could be

used in combination with CO measurements to infer which of the O atoms in these molecules

forms CO vs other oxygenated species. Numerous other applications of isotopic labeling of C

atoms could also be used to infer branching during the pyrolysis and oxidation of fuel molecules

and their fragments.

Finally, the acetylene diagnostic developed here could be used a as a powerful tool for

studying the pyrolysis of various hydrocarbons, especially alkenes. The utility of this diagnostic

could be improved if simultaneous measurements of acetylene, ethylene, and methane were

performed, because these species are the primary products of the pyrolysis of many

hydrocarbons. Simultaneous measurements of acetylene and ethylene are particularly useful,

because acetylene is a pyrolysis product of ethylene. Therefore, during the pyrolysis of larger

alkenes, it is unclear whether the production of acetylene is caused by the eventual decomposition

of ethylene, or whether it is being produced by more direct decomposition pathways unique to the

alkenes themselves. Simultaneous measurements of both ethylene and acetylene would help

clarify the overall reaction pathways for the production of both species.

130

7.3 Publications

The work described here has been published and presented in a variety of academic

journals and conferences. Below is a list of the publications that resulted from this work.

Journal Articles

I. Stranic, R. K. Hanson, “Laser Absorption Diagnostic for Measuring Acetylene

Concentrations in Shock Tubes,” Journal of Quantitative Spectroscopy and Radiative

Transfer (Submitted)

I. Stranic, G. A. Pang, R. K. Hanson, D. M. Golden, C. T. Bowman, “Shock tube

measurements of the rate constant for the reaction ethanol + OH,” Journal of Physical

Chemistry A 118 (2014), pp. 822-828

I. Stranic, D. F. Davidson, R. K. Hanson, “Shock tube measurements of the rate constant for

the reaction cyclohexene → ethylene + 1,3-butadiene,” Chemical Physics Letters 584

(2013), pp. 18-23

I. Stranic, G. A. Pang, R. K. Hanson, D. M. Golden, C. T. Bowman, “Shock tube

measurements of the tert-butanol + OH reaction rate and the tert-C4H8OH radical β-

scission branching ratio using isotopic labeling,” Journal of Physical Chemistry A 117

(2013), pp. 4777-4784

I. Stranic, S. H. Pyun, D. F. Davidson, R. K. Hanson, “Multi-species measurements of 2-

butanol and i-butanol pyrolysis behind reflected shock waves,” Combustion and Flame

160 (2013), pp. 1012-1019

131

I. Stranic, S. H. Pyun, D. F. Davidson, R. K. Hanson, “Multi-species measurements of 1-

butanol pyrolysis behind reflected shock waves,” Combustion and Flame 159 (2012), pp.

3242-3250

I. Stranic, D. P. Chase, J. T. Harmon, S. Yang, D. F. Davidson, R. K. Hanson. “Shock tube

measurements of ignition delay times for the butanol isomers,” Combustion and Flame

159 (2012), pp. 516-527

Conference Presentations

I. Stranic, G. A. Pang, D. F. Davidson, R. K. Hanson, D. M. Golden, C. T. Bowman, “Shock

tube measurements of the tert-butanol + OH reaction rate and the tert-C4H8OH radical β-

scission branching ratio using isotopic labeling,” 8th US National Combustion Meeting

(2013), Park City UT, United States


measurements of ignition delay times for the butanol isomers,” 23rd

International

Colloquium on the Dynamics of Explosions and Reacting Systems (2011), Irvine CA,

United States


measurements of ignition delay times for the butanol isomers,” 7th US National

Combustion Meeting (2011), Atlanta GA, United States

132

APPENDIX A: TABLES OF RAW DATA

A.1 Ignition delay times for the butanol isomers

The data presented here pertains to ignition delay times measurements for the butanol

isomers discussed in Chapter 3.

133

XO2 ϕ P [atm] T [K] τign [µs] XO2 ϕ P [atm] T [K] τign [µs]

0.04 1.0 1.51 1274 1013 0.04 0.60-0.75 17.58 1354 73

0.04 1.0 1.38 1420 207 0.04 0.60-0.75 17.71 1311 120

0.04 1.0 1.38 1275 993 0.04 0.60-0.75 17.58 1177 628

0.04 1.0 1.42 1344 468 0.04 0.75-1.0 43.17 1065 1141

0.04 1.0 1.36 1450 158 0.04 0.75-1.0 38.93 1135 532

0.04 1.0 1.47 1320 575 0.04 0.75-1.0 43.04 1118 612

0.04 1.0 1.47 1432 172 0.04 0.75-1.0 41.40 1270 111

0.04 1.0 1.51 1380 296 0.04 0.75-1.0 43.33 1199 226

0.04 1.0 1.34 1458 148 0.04 0.75-1.0 39.61 1111 700

0.04 1.0 1.73 1332 430 0.04 0.75-1.0 46.01 1054 1221

0.04 1.0 1.71 1384 259 0.04 0.75-1.0 43.71 1280 92

0.04 0.5 1.68 1405 153 0.04 0.75-1.0 44.72 1205 207

0.04 0.5 1.76 1339 328 0.04 0.75-1.0 40.92 1198 252

0.04 0.5 1.78 1289 574 0.04 0.75-1.0 40.77 1139 493

0.04 0.5 1.86 1245 1057 0.04 0.75-1.0 40.78 1144 466

0.04 0.5 1.75 1413 134 0.04 0.75-1.0 42.27 1175 320

0.04 1.0 2.78 1336 312 0.04 0.75-1.0 44.02 1205 213

0.04 1.0 2.97 1374 213 0.04 0.75-1.0 44.06 1207 216

0.04 1.0 3.05 1291 506 0.04 0.75-1.0 45.14 1164 330

0.04 1.0 3.19 1247 832 0.04 0.2-0.3 18.92 1239 317

0.04 1.0 3.15 1217 1133 0.04 0.2-0.3 19.74 1156 959

0.04 1.0 3.18 1199 1382 0.04 0.2-0.3 18.65 1321 106

0.04 1.0 2.88 1425 128 0.04 0.2-0.3 19.34 1302 133

0.03 1.0 1.01 1301 1324 0.04 0.2-0.3 19.98 1197 527

0.03 1.0 0.97 1418 326 0.04 0.2-0.3 18.49 1246 289

0.03 1.0 0.99 1355 628 0.04 0.2-0.3 20.19 1138 1119

0.03 1.0 0.93 1505 151 0.04 0.2-0.3 18.58 1302 138

0.03 1.0 1.17 1381 401 0.04 0.2-0.3 18.56 1240 308

0.03 1.0 1.16 1495 141 0.04 0.2-0.3 19.50 1314 111

0.045 1.0 0.95 1230 1560 0.04 1.0 17.94 1317 118

0.045 1.0 0.93 1388 293 0.04 1.0 17.73 1245 283

0.045 1.0 0.96 1312 653 0.04 1.0 18.51 1224 341

0.045 1.0 0.91 1534 90 0.04 1.0 41.12 1268 113

0.04 0.60-0.75 18.24 1166 702 0.04 1.0 44.95 1211 196

0.04 0.60-0.75 18.30 1186 528 0.04 1.0 45.12 1169 314

0.04 0.60-0.75 17.95 1233 297 0.04 1.0 18.71 1263 235

0.04 0.60-0.75 18.47 1137 962 0.04 1.0 18.77 1183 723

0.04 0.60-0.75 18.63 1087 1750 0.04 1.0 18.56 1316 113

0.04 0.60-0.75 17.41 1272 197 0.04 1.0 18.91 1220 434

0.04 0.60-0.75 18.75 1121 1157



134


0.04 1.0 1.59 1360 564 0.03 1.0 1.17 1424 404

0.04 1.0 1.54 1434 263 0.03 1.0 1.24 1331 1094

0.04 1.0 1.44 1503 138 0.06 1.0 1.23 1309 736

0.04 1.0 1.58 1306 1066 0.06 1.0 1.20 1357 430

0.04 1.0 1.42 1549 90 0.06 1.0 1.24 1287 1041

0.04 1.0 1.55 1409 323 0.06 1.0 1.19 1393 292

0.04 1.0 1.47 1465 180 0.06 1.0 1.18 1425 226

0.04 1.0 1.48 1321 936 0.06 1.0 1.27 1300 810

0.04 1.0 1.48 1339 699 0.06 1.0 1.24 1382 330

0.04 1.0 3.26 1406 220 0.04 0.65-0.75 18.12 1192 806

0.04 1.0 3.19 1403 226 0.04 0.65-0.75 18.40 1315 164

0.04 1.0 3.37 1405 217 0.04 0.65-0.75 18.42 1258 337

0.04 1.0 3.41 1385 265 0.04 0.65-0.75 18.47 1125 1697

0.04 1.0 3.53 1367 313 0.04 0.65-0.75 18.69 1242 411

0.04 1.0 3.30 1274 830 0.04 0.65-0.75 18.51 1166 1099

0.04 1.0 3.28 1281 861 0.04 0.65-0.75 17.99 1347 122

0.04 1.0 3.30 1408 214 0.04 0.80-1.05 43.99 1124 780

0.04 1.0 3.44 1329 457 0.04 0.80-1.05 40.49 1176 455

0.04 1.0 3.44 1308 622 0.04 0.80-1.05 42.40 1064 1599

0.04 1.0 3.23 1443 149 0.04 0.80-1.05 44.26 1195 339

0.04 1.0 3.42 1293 721 0.04 0.80-1.05 37.83 1132 820

0.04 1.0 3.56 1294 713 0.04 0.80-1.05 43.21 1242 204

0.04 1.0 3.05 1417 202 0.04 0.80-1.05 42.34 1253 186

0.04 1.0 3.10 1475 113 0.04 0.80-1.05 45.37 1165 472

0.04 1.0 3.46 1260 1011 0.04 0.80-1.05 43.64 1136 672

0.04 0.5 1.74 1385 260 0.04 0.80-1.05 40.75 1069 1505

0.04 0.5 1.80 1334 456 0.04 0.80-1.05 41.31 1308 104

0.04 0.5 1.81 1300 705 0.04 1.0 18.36 1235 483

0.04 0.5 1.87 1269 973 0.04 1.0 18.76 1292 257

0.04 0.5 1.73 1441 137 0.04 1.0 18.59 1337 149

0.04 0.5 3.34 1362 238 0.04 1.0 15.56 1242 457

0.03 1.0 1.19 1468 267 0.04 1.0 41.77 1193 409

0.03 1.0 1.23 1383 602 0.04 1.0 41.93 1270 170

0.03 1.0 1.19 1532 141 0.04 1.0 42.91 1209 334

0.03 1.0 1.16 1399 493 0.04 1.0 43.87 1235 243

0.03 1.0 1.17 1436 349 0.04 1.0 43.77 1119 892



135


0.04 1.0 1.41 1433 322 0.04 0.65-0.90 18.84 1249 304

0.04 1.0 1.51 1381 501 0.04 0.65-0.90 18.86 1189 588

0.04 1.0 1.56 1284 1210 0.04 0.65-0.90 18.11 1322 147

0.04 1.0 1.49 1319 898 0.04 0.65-0.90 18.95 1106 1395

0.04 1.0 1.50 1349 675 0.04 0.65-0.90 17.96 1186 625

0.04 1.0 1.37 1519 142 0.04 0.65-0.90 19.13 1152 866

0.04 1.0 1.41 1483 189 0.04 0.65-0.90 18.90 1136 1020

0.04 1.0 1.49 1486 190 0.04 0.65-0.90 19.02 1120 1207

0.04 1.0 1.51 1485 178 0.04 0.65-0.90 19.76 1121 1148

0.04 1.0 1.38 1588 87 0.04 0.65-0.90 19.42 1070 1949

0.04 1.0 1.69 1376 452 0.04 0.65-0.90 17.88 1358 95

0.04 1.0 1.60 1372 497 0.04 0.65-0.90 18.78 1271 232

0.04 1.0 1.56 1401 371 0.04 0.90-1.05 43.88 1155 381

0.04 1.0 3.38 1437 167 0.04 0.90-1.05 40.92 1072 1041

0.04 1.0 3.27 1363 348 0.04 0.90-1.05 44.61 1143 423

0.04 1.0 3.42 1367 343 0.04 0.90-1.05 44.74 1166 342

0.04 1.0 3.42 1343 406 0.04 0.90-1.05 44.72 1204 225

0.04 1.0 3.30 1286 792 0.04 0.90-1.05 45.75 1131 481

0.04 1.0 3.49 1310 528 0.04 0.90-1.05 44.56 1086 851

0.04 1.0 3.22 1493 107 0.04 0.90-1.05 45.19 1080 903

0.04 1.0 3.41 1271 805 0.04 0.90-1.05 46.36 1225 175

0.04 1.0 3.54 1278 751 0.04 0.90-1.05 47.33 1131 472

0.04 1.0 3.55 1240 1032 0.04 0.90-1.05 47.88 1095 731

0.04 0.5 1.57 1410 250 0.04 0.90-1.05 48.47 1045 1303

0.04 0.5 1.65 1344 487 0.04 0.90-1.05 42.78 1176 332

0.04 0.5 1.72 1298 827 0.04 0.90-1.05 48.50 1022 1840

0.04 0.5 1.74 1265 1133 0.04 0.90-1.05 46.82 1257 132

0.04 0.5 1.56 1496 103 0.04 0.90-1.05 45.44 1281 103

0.03 1.0 1.17 1438 441 0.04 1.0 18.54 1287 234

0.03 1.0 1.13 1551 149 0.04 1.0 18.58 1208 531

0.03 1.0 1.14 1483 293 0.04 1.0 17.84 1314 178

0.03 1.0 1.12 1493 264 0.04 1.0 19.06 1167 770

0.03 1.0 1.18 1586 112 0.04 1.0 43.37 1140 509

0.03 1.0 1.21 1526 188 0.04 1.0 43.55 1223 216

0.04 1.0 43.30 1089 848

Table A-3: Summary of measured ignition delay times for iso-butanol diluted in argon. T and P


136


0.04 1.0 1.47 1464 635 0.03 1.0 1.30 1463 819

0.04 1.0 1.45 1507 370 0.03 1.0 1.28 1510 453

0.04 1.0 1.44 1540 263 0.03 1.0 1.26 1563 226

0.04 1.0 1.39 1615 126 0.03 1.0 1.21 1568 234

0.04 1.0 1.55 1425 995 0.03 1.0 1.26 1656 102

0.04 1.0 1.45 1593 141 0.04 0.75-0.95 18.00 1377 247

0.04 1.0 1.67 1453 625 0.04 0.75-0.95 18.58 1310 515

0.04 1.0 1.70 1405 1135 0.04 0.75-0.95 18.97 1276 847

0.04 1.0 1.48 1458 640 0.04 0.75-0.95 18.29 1442 123

0.04 1.0 1.50 1534 254 0.04 0.75-0.95 17.70 1316 533

0.04 1.0 1.59 1626 106 0.04 0.75-0.95 19.72 1270 853

0.04 1.0 1.61 1447 673 0.04 0.75-0.95 19.62 1240 1214

0.04 1.0 3.06 1503 225 0.04 0.75-0.95 18.25 1319 498

0.04 1.0 3.10 1487 277 0.04 0.75-0.95 19.68 1225 1462

0.04 1.0 3.02 1504 248 0.04 0.75-0.95 17.62 1471 84

0.04 1.0 3.03 1513 220 0.04 0.75-0.95 17.81 1395 207

0.04 1.0 3.00 1516 212 0.04 0.75-0.95 17.91 1469 87

0.04 1.0 3.14 1578 106 0.04 0.95-1.05 46.15 1205 997

0.04 1.0 3.07 1469 358 0.04 0.95-1.05 46.69 1181 1241

0.04 1.0 2.97 1511 239 0.04 0.95-1.05 46.81 1267 427

0.04 1.0 2.96 1516 213 0.04 0.95-1.05 44.00 1249 575

0.04 1.0 2.98 1527 201 0.04 0.95-1.05 45.84 1310 264

0.04 1.0 3.01 1539 161 0.04 0.95-1.05 47.14 1244 575

0.04 1.0 3.19 1489 278 0.04 0.95-1.05 42.97 1286 377

0.04 1.0 3.24 1451 426 0.04 0.95-1.05 44.50 1329 221

0.04 1.0 3.17 1395 804 0.04 0.95-1.05 43.60 1336 212

0.04 1.0 3.24 1428 532 0.04 0.95-1.05 44.44 1223 768

0.04 1.0 3.19 1385 853 0.04 0.95-1.05 43.59 1300 302

0.04 1.0 3.31 1405 690 0.04 0.95-1.05 44.92 1403 91

0.04 1.0 3.33 1395 784 0.04 0.95-1.05 45.21 1374 124

0.04 0.5 1.60 1459 347 0.04 1.0 17.29 1533 52

0.04 0.5 1.67 1389 756 0.04 1.0 17.20 1388 252

0.04 0.5 1.55 1497 212 0.04 1.0 18.52 1317 545

0.04 0.5 1.50 1562 105 0.04 1.0 16.79 1464 111

0.03 1.0 1.02 1479 756 0.04 1.0 42.28 1221 810

0.03 1.0 1.02 1515 472 0.04 1.0 41.78 1322 269

0.03 1.0 0.99 1538 352 0.04 1.0 41.61 1288 382

0.03 1.0 1.36 1432 1112 0.04 1.0 39.93 1345 218

0.03 1.0 1.35 1453 893

Table A-4: Summary of measured ignition delay times for tert-butanol diluted in argon. T and P


137

P [atm] T [K] τign [µs]

19.67 1095 258

20.44 1029 578

21.34 989 1008

19.04 1174 87

22.21 964 1047

22.80 906 1466

24.63 887 1719

26.20 871 1918

24.49 871 1884

22.97 944 1362

25.04 833 2715

24.85 856 2146

Table A-5: Summary of measured ignition delay times for 1-butanol in stoichiometric air.

Mixtures made with N2 and O2 only. T and P values correspond to the initial post-shock

conditions.

138

A.2 Ethanol + OH Rate Constant Measurements

The data presented here pertains to ethanol + OH rate constant measurements discussed

in Chapter 4.

Mixture T [K] P [atm] koverall x 10

-12

[cm3mol

-1s

-1]

349 ppm ethan18

ol

108 ppm TBHP +

H2O

1032 1.08 7.90

1113 1.04 9.08

1078 1.06 8.56

1191 1.04 10.35

353 ppm ethan18

ol

93 ppm TBHP + H2O

1232 1.03 11.00

1230 0.98 10.90

1263 1.00 11.40

995 1.13 7.75

963 1.17 7.54

954 1.19 7.40

285 ppm ethan18

ol

80 ppm TBHP + H2O

935 1.20 7.27

926 1.23 7.03

917 1.16 7.28

1110 1.10 9.20

1141 1.08 9.73

Table A-6: Summary of the measurements of the overall rate constant for the ethanol + OH


139

Mixture T [K] P [atm] knon-β x 10

-12

[cm3mol

-1s

-1]

354 ppm ethan16

ol

64 ppm TBHP + H2O

1032 1.05 6.23

979 1.08 5.62

1023 1.03 6.04

1075 0.99 6.44

1147 0.94 7.18

205 ppm ethan16

ol

60 ppm TBHP + H2O

1137 0.98 7.10

914 1.05 5.65

951 1.05 5.78

988 1.07 5.95

386 ppm ethan16

ol

133 ppm TBHP + H2O

1090 0.85 6.41

1274 1.03 8.45

1196 0.99 7.76

1207 0.98 7.80

1247 1.01 8.15

1148 1.02 7.20

1111 1.03 6.83

229 ppm ethan16

ol

65 ppm TBHP + H2O

986 1.09 5.90

959 1.10 5.84

939 1.13 5.74

921 1.14 5.60

932 1.13 5.74

885 ppm ethan16

ol

170 ppm TBHP + H2O

1065 1.12 6.40

1024 1.16 6.04

207 ppm ethan16

ol

59 ppm TBHP + H2O

930 1.22 5.83

913 1.18 5.62

800 ppm ethan16

ol

59 ppm TBHP + H2O

1020 1.20 5.90

930 1.26 5.50

1123 1.16 6.70

1213 1.08 7.60

910 1.29 5.49

922 1.27 5.60

Table A-7: Summary of the measurements of the non-β rate constant for the ethanol + OH


140

A.3 tert-Butanol + OH Rate Constant Measurements

The data presented here pertains to tert-butanol + OH rate constant measurements

discussed in Chapter 4.

Mixture T [K] P [atm] 16

k' x 1012

[cm3molecule

-1s

-1]

2080 ppm tert-

butan16

ol 100 ppm

TBHP/H2O

948 1.25 1.63

1018 1.25 2.00

1068 1.16 2.37

906 1.26 1.64

1147 1.18 2.93

896 1.32 1.52

997 1.26 1.88

1124 1.12 2.87

1063 ppm tert-

butan16

ol 99 ppm

TBHP/H2O

1113 1.19 2.62

1074 1.22 2.41

976 1.28 1.80

1204 1.16 3.43

1186 1.12 3.52

1056 1.24 2.26

923 1.29 1.59

498 ppm tert-

butan16

ol 100 ppm

TBHP/H2O

1039 1.25 2.10

1149 1.17 2.97

907 1.33 1.58

1161 1.18 3.21

1019 1.27 2.12

307 ppm tert-

butan16

ol 57 ppm

TBHP/H2O

1113 0.99 2.90

1197 0.93 3.47

974 1.15 2.05

1162 0.97 3.23

1166 0.98 3.22

1020 1.05 2.35

1079 1.03 2.55

445 ppm tert-

butan16

ol 52 ppm

TBHP/H2O

943 1.20 1.65

1058 1.06 2.50

902 1.21 1.63

1004 1.13 2.00

962 1.16 1.91



141

Mixture T [K] P [atm] 18

k' x 1012

[cm3molecule

-1s

-1]


ol

168 ppm TBHP/H2O

999 1.23 10.00

1089 1.21 12.40

1047 1.23 11.10

921 1.23 8.66


ol

126 ppm TBHP/H2O

1020 1.22 10.60

1000 1.29 9.47

896 1.34 7.67

1131 1.19 13.80

910 1.32 8.16

1208 1.15 16.00


ol

122 ppm TBHP/H2O

1141 1.21 14.10

1016 1.27 10.50

966 1.33 9.03

1167 1.20 14.40

969 1.30 9.23


ol

133 ppm TBHP/H2O

938 1.30 8.53

928 1.33 8.31



142

A.4 Cyclohexene Decomposition Rate Constant Measurements

The data presented here pertains to rate constant measurements for cyclohexene

decomposition discussed in Chapter 5.

xcyclohexene T [K] P [atm] k [s-1

]

1.00 %

1235 1.91 2830

1172 2.04 764

1080 2.11 68

1027 2.11 15.0

1087 3.72 92

1192 3.52 1230

1227 1.89 2490

1087 3.69 100

1043 3.80 26.4

0.333 %

1265 1.93 5570

1276 3.49 6840

1300 1.24 9610

1126 1.94 245

3.00 %

997 2.03 5.7

1042 1.94 23.6

959 0.82 1.77

975 0.88 3.0

985 1.93 4.2

Table A-10: Summary of the rate constant measurements for cyclohexene decomposition. All

mixtures are balanced in argon.

143

APPENDIX B: ADDITIONAL DATA ON THE PYROLYSIS AND

OXIDATION OF THE BUTANOL ISOMERS

B.1 Ignition Delay Times of 2-Butanol and tert-Butanol

Figures B-1 and B-2 show the measured ignition delay times of 2-butanol and tert-

butanol at various pressures. These data are an extension of the work presented in Chapter 3.

0.65 0.70 0.75 0.80 0.85 0.90 0.95

100

1000

XO

2

= 0.04

P = 43P = 19

P = 3.0

P = 1.5

1111 K1250 K1429 K

= 1

= 0.65-0.75

= 0.80-1.05

t ign [s]

1000/T5 [1/K]

Figure B-1: Measured ignition delay times for 2-butanol, xO2 = 0.04, diluted in argon. Pressure

in atmospheres. Uncertainties are approximately equal to twice the height of the data points.

144

0.60 0.65 0.70 0.75 0.80 0.85

100

1000

P = 43P = 19

P = 3.0

= 1

= 0.75-0.95

= 0.95-1.05

1667 K 1250 K

t ign [s]

1000/T5 [1/K]

1429 K

XO

2

= 0.04

P = 1.5

Figure B-2: Measured ignition delay times for tert-butanol, xO2 = 0.04, diluted in argon.


points.

B.2 Ignition Delay Times of 1-Butanol in Air

Figure B-3 shows measurements of ignition delay times of 1-butanol in stoichiometric air

at high pressures, as well as a comparison with shock tube experiments by Heufer et al.34

.

Relatively good agreement exists at high temperatures, but poor agreement is observed at low

temperatures. This discrepancy is likely associated with significant pre-ignition pressure increases

that are observed at temperatures below 1000 K, as shown in Figures B-4 and B-5. Pre-ignition

pressure increases at low temperatures were also observed in the study by Heufer et al.34

, though

their magnitude is much larger than would be expected if they were caused by typical non-

reactive pressure increases associated with non-ideal shock tube behavior. Experiments

containing pre-ignition pressure increases must be carefully interpreted because significant pre-

ignition pressure increases can cause shock tubes to deviate from their ideal constant-volume

(CV) behavior, and such deviations may vary between different shock tube facilities. The shock

145

tube used in this study (HPST) has an inner diameter of 5 cm, whereas the shock tube used in the

study by Heufer et al.34

has an inner diameter of 14 cm. Therefore, a possible explanation for the

shorter ignition delay times in this study at low temperatures compared to those of Heufer et al. 34

is that the measurement volume in the smaller diameter shock tube used in this study is more

constrained than the measurement volume in shock tube used by Heufer et al.34

. As discussed in

Section 3.2.1, constraining the measurement volume amplifies the temperature increases

associated with pre-ignition heat release, which increases the speed of subsequent chemical

reactions and ultimately reduces the ignition delay time. The increased significance of non-

idealities caused by excessive pre-ignition heat release compared to non-idealities caused by non-

reactive pressure increases associated with shock wave-boundary layer interactions are evident by

the fact that the measured data in this study at low temperatures are shorter than the data in the

study by Heufer et al.34

. In the absence of pre-ignition heat release, one would expect that the

ignition delay time measurements in this study at low temperatures would be longer than those

measured by Heufer et al.34

, because the data by Heufer et al.34

are also subject to a slight non-

reactive pre-ignition pressure rise.

146

0.8 0.9 1.0 1.1 1.2 1.3

100

1000

10000

100000

833 K1000 K

Current Data

Heufer et al.

Vranckx et al.

t ign [s]

1000/T [K-1]

1250 K

Figure B-3:Measured ignition delay times for 1-butanol, P = 20 bar, ϕ = 1, in air. Heufer et

al.34

data is subject to non-reactive, facility-dependent, pre-ignition pressure increases.

0 500 1000 1500 2000

0.0

0.5

1.0

1.5

Sig

na

l [V

]

time [s]

Photodetector - Sidewall



ign



147

0 500 1000 1500 2000 2500 3000 3500

0.0

0.5

1.0

1.5

2.0

ign

Photodetector - Sidewall



Sig

na

l [V

]

time [us]

Figure B-5: Ignition delay time measurement of 1-butanol in stoichiometric air. Initial

reflected shock conditions: T = 833 K, P = 25.0 atm.

The hypothesis that pre-ignition pressure increases are associated with heat release due to

exothermic chemical reactions is further supported by the measured pre-ignition sidewall

photodetector signal increases shown in Figures B-4 and B-5, which suggest that some degree of

burning is occurring inside the measurement volume. However, local ignition outside of the

reaction volume where data are collected can also contribute to the pressure increases observed

inside the measurement volume. Ignition outside of the measurement volume would send

pressure waves into the measurement volume, therefore increasing pressure, temperature, and

speeding up critical chemical reactions. Chaos et al.147

discuss these effects in great detail and

suggest various modeling approaches for interpreting ignition delay time data that contains pre-

ignition pressure increases. However, the study by Chaos et al.147

does not clearly distinguish

non-idealities originating from pre-ignition pressure increase caused by non-ideal shock tube

effects such as shock wave-boundary layer interactions, and non-idealities originating from pre-

ignition pressure increases caused by chemical heat release. These two hypotheses often require

148

different treatment when interpreting shock tube experimental data containing pre-ignition

pressure increases.

In the case of facility dependent pressure rises caused by phenomena unrelated to genuine

pre-ignition heat release, i.e. shock wave-boundary layer interactions or ignition outside of the

measurement volume, the post-shock temperature profile in shock tube ignition time experiments

is effectively higher than the post temperature profile expected in a true CV experiment. In this

case, experimental data underestimates the ignition delay time that would be expected in a true 147

CV experiment due to the temperature increasing non-idealities that are present in a shock tube.

Therefore, a possible correction for the ignition delay time data is to estimate a temperature

higher that the post-reflected shock temperature that more accurately represents the “effective”

temperature that drives chemical processes. A more sophisticated approach is to recognize that a

shock tube does not always behave like an ideal CV reactor, and to model experimental data

using gas-dynamic models that take into account time varying reactor pressure and/or volume.

Several versions of such models are discussed and compared in the study by Chaos et al. 147

.

These models, as well as a “worst case” temperature estimate are used to interpret the ignition

delay time data in the study by Vranckx et al.33

.

However, in the case of pre-ignition pressure increases caused by genuine heat release,

the validity of current time varying pressure/volume models to interpret shock tube experiments

is uncertain. Specifying the time varying pressure/volume profile in simulations is valid when the

observed pre-ignition pressure perturbations are mostly caused by events unrelated to real fuel

chemistry inside the measurement volume, i.e. shock wave boundary layer interactions or perhaps

ignition outside of the measurement volume. In the case of pre-ignition pressure increases

observed in this study, which are too severe to be entirely explained by non-ideal shock tube

behavior, extracting measured pressure profiles for use in simulations may be an invalid approach

because the experimental pressure profile is a sensitive kinetics-driven variable. This is evident

by the difference of the observed pressure profiles at different temperatures, as shown in Figures

149

B-4 and B-5. Furthermore, the significant temperature dependence on pressure means that

specifying large pre-ignition pressure increases in shock tube models constrains the kinetics in

simulations to the underlying temperature profile. Finally, shown in Figures B-4 and B-5, pre-

ignition pressure profiles are often non-linear in which case it becomes difficult to determine a

consistent method for extracting pressure profiles for use in shock tube models, especially after

the measured time of ignition.

Therefore, detailed modeling of 1-butanol ignition delay times in air, including possible

facility-dependent and chemistry dependent-effects, is reserved for future work. Such modeling

would include a 1D description of the shock tube that takes into account interactions between the

reflected shock wave and boundary layer, as well as the interaction between the reflected shock

speed and reflected-shock-region pressure changes.

While there is some uncertainty in the interpretation of shock tube experiments

containing significant pre-ignition pressure increases, similar trends are observed in this study

and in the study by Heufer et al.34

. As shown in Figure B-3, significant rollover in ignition delay

times is observed in both studies, although the precise magnitude of this rollover is unclear. A CV

shock tube model is chosen for comparison with experimental data due limitations of more

sophisticated models discussed above. The mechanism developed by Vranckx et al.33

was

preferred for modeling the experimental data because it includes detailed treatment of low-

temperature/high-pressure chemistry such as that related to H2O2, HO2, and peroxy radicals. As

shown in Figure B-3, kinetic simulations predict significant rollover of ignition delay times,

which are consistent with the experimental data. Simulations also predict significant pre-ignition

pressure increases shown in Figure B-4, or two stage ignition at low temperatures shown in

Figure B-5. The simulated CV pressure traces shown in Figure B-6 exhibit typical autoignition

behavior at temperatures above 900 K. However, at lower temperatures near 850 K, significant

pre-ignition is predicted, eventually leading to two stage ignition at even lower temperatures near

750 K. It should be noted that measured pre-ignition pressure increases at 906 K and measured

150

two-state ignition pressure increases at 833 K occur at higher temperatures than the temperatures

at which similar phenomena are predicted by the Vranckx et al.33

mechanism. This is consistent

with the observation that rollover in ignition delay times occur at higher temperature in this study

compared to simulations. Nonetheless, it is evident that the addition of the simplified butyl

peroxy chemistry in the Vranckx et al.33

mechanism at least partially explains several

observations made in this study.

0 2000 4000 6000 8000

20

22

24

26

28

30

83

3 K

80

0 K

87

0 K

76

9 K

90

9 K

95

2 K

Pre

ss

ure

[a

tm]

time [s]

10

00

K

Figure B-6: Pressure traces from CV autoignition simulations of 1-butanol in stoichiometric air

using the Vranckx et al.33

mechanism. Pinitial = 20 atm. Temperature refers to Tinitial.

B.2 Multi-Species Time-histories for 2-Butanol Pyrolysis

OH and H2O Measurements

Figures B-7 and B-8 show measured OH and H2O time-histories as well as comparisons

with simulations using the Sarathy et al.8,9

mechanism. Peak mole fractions of OH and H2O are

generally underpredicted, though OH is overpredicted at intermediate-to-long time scales. As

discussed in Section 3.3, mole fractions of these two species are highly interdependent because H-

abstraction from butanol by OH is a major production pathway of H2O.

151

0 10 20 30 40 500

20

40

60

OH

Mo

le F

racti

on

[p

pm

]

time [s]

1345 K, 1.89 atm

1382 K, 1.84 atm

1400 K, 1.82 atm

1449 K, 1.80 atm

1498 K, 1.76 atm

1527 K, 1.70 atm

Figure B-7: Measured OH mole fraction for 1% 2-butanol pyrolysis. Solid lines represent


mechanism.

0 200 400 600 8000.000

0.001

0.002

0.003

0.004

H2O

Mo

le F

racti

on

time [s]

1345 K, 1.89 atm

1382 K, 1.84 atm

1400 K, 1.82 atm

1449 K, 1.80 atm

1498 K, 1.76 atm

1527 K, 1.70 atm

Figure B-8: Measured H2O mole fraction for 1% 2-butanol pyrolysis. Solid lines represent


mechanism.

152

However, radical production in 2-butanol pyrolysis is affected by a complicated network

of chemical reactions. First, as shown in Figure B-9, OH time-histories are highly sensitive to the

rate of Reaction B-1, because it is the primary initiator of radical production. 2-C2H4OH and

C2H5, the products of Reaction B-1, decompose to form H radicals, which are then able to abstract

H radicals from 2-butanol to form 2-C4H8OH radicals. Two of these radicals, 2-C4H8OH-m and

sC4H8OH-β, are able to undergo beta-scission to form OH, as shown in Reactions B-2a and B-3a.

2-C4H9OH + M → C2H5+2-C2H4OH Reaction B-1

2-C4H8OH-m → C4H8-1 + OH Reaction B-2a

2-C4H8OH-m → C2H5 + CH2CHOH Reaction B-3b

2-C4H8OH-β → C4H8-2 + OH Reaction B-4a

2-C4H8OH-β → CH3 + CH3CHCHOH Reaction B-5b

However, 2-C4H8OH-m and 2-C4H8OH-β radicals shown in Reactions B-2a and B-3a,

also have competing decomposition pathways that do not form OH, as shown in Reactions B-2b

and B-3b. Therefore, as shown in Figure B-9, the OH mole fraction is sensitive to H-abstraction

branching ratios, as well as to β-scission branching ratios between Reactions B-3a and B-3b. It is

noted that the Sarathy et al.8,9

mechanism describes Reactions B-2a-B-3b in the 2-C4H8OH

formation direction, although they proceed in the sC4H8OH decomposition direction at the

conditions in this study (this convention is used above). Branching ratios between Reactions B-2a

and B-2b are also important, but they do not appear in the sensitivity analysis in Figure B-9

because Reaction B-2b (non-OH producing) is favored by an order of magnitude in the Sarathy et

al.8,9

mechanism. If Reactions B-2a/b had similar rates, OH would have high sensitivity to both.

153

0 20 40 60 80 100

-0.4

0.0

0.4

0.8

1.2

OH

Sen

sit

ivit

y

time [s]

2-C4H

9OH = C

2H

5+2-C

2H

4OH

2-C4H

9OH+H = 2-C

4H

8OH-+H

2

2-C4H

9OH+OH = 2-C

4H

8OH-+H

2O

2-C4H

8OH- = CH

3CHCHOH+CH

3

2-C4H

8OH- = C

4H

8-2+OH

Figure B-9: OH sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1449 K, P = 1.8


mechanism.

The method of macroscopic reversibility, which is used to calculate the reaction rates of

the above beta-scission reactions in the Sarathy et al.8,9

mechanism, has significant uncertainty,

because the thermodynamic information for 2-C4H8OH radicals is not accurately known.

Furthermore, as shown in Figures B-10 and B-11, branching ratios between Reactions B-2a/b and

B-3a/b can be modified to produce a similar effect on OH and H2O time-histories. Therefore,

from our data, it is not clear which of these reactions must be modified, and further study is

necessary in order to improve the 2-butanol kinetic mechanism. It is also unclear from the

sensitivity analysis using the Sarathy et al.8,9

mechanism which reaction rates could be modified

to significantly increase OH mole fractions at early times (<10µs), while significantly reducing

the OH mole fraction at longer times (10µs+), in order to improve agreement with measurements.

154

0 10 20 30 40 500

10

20

30

40

OH

Mo

le F

racti

on

[p

pm

]

time [s]

Measurements

CV Simulations

Unmodified (B-2a/2b = 0.1, B-3a/3b = 0.4)

Modified (B-2a/2b = 1.0, B-3a/3b = 0.4)

Modified (B-2a/2b = 0.1, B-3a/3b =1.7)

Figure B-10: Measured OH mole fraction for 1% 2-butanol pyrolysis. Initial post-reflected-shock

conditions: T = 1449 K, P = 1.8 atm Solid lines represent measurements, dotted lines represent

CV simulations performed using the Sarathy et al.8,9

mechanism.

0 200 400 6000.000

0.001

0.002

0.003

0.004

0.005

0.006

H2O

Mo

le F

racti

on

time [s]

Measurement

CV Simulations

Unmodified (B-2a/2b = 0.1, B-3a/3b = 0.4)

Modified (B-2a/2b = 1.0, B-3a/3b = 0.4)

Modified (B-2a/2b = 0.1, B-3a/3b =1.7)

Figure B-11: Measured H2O mole fraction for 1% 2-butanol pyrolysis. Initial post-reflected-

shock conditions: T = 1449 K, P = 1.8 atm Solid lines represent measurements, dotted lines

represent CV simulations performed using the Sarathy et al.8,9

mechanism

155

C2H4 Measurements

Figure B-12 shows measured C2H4 time-histories for 1% 2-butanol pyrolysis as well as

comparisons with modeling using the Sarathy et al.8,9

mechanism. The experimental data are

overpredicted by simulations, considering the uncertainty in the measurement. As shown in

Figure B-13, C2H4 time-histories are sensitive to Reaction B-1 due to the subsequent

decomposition of C2H5 into C2H4. Though CO, OH, and H2O time-histories suggest that Reaction

B-1 may be too slow, C2H4 time-histories indicate the opposite. In fact, attempts to improve

agreement between measurements and simulations of CO, OH, and H2O by increasing the rate of

Reaction B-1 resulted in far too much C2H4. Therefore, it is unlikely that the Sarathy et al.8,9

mechanism underpredicts the rate of Reaction B-1. Though not shown here, both modifications in

reaction rate ratios shown in Figures B-10 and B-11 slightly improve agreement between

measurements and simulations for C2H4 time-histories.

0 200 400 600 800 10000.000

0.002

0.004

0.006

0.008

C2H

4 M

ole

Fra

cti

on

time [s]

1345 K, 1.89 atm

1382 K, 1.84 atm

1400 K, 1.82 atm

1498 K, 1.76 atm

1527 K, 1.70 atm

Figure B-12: Measured C2H4 mole fraction for 1% 2-butanol pyrolysis. Solid lines represent


mechanism.

156

0 200 400 600 800 1000-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

C2H

4 S

en

sit

ivit

y

time [s]

2-C4H

9OH = C

2H

5+2-C

2H

4OH

C2H

6+H = C

2H

5+H

2

C2H

4+OH = C

2H

3OH+H

C2H

4+CH

3 = C

2H

3+CH

4

2-C4H

9OH+H = 2-C

4H

8OH-+H

2

Figure B-13: C2H4 sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1449 K, P =

1.8 atm. CV simulations performed using the Sarathy et al.8,9

mechanism.

CO Measurements:

Figure B-14 shows measured CO time-histories for 1% 2-butanol pyrolysis at a variety of

temperatures as well as comparisons with modeling using the Sarathy et al.8,9

mechanism. At long

times and high temperatures, CO mole fractions are slightly overpredicted by the simulations.

However, at early times, the simulations greatly underpredict the CO mole fractions. Rate of

production (ROP) analysis indicates that CO is largely produced by the unimolecular

decomposition of CH3CO and HCO, both of which primarily originate from sC2H4OH, which is a

product of Reaction B-1. Therefore, as shown in Figure B-15, CO exhibits strong sensitivity to

this reaction. The most straightforward method for improving agreement between measurements

and simulations of CO at early times is to increase the rate of Reaction B-1. However, as

discussed previously, it is unlikely that this reaction is too slow. Figure B-15 also indicates that

other reactions, none of which have been well studied, exhibit high early-time sensitivity and low

long-time sensitivity and could thus be modified to improve agreement between CO measurement

and simulations. Since there are multiple candidates, modifications to these reaction rates are not

157

proposed in this study. It is important to note that as discussed in Section 3.3.3.2, CO and H2O

contain the majority of O atoms in the system at long times and high temperatures, 90% of which

are accounted for in measurements of CO and H2O. Therefore, it is expected that the CO mole

fraction is overpredicted by simulations at high temperatures and long times given that the H2O

mole fraction is underpredicted.

0 20 40 60 80 400 8000.000

0.001

0.002

0.003

0.004

0.005

0.006

CO

Mo

le F

racti

on

time [s]

1315 K, 1.46 atm

1420 K, 1.40 atm

1565 K, 1.36 atm

Figure B-14: Measured CO mole fraction for 1% 2-butanol pyrolysis. Solid lines represent


mechanism.

158

0 100 200 300 400 500 600-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

CO

Sen

sit

ivit

y

time [s]

2-C4H

9OH = C

2H

5+2-C

2H

4OH

CH3CHO+H = CH

3CO+H

2

2-C2H

4OH = C

2H

3OH+H

2-C4H

9OH+H = 2-C

4H

8OH-m+H

2

2-C4H

9OH+H = 2-C

4H

8OH-+H

2

Figure B-15: CO sensitivity for 1% 2-butanol pyrolysis. Initial Conditions: T = 1603 K, P = 1.36


mechanism.

159

APPENDIX C: UNCERTAINTY ANALYSIS OF ALCOHOL + OH

REACTION RATE CONSTANT MEASUREMENTS

The total uncertainty in the ethanol + OH and tert-butanol + OH reaction rate constant

measurements was calculated by adding the root-mean square sum of the random errors to the

linear sum of systematic errors. The propagated uncertainty in a representative measurement of

the overall rate constant in representative ethanol and tert-butanol experiments due to all

considered uncertainty factors is shown in Figures C-1 and C-2. It is noted that the magnitude of

the uncertainties in several of the uncertainty factors shown in Figures C-1 and C-2 are

temperature dependent. These uncertainties are propagated into the overall uncertainties of the

inferred values for the various branching ratios that were inferred in this work.

0 2 4 6 8

0 2 4 6 8

positive

negative

overall uncertainty

negative only

Total Uncertainty = +21, -26 %

% Uncertainty in koverall

*Temperature (0.3%)

*Pressure (0.6%)

*Absorption baseline (0.05%)

*Wavelength drift (0.032 cm-1)

16OH absorption coefficient (3%)

*Fitting error (3%)

*Time zero (1s)

ethan18

ol enrichment (-1.5%)

*Initial ethan18

ol concentration (2%)

TBHP decomposition rate (30%)

Overall CH3 + OH reaction rate (30%)

k4.1c

/k4.1a

(0 to 1)

CH3CHOH Chemistry

(see discussion){


ethanol + OH associated with each factor considered in the analysis. Random uncertainty factors

are indicated by *, the rest are systematic. Uncertainties are ±, unless specified otherwise. 205

ppm ethan18

ol, 12 ppm TBHP, 35 ppm H2O, diluted in argon. T = 914 K, P = 1.09 atm.

160

0 2 4 6

0 2 4 6

Total Uncertainty = 13%

Rate of Reactions (4.4a/b) (Factor of 3)

% Uncertainty in 18

k'

TBHP decomposition rate (30%)

*Temperature (0.3%)

*Pressure (0.6%)

*Absorption baseline (0.05%)

*Wavelength drift (0.032 cm-1)

16OH absorption coefficient (3%)

*Fitting error (3%)

*Time zero (1s)

tert-butan18

ol enrichment (-1%)

*Initial tert-butan18

ol concentration (2.5%)

Overall CH3 + OH reaction rate (30%)

iso-C4H

8 + OH reaction rate (30%)

negative only


tert-butanol + OH associated with each factor considered in the uncertainty analysis. Random

uncertainty factors are indicated by *, the rest are systematic. Uncertainties are ±, unless

specified otherwise. 500 ppm tert-butan18

ol, 28 ppm TBHP, 81 ppm H2O, diluted in argon. T =

1167 K, P = 1.20 atm.

Though most of the uncertainty factors depicted in Figures C-1 and C-2 are

straightforward, the uncertainty due in the measured rate constant for the reaction ethanol + OH

due to CH3CHOH radical chemistry must be discussed in further detail. The uncertainties in the

decomposition rate of CH3CHOH and the rate of reaction CH3CHOH + OH are considered to be a

factor of 3 and 4, respectively. Uncertainties in these reactions rate constants manifest themselves

as uncertainties in the measurement of the rate constant for the title reaction depending on the

extent to which the CH3CHOH radical acts a sink for 16

OH radicals. An extreme scenario for

secondary 16

OH removal by CH3CHOH occurs if the decomposition rate of CH3CHOH is low,

thus resulting in higher concentrations of this radical, and if the rate constant for the reaction

CH3CHOH + OH is high, thus allowing rapid removal of 16

OH. If this worst case scenario is

161

assumed in the kinetic mechanism, a lower overall and non-β rate constant for the title reaction is

required in order for the kinetic simulations to fit the experimental data. Similarly, the converse

scenario occurs if the decomposition rate of CH3CHOH is high, thus resulting in lower

concentrations of the radical, and if the rate constant of the reaction CH3CHOH + OH is low, thus

reducing the secondary removal of 16

OH. In this case, a higher rate constant for the title reaction

will be required in order for the kinetic simulations to match the experimental data. It is noted that

reactions of 16

OH with other stable secondary species such as ethylene or acetaldehyde do not

significantly contribute to the uncertainties in this study because their rate constants are known

relatively accurately, and they are slower by approximately a factor of 5 compared to the rate

constant for the reaction CH3CHOH + OH.

Since measurements with tert-butan18

ol and ethan18

ol were used to infer the rate constant

for the overall tert-butanol + OH and ethanol + OH reactions, it must be confirmed that kinetic

isotope effects (KIE) do not cause variations in the reaction rates of H-atom abstraction by OH

radicals between the labeled and unlabeled alcohols. Primary KIE are those that involve the

breaking of a bond at the site of kinetic substitution, which in this study occurs at the alcohol

group that reacts with OH through Reaction 4.1c and 4.3b. Due to small changes in both the

overall molecular weight of the alcohols in this study and the vibrational frequency of the OH

bond in the alcohol group, transition state theory predicts that KIE will have a negligible effect on

the rate of Reaction 4.1c and 4.3b. Previous studies have shown that KIE involving breaking of

bonds at molecular sites away from the site of isotopic substitution do not significantly affect

reaction rate constants148,149

. Therefore, given that KIE are negligible for Reactions 4.1c and 4.3b,

they are assumed to be nearly zero for reactions away from the OH site. Since reactions away

from the OH site accounts for the majority of the overall ethanol/tert-butanol + OH reaction, KIE

do not affect the extrapolation of the measurements of the title parameters involving labeled

alcohols to the respective kinetic parameters involving unlabeled alcohols.

162

Kinetic simulations were also used to verify that conversion of 18

OH to 16

OH through the

reaction 18

OH + H216

O ↔ 16

OH + H218

O does not perturb the inferred values of the rate constants

of interest in this work. The rate constant for this reaction was computed using the "Thermo"

code in the MultiWell150

software suite with structures, frequencies and energies from theoretical

calculations by Uchimaru et al.151

. Tunneling corrections were included, and the estimated rate

constant from this study is good agreement with theoretical calculations by Masgrau et al.152

.

163

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SHOCK TUBE STUDIES OF BIOFUEL KINETICS · Units: s-1 3(unimolecular), cm mol-1s-1(bimolecular) Table A-1: Summary of measured ignition delay times for 1-butanol diluted in argon