KINETIC MODELS FOR THE PREDICTION OF WEATHERING OF COMPLEX
MIXTURES ON NATURAL WATERS
By
John McIlroy

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Chemistry—Doctor of Philosophy
2014

ABSTRACT
KINETIC MODELS FOR THE PREDICTION OF WEATHERING OF COMPLEX
MIXTURES ON NATURAL WATERS
By
John McIlroy
Models play a vital role in predicting environmental fates of pollutants, which is
critical for effective remediation. However, many fate and transport models for complex
mixtures, e.g. petroleum products, do not incorporate the individual compounds, which
are responsible for toxicity and environmental persistence.

In this research, a

diesel/water microcosm mimicked an environmental fuel spill with simulated weathering
by evaporation and irradiation. Temporal changes in composition were assessed by gas
chromatography-mass spectrometry (GC-MS) and time of flight mass spectrometry (ToFMS) with atmospheric pressure chemical ionization (APCI).
During evaporation, first-order kinetic rate constants were calculated for selected
compounds and employed to develop predictive models, based on GC retention indices.
Models were initially developed for compounds from individual classes (normal alkane,
branched alkane, alkyl benzene, and polycyclic hydrocarbon) and later expanded to
include compounds from all classes (comprehensive model). Using the comprehensive
model, the rate constants were predicted with an average error of 10%, whereas the class
specific models resulted in less error (4 – 8%). A model was also developed that
incorporated varying temperature (5 to 35 °C), allowing for the prediction of the rate
constants over environmentally relevant temperatures (16 % error).

Using the rate

constant, the fraction remaining of individual compounds was determined. The fraction

ii

remaining of individual compounds was used to calculate the fraction remaining of the
total fuel (± 6%), and was in good agreement with currently available evaporation models.
The variable-temperature model successfully applied to predict the fraction remaining of
other petroleum products, demonstrating applicability beyond diesel fuel. The variabletemperature model was also used to predict chromatographic profiles of a fuel after
evaporation, estimated the length of time a fuel has been evaporated using the predicted
chromatogram, and estimate the time to reach a specific percent evaporated for an
individual compound or for the entire fuel.
First-order kinetic rate constants were also determined for diesel fuel irradiated
with simulated sunlight for 10 hours by GC-MS and APCI-ToF-MS.

The decay of

hydrocarbons and formation of oxygenated compounds began within the first hour of
irradiation. Using GC-MS, a two-fold increase in the rate constant was observed during
irradiation (0.004 – 1.211 h-1) than predicted from the variable-temperature evaporation
model (0.000 – 0.379 h-1). Compounds unlikely to evaporate also decayed, indicating
they were precursors to photooxidation.

In the APCI-ToF-MS, rate constants were

determined for decay of hydrocarbons (0.003 – 0.210 h-1) and formation of oxygenated
compounds (0.002 – 1.173 h-1).

The kinetic rate constants developed in this work

provided valuable information about changes in individual compounds during the
weathering of petroleum products. Predicting changes in individual compounds provides
additional information not available in most current models impact assessment and guide
remediation of petroleum releases.

iii

ACKNOWLEDGEMENTS

I would like to thank everyone that has helped me throughout my time at Michigan
State. I appreciate my advisors, Vicki McGuffin and Dan Jones, for all of their help,
support, and weekly discussions while completing my Ph.D. and Master’s research. I
would also like to thank Ruth Smith for serving as my Master’s advisor, providing help
and guidance throughout my research, and for serving on my committee. Also, thank you
to John McCracken and Ned Jackson for serving on my committee and providing helpful
comments and suggestions in the formulation of this project.
I could not have done this without the support of all of the MSU Chemistry
Department and the current and former members of the McGuffin, Jones, and Forensic
Chemistry research groups. I would like to specifically thank Kathy Severin for help with
instrumentation and Steven Halpin for assistance in writing Matlab algorithms. I have
also been fortunate to receive financial support through the U.S Environmental Protection
Agency’s STAR Fellowship, the J. Edgar Hoover Scientific Scholarship, and Pfizer.
Last, I would like to thank all my friends and family for all of their help and support
throughout the process. In particular I want to thank my wife Katie for everything she did
to help me throughout graduate school.
This document was developed under STAR Fellowship Assistance Agreement no.
FP917295 awarded by the U.S. Environmental Protection Agency (EPA). This work has
not been formally reviewed by EPA. The views expressed in this publication are solely
those of the authors, and EPA does not endorse any products or commercial services
mentioned in this publication.
iv

TABLE OF CONTENTS

LIST OF TABLES ..................................................................................... viii 
LIST OF FIGURES ................................................................................... xiii 
1.  Introduction .......................................................................................... 1 
1.1  Petroleum Release into the Environment ....................................................... 1 
1.2  Petroleum Composition .................................................................................... 2 
1.2.1  Composition of Crude Oil ......................................................................... 2 
1.2.2  Refined Petroleum Products ..................................................................... 7 
1.2.3  Composition of Diesel Fuel ....................................................................... 8 
1.3  Oil Spill Weathering ........................................................................................ 11 
1.3.1  Physical Weathering Processes ............................................................. 12 
1.3.1.1  Evaporation .................................................................................... 12 
1.3.1.2  Spreading ....................................................................................... 14 
1.3.1.3  Dissolution ...................................................................................... 14 
1.3.1.4  Emulsification ................................................................................. 15 
1.3.1.5  Natural Dispersion .......................................................................... 15 
1.3.1.6  Sedimentation ................................................................................ 15 
1.3.2  Chemical Weathering: Photooxidation.................................................... 16 
1.3.3  Biological Weathering: Biodegradation ................................................... 16 
1.4  Analytical Strategies for Characterization of Crude Oil and Petroleum
Products........................................................................................................... 17 
1.4.1  Gas Chromatography ............................................................................. 18 
1.4.2  Liquid Chromatography .......................................................................... 18 
1.4.3  Mass Spectrometry................................................................................. 19 
1.4.4  Strategies for Analysis of Diesel Fuel ..................................................... 21 
1.5  Basis of Predictive Models ............................................................................. 23 
1.5.1  Physical Properties ................................................................................. 23 
1.5.2  Chromatographic Retention Index .......................................................... 24 
1.5.3  Kendrick Mass Defect............................................................................. 25 
1.6  Oil Spill Modeling ............................................................................................ 26 
1.6.1  Fate and Transport Modeling of Oil Spills ............................................... 26 
1.6.2  Evaporation of Petroleum Constituents .................................................. 27 
1.6.2.1  Theory ............................................................................................ 27 
1.6.2.2  Empirical Models ............................................................................ 29 
1.6.2.3  Analytical Model ............................................................................. 32 
1.6.2.4  Pseudo-component Model.............................................................. 38 
1.6.2.5  Kinetic Models ................................................................................ 42 
1.6.3  Photodegradation of Petroleum Products ............................................... 45 
1.6.3.1  Direct photolysis ............................................................................. 46 
1.6.3.2  Indirect Photolysis .......................................................................... 47 
1.6.3.3  Photooxidation Studies ................................................................... 49 
v

1.7  Objectives and Aims ....................................................................................... 52 
REFERENCES .......................................................................................................... 55

2.  Gas Chromatographic Retention Index as a Basis for Predicting
Evaporation Rates of Complex Mixtures ......................................... 67 
2.1  Introduction ..................................................................................................... 67 
2.2  Materials and Methods.................................................................................... 69 
2.2.1  Sample Collection................................................................................... 69 
2.2.2  Evaporation Chamber............................................................................. 70 
2.2.3  Evaporation of Diesel Fuel ..................................................................... 72 
2.2.4  Gas Chromatography-Mass Spectrometry Analysis ............................... 72 
2.2.5  Identification and Quantification of Selected Compounds ...................... 74 
2.3  Results and Discussion .................................................................................. 93 
2.3.1  Determination of Kinetic Rate Constants ................................................ 93 
2.3.2  Predicting Kinetic Rate Constant Based on Boiling Point ..................... 105 
2.3.3  Predicting Kinetic Rate Constant Based on Retention Index ................ 106 
2.3.4  Correction of Retention Indices using McReynolds Constants ............. 115 
2.3.5  Model Validation ................................................................................... 120 
2.4  Applications of the Models........................................................................... 120 
2.5  Conclusions................................................................................................... 132 
REFERENCES ........................................................................................................ 134

3.  Variable-Temperature Model for Predicting Environmental
Evaporation Rates of Petroleum Products using Gas
Chromatographic Retention Indices .............................................. 139 
3.1  Introduction ................................................................................................... 139 
3.2  Materials and Methods.................................................................................. 140 
3.2.1  Sample Collection................................................................................. 140 
3.2.2  Evaporation of Fuel Samples ............................................................... 140 
3.2.3  Gas Chromatography-Mass Spectrometry Analysis ............................. 141 
3.2.4  Data Analysis ....................................................................................... 142 
3.3  Results ........................................................................................................... 154 
3.3.1 
Arrhenius Plots ................................................................................... 202 
3.3.2  Fixed-temperature Models .................................................................... 208 
3.3.3  Variable-Temperature Model ................................................................ 214 
3.3.4  Applications of Model ........................................................................... 215 
3.3.4.1  Calculation of Fraction Remaining with Fluctuating Temperatures
..................................................................................................... 215 
3.3.4.2  Compound Distribution ................................................................. 221 
3.3.4.3  Evaporation Rates of Other Complex Mixtures ............................ 224 
3.3.4.4  Evaporation Time ......................................................................... 230 
3.3.4.5  Time to Specific Fraction Remaining ............................................ 231 
3.3.4.6  Comparison to Other Evaporation Models.................................... 235 
3.4  Discussion and Conclusions ....................................................................... 236 
REFERENCES ........................................................................................................ 240
vi

4.  Determination of Kinetic Rate Constants during Solar-Simulated
Irradiation of Diesel Fuel by Gas Chromatography-Mass
Spectrometry and High Resolution Mass Spectrometry .............. 243 
4.1  Introduction ................................................................................................... 243 
4.2  Materials and Methods.................................................................................. 244 
4.2.1  Collection of Diesel Fuel ....................................................................... 244 
4.2.2  Irradiation of Diesel Fuel....................................................................... 244 
4.2.3  Sample Extraction ................................................................................ 252 
4.2.4  Selection of an Internal Standard ......................................................... 253 
4.2.5  Gas Chromatography-Mass Spectrometry ........................................... 254 
4.2.6  Time of Flight-Mass Spectrometry ........................................................ 255 
4.3  Results ........................................................................................................... 255 
4.3.1  Visual Observations and Mass Change of Diesel Residue................... 255 
4.3.2  Gas Chromatography-Mass Spectrometry of Diesel Residue .............. 256 
4.3.3  Determination of Elemental Formulas by High Resolution Mass
Spectrometry ............................................................................................. 266 
4.3.4  Kendrick Mass Defect........................................................................... 267 
4.3.5  Principal Component Analysis .............................................................. 271 
4.3.6  Determination of Photooxidation Rate Constants ................................. 274 
4.3.6.1  Kinetic Rate Constants Determined from Gas Chromatography-Mass
Spectrometry ................................................................................ 277 
4.3.6.2  Kinetic Rate Constants Determined from High Resolution Mass
Spectrometry ................................................................................ 279 
4.3.7  Analysis of Precipitate formed during Irradiation of Diesel Fuel ........... 298 
4.4  Discussion and Conclusions ....................................................................... 303 
REFERENCES ........................................................................................................ 308

5.  Conclusions and Future Works ...................................................... 312 
5.1  Evaporation ................................................................................................... 312 
5.1.1  Conclusions .......................................................................................... 312 
5.1.2  Limitations ............................................................................................ 314 
5.1.3  Future Directions .................................................................................. 315 
5.2  Photooxidation .............................................................................................. 317 
5.2.1  Conclusions .......................................................................................... 317 
5.2.2  Limitations ............................................................................................ 318 
5.2.3  Future Directions .................................................................................. 320 
REFERENCES ........................................................................................................ 322 

vii

LIST OF TABLES

Table 1-1. Common defined compound classes found in crude oil. For each class,
several example compounds are listed. The example structure is of the bolded example
compound. ...................................................................................................................... 4 
Table 1-2. Selected properties of petroleum and petroleum products. ............................ 5 
Table 1-3. Distillation temperature and carbon range for typical petroleum products [10,
11].
10 
Table 2-1. The injection parameters optimized using the precision in peak area of a
mixture of five normal alkanes. ...................................................................................... 75 
Table 2-2. Selected compounds monitored during evaporation of diesel fuel to develop
the model. The following information is listed for each compound: compound class,
peak number (#) (corresponding to peaks labeled in Figure 2-3 – Figure 2-8), mass-tocharge ratio (m/z) of extracted ion chromatogram used for quantification, retention time
(tTR), boiling point (TB), retention index (IT), rate constant (k), characteristic lifetime (),
and number of  in 300 hours. For the compound class the follow abbreviations were
used: normal alkane (Norm), branched alkane (Bran), alkyl aromatic (Arom), polycyclic
hydrocarbon (Poly). ....................................................................................................... 77 
Table 2-3. Selected compounds monitored during evaporation of diesel fuel to validate
the model. The following information is listed for each unidentified compound:
compound class, mass-to-charge ratio (m/z) of extracted ion chromatogram used for
quantification, retention time (tTR), retention index (IT), rate constant (k), characteristic
lifetime (), and number of  in 300 hours. The absolute percent error (APE) between
the experimental and predicted rate constant is also shown. ........................................ 91 
Table 2-4. Compounds utilized to confirm linearity of calibration curves. For each
compound, the retention time (tTR), concentration range, slope (m), intercept (b), and
coefficient of determination (R2) are shown. .................................................................. 94 
Table 2-5. Class-specific models developed to predict the rate constant, based on the
uncorrected retention index. For each model, the number of compounds used to create
the model (n) as well as the slope (m), intercept (b), and coefficient of determination
(R2) for Equation 2-3 are shown. In addition, the mean absolute percent error (MAPE)
for predicting compounds in each class is shown. For the compound class the follow
abbreviations were used: normal alkane (Norm), branched alkane (Bran), alkyl aromatic
(Arom), polycyclic hydrocarbon (Poly). ........................................................................ 110 
Table 2-6. Class-specific models developed to predict the rate constant, based on the
corrected retention index. For each model, the number of compounds used to create
the model (n) as well as the slope (m), intercept (b), and coefficient of determination
viii

(R2) for Equation 2-3 are shown. In addition, the mean absolute percent error (MAPE)
for predicting compounds in each class is shown. For the compound class the follow
abbreviations were used: normal alkane (Norm), branched alkane (Bran), alkyl aromatic
(Arom), polycyclic hydrocarbon (Poly). ........................................................................ 119 
Table 2-7. Fraction remaining (FIT) for selected compounds in evaporated diesel fuel
(20 °C, 100 h), experimental and predicted using the comprehensive model with
retention index (IT) correction. The absolute percent error (APE) is also shown. ....... 124 
Table 3-1. Selected compounds monitored during evaporation of diesel fuel for
development of fixed-temperature and variable-temperature models. The following
information is listed for each compound: Peak number in Table 3-3 – Table 3-12 (Peak
#), the identity of the compound, the class to which the compound was assigned, the
mass-to-charge (m/z) ratio of the extracted ion chromatogram (EIC) used to quantify the
compound, the retention time (tTR), the boiling point (Tb), and retention index (IT) before
and after correction. .................................................................................................... 143 
Table 3-2. Selected compounds monitored during evaporation of diesel fuel for
validation of fixed-temperature and variable-temperature models. The following
information is listed for each compound: Peak number in Table 3-3 – Table 3-12 (Peak
#), the class to which the compound was assigned, the mass-to-charge (m/z) ratio of
the extracted ion chromatogram (EIC) used to quantify the compound, the retention time
(tTR), and retention index (IT) before and after correction. ........................................... 151 
Table 3-3. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 5 °C. The predicted rate constant (kpred) and absolute
precent error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 16 – 37, 43 – 45, 72 – 77). Several compounds had retention indices
less than 800 (peaks 1, 38, 46) and were also excluded, as the retention index could not
be accurately extrapolated. ......................................................................................... 156 
Table 3-4. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel
evaporated at 5 °C. The predicted rate constant (kpred) and absolute precent error
(APE) was calculated using the fixed-temperature (fixed T) and variable-temperature
(variable T) models. Compounds with  > 0.5 in 300 h were excluded from the table
(peaks 80, 84, 85, 105, 106). ...................................................................................... 162 
Table 3-5. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 10 °C. The predicted rate constant (kpred) and absolute
precent error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 19 – 37, 43 – 45, 73 – 77). Several compounds had retention indices

ix

lower than 800 (peaks 1, 38, 46) and were also excluded, as the retention index could
not be accurately extrapolated. ................................................................................... 165 
Table 3-6. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel
evaporated at 10 °C. The predicted rate constant (kpred) and absolute precent error
(APE) was calculated using the fixed-temperature (fixed T) and variable-temperature
(variable T) models. Compounds with  > 0.5 in 300 h were excluded from the table
(peaks 80, 84, 85, 105, 106). ...................................................................................... 171 
Table 3-7. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 20 °C. The predicted rate constant (kpred) and absolute
precent error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 23-37, 44, 45, 57). Several compounds had retention indices lower
than 800 (peaks 1, 38, 46) and were also excluded, as the retention index could not be
accurately extrapolated. .............................................................................................. 174 
Table 3-8. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel
evaporated at 20 °C. The predicted rate constant (kpred) and absolute precent error
(APE) was calculated using the fixed-temperature (fixed T) and variable-temperature
(variable T) models. Compounds with  > 0.5 in 300 h were excluded from the table
(peaks 80, 85, 105, 106). ............................................................................................ 180 
Table 3-9. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 30 °C. The predicted rate constant (kpred) and absolute
precent error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 24 – 37, 45, 77). Several compounds had retention indices lower than
800 (peaks 1, 38, 46) and were also excluded, as the retention index could not be
accurately extrapolated. .............................................................................................. 183 
Table 3-10. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel
evaporated at 30 °C. The predicted rate constant (kpred) and absolute precent error
(APE) was calculated using the fixed-temperature (fixed T) and variable-temperature
(variable T) models. Compounds with  > 0.5 in 300 h were excluded from the table.189 
Table 3-11. For model development, the experimental rate constant (kexp),
characteristic lifetime (), and the number of  in 300 h for selected compounds
monitored during the evaporation of diesel fuel at 35 °C. The predicted rate constant
(kpred) and absolute precent error (APE) was calculated using the fixed-temperature
(fixed T) and variable-temperature (variable T) models. Compounds with  > 0.5 in 300

x

h were excluded from the table (peaks 26 – 37, 45). Several compounds had retention
indices lower than 800 (peaks 1, 38, 46) and were also excluded, as the retention index
could not be accurately extrapolated. .......................................................................... 192 
Table 3-12. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel
evaporated at 35 °C. The predicted rate constant (kpred) and absolute precent error
(APE) was calculated using the fixed-temperature (fixed T) and variable-temperature
(variable T) models. Compounds with  > 0.5 in 300 h were excluded from the table.199 
Table 3-13. The activation energy (EA), pre-exponential factor (A), coefficient of
determination (R2) determined from the Arrhenius plot of using all temperatures (5, 10,
20, 30, 35 °C). ............................................................................................................. 204 
Table 3-14. The activation energy (EA), pre-exponential factor (A), coefficient of
determination (R2) determined from the Arrhenius plot of using the three highest
temperatures (20, 30, 35 °C). The enthalpy of vaporization (Hvap) from the literature and
the enthalpy of activation (HA) determined from the Arrhenius plot and Equation 3-3 as
well as the difference between the two values (Hvap - HA) are also shown. ................. 206 
Table 3-15. The fixed temperature models developed for each temperature, including
the number of compounds (n), the slope (m), intercept (b), and coefficient of
determination (R2) for linear regression with Equation 3-4 are shown. Also shown is the
mean absolute percent error (MAPE) in the prediction of the rate consent for each
temperature using the fixed temperature models as well as the variable temperature
model (Equation 3-6). .................................................................................................. 210 
Table 3-16. The rate constant (k) at each temperature for decalin (RI = 1045), which
was not included in the original model. The observed rate constant (kobs) as well as the
experimentally predicted (kexp) rate constant using the fixed temperature and variable
model is also shown. The absolute percent error (APE) between the experimental and
predicted rate constants are shown for each model. ................................................... 213 
Table 3-17. The mean absolute percent error (MAPE) for 29 compounds using the
corresponding fixed temperature model (Table 3-15) and the variable temperature
model (Equation 3-6). .................................................................................................. 216 
Table 3-18. The fraction of fuel remaining predicted using the variable-temperature
model with temperature data collected every two minutes, every five hours, every twelve
hours, and the running average temperature (Figure 3-3). The experimental fraction of
fuel remaining (FIT) based on the average change in mass was 0.83. The percent error
between the experimental and predicted values using the model is also shown. In
addition, the percent error between the models using the 2-min temperature interval
compared to the longer intervals is shown. ................................................................. 219 
Table 4-1. A list of compounds monitored by the GC-MS experiment. For each
compound the mass-to-charge (m/z) ratio for the extracted ion chromatogram, the

xi

retention time (tR), retention index (IT), the observed rate constant (kobs), and a predicted
rate constant (kpre) for evaporation available from Chapter 3. ..................................... 259 
Table 4-2. The exact mass, the number of carbon atoms (C), the number of hydrogen
atoms (H), the number of oxygen atoms (O), the double bond equivalence (DBE), the
Kendrick mass defect (KMD), the rate constant for decay (kd), and the uncertainty in the
rate constant for compounds identified using mass spectrometry. .............................. 281 
Table 4-3. The exact mass, the number of carbon atoms (C), the number of hydrogen
atoms (H), the number of oxygen atoms (O), the double bond equivalence (DBE), the
Kendrick mass defect (KMD), the first (1st) and zeroth (0th) rate constant for formation
(kf), and the uncertainty in the rate constant for compounds identified using mass
spectrometry. .............................................................................................................. 291 

xii

LIST OF FIGURES

Figure 1-1. Sample distillation curve of Alaska North Slope oil (southern pipeline).
Distillation data from National Oceanic and Atmospheric and Administration’s ADIOS 2
modelling program [18].................................................................................................... 9 
Figure 1-2. Different weathering processes effecting a petroleum release in the
environment. The thickness of the line indicates the contribution of weathering process.
Figure adapted from National Oceanic and Atmospheric and Administration and the
American Petroleum Institute [6, 22]. ............................................................................ 13 
Figure 1-3. A compound in oil (C) becoming oxidized (Cox) via indirect photolysis. A
sensitizer (S) absorbs sunlight and enters an excited singlet state (1S*). The sensitizer
can react with oxygen to form reactive oxygen species (ROS), which can then oxidize
C. Through intersystem crossing, the 1S* can enter the triplet state (3S*), which can
directly oxidize C or can react with oxygen, to form singlet oxygen (1O2). Singlet oxygen
can then oxidize C. Figure adapted from Schwarzenbach et al. [87]........................... 48 
Figure 2-1. Schematic diagram of the evaporation chamber in temperature-controlled
incubator. See Section 2.2.2 for detailed description. .................................................. 71 
Figure 2-2. Total ion chromatogram for diesel fuel. The bottom trace is an expanded
portion of the chromatogram, showing the region where more volatile compounds are
observed. ...................................................................................................................... 83 
Figure 2-3. Extracted ion chromatogram of m/z 57 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2. ...................................................................................................................... 84 
Figure 2-4. Extracted ion chromatogram of m/z 83 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2. ...................................................................................................................... 85 
Figure 2-5. Extracted ion chromatogram of m/z 91 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2. ...................................................................................................................... 86 
Figure 2-6. Extracted ion chromatogram of m/z 105 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2. ...................................................................................................................... 87 
xiii

Figure 2-7. Extracted ion chromatogram of m/z 117 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2. ...................................................................................................................... 88 
Figure 2-8. Extracted ion chromatogram of m/z 128 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak number corresponds to the compound listed in
Table 2-2. ...................................................................................................................... 89 
Figure 2-9. Total ion chromatograms of diesel fuel evaporated at 20 °C for 0 – 300 h.
For reference, selected n-alkanes are labeled by carbon number. n-Heneicosane (C21)
was used for normalization (*). ...................................................................................... 96 
Figure 2-10. Residual abundances of n-octane (a), n-decane (b), n-dodecane (c), and
n-tetradecane (d) as a function of evaporation time normalized to the peak height of nheneicosane in the EIC at m/z 57. Linear regression equations: n-octane: Ct = 0.448 *
exp (-2.26 * 10-1 * t), R2 = 0.980, F = 3882; n-decane: Ct = 5.926 * exp (-2.01 * 10-2 * t),
R2 = 0.982, F = 4359; n-dodecane: Ct = 10.475 * exp (-2.20 *10-3 * t), R2 = 0.807, F =
330; n-tetradecane: Ct = 9.276 * exp (-0.00 * 100 * t), R2 = 0.000, F = 0. The rate
constant, k, is underlined in each equation. .................................................................. 97 
Figure 2-11. A chromatogram of unevaporated diesel fuel showing the compounds with
decay curves corresponding to >5  (blue), 5 – 1  (yellow), 1 – 0.5  (red), and <0.5 
(green). 101 
Figure 2-12. The coefficient of determination (a) F-statistic (b), and relative standard
deviation for each compound versus the number of tau () in the decay curve. The inset
in a shows an expanded region, from 0 – 5. .............................................................. 103 
Figure 2-13. Natural logarithm of evaporation rate constant (ln (k)) versus boiling point
for normal alkanes (a). Linear regression equation: y = -5.09 * 10-2 * x + 18.83, R2 =
0.999, n = 5. Natural logarithm of evaporation rate constant (ln(k)) versus boiling point
for all selected compound classes (b): normal alkanes (), branched alkanes (), alkyl
benzenes (), and polycyclic hydrocarbons (). Linear regression equation: y = -4.51 *
10-2 * x + 16.71, R2 = 0.961, n = 23. Compound with the * indicates naphthalene, which
sublimes and likely contains large error in the boiling point. Boiling point versus
chromatographic retention index on HP-1MS stationary phase (c). Linear regression
equation: y = 2.33 * 10-1 * x + 213.2, R2 = 0.991, n = 23. ............................................ 107 
Figure 2-14. Natural logarithm of evaporation rate constant (ln (k)) versus
chromatographic retention index on HP-1MS stationary phase for all selected
compound classes: normal alkanes (), branched alkanes (), alkyl benzenes (), and
polycyclic hydrocarbons (). The linear regression of each model is shown: normal
alkanes (green), branched alkanes (blue), alkyl benzenes (red), polycyclic hydrocarbons
(purple), and comprehensive (black). The regression equations are shown in Table 2-5.
111 

xiv

Figure 2-15. Natural logarithm of evaporation rate constant (ln (k)) versus
chromatographic retention index on HP-1MS stationary phase for all compound classes:
normal alkanes (), branched alkanes (), alkyl benzenes (), and polycyclic
hydrocarbons (). Linear regression equation: y = -1.04 * 10-2 * x + 6.70, R2 = 0.981, n
= 51. 113 
Figure 2-16. Natural logarithm of evaporation rate constant (ln (k)) versus corrected
chromatographic retention index on HP-1MS stationary phase for all selected
compound classes: normal alkanes (), branched alkanes (), alkyl benzenes (), and
polycyclic hydrocarbons (). The linear regression of each model is shown: normal
alkanes (green), branched alkanes (blue), alkyl benzenes (red), polycyclic hydrocarbons
(purple), and comprehensive (black). .......................................................................... 117 
Figure 2-17. Natural logarithm of evaporation rate constant (ln (k)) versus corrected
chromatographic retention index on HP-1MS stationary phase for all compound classes:
normal alkanes (), branched alkanes (), alkyl benzenes (), and polycyclic
hydrocarbons (). Linear regression equation: y = -1.05 *10-2 * x + 6.71, R2 = 0.990, n
= 51. 118 
Figure 2-18. Total ion chromatogram of diesel fuel with the fraction remaining at each
retention index (red dashed line) for evaporation at 20 °C for 100 h. .......................... 122 
Figure 2-19. Total ion chromatogram for kerosene (a) and marine fuel stabilizer (b).
The peak numbers correspond to the compounds listed in Table 2-2. ........................ 131 
Figure 3-1. Representative total ion chromatograms of diesel samples prior to
evaporation and after evaporation for 300 h at 5 – 35 °C. Even-numbered normal
alkanes are labeled for reference. ............................................................................... 155 
Figure 3-2. Natural logarithm of evaporation rate constant (ln (k)) versus retention index
for selected compounds. Linear regression equations: 5 °C (×) y = -1.12 * 10-2 * x +
6.78, R2 = 0.987, n = 42; 10 °C (), y = -1.05 * 10-2 * x + 6.17, R2 = 0.982, n = 46; 20 °C
(), y = -1.05 * 10-2 * x + 6.71, R2 = 0.990, n = 51; 30 °C (), y = -1.02 * 10-2 * x + 7.35,
R2 = 0.995, n = 58; 35 °C (), y = -1.00 * 10-2 * x + 7.62, R2 = 0.993, n = 61. .............. 209 
Figure 3-3. The temperature profile (a) of the fluctuating evaporation experiment with
the temperature recorded every two minutes (solid line) and as a running average
temperature (dashed line). The temperatures at 5-h intervals (circles) and 12-h
intervals (stars) are also shown. The fraction of fuel remaining (b) calculated using the
variable temperature model using the temperature at 2 min intervals (solid line) 5-h
intervals (circles), 12-h intervals (stars), and running average temperature (dashed line).
The percent fuel remaining is shown in Table 3-18. .................................................... 218 
Figure 3-4. The fraction remaining curve (a) predicted using the variable temperature
model, using the average temperature (17.1 °C) during the fluctuating temperature
experiment (100 h). Also shown are chromatograms of diesel fuel (normalized to
heneicosane), unevaporated (b), predicted by multiplying the unevaporated

xv

chromatogram (b) by the fraction remaining curve (a), and the actual chromatogram of
diesel fuel after the fluctuating temperature experiment (d). ....................................... 222 
Figure 3-5. A chromatogram of diesel fuel prior to evaporation (a) and after 100 h
evaporation at 20 °C (b). In part b, the solid black chromatogram represents the
experimentally evaporated fuel, while the red dashed line represents the predicted
distribution of compounds, using the variable temperature model. The numbers
correspond to peak numbers given in Table 3-1. ........................................................ 226 
Figure 3-6. A chromatogram of kerosene prior to evaporation (a) and after 100 h
evaporation at 20 °C (b). In part b, the solid black chromatogram represents the
experimentally evaporated fuel, while the red dashed line represents the predicted
distribution of compounds, using the variable temperature model. The numbers
correspond to peak numbers given in Table 3-1. ........................................................ 227 
Figure 3-7. A chromatogram of marine fuel stabilizer prior to evaporation (a) and after
100 h evaporation at 20 °C (b). In part b, the solid black chromatogram represents the
experimentally evaporated fuel, while the red dashed line represents the predicted
distribution of compounds, using the variable temperature model. The numbers
correspond to peak numbers given in Table 3-1. ........................................................ 228 
Figure 3-8. The Pearson product-moment correlation (PPMC) coefficients between a
chromatogram of diesel fuel evaporated on water for 100 h at 20 °C and the predicted
evaporation chromatogram, based on the variable-temperature model for 0 – 1000 h
tested at 1-h intervals. The PPMC coefficient maximized at 117 h (0.9986), with values
greater than 0.998 from 89 – 151 h. ............................................................................ 233 
Figure 3-9. The predicted fraction remaining, using the variable-temperature model
(Equation 10), over 10,000 h (approximately 1 year) at an average temperature of 20
°C.
234 
Figure 4-1. A diagram depicted the solar simulator used for irradiation. A commercially
available xenon light source was utilized along with several plano-convex lens to
homogenize the beam. A beam turner redirected the beam from the source to the
sample. The sample was placed on an aluminum block, connected to a circulating
water bath to maintain constant temperature. The sample and block were housed
inside a Plexiglas box with a hole in the top to allow light to pass. Two filters (KG2)
were placed over the hole to reduce the infrared light reaching the sample. A ray
tracing is shown as the red dashed line. ..................................................................... 246 
Figure 4-2. A diagram showing how uniformity was measured. The irradiated sample
was contained in a petri dish (dashed line, diameter ~5.5 cm). Intensity measurements
were taken at the points where the grid lines intersect. ............................................... 248 
Figure 4-3. A spectrum of the sun [7] (black dotted line) compared to the spectrum of a
xenon light source (dashed blue line) and the xenon light source with 2 KG2 filters (solid
red line) (a). The same spectra are shown in b, but all were collected using the same
spectrometer. The spectra were normalized to the average intensity between 500 – 550
xvi

nm. The spectral irradiance of the sun and the xenon source with the 2 KG2 filters is
shown in part c. ........................................................................................................... 250 
Figure 4-4. Total ion chromatograms (a) and extracted ion chromatograms (b) of m/z
216 of diesel fuel irradiated for 0 – 10 h as well as a 10 h dark control. In the total ion
chromatogram the even numbered normal alkanes are labeled for reference. The
peaks at 34.39 min and 34.77 min correspond to methyl pyrenes. ............................. 258 
Figure 4-5. The output from mass spectrometry analysis of diesel fuel. An example TIC
chromatogram (a) is representative of all chromatograms indicating the region over
which the spectra were averaged (red line). The mass spectrum prior to irradiation (b)
and after irradiation for 10 h (c) and the 10 hour dark control (d) are also shown.
Quinoline-d7 (*) was used at the lock mass. The formulas for each mass is in Table 4-2
and Table 4-3. ............................................................................................................. 264 
Figure 4-6. The Kendrick mass defect versus the nominal mass for an unirradiated
diesel sample (a). Compounds in a horizontal row have the same double bond
equivalence (DBE) and differ by 14 Da, indicating a difference in one methylene group.
Compounds in a diagonal line, indicate the same number of carbon atoms, and differ by
2 Da, indicating a difference in 2 hydrogen atoms. The Kendrick mass defect versus
the nominal mass for the unirradiated diesel fuel (large red circles) overlaid with the 10
hour dark control (small black circles) (b), and the 10 hour irradiated sample (small
black diamonds) (c). .................................................................................................... 269 
Figure 4-7. The PCA scores plot (a) and loadings plot (b) for samples irradiated for 0 h
(), 1 h (■), 2 h (♦), 4 h (▲), 6 h (+),8 (▼), and 10 h ( ). ............................................ 272 
Figure 4-8. Decay and formation curves for various compounds. The regression
equation is shown and the first order rate constant is underlined. From the GC-MS
analysis: methyl pyrene (a) (retention time 34.77 min, y = 0.033 * exp (-0.243 * t)).
From the HR-MS analysis: C16H19 (b) (m/z: 211.15, y = 1.840 * exp (-0.205 * t)),
C13H17O1 (c) (m/z: 189.13, y = 6.291 * exp (-0.0165 * t)), C18H21O2 (d) (m/z: 269.15, y =
0.097 * exp (-0.045 * t)). .............................................................................................. 275 
Figure 4-9. The rate constant for decay (a) and formation (b) of selected compounds
versus the mass of the compound. Compounds are classified based on the number of
double bond equivalences (4: red, 5: orange, 6: yellow, 7: light green, 8: dark green, 9:
light blue, 10: dark blue, 11: purple) and number of oxygens (0: , 1: ▲, 2: ■). .......... 296 
Figure 4-10. An infrared spectrum of the precipitate formed from diesel after 10 hours
of irradiation. Several peaks are labeled for reference. .............................................. 299 
Figure 4-11. The mass spectrum of the precipitate formed from diesel fuel after 10 h of
irradiation. The peak marked with “x” at 391.28 is from a phthalate and is present in the
blank. It was used as a lock mass in this analysis. ..................................................... 300 

xvii

1. Introduction
1.1 Petroleum Release into the Environment
Petroleum and petroleum products have become a major part of everyday life, with
over 18.5 million barrels of oil used each day in the United States [1]. Due to this
widespread use of petroleum, there are unintentional releases of petroleum and
petroleum products into the environment. Each year, an estimated 380,000,000 gallons
of petroleum and petroleum products are released into the environment by natural seeps
and through man-made activities [2].

The release by natural seeps accounts for

approximately 45% of the oil released worldwide, but these releases are slow and
distributed over a wide range of locations. As a result, contamination levels at most
locations are low, which allows local environments to adapt in part through physical and
chemical processes that disperse and degrade petroleum constituents [2-4].

The

remaining oil released into the environment (over 200,000,000 gallons) results from
human activities, and many of which are accidental spills. These spills can occur at
various points during distribution, including the extracting, transporting, and consuming
phases [2]. Oil spilled during extraction accounts for approximately 5% of oil spills
worldwide, while transport accounts for approximately 25%.

Activities related to

consumption of oil and oil products account for the remaining 70% of the oil released into
the environment worldwide [2].
These releases can have a devastating effect on the surrounding environment for
years after the release [2, 5, 6].

Many of the components in oil are toxic to plant and

animal life, and exposure can result in acute and chronic problems [2, 5]. In addition to

1

ecological impacts, oil spills often have a devastating impact on the local economy [5, 7],
particularly when commercial fishing or agricultural production is reduced.

These

activities usually do not resume until the risks of exposure have dwindled to acceptable
levels, but there is great uncertainty in predicting when it is safe to resume these activities.
Environmental modeling of oil spills provides an important tool to help assess potential
health and economic impacts. Modeling the fate and transport of petroleum products can
be used to determine exposure risks, direct remediation, and mitigate disruption to
commercial activities [5]. More about modeling the fate of petroleum products will be
discussed in Section 1.6
1.2 Petroleum Composition
Crude oil was formed from the incomplete decay of organic material, primarily
algae, archaea, bacteria, and zooplankton that inhabited aquatic environments. These
dead organisms settled and were covered by sediment, which compressed and trapped
it. When elevated pressures were accompanied by elevated temperatures for millions of
years, crude oil was formed from chemical transformations and physical migration
through rock [8-10]. Each deposit of oil experienced different temperatures and starting
material, therefore each oil has specific properties including viscosity, specific gravity, and
vapor pressure which generated specific markers that can be used to identify the source
and influence the fate of the oil after a spill [5, 9, 11].
1.2.1 Composition of Crude Oil
Crude oil consists mostly of hydrocarbons, but also has oxygen-, sulfur-, and
nitrogen-containing compounds, as well as trace amounts of metals [8, 9]. Using gas

2

chromatography-mass spectrometry (GC-MS), more than 300 different compounds were
identified in crude oil [12, 13]. Using high-resolution mass spectrometry, elemental
formulas for over 17,000 unique petroleum constituents have been assigned [14].
There are four major classes of compounds found in crude oil: alkanes, aromatic
hydrocarbons, resins, and asphaltenes (Table 1-1).

The alkane class contains

hydrocarbons that are bonded through covalent  bonds. This class comprises 25 – 90
percent of the composition of most crude oils (Table 1-2) and this group can be further
sorted into sub-classifications as normal alkanes, branched alkanes, and cyclic alkanes.
The normal alkanes are defined as those hydrocarbons with straight saturated alkyl
chains. In crude oils, the chain lengths of normal alkanes typically range from n-pentane
(n-C5) to n-tetracontane (n-C40). Branched alkanes are structural isomers of the normal
alkanes, consisting of the same chemical formula, but with branching rather than a linear
arrangement of carbons. The branched alkanes reflect different biosynthetic origins than
the linear alkanes. Cyclic alkanes are characterized by the presence of a ring. Crude
oils typically contain five- or six-membered aliphatic rings with 1 – 14 alkyl substitutions
[9, 11]. Terpanes and steranes usually have three six-membered rings with either an
additional six-membered (terpanes) or a five-membered (steranes) ring. Alkenes and
alkynes, which are related to alkanes, are rarely found in petroleum.

3

Table 1-1. Common defined compound classes found in crude oil. For each class,
several example compounds are listed. The example structure is of the bolded example
compound.

Class

Example Compounds

Example Structure

Alkane
Normal

Decane (C10H22)
Pentadecane (C15H32)
Eicosane (C20H42)

Branched

2,6,10-Trimethyldodecane
(C15H32)
Phytane (C20H42)

Cyclic

Butylcyclohexane (C10H20)
Cyclopentane (C5H10)

Aromatic
BTEX

Ethylbenzene (C8H10)
1,3,5-trimethylbenzene (C9H12)

PAH

Anthracene (C14H10)
Tetralin (C10H12)
Pyrene (C16H10)

Polar Compounds
Resins

Asphaltenes

Dibenzothiophene (C12H8S)
Carbazole (C12H9N)
Dibenzofuran (C12H8O)
No defined formula

4

Varies: contains heteroatoms,
aromatic and alkane portions

Table 1-2. Selected properties of petroleum and petroleum products.

Crude Oil
Light
Heavy
Crude
Crude
% Composition1
Alkane
Aromatic
Polar
% Distilled2
100 °C
200 °C
300 °C
400 °C
Residual

Gasoline

Refined Product
Intermediate
Diesel
Fuel oil

Bunker
Oil

55 – 90
10 – 35
1 – 15

25 – 80
15 – 40
5 – 40

50 – 60
25 – 40
0

65 – 95
5 – 25
0–2

25 – 35
40 – 60
15 – 25

20 – 30
30 – 50
10 – 30

2 – 15
15 – 40
30 – 60
45 – 85
15 – 55

1 – 10
2 – 25
15 – 45
25 – 75
25 – 75

70
100
-

1
30
85
100
-

2–5
15 – 25
30 – 40
60 – 70

2–5
5 – 15
15 – 25
75 – 85

°API Gravity

30 – 50

10 – 30

65

35

10 – 20

5 – 15

Density
(g/mL @ 15 °C)

0.78 –
0.88

0.88 –
1.00

0.72

0.84

0.94 – 0.99

0.96 –
0.104

0.5

2

1000 – 15000

10000 –
50000

Viscosity
50 –
5 – 50
(cSt)
50000
1. Adapted from Fingas [11].
2. Adapted from Wang et al. [9].

5

Aromatic compounds contain at least one benzene ring, which is a six-membered
ring with three delocalized  bonds (Table 1-1). This class comprises 10 – 40 percent of
the composition of crude oils (Table 1-2) and can be further classified as benzene,
toluene, ethylbenzene, and xylene (BTEX) or polycyclic aromatic hydrocarbons (PAHs).
BTEX compounds contain a single benzene ring with alkyl substitutions. In crude oils,
PAHs typically contain between 2 – 6 rings and contain multiple alkyl substitutions [5, 9].
BTEX and PAHs are of great concern when released into the environment owing to their
toxicity and carcinogenic potential [9]. BTEX compounds are more volatile and pose a
greater risk to first responders. PAHs pose a greater long-term risk, because they are
more carcinogenic and less volatile, and therefore more persistent in the environment [2].
Resins are a large group of polar molecules containing a heteroatom, such as
nitrogen, oxygen, or sulfur (Table 1-1). These polar compounds are responsible for the
adhesion observed in crude oil [11]. Resins make up a relatively small amount of crude
oils, often ranging from 2 – 20 % (Table 1-2) [9]. Sulfur-containing resins account for 0.1
– 6% of crude oil, while the oxygen- and nitrogen-containing resins account for 0.1 – 3%
[9]. Another group of polar molecules is defined as asphaltenes, which are compounds
with minimal solubility in hydrocarbon solvents. These compounds are not dissolved in
the crude oil, rather exist as colloidal suspensions in the oil. The exact formulas and
compositions of asphaltene constituents are largely unknown, but are estimated to have
masses ranging from several hundred to over 5000 g/mol when they are aggregated
together.
Crude oil is typically classified as either light or heavy crude. Heavy crude oil is
defined as having an American Petroleum Institute gravity (°API) above 30°. The API

6

gravity is calculated based on the relative density (RD) of the oil compared to water at 60
°F.


API 

Equation 1-1

141.5
 131.5
RD

The °API gravity scale for oils typically ranges from 10 – 70° and varies inversely with the
density of the oil. Heavy crude oil, which typically is found in oil sands, has a higher
abundance of resins and asphaltenes, resulting in the oil being more viscous (Table 1-2)
and requiring additional refining before use as transportation fuels [9]. The °API gravity
is often readily available for each crude oil and is, therefore, commonly used in
environmental models as a predictor of physical properties.
1.2.2 Refined Petroleum Products
Crude oil is refined into a number of more useful petroleum products for distribution
and consumption, with a wide range of physical properties, depending on the use.
Fractional distillation is used to separate crude oil into five to seven fractions, based on
boiling point. A sample distillation curve, showing the volume of petroleum distilled at
each temperature, is shown in Figure 1-1. Distillation curves are often utilized to predict
physical properties for modeling the fate and transport of the oil during an environmental
release. However, distillation curves are far less widely available than °API gravity. When
available, distillation data provides more accurate prediction of properties for
environmental models [15].
After distillation, some fractions are used as is, while other fractions undergo
additional distillation or chemical conversion. Chemical conversion breaks down large

7

molecules or rearranges molecules to produce compounds with a desired set of
properties including volatility and speed of ignition. Catalytic cracking is one of the most
common chemical conversions, which, with the help of a catalyst, breaks apart large
molecules, increasing their volatility [8]. The chemical composition of the refined product
can vary greatly based on the starting material, differences in the refining process, and
blending of the fuels [16, 17]. Common refined petroleum products include gasoline,
kerosene, diesel fuel, and heating oils. Common distillation temperature ranges (Table
1-3) and physical properties (Table 1-2) are shown for selected petroleum products [9,
11]. Fractions distilled at lower temperatures are more volatile (e.g. gasoline), and less
dense and less viscous.

These fractions tend to evaporate very quickly and will pose

little environmental hazard. Fractions distilled at higher temperature are less volatile and
will be more persistent in the environment (e.g. diesel fuel). Fractions distilled at the
highest temperatures (e.g. bunker oil) are viscous and dense, which can cause the fuel
to sink in water. These fractions are persistent in the environment and can pose a
challenge during remediation [2].
1.2.3 Composition of Diesel Fuel
Diesel fuel, which was the primary sample used in the research described in
subsequent chapters, consists mostly of alkanes (65 – 95 %), but also contains up to 25%
aromatic compounds and up to 2% resins (Table 1-2). The compounds in diesel fuel also
have a wide range of boiling points (~100 – 400 °C), encompassing volatile and
nonvolatile compounds. Depending on the starting material, diesel fuel is produced

8

800
700

Temperature (°C)

600
500
400
300
200
100
0
0

20

40
60
Volume Fraction Distilled (%)

80

100

Figure 1-1. Sample distillation curve of Alaska North Slope oil (southern pipeline).
Distillation data from National Oceanic and Atmospheric and Administration’s ADIOS 2
modelling program [18].

9

Table 1-3. Distillation temperature and carbon range for typical petroleum products [10,
11].

Petroleum Product

Distillation
Temperature (°C)

Carbon Range

Liquefied Petroleum Gas
Petroleum ether
Ligroin
Gasoline
Jet Fuel
Kerosene
Diesel fuel
Gas Oil
Bunker Oil
Lubricating Oil
Asphalt / coke

< 30
20 – 60
60 – 100
40 – 205
105 – 265
175 – 315
170 – 400
>275
>365
Nonvolatile (liquid)
Nonvolatile (solid)

1–4
5–6
6–7
5 – 10
8 – 14
10 – 16
9 – 24
12 – 70
20 – 70
variable
variable

10

directly after fractional distillation or may be blended with other products after chemical
conversion. For example, diesel fuel is often blended with more volatile fractions, such
as kerosene or jet fuel, to lower the gel point for use in cold weather. This is typically
referred to as winter diesel. Diesels that are not blended with a more volatile fraction are
summer diesels [17]. Before distribution, diesel fuel is treated to remove sulfur, in order
to comply with ultra-low sulfur regulations (<15 ppm) [17]. Other compounds containing
heteroatoms are removed in this process and are generally present at low ppm levels
[19]. While the starting material and refining can result in a variable chemical composition
for diesel fuel, diesel specifications are tightly regulated [20]. Diesel fuel is often blended
with additives such as antioxidants (e.g. 2,4-dimethyl-1-6-t-butyl phenol) and ignition
improvers (e.g. isopropyl nitrate) that could be present during an analysis [17].
1.3 Oil Spill Weathering
After an environmental release of a petroleum product, the oil begins undergoing
physical, chemical, and biological weathering almost immediately.

The physical

properties of the fuel as well as the extent of weathering play important roles in predictions
of the environmental fate and impact of an oil spill [5, 21]. As the oil is weathered, the
density and viscosity change. In some cases, the viscosity of an oil can increase by an
order of magnitude in the first twenty-four hours and an increase in density can result in
the residual oil sinking in water [6].

Weathering also plays an important role in

remediation. Chemical dispersants, for example, are typically most effective for oils with
low viscosities, so they should be applied before the oil becomes too viscous. The
weathering processes that occur are dependent on the type of oil that has been spilled,

11

the location of the spill (on land, in fresh water, in salt water), the temperature, and many
other environmental factors [21, 22].
The most common weathering processes are shown in Figure 1-2.

Most

weathering processes described in the figure are physical weathering processes with the
exception of photooxidation, which is a chemical weathering process, and biodegradation,
which is a biochemical weathering process. Each of these weathering processes will be
discussed in more detail in the following sections.
1.3.1 Physical Weathering Processes
1.3.1.1 Evaporation
Evaporation is the process of the volatile components at the surface of the oil
escaping and entering the vapor phase, leaving behind the heavier, less-volatile
components [5, 23, 24]. Evaporation is typically the most dominant weathering process;
it begins immediately after a spill and can continue throughout the oil spill cleanup [6, 15,
25]. Most material losses due to evaporation occur within the first few days [2, 22].
Evaporation can account for 100% of the mass lost in refined fuels, such as gasoline, to
as little as 5% of the mass lost in the heavier Bunker C oil [2, 15]. For typical crude oil,
the mass lost due to evaporation ranges from 40 – 75% [2, 22]. The rate of evaporative
mass loss is dependent on temperature (including air and water temperature, as well as
solar heating) and the composition of the fuel [6, 22]. Some debate still exists whether
evaporation is dependent on surface area and wind speed [2, 26]. This will be discussed

12

Figure 1-2. Different weathering processes effecting a petroleum release in the
environment. The thickness of the line indicates the contribution of weathering process.
Figure adapted from National Oceanic and Atmospheric and Administration and the
American Petroleum Institute [6, 22].

13

in more detail in Section 1.6.2. Evaporation has the greatest effect on many physical
properties of fuels, including density and viscosity. By the removal of the small, volatile
component, the remaining fuel is more dense and viscous [5, 6]. Evaporation can also
affect the toxicity of the fuel. Many of the compounds considered to be the most toxic to
aquatic life, typically the BTEX and naphthalene compounds, are removed by evaporation
[22] and may undergo photodegradation in the atmosphere. PAHs are more toxic, but
are less water soluble and have lower bioavailabilities than BTEX compounds, resulting
in a decreased acute toxicity for PAHs in the aquatic environment [27].
1.3.1.2 Spreading
Spreading is the horizontal movement of the oil on water, due to gravity, currents,
and wind, producing the characteristic oil slick [21, 22]. The spreading is slowed by
increasing viscosity of the oil [26]. Oils with low viscosity form thin layers on water (~0.01
mm), while more viscous oils have greater thicknesses (~1 mm) [15, 22, 28]. After
forming, these slicks can move with the wind and currents [21]. Wave action can break
slicks into multiple smaller slicks over time [29].

The spreading of the oil begins

immediately after a spill and can continue throughout the course of the spill [22].
1.3.1.3 Dissolution
Dissolution describes the dissolving of water-soluble components of oil into the
water layer, creating an underwater oil slick [15]. The BTEX compounds are the most
water-soluble and, due to their toxicity, the most dangerous to aquatic life [6]. These
compounds also are volatile and, therefore, may quickly evaporate from the spill zone
[27]. As a result, dissolution accounts for only a small amount (0 – 5 %) of mass loss

14

from an oil spill [15, 22]. The rates of mass loss caused by dissolution depends on the
temperature, chemical composition of the spill, the solubilities of the compounds in water,
and the surface area [22, 27].
1.3.1.4 Emulsification
Emulsification describes the process of a liquid being dispersed within another
immiscible liquid, forming small droplets. These droplets are typically formed through
wave action in the ocean [5]. Formation of emulsions increases the density and viscosity
of the oil, slows most other weathering processes, and increases the total volume of the
spill [2, 22], which hampers remediation [5]. The major factor that affects emulsification
is the wave energy, which causes the oil and water emulsions to form [22].
1.3.1.5 Natural Dispersion
Dispersion describes the formation and transport of suspended oil droplets in water
[2, 6, 22]. These droplets are formed through wave action and can then be spread both
vertically and horizontally in the water column [2, 22, 29]. Dispersion is a significant
weathering process accounting for 10 – 60% of the mass loss of a spill [22]. Rates of
dispersion depend on the wave action, as well as the properties of the oil and rates of
other weathering processes [26]. Dispersed oil will often dissolve into the water and
biodegrade more rapidly than emulsions or surface slicks due to the high surface areato-volume ratio in the small droplets [6].
1.3.1.6 Sedimentation
Sedimentation occurs when oil droplets adhere to sediments in the seawater or
from the shore and become denser than water and sink. Oil droplets can also be ingested
15

by aquatic organisms, which excrete the oil in fecal matter [6, 22]. Sedimentation typically
occurs with resins and asphaltenes and can make up 10% of the mass lost during a spill.
The oil sediment can be harmful to aquatic organisms and can remain in the environment
for decades [15].
1.3.2 Chemical Weathering: Photooxidation
Photooxidation describes the oxidation of compounds in oil by sunlight.
Chromophores in the oil and seawater absorb ultraviolet and visible radiation from the
sun, and react to form oxidized products including alcohols, ketones, and carboxylic acids
[2]. These oxidized products are more polar and water-soluble than their precursors,
which can lead to increased dispersion after photooxidation [30]. Photooxidation alters
the physical properties of the fuel and results in the formation of more toxic compounds
[2, 22]. Photooxidation is not believed to account for much of the mass lost during
weathering, but the formation of toxic compounds makes photooxidation an important
weathering process. In addition, photooxidation can convert larger molecules, which
resist evaporation, dissolution, and biodegradation, into molecules that are more readily
degraded [31]. For remediation, photo-catalysts such as titanium dioxide are added to
the oil to encourage photo-degradation [31]. The extent of photooxidation depends on
levels of exposure to sunlight and the presence of chromophores and quenchers in the
environment. There will be more discussion of photooxidation in Section 1.6.3.
1.3.3 Biological Weathering: Biodegradation
Biodegradation is the degradation of oil by organisms, mostly bacteria and fungi,
breaking the compounds in oil into oxidized products or carbon dioxide and water if the

16

process proceeds to completion [22].

There are multiple enzymatic pathways for

biodegradation, and complete degradation of complex compounds, such as PAHs, likely
requires several different organisms [2, 32]. Normal alkanes have been shown to be the
most readily degraded, while PAHs and resins typically take much longer [32].
Biodegradation is considered to be a major source of the mass loss during weathering,
however it is a slow process [15, 22]. Many factors affect rates of microbial degradation
including the organisms that are present, temperature, oxygen availability, nutrients in the
seawater, and the properties of the oil [2, 22].
1.4 Analytical Strategies for Characterization of Crude Oil and Petroleum Products
Many analytical techniques have been applied to the analysis of crude oil and
petroleum products [33]. However, no single technique has yet to provide a complete
analysis of oil, due to its complexity, and complementary techniques are necessary to
investigate the wide range of compounds. The number of compounds estimated to be
present in crude oil is 10,000 – 100,000, with a large range in mass and heteroatom
containing compounds [34].

Some techniques, such as infrared and ultraviolet

spectroscopy are not sufficiently specific for individual compound identification, but are
useful in screening for certain classes of compounds or functional groups.

Other

methods, such as mass spectrometry, are more specific and allow for the identification of
individual compounds [9]. Several of the most common instrumental techniques for
petroleum analysis are highlighted, which will provide insight into the need for
complementary techniques for the comprehensive analysis of petroleum.

17

1.4.1 Gas Chromatography
Gas chromatography (GC) has been the most common method for analysis of
petroleum. The GC is often coupled with a flame ionization detector (FID) or mass
spectrometer (MS) detector [9, 12, 13, 16, 35, 36]. Chromatography is used to separate
compounds in the complex mixture so they do not all arrive at the detector at the same
time. When GC is coupled to MS (GC-MS), the chromatographic separation provides
high separation efficiency, after which the analytes are ionized in the mass spectrometer.
This process may yield both molecular and fragment ions, and the masses of these ions
are helpful for analyte identification based on the mass-to-charge (m/z) ratios of the ions
[9, 37]. In order to improve separation peak capacity, two-dimensional GC x GC methods
have also been utilized [37-40]. These methods resolve peaks that co-elute in the first
GC separation by performing a second, very fast separation using a stationary phase with
a different polarity than the first [40]. GC methods offer great advantages, because the
separation is fast and simple and can easily be coupled with a mass spectrometer.
However, GC analysis is limited to analytes that can partition into the gas phase, so the
analyte must be volatile. This corresponds to nonpolar compounds with boiling points up
to ~425 °C or molar masses up to ~1200 Da [41]. In particular, refined petroleum products
are well suited for GC-MS analysis, given the boiling point range and the nonpolar nature
of hydrocarbons [37, 40].
1.4.2 Liquid Chromatography
Another common method for analyzing petroleum is liquid chromatography (LC)
[9, 33, 42, 43]. In many cases, the LC system is also coupled to a mass spectrometer,
although other detection methods are available [42-44] LC is capable of separating small
18

and large molecules (over 100,000 Da), but can be complicated by method development,
including selection of the mobile phase to achieve selective retention, choice of stationary
phase (packing material, particle size, and pore size), and detector [44, 45]. LC is not
limited by volatility, making it useful for the analysis of high molecular weight PAHs, resins
and asphaltenes [33, 35]. LC is typically useful in analyzing alkanes with greater than 16
carbons and PAHs with 2 – 6 rings.
1.4.3 Mass Spectrometry
Mass spectrometry methods can be coupled to GC, LC, or samples can be directly
injected into the MS using flow injection analysis (FIA) [46]. Using mass spectrometry
allows for the determination of the molecular or fragment ion masses, which in turn can
be used to determine elemental formulas of each if sufficient mass measurement
accuracy is available. Additional stages of mass spectrometry (MSn) can be utilized to
further fragment the ions, to help elucidate their structures. The single quadrupole mass
spectrometer often coupled with GC typically provides low mass resolution (m/∆m =
2000), yielding only nominal masses (masses accurate to integer values). Assignments
of exact elemental formulas require higher mass resolution and mass measurement
accuracy. High-resolution mass spectrometers (m/∆m > 10,000), such as time-of-flight
(ToF) and Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR MS),
have allowed for the visualization of previously unresolved masses and the assignments
of elemental formulas for a large number of detected analytes [46]. In recent years, these
high-resolution mass analyzers have been widely applied to analysis of crude oils,
eliciting tens of thousands of unique elemental formulas.

This has resulted in the

emergence of a sub-discipline known as petroleomics, which applies analytical technique

19

in efforts to determine comprehensive chemical composition as well as establish physical
properties and reactivities of all petroleum constituents [14, 34].
An important consideration that affects the MS analysis is the selection of
ionization method [46]. Mass spectrometers measure mass-to-charge (m/z) ratios by
accelerating ions by application of an electric field.

Uncharged molecules do not

experience such acceleration, therefore, ionization determines which compounds can be
detected [47]. Typically, electron ionization (EI) is used for GC-MS analysis, and it
provides universal ionization of all molecules that elute from the GC column. Moreover,
using electron ionization facilitates identification because the fragmentation of a
compound can be compared to mass spectrum libraries [16, 37, 48]. For less volatile
compounds not amenable to GC, electrospray ionization (ESI), atmospheric pressure
photoionization (APPI), and atmospheric pressure chemical ionization (APCI) [14, 33, 34,
49-51]. ESI is typically used for compounds with high molecular weights or compounds
that have polar (acidic or basic) functional groups. In ESI, compounds are ionized by
creating a charged droplet, containing solvent and the compound to be ionized. The
solvent is evaporated and the charge is transferred onto the compound. The analyte
must have a higher proton affinity than the solvent. Methanol has a proton affinity of
approximately 760 kJ/mol. APPI and APCI are preferred for smaller (~1000 Da) and lesspolar compounds, and have been less widely applied in the analysis of petroleum than
ESI [46, 47]. In APCI, the sample in solution is introduced into the ion source where it is
vaporized and a corona discharge is used to ionize the reagent gas. The regent gas can
then transfer the charge to the analyte. At atmospheric pressure there is excess reagent
gas, resulting in efficient ionization. In APPI, compounds are ionized using photons.

20

Polar compounds have higher ionization potentials and are not as well ionized as
nonpolar compounds.
The complexity of petroleum requires the use of a range of complementary
analytical techniques if comprehensive information is to be generated. While nonpolar,
volatile compounds including alkanes and small aromatics are effectively analyzed by
GC, larger aromatic compounds as well as the polar and resin fractions lack the volatility
needed for GC separation. LC or FIA coupled to MS allows for the analysis of more polar
compounds, however most LC-compatible ionization methods will not ionize alkanes.
The most polar compounds are more efficiently ionized using ESI, while moderately polar
compounds including aromatic hydrocarbons are more effectively ionized using APCI or
APPI.
1.4.4 Strategies for Analysis of Diesel Fuel
In the analysis of diesel fuel, GC-MS is by far the most common instrumental
approach because most of the compounds are volatile and have been distilled [37, 52].
However, chromatographic separation by GC cannot resolve all compounds in a mixture
as complex as diesel, therefore, many low abundance compounds are obscured by more
abundant compounds. In GC-MS analysis, approximately 100 separate peaks have been
reported in analyses of diesel fuels [40]. Two-dimensional gas chromatography (GC x
GC) has been applied to achieve additional separation [40, 53]. In GC x GC, a mixture
is first separated on a column with a nonpolar stationary phase, where the separation is
based on boiling point. The eluent is transferred to a second column with a more polar
stationary phase, where compounds are separated based on molecular interactions with

21

the stationary phase. This increases the peak capacity of the analysis, resulting in the
observation of over 1000 resolved compounds [40].
While high-resolution instrumentation has been widely applied to crude oils [54,
55], surprisingly, few studies have used these high-resolution instruments with diesel fuel,
even though diesel contains polar compounds, which would not be observed by GC.
Hughey et al. used ESI-FT-ICR-MS to compare the heteroatomic hydrocarbon content
during different stages of the refining process of diesel fuel [19]. ESI allowed for efficient
ionization of heterocyclic constituents, however, hydrocarbons without a heteroatom were
not observed [19]. Rostad and Hostettler utilized ESI in negative ion mode with a
quadrupole mass analyzer to identify polar acidic compounds in refined fuels [56], but
only heteroatom-containing compounds were observed and therefore, pure hydrocarbons
were not included [56].
Diesel fuel has been analyzed using Penning ionization with FT-ICR-MS, resulting
in ionization of PAHs and heteroatom-containing compounds [57]. APCI has also been
shown to ionize more moderately polar molecules, such as PAHs, in addition to
heteroatom-containing constituents [58, 59]. This ionization of PAHs was enhanced by
the use of an aprotic solvent to transport the fuel into the mass spectrometer ion source
[58]. This makes APCI a useful ionization method for diesel fuel, which contains both
PAHs and heteroatomic hydrocarbons. However, there are no literature reports of using
APCI for the analysis of diesel fuel.

22

1.5 Basis of Predictive Models
In most environmental models, an easily obtained property is typically the basis of
the model and is used to predict the hard to obtain values. For example, the vapor
pressure of compound can be used to predict that compounds rate of evaporation.
Physical properties (e.g. vapor pressure, boiling point etc.) are often used at the basis for
models because they are easy to obtain.

However, for complex mixture, such as

petroleum, obtaining physical properties can be challenging and therefore, other
methodologies, such as analytical measurement, are needed.
1.5.1 Physical Properties
Many of the predictive models for weathering of oil spills rely on using the known
physical properties of a compound or oil, such as the vapor pressure and boiling point.
Such properties are often used as the basis for predictive modeling [29, 60]. The vapor
pressures, boiling points, and other physical properties for some compounds are available
in the literature [61-63]. However, many compounds abundant in petroleum are not
included in these references.

Moreover, identification of a specific compound in a

complex petroleum mixture is challenging, given the large number of isomers and
structurally-related compounds that yield similar mass spectra. Physical properties of
many fuels are typically not available, requiring the properties to be estimated from the
distillation curve or °API gravity.

As a fuel is weathered, these estimates become

unreliable, leading to increased uncertainty in the predictive model.

23

1.5.2 Chromatographic Retention Index
The physical properties of a compound can be estimated using analytical
measurements as a surrogate. One common example is the retention of a compound
during a chromatographic separation.

Quantitative structure-retention relationships

(QSRRs) have been applied to predict physical and chemical properties based on linear
free-energy relationships [62, 64]. QSRRs were first observed as a log-linear relationship
between retention time and carbon number. Kováts expanded on this relationship and
demonstrated a correlation between retention on a nonpolar stationary phase and boiling
point [65]. This led to the generation of Kováts retention indices. Retention indices
provide broadly applicable retention scale relative to the normal alkanes, resulting in a
retention index value, independent from many GC parameters including stationary phase,
column dimensions, and temperature. For temperature-programmed GC, retention
indices (IT) are calculated for a compound of interest based on the retention time of that
compound (tTR,i) and the retention time of the normal alkanes of carbon number z that
elute before (tTR,z) and after (tTR,z+1) [66, 67].

 tT  tT

I T  100  T R,i RT,z  z
 t R, z1  t R,z 

Equation 1-2

QSRRs have been applied to predict physical properties such as solubility, vapor
pressure, reactivity, octanol-water partition coefficient, and many other physical and
structural properties [62, 68]. Retention indices as a predictor for physical properties in a
complex mixture are advantageous because the compound does not require definitive
identification and can be determined from a GC experiment. Previous predicative models,
which required known physical properties, would become more broadly applicable by

24

applying an analytically-derived surrogate in place of the physical property. Moreover,
retention indices are available in the literature for many compounds [69], therefore, if the
identity compound is known, no GC experiment is necessary to obtain the retention index.
1.5.3 Kendrick Mass Defect
Another analytical measurement that has been useful in grouping petroleum
constituents with similar structural features is the Kendrick mass defect. High-resolution
mass spectrometers measure ion masses with accuracies within a few parts-per-million
(ppm), which can be used to calculate a short list of molecular formulas that are within
experimental error for each ion [51]. Accurate masses have been useful in petroleomics,
resulting in the assignments of thousands of unique formulas to ions generated from
crude oil [34, 55]. In the mass spectra of petroleum samples, series of peaks are
observed separated by approximately 2 mass units or 14 mass units, corresponding to a
difference of two hydrogen atoms (relating to a double bond or ring) or a methylene (CH2)
group, respectively [51]. The repeating pattern of methylene groups can be used to group
compounds using the Kendrick mass defect, which groups compounds together if they
differ only by the number of methylene groups. For example, the Kendrick mass defect
would be common for all alkanes, as they are a homologous series differing by the
number of methylene groups. The Kendrick mass scale (mK) makes the exact mass (mE),
of CH2 equal to exactly 14, instead of

12

C equal to 12 (or mass of methylene being

14.01565 Da).

 14.00000 
mK  mE 

 14.01565 

Equation 1-3

25

The Kendrick mass defect (KMD) can then be calculated as the difference between the
Kendrick mass and the nominal mass (mN).

KMD  mK  mN

Equation 1-4

This conversion results in the mass defect for compounds that differ by the number of
methylene groups, but have the same heteroatoms and double bond equivalences (DBE),
which can be calculated based on the number of carbon, hydrogen and nitrogen atoms.
DBE  C 

Equation 1-5

H N
 1
2 2

The Kendrick mass defect allows for rapid grouping of compounds based on differences
in the number of rings or double bonds, as these are not differences of only the number
of methylene groups.
1.6 Oil Spill Modeling
The ultimate goal of most oil spill modeling is to predict the movement of the oil in
the environment in order to direct remediation and assess potential impacts.

The

movement of the oil in the environment is closely tied to the weathering, therefore most
comprehensive predictive models also include a weathering component [15]. These
weathering models were developed using empirical measurements of oil spills in the
environment using the analytical instrumentation discussed above.
1.6.1 Fate and Transport Modeling of Oil Spills
There are many types of predictive models used in impact assessment after oil
spills. Many focus on modeling the three-dimensional transport and fate of the oil in the
environment, and are typically developed by government agencies or companies. The
26

National Oceanic and Atmospheric Administration (NOAA) utilizes two modeling software
packages, General NOAA Operational Modeling Environment (GNOME) and Automated
Data Inquiry for Oil Spills version 2 (ADIOS2) [29, 70]. GNOME is used for trajectory
modeling while ADIOS2 models the weathering [18, 71]. The OILTRANS model was
developed for the Atlantic Regions’ Coastal Pollution Response (ARCOPOL) in Europe
[72, 73]. SIMAP is an example of commercially available oil spill modeling software [2,
27, 74]. Other sophisticated three-dimensional oil modeling programs include: COZOIL
[75], SINTEF OSCAR [76, 77], OILMAP [78], GULFSPILL [79], MOHAD [80], POSEISON
OSM [81], OD3D [82], MEDSLIK [83-85], and BioCast [86].
Each fate and transport model consists of many smaller models used to predict
the transport and weathering processes during an oil spill [2]. The overall fate and
trajectory is determined by combining the outcome of each of the individual processes.
The performance of one algorithm within the comprehensive model can greatly affect the
results and accuracy of the other algorithms [26, 60].

Comprehensive models are

continually being refined to incorporate more accurate individual models and estimations
to provide a comprehensive and accurate prediction. In this work, new methods, based
on kinetic rate constants, were developed as predictive models for evaporation and
photooxidation.
1.6.2 Evaporation of Petroleum Constituents
1.6.2.1 Theory
Evaporation is the movement of a molecule from the liquid phase into the gaseous
phase. In order to move into the gas phase, the molecule must have more energy than

27

the intermolecular forces that keep it in the liquid. At a given temperature, molecules
have a range of kinetic energies, which allows some of those molecules to break the
intermolecular forces and reach the gas phase. The pressure of the molecules in the gas
phase above the liquid is the vapor pressure [87]. In pure liquids, the rate of evaporation
is constant over time, however, that is not the case in a mixture [88, 89]. In a mixture, the
vapor pressure of a compound can be expressed in terms of Raoult’s Law, which states
that the vapor pressure of a liquid is proportional to the mole fraction of the liquid in a
mixture [90]. As the mixture evaporates, the composition and, therefore, the equilibrium
vapor pressure changes, which make predicting the rate of evaporation as a function of
time challenging. In addition, evaporation of a mixture results in an increase in viscosity
and density, leading to increased diffusion coefficients.
The vapor pressure of a compound at equilibrium can be determined using the
Clausius-Clapeyron equation.

 ln(P) Hvap

T
RT 2

Equation 1-6

The equilibrium vapor pressure (P) is related to enthalpy of vaporization (Hvap) and the
absolute temperature (T) and the gas constant (R) [90]. The enthalpy of vaporization is
typically independent of temperature under most environmental conditions. However,
phase changes and variation in mixture composition can lead to changes in the enthalpy
of vaporization [90]. Many of the models commonly used to predict evaporative loss are
based on the correlation between the vapor pressure and the evaporation rate [29, 60,
72, 91-96]. However, little is still understood about the physics and chemistry that occur
during evaporation in a complex mixture released into the environment [2, 24, 97].

28

Comprehensive oil modeling software is typically a combination of many different
fate and transport models. In a petroleum release, evaporation is a major weathering
process and must be account for in environmental models. The evaporation model within
comprehensive modeling software typically falls into one of three types of models:
empirical [88, 98, 99], analytical [26, 100], and pseudo-component [26, 29, 60, 73, 101,
102]. Each type requires different inputs and makes different assumptions about how the
rate of evaporation is affected over time.

Some software only includes a single

evaporation model, while other programs include several models from which the analyst
can choose [2, 26, 72].
1.6.2.2 Empirical Models
The empirical models use laboratory measurements of specific fuels to predict
temporal changes in mass at various temperatures [99, 103, 104]. Much of the work to
develop these predictive models has been conducted by Fingas, who used the temporal
changes in mass of crude oils and refined fuels placed into petri dishes to determine the
percent evaporated [15, 24, 88, 98, 103, 104]. A plot of the percent evaporated versus
time was generated and fit to either a logarithmic or square root function using curvefitting software [98]. This procedure was repeated for hundreds of different fuels at
various temperatures [24]. These empirical models are easy to apply and have been
used to predict the percent evaporated (by mass) based on the fuel source, the
temperature (T), and the time (t) [60, 72, 98]. An example of an empirical model for
southern diesel fuel (diesel fuel for use in the southern United States) evaporated for less
than 5 days:

29

Equation 1-7

%Evap  (0.02  0.013 T ) t

The empirical models determined by Fingas for many crude oils and refined petroleum
products are available in the literature [24].
Fingas also developed two general equations to predict the percent evaporated
using the percent (by mass) distilled on a distillation curve for a specific fuel at 180 °C (D)
[25]. One model is for oils that evaporate in a logarithmic fashion with time, which Fingas
concluded would encompass most crude oils and petroleum products [24].
% Evap  (0.165 D  0.045 (T  15)) ln( t )

Equation 1-8

A second empirical model was developed for oils that evaporate with the square root of
time, which was diesel fuel and some crude oils [21, 24].
Equation 1-9

%Evap  (0.0254 D  0.01(T 15)) t

While these more general empirical models do not require that the source of the fuel be
known or have an existing empirical model, they do require that the percent distilled at
180 °C be known. These data are often not readily available and would still require
knowing the type and composition of fuel that was spilled. Typical percent distilled at 180
°C for diesel fuel is 5 – 20% [18].

In addition, as empirical models there is no direct

relationship to thermodynamic principles. There is no fundamental explanation why some
of the oils that were tested evaporated with a logarithmic or square root relationship with
time. This makes further application of these models cumbersome.
Another interesting aspect of the empirical models is that they assume oil
evaporation is not boundary layer-regulated, unlike the other evaporation models [88].
The boundary layer is the thin layer of air (typically less than 1 mm), just above the oil,
30

that the evaporated molecules enter [25, 105]. If the boundary layer becomes saturated
over the course of the evaporation, the process is considered to be boundary layerregulated. The result is that the air layer becomes saturated and evaporation slows [25].
This is true of compounds that evaporate quickly. Evaporation of water is also boundary
layer-regulated. Fingas argues that this assumption is invalid for crude oil or petroleum
product because many of the compounds evaporate slowly [25].

If evaporation is not

boundary layer-regulated, then many factors, including the surface area of the spill or the
wind speed, do not affect the rate of evaporation [25, 88, 97]. While this assumption is
contrary to most oil spill modeling [26], the models proposed by Fingas are generally
comparable to the other models [28, 60] and are included in some oil spill modeling
software programs [72, 73].
By varying the surface area, wind speed, and volume of liquid, Fingas
demonstrated that water demonstrated boundary layer regulation, while oil and petroleum
products did not [88]. For water, Fingas observed a significant increase in the rate of
evaporation with increasing wind speed, demonstrating boundary layer regulation.
However, for oil, petroleum products and hydrocarbons greater than nonane, Fingas
observed only a small increase in the rate of evaporation with increasing wind. In addition,
Fingas also demonstrated that increasing the area of the spill does not affect the rate of
evaporation, indicating a lack of boundary layer regulation [88].
The advantage of the empirical model is the simplicity and the ease of prediction.
Moreover, these simplistic models correlate well with the more complex models discussed
below. This allows for fast estimations of the percent evaporated without the need for
complex computer programs. The major drawback of this method is that the type of oil

31

must be known and an empirical model must already have been developed. Even when
utilizing the general models, the percent distilled at 180 °C and the temporal relationship
(logarithmic or square root) with evaporation must be known.
1.6.2.3 Analytical Model
The analytical models use a fundamental thermodynamic approach combined with
empirical measurements for the development. In order to develop this semi-empirical
approach, many assumptions and empirical measurements were used [60, 97]. This
approach assumes that the oil behaves as a single component, which has physical
properties that change linearly over time as weathering progresses [29]. The derivation
of the analytical model and
A generic, semi-empirical evaporation equation was proposed, demonstrating the
major factors in rate of evaporation (E), including the mass transfer coefficient (km), the
concentration (Cs) of the liquid being evaporated, wind speed (U), and diffusion at the
boundary layer (S) [25].

E  K Cs U S

Equation 1-10

Sutton proposed a model to predict the rate of evaporation of a pure liquid, specifically
water, based on Equation 1-10, using empirical measurements [106].
E  K CS U

7

9

a

1

9

Equation 1-11

Sc  r

This equation introduced the dependence of spill area (a), and Schmidt number (Sc) in
the rate of evaporation. The Schmidt number is the ratio of the air’s kinematic viscosity
to the evaporating molecule’s diffusion coefficient in air. The exponent (r) relates to the

32

effect of diffusion, and typically ranges from 0 – 2/3 [25, 106]. The powers associated
with each variable were empirically determined.
MacKay and Matsugu proposed an equation relating the rate of evaporation (E) or
change in concentration over time, based on vapor pressure (P), temperature of the pool
of liquid (T), gas constant (R), and mass transfer coefficient (km) [107].

E

Equation 1-12

km P
RT

The equation for the mass transfer coefficient was based on the work by Sutton [106].
7

km  0.0292 U 9 a

1
9

Sc

2

Equation 1-13

3

The coefficients for the equation were empirically determined using the evaporation of
water, the aromatic hydrocarbon cumene, and gasoline from large evaporation pans [100,
106, 107]. They also investigated the effect of spill area and wind speed. The rate of
evaporation was based on the volume change over time. MacKay and Matsugu found
that Equation 1-12 worked well to predict the evaporation of a pure liquid, but did not work
well for gasoline, which had a variable vapor pressure due to evaporation [107]. For this
work, MacKay and Matsugu concluded that Equation 1-12 could describe evaporation
when there is a constant vapor pressure.
Stiver and MacKay developed several experiments to determine the rate of
evaporation for individual compounds in a complex mixture, using four crude oils and a
“synthetic oil”, which was a mixture of n-alkanes [100]. Three different evaporation
methods were applied, evaporation of a thin film from a tray, gas stripping, and distillation.
Oil samples evaporated from a thin film allowed for monitoring temporal changes in mass,

33

and gas stripping allowed for monitoring temporal changes in both mass and volume.
Distillation was performed to generate a distillation curve, monitoring volume distilled at
various temperatures.
Stiver and Mackay adapted Equation 1-12 to predicting the evaporation rate for an
individual compound (i) from a thin film, within a complex mixture [100].

Ni 

km a i  i Pi
RT

Equation 1-14

The vapor pressure of a compound in a mixture was determined using Raoult’s law, based
on the vapor pressure of the pure compound (Pi), the mole fraction (i), and the activity
coefficient (i). Equation 1-14 can be expressed in terms of the change in the number of
moles of an individual compound (ni) at time (t).

n 
km a  i   i Pi
ni
 nt 

t
RT

Equation 1-15

The total moles (nt) present can be determined from the fraction evaporated (FE), the
initial volume of oil (V0), and the initial oil molar volume (c0) [93].

nt 

(1  FE ) V0

c

Equation 1-16

0

Equation 1-16 can be substituted into Equation 1-15 and rearranged to form Equation
1-17.

c0  i Pi km a t
ni

(1  FE ) R T
ni
V0

Equation 1-17

34

The evaporative exposure (θ) incorporates the terms that are a function of the size
of the spill.



km a t
V0

Equation 1-18

The mean effective oil molar volume (c) was used to account for the changes in the
activity coefficient and oil molar volume due to evaporation.

c 

c  i

Equation 1-19

0

(1  FE )

By substituting Equation 1-18 and Equation 1-19 into Equation 1-17 and rearranging, the
fraction remaining can be predicted for an individual compound [93].

ni c Pi


ni
RT

Equation 1-20

Equation 1-20 is further simplified using the Henry’s Law constant (H), which is the ratio
of the compound in the gas phase (P/RT) to the compound in the liquid phase (1/ ), at
equilibrium [100].

H

c Pi

Equation 1-21

RT

Substituting Equation 1-21 into Equation 1-20, the fraction remaining (Fi), or change in
moles over the initial moles, for an individual compound can be calculated based on the
Henry’s Law constant and the evaporative exposure.

Fi  H 

Equation 1-22

35

If H is independent of F, Equation 1-22 can be integrated, to calculate the fraction
remaining [93, 100].
F H

Equation 1-23
To this point, all calculations were for an individual compound. However, this

can be extended to a complex mixture. However, physical properties, such as activity
coefficients or vapor pressure, which were used to determine the fraction remaining for
an individual compound now must be estimated for the bulk fuel. Also, in a complex
mixture or at concentrations above infinite dilution, H is not independent of F, so an
equivalence must be established. This can be achieved using a form of the ClausiusClapeyron equation.
 P  Hvap
ln  1  
R
 P2 

 1 1
  
 T2 T1 

Equation 1-24

The Clausius-Clapeyron equation can be rearranged, so that PA is the atmospheric
pressure at which the boiling point (Tb) is recorded, and P is the vapor pressure at
temperature T.
 P 
Tb 

ln 
  B 1
T 

 PA 

Equation 1-25

The B term is dimensionless and equal to the heat of vaporization (Hvap) over the gas
constant (R) and the boiling point.

B

H vap

Equation 1-26

RTb

Equation 1-21 can be rearranged based on Equation 1-25.

36

P 
ln(H )  ln  A c
 RT

B Tb

B T


Equation 1-27

Equation 1-27 can then be simplified.

ln(H)  A 

BTb
T

Equation 1-28

A is a constant that can be determined for an oil, based on experimental distillation. Stiver
and MacKay determined empirical values for A and B by linear regression of ln(H) versus
Tb. Empirically determined values using five crude oils were A = 6.3 and B = 10.3 [23,
100]. These oils are likely not representative of all possible petroleum products, so new
fitting coefficients might be required.
As previously noted, the boiling point of a fuel is needed. A mixture does not
have a true boiling point, but Stiver and MacKay proposed a simplified equation predict
the boiling point, based on experimental distillations.

Tb  T0  TG  F

Equation 1-29

In this equation, T0 is the initial boiling point of the distillation, where the fraction
evaporated is 0 and TG is the temperature gradient of the distillation curve [100].
Combining Equation 1-22, Equation 1-28, and Equation 1-29 yields


T  T  F 
F  exp  A  0 G  
T



Equation 1-30

When utilizing the analytical model, several temperatures (T0 and TG) must be
estimated from the distillation curve. The distillation curves utilized to develop this model,
were based on small-scale laboratory distillations, and these distillation data are not

37

available for most oils [60, 108]. In addition, the estimation for the A and B terms were
determined from the distillation of only a few oils, and may not be representative of all
oils. The analytical method also assumes a linear relationship between the fraction
evaporated and the boiling point, making the analytical model better suited for oils with a
linear distribution of distillation cuts [26, 108].

These estimates present significant

sources of uncertainty in the predictive capacity of the model [28, 29, 100, 107].
1.6.2.4 Pseudo-component Model
The most common method currently used for estimating extent of evaporation is
the pseudo-component model. This model, which is based on the analytical model
developed by Stiver and MacKay, approximates the composition of the complex fuel as
several discrete and independent components, rather than as a single component, as is
done with the analytical method. The total evaporation of the fuel is based on the sum of
the evaporation of the pseudo-components.

This allows for a more accurate

determination of vapor pressure and molar volume, but requires additional assumptions
and empirical data.
Payne et al. developed a method for predicting the rate of evaporation for oil based
on several well-characterized pseudo-components, which were selected based on
distillation [102]. The oil was distilled and each fraction became a pseudo-component.
The temperature of the distillation, volume fraction distilled, and °API gravity (Equation
1-1) were then determined for each cut [102]. However, these data are not widely
available for most oils, making broad applicability challenging [60]. Jones expanded on
a pseudo-component model (discussed below) using standard distillation data [109]
without requiring the °API gravity [60]. In order to accomplish this, Jones used empirical
38

relationships between boiling point and molar volume for the normal alkanes. In addition,
Jones developed an empirical function relating the vapor pressure of pseudo-components
to the boiling point using Antoine’s equation rather than the Clausius-Clapeyron equation
used in the analytical model [26, 60].
Like the analytical model, the pseudo-component model is based on the rate of
evaporation (similar to Equation 1-14) proposed by Stiver and MacKay [100].
Equation 1-31

Vi k m ,i a(t ) Pi Vi  i (t )

RT
t

Equation 1-31 can be used to predict the volume (Vi) of a pseudo-component (i) at time
(t), based on the mass transfer coefficient (km,i), vapor pressure (Pi), relative molar volume
(Vi ), and mole fraction at t (i(t)) for each pseudo-component as well as water
temperature (T), spill area at t, (a(t)), and the gas constant (R) [72, 73]. The mass transfer
coefficient was calculated with slight modifications in the equation determined from
Mackay and Matsugu (Equation 1-13), using the wind speed (U), the length of the oil slick
downwind of the source (X), and the Schmidt number (Sc) [107].

km,i  0.0048 U

7

9

a

1
9

Sc

2

Equation 1-32

3

An approximation for the Schmidt number was used, based on the mole-weighted
average of the oil (MWave) [73].

 0.018 
Sc  1.3676 

 MWave 

1
2

Equation 1-33

The mole-weighted average is calculated from the molecular weight (MWi), the initial
molar volume (Vi0) and relative molar volume of each pseudo-component.
39



MWi * Vi0

MWave 


Vi
Vi0

Equation 1-34

Vi

Using the boiling point of each pseudo-component (Tb,i), the molecular weight, and
relative molar volume can be calculated, using a correction derived from the normal
alkanes between propane (C3) and eicosane (C20) [18].

The boiling point for each

pseudo-component is the average temperature between the beginning and end of the
cuts on the distillation curve [102].



 

M W i  0.04132  1.985 * 10  4 T b , i  9.494 * 10  7 T b , i 2



 

Vi  7.0 * 105  2.102 * 10 7 Tb,i  1.0 * 10 9 Tb,i 2





Equation 1-35
Equation 1-36

The vapor pressure of each pseudo-component can be estimated using Antoine’s
equation, based on the atmospheric pressure (Pa), water temperature, and boiling point,
2

 P  8.75  1.987 * log(Tb,i ) Tb,i  C   1
1 
ln  i  



RTb,i
 Pa 
Tb,i  C T  C 

Equation 1-37

where C is
C  0.19 Tb,i  18.0 

Equation 1-38

The mole fraction was calculated based on the molar volumes.

Vi
V
i (t )  i i
max V
j

j 1 V
j

Equation 1-39

40

Equation 1-31 through Equation 1-39 can be combined to estimate the volume remaining
of each pseudo-component.
1

 0.018  3
0.0656 * U 9 

MWave  a(t ) Pi Vi
Vi


1
R T imax V j
t
X 9

j 1 V
j
7

Equation 1-40

To calculate the fraction evaporated (v/v) for each pseudo-component, Equation 1-40 is
solved at each time step (which is typically about 1 hour). The total fraction evaporated
(v/v) is the sum of the fraction evaporated of each of the pseudo-components, divided by
the initial volume of oil spilled [73].
Jones compared theoretical evaporations of a light, medium, and heavy crude oil
using the empirical, analytical, and pseudo-component models [60].

The fraction

remaining over time was compared when the temperature, volume, thickness, and wind
speed were individually varied for each oil. Overall, the models performed similarly,
predicting fractions remaining within ~10% of each other, despite the large differences in
how each model was developed. Jones reported that the models were only moderately
sensitive (± 10%) to changes in temperatures, thicknesses, and wind speeds that would
be commonly observed in the environment [60].
Variations of the pseudo-component model are currently the most widely utilized
in comprehensive oil modeling software [18, 26, 28, 29, 72, 73]. In general, the empirical
[88, 98], analytical [93, 100], and pseudo-component [60, 102] models result in similar
percent of fuel remaining after evaporation [26, 28, 60]. However, the use of the ClausiusClapeyron equation in the analytical model has been reported to result in vapor pressures

41

that are higher than actual values for the less volatile compounds [18]. The vapor
pressure calculation based on Antoine’s equation was shown to be more reliable [29].
Because the rate of evaporation is directly related to vapor pressure, this is a critical
calculation in the model [91, 110]. However, in the pseudo component model, estimates
are used to obtain the molar volume is based on the molar volumes of n-alkanes from 3
– 20 carbons. This estimates can result in wide errors, especially for fuels with large
aromatic content.
1.6.2.5 Kinetic Models
The models for evaporation discussed in Sections 1.6.2.2 to 1.6.2.4 all utilize
empirically derived fitting coefficients for at least some of the estimates included in the
model.

The empirical models developed by Fingas have no thermodynamic basis,

making extension of the model challenging.

The analytical and pseudo-component

models have a thermodynamic basis, however they require extensive estimations and
assumptions.

These models require empirical fitting coefficients to obtain physical

properties of a fuel.
Another method proposed for estimating the rate of evaporation is using kinetic
models. Evaporation can be thought of as process of a molecule moving from the liquid
to the gas phase, with a rate constant of k. Kinetic equations allow for the determination
of analyte concentration at a specific time, given the reaction order. Rate constants for
evaporation from a complex mixture were found to be first-order decays [92].

Ct  C0 * exp(k * t )

Equation 1-41

42

where Ct is the concentration at time t and C0 is the initial concentration [105, 111, 112].
As an alternative to the rate constant, the characteristic lifetime ( = 1/k) or the half-life
(t½), which is the time in which the concentration of analyte decreases by one-half, can
be used.
Regnier and Scott experimentally determined the kinetic rate constant for normal
alkanes in diesel fuel at four temperatures (5, 10, 20, and 30 °C) with constant wind (13
mi hr-1) [92]. Diesel fuel was evaporated in petri dishes and an aliquot was removed for
GC-MS analysis. The normal alkanes in the diesel samples were quantified after various
evaporation times and used to determine kinetic rate constants. Using the vapor pressure
(P) and rate constant (k) of the normal alkane at each temperature, the rate constant
could be predicted [92].
log( P )  1.25 log( k )  0.160

Equation 1-42

This vapor pressure model was only applied to the normal alkanes, but the authors
hypothesized that it could be applied to all compounds. One of the major drawbacks is
that in order to utilize the model, the vapor pressure of the compound had to be known.
Moreover, this model was only capable of predicting the evaporation of individual
compounds, not the entire oil. However, this work demonstrated that the evaporation rate
constant did correlate with the vapor pressure of a compound.
Another kinetic model was developed by Butler to predict the age of tar balls [113].
This model assumed that the fraction remaining of an individual compound is proportional
to vapor pressure. The fraction remaining (x/x0) of an individual compound can be
determined based on the based on the rate constant (k), the vapor pressure (P), the time
(t), and the initial amount (x0) [25, 113, 114].
43

 kPt
x
 exp  

x0
x0 


Equation 1-43

The vapor pressure was determined as a function of carbon number (N), using the normal
alkanes [113].
P  exp(10.94  1.06 N )

Equation 1-44

Equation 1-43 and Equation 1-44 can be combined to predict the fraction remaining for a
compound, based on the carbon number [114].

 k t 

x
 exp    exp(10.94  1.06N )
x0
  x0 


Equation 1-45

However, this prediction required an estimation of the rate constant, which required
experimental determination, based on the weathering of the oil [113]. While this model
did not require identification of a compound, an assumption was made that the vapor
pressure of a compound was related to the normal alkane with the same number of
carbon atoms.
Kinetic models are useful in determining rate constants for evaporation of an
individual compound. The fraction remaining of that compound can then be determined
using the rate constant and Equation 1-41. The initial concentration of analyte is not
required when determining the fraction remaining, it is only necessary to obtain an
absolute concentration. Identification of the compound is also unnecessary, as long as
the vapor pressure can be determined. Determination of the vapor pressure without
identifying a compound can be challenging, but analytical properties such as retention
index on a nonpolar stationary phase have been shown to predict the vapor pressure [40].
Existing kinetic models for evaporation have not been applied to an entire fuel, only to
44

individual compounds from a complex mixture. In order for kinetic models to be useful,
they must be capable of predicting evaporation of a bulk fuel as well as individual
compounds.
1.6.3 Photodegradation of Petroleum Products
Most comprehensive oil spill modeling software programs do not include fate
models due to photodegradation [2, 73, 115].

Many consider photodegradation to

account for a very small amount of the mass loss for oil, making it insignificant compared
to other weathering processes [21, 22, 116]. Photodegradation typically consists of
oxidation of compounds, however, other degradation pathways, such as direct photolysis
also occurs. Photooxidation typically results in increased toxicity and water solubility for
a number of compounds [21, 70, 116]. Even if photodegradation does not account for
significant mass loss, the formation of toxic products can have a significant environmental
impact.
Many compounds in crude oil can absorb the UV and visible components of
sunlight, resulting in the promotion of that compound to the excited state. The energy
absorbed by the compound can be dissipated in several ways. The compound can return
to the ground state, without resulting in a structural change. The energy can be released
into the environment as heat, via internal conversion. A photon of light can also be
released through fluorescence or phosphorescence. The energy can be transferred to
another molecule (photosensitization), which can dissipate the energy or undergo a
reaction.

Last, the energy can directly break the bonds in the compound, forming

fragments, peroxides, or radicals that can react with other compounds.

[87, 117].

Reactions through photosensitization is thought to be the dominant pathway for
45

photodegradation.

Many compounds found in the environment, such as dissolved

organic matter in water, serve as photosensitizers [116, 118].
In general, the processes and mechanisms responsible for photodegradation of
the components in oils are not well understood [118-120]. Photooxidation, the most
common photodegradation method, has been shown to result from direct photolysis as
well as through photosensitization, typically with singlet oxygen (1O2) or electron transfer
involving free radicals [31, 118, 120-126]. Previous work has focused on determining the
mechanism and predicting the rate of photooxidation of individual compounds.

For

petroleum products released into the environment, there are many factors that influence
the degradation including composition of the oil, presence of photosensitizers or
quenchers in the environment, intensity of solar irradiation, temperature, and extent of
weathering [30, 118, 119, 124, 126]. Moreover, in environmental studies, differentiating
between the effects of photooxidation and biodegradation is challenging, because both
result in oxidized products [115, 116, 122, 123, 127]. In laboratory studies, experimental
conditions vary widely among researchers. Light sources have varied from mercury and
xenon arc lamps to natural sunlight. The irradiance of the source (250 W/m2 [30] – 1260
W/m2 [119]) and irradiation times widely varied.

These differences in experimental

conditions, which could lead to different mechanisms, resulted in contradictory
conclusions between investigations [122, 123, 128]. Most research supports that normal
alkanes in oil are largely unaffected by photooxidation, while aromatic compounds are
typically converted into polar compounds or resins through the addition of oxygen [33,
118, 119, 129].
1.6.3.1 Direct photolysis

46

Direct photolysis is the absorption of light energy by a chromophore resulting in
the breaking of bonds.

While direct photolysis has been demonstrated for many

compounds in petroleum products, photosensitized reactions are more likely in
environmental spills due to the large number of sensitizers in the environment. Oil also
has low photon energies relative to carbon-carbon or carbon-hydrogen bond energies
[122-124, 130, 131]. For example, a photon of 315 nm, the short-wavelength end of the
UVA range, deposits about 91 kcal/mol, which is slightly more than weak C-H and C-C
bonds. Direct photolysis has been proposed to be the dominant mechanism in dilute
solutions, owing to the short lifespan of reactive oxygen species [128].
1.6.3.2 Indirect Photolysis
Photodegradation is believed to occur via indirect photolysis, due to the large
number of sensitizers in the environment and in petroleum. Indirect photolysis requires
a sensitizer (S) to absorb light, resulting in the sensitizer entering the excited singlet state
(1S*) (Figure 1-3) [87, 117, 131]. Once the energy is absorbed, it is transferred to another
compound. The excited-state sensitizer (1S*) can react with oxygen in the ground state
(3O2) to form reactive oxygen species (e.g. OH, O2 ,H2O2, etc.), which can oxidize a

compound in oil. Some sensitizers (1S*) can also undergo intersystem crossing, resulting

47

C
1

3

S*

h

O2

Cox

ROS (OH, O2 -, ROO , RO ) 
3

O2

3

S

3

Cox

S*

1

O2

O2

C
Cox

Figure 1-3. A compound in oil (C) becoming oxidized (Cox) via indirect photolysis. A
sensitizer (S) absorbs sunlight and enters an excited singlet state (1S*). The sensitizer
can react with oxygen to form reactive oxygen species (ROS), which can then oxidize C.
Through intersystem crossing, the 1S* can enter the triplet state (3S*), which can directly
oxidize C or can react with oxygen, to form singlet oxygen (1O2). Singlet oxygen can then
oxidize C. Figure adapted from Schwarzenbach et al. [87].

48

in an excited sensitizer in the triplet excited state (3S*) [87]. This sensitizer can react with
triplet oxygen (3O2), resulting in the formation of singlet oxygen (1O2), which can oxidize
the oil constituent. Last, the sensitizer (3S*) can directly react with the oil compound,
resulting in oxidation [87, 132].
1.6.3.3 Photooxidation Studies
Predicting the products and rates of photooxidation for some pure compounds is
fairly well established. Much of the initial work was performed by Zepp and Schlotzhauer,
who experimentally determined the half-life for the direct photolysis of 13 PAHs, which
ranged from 0.034 h for naphthacene to 71 h for naphthalene [131, 133]. They then
predicted the half-life for these PAHs at various depths in water, where light would be
attenuated by absorption.
This led to the development of a model in which the first-order rate constant for
direct photolysis of a pure compound (kp) is related to the rate constant for light absorption
(ka) and the quantum yield () of the number of reactions per photon of absorbed light
[87].

kp   * ka

Equation 1-46

The rate constant for light absorption is calculated from the irradiance of the light (W),
the molar absorptivity (), the attenuation of light () though a layer of thickness (z),
where  indicates the wavelength of light [128, 130, 134].

ka 

W *  
z * 

Equation 1-47

49

Plata et al. compared rate constants for direct photolysis of pure PAHs found in
the literature to actual rates for PAHs in No. 6 fuel oil coated on rocks after a spill [128].
The observed rate of photodegradation was substantially higher than those from the
literature, indicating that other reactions must be occurring simultaneously, and direct
photolysis cannot account completely for photooxidation [128].
The rate of indirect photolysis for a pure compound is more complicated to predict.
Indirect photolysis depends on sensitizer was well as the reactant, resulting in pseudofirst-order or second-order kinetics [135, 136].

The overall reaction rate (Rox) is

dependent on the compound of interest (C), the concentration of each oxidant (Ox), and
the rate constant (kox) for each oxidant [135].

Rox 

d C 
dt

  kox * Ox  * C 

Equation 1-48

The oxidants must be identified and their concentrations directly measured. In addition,
the rate constant for these oxidants must be known and are wavelength and compound
dependent as seen in Equation 1-47 [135]. These models have limited utility in estimation
of photooxidation of petroleum products, because they were developed for systems with
a single compound being oxidized by a few well-known sensitizers. In the photooxidation
of petroleum, many compounds are simultaneously oxidized, with compounds in the
petroleum as well as in the environment acting as sensitizers [121-123]. Therefore, the
rate of photodegradation depends on the composition of the petroleum product as well
as the environmental conditions including the dissolved organic and inorganic matter, the
intensity of the sunlight and the temperature [30, 137].

50

Most recent studies have focused on using new analytical instrumentation to
identify products formed by photooxidation during weathering of petroleum spills. In many
previous studies, instrumental limitations made identifying oxidized products in crude oil
challenging [116]. For example, most oxidize products could not be analyzed by GC-MS.
In addition, GC-MS did not provide adequate separation compounds in crude oil. Recent
experiments have utilized two dimensional gas chromatography and high-resolution mass
spectrometry for the analysis of petroleum [34, 40, 116].
Islam et al. divided the fuel into fractions (saturate, aromatic, resin, and
asphaltene) and analyzed each fraction after photooxidation using gravimetric analysis
and Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) with
atmospheric pressure photoionization (APPI) [33]. The gravimetric analysis of petroleum
fractions is common for assessing weathering. Based on the gravimetric analysis, Islam
et al. showed that after photooxidation there was no statistical difference in the saturate
fraction, a significant increase in the resin fraction, and a significant decrease in the
aromatic fraction, which is consistent with most previous work [33, 138]. However, using
FT-ICR MS, substantial changes in the saturate fraction was observed.

After

photooxidation, there was a decrease in abundances of heteroatom-containing
compounds, particularly those containing sulfur, in the saturate fraction. There was also
an observed decrease in the number of compounds in the saturate fraction with high
double-bond equivalences (DBE), indicating preferential degradation of these
hydrocarbons [33]. This is contradictory to most work, which indicated that the saturate
fraction is relatively unchanged by photooxidation.

51

Radovic et al. showed preferential degradation for certain compounds, using
samples collected from the Deepwater Horizon platform blowout, treating them by
irradiation with a xenon source [118].

Samples were fractionated using thin-layer

chromatography followed by analysis using GC-MS and infrared spectroscopy. After
irradiation, there was a decrease in abundances of the aromatic fraction, an increase in
the resin fraction, and an increase in the oxygen content of the resin and asphaltenes.
Radovic et al. also observed preferential photooxidation for compounds with increased
alkyl substitution and additional aromatic rings [118].

In addition, Radovic et al.

demonstrated that PAHs with the same number of rings but with a peri-condensed
structure were preferentially degraded compared to those with a cata-condensed
structure [118, 139]. A peri-condensed PAH is more compact, with at least one carbon
atom shared between three aromatic rings.

They also observed degradation of

triaromatic steranes, which are typically thought of as unaltered by weathering and are
often used to determine the origin of the oil [118]. These findings demonstrated many of
the analytical challenges and conflicting conclusions still persistent in much published
literature dealing with the weathering of petroleum.
1.7 Objectives and Aims
Part of the challenge in assessing petroleum discharges arises from the complexity
of the sample and the changes in the physical and chemical properties that occur due to
weathering. Better understanding of the fundamentals of these weathering processes
shows promise to improve impact assessments of discharges and to assess remediation
effectiveness.

Current evaporation models rely on physical properties not readily

available for most fuels. This leads to estimations which can introduce additional error.

52

No model currently exists for predicting photodegradation in a complex mixture such as
petroleum. There are still significant knowledge gaps concerning what compounds in the
oil react, what products are formed, and by what mechanisms.
The objective of this research is to develop empirical rate constants for individual
compounds undergoing relevant weathering processes that will provide a better
understanding of the fundamental changes that occur during weathering. These rate
constants serve as the foundation for predictive models of the fate of petroleum in the
environment. In order to accomplish this objective, the following aims were outlined:
1. Generate rate constants capable of characterizing environmental weathering
processes.
2. Associate physical properties of compounds with analytical measurements, as a basis
for a model to predict the rate constant associated with the weathering processes.
3. Apply rate constants and subsequent models to weathering processes to elicit better
understanding of the fundamental changes that occur.
In this work, diesel fuel was subjected to evaporation and photodegradation. GCMS and ToF-MS were utilized to monitor the fuel during each weathering process. Kinetic
rate constants for individual compounds in each weathering process were generated
using the temporal change in abundance.

The kinetic rate constants allowed for

comparisons of individual compounds during weathering. From this work, models for
predicting evaporation over environmentally relevant temperature were developed. Rate
constants from photodegradation provided key insights into the decay and formation of
compounds during irradiation. The models developed from this work will predict rates of

53

specific weathering processes, rather than the comprehensive fate and transport of the
fuel. However, these models can be incorporated into more comprehensive models that
encompass other fate and transport models.

Moreover, this work will provide

methodologies for developing predictive models based on analytical properties, which
could be applied to other weathering processes such as dissolution or biodegradation.

54

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55

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66

2. Gas Chromatographic Retention Index as a Basis for Predicting
Evaporation Rates of Complex Mixtures
2.1 Introduction
The 2010 Deepwater Horizon oil spill in the Gulf of Mexico highlighted the
environmental hazards of petroleum discharges and the knowledge gaps that hinder
accurate impact assessment and remediation [1]. In particular, predicting the fate and
transport of petroleum continues to be an ongoing challenge. Discharged petroleum
constituents are distributed between air, water, and sediment on the basis of their physical
and chemical properties. The composition of a spill is continuously altered by physical,
chemical, and biological weathering processes that begin immediately after a release
occurs [2].

Physical weathering processes, including evaporation, change pollutant

distribution by transporting constituents away from the initial point of release [2].
Evaporation is the most prevalent contributor to losses of volatile petroleum constituents,
often accounting for up to 75% of the mass loss, and is therefore a critical component to
oil spill models [2-11]. The weathering processes continuously change the composition
of the fuel, as well as altering physical properties such as viscosity and density, making
comprehensive modeling very challenging [9, 12, 13]. Accurate predictive models are
necessary to determine the presence and loss of compounds, time of release [14, 15],
and source [16-18] of environmental spills.
The current models used to predict evaporation (Chapter 1) rely on estimations of
physical properties which increases uncertainty in the model or empirical measurements
which make extrapolation of the model challenging. Also, current models focus on

67

monitoring the evaporation of the bulk fuel, rather than the individual compounds within
the fuel. In this work, empirical measurements were utilized to determine evaporation
rate constants for individual compounds within the complex mixture.

These rate

constants were employed to build mathematical expressions to predict evaporation rates
for each compound. This approach has been previously used to determine evaporation
rate constants for normal alkanes in diesel fuel [19]. Regnier and Scott [19] demonstrated
that evaporation rate constants for the normal alkanes between n-nonane and noctadecane were first-order and could be predicted based on the vapor pressure of the
normal alkane.

In work by Smith [20], first-order evaporation rate constants were

calculated for individual compounds in a simple mixture based on the vapor pressure and
mass transfer coefficient of that compound, as well as the surface area, temperature, and
total number of moles in the spill. These works have demonstrated that first-order rate
constants can be utilized to determine the evaporation rate for individual compounds from
a simulated petroleum spill. However, in these previous works, only major constituents
were monitored, and no predictive model for all compounds was developed.
The use of physical properties, such as vapor pressure and boiling point, to predict
evaporation rates is theoretically based and accurate. However, it is cumbersome for
complex mixtures because of the large number of compounds. The use of physical
properties requires that the individual compounds be identified and that the corresponding
magnitude of the property be known. The prediction of physical properties by means of
analytical measurements is well reported in the literature [21-23]. Arey et al. [24] showed
that the retention index (I) in gas chromatography (GC) on a non-polar stationary phase
can be used to estimate the vapor pressure and boiling point. In addition, the retention

68

index on a second, polar stationary phase (i.e., 2-dimensional GC, or GC x GC) can be
used to estimate other physical properties such as water solubility and octanol–water
partition coefficient. GC x GC can also provide better separation of compounds, which
can assist in compound identification, especially when used with in conjunction with mass
spectrometry [25, 26].
An empirically-derived surrogate measurement, such as GC retention index, has
several distinct advantages. First, it will allow the development of a theoretically based
and accurate model of evaporation, without the challenges associated with using physical
properties. Moreover, it will obviate the need to identify the compounds present in a
complex mixture in order to predict the evaporation rates.

To demonstrate these

concepts, models were developed in this study to predict the kinetic rate constant for
evaporation of individual compounds, first based on boiling point, then based on GC
retention index. From the predicted kinetic rate constants, the fraction remaining of each
individual compound, as well as the fraction remaining of total fuel can be estimated.
2.2 Materials and Methods
2.2.1 Sample Collection
Diesel fuel was chosen as an illustrative complex mixture because of its wide range
of compounds (aliphatic, substituted aromatics, and polycyclic aromatic hydrocarbons)
and boiling points (~ 100 – 400 °C). Diesel fuel is also well suited for analysis by gas
chromatography-mass spectrometry (GC-MS). Diesel fuel was collected from a local
service station in East Lansing, Michigan in July of 2010. The fuel was transferred to
acid-washed amber bottles and stored at approximately 5 °C until use.

69

Several other petroleum fuels were used for the validation studies. Kerosene was
purchased from a local service station in July of 2010 and stored in amber bottles at
approximately 5 °C. Marine fuel stabilizer (Pennzoil, Houston, TX) was purchased and
stored in its original container.
2.2.2 Evaporation Chamber
An evaporation chamber was constructed to isolate external vibrations, maintain
constant temperature and humidity, control air flow, and minimize explosion hazards
(Figure 2-1). The chamber was fabricated from aluminum owing to its favorable thermal
properties. A Plexiglas front panel allowed for viewing of the samples, while a door in the
panel provided access to the interior of the chamber. A vibration-isolated shelf was
constructed to minimize any external disturbance of the samples. To control temperature,
the evaporation chamber was placed into an Ambi-Hi-Lo incubator (5 – 50 °C ± 0.5 °C,
model 3550DT, Lab-Line, Melrose Park, IL). To control relative humidity (RH), trays of
distilled water were placed inside the evaporation chamber. Temperature and humidity
were monitored and recorded at two-minute intervals using a data logger (0 – 55 °C ± 0.3
°C , 10 – 95% RH ± 5% RH, model TR-74Ui, T & D Corporation, Nagano, Japan). A
peristaltic pump (Masterflex L/S drive, model 7523-40, with L/S Easy-Load II pump head,
model 77200-62, Cole-Parmer, Vernon Hills, IL) with Viton tubing (Cole-Parmer)
circulated the air within the chamber (~ 80 mL min-1). A copper tube (12 in x 0.5 in OD x
0.37 in ID) filled with activated carbon (6 – 14 mesh, Fisher Scientific, Waltham, MA) was
placed in-line to remove volatile compounds as they evaporated from the diesel fuel,

70

Figure 2-1. Schematic diagram of the evaporation chamber in temperature-controlled
incubator. See Section 2.2.2 for detailed description.

71

thereby minimizing the explosion hazard. Additional dishes of activated carbon were
placed in the evaporation chamber and Ambi-Hi-Lo Incubator. High purity air was also
introduced to the chamber (~ 30 mL min-1) after being sparged through distilled water
located in the temperature-controlled oven.
2.2.3 Evaporation of Diesel Fuel
To develop the models, a thin film of diesel fuel (1.0 mL, ~0.5 mm) on distilled
water (15 mL) was evaporated in glass petri dishes (60 mm ID x 15 mm). Diesel samples
were evaporated at 20 °C in triplicate for nine different lengths of time (0 – 300 h). For
the validation studies, three different fuel samples, diesel, kerosene, and marine fuel
stabilizer, were evaporated at 20 °C for 100 h. For diesel fuel, three petri dishes were
prepared with fuel and water as previously described. An additional three dishes were
prepared with the fuel alone.

These latter dishes were weighed before and after

evaporation in order to determine the mass lost. For kerosene and marine fuel stabilizer,
two petri dishes were prepared with fuel and water and another dish with the fuel alone.
2.2.4 Gas Chromatography-Mass Spectrometry Analysis
After evaporation, the fuel residues were extracted from the petri dishes for GCMS analysis. Approximately 1 mL of dichloromethane was added to each dish, then the
diesel/water/dichloromethane mixture was quantitatively transferred to a separatory
funnel. The petri dish was rinsed with additional 2 – 3 mL aliquots of dichloromethane,
which were combined with the first in the separatory funnel. The organic layer was
transferred to a 10.0 mL volumetric flask. The extracted diesel residue was further diluted

72

(1:50) in dichloromethane and transferred to a sealed autosampler vial for GC-MS
analysis.
All analyses were performed using a gas chromatograph (model 7890N, Agilent
Technologies, Santa Clara, CA) with an automatic liquid sampler (model 7693, Agilent
Technologies) that was coupled to a mass spectrometer (model 5975, Agilent
Technologies).

The GC was equipped with a capillary column containing a 100%

poly(dimethylsiloxane) stationary phase (HP-1MS, 30 m x 0.25 mm x 0.25 μm, Agilent
Technologies). Compounds generally elute from this nonpolar stationary phase based
on boiling point owing to the weak interactions between the compound and stationary
phase. Ultra-high-purity helium was used as the carrier gas (1 mL min-1). The diluted
diesel extract (1 µL) was injected using a pulsed (15 psi for 0.25 min) split (50:1) injection
at 280 °C (the injection optimization is discussed below). The GC temperature program
began at 50 °C with a 5 °C min-1 ramp rate to 280 °C and a final hold time of 4 min. The
transfer line was maintained at 300 °C. The mass spectrometer employed electron
ionization (70 eV) with a quadrupole mass analyzer, which scanned mass-to-charge
ratios (m/z) 40 – 550 at a scan rate of 2.91 scans s-1.
An optimization was performed to minimize variation from injection in the GC-MS
analysis. Five normal alkanes (C8, C10, C12, C14, and C16), spanning a large range of
volatilities, were analyzed five times by GC-MS and the precision of the injection was
monitored using percent relative standard deviation (RSD) in the peak area. The injection
parameters that were tested included the pre- and post-injection dwell time, the pulsed
injection pressure and time, and the gas saver on or off (Table 2-1). The injection dwell
time is the length of time that the syringe is left in the injection port prior to or after injection.

73

A longer pre-injection dwell time helps the syringe to heat prior to injection, resulting in
more efficient volatilization. A longer post-injection dwell time ensures all of the sample
is delivered from the syringe. The pressure pulse prior to injection forces the sample onto
the column more quickly and minimizes degradation of the sample. The gas saver
reduces the flow rate from the split valve to minimize consumption of carrier gas.
Optimization (Table 2-1) resulted in increased precision of injection, with the average
RSD of the five normal alkanes decreasing from 8.5% prior to optimization to 2.9% after
optimization.
2.2.5 Identification and Quantification of Selected Compounds
After GC-MS analysis of the diesel fuel, individual compounds were identified and
quantified (Table 2-2). First, compound classes were assigned based on characteristic
fragment ions: normal alkanes (m/z 57), branched and cyclic alkanes (m/z 57 and m/z
83), alkyl aromatics (m/z 91 and m/z 105), and polycyclic hydrocarbons (m/z 91, m/z 117,
and m/z 128) [18, 27]. The m/z values of these fragments were used to generate
extracted ion chromatograms (EICs) that were characteristic of each compound class
[18]. By employing EICs, there was less interference from co-eluting compounds and an
increased signal-to-noise ratio, which allowed for detection of low-abundance
compounds. The total ion chromatogram (TIC) and example EICs for each compound
class are shown in Figure 2-2 to Figure 2-8. The selected compounds that are numbered
correspond to the peak numbers in Table 2-2.

74

Table 2-1. The injection parameters optimized using the precision in peak area of a
mixture of five normal alkanes.

Parameter

Range tested

Optimized Value

Pre-injection dwell time

0 – 0.06 min

0.02 min

Post-injection dwell time

0 – 0.08 min

0.05 min

Pressure pules

No pulse – 40 psi

15 psi

Pulse duration

0.1 – 1 min

0.25 min

Gas saver

On/off

Off

75

Compounds were identified by searching against a database of mass spectra
(NIST/EPA/NIH Mass Spectral Library 02, Version 2.0a, Agilent Technologies). To help
identify some structural isomers, relative retention indices were compared to literature
values [28]. In some cases, compounds could only be provisionally identified and were
assigned to a compound class based on characteristic ions from their mass spectra.
Seventy-eight selected compounds were monitored over the course of the evaporation
experiments, of which forty-six were definitively identified. Selection of compounds to
monitor was based on the ability to identify/classify the compound, the volatility of the
compound, and the abundance being greater than ~20% of the maximum peak in the
EIC.
To assist in identifying compounds and as part of the model development, the
retention index under temperature-programmed conditions (IT) was calculated for each
selected compound. The retention index is calculated based on the retention time of the
compound of interest (tTR,i) and the retention time of the normal alkanes of carbon number
z that elute before (tTR,z) and after (tTR,z+1) [29, 30].

 tT  tT

I T  100  T R,i RT,z  z
 t R, z1  t R,z 

Equation 2-1

The index is independent of GC parameters such as column dimensions,
stationary phase thickness, flow rate, and temperature program and, hence, is more
broadly applicable than retention time or retention factor. The retention index is an
advantageous surrogate over physical properties in the development of the model,

76

Table 2-2. Selected compounds monitored during evaporation of diesel fuel to develop
the model. The following information is listed for each compound: compound class, peak
number (#) (corresponding to peaks labeled in Figure 2-3 – Figure 2-8), mass-to-charge
ratio (m/z) of extracted ion chromatogram used for quantification, retention time (tTR),
boiling point (TB), retention index (IT), rate constant (k), characteristic lifetime (), and
number of  in 300 hours. For the compound class the follow abbreviations were used:
normal alkane (Norm), branched alkane (Bran), alkyl aromatic (Arom), polycyclic
hydrocarbon (Poly).
k (h-1)

 (h)

#  in
300 h

0.308

3.24

92.52

800

0.226

4.43

67.69

415

862

0.108

9.27

32.36

4.948

417

869

0.097

10.29

29.15

57

5.479

424

900

0.066

15.19

19.75

6

57

6.248

933

0.045

22.08

13.59

Bran

7

57

6.411

940

0.044

22.76

13.18

Methyl
nonane
isomer

Bran

8

57

6.883

960

0.033

30.30

9.90

Unidentified

Bran

9

57

7.105

970

0.029

34.67

8.65

Decane

Norm

10

57

7.816

447

1000

0.020

49.75

6.03

4-Methyl
decane

Bran

11

57

8.434

460

1024

0.016

61.08

4.91

5-Methyl
decane

Bran

12

57

9.326

1058

0.012

84.53

3.55

Compound

Class

#

m/z

tTR
(min)

TB
(K)*

2-Methyl
heptane

Bran

1

57

3.398

391

Octane

Norm

2

57

3.748

399

4-Methyl
octane

Bran

3

57

4.814

3-Methyl
octane

Bran

4

57

Nonane

Norm

5

Dimethyl
octane
isomer

Bran

Ethyl methyl
heptane
isomer

77

IT

Table 2-2 cont’d

Compound

Class

#

m/z

tTR
(min)

TB
(K)*

IT

k (h-1)

 (h)

#  in
300 h

2-Methyl
decane

Bran

13

57

9.506

462

1064

0.011

95.18

3.15

3-Methyl
decane

Bran

14

57

9.670

1071

0.010

97.63

3.07

Undecane

Norm

15

57

10.439

1100

0.007

134.07

2.24

Unidentified

Bran

16

57

11.960

1155

0.005

219.07

1.37

Methyl
undecane
isomer

Bran

17

57

12.217

1165

0.004

255.54

1.17

Unidentified

Bran

18

57

12.392

1171

0.004

258.38

1.16

Dodecane

Norm

19

57

13.184

1200

0.002

453.77

0.66

2,6-Dimethyl
undecane

Bran

20

57

13.616

1216

0.002

495.57

0.61

Unidentified

Bran

21

57

14.618

1254

0.001

771.87

0.39

Unidentified

Bran

22

57

15.213

1276

0.001

1182.54

0.25

Tridecane

Norm

23

57

15.848

1300

0.000

2041.5

0.15

Unidentified

Bran

24

57

17.527

1365

0.000

40719.8

0.01

2,6,10Trimethyl
decane

Bran

25

57

17.900

1379

Tetradecane

Norm

26

57

18.430

Unidentified

Bran

27

57

20.027

78

468

489

507

523

1400
1465

Table 2-2 cont’d

k (h-1)

 (h)

#  in
300 h

0.621

1.61

186.37

828

0.181

5.53

54.25

429

925

0.059

17.06

17.59

8.527

453

1027

0.018

54.77

5.48

11.272

477

1130

0.007

146.06

2.05

Compound

Class

#

m/z

tTR
(min)

TB
(K)*

IT

Pentadecane

Norm

28

57

20.890

540

1500

Hexadecane

Norm

29

57

23.186

554

1600

2,6,10Trimethyl
pentadecane

Bran

30

57

24.369

Heptadecane

Norm

31

57

25.395

Pristane

Bran

32

57

25.628

Octadecane

Norm

33

57

27.488

Phytane

Bran

34

57

27.791

1815

Nonadecane

Norm

35

57

29.539

1900

Eicosane

Norm

36

57

31.400

616

2000

Heneicosane

Norm

37

57

33.276

635

2100

Methyl
cyclohexane

Bran

38

83

2.856

374

Ethyl
cyclohexane

Bran

39

83

4.226

405

Propyl
cyclohexane

Bran

40

83

6.067

Butyl
cyclohexane

Bran

41

83

Pentyl
cyclohexane

Bran

42

83

79

1654
575

1700
1711

589

1800

Table 2-2 cont’d

Compound

Class

#

m/z

tTR
(min)

TB
(K)*

IT

k (h-1)

 (h)

#  in
300 h

Hexyl
cyclohexane

Bran

43

83

14.288

498

1241

0.002

491.22

0.61

Heptyl
cyclohexane

Bran

44

83

16.833

510

1338

0.000

2371.08

0.13

Octyl
cyclohexane

Bran

45

83

19.462

528

1442

Toluene

Arom

46

91

3.194

384

0.486

2.06

145.81

Ethyl
benzene

Arom

47

91

4.511

409

844

0.170

5.89

50.95

m/p-Xylene

Arom

48

91

4.663

412

853

0.135

7.39

40.57

o-Xylene

Arom

49

91

5.071

417

876

0.111

9.03

33.24

Propyl
benzene

Arom

50

91

6.365

432

938

0.055

18.05

16.62

Butyl
benzene

Arom

51

91

8.871

456

1040

0.017

57.36

5.23

Unidentified

Arom

52

91

10.171

1090

0.011

94.32

3.18

1,2,3,4Tetrahydronaphthalene

Poly

53

91

11.465

1137

0.008

133.32

2.25

Pentyl
benzene

Arom

54

91

11.576

1141

0.007

148.60

2.02

Methyl
tetralin
isomer

Poly

55

91

12.980

1193

0.004

227.41

1.32

Unidentified

Poly

56

91

17.066

1347

0.001

1980.24

0.15

Unidentified

Poly

57

91

19.660

1450

80

480

Table 2-2 cont’d

IT

k (h-1)

 (h)

#  in
300 h

945

0.047

21.50

13.96

953

0.037

26.99

11.11

962

0.040

25.02

11.99

978

0.032

31.40

9.56

996

0.028

35.28

8.50

1005

0.025

39.49

7.60

8.754

1036

0.018

56.47

5.31

105

8.854

1040

0.017

59.02

5.08

66

105

9.139

1050

0.016

62.08

4.83

Arom

67

105

10.113

1088

0.011

91.90

3.26

Indane

Poly

68

117

8.212

1015

0.027

37.16

8.07

Methyl
indane
isomer

Poly

69

117

9.565

1067

0.015

66.96

4.48

Compound

Class

#

m/z

tTR
(min)

Ethyl methyl
benzene
isomer

Arom

58

105

6.534

1,3,5Trimethyl
benzene

Arom

59

105

6.720

Ethyl Methyl
benzene
isomer

Arom

60

105

6.930

1,2,4Trimethyl
benzene

Arom

61

105

7.291

Unidentified

Arom

62

105

7.734

1,2,3Trimethyl
benzene

Arom

63

105

7.950

Methyl propyl
benzene
isomer

Arom

64

105

Methyl propyl
benzene
isomer

Arom

65

Methyl propyl
benzene
isomer

Arom

Unidentified

81

TB
(K)*

438

442

449

450

Table 2-2 cont’d

IT

k (h-1)

 (h)

#  in
300 h

10.958

1119

0.009

112.48

2.67

117

11.220

1128

0.008

118.47

2.53

72

117

13.516

1212

0.004

271.36

1.11

Poly

73

117

14.303

1242

0.003

379.08

0.79

Methyl
tetralin
isomer

Poly

74

117

14.974

1267

0.002

468.15

0.64

Methyl
tetralin
isomer

Poly

75

117

15.760

1297

0.001

787.51

0.38

Methyl
tetralin
isomer

Poly

76

117

16.349

1319

0.001

1110.96

0.27

Methyl
tetralin
isomer

Poly

77

117

17.591

1368

0.000

2785.81

0.11

Naphthalene

Poly

78

128

11.949

1155

0.008

127.33

2.36

Compound

Class

#

m/z

tTR
(min)

Unidentified

Poly

70

117

Unidentified

Poly

71

Unidentified

Poly

Methyl
tetralin
isomer

* Source reference [31]

82

TB
(K)*

491

Figure 2-2. Total ion chromatogram for diesel fuel. The bottom trace is an expanded
portion of the chromatogram, showing the region where more volatile compounds are
observed.

83

Figure 2-3. Extracted ion chromatogram of m/z 57 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2.

84

Figure 2-4. Extracted ion chromatogram of m/z 83 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2.

85

Figure 2-5. Extracted ion chromatogram of m/z 91 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2.

86

Figure 2-6. Extracted ion chromatogram of m/z 105 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2.

87

Figure 2-7. Extracted ion chromatogram of m/z 117 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak numbers correspond to the compounds listed in
Table 2-2.

88

Figure 2-8. Extracted ion chromatogram of m/z 128 for diesel fuel. The bottom trace is
an expanded portion of the chromatogram, showing the region where more volatile
compounds are observed. The peak number corresponds to the compound listed in
Table 2-2.

89

because many of the constituents in diesel fuel do not have known identities, boiling
points, or vapor pressures, which are required for most currently available evaporation
models. For the selected compounds, the identity, class membership, retention time,
retention index, and boiling point are also summarized in Table 2-2.
In addition to these compounds used for model development, a second set that
spanned the same range of retention times was selected for model validation. These
compounds (n = 27) were provisionally identified and assigned to one of the compound
classes described above (branched alkane: m/z 57, m/z 97, alkyl aromatic: m/z 105, m/z
117, m/z 119, polycyclic hydrocarbon: m/z 117, m/z 137, m/z 138). For these compounds,
the class membership, retention time, and retention index are summarized in Table 2-3.
For both the model development and validation sets, the compounds were
quantified based on their peak heights in the EIC. Peak heights, rather than peak areas,
were chosen for quantification because they were more precise. Precision was measured
using RSD for all selected compounds in the EIC of m/z 57 across nine replicates. The
precision using peak heights was 8.4% compared to 11.3% for peak areas. For peaks
that were not baseline resolved, reproducible determination of the baseline was
challenging, leading to variability in determination of peak areas. To further improve
precision, the peak heights of all selected compounds were normalized to the height of
n-heneicosane (C21) in the EIC of m/z 57. n-Heneicosane was selected for normalization
since it was a late-eluting peak and was unaffected by evaporation during the time course

90

Table 2-3. Selected compounds monitored during evaporation of diesel fuel to validate
the model. The following information is listed for each unidentified compound: compound
class, mass-to-charge ratio (m/z) of extracted ion chromatogram used for quantification,
retention time (tTR), retention index (IT), rate constant (k), characteristic lifetime (), and
number of  in 300 hours. The absolute percent error (APE) between the experimental
and predicted rate constant is also shown.
Class

m/z

tTR
(min)

IT

k (h-1)

 h

# t in
300 h

k (h-1)
predicted

APE

Branched
Alkane

57

12.094

1160

0.004

238.67

1.26

0.004

6.2

Branched
Alkane

97

3.800

803

0.244

4.10

73.26

0.186

23.8

Branched
Alkane

97

5.205

884

0.087

11.52

26.03

0.080

8.2

Branched
Alkane

97

5.578

904

0.076

13.11

22.89

0.065

15.3

Branched
Alkane

97

7.326

979

0.027

36.74

8.16

0.030

8.6

Branched
Alkane

97

7.390

982

0.028

35.63

8.42

0.029

2.3

Branched
Alkane

97

7.647

993

0.027

37.49

8.00

0.026

4.0

Branched
Alkane

97

9.943

1081

0.010

98.74

3.04

0.010

0.5

Branched
Alkane

97

10.241

1092

0.010

104.42

2.87

0.009

5.6

Alkyl
Aromatic

105

5.723

910

0.075

13.32

22.51

0.061

19.3

Alkyl
Aromatic

105

11.605

1142

0.006

156.74

1.91

0.005

16.0

Alkyl
Aromatic

105

11.832

1151

0.006

160.77

1.87

0.005

21.0

91

Table 2-3 cont’d

Class

m/z

tTR
(min)

IT

k (h-1)

 h

# t in
300 h

k (h-1)
predicted

APE

Alkyl
Aromatic

117

14.641

1255

0.002

465.88

0.64

0.002

22.7

Alkyl
Aromatic

119

8.002

1007

0.024

42.45

7.07

0.022

6.4

Alkyl
Aromatic

119

8.084

1010

0.022

44.63

6.72

0.021

4.7

Alkyl
Aromatic

119

8.864

1033

0.018

55.20

5.43

0.017

7.3

Alkyl
Aromatic

119

8.941

1043

0.015

68.31

4.39

0.015

3.6

Alkyl
Aromatic

119

9.617

1069

0.012

80.56

3.72

0.012

6.6

Alkyl
Aromatic

119

11.686

1145

0.006

154.72

1.94

0.005

19.6

Alkyl
Aromatic

119

11.797

1149

0.006

168.58

1.78

0.005

16.0

Alkyl
Aromatic

119

12.036

1158

0.005

182.92

1.64

0.005

16.8

Polycyclic
Hydrocarbon

119

10.650

1104

0.009

115.55

2.60

0.008

7.5

Polycyclic
Hydrocarbon

119

11.360

1134

0.007

138.98

2.16

0.006

18.3

Polycyclic
Hydrocarbon

137

10.532

1103

0.009

115.01

2.61

0.008

7.3

Polycyclic
Hydrocarbon

137

13.645

1217

0.003

345.93

0.87

0.002

15.2

Polycyclic
Hydrocarbon

137

13.907

1227

0.003

367.34

0.82

0.002

18.7

Polycyclic
Hydrocarbon

138

9.052

1047

0.016

62.65

4.79

0.015

9.1

92

of these experiments. To confirm linear response for the purposes of quantification,
calibration curves for 27 selected compounds were obtained over the range of
concentrations typically found in diesel fuel (0 – 1.4 mM), with coefficients of
determination (R2) in the range of 0.992 – 0.999 (Table 2-4).
2.3 Results and Discussion
2.3.1 Determination of Kinetic Rate Constants
Example TICs of diesel fuel evaporated for 0, 7, 30, and 300 h are shown in Figure
2-9. Early eluting compounds are the most volatile and evaporate first, whereas later
eluting compounds remain relatively unchanged over the course of the evaporation
experiment. For each compound of interest (Section 2.2.5), a decay curve was generated
by plotting the normalized abundance as a function of evaporation time. Example decay
curves for four normal alkanes are shown in Figure 2-10. As expected, abundances of
the more volatile compounds, such as n-octane (Figure 2-10a), decay more quickly than
less volatile compounds, such as n-tetradecane (Figure 2-10d).

93

Table 2-4. Compounds utilized to confirm linearity of calibration curves. For each
compound, the retention time (tTR), concentration range, slope (m), intercept (b), and
coefficient of determination (R2) are shown.
Compound

tTR
(min)

Concentration
(M)

m

b

R2

Toluene

3.141

2.34E-04 – 1.17E-03

3E+10

-1E+06

0.997

Ethylbenzene

4.514

2.32E-04 – 1.16E-03

3E+10

-2E+05

0.998

p-Xylene

4.660

2.28E-04 – 1.14E-03

3E+10

-2E+05

0.997

o-Xylene

5.105

2.36E-04 – 1.18E-03

3E+10

-6E+05

0.998

Nonane

5.178

2.30E-04 – 1.15E-03

2E+10

3E+05

0.997

Propylbenzene

6.408

2.34E-04 – 1.17E-03

4E+10

-2E+06

0.997

1,2,4Trimethylbenzene

7.366

2.29E-04 – 1.15E-03

4E+10

-1E+06

0.997

Decane

7.471

2.24E-04 – 1.12E-03

3E+10

9E+05

0.998

Butyl Cyclohexane

8.314

2.26E-04 – 1.13E-03

4E+10

5E+05

0.998

Indan

8.448

2.31E-04 – 1.15E-03

4E+10

-1E+05

0.997

Butylbenzene

8.976

2.29E-04 – 1.15E-03

5E+10

-3E+06

0.997

Undecane

10.114

2.29E-04 – 1.15E-03

3E+10

-3E+05

0.998

1,2,4,5Tetramethylbenzene

10.590

2.31E-04 – 1.16E-03

5E+10

-1E+06

0.996

Tetralin

11.853

2.27E-04 – 1.14E-03

5E+10

-4E+05

0.998

Naphthalene

12.463

2.30E-04 – 1.15E-03

5E+10

-3E+06

0.992

94

Table 2-4 cont’d

Compound

tTR
(min)

Concentration
(M)

m

b

R2

Dodecane

12.856

2.70E-04 – 1.35E-03

3E+10

-3E+05

0.998

Tridecane

15.555

2.28E-04 – 1.14E-03

4E+10

-1E+06

0.998

Tetradecane

18.147

2.27E-04 – 1.14E-03

5E+10

-1E+06

0.998

Pentadecane

20.618

2.29E-04 – 1.15E-03

5E+10

-2E+06

0.998

Fluorene

22.611

2.28E-04 – 1.14E-03

8E+10

-7E+06

0.995

Hexadecane

22.964

2.28E-04 – 1.14E-03

6E+10

-1E+06

0.998

Heptadecane

25.197

2.29E-04 – 1.15E-03

6E+10

-3E+06

0.998

Octadecane

27.322

2.22E-04 – 1.11E-03

7E+10

-4E+06

0.999

Nonadecane

29.348

2.27E-04 – 1.14E-03

7E+10

-5E+06

0.999

Eicosane

31.283

2.27E-04 – 1.13E-03

8E+10

-6E+06

0.999

Pyrene

33.405

2.27E-04 – 1.13E-03

1E+11

-8E+06

0.997

95

Figure 2-9. Total ion chromatograms of diesel fuel evaporated at 20 °C for 0 – 300 h.
For reference, selected n-alkanes are labeled by carbon number. n-Heneicosane (C21)
was used for normalization (*).

96

Figure 2-10. Residual abundances of n-octane (a), n-decane (b), n-dodecane (c), and ntetradecane (d) as a function of evaporation time normalized to the peak height of nheneicosane in the EIC at m/z 57. Linear regression equations: n-octane: Ct = 0.448 *
exp (-2.26 * 10-1 * t), R2 = 0.980, F = 3882; n-decane: Ct = 5.926 * exp (-2.01 * 10-2 * t),
R2 = 0.982, F = 4359; n-dodecane: Ct = 10.475 * exp (-2.20 *10-3 * t), R2 = 0.807, F =
330; n-tetradecane: Ct = 9.276 * exp (-0.00 * 100 * t), R2 = 0.000, F = 0. The rate constant,
k, is underlined in each equation.

97

Figure 2-10 cont’d

98

Based on the decay curve for each compound, the kinetic rate constant, k, was
determined by non-linear regression (TableCurve 2D, version 5.01, Jandel Scientific, San
Rafael, CA). All compounds were assumed to have a first-order kinetic decay [20],

C t  C 0 exp(  k t )

Equation 2-2

where Ct is the concentration at time t and C0 is the initial concentration [11, 32]. The
resulting decay curve and regression line for the normal alkanes is shown in Figure 2-10.
Based on the curve fitting, the evaporation rate constant for n-octane (Figure 2-10a) was
determined to be 2.3 * 10-1 h-1 with a coefficient of determination (R2) of 0.98, indicating
a good quality of fit [33]. The rate constants for n-decane (Figure 2-10b) and n-dodecane
(Figure 2-10c) were 2.0 * 10-2 h-1 (R2 = 0.98) and 2.2 *10-3 h-1 (R2 = 0.81), respectively.
The rate constant for n-tetradecane (Figure 2-10d) was 0.0 h-1, indicating that the
concentration did not change measurably over the course of 300 h. Rate constants for
all selected compounds are available in Table 2-2. As demonstrated by the rate constants
in the tables, compounds with larger IT values and, hence, lower volatility, exhibited
smaller rate constants. An increase in retention index of about 200 (or two methylene
groups) resulted in approximately one order-of-magnitude decrease in k.
In order to accurately determine the rate constant, it is important that experimental
data represent an adequate portion of the decay curve. The completeness of a decay
curve can be expressed in terms of the characteristic lifetime,, which is equal to 1/k. A
minimum of 5  (99.3% completion for a first-order decay) is considered necessary to
adequately fit the decay curve [34]. However, in 300 h, many of the selected compounds

99

had less than 5  (Table 2-2). A chromatogram which highlights the regions with decay
curves corresponding to various number of  is shown in Figure 2-11.
In order to include more compounds in the development of the model, the error
introduced when fitting decay curves with less than 5  was investigated. For 14 selected
compounds, each yielding measurements spanning more than 5 , the number of  was
altered by removing the last time point of the decay curves. The rate constant was then
recalculated, based on fewer , using the curve-fitting software.

This process was

repeated until only three points remained in each curve, resulting in a number of  ranging
from approximately 0.01 to 163.
The error calculation for this work was based on the mean absolute percent error
(MAPE) [35, 36]. The absolute error is calculated between the rate constant from the
complete decay curve (k) and the observed rate constant from the truncated decay curve
(kobs), and then averaged across all observations (n).
n



MAPE 

i 1

k i  k obs ,i
ki
n

Equation 2-3

100

While there are a number of valid methods for calculating error, the MAPE is commonly
applied and easy to interpret [36].
The MAPE between the original k (fit over 300 h) and the new k (< 300 h) was

100

Figure 2-11. A chromatogram of unevaporated diesel fuel showing the compounds with
decay curves corresponding to >5  (blue), 5 – 1  (yellow), 1 – 0.5  (red), and <0.5 
(green).

101

calculated for each iteration. When more than 5  was used for the curve fitting, there
was little difference (0.0003%) between the newly determined rate constant and the
original. When 1 – 5  was used for the curve fitting, 1% error in k was observed and for
the evaporation rate constant, with a mean average percent error of 3%. When 0.5 – 1 
was used, 13% error was observed. When less than 0.5  was used, the error in k
increased significantly to 38%. Therefore, compounds with more than 0.5  were selected
for inclusion in the development of the predictive model
When the decay curves for selected compounds were fit, the coefficient of
determination (R2) and the F-statistic were found to scale with the number of  (Figure
2-12). The coefficient of determination consistently increased with an increase in the
number of . More spread is observed for the F-statistic. This likely arise from the
increased uncertainty when the decay occurs quickly, and there are only a few points
before the decay is completed. When less than 0.5  was used to determine the rate
constant, the R2 was constantly below 0.7 (Figure 2-12a) and the F-statistic was
consistently below 200 (Figure 2-12b), at which point curves were considered to have a
questionable fit. When greater than 0.5  was used in the decay curve, the R2 was
consistently above 0.7 and maximized at 0.98 while the F-statistic was over 200, and
maximized at 6800. The relative standard deviation was consistently below 8% when
using greater than 0.5 . This demonstrates that a decay curve with greater than 0.5
provided sufficient data to obtain an appropriate fitting with minimal error.

102

a

b

Figure 2-12. The coefficient of determination (a) F-statistic (b), and relative standard
deviation for each compound versus the number of tau () in the decay curve. The inset
in a shows an expanded region, from 0 – 5.

103

Figure 2-12 cont’d

c

104

For the 300 h evaporation time, only those compounds eluting during the first 15%
of the chromatogram (IT < 1040) yielded data with greater than 5  (Figure 2-11). This
corresponded to 29 of the selected compounds. By utilizing rate constants generated
from decay curves with greater than 0.5  (rather than 5 ), 30% of the chromatogram (IT
< 1260) could be used for model development (Figure 2-11). This corresponded to 51 of
the selected compounds, with rate constants varying from 0.002 to 0.621 h-1. The cutoff
of 0.5  allows for the inclusion of more compounds, while still enabling the accurate
determination of rate constants, which is critical for the development of robust predictive
models. The values for IT, k, , and number  in 300 h are summarized in Table 2-2 for
all selected compounds.
2.3.2 Predicting Kinetic Rate Constant Based on Boiling Point
Initially, a model was developed to predict the evaporation rate constant based on
known boiling points. Figure 2-13a shows the natural logarithm of the rate constant as a
function of boiling point for five normal alkanes (C8 – C12). For a homologous series (in
this case, normal alkanes), correlation is observed between the number of methylene
groups and physical properties such as boiling point. This relationship exists because
the change in free energy of evaporation upon addition of each methylene group is
constant [37, 38]. The natural logarithm of the rate constant versus boiling point plot is
linear for the normal alkanes with a high coefficient of determination (R2 = 0.999),
indicating that boiling point is an appropriate predictor for the rate constant. A linear
relationship (R2 = 0.961) is still observed when additional compounds from other classes
(normal alkanes, branched and cyclic alkanes, alkyl aromatics, and polycyclic

105

hydrocarbons) were included in the plot (Figure 2-13b). This demonstrates that the
boiling point of a compound can reliably be used to predict the rate constant for
evaporation.
In order to develop a widely applicable model, the basis of the model must be
derived from an easily obtained property. However, physical properties such as boiling
point present a substantial challenge when used as the basis of a model, because the
compound must be identified and the boiling point must be known.

Unambiguous

identification by GC-MS is often challenging, especially when structural and positional
isomers are present. In addition, values of the physical properties are not available for
many compounds found in diesel fuel.
2.3.3 Predicting Kinetic Rate Constant Based on Retention Index
An empirical surrogate for boiling point would provide a promising basis for
predictive models of evaporation, because definitive identification would not be
necessary. In this work, a 100% poly(dimethylsiloxane) stationary phase was utilized in
the GC-MS analysis. Molecular interactions with this stationary phase are dominated by
weak London dispersion forces, such that compounds elute from the column based on
their boiling points [39]. Figure 2-13c shows the relationship between boiling point and
chromatographic retention index for 23 compounds from the four compounds classes
previously discussed. A linear relationship exists between the boiling point and retention
index (R2 = 0.991), which demonstrates that retention index is a suitable surrogate for
boiling point.

106

Figure 2-13. Natural logarithm of evaporation rate constant (ln (k)) versus boiling point
for normal alkanes (a). Linear regression equation: y = -5.09 * 10-2 * x + 18.83, R2 =
0.999, n = 5. Natural logarithm of evaporation rate constant (ln(k)) versus boiling point
for all selected compound classes (b): normal alkanes (), branched alkanes (), alkyl
benzenes (), and polycyclic hydrocarbons (). Linear regression equation: y = -4.51 *
10-2 * x + 16.71, R2 = 0.961, n = 23. Compound with the * indicates naphthalene, which
sublimes and likely contains large error in the boiling point. Boiling point versus
chromatographic retention index on HP-1MS stationary phase (c). Linear regression
equation: y = 2.33 * 10-1 * x + 213.2, R2 = 0.991, n = 23.

107

Figure 2-13 cont’d
-1

b

-2

ln (k) (h-1)

-3
-4
*

-5
-6
-7
375

400

425
450
Boiling Point (K)

475

500

525

c

Boiling Point (K)

500

*

475
450
425
400
375
750

850

950
1050
Retention Index

108

1150

1250

Models were developed to predict evaporation rate constants by linear regression
of the natural logarithm of the experimentally determined rate constant (ln (k)) versus the
retention index (IT)
Equation 2-4

ln(k)  m IT  b

where m and b are the slope and intercept determined from the regression. When the
regression was performed using only the normal alkanes, there was a strong linear
relationship with a high coefficient of determination (R2 = 0.999), which is expected for a
homologous series based on linear free energy relationships [37, 38, 40]. The regression
of other homologous series behaved similarly.

For example, the alkyl-substituted

cyclohexanes (methyl to hexyl) from the branched alkane class and the mono-substituted
alkyl benzenes (methyl to pentyl) from the alkyl aromatic class demonstrated a similar
coefficient of determination (R2 = 0.999) for the linear regression of Equation 2-4 to that
of the normal alkanes.
Class-specific models were developed to predict evaporation rate constants (Table
2-5). The goodness of fit to the linear regression model for the branched alkane (R2 =
0.994), alkyl aromatic (R2 = 0.992), and polycyclic hydrocarbon (R2 = 0.992) classes was
lower than that for the homologous series discussed above.

The coefficient of

determination was expected to decrease in the absence of a repeating structural unit.
The R2 value from the linear regression of the boiling point versus the retention index
(Figure 2-13c, R2 = 0.991) serves as a measure of the expected goodness of fit for a nonhomologous series. Each of the class-specific models had coefficients of determination
equal to or greater than the expected value. A plot showing the regression for each
compound class is shown in Figure 2-14.
109

Table 2-5. Class-specific models developed to predict the rate constant, based on the
uncorrected retention index. For each model, the number of compounds used to create
the model (n) as well as the slope (m), intercept (b), and coefficient of determination (R2)
for Equation 2-3 are shown. In addition, the mean absolute percent error (MAPE) for
predicting compounds in each class is shown. For the compound class the follow
abbreviations were used: normal alkane (Norm), branched alkane (Bran), alkyl aromatic
(Arom), polycyclic hydrocarbon (Poly).
MAPE in k for Compounds in Each Class
Model
Basis

n

ma

bb

R2

Norm

Bran

Arom

Poly

All

Norm

5

-1.14 * 10-2

7.61

0.999

4.9

10

19

43

19

Bran

19

-1.08 * 10-2

7.05

0.994

12

8.2

14

32

15

Arom

17

-1.08 * 10-2

7.20

0.992

26

17

5.7

22

15

Poly

10

-1.00 * 10-2

6.47

0.992

44

36

15

4.0

23

All

51

-1.04 * 10-2

6.70

0.981

24

15

6.9

20

14

a. Slope (h-1)
b. Intercept (h-1)

110

Figure 2-14.
Natural logarithm of evaporation rate constant (ln (k)) versus
chromatographic retention index on HP-1MS stationary phase for all selected compound
classes: normal alkanes (), branched alkanes (), alkyl benzenes (), and polycyclic
hydrocarbons (). The linear regression of each model is shown: normal alkanes (green),
branched alkanes (blue), alkyl benzenes (red), polycyclic hydrocarbons (purple), and
comprehensive (black). The regression equations are shown in Table 2-5.

111

A comprehensive model was also developed that incorporated compounds from
all classes (Figure 2-15). When the linear regression was performed, an unexpected
decrease in the coefficient of determination (R2 = 0.981) was observed, relative to the
class specific models. In order to test the origin of this discrepancy, each class (normal
alkane, branched alkane, branched aromatic, and polycyclic hydrocarbon) was
sequentially added into the comprehensive model (Table 2-5). The decrease in R2 was
observed after the aromatic and polycyclic hydrocarbon classes were included. Many of
the alkyl aromatic and polycyclic hydrocarbons were positioned above the regression line
(Figure 2-15), indicating that these compounds behaved differently than the normal and
branched alkanes, the origin of which will be discussed in Section 3.4.
The four class-specific models and the comprehensive model were used to predict
evaporation rate constants for the selected compounds (n = 5 – 19, Table 2-2 and Table
2-5). The absolute percent error between the predicted and observed rate constant was
determined, and the mean absolute percent error (Equation 2-3) for each model was
calculated (Table 2-5). The lowest errors were observed when a class-specific model
was used to predict the rate constants for compounds in that class. For example, when
the model for normal alkanes was used to predict the rate constants for normal alkanes,
the average error was 4.9%. Using the branched alkane, alkyl aromatic, and polycyclic
hydrocarbon models to predict the rate constant for compounds from those classes, the
MAPE was 8.2%, 5.7%, and 4.0%, respectively. However, when the incorrect class-

112

Figure 2-15.
Natural logarithm of evaporation rate constant (ln (k)) versus
chromatographic retention index on HP-1MS stationary phase for all compound classes:
normal alkanes (), branched alkanes (), alkyl benzenes (), and polycyclic
hydrocarbons (). Linear regression equation: y = -1.04 * 10-2 * x + 6.70, R2 = 0.981, n
= 51.

113

specific model was applied to predict the rate constant, the error was much larger. For
example, when the normal alkane model was used to predict compounds from the
polycyclic hydrocarbon class, the MAPE was 43%. This illustrates the importance of
proper classification of compounds when applying class-specific models.

However,

classification can be challenging for many compounds found in complex samples such as
diesel fuel.
If class membership is not known, the comprehensive model allows prediction of
the evaporation rate constant with a mean absolute percent error of 14.2%. When the
comprehensive model was used, there was greater error than with the correct classspecific model. The largest error was observed for the prediction of compounds from the
normal alkane class (24.3%). The mean absolute percent error for the branched alkane,
alkyl aromatic, and polycyclic hydrocarbon classes was 15.0%, 6.9%, and 19.7%,
respectively. The greater error observed for the normal alkane class is likely due to the
relatively few compounds included in that class (n = 5). The lower error observed for the
alkyl aromatic class is likely due to the large number of compounds (n = 17), observed
over a narrow retention index range (844  IT  1141). In addition, many of these
compounds are volatile, which means that a greater number of  is included in the decay
curve to determine the rate constant. The comprehensive model is advantageous since
knowledge of class membership is not necessary. However, if class membership is
known, the class-specific models result in approximately 10% less error in the
determination of the rate constant.

114

2.3.4 Correction of Retention Indices using McReynolds Constants
As noted above, many of the compounds from the alkyl aromatic and polycyclic
hydrocarbon classes are positioned above the regression line in the plot of the natural
logarithm of the rate constant versus the retention index (Figure 2-15). This error in
position occurs because many of these compounds are more retained on the stationary
phase than expected, based on the compound’s boiling point.

Using a 100%

poly(dimethylsiloxane) stationary phase, compounds are expected to elute based on
boiling point. However, some compounds appear to be more retained than expected due
to additional analyte/stationary phase interactions.

To evaluate the extent of this

additional retention, the McReynolds constants (IT) were utilized. The McReynolds
constant for a particular probe molecule is calculated by subtracting the retention index
of that probe on a stationary phase of interest from that on squalane. Squalane is a
nonpolar, purely hydrocarbon stationary phase capable only of London forces [39]. For
example, the McReynolds number for benzene on a 100% poly(dimethylsiloxane)
stationary phase (specifically OV-101) is 17 [41]. A shift of 100 IT units corresponds to a
shift of one methylene group. Therefore, an increase in retention index of 17 indicates
that the compound is more retained by approximately 0.17 methylene units on the 100%
poly(dimethylsiloxane) stationary phase. The additional retention is likely due to electron
donor/acceptor interactions between benzene and the oxygen atoms in the backbone of
the polysiloxane stationary phase. This suggests that alkyl aromatic and polycyclic
hydrocarbons also have additional interactions with the stationary phase.
To correct the retention index for these additional interactions, the McReynolds
constant for benzene on the 100% poly(dimethylsiloxane) stationary phase (IT = 17) was

115

subtracted from the retention indices for all compounds from the alkyl aromatic and
polycyclic hydrocarbon classes. Within the McReynolds system, benzene is considered
to be the representative probe for aromatic hydrocarbons. Specific probes do not exist
for alkyl aromatic and polycyclic aromatic hydrocarbons; however the difference in
retention index between the 100% poly(dimethylsiloxane) and squalane stationary
phases for these compounds is very similar to that for benzene [28]. When this correction
is applied, the retention index more accurately represents the boiling point for these
compounds, which improves the performance of the model.
The class-specific and comprehensive models were reconstructed using the
corrected retention indices (Figure 2-16 and Figure 2-17). The class-specific models had
the same coefficient of determination and prediction error as those prior to retention index
correction (Table 2-6). However, the coefficient of determination for the comprehensive
model increased from R2 = 0.981 to R2 = 0.990 when the corrected IT values were utilized.
This coefficient of determination was more similar to those for the class-specific models.
This improvement in goodness of fit for the comprehensive model resulted in an increase
in prediction accuracy (Table 2-6). The mean absolute percent error for all compounds
decreased from 14.2% to 10.3%.
These results suggest that the methodologies developed in this work may be more
broadly applicable to chromatographic separations on other stationary phases. To test
this hypothesis, retention indices of all selected compounds were experimentally
determined on a 5%-phenyl-95%-methylpolysiloxane stationary phase (HP-5MS, 30 m x

116

Figure 2-16. Natural logarithm of evaporation rate constant (ln (k)) versus corrected
chromatographic retention index on HP-1MS stationary phase for all selected compound
classes: normal alkanes (), branched alkanes (), alkyl benzenes (), and polycyclic
hydrocarbons (). The linear regression of each model is shown: normal alkanes (green),
branched alkanes (blue), alkyl benzenes (red), polycyclic hydrocarbons (purple), and
comprehensive (black).

117

Figure 2-17. Natural logarithm of evaporation rate constant (ln (k)) versus corrected
chromatographic retention index on HP-1MS stationary phase for all compound classes:
normal alkanes (), branched alkanes (), alkyl benzenes (), and polycyclic
hydrocarbons (). Linear regression equation: y = -1.05 *10-2 * x + 6.71, R2 = 0.990, n =
51.

118

Table 2-6. Class-specific models developed to predict the rate constant, based on the
corrected retention index. For each model, the number of compounds used to create the
model (n) as well as the slope (m), intercept (b), and coefficient of determination (R2) for
Equation 2-3 are shown. In addition, the mean absolute percent error (MAPE) for
predicting compounds in each class is shown. For the compound class the follow
abbreviations were used: normal alkane (Norm), branched alkane (Bran), alkyl aromatic
(Arom), polycyclic hydrocarbon (Poly).

MAPE in k for Compounds in Each Class

a.
b.

Model
Basis

n

ma

bb

R2

Norm

Bran

Arom

Poly

All

Norm

5

-1.14 * 10-2

7.61

0.999

4.9

10

6.8

30

13

Bran

19

-1.08 * 10-2

7.05

0.994

12

8.2

6.8

19

10

Arom

17

-1.08 * 10-2

7.02

0.992

9.7

8.1

5.7

22

10

Poly

10

-1.00 * 10-2

6.31

0.992

28

18

15

4.0

15

All

51

-1.05 * 10-2

6.71

0.990

16

9.3

7.8

14

10

Slope (h-1)
Intercept (h-1)

119

0.25 mm x 0.25 μm, Agilent Technologies). These retention indices were corrected based
on the McReynolds constant for benzene on an equivalent stationary phase (specifically,
OV-73,  IT = 40) in the same manner as described above. The model developed for the
5% phenyl stationary phase (y = -1.04 * 10-2 IT + 6.59, R2 = 0.984) was not statistically
different ( = 0.005) from that for the 100% poly(dimethylsiloxane) stationary phase (y =
-1.05 * 10-2 IT + 6.71, R2 = 0.990). This demonstrates that retention indices measured on
any stationary phase can be utilized in this model, provided there are appropriate
McReynolds constants available for the stationary phase and compounds of interest.
2.3.5 Model Validation
Twenty seven additional compounds were selected for model validation from the
branched alkane, alkyl benzene, and polycyclic hydrocarbon classes.

Kinetic rate

constants were experimentally determined in the same manner as those used to develop
the model (Section 2.3.1). The experimental rate constants were compared to the values
predicted by using Equation 2-4, after retention index correction (Table 2-3). The MAPE
was 7.6%, with a range of 0.3% – 23.8%. This is comparable to or better than the 10.3%
MAPE observed for the prediction of the rate constant of the 51 compounds used to
generate the model (Table 2-6).
2.4 Applications of the Models
The models developed in Section 1.3 allow prediction of the evaporation rate
constant (k) for each compound based on retention index (IT). Once k is determined, the
fraction remaining (FIT) can be predicted at time t by rearranging Equation 2-2.

120

FIT  CIT ,t / CIT ,0  exp(k t )

Equation 2-5

The equation to predict the rate constant (Equation 2-4) can be substituted in Equation
2-5 to generate a predictive model for the fraction remaining of an individual compound
Equation 2-6

FIT  exp((exp(m I T  b) t ))

where the slope (m) and intercept (b) are model specific (Tables 2 and 3). For example,
the fraction remaining predicted by using the comprehensive model with retention index
correction is
Equation 2-7

FIT  exp((exp(0.105 I T  6.71) t ))

To test the accuracy of predicting the fraction remaining of a compound, a
validation set of six diesel samples, evaporated at 20 °C, was used. The predicted
fraction remaining of each compound was calculated based on Equation 2-7, using the
corrected retention index (IT) and evaporation time (t) of 100 h. The fraction remaining
(ranging from 0 – 1) can be plotted as a function of the retention index, showing the
fraction remaining for each compound. Figure 2-18 shows the fraction remaining at each
retention index, superimposed over a chromatogram of diesel fuel. For example, the
predicted fraction remaining of n-undecane (IT = 1100) was calculated as 0.434, indicating
that 43% of n-undecane remains after 100 h of evaporation.

121

Figure 2-18. Total ion chromatogram of diesel fuel with the fraction remaining at each
retention index (red dashed line) for evaporation at 20 °C for 100 h.

122

The experimental fraction remaining was calculated by dividing the average
normalized peak height in the EIC of each selected compound in the evaporated samples
by that in the unevaporated samples. For n-undecane, the fraction remaining based on
the EIC of m/z 57 was 0.413, a 5.0% absolute error from the predicted value. For all
compounds, the absolute percent error (APE) ranged from 0.0 to 300% and had a MAPE
of 55% (Table 2-7). When FIT was less than 0.1 (IT < 1050), the MAPE was 131%. The
large error in FIT at retention indices below 1050 was due to the very small fraction
remaining (Table 2-7). When a relative error calculation is used for small numbers, the
error appears inflated [36]. The mean absolute error in this region was only 0.03. When
FIT was 0.1 – 0.5 (1050 < IT < 1150), the MAPE was 42%. The higher error in this region
was not surprising as this is where the fraction remaining curve increases sharply at the
inflection point (Figure 7). In this region, small variations in the retention index of a
compound could result in larger errors in the fraction remaining. When FIT was greater
than 0.5 (IT > 1150), the MAPE was 5.9%. The change in the fraction remaining curve in
this region is relative small, leading to the lower error.

When the low abundance

compounds are excluded from the MAPE calculation, (FIT = 0.1 – 1), the MAPE was 13%.
In addition to the fraction remaining of individual compounds of interest, the models
developed in this work can also be utilized to predict the total fraction remaining (Ftot).
The Ftot is calculated by summing Equation 2-7 over the relevant range of retention
indices (for this study, ITi = 739 and ITf = 3238)

123

Table 2-7. Fraction remaining (FIT) for selected compounds in evaporated diesel fuel (20
°C, 100 h), experimental and predicted using the comprehensive model with retention
index (IT) correction. The absolute percent error (APE) is also shown.
Compound

IT
Corrected

FIT
Experimental

FIT
Predicted

APE

Octane

800

2.39E-03

4.56E-09

100

Ethyl benzene

827

1.09E-03

5.19E-07

100

Ethyl cyclohexane

828

8.84E-04

5.63E-07

100

m/p-Xylene

836

9.49E-04

1.85E-06

100

o-Xylene

859

1.54E-03

3.30E-05

98

4-Methyl octane

862

1.47E-03

4.15E-05

97

3-Methyl octane

869

7.11E-04

9.09E-05

87

Nonane

900

1.20E-03

1.17E-03

2.8

Propyl benzene

921

2.46E-03

4.39E-03

79

Propyl cyclohexane

925

2.27E-03

5.56E-03

145

Ethyl methyl
benzene isomer

928

3.22E-03

6.52E-03

102

Dimethyl octane
isomer

933

2.40E-03

8.33E-03

246

1,3,5-Trimethyl
benzene

936

7.53E-03

9.74E-03

29

Ethyl methyl
heptane isomer

940

2.92E-03

1.17E-02

299

Ethyl methyl
benzene isomer

945

5.78E-03

1.48E-02

155

124

Table 2-7 cont’d

Compound

IT
Corrected

FIT
Experimental

FIT
Predicted

APE

Methyl nonane
isomer

960

8.72E-03

2.72E-02

212

1,2,4-Trimethyl
benzene

961

1.14E-02

2.77E-02

143

Unidentified

970

1.30E-02

3.82E-02

195

Unidentified

979

1.54E-02

5.27E-02

243

1,2,3-Trimethyl
benzene

988

2.73E-02

6.79E-02

149

Indane

998

2.56E-02

8.87E-02

246

Decane

1000

4.30E-02

9.30E-02

116

Methyl propyl
benzene isomer

1019

7.32E-02

1.42E-01

94

Methyl propyl
benzene isomer

1023

7.90E-02

1.53E-01

94

Butyl benzene

1023

7.94E-02

1.55E-01

95

4-Methyl decane

1024

8.19E-02

1.56E-01

91

Butyl cyclohexane

1027

6.16E-02

1.67E-01

171

Methyl propyl
benzene isomer

1033

9.41E-02

1.87E-01

99

Methyl indane
isomer

1050

1.13E-01

2.43E-01

116

5-Methyl decane

1058

1.86E-01

2.72E-01

46

125

Table 2-7 cont’d

Compound

IT
Corrected

FIT
Experimental

FIT
Predicted

APE

2-Methyl decane

1064

2.31E-01

2.98E-01

29

Unidentified

1071

2.11E-01

3.21E-01

52

3-Methyl decane

1071

2.45E-01

3.22E-01

31

Unidentified

1073

2.42E-01

3.30E-01

36

Undecane

1100

4.13E-01

4.34E-01

5.0

Unidentified

1102

2.96E-01

4.41E-01

49

Unidentified

1111

3.28E-01

4.77E-01

45

1,2,3,4-Tetrahydronaphthalene

1120

3.75E-01

5.09E-01

36

Pentyl benzene

1124

4.41E-01

5.24E-01

19

Pentyl cyclohexane

1130

4.34E-01

5.44E-01

25

Naphthalene

1138

3.52E-01

5.70E-01

62

Unidentified

1155

6.15E-01

6.26E-01

1.8

Methyl undecane
isomer

1165

6.80E-01

6.54E-01

3.8

Unidentified

1171

6.86E-01

6.72E-01

2.0

Methyl tetralin
isomer

1176

6.06E-01

6.84E-01

13

126

Table 2-7 cont’d

Compound

IT
Corrected

FIT
Experimental

FIT
Predicted

APE

Unidentified

1195

6.47E-01

7.35E-01

14

Dodecane

1200

8.24E-01

7.45E-01

10

2,6-Dimethyl
undecane

1216

8.29E-01

7.80E-01

5.9

Methyl tetralin
isomer

1225

7.56E-01

7.98E-01

5.5

Hexyl cyclohexane

1241

8.17E-01

8.27E-01

1.2

Methyl tetralin
isomer

1250

7.87E-01

8.40E-01

6.8

Unidentified

1254

9.09E-01

8.46E-01

7.0

Unidentified

1276

9.35E-01

8.76E-01

6.4

Methyl tetralin
isomer

1280

8.65E-01

8.80E-01

1.8

Tridecane

1300

1.01E+00

9.02E-01

10

Methyl tetralin
isomer

1302

9.28E-01

9.04E-01

2.6

Unidentified

1330

9.85E-01

9.27E-01

5.9

Heptyl cyclohexane

1338

9.57E-01

9.33E-01

2.5

Methyl tetralin
isomer

1351

1.00E+00

9.41E-01

6.3

Unidentified

1365

1.03E+00

9.49E-01

8.1

127

Table 2-7 cont’d

Compound

IT
Corrected

FIT
Experimental

FIT
Predicted

APE

2,6,10-Trimethyl
decane

1379

1.03E+00

9.56E-01

7.3

Tetradecane

1400

1.04E+00

9.64E-01

7.3

Unidentified

1433

1.04E+00

9.75E-01

6.4

Octyl cyclohexane

1442

1.04E+00

9.77E-01

6.3

Unidentified

1465

1.04E+00

9.82E-01

5.8

Pentadecane

1500

1.06E+00

9.87E-01

6.7

Hexadecane

1600

1.05E+00

9.96E-01

5.3

2,6,10-Trimethyl
pentadecane

1654

1.06E+00

9.97E-01

5.9

Heptadecane

1700

1.02E+00

9.98E-01

1.6

Pristane

1711

1.05E+00

9.99E-01

4.8

Octadecane

1800

1.01E+00

9.99E-01

1.5

Phytane

1815

1.02E+00

1.00E+00

2.4

Nonadecane

1900

9.94E-01

1.00E+00

0.6

Eicosane

2000

1.01E+00

1.00E+00

1.3

Heneicosane

2100

1.00E+00

1.00E+00

0.0

128

Table 2-7 cont’d

Compound

IT
Corrected

FIT
Experimental

FIT
Predicted

APE

Docosane

2200

1.03E+00

1.00E+00

3.0

Tricosane

2300

1.07E+00

1.00E+00

6.8

Tetracosane

2400

1.08E+00

1.00E+00

7.7

Pentacosane

2500

1.14E+00

1.00E+00

12

129

T

If
 T Fj Aj
j I
Ftot  i T
If
 T Aj
j I
i

Equation 2-8

where Aj is the normalized abundance at each retention index in the chromatogram of the
unevaporated fuel sample.
To test the accuracy of predicting the fraction remaining, three aliquots of diesel
fuel were evaporated at 20 °C for 100 h without water in order to obtain accurate masses
of the remaining fuel. The average fraction remaining based on the mass of the three
diesel samples was 0.8176. Using the comprehensive, retention index corrected model,
the predicted total fraction remaining is 0.8627, a 5.5% error. This error is lower than the
MAPEs for the individual compounds discussed above. Many of the selected compounds
used to develop and test the model were volatile, with a correspondingly higher APE
because of their low abundance after evaporation. However, when calculating the total
fraction remaining, the contributing compounds are relatively unaffected by evaporation,
thereby reducing the error in the model.
To demonstrate the applicability of the model to other fuels, kerosene and marine
fuel stabilizer were also utilized Figure 2-19 a and b respectively. These fuels differ
significantly from diesel in chemical composition. A petri dish containing only the fuel was
weighed before and after evaporation at 20 °C for 100 h. For kerosene, the fraction
remaining by mass was 0.6171.

The predicted fraction remaining using the

comprehensive, retention index corrected model was 0.7253, a 17.5% error. For marine

130

Figure 2-19. Total ion chromatogram for kerosene (a) and marine fuel stabilizer (b). The
peak numbers correspond to the compounds listed in Table 2-2.

131

fuel stabilizer, the fraction remaining by mass was 0.5576.

The predicted fraction

remaining was 0.6108, resulting in a 9.5% error. These errors are of similar magnitude
to those for prediction of the individual rate constants as well as for the total fraction
remaining of diesel fuel, demonstrating that the model is extensible to other petroleum
products.
2.5 Conclusions
This study has demonstrated that models based on retention index of a compound
can accurately predict its evaporation rate constant. The class-specific models are more
accurate, but require assigning each compound to a structural class. The comprehensive
model, based on all compound classes, is advantageous because knowledge of class
membership is not required. Utilizing the developed models, the fraction remaining of an
individual compound, as well as the total fraction remaining of the fuel, can be accurately
predicted based on the retention index and evaporation time. This can be done without
any prior knowledge of the fuel’s composition or physical properties, which is critical in
environmental and petrochemical applications where exact composition of a fuel is often
unknown.
McReynolds constants were applied to further refine the comprehensive model to
correct for differences in retention indices that resulted from interactions of the aromatic
compounds with the polysiloxane stationary phase.

The retention index correction

strategies resulted in a closer representation of boiling point and resulted in a more
accurate model. In addition chromatographic data generated on a number of widely
available stationary phases could be utilized in the model after retention index correction.

132

Model flexibility, including the input GC data and models for different compound classes,
will allow end-users to decide which is most appropriate based on the available data.
While this work has been developed for evaporation of petroleum products, the
methodologies have many other potential applications. Other weathering processes on
petroleum spills, such as dissolution, could be predicted using similar kinetic models.
These methodologies could also be applied for explosives detection, where the vapor
pressure and rate of decomposition are critical aspects in the development of detection
schemes. Tracking the release and exposure of chemical warfare agents could be
accomplished with similar kinetic models. In addition, monitoring and predicting the fate
of other pollutants released into the environment, for which there is no established model,
could be accomplished using these methodologies. These potential applications are
worthy of additional investigation.

133

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134

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138

3. Variable-Temperature
Evaporation

Rates

Model
of

for

Petroleum

Predicting
Products

Environmental
using

Gas

Chromatographic Retention Indices
3.1 Introduction
Effective remediation and impact assessment of environmental releases of
petroleum fuels depends upon reliable modeling of their fate. Because these devastating
releases can occur anywhere in the world, variations in environmental conditions,
particularly temperature, must be incorporated into predictive models to facilitate accurate
predictions [1-5]. In the previous chapter, a novel kinetic method was proposed to predict
evaporation of petroleum constituents. An extensive set of empirical rate constants was
determined at 20 °C, which was then fit to a regression equation based on the gas
chromatographic retention index.

This chapter expands on the previous efforts by

incorporating variable temperature into the predictive model. Fixed-temperature models
were initially developed from empirical measurements at five temperatures (5, 10, 20, 30,
35 °C). Multiple linear regression of the rate constants determined for each compound at
each temperatures was used to create a variable temperature model. The variable
temperature model could be used to predict the fraction remaining of an individual
compound or the entire fuel. The variable-temperature model was also used to estimate
the length of time the fuel has been evaporated from an experimental chromatogram, to
predict the chromatogram of the fuel after evaporation for a given time, and to predict the
time to reach a specific percent evaporated for an individual compound or for the entire
fuel.

139

3.2 Materials and Methods
3.2.1 Sample Collection
Diesel fuel was utilized for model development because it contains a wide range
of compounds (normal alkanes, branched and cyclic alkanes, alkyl aromatics, and
polycyclic aromatics), representative of the compound classes in crude oil. The range of
boiling points in diesel fuel (~100 – 400 °C) is appropriate for analysis by gas
chromatography-mass spectrometry (GC-MS). A large volume (~5 gallons) of diesel fuel
was collected from a service station in East Lansing, MI, placed into acid-washed amber
bottles, and stored at ~5 °C. This fuel sample was used over the entire course of the
study. Kerosene was also collected from a local service station and stored in amber
bottles at ~5 °C until use. Marine fuel stabilizer (Pennzoil, Houston, TX) was purchased
and stored in its original container until use.
3.2.2 Evaporation of Fuel Samples
Diesel fuel samples were evaporated in an evaporation chamber designed in house [6].
Temperature was controlled by an Ambi-Hi-Lo incubator (5 – 50 °C ± 0.5 °C, model
3550DT, Lab-Line, Melrose Park, IL). Relative humidity (RH) was controlled by placing
trays of water, totaling approximately 300 mL, inside the chamber. Temperature and
humidity were monitored and recorded at two-minute intervals using a data logger (0 –
55 °C ± 0.3 °C, 10 – 95% RH ± 5% RH, TR-74Ui, T & D Corporation, Nagano, Japan).
Glass Petri dishes (60 mm diameter x 15 mm high) with a thin film of diesel fuel (1.0 mL,
~0.5 mm) on distilled water (15 mL) were used to simulate an environmental spill. The

140

samples were evaporated in triplicate for nine different lengths of time (0 – 300 h) at each
temperature (5, 10, 20, 30, and 35 °C).
For model validation, several other evaporation experiments were performed. In
one experiment, three diesel fuel samples were prepared as previously described, while
three additional samples were prepared without the water layer. The latter fuel samples
were weighed before and after evaporation at 20 °C for 100 h to determine the mass loss.
In separate experiments, three samples of kerosene and marine fuel stabilizer were
evaporated at 20 °C for 100 h. In each experiment, two dishes contained the fuel and
water, while the third dish contained the fuel alone. To test the model under fluctuating
temperatures, three samples of diesel fuel with water and three samples with fuel alone
were evaporated. The temperature was varied in the range of 12 – 27 °C approximately
every 12 h, for a total time of 100 h, in order to simulate diurnal variations.
3.2.3 Gas Chromatography-Mass Spectrometry Analysis
The

evaporated

diesel

residues

were

extracted

from

water

using

dichloromethane. The contents of the Petri dish were quantitatively transferred to a
separatory funnel and the dish was rinsed several times with approximately 1 mL of
dichloromethane. The organic layer was then transferred to a 10.0 mL volumetric flask.
An additional dilution (1:50) was performed prior to GC-MS analysis [6].
The analytical system consisted of a gas chromatograph (model 7890N, Agilent
Technologies, Santa Clara, CA) with an automatic liquid sampler (model 7693, Agilent
Technologies), coupled to a single-quadrupole mass spectrometer (model 5975, Agilent
Technologies). The GC separation was performed on a capillary column with 100%

141

poly(dimethylsiloxane) stationary phase (HP-1MS, 30 m x 0.25 mm x 0.25 μm, Agilent
Technologies), using ultra-high purity helium (1 mL/min) as the carrier gas. The diluted
diesel extract was introduced via a pulsed (15 psi for 0.25 min), split (50:1) injection at
280 °C. The GC temperature program had an initial temperature of 50 °C, linear ramp of
5 °C/min to a final temperature of 280 °C, with a 4-min hold. In the mass spectrometer,
the samples were ionized (70 eV) and the fragment ions were separated using a
quadrupole mass analyzer, which scanned mass-to-charge (m/z) ratios of 40 – 550 at
2.91 scans/s. Compounds were identified by means of the m/z ratio of prominent ions as
well as the GC retention indices [6]. They were quantified by means of the abundance
from extracted ion chromatograms (EIC), normalized to the abundance of heneicosane
(C21) in the EIC at m/z 57 [6]. A list of the 78 compounds selected for model development
and 29 compounds selected for model validation is provided in Table 3-1 and Table 3-2.
3.2.4 Data Analysis
The first-order rate constants (k) were determined by using the methodology
developed in the previous work [17]. The first-order kinetic rate constant (k) can be used
to calculate the concentration of a compound (Ct) at time (t), given its initial concentration
(C0).

Ct  C0 exp(k t )

Equation 3-1

142

Table 3-1. Selected compounds monitored during evaporation of diesel fuel for
development of fixed-temperature and variable-temperature models. The following
information is listed for each compound: Peak number in Table 3-3 – Table 3-12 (Peak
#), the identity of the compound, the class to which the compound was assigned, the
mass-to-charge (m/z) ratio of the extracted ion chromatogram (EIC) used to quantify the
compound, the retention time (tTR), the boiling point (Tb), and retention index (IT) before
and after correction.
Peak
#

Compound

Class

m/z

tTR
(min)

Tb
(K)1

IT

IT
Corrected2

1

2-Methyl
heptane

Branched
Alkane

57

3.398

2

Octane

Normal
Alkane

57

3.748

399

800

800

3

4-Methyl
octane

Branched
Alkane

57

4.814

415

862

862

4

3-Methyl
octane

Branched
Alkane

57

4.948

417

869

869

5

Nonane

Normal
Alkane

57

5.479

424

900

900

6

Dimethyl
octane
isomer

Branched
Alkane

57

6.248

933

933

7

Ethyl methyl
heptane
isomer

Branched
Alkane

57

6.411

940

940

8

Methyl
nonane
isomer

Branched
Alkane

57

6.883

960

960

9

Unidentified

Branched
Alkane

57

7.105

970

970

143

Table 3-1 cont’d

Peak
#

Compound

Class

m/z

tTR
(min)

Tb
(K)1

IT

IT
Corrected2

10

Decane

Normal
Alkane

57

7.816

447

1000

1000

11

4-Methyl
decane

Branched
Alkane

57

8.434

460

1024

1024

12

5-Methyl
decane

Branched
Alkane

57

9.326

1058

1058

13

2-Methyl
decane

Branched
Alkane

57

9.506

1064

1064

14

3-Methyl
decane

Branched
Alkane

57

9.670

1071

1071

15

Undecane

Normal
Alkane

57

10.439

1100

1100

16

Unidentified

Branched
Alkane

57

11.960

1155

1155

17

Methyl
undecane
isomer

Branched
Alkane

57

12.217

1165

1165

18

Unidentified

Branched
Alkane

57

12.392

1171

1171

19

Dodecane

Normal
Alkane

57

13.184

1200

1200

20

2,6-Dimethyl
undecane

Branched
Alkane

57

13.616

1216

1216

144

462

468

489

Table 3-1 cont’d

Peak
#

Compound

Class

m/z

tTR
(min)

IT

IT
Corrected2

21

Unidentified

Branched
Alkane

57

14.618

1254

1254

22

Unidentified

Branched
Alkane

57

15.213

1276

1276

23

Tridecane

Normal
Alkane

57

15.848

1300

1300

24

Unidentified

Branched
Alkane

57

17.527

1365

1365

25

2,6,10Trimethyl
decane

Branched
Alkane

57

17.900

1379

1379

26

Tetradecane

Normal
Alkane

57

18.430

1400

1400

27

Unidentified

Branched
Alkane

57

20.027

1465

1465

28

Pentadecane

Normal
Alkane

57

20.890

540

1500

1500

29

Hexadecane

Normal
Alkane

57

23.186

554

1600

1600

30

2,6,10Trimethyl
pentadecane

Branched
Alkane

57

24.369

1654

1654

31

Heptadecan
e

Normal
Alkane

57

25.395

1700

1700

145

Tb
(K)1

507

523

575

Table 3-1 cont’d

Peak
#

Compound

Class

m/z

tTR
(min)

IT

IT
Corrected2

32

Pristane

Branched
Alkane

57

25.628

1711

1711

33

Octadecane

Normal
Alkane

57

27.488

1800

1800

34

Phytane

Branched
Alkane

57

27.791

1815

1815

35

Nonadecane

Normal
Alkane

57

29.539

1900

1900

36

Eicosane

Normal
Alkane

57

31.400

616

2000

2000

37

Heneicosane

Normal
Alkane

57

33.276

635

2100

2100

38

Methyl
cyclohexane

Branched
Alkane

83

2.856

374

39

Ethyl
cyclohexane

Branched
Alkane

83

4.226

405

828

828

40

Propyl
cyclohexane

Branched
Alkane

83

6.067

429

925

925

41

Butyl
cyclohexane

Branched
Alkane

83

8.527

453

1027

1027

42

Pentyl
cyclohexane

Branched
Alkane

83

11.272

477

1130

1130

146

Tb
(K)1

589

Table 3-1 cont’d

Peak
#

Compound

Class

m/z

tTR
(min)

Tb
(K)1

IT

IT
Corrected2

43

Hexyl
cyclohexane

Branched
Alkane

83

14.288

498

1241

1241

44

Heptyl
cyclohexane

Branched
Alkane

83

16.833

510

1338

1338

45

Octyl
cyclohexane

Branched
Alkane

83

19.462

528

1442

1442

46

Toluene

Alkyl
Aromatic

91

3.194

384

47

Ethyl
benzene

Alkyl
Aromatic

91

4.511

409

844

827

48

m/p-Xylene

Alkyl
Aromatic

91

4.663

412

853

836

49

o-Xylene

Alkyl
Aromatic

91

5.071

417

876

859

50

Propyl
benzene

Alkyl
Aromatic

91

6.365

432

938

921

51

Butyl
benzene

Alkyl
Aromatic

91

8.871

456

1040

1023

52

Unidentified

Alkyl
Aromatic

91

10.171

1090

1073

53

1,2,3,4Tetrahydronaphthalene

Polycyclic
Hydrocarbon

91

11.465

1137

1120

147

490

Table 3-1 cont’d

Peak
#

Compound

Class

m/z

tTR
(min)

IT

IT
Corrected2

54

Pentyl
benzene

Alkyl
Aromatic

91

11.576

1141

1124

55

Methyl
tetralin
isomer

Polycyclic
Hydrocarbon

91

12.980

1193

1176

56

Unidentified

Polycyclic
Hydrocarbon

91

17.066

1347

1330

57

Unidentified

Polycyclic
Hydrocarbon

91

19.660

1450

1433

58

Ethyl methyl
benzene
isomer

Alkyl
Aromatic

105

6.534

945

928

59

1,3,5Trimethyl
benzene

Alkyl
Aromatic

105

6.720

953

936

60

Ethyl methyl
benzene
isomer

Alkyl
Aromatic

105

6.930

962

945

61

1,2,4Trimethyl
benzene

Alkyl
Aromatic

105

7.291

978

961

62

Unidentified

Alkyl
Aromatic

105

7.734

996

979

63

1,2,3Trimethyl
benzene

Alkyl
Aromatic

105

7.950

1005

988

148

Tb
(K)1

438

442

449

Table 3-1 cont’d

Peak
#

64

65

66

Compound
Methyl
propyl
benzene
isomer
Methyl
propyl
benzene
isomer
Methyl
propyl
benzene
isomer

Class

m/z

tTR
(min)

IT

IT
Corrected2

Alkyl
Aromatic

105

8.754

1036

1019

Alkyl
Aromatic

105

8.854

1040

1023

Alkyl
Aromatic

105

9.139

1050

1033

1088

1071

1015

998

Tb
(K)1

67

Unidentified

Alkyl
Aromatic

105

10.113

68

Indane

Polycyclic
Hydrocarbon

117

8.212

69

Methyl
indane
isomer

Polycyclic
Hydrocarbon

117

9.565

1067

1050

70

Unidentified

Polycyclic
Hydrocarbon

117

10.958

1119

1102

71

Unidentified

Polycyclic
Hydrocarbon

117

11.220

1128

1111

72

Unidentified

Polycyclic
Hydrocarbon

117

13.516

1212

1195

73

Methyl
tetralin
isomer

Polycyclic
Hydrocarbon

117

14.303

1242

1225

149

450

507

Table 3-1 cont’d

Peak
#

Compound

Class

m/z

tTR
(min)

IT

IT
Corrected2

74

Methyl
tetralin
isomer

Polycyclic
Hydrocarbon

117

14.974

1267

1250

75

Methyl
tetralin
isomer

Polycyclic
Hydrocarbon

117

15.760

1297

1280

76

Methyl
tetralin
isomer

Polycyclic
Hydrocarbon

117

16.349

1319

1302

77

Methyl
tetralin
isomer

Polycyclic
Hydrocarbon

117

17.591

1368

1351

78

Naphthalene

Polycyclic
Hydrocarbon

128

11.949

1155

1138

Tb
(K)1

490

1

Source: R.L. Brown, S.E. Stein, in: P.J. Linstrom, W.G. Mallard (Eds.), NIST Chemistry
WebBook, NIST Standard Reference Database Number 69, National Institute of
Standards and Technology, Gaithersburg MD, 2011. http//webbook.nist.gov, (retrieved
February 26, 2014).

2

For compounds in the alkyl aromatic and polycyclic aromatic classes, retention index is
corrected using the McReynolds constant for benzene on 100% poly(dimethylsiloxane)
stationary phase. IT corrected = IT – 17

150

Table 3-2. Selected compounds monitored during evaporation of diesel fuel for
validation of fixed-temperature and variable-temperature models. The following
information is listed for each compound: Peak number in Table 3-3 – Table 3-12 (Peak
#), the class to which the compound was assigned, the mass-to-charge (m/z) ratio of
the extracted ion chromatogram (EIC) used to quantify the compound, the retention time
(tTR), and retention index (IT) before and after correction.

Peak #

Class

m/z

tTR (min)

IT

IT
Corrected1

79

Branched
Alkane

57

12.094

1160

1160

80

Branched
Alkane

57

15.078

1271

1271

81

Alkyl
Aromatic

105

5.723

910

893

82

Alkyl
Aromatic

105

11.605

1142

1125

83

Alkyl
Aromatic

105

11.832

1151

1134

84

Alkyl
Aromatic

117

14.641

1255

1238

85

Polycylic
Hydrocarbon

117

16.728

1334

1317

86

Branched
Alkane

97

3.800

803

803

87

Branched
Alkane

97

5.205

884

884

151

Table 3-2 cont’d

Peak #

Class

m/z

tTR (min)

IT

IT
Corrected1

88

Branched
Alkane

97

5.578

904

904

89

Branched
Alkane

97

7.326

979

979

90

Branched
Alkane

97

7.390

982

982

91

Branched
Alkane

97

7.647

993

993

92

Branched
Alkane

97

9.943

1081

1081

93

Branched
Alkane

97

10.241

1092

1092

94

Alkyl
Aromatic

119

8.002

1007

990

95

Alkyl
Aromatic

119

8.084

1010

993

96

Alkyl
Aromatic

119

8.864

1033

1016

97

Alkyl
Aromatic

119

8.941

1043

1026

98

Alkyl
Aromatic

119

9.617

1069

1052

152

Table 3-2 cont’d

Peak #

Class

m/z

tTR (min)

IT

IT
Corrected1

99

Alkyl
Aromatic

119

10.650

1104

1087

100

Alkyl
Aromatic

119

11.360

1134

1117

101

Alkyl
Aromatic

119

11.686

1145

1128

102

Alkyl
Aromatic

119

11.797

1149

1132

103

Alkyl
Aromatic

119

12.036

1158

1141

104

Polycyclic
Hydrocarbon

137

10.532

1103

1086

105

Polycyclic
Hydrocarbon

137

13.645

1217

1200

106

Polycyclic
Hydrocarbon

137

13.907

1227

1210

1

For compounds in the alkyl aromatic and polycyclic aromatic classes, retention index
is corrected using the McReynolds constant for benzene on 100%
poly(dimethylsiloxane) stationary phase. IT corrected = IT – 17

153

The normalized abundance of each selected compound was plotted as a function
of time, and the resulting decay curve was fit by nonlinear regression to Equation 3-1
(TableCurve 2D, version 5.01, Systat Software, Richmond, CA).

The characteristic

lifetime (), which is equal to 1/k, is often used to describe the completeness of the decay
curve. Only rate constants for compounds with greater than 0.5  in the decay curve were
included in the models. This allowed for inclusion of 78 selected compounds, while
introducing only minimal error of 2.9% [17].
For development of the fixed-temperature and variable-temperature kinetic
models, linear and multiple linear regression were performed using Excel (Office 2013,
version 15.0, Microsoft Corporation, Redmond, WA).
3.3 Results
Figure 3-1 shows representative total ion chromatograms (TIC) of diesel fuel prior
to evaporation and after 300 h of evaporation at temperatures of 5, 10, 20, 30, and 35 °C.
As expected, an increase in temperature resulted in additional evaporation.

Some

compounds, such as n-octane (C8), were completely evaporated after 300 h at all
temperatures.

Other compounds, such as n-tetradecane (C14), remained relatively

unchanged at all temperatures. The rate constants for evaporation are summarized for
all selected compounds at each temperature in Table 3-3 – Table 3-12.

154

Figure 3-1. Representative total ion chromatograms of diesel samples prior to
evaporation and after evaporation for 300 h at 5 – 35 °C. Even-numbered normal alkanes
are labeled for reference.

155

Table 3-3. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 5 °C. The predicted rate constant (kpred) and absolute precent
error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 16 – 37, 43 – 45, 72 – 77). Several compounds had retention indices
less than 800 (peaks 1, 38, 46) and were also excluded, as the retention index could not
be accurately extrapolated.
Peak #

ke (h-1)

 (h)

#  in
300 h

1

1.83E-01

5.5

54.9

2

1.28E-01

7.8

3

5.04E-02

4

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

38.3

1.10E-01

7.36E-02

14.1

42.4

19.8

15.1

5.49E-02

3.90E-02

9.0

22.6

4.97E-02

20.1

14.9

5.04E-02

3.60E-02

1.3

27.5

5

3.34E-02

29.9

10.0

3.57E-02

2.63E-02

6.7

21.4

6

2.32E-02

43.1

7.0

2.46E-02

1.87E-02

6.2

19.3

7

2.27E-02

44.0

6.8

2.28E-02

1.74E-02

0.4

23.2

8

1.63E-02

61.3

4.9

1.82E-02

1.42E-02

11.4

13.2

9

1.48E-02

67.7

4.4

1.63E-02

1.28E-02

10.5

13.1

156

Table 3-3 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

10

1.02E-02

98.5

3.0

1.16E-02

9.38E-03

14.1

7.6

11

8.24E-03

121.3

2.5

8.90E-03

7.36E-03

7.9

10.7

12

5.56E-03

179.9

1.7

6.07E-03

5.19E-03

9.2

6.7

13

4.98E-03

201.0

1.5

5.62E-03

4.83E-03

12.9

2.8

14

4.79E-03

208.6

1.4

5.24E-03

4.53E-03

9.2

5.4

15

3.13E-03

320.0

0.9

3.77E-03

3.35E-03

20.5

7.3

16

1.51E-03

660.7

0.5

2.02E-03

1.89E-03

17

1.31E-03

760.8

0.4

1.82E-03

1.72E-03

18

1.26E-03

793.4

0.4

1.69E-03

1.61E-03

19

6.96E-04

1437.5

0.2

1.22E-03

1.20E-03

20

6.14E-04

1629.5

0.2

1.02E-03

1.01E-03

157

Table 3-3 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

21

2.54E-04

3943.1

0.1

6.68E-04

6.88E-04

22

1.41E-04

7107.7

0.0

5.20E-04

5.47E-04

38

4.40E-01

2.3

132.1

39

1.04E-01

9.6

31.3

8.05E-02

40

2.98E-02

33.5

8.9

41

9.46E-03

105.7

42

2.86E-03

43

APE
fixed T

APE
variable T

5.54E-02

23.0

47.0

2.69E-02

2.03E-02

9.9

32.0

2.8

8.55E-03

7.10E-03

9.6

24.9

350.1

0.9

2.68E-03

2.45E-03

6.2

14.1

5.11E-04

1957.9

0.2

7.68E-04

7.81E-04

46

3.04E-01

3.3

91.3

47

9.70E-02

10.3

29.1

8.10E-02

5.57E-02

16.5

42.6

48

7.42E-02

13.5

22.3

7.34E-02

5.09E-02

1.1

31.4

158

Table 3-3 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

49

5.84E-02

17.1

17.5

5.63E-02

3.99E-02

3.6

31.7

50

2.94E-02

34.0

8.8

2.82E-02

2.12E-02

4.0

27.9

51

8.80E-03

113.6

2.6

8.93E-03

7.39E-03

1.4

16.1

52

5.00E-03

200.1

1.5

5.12E-03

4.44E-03

2.4

11.2

53

3.36E-03

297.5

1.0

3.00E-03

2.72E-03

10.9

19.1

54

2.74E-03

365.0

0.8

2.86E-03

2.61E-03

4.5

4.9

55

1.70E-03

589.0

0.5

1.61E-03

1.54E-03

5.1

9.3

58

2.42E-02

41.3

7.3

2.60E-02

1.97E-02

7.3

18.8

59

1.78E-02

56.3

5.3

2.38E-02

1.81E-02

33.8

2.0

60

2.02E-02

49.6

6.0

2.15E-02

1.65E-02

6.6

18.1

61

1.64E-02

61.0

4.9

1.81E-02

1.41E-02

10.1

14.1

159

Table 3-3 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

62

1.52E-02

66.0

4.5

1.46E-02

1.16E-02

3.7

23.5

63

1.19E-02

84.1

3.6

1.33E-02

1.06E-02

11.4

10.8

64

8.57E-03

116.7

2.6

9.39E-03

7.74E-03

9.5

9.7

65

8.80E-03

113.6

2.6

8.99E-03

7.44E-03

2.2

15.5

66

7.67E-03

130.3

2.3

7.96E-03

6.65E-03

3.7

13.3

67

5.00E-03

200.1

1.5

5.24E-03

4.54E-03

4.9

9.2

68

1.40E-02

71.3

4.2

1.18E-02

9.57E-03

15.5

31.7

69

7.43E-03

134.6

2.2

6.63E-03

5.63E-03

10.7

24.2

70

4.08E-03

245.1

1.2

3.69E-03

3.29E-03

9.6

19.5

71

3.77E-03

265.6

1.1

3.31E-03

2.98E-03

12.0

20.9

72

1.24E-03

809.4

0.4

1.29E-03

1.25E-03

160

Table 3-3 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

73

8.51E-04

1174.6

0.3

9.24E-04

9.25E-04

74

5.41E-04

1848.8

0.2

6.96E-04

7.14E-04

75

2.19E-04

4569.2

0.1

5.00E-04

5.27E-04

78

3.56E-03

281.2

1.1

2.46E-03

2.27E-03

161

APE
fixed T

APE
variable T

30.9

36.3

Table 3-4. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel evaporated
at 5 °C. The predicted rate constant (kpred) and absolute precent error (APE) was
calculated using the fixed-temperature (fixed T) and variable-temperature (variable T)
models. Compounds with  > 0.5 in 300 h were excluded from the table (peaks 80, 84,
85, 105, 106).
Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

79

1.52E-03

657.5

0.5

1.91E-03

1.80E-03

25.8

18.5

81

2.94E-02

34.1

8.8

3.84E-02

2.81E-02

30.7

4.3

82

1.86E-03

538.5

0.6

2.83E-03

2.58E-03

52.4

38.9

83

1.90E-03

526.6

0.6

2.58E-03

2.37E-03

35.7

24.7

86

1.51E-01

6.6

45.3

1.06E-01

7.13E-02

29.8

52.8

87

4.52E-02

22.1

13.6

4.26E-02

3.09E-02

5.7

31.6

88

3.88E-02

25.8

11.6

3.40E-02

2.52E-02

12.3

35.1

89

1.45E-02

69.1

4.3

1.47E-02

1.16E-02

1.5

19.5

90

1.50E-02

66.7

4.5

1.42E-02

1.13E-02

5.1

24.5

162

Table 3-4 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

91

1.39E-02

71.8

4.2

1.26E-02

1.01E-02

9.7

27.4

92

4.75E-03

210.7

1.4

4.66E-03

4.07E-03

1.9

14.2

93

4.66E-03

214.4

1.4

4.10E-03

3.62E-03

12.1

22.3

94

1.19E-02

83.8

3.6

1.30E-02

1.04E-02

8.6

12.9

95

1.14E-02

87.4

3.4

1.25E-02

1.01E-02

9.3

12.0

96

9.01E-03

111.0

2.7

9.67E-03

7.95E-03

7.3

11.8

97

7.14E-03

140.0

2.1

8.67E-03

7.19E-03

21.3

0.7

98

6.07E-03

164.7

1.8

6.49E-03

5.51E-03

6.8

9.2

99

3.85E-03

260.1

1.2

4.36E-03

3.83E-03

13.3

0.4

100

3.08E-03

324.8

0.9

3.13E-03

2.83E-03

1.6

8.2

101

2.51E-03

398.6

0.8

2.74E-03

2.50E-03

9.1

0.3

163

Table 3-4 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

102

2.32E-03

431.3

0.7

2.62E-03

2.40E-03

12.8

3.5

103

2.08E-03

480.5

0.6

2.37E-03

2.19E-03

13.9

5.4

104

4.13E-03

242.0

1.2

4.39E-03

3.86E-03

6.3

6.7

107

8.41E-03

119.0

2.5

8.26E-03

6.88E-03

0.7

18.1

164

Table 3-5. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 10 °C. The predicted rate constant (kpred) and absolute
precent error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 19 – 37, 43 – 45, 73 – 77). Several compounds had retention indices
lower than 800 (peaks 1, 38, 46) and were also excluded, as the retention index could
not be accurately extrapolated.
Peak #

ke (h-1)

 (h)

#  in
300 h

1

2.13E-01

4.7

63.8

2

1.51E-01

6.6

3

5.49E-02

4

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

45.2

1.05E-01

1.10E-01

30.2

26.8

18.2

16.5

5.50E-02

5.85E-02

0.2

6.6

5.33E-02

18.8

16.0

5.07E-02

5.40E-02

4.9

1.4

5

3.47E-02

28.8

10.4

3.67E-02

3.94E-02

5.7

13.4

6

2.45E-02

40.8

7.4

2.60E-02

2.81E-02

5.9

14.4

7

2.35E-02

42.5

7.1

2.41E-02

2.61E-02

2.7

11.2

8

1.72E-02

58.1

5.2

1.95E-02

2.12E-02

13.4

23.4

9

1.59E-02

62.8

4.8

1.77E-02

1.93E-02

10.9

20.9

165

Table 3-5 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

10

1.08E-02

92.5

3.2

1.28E-02

1.41E-02

18.6

30.2

11

9.51E-03

105.2

2.9

1.00E-02

1.10E-02

5.2

16.2

12

6.82E-03

146.6

2.0

6.99E-03

7.78E-03

2.5

14.1

13

6.17E-03

162.1

1.9

6.50E-03

7.25E-03

5.5

17.6

14

6.06E-03

164.9

1.8

6.09E-03

6.80E-03

0.4

12.1

15

4.25E-03

235.5

1.3

4.47E-03

5.03E-03

5.3

18.4

16

2.31E-03

433.8

0.7

2.50E-03

2.84E-03

8.3

23.2

17

1.99E-03

502.3

0.6

2.26E-03

2.58E-03

13.6

29.6

18

1.90E-03

526.1

0.6

2.11E-03

2.42E-03

11.3

27.1

19

1.08E-03

924.5

0.3

1.56E-03

1.80E-03

20

9.78E-04

1022.2

0.3

1.32E-03

1.52E-03

166

Table 3-5 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

21

5.65E-04

1768.8

0.2

8.86E-04

1.03E-03

22

4.00E-04

2497.0

0.1

7.00E-04

8.20E-04

23

1.98E-04

5055.7

0.1

5.45E-04

6.41E-04

38

5.10E-01

2.0

153.1

39

1.13E-01

8.9

33.8

7.87E-02

40

3.07E-02

32.6

9.2

41

1.00E-02

100.0

42

3.80E-03

43

APE
fixed T

APE
variable T

8.30E-02

30.1

26.2

2.82E-02

3.04E-02

8.3

1.0

3.0

9.63E-03

1.06E-02

3.7

6.4

263.1

1.1

3.25E-03

3.68E-03

14.5

3.3

9.85E-04

1014.9

0.3

1.01E-03

1.17E-03

44

1.33E-04

7493.3

0.0

3.65E-04

4.33E-04

46

3.62E-01

2.8

108.7

167

Table 3-5 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

47

9.57E-02

10.5

28.7

7.91E-02

8.35E-02

17.3

12.7

48

7.23E-02

13.8

21.7

7.21E-02

7.63E-02

0.3

5.4

49

5.75E-02

17.4

17.3

5.63E-02

5.98E-02

2.1

4.0

50

2.83E-02

35.3

8.5

2.95E-02

3.18E-02

4.1

12.3

51

9.41E-03

106.2

2.8

1.00E-02

1.11E-02

6.6

17.7

52

5.55E-03

180.2

1.7

5.96E-03

6.65E-03

7.4

19.9

53

4.17E-03

239.7

1.3

3.61E-03

4.08E-03

13.5

2.3

54

3.59E-03

278.7

1.1

3.46E-03

3.91E-03

3.6

8.9

55

2.30E-03

434.1

0.7

2.02E-03

2.31E-03

12.4

0.2

58

2.33E-02

42.9

7.0

2.73E-02

2.95E-02

17.1

26.4

59

1.79E-02

56.0

5.4

2.51E-02

2.72E-02

40.6

52.1

168

Table 3-5 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

60

1.99E-02

50.1

6.0

2.28E-02

2.48E-02

14.5

24.2

61

1.58E-02

63.1

4.8

1.94E-02

2.11E-02

22.5

33.3

62

1.47E-02

67.9

4.4

1.59E-02

1.74E-02

8.1

18.1

63

1.26E-02

79.5

3.8

1.45E-02

1.59E-02

15.4

26.4

64

9.24E-03

108.2

2.8

1.05E-02

1.16E-02

13.8

25.6

65

9.11E-03

109.8

2.7

1.01E-02

1.12E-02

10.9

22.5

66

8.75E-03

114.3

2.6

9.01E-03

9.97E-03

3.0

14.0

67

6.09E-03

164.3

1.8

6.10E-03

6.81E-03

0.1

11.8

68

1.36E-02

73.6

4.1

1.31E-02

1.44E-02

3.7

5.7

69

8.00E-03

125.1

2.4

7.60E-03

8.44E-03

5.0

5.5

70

5.05E-03

198.1

1.5

4.38E-03

4.93E-03

13.1

2.3

169

Table 3-5 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

71

4.74E-03

211.0

1.4

3.96E-03

4.47E-03

16.3

5.7

72

1.77E-03

564.6

0.5

1.64E-03

1.88E-03

7.6

6.2

73

1.04E-03

960.1

0.3

1.20E-03

1.39E-03

74

7.30E-04

1369.8

0.2

9.20E-04

1.07E-03

75

2.81E-04

3559.8

0.1

6.75E-04

7.90E-04

76

7.14E-05

14006

0.0

5.31E-04

6.26E-04

78

4.82E-03

207.7

1.4

3.00E-03

3.40E-03

37.7

29.4

170

Table 3-6. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel evaporated
at 10 °C. The predicted rate constant (kpred) and absolute precent error (APE) was
calculated using the fixed-temperature (fixed T) and variable-temperature (variable T)
models. Compounds with  > 0.5 in 300 h were excluded from the table (peaks 80, 84,
85, 105, 106).
Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

79

2.18E-03

459.2

0.7

2.37E-03

2.70E-03

8.9

24.1

81

3.84E-02

26.0

11.5

3.93E-02

4.21E-02

2.4

9.7

82

3.51E-03

284.7

1.1

3.42E-03

3.87E-03

2.6

10.1

83

3.39E-03

295.2

1.0

3.14E-03

3.55E-03

7.4

4.8

86

1.61E-01

6.2

48.2

1.02E-01

1.07E-01

36.6

33.5

87

4.63E-02

21.6

13.9

4.34E-02

4.64E-02

6.2

0.2

88

3.91E-02

25.6

11.7

3.51E-02

3.77E-02

10.2

3.5

89

1.45E-02

68.8

4.4

1.60E-02

1.75E-02

10.0

20.2

90

1.50E-02

66.8

4.5

1.55E-02

1.70E-02

3.6

13.3

171

Table 3-6 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

91

1.39E-02

72.0

4.2

1.38E-02

1.52E-02

0.4

9.1

92

5.87E-03

170.4

1.8

5.46E-03

6.10E-03

7.0

4.0

93

5.65E-03

176.9

1.7

4.84E-03

5.43E-03

14.3

3.9

94

1.19E-02

84.2

3.6

1.42E-02

1.56E-02

19.7

31.2

95

1.15E-02

86.8

3.5

1.38E-02

1.51E-02

19.4

30.9

96

9.48E-03

105.4

2.8

1.08E-02

1.19E-02

14.0

25.7

97

7.92E-03

126.2

2.4

9.76E-03

1.08E-02

23.2

36.1

98

6.98E-03

143.2

2.1

7.44E-03

8.27E-03

6.6

18.4

99

4.83E-03

207.0

1.4

5.13E-03

5.74E-03

6.1

18.9

100

3.96E-03

252.3

1.2

3.76E-03

4.24E-03

5.2

6.9

101

3.43E-03

291.5

1.0

3.32E-03

3.75E-03

3.3

9.4

172

Table 3-6 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

102

3.14E-03

318.3

0.9

3.18E-03

3.60E-03

1.1

14.5

103

2.87E-03

348.8

0.9

2.90E-03

3.29E-03

1.1

14.8

104

4.81E-03

207.7

1.4

5.16E-03

5.78E-03

7.2

20.1

107

8.78E-03

113.9

2.6

9.33E-03

1.03E-02

6.3

17.6

173

Table 3-7. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 20 °C. The predicted rate constant (kpred) and absolute
precent error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 23-37, 44, 45, 57). Several compounds had retention indices lower than
800 (peaks 1, 38, 46) and were also excluded, as the retention index could not be
accurately extrapolated.
Peak #

ke (h-1)

 (h)

#  in
300 h

1

3.08E-01

3.2

92.5

2

2.26E-01

4.4

3

1.08E-01

4

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

67.7

1.92E-01

2.31E-01

14.9

2.3

9.3

32.4

1.01E-01

1.22E-01

6.5

13.6

9.72E-02

10.3

29.2

9.31E-02

1.13E-01

4.2

16.4

5

6.58E-02

15.2

19.8

6.75E-02

8.25E-02

2.6

25.3

6

4.53E-02

22.1

13.6

4.79E-02

5.88E-02

5.7

29.8

7

4.39E-02

22.8

13.2

4.45E-02

5.47E-02

1.3

24.5

8

3.30E-02

30.3

9.9

3.60E-02

4.44E-02

9.2

34.6

9

2.88E-02

34.7

8.7

3.26E-02

4.03E-02

13.2

39.7

174

Table 3-7 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

10

2.01E-02

49.8

6.0

2.38E-02

2.95E-02

18.2

46.6

11

1.64E-02

61.1

4.9

1.86E-02

2.31E-02

13.4

41.2

12

1.18E-02

84.5

3.5

1.30E-02

1.63E-02

10.0

37.7

13

1.05E-02

95.2

3.2

1.21E-02

1.52E-02

15.3

44.4

14

1.02E-02

97.6

3.1

1.13E-02

1.42E-02

10.8

38.9

15

7.46E-03

134.1

2.2

8.35E-03

1.05E-02

12.0

41.1

16

4.56E-03

219.1

1.4

4.68E-03

5.95E-03

2.5

30.3

17

3.91E-03

255.5

1.2

4.24E-03

5.40E-03

8.5

38.0

18

3.87E-03

258.4

1.2

3.97E-03

5.06E-03

2.6

30.7

19

2.20E-03

453.8

0.7

2.94E-03

3.76E-03

33.3

70.5

20

2.02E-03

495.6

0.6

2.48E-03

3.18E-03

22.9

57.6

175

Table 3-7 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

21

1.30E-03

771.9

0.4

1.67E-03

2.16E-03

22

8.46E-04

1182.5

0.3

1.33E-03

1.72E-03

23

4.90E-04

2041.5

0.1

1.03E-03

1.34E-03

38

6.21E-01

1.6

186.4

39

1.81E-01

5.5

54.3

1.44E-01

40

5.86E-02

17.1

17.6

41

1.83E-02

54.8

42

6.85E-03

43

APE
fixed T

APE
variable T

1.74E-01

20.4

3.9

5.19E-02

6.37E-02

11.4

8.6

5.5

1.79E-02

2.23E-02

2.0

22.1

146.1

2.1

6.08E-03

7.70E-03

11.2

12.4

2.04E-03

491.2

0.6

1.90E-03

2.45E-03

6.4

20.5

44

4.22E-04

2371.1

0.1

6.93E-04

9.06E-04

46

4.86E-01

2.1

145.8

176

Table 3-7 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

47

1.70E-01

5.9

51.0

1.45E-01

1.75E-01

14.8

2.9

48

1.35E-01

7.4

40.6

1.32E-01

1.60E-01

2.4

18.0

49

1.11E-01

9.0

33.2

1.03E-01

1.25E-01

6.9

13.0

50

5.54E-02

18.1

16.6

5.43E-02

6.65E-02

2.0

20.0

51

1.74E-02

57.4

5.2

1.86E-02

2.32E-02

6.9

33.0

52

1.06E-02

94.3

3.2

1.11E-02

1.39E-02

4.7

31.3

53

7.50E-03

133.3

2.3

6.75E-03

8.53E-03

10.0

13.7

54

6.73E-03

148.6

2.0

6.47E-03

8.18E-03

3.8

21.6

55

4.40E-03

227.4

1.3

3.79E-03

4.83E-03

13.8

9.9

56

5.05E-04

1980.2

0.2

7.54E-04

9.84E-04

58

4.65E-02

21.5

14.0

5.03E-02

6.17E-02

8.2

32.7

177

Table 3-7 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

59

3.70E-02

27.0

11.1

4.63E-02

5.69E-02

25.0

53.5

60

4.00E-02

25.0

12.0

4.22E-02

5.18E-02

5.5

29.7

61

3.19E-02

31.4

9.6

3.59E-02

4.42E-02

12.6

38.8

62

2.83E-02

35.3

8.5

2.94E-02

3.64E-02

3.8

28.4

63

2.53E-02

39.5

7.6

2.69E-02

3.33E-02

6.2

31.5

64

1.77E-02

56.5

5.3

1.95E-02

2.43E-02

10.2

37.1

65

1.69E-02

59.0

5.1

1.88E-02

2.34E-02

10.7

37.8

66

1.61E-02

62.1

4.8

1.67E-02

2.09E-02

4.0

29.6

67

1.09E-02

91.9

3.3

1.14E-02

1.42E-02

4.4

30.9

68

2.69E-02

37.2

8.1

2.42E-02

3.00E-02

10.0

11.6

69

1.49E-02

67.0

4.5

1.41E-02

1.77E-02

5.4

18.3

178

Table 3-7 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

70

8.89E-03

112.5

2.7

8.19E-03

1.03E-02

7.9

16.0

71

8.44E-03

118.5

2.5

7.41E-03

9.35E-03

12.2

10.8

72

3.69E-03

271.4

1.1

3.08E-03

3.94E-03

16.4

6.9

73

2.64E-03

379.1

0.8

2.26E-03

2.91E-03

14.3

10.1

74

2.14E-03

468.1

0.6

1.74E-03

2.24E-03

18.6

4.9

75

1.27E-03

787.5

0.4

1.28E-03

1.65E-03

76

9.00E-04

1111.0

0.3

1.01E-03

1.31E-03

77

3.59E-04

2785.8

0.1

6.09E-04

7.98E-04

78

7.85E-03

127.3

2.4

5.61E-03

7.11E-03

28.5

9.4

179

Table 3-8. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel evaporated
at 20 °C. The predicted rate constant (kpred) and absolute precent error (APE) was
calculated using the fixed-temperature (fixed T) and variable-temperature (variable T)
models. Compounds with  > 0.5 in 300 h were excluded from the table (peaks 80, 85,
105, 106).
Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

79

4.19E-03

238.7

1.3

4.45E-03

5.66E-03

6.2

35.0

81

7.50E-02

13.3

22.5

7.23E-02

8.82E-02

3.7

17.5

82

6.38E-03

156.7

1.9

6.40E-03

8.09E-03

0.3

26.9

83

6.22E-03

160.8

1.9

5.87E-03

7.43E-03

5.6

19.5

84

2.15E-03

465.9

0.6

1.98E-03

2.55E-03

7.7

18.8

86

2.44E-01

4.1

73.3

1.86E-01

2.24E-01

23.8

8.3

87

8.68E-02

11.5

26.0

7.97E-02

9.71E-02

8.2

11.9

88

7.63E-02

13.1

22.9

6.46E-02

7.90E-02

15.3

3.5

89

2.72E-02

36.7

8.2

2.96E-02

3.66E-02

8.6

34.3

180

Table 3-8 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

90

2.81E-02

35.6

8.4

2.87E-02

3.55E-02

2.3

26.6

91

2.67E-02

37.5

8.0

2.56E-02

3.17E-02

4.0

19.0

92

1.01E-02

98.7

3.0

1.02E-02

1.28E-02

0.5

26.2

93

9.58E-03

104.4

2.9

9.04E-03

1.14E-02

5.6

18.8

94

2.36E-02

42.4

7.1

2.63E-02

3.26E-02

11.8

38.4

95

2.24E-02

44.6

6.7

2.55E-02

3.16E-02

13.8

41.0

96

1.81E-02

55.2

5.4

2.01E-02

2.50E-02

10.8

37.7

97

1.46E-02

68.3

4.4

1.81E-02

2.26E-02

23.8

54.1

98

1.24E-02

80.6

3.7

1.38E-02

1.73E-02

11.5

39.4

99

8.65E-03

115.5

2.6

9.56E-03

1.20E-02

10.5

38.9

100

7.20E-03

139.0

2.2

7.03E-03

8.87E-03

2.4

23.3

181

Table 3-8 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

101

6.46E-03

154.7

1.9

6.21E-03

7.85E-03

4.0

21.5

102

5.93E-03

168.6

1.8

5.95E-03

7.53E-03

0.3

27.0

103

5.47E-03

182.9

1.6

5.43E-03

6.89E-03

0.6

26.0

104

8.69E-03

115.0

2.6

9.63E-03

1.21E-02

10.7

39.2

105

2.89E-03

345.9

0.9

2.93E-03

3.75E-03

1.3

29.6

106

2.72E-03

367.3

0.8

2.64E-03

3.39E-03

3.0

24.4

107

1.60E-02

62.6

4.8

1.73E-02

2.16E-02

8.6

35.3

182

Table 3-9. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 30 °C. The predicted rate constant (kpred) and absolute
precent error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 24 – 37, 45, 77). Several compounds had retention indices lower than
800 (peaks 1, 38, 46) and were also excluded, as the retention index could not be
accurately extrapolated.
Peak #

ke (h-1)

 (h)

#  in
300 h

1

6.81E-01

1.5

204.2

2

5.42E-01

1.8

3

2.26E-01

4

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

162.5

4.40E-01

4.63E-01

18.8

14.5

4.4

67.9

2.34E-01

2.46E-01

3.5

8.4

2.19E-01

4.6

65.8

2.17E-01

2.27E-01

1.2

3.4

5

1.62E-01

6.2

48.6

1.58E-01

1.65E-01

2.2

2.1

6

1.07E-01

9.3

32.2

1.13E-01

1.18E-01

5.3

9.7

7

1.04E-01

9.6

31.3

1.05E-01

1.10E-01

1.1

5.2

8

7.82E-02

12.8

23.4

8.57E-02

8.91E-02

9.7

14.0

9

7.17E-02

14.0

21.5

7.78E-02

8.08E-02

8.5

12.7

183

Table 3-9 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

10

5.03E-02

19.9

15.1

5.70E-02

5.91E-02

13.3

17.4

11

3.99E-02

25.1

12.0

4.48E-02

4.63E-02

12.3

16.1

12

2.87E-02

34.8

8.6

3.17E-02

3.26E-02

10.3

13.7

13

2.51E-02

39.9

7.5

2.95E-02

3.04E-02

17.8

21.4

14

2.44E-02

41.1

7.3

2.77E-02

2.85E-02

13.7

17.1

15

1.84E-02

54.3

5.5

2.05E-02

2.11E-02

11.6

14.6

16

1.08E-02

92.5

3.2

1.17E-02

1.19E-02

7.9

10.3

17

9.87E-03

101.4

3.0

1.06E-02

1.08E-02

7.4

9.8

18

9.34E-03

107.0

2.8

9.92E-03

1.01E-02

6.2

8.5

19

6.21E-03

161.0

1.9

7.39E-03

7.53E-03

19.0

21.3

20

6.12E-03

163.3

1.8

6.26E-03

6.38E-03

2.3

4.1

184

Table 3-9 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

21

4.38E-03

228.5

1.3

4.26E-03

4.33E-03

2.5

1.1

22

3.34E-03

299.8

1.0

3.39E-03

3.44E-03

1.8

3.1

23

2.24E-03

445.8

0.7

2.66E-03

2.69E-03

18.6

20.0

24

1.02E-03

984.0

0.3

1.37E-03

1.38E-03

25

7.98E-04

1253.1

0.2

1.18E-03

1.19E-03

38

1.41E+00

0.7

423.4

39

4.07E-01

2.5

122.2

3.32E-01

3.48E-01

18.6

14.5

40

1.39E-01

7.2

41.8

1.22E-01

1.28E-01

12.1

8.4

41

4.42E-02

22.6

13.3

4.32E-02

4.47E-02

2.2

1.1

42

1.54E-02

64.9

4.6

1.51E-02

1.54E-02

2.2

0.2

43

5.33E-03

187.8

1.6

4.84E-03

4.92E-03

9.1

7.7

185

Table 3-9 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

44

1.89E-03

528.8

0.6

1.80E-03

1.82E-03

4.7

3.9

46

1.09E+00

0.9

325.8

47

3.87E-01

2.6

116.1

3.34E-01

3.50E-01

13.8

9.5

48

3.09E-01

3.2

92.6

3.05E-01

3.20E-01

1.3

3.6

49

2.57E-01

3.9

77.2

2.40E-01

2.51E-01

6.9

2.5

50

1.37E-01

7.3

41.1

1.28E-01

1.33E-01

6.6

2.6

51

4.17E-02

24.0

12.5

4.50E-02

4.65E-02

7.7

11.4

52

2.53E-02

39.5

7.6

2.71E-02

2.79E-02

7.1

10.3

53

1.73E-02

57.8

5.2

1.67E-02

1.71E-02

3.7

1.2

54

1.51E-02

66.1

4.5

1.60E-02

1.64E-02

5.7

8.4

55

1.01E-02

99.5

3.0

9.49E-03

9.69E-03

5.6

3.6

186

Table 3-9 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

56

1.92E-03

520.1

0.6

1.96E-03

1.97E-03

1.7

2.6

58

1.20E-01

8.3

36.1

1.19E-01

1.24E-01

1.2

3.0

59

9.14E-02

10.9

27.4

1.10E-01

1.14E-01

19.8

24.8

60

9.86E-02

10.1

29.6

9.99E-02

1.04E-01

1.3

5.4

61

7.99E-02

12.5

24.0

8.53E-02

8.87E-02

6.8

11.0

62

7.23E-02

13.8

21.7

7.03E-02

7.29E-02

2.7

0.9

63

6.12E-02

16.3

18.4

6.44E-02

6.67E-02

5.2

9.1

64

4.27E-02

23.4

12.8

4.71E-02

4.87E-02

10.1

13.9

65

4.08E-02

24.5

12.2

4.53E-02

4.68E-02

11.0

14.8

66

3.86E-02

25.9

11.6

4.05E-02

4.19E-02

4.9

8.4

67

2.48E-02

40.4

7.4

2.77E-02

2.86E-02

11.9

15.2

187

Table 3-9 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

68

6.59E-02

15.2

19.8

5.81E-02

6.02E-02

11.8

8.6

69

3.55E-02

28.2

10.6

3.43E-02

3.54E-02

3.3

0.2

70

2.10E-02

47.6

6.3

2.01E-02

2.07E-02

4.2

1.6

71

1.96E-02

51.1

5.9

1.83E-02

1.87E-02

6.7

4.2

72

8.76E-03

114.2

2.6

7.74E-03

7.89E-03

11.6

9.9

73

6.85E-03

146.0

2.1

5.73E-03

5.82E-03

16.4

15.0

74

5.51E-03

181.4

1.7

4.43E-03

4.49E-03

19.7

18.5

75

3.90E-03

256.4

1.2

3.27E-03

3.32E-03

16.0

15.0

76

2.92E-03

342.5

0.9

2.60E-03

2.63E-03

11.1

10.1

77

1.62E-03

617.6

0.5

1.59E-03

1.60E-03

78

1.67E-02

59.9

5.0

1.39E-02

1.43E-02

16.6

14.5

188

Table 3-10. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel evaporated
at 30 °C. The predicted rate constant (kpred) and absolute precent error (APE) was
calculated using the fixed-temperature (fixed T) and variable-temperature (variable T)
models. Compounds with  > 0.5 in 300 h were excluded from the table.
Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

79

1.03E-02

97.1

3.1

1.11E-02

1.13E-02

7.7

10.2

80

3.43E-03

291.2

1.0

3.57E-03

3.62E-03

4.1

5.5

81

1.75E-01

5.7

52.4

1.69E-01

1.77E-01

3.1

1.3

82

1.44E-02

69.4

4.3

1.58E-02

1.62E-02

9.9

12.7

83

1.45E-02

69.1

4.3

1.45E-02

1.49E-02

0.5

2.9

84

5.97E-03

167.6

1.8

5.03E-03

5.11E-03

15.7

14.3

85

2.75E-03

363.2

0.8

2.24E-03

2.26E-03

18.8

18.0

86

5.60E-01

1.8

168.0

4.27E-01

4.49E-01

23.8

19.8

87

1.98E-01

5.1

59.3

1.86E-01

1.95E-01

5.9

1.6

88

1.70E-01

5.9

51.0

1.52E-01

1.58E-01

10.9

7.0

189

Table 3-10 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

89

6.70E-02

14.9

20.1

7.06E-02

7.33E-02

5.5

9.5

90

6.72E-02

14.9

20.1

6.87E-02

7.12E-02

2.2

6.0

91

6.24E-02

16.0

18.7

6.14E-02

6.36E-02

1.6

2.0

92

2.31E-02

43.3

6.9

2.49E-02

2.56E-02

7.7

10.8

93

2.22E-02

45.0

6.7

2.22E-02

2.28E-02

0.1

2.7

94

5.73E-02

17.5

17.2

6.31E-02

6.54E-02

10.1

14.1

95

5.38E-02

18.6

16.1

6.11E-02

6.33E-02

13.6

17.7

96

4.29E-02

23.3

12.9

4.84E-02

5.00E-02

12.6

16.5

97

3.54E-02

28.3

10.6

4.38E-02

4.52E-02

23.7

27.8

98

2.95E-02

33.9

8.8

3.36E-02

3.47E-02

14.2

17.8

99

1.99E-02

50.3

6.0

2.34E-02

2.41E-02

17.8

21.2

190

Table 3-10 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

100

1.68E-02

59.7

5.0

1.73E-02

1.78E-02

3.4

6.1

101

1.45E-02

68.9

4.4

1.54E-02

1.57E-02

5.8

8.5

102

1.39E-02

71.8

4.2

1.47E-02

1.51E-02

5.8

8.5

103

1.27E-02

78.5

3.8

1.35E-02

1.38E-02

5.8

8.4

104

1.95E-02

51.3

5.8

2.36E-02

2.43E-02

21.0

24.5

105

7.39E-03

135.3

2.2

7.37E-03

7.51E-03

0.3

1.6

106

7.26E-03

137.7

2.2

6.66E-03

6.79E-03

8.2

6.6

107

3.92E-02

25.5

11.8

4.19E-02

4.33E-02

6.8

10.4

191

Table 3-11. For model development, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds monitored during the
evaporation of diesel fuel at 35 °C. The predicted rate constant (kpred) and absolute
precent error (APE) was calculated using the fixed-temperature (fixed T) and variabletemperature (variable T) models. Compounds with  > 0.5 in 300 h were excluded from
the table (peaks 26 – 37, 45). Several compounds had retention indices lower than 800
(peaks 1, 38, 46) and were also excluded, as the retention index could not be accurately
extrapolated.

Peak #

ke (h-1)

 (h)

#  in
300 h

1

1.44E+00

0.7

432.4

2

1.00E+00

1.0

3

3.95E-01

4

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

300.0

6.82E-01

6.46E-01

31.8

35.4

2.5

118.5

3.68E-01

3.43E-01

6.8

13.3

3.79E-01

2.6

113.8

3.41E-01

3.16E-01

10.1

16.6

5

2.54E-01

3.9

76.1

2.51E-01

2.31E-01

1.2

9.1

6

1.75E-01

5.7

52.6

1.80E-01

1.64E-01

2.8

6.3

7

1.69E-01

5.9

50.7

1.68E-01

1.53E-01

0.4

9.5

8

1.26E-01

7.9

37.9

1.37E-01

1.24E-01

8.7

1.7

192

Table 3-11 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

9

1.11E-01

9.0

33.3

1.25E-01

1.13E-01

12.4

1.4

10

7.66E-02

13.0

23.0

9.22E-02

8.24E-02

20.2

7.5

11

6.34E-02

15.8

19.0

7.28E-02

6.46E-02

14.8

1.9

12

4.68E-02

21.3

14.1

5.18E-02

4.55E-02

10.6

2.8

13

4.20E-02

23.8

12.6

4.84E-02

4.24E-02

15.3

1.1

14

4.04E-02

24.8

12.1

4.54E-02

3.98E-02

12.5

1.5

15

2.89E-02

34.6

8.7

3.39E-02

2.94E-02

17.2

1.8

16

1.82E-02

54.9

5.5

1.95E-02

1.66E-02

6.9

8.6

17

1.61E-02

62.2

4.8

1.77E-02

1.51E-02

10.3

6.0

18

1.52E-02

65.9

4.6

1.66E-02

1.41E-02

9.6

6.8

19

1.10E-02

90.5

3.3

1.25E-02

1.05E-02

12.8

4.9

193

Table 3-11 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

20

9.98E-03

100.2

3.0

1.06E-02

8.89E-03

6.2

10.9

21

7.28E-03

137.5

2.2

7.27E-03

6.04E-03

0.1

17.0

22

5.87E-03

170.4

1.8

5.81E-03

4.80E-03

0.9

18.3

23

4.04E-03

247.7

1.2

4.58E-03

3.75E-03

13.4

7.0

24

2.41E-03

414.2

0.7

2.39E-03

1.92E-03

1.0

20.4

25

2.16E-03

463.4

0.6

2.07E-03

1.66E-03

4.2

23.3

26

1.48E-03

674.4

0.4

1.68E-03

1.34E-03

27

7.43E-04

1345.9

0.2

8.79E-04

6.87E-04

28

3.22E-04

3105.8

0.1

6.19E-04

4.79E-04

38

2.86E+00

0.3

858.6

39

7.52E-01

1.3

225.6

5.17E-01

4.86E-01

31.2

35.4

194

Table 3-11 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

40

2.14E-01

4.7

64.1

1.95E-01

1.78E-01

8.7

16.6

41

6.86E-02

14.6

20.6

7.03E-02

6.23E-02

2.4

9.2

42

2.55E-02

39.3

7.6

2.50E-02

2.15E-02

1.8

15.5

43

8.69E-03

115.1

2.6

8.23E-03

6.86E-03

5.3

21.1

44

3.91E-03

255.7

1.2

3.13E-03

2.53E-03

20.1

35.2

46

2.13E+00

0.5

637.9

47

6.74E-01

1.5

202.1

5.20E-01

4.89E-01

22.8

27.5

48

5.46E-01

1.8

163.7

4.76E-01

4.46E-01

12.7

18.2

49

4.34E-01

2.3

130.1

3.76E-01

3.50E-01

13.3

19.3

50

2.11E-01

4.7

63.2

2.03E-01

1.86E-01

3.4

11.7

51

6.43E-02

15.5

19.3

7.31E-02

6.49E-02

13.6

0.8

195

Table 3-11 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

52

3.95E-02

25.3

11.8

4.45E-02

3.89E-02

12.7

1.4

53

2.75E-02

36.3

8.3

2.76E-02

2.39E-02

0.4

13.4

54

2.50E-02

40.0

7.5

2.65E-02

2.29E-02

6.2

8.5

55

1.64E-02

60.9

4.9

1.59E-02

1.35E-02

3.1

17.7

56

3.84E-03

260.6

1.2

3.39E-03

2.75E-03

11.7

28.3

58

1.75E-01

5.7

52.6

1.89E-01

1.73E-01

7.9

1.5

59

1.42E-01

7.1

42.5

1.75E-01

1.59E-01

23.4

12.4

60

1.49E-01

6.7

44.7

1.60E-01

1.45E-01

7.1

2.7

61

1.18E-01

8.5

35.3

1.37E-01

1.24E-01

16.2

5.0

62

1.06E-01

9.5

31.7

1.13E-01

1.02E-01

7.2

3.6

63

9.04E-02

11.1

27.1

1.04E-01

9.31E-02

14.9

3.0

196

Table 3-11 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

64

6.49E-02

15.4

19.5

7.64E-02

6.79E-02

17.7

4.6

65

6.30E-02

15.9

18.9

7.35E-02

6.53E-02

16.7

3.6

66

5.94E-02

16.8

17.8

6.60E-02

5.84E-02

11.1

1.7

67

4.03E-02

24.8

12.1

4.55E-02

3.98E-02

12.7

1.3

68

1.01E-01

9.9

30.3

9.39E-02

8.40E-02

7.0

16.9

69

5.42E-02

18.4

16.3

5.61E-02

4.94E-02

3.4

8.9

70

3.32E-02

30.1

10.0

3.32E-02

2.88E-02

0.0

13.2

71

3.06E-02

32.7

9.2

3.02E-02

2.61E-02

1.2

14.5

72

1.45E-02

68.8

4.4

1.30E-02

1.10E-02

10.3

24.2

73

1.09E-02

91.9

3.3

9.70E-03

8.12E-03

10.8

25.3

74

8.71E-03

114.7

2.6

7.54E-03

6.27E-03

13.5

28.1

197

Table 3-11 cont’d

Peak #

ke (h-1)

 (h)

#  in
300 h

kp
fixed T

kp
variable T

APE
fixed T

APE
variable T

75

6.42E-03

155.7

1.9

5.61E-03

4.63E-03

12.6

28.0

76

5.19E-03

192.8

1.6

4.47E-03

3.66E-03

13.8

29.4

77

3.34E-03

299.2

1.0

2.76E-03

2.23E-03

17.3

33.3

78

2.82E-02

35.4

8.5

2.32E-02

1.99E-02

17.9

29.5

198

Table 3-12. For model validation, the experimental rate constant (kexp), characteristic
lifetime (), and the number of  in 300 h for selected compounds in diesel fuel evaporated
at 35 °C. The predicted rate constant (kpred) and absolute precent error (APE) was
calculated using the fixed-temperature (fixed T) and variable-temperature (variable T)
models. Compounds with  > 0.5 in 300 h were excluded from the table.
Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

79

1.73E-02

57.9

5.2

1.85E-02

1.58E-02

7.3

8.5

80

6.10E-03

163.9

1.8

6.11E-03

5.05E-03

0.2

17.2

81

2.92E-01

3.4

87.7

2.68E-01

2.47E-01

8.5

15.7

82

2.43E-02

41.1

7.3

2.63E-02

2.26E-02

7.9

7.0

83

2.35E-02

42.5

7.1

2.42E-02

2.08E-02

2.8

11.6

84

9.24E-03

108.2

2.8

8.54E-03

7.13E-03

7.6

22.9

85

4.86E-03

205.7

1.5

3.86E-03

3.15E-03

20.6

35.3

86

1.06E+00

0.9

317.7

6.62E-01

6.26E-01

37.5

40.9

87

3.10E-01

3.2

93.0

2.94E-01

2.71E-01

5.3

12.4

88

2.74E-01

3.7

82.2

2.40E-01

2.21E-01

12.3

19.4

199

Table 3-12 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

89

1.05E-01

9.5

31.4

1.14E-01

1.02E-01

8.5

2.4

90

1.05E-01

9.5

31.5

1.11E-01

9.93E-02

5.2

5.5

91

9.82E-02

10.2

29.5

9.91E-02

8.87E-02

0.9

9.7

92

3.84E-02

26.0

11.5

4.09E-02

3.57E-02

6.6

7.0

93

3.65E-02

27.4

10.9

3.65E-02

3.18E-02

0.2

12.8

94

8.99E-02

11.1

27.0

1.02E-01

9.12E-02

13.2

1.4

95

8.43E-02

11.9

25.3

9.86E-02

8.83E-02

17.0

4.8

96

6.57E-02

15.2

19.7

7.84E-02

6.98E-02

19.4

6.2

97

5.60E-02

17.8

16.8

7.11E-02

6.31E-02

27.0

12.6

98

4.71E-02

21.2

14.1

5.50E-02

4.84E-02

16.8

2.8

99

3.22E-02

31.0

9.7

3.86E-02

3.36E-02

19.6

4.2

200

Table 3-12 cont’d

Peak #

kexp (h-1)

 (h)

#  in
300 h

kpred
fixed T

kpred
variable T

APE
fixed T

APE
variable T

100

2.70E-02

37.0

8.1

2.87E-02

2.48E-02

6.2

8.2

101

2.46E-02

40.7

7.4

2.55E-02

2.20E-02

3.7

10.7

102

2.27E-02

44.0

6.8

2.45E-02

2.11E-02

7.7

7.4

103

2.07E-02

48.2

6.2

2.24E-02

1.93E-02

8.2

7.1

104

3.23E-02

31.0

9.7

3.88E-02

3.38E-02

20.4

4.9

105

1.16E-02

86.4

3.5

1.24E-02

1.05E-02

7.3

9.5

106

1.13E-02

88.9

3.4

1.13E-02

9.47E-03

0.0

15.9

107

5.87E-02

17.0

17.6

6.82E-02

6.04E-02

16.1

2.9

201

Based on these experimental data, several models were developed to predict the
rate constants for evaporation. The fixed-temperature models were developed to predict
rate constants at a single temperature at which the data were acquired (5 – 35 °C). The
data from these experiments were then combined to develop the variable-temperature
model.

The variable-temperature model was utilized in two ways:

under constant

temperature, to compare with the performance of the fixed-temperature models, and
under fluctuating temperature, to simulate diurnal and seasonal changes.

Once

developed, these models were applied to predict the fraction remaining of an individual
compound and the entire fuel. Prior to model development, data were evaluated by
constructing Arrhenius plots to determine evaluate the effect of temperature on the rate
constant and determine the activation energy and pre-exponential term in the Arrhenius
equation.
3.3.1

Arrhenius Plots
The dependence of the rate constant on temperature can be described by the

Arrhenius equation

ln k  ln A 

EA
RT

Equation 3-2

where k is the rate constant, A is the pre-exponential factor, EA is the activation energy,
R is the gas constant and T is temperature.

Arrhenius plots were constructed for

seventeen selected compounds by plotting the ln (k) vs 1/T, and linear regression was
performed. The activation energy was determined from the slope and the pre-exponential
factor was determined from the intercept. The pre-exponential factor incorporates a

202

frequency factor, accounting for the number of collisions, as well as a steric factor, related
to the cross-sectional area of a molecule.
Arrhenius plots were constructed using rate constants from all 5 temperatures
(Table 3-13). There was a deviation from linearity at the lower temperatures (R2 = 0.937
– 0.988). This deviation may be due to an increased temperature experienced when the
evaporation chamber was opened to place the samples inside. A phase change occurring
at the lower temperatures could also explain the deviation from linearity. The temperature
at which saturates form a wax and precipitate out of solution, or the cloud point, is
approximately 0 – 5 °C for diesel fuel [7]. Therefore, at the lower temperatures, a phase
change may be occurring. The activation energy determined for each compound was
relatively similar (Table 3-13), however, due to the deviation in linearity, only limited
conclusions can be made from these values.
Arrhenius plots were constructed using only the three highest temperatures (20,
30, and 35 °C) where the plots were linear (TABLE, R2 = 0.986 – 1.000). The activation
energy was similar for all the individual compounds.

The pre-exponential factor was

larger using the three highest temperatures, suggesting a lower frequency of collision
when incorporating the lower temperatures may be due to a phase change. Using the
activation energy, the activation enthalpy (HA) was determined from the temperature (T)
the pressure (P) and the change in molar volume (ΔV).

203

Table 3-13. The activation energy (EA), pre-exponential factor (A), coefficient of
determination (R2) determined from the Arrhenius plot of using all temperatures (5, 10,
20, 30, 35 °C).
Compound Identity

EA

A

R2

Octane

49.25

1.87E+08

0.939

Ethyl benzene

48.54

9.85E+07

0.940

Ethyl cyclohexane

47.89

8.27E+07

0.937

Nonane

51.72

1.37E+08

0.961

Propyl benzene

51.14

9.09E+07

0.952

Propyl cyclohexane

50.43

7.05E+07

0.962

1,3,5 trimethyl
benzene

53.60

1.62E+08

0.963

1,2,4 trimethyl
benzene

51.66

6.39E+07

0.956

1,2,3 trimethyl
benzene

52.26

6.30E+07

0.971

Indane

51.28

4.64E+07

0.954

204

Table 3-13 cont’d

Compound Identity

EA
(kJ/mol)

A
(s-1)

R2

Decane

51.63

4.05E+07

0.963

Butyl benzene

50.53

2.20E+07

0.965

4-methyl decane

50.79

2.37E+07

0.966

Butyl cyclohexane

50.35

2.18E+07

0.961

Undecane

54.36

4.51E+07

0.983

1,2,3,4
tetrahydronaphthalene

51.78

1.55E+07

0.980

Dodecane

66.77

2.17E+09

0.988

205

Table 3-14. The activation energy (EA), pre-exponential factor (A), coefficient of
determination (R2) determined from the Arrhenius plot of using the three highest
temperatures (20, 30, 35 °C). The enthalpy of vaporization (Hvap) from the literature and
the enthalpy of activation (HA) determined from the Arrhenius plot and Equation 3-3 as
well as the difference between the two values (Hvap - HA) are also shown.

Compound Identity

Hvap
EA
(kJ/mol)1 (kJ/mol)

A (s-1)

R2

HA
(kJ/mol)

Hvap HA

Octane

41.5

75.6

6.74E+12

0.990

73.22

31.7

Ethyl benzene

42.3

70.1

5.36E+11

0.992

67.74

25.5

Ethyl cyclohexane

40.6

72.1

1.26E+12

0.986

69.69

29.1

Nonane

46.4

69.8

1.83E+11

1.000

67.38

20.9

Propyl benzene

46.2

69.2

1.22E+11

1.000

66.81

20.6

Propyl cyclohexane

45.1

66.9

4.98E+10

1.000

64.49

19.4

1,3,5 trimethyl
benzene

47.5

69.4

8.90E+10

1.000

67.02

19.5

1,2,4 trimethyl
benzene

47.9

68.2

4.64E+10

0.999

65.78

17.8

1,2,3 trimethyl
benzene

49.1

66.2

1.63E+10

1.000

63.79

14.7

206

Table 3-14 cont’d

Compound Identity

EA
Hvap
1
(kJ/mol) (kJ/mol)

A (s-1)

R2

HA
(kJ/mol)

Hvap HA

Indane

48.8

68.6

4.57E+10

1.000

66.17

17.4

Decane

51.4

69.5

5.05E+10

1.000

67.12

15.7

Butyl benzene

51.4

67.5

1.94E+10

1.000

65.14

13.8

4-methyl decane

53.8

69.9

4.80E+10

1.000

67.51

13.7

Butyl cyclohexane

49.4

68.5

2.98E+10

1.000

66.08

16.7

Undecane

56.4

70.1

2.32E+10

1.000

67.65

11.2

1,2,3,4
tetrahydronaphthalene

55.0

66.9

6.34E+09

0.999

64.49

9.5

Dodecane

61.5

82.9

1.33E+12

0.999

80.50

19.0

1. From reference [8].

207

EA  HA  (RT  P V)

Equation 3-3

The molar volume was calculated as 10 times the volume in the liquid phase, because
the molecule is moving from the gas to liquid phase. The activation enthalpy was similar,
but slightly lower than the activation energy, demonstrating that the temperature and
change in volume only have minor contributions. The activation enthalpy was compared
to the enthalpy of vaporization (TABLE).

The enthalpy of vaporization is large,

contributing 55 – 85% of the total enthalpy of activation.
3.3.2 Fixed-temperature Models
To develop the fixed-temperature models, the natural logarithm of the rate constant
(ln (k)) was plotted versus the retention index for all selected compounds (Figure 3-2).
Linear regression was used to calculate the slope (m) and intercept (b) of
Equation 3-4

ln(k)  m I T  b

as summarized in Table 3-15. At all temperatures, a high coefficient of determination (R2
= 0.982 – 0.995) indicated a good quality of fit to the linear equation. Slightly lower R2
values were observed at the lower temperatures of 5 and 10 °C, which may be due to a
change in temperature when the evaporation chamber was opened to insert and remove
the samples. It is noteworthy that both the slope (1.00 * 10-2 – 1.12 * 10-2) and the
intercept (6.17 – 7.62) of Equation 3-4 were temperature dependent.

208

Figure 3-2. Natural logarithm of evaporation rate constant (ln (k)) versus retention index
for selected compounds. Linear regression equations: 5 °C (×) y = -1.12 * 10-2 * x +
6.78, R2 = 0.987, n = 42; 10 °C (), y = -1.05 * 10-2 * x + 6.17, R2 = 0.982, n = 46; 20 °C
(), y = -1.05 * 10-2 * x + 6.71, R2 = 0.990, n = 51; 30 °C (), y = -1.02 * 10-2 * x + 7.35,
R2 = 0.995, n = 58; 35 °C (), y = -1.00 * 10-2 * x + 7.62, R2 = 0.993, n = 61.

209

Table 3-15. The fixed temperature models developed for each temperature, including
the number of compounds (n), the slope (m), intercept (b), and coefficient of
determination (R2) for linear regression with Equation 3-4 are shown. Also shown is the
mean absolute percent error (MAPE) in the prediction of the rate consent for each
temperature using the fixed temperature models as well as the variable temperature
model (Equation 3-6).
Model
Temperature
(K)

n

m

b

R2

278

42

-1.12 * 10-2

6.78

283

46

-1.05 * 10-2

293

51

303
308

MAPE (%)

MAPE (%)

Fixed T

Variable T

0.987

9.6

19

6.17

0.982

10.8

16

-1.05 * 10-2

6.71

0.990

10.3

26

58

-1.02 * 10-2

7.35

0.995

8.6

9.4

61

-1.00 * 10-2

7.62

0.993

10.5

13

10.0

16.4

Average

210

The performance of the fixed-temperature models was evaluated by calculating
the predicted rate constant (kpred) and comparing it to the experimental evaporation rate
constant (kexp) for each selected compound. The absolute percent error (APE) was
calculated for each compound and then averaged to yield the mean absolute percent
error (MAPE) [9].
n

kexp,i  kpred,i

i 1

kexp,i



MAPE 

n

Equation 3-5

100

The APE for the selected compounds is summarized in the odd numbered tables between
Table 3-3 – Table 3-12 and the MAPE is summarized in Table 3-15 for each fixedtemperature model. Errors for individual compounds ranged from 0.1 – 40.6%. The
MAPE for each model ranged from 8.6 – 10.8%, with an overall average of 10.0%.
To validate the fixed-temperature models, 29 additional compounds were
selected that spanned a similar range of retention indices as those used to develop the
models. The rate constants were experimentally determined at temperatures of 5, 10,
20, 30, and 35 °C, as summarized in the even numbered tables between Table 3-3 –
Table 3-12. The experimental rate constants were then compared to the values predicted
by the fixed-temperature models at the corresponding temperature. As a representative
example, the experimental and predicted rate constants for decalin (m/z = 138, IT = 1045)
are shown in Table 3-16. The APE for each model ranged from 0.5 – 17.4%, with an
overall average

211

212

Table 3-16. The rate constant (k) at each temperature for decalin (RI = 1045), which was
not included in the original model. The observed rate constant (kobs) as well as the
experimentally predicted (kexp) rate constant using the fixed temperature and variable
model is also shown. The absolute percent error (APE) between the experimental and
predicted rate constants are shown for each model.
Model
Temperature
(K)

kobs (h-1)

278

kexp (h-1):

kexp (h-1):

Fixed T Model

APE
(%)

Variable T Model

APE
(%)

8.41 * 10-3

6.95 * 10-3

17

5.87 * 10-3

30

283

8.78 * 10-3

7.93 * 10-3

9.6

8.80 * 10-3

0.3

293

1.60 * 10-2

1.48 * 10-2

7.6

1.84 * 10-2

15

303

3.92 * 10-2

3.58 * 10-2

8.7

3.69 * 10-2

5.8

308

5.87 * 10-2

5.84 * 10-2

0.5

5.15 * 10-2

12

Average

8.8

213

13

of 8.8%.

The MAPE for all validation compounds using the corresponding fixed-

temperature models ranged from 0.02 – 52%, with an overall average of 10.1% (even
numbered tables between Table 3-3 – Table 3-12). The error observed for the validation
compounds is comparable to that for the selected compounds used to develop the model
(Table 3-15). This demonstrates that the models are broadly applicable to a wide range
of compounds, not only those used to develop the model. Extensibility of the model is
critical because of the large number and wide variety of compounds in petroleum fuels.
3.3.3 Variable-Temperature Model
The models developed to this point were generated for five fixed temperatures (5 – 35
°C), but do not include temperature as a variable. Using the same experimental data, a
variable-temperature model to predict the rate constant was developed. Multiple linear
regression was performed to determine the fitting coefficients for the slopes (m1 and m2)
and the intercept (b). As for the fixed-temperature models, all selected compounds with
greater than 0.5  in the 300 h evaporation experiment were included in the regression (n
= 258, R2 = 0.979) [6].

 1
ln(k )  0.0103 I T  6410    28.7
T 

Equation 3-6

The APE for predicting the rate constant for each selected compound is summarized in
Table 3-3 – Table 3-12, and the MAPE is summarized in Table 3-15. Errors for individual
compounds ranged from 0.2 – 71 %. The MAPE ranged from 9.4 – 26%, with an overall
average of 16.4%. As expected, these errors are slightly greater than those for the fixedtemperature models.

214

The rate constants for the 29 validation compounds were also predicted at each
temperature using the variable-temperature model. As a representative example, the
experimental and predicted rate constants for decalin (m/z = 138, IT = 1045) are shown
in Table 3-16. The APE at each temperature ranged from 0.3 – 30%, with an overall
average of 13%. The MAPE for all validation compounds ranged from 0.2 – 54%, with
an overall average of 16.8% (Table 3-17 and even numbered tables between Table 3-3
– Table 3-12).

Again, the error for the validation compounds using the variable-

temperature model is consistent with that observed for the compounds used to develop
the model (Table 3-15).

This demonstrates that the variable-temperature model is

broadly applicable to a wide range of compounds, not only those used to develop the
model. This model can be utilized over a range of environmentally relevant temperatures
with low error and only a 6.4% increase over the fixed-temperature models.
3.3.4 Applications of Model
3.3.4.1 Calculation of Fraction Remaining with Fluctuating Temperatures
In Chapter 2, the fraction remaining of an individual compound (FIT) was calculated
by combining Equation 3-1 and Equation 3-4 [6]. To predict the fraction remaining at
variable temperature, Equation 3-6 was combined with Equation 3-1.

FIT 

CIT ,t
CIT ,0

 1
 exp( (exp(0.0103 I T  6410    28.7) t )
T 

215

Equation 3-7

Table 3-17. The mean absolute percent error (MAPE) for 29 compounds using the
corresponding fixed temperature model (Table 3-15) and the variable temperature model
(Equation 3-6).
Model
Temperature
(K)

MAPE (%)
Fixed T Model

MAPE (%)
Variable T Model

278

13.4

16.7

283

9.3

17.9

293

7.6

27.5

303

9.2

10.8

308

10.8

11.3

Average

10.1

16.8

216

The total fraction of fuel remaining (Ftot), based on the individual compounds, could then
be calculated
T

If
 T Fj Cj,0
j I
Ftot  i T
If
 T Cj,0
j I
i

Equation 3-8

using Equation 3-7 for compounds with ITi = 739 and ITf = 3238. with ITi = 739 and ITf =
3238. The iterative calculations to determine the fraction remaining were performed using
an algorithm written in house (Matlab, version 7.12.0.635 R2011a, Mathworks, Natick,
MA).
This model was validated by evaporating three samples of diesel fuel with water
and three samples of fuel alone under conditions of fluctuating temperature, in order to
simulate diurnal variations. The temperature was varied in the range of 12 – 27 °C
approximately every 12 h, for a total time of 100 h. The temperature profile, recorded in
the evaporation chamber at 2-min intervals, is shown in Figure 3-3a (solid line). The
experimental fraction remaining of diesel fuel was determined from the change in mass
of the samples without water, before and after evaporation.
remaining was 0.83.

The average fraction

Using the variable-temperature model with the temperatures

recorded at 2-min intervals, the fraction remaining was predicted to be 0.87.

The

predicted fraction remaining represents only 5.4% error, compared with the experimental
value (Table 3-18). The fraction remaining calculation is based on the change in GC-MS

217

Figure 3-3. The temperature profile (a) of the fluctuating evaporation experiment with the
temperature recorded every two minutes (solid line) and as a running average
temperature (dashed line). The temperatures at 5-h intervals (circles) and 12-h intervals
(stars) are also shown. The fraction of fuel remaining (b) calculated using the variable
temperature model using the temperature at 2 min intervals (solid line) 5-h intervals
(circles), 12-h intervals (stars), and running average temperature (dashed line). The
percent fuel remaining is shown in Table 3-18.

218

Table 3-18. The fraction of fuel remaining predicted using the variable-temperature model
with temperature data collected every two minutes, every five hours, every twelve hours,
and the running average temperature (Figure 3-3). The experimental fraction of fuel
remaining (FIT) based on the average change in mass was 0.83. The percent error
between the experimental and predicted values using the model is also shown. In
addition, the percent error between the models using the 2-min temperature interval
compared to the longer intervals is shown.
Temperature
Interval

Predicted
FIT

Error (%) from
Prediction using 2-min
Temperature Interval

Error (%) from
Experimental
Fraction Remaining

2 min

0.870

0.00

5.4

1h

0.870

0.01

5.4

5h

0.869

-0.15

5.3

12 h

0.872

0.18

5.6

100 h
Average

0.874

0.43

5.9

219

abundance between the evaporated and unevaporated chromatograms, whereas the
experimental fraction remaining is based on the change in mass. This could account for
some of the difference between the predicted and experimental values. The error in the
prediction of the fraction remaining of fuel is similar to that observed using the fixedtemperature model (20 °C, 7.3% error) in our previous work [6]. This demonstrates that
the variable-temperature model, using fluctuating temperature, can predict the fraction
remaining of fuel with similar error to existing models that lack the temperature variable.
For many practical applications, such highly accurate and detailed temperature
data may not be available.

For example, temperature data are available at hourly

intervals for many areas in the United States using the National Oceanic and Atmospheric
Administration (NOAA) National Climatic Data Center [10].

In order to simulate

temperature data that are more readily available, profiles with the temperature collected
at 1-h, 5-h, and 12-h intervals were also utilized. The temperature at 5-h intervals (circles)
and 12-h intervals (asterisks) are shown on Figure 3-3a. In addition, the running average
temperature was calculated (dashed line). The variable-temperature model was used to
calculate the fraction remaining using each temperature interval. The predicted fraction
remaining over the duration of the 100-h experiment is shown in Figure 3-3b. The
predicted fraction remaining for the 5-h and 12-h intervals is very similar to that for the 2min interval at all times. When the running average temperature was used, the fraction
remaining was slightly different because the average temperature was less sensitive to
the high and low temperature fluctuations (Figure 3-3a). However, by 100 h, the predicted
fraction remaining using the running average temperature became more similar to that
from the other temperature profiles.

220

The predicted fraction remaining at the end of the 100-h experiment is
summarized in Table 3-18. In general, the fraction remaining is similar (± 0.005) for all
temperature profiles. The 2-min interval is expected to be the most accurate (FIT = 0.870),
since it most closely reflects the actual temperature. The running average temperature
is expected to be the least accurate (FIT = 0.874), yet there was only a 0.43% difference
between these two values. This suggests that the use of the average temperature over
the course of an environmental spill is a reasonable approximation. This is advantageous
because the average temperature is easier to obtain and allows for easier application of
the predictive models.
3.3.4.2 Compound Distribution
The variable-temperature model in Equation 3-6 can be utilized to predict the
fraction remaining, ranging from 0 to 1, at each retention index. An example for diesel
fuel is shown in Figure 3-4. In this example, the fraction remaining curve was calculated
at the average temperature (17.1 °C) and time (100 h) for the temperature profile shown
in Figure 3-3a.

This fraction remaining curve can be employed to predict the

chromatographic profile, or the distribution of all individual compounds in the
chromatogram after evaporation. The fraction remaining at each retention index (Figure
3-4a) was multiplied by the corresponding normalized abundance from the chromatogram
(Figure 3-4b) to generate the predicted distribution of compounds after evaporation

221

Figure 3-4. The fraction remaining curve (a) predicted using the variable temperature
model, using the average temperature (17.1 °C) during the fluctuating temperature
experiment (100 h). Also shown are chromatograms of diesel fuel (normalized to
heneicosane), unevaporated (b), predicted by multiplying the unevaporated
chromatogram (b) by the fraction remaining curve (a), and the actual chromatogram of
diesel fuel after the fluctuating temperature experiment (d).
222

Figure 3-4 cont’d

223

(Figure 3-4c).

The predicted chromatogram was compared to the experimental

chromatogram (Figure 3-4d) generated from the fluctuating temperature experiment
(Section 3.3.4.1).
A visual comparison of the predicted and experimental chromatograms (Figure
3-4c and Figure 3-4d) suggests a relatively high degree of similarity. In order to quantify
this similarity, Pearson product-moment correlation (PPMC) coefficients were used.
PPMC coefficients (r) measure how two variables (x and y) change with respect to one
another (covariance), compared to the degree to which each variable changes
independently (standard deviation) [11].








  xi  x yi  y 
r
2
2
 xi  x  yi  y

 

Equation 3-9



PPMC coefficients can range from -1 – +1, where -1 indicates a negative correlation, and
+1 indicates a positive correlation. Correlations can be classified as strong (0.8 ≤ |r| ≤ 1),
moderate, (0.5 < |r| < 0.8) or weak (0.5 ≤ |r| ≤ 0.8) [11]. For this case, the x and y variables
are the abundances in the predicted and experimental chromatograms at each retention
index. The PPMC coefficient was 0.991, indicating that the two chromatograms were
strongly correlated.

This demonstrates that this model can accurately predict the

distribution of individual compounds after evaporation.
3.3.4.3 Evaporation Rates of Other Complex Mixtures
To demonstrate the applicability of the model to other complex mixtures, the
variable-temperature model was applied to predict the fraction of fuel remaining and
distribution of compounds for diesel fuel, kerosene, and marine fuel stabilizer, each
224

evaporated at a constant temperature near 20 °C for 100 h, similar to that discussed in
Section 3.3.4.1. An example chromatogram of each liquid before and after evaporation
is shown in Figure 3-5 – Figure 3-7. Kerosene has a similar composition and distribution
of compounds compared to diesel fuel but contains more short-chain normal alkanes.
Kerosene is therefore more volatile than diesel fuel. Marine fuel stabilizer contains mostly
branched and cyclic alkanes, with very low abundances of normal alkanes or aromatic
compounds. Marine fuel stabilizer is more volatile than diesel fuel or kerosene. For
normalization, heneicosane was used for diesel, pentadecane was used for kerosene,
and tetradecane was used for marine fuel stabilizer.
Based on the weight of the diesel fuel before and after evaporation, the fraction
remaining was 0.82. The predicted fraction remaining, using the variable-temperature
model was 0.84, a 3.1% absolute error. This error is similar to that observed when
calculating the fraction remaining using the fluctuating temperature (5.4%). For kerosene,
the fraction remaining based on weight was 0.62. Using the variable-temperature model,
the predicted fraction remaining of kerosene was 0.70, a 12.7% difference. For marine
fuel stabilizer, the fraction remaining based on weight was 0.56. Using the variabletemperature model, the predicted fraction remaining was 0.55, a 2.0% difference. The
low errors demonstrate the success at applying these models to predict the fraction of
fuel remaining for a range of petroleum products.

225

b

Figure 3-5. A chromatogram of diesel fuel prior to evaporation (a) and after 100 h
evaporation at 20 °C (b). In part b, the solid black chromatogram represents the
experimentally evaporated fuel, while the red dashed line represents the predicted
distribution of compounds, using the variable temperature model. The numbers
correspond to peak numbers given in Table 3-1.

226

b

Figure 3-6. A chromatogram of kerosene prior to evaporation (a) and after 100 h
evaporation at 20 °C (b). In part b, the solid black chromatogram represents the
experimentally evaporated fuel, while the red dashed line represents the predicted
distribution of compounds, using the variable temperature model. The numbers
correspond to peak numbers given in Table 3-1.

227

b

Figure 3-7. A chromatogram of marine fuel stabilizer prior to evaporation (a) and after
100 h evaporation at 20 °C (b). In part b, the solid black chromatogram represents the
experimentally evaporated fuel, while the red dashed line represents the predicted
distribution of compounds, using the variable temperature model. The numbers
correspond to peak numbers given in Table 3-1.

228

The model was also used to predict the distribution of compounds for diesel,
kerosene, and marine fuel stabilizer as discussed in Section 3.3.4.2. After prediction of
the chromatogram, a visual comparison and quantitative comparison using PPMC
coefficients were applied between the predicted and experimental chromatograms. For
diesel fuel, the visual comparison of overlaid chromatograms (Figure 3-5) showed a good
agreement between the evaporated and predicted chromatogram. The PPMC coefficient
between these chromatograms was 0.9983, indicating strong correlation. For kerosene,
the visual comparison of the chromatograms (Figure 3-6) showed that the more volatile
compounds were at a higher abundance in the predicted chromatogram while the less
volatile compounds were at a higher abundance in the experimental chromatogram. The
PPMC coefficient between these chromatograms was 0.9874. In the comparison of the
chromatograms for marine fuel stabilizer (Figure 3-7), similar trends were observed to
those observed in kerosene.

The PPMC coefficient between the predicted and

experimentally determined chromatogram for evaporated marine fuel stabilizer was
0.9864. These results demonstrate that the model can be applied to other complex
mixtures.
While this PPMC coefficient for kerosene and marine fuel stabilizer still indicates
strong correlation, they were lower than observed in the predictions using diesel
chromatogram predictions. There are several possible reasons for this. First, the model
is based on retention index, which require normal alkanes in order to calculate. In
particular for marine fuel stabilizer, the normal alkanes were at low abundance or were
not present, requiring extrapolation of retention indices from other samples analyzed at
the same time. Another possible problem arises from the increased volatility of kerosene

229

and marine fuel stabilizer. In order to correct for variation in sample preparation and
analysis, normalization was applied. Ideally a nonvolatile compound would be used for
normalization. However, in both kerosene and marine fuel stabilizer, it is possible that
some of the compound used for normalization evaporated, which could have introduced
additional variation into the prediction.
3.3.4.4 Evaporation Time
The models developed in this work can also be used to estimate the evaporation
time from the chromatograms of an unevaporated and evaporated fuel sample. This
would be useful in environmental applications to estimate when a spill occurred. To do
so, a fraction remaining curve is created for each possible evaporation time.

The

abundance at each retention time in the chromatogram of the unevaporated fuel sample
is multiplied by the fraction remaining, to generate the predicted chromatogram (as
discussed in Section 3.3.4.2). The predicted chromatogram at each possible evaporation
time is compared to the actual evaporated chromatogram, using PPMC coefficients. The
time at which the PPMC coefficient reaches a maximum value is considered the best
estimate of the evaporation time.
This prediction was tested using the diesel fuel evaporated at 20 °C for 100
hours, discussed in Section 3.3.4.3. The diesel fuel was extracted from six different petri
dishes, three containing water and three without water, and each was analyzed by GCMS in triplicate, creating eighteen total trials. The variable-temperature model with the
average temperature was used to predict the evaporated chromatograms at times from 0
– 1000 h, at 1 hour intervals. An example of the distribution of PPMC coefficients is

230

shown

in

Figure 3-8. There is a relatively large region with a similarly high PPMC coefficient (r
>0.998), ranging from 89 – 151 h. While this region has similar PPMC coefficients, it
brackets the actual evaporation time of 100 h. Also, the time at which this replicate had
a maximum PPMC coefficient was 117 h (r = 0.9986), a 17% error from the actual
evaporation time. For all 18 replicates, the average predicted evaporation time was 105
h (range: 77 – 141), only a 5% error from the actual time, with an average PPMC
coefficient of 0.9990 (range: 0.9986 – 0.9992). The demonstrated the utility of this model
in predicting the length of time a sample has been evaporated, given the temperature and
the original distribution of compounds.
3.3.4.5 Time to Specific Fraction Remaining
These models have been shown to accurately predict the evaporation time
(Section 3.3.4.4) and could therefore be used to estimate the time required for the entire
fuel or an individual compound to reach a specific level, such as an LD50 or a limit of
detection. This information is critical for assessing safety at spill sites and predicting
persistence in the environment. Using the total fraction remaining (Equation 3-8) with the
variable-temperature model (Equation 3-7), numerical integration can be used to
determine the time to reach a specific concentration.

A plot of the fraction remaining

versus time at 20 °C is shown in Figure 3-9 on a logarithmic scale. The fraction remaining
decreases quickly for the first day and into the first week, then decreased more slowly. A
plot such as this is useful in assessing temporal changes in the fuel due to evaporation.

231

232

Figure 3-8. The Pearson product-moment correlation (PPMC) coefficients between a
chromatogram of diesel fuel evaporated on water for 100 h at 20 °C and the predicted
evaporation chromatogram, based on the variable-temperature model for 0 – 1000 h
tested at 1-h intervals. The PPMC coefficient maximized at 117 h (0.9986), with values
greater than 0.998 from 89 – 151 h.

233

Figure 3-9. The predicted fraction remaining, using the variable-temperature model
(Equation 10), over 10,000 h (approximately 1 year) at an average temperature of 20 °C.

234

A similar calculation can be performed for any compound in petroleum. For
example, benzene is commonly highlighted due to its high toxicity in the environment.
Benzene makes up approximately 1% of commercial gasoline by volume [12]. If 15
gallons of gasoline (approximately the size of a car’s gas tank) leaked into a stream, there
would be over 500,000 mg of benzene released into the environment. For rainbow trout,
the lethal concentration (LC50) is approximately 22 mg/gal for 96 h [13]. In a pool of
10,000 gallons, the concentration is 50 mg/gal. The time until the concentration reaches
below the LC50 (approximately 0.44 remaining) can be solve using Equation 3-7 for
benzene (IT = 650 [14]). The time to reach below the LC50 is approximately 0.7 h and the
time to reach 0.01 (or 1% remaining) is approximately 4 h. While this is a simple example,
it serves to demonstrate the utility of the model in predicting removal of a compound from
the environment due to evaporation.
3.3.4.6 Comparison to Other Evaporation Models
The accuracy of the model developed in this work has been amply demonstrated
in the previous sections. To further validate this model, fraction remaining predicted using
this model was compared to an existing evaporation model.

An empirical model

developed by Fingas for southern diesel fuel evaporated for less than five days was used
for the comparison [15]. The model for the percent evaporated (%Evap) is based on time
(t, min) and temperature (T, °C).

%Evap   0.02  0.013 T  t

Equation 3-10

While this is the simplest evaporation model, Jones demonstrated that this model
provides similar results to other commonly used evaporation models [16], including those

235

by MacKay (known as the analytical model) [17, 18] and Jones (known as the pseudocomponent model) [3, 16].
The experimentally determined percent remaining by weight for diesel fuel
allowed to evaporate at 20 °C for 100 h and was 82% (Section 3.3.4.3). Using the total
fraction remaining and variable-temperature model the predicted percent remaining was
84%.

Using the empirically developed model by Fingas (Equation 3-10) [15], the

predicted percent remaining was 81%. The prediction using the model by Fingas is
remarkably similar to the model developed in this work. Moreover, the model from this
work also incorporated predicting the evaporation of individual compounds.

This

demonstrates that the model in this work can predict the evaporation comparably to other
models, but also provides additional tools, such as the prediction of individual
compounds, not available in existing models.
3.4 Discussion and Conclusions
In this work, the model for predicting the rate constant based on retention index
offers potential multiple applications in environmental modeling. The evaporation rate
constant can be predicted based on retention index and temperature. The predicted rate
constant can then be used to predict the fraction remaining of a fuel at a given time, with
similar accuracy to existing models. Many existing models rely on estimations of physical
properties, which are determined from the pure compound. As demonstrated using the
enthalpy of vaporization, the physical property of a pure compound can vary greatly in a
complex mixture. The development of a semi-empirical evaporation model is necessary
in order to account of these differences.

236

The model has also been shown to be applicable to a range of petroleum fuels.
Moreover, because the model was developed using individual compounds, further
information accessible over existing models, which can only predict the evaporation of
the entire fuel. Additionally, the use of many existing models, require knowledge of
physical properties, such as the boiling point or vapor pressure. When these properties
are not known, they must be estimated using information about the fuel, such as the
distillation curve, which is not readily available for most refined petroleum products. In
this model, only the retention index for the compounds of interest required. A simple GCMS experiment can be used to determine the retention index of all compounds in a fuel
sample. Alternatively, the retention index for many compounds is available in reference
libraries, such as the NIST Webbook [14], negating the need the GC-MS experiment.
In addition to predicting the fraction remaining, the model develop in this work
provides a method for determining the distribution of compounds at a given time (Section
3.3.4.2), the length of time over which the evaporation has occurred (Section 3.3.4.4),
and the time to reach safe exposure levels (Section 3.3.4.5). Determination of the
distribution of compound helps to assess what losses would be expected due to
evaporation. The expected losses could be compared to losses experienced during
remediation, to evaluate effectiveness. For example, if the application of a remediation
method results in a greater reduction of compounds than expected from the model, it
could be judged to be effective. This model also allows for a determination of exposure
time, which would be necessary for determination of the source or blame for the spill.
Last, the prediction of evaporation rates of potentially toxic and volatile compounds, such

237

as benzene, can be readily estimated, which is important for assessing hazards for
cleanup workers [3].
For the implementation of this model, there are several other important
considerations. First, this model only calculated the fraction remaining, therefore in order
to obtain an absolute weight or concentration, the initial amount is required. The initial
amount could be quantified using an analytical technique such as GC or may be known
from the source. Second, determination of an appropriate compound for normalization is
challenging in refined petroleum products that contain mostly volatile components. Lastly,
this model has only been applied to petroleum distillates. Crude oil contains many
compounds that are not volatile enough to be analyzed by GC-MS, including polar
compounds such as resins and asphaltenes, which can account for up to 50% of the
composition of crude oil [19, 20]. Therefore, a correction factor may be necessary to
determine a total fraction remaining of crude oil.
In conclusion, the model presented in this work is capable of predicting a firstorder kinetic constant for the evaporation of an individual compound, based on the
retention index of that compound and the temperature. The rate constant can then be
utilized to predict the fraction remaining of individual compounds and the fraction
remaining of the entire fuel. Existing models cannot predict the fraction remaining of
individual compounds and require the estimation of a physical properties of the fuel,
making this model more versatile than existing models. The model developed in this work
was shown to have a wide range of applications include to predict the distribution of
compounds after evaporation, to predict the length of time since the evaporation began,

238

and predict the time to reach a specific fraction remaining. The model was also shown to
be applicable to the evaporation of other complex mixtures.

239

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240

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[12] E.P. Agency, Summary and Analysis of the 2011 Gasoline Benzene PreCompliance Reports. <http://www.epa.gov/otaq/regs/toxics/420r12007.pdf>. 08/16/2014.

241

[13]

Sigma-Aldrich, Benzene Material Safety Data Sheet, 2014

[14] S.E. Stein, in: P.J. Linstrom, W.G. Mallard (Eds.), NIST Chemistry Webbook, NIST
Standard Reference Database Number 69, National Institute of Standards and
Technology, Mass Spec Data Center, Gaithersburg, MD, 2011. http//webbook.nist.gov,
(retrieved February 26, 2014).
[15] M. Fingas, in: M. Fingas (Ed.), Oil Spill Science and Technology (Chapt. 9),
Elsevier, Burlington, MA, 2011.
[16] R.K. Jones, Proceedings; Environmental Canada Twentieth Arctic and Marine
Oilspill Program Technical Seminar, 1 (1997) 43.
[17]

W. Stiver, D. Mackay, Environ. Sci. Technol., 18 (1984) 834.

[18]

W. Stiver, W.Y. Shiu, D. Mackay, Environ. Sci. Technol., 23 (1989) 101.

[19] Z. Wang, M. Fingas, C. Yang, J. Christensen, in: R.D. Morrison, B.L. Murphy
(Eds.), Environ. Forensics, Elsevier, Burlington, MA, 2006.
[20] M. Fingas, in: M. Fingas (Ed.), Oil Spill Science and Technology (Chapt. 5),
Elsevier, Burlington, MA, 2011.

242

4. Determination of Kinetic Rate Constants during Solar-Simulated
Irradiation

of

Diesel

Fuel

by

Gas

Chromatography-Mass

Spectrometry and High Resolution Mass Spectrometry
4.1 Introduction
Until recently, photooxidation of petroleum after an environmental release was
considered an insignificant weathering process as it did not account for a substantial
source of mass loss during weathering [1]. Photooxidation is not included in many
comprehensive petroleum weathering models [1-3].

However, photooxidation of a

compound increases its water solubility and toxicity, leading to increased rates of
transport as well as environmental and health risks [4]. Photooxidation of oil can also
change the physical properties of the oil, forming high-molecular weight tars and gum
residues [1].

Therefore, understanding photooxidation is an important aspect of

comprehensive environmental modeling of a petroleum spill.
In this work, the effect of photooxidation on diesel fuel was investigated. The goal
of this work was to identify and quantify the degradation and formation of compounds. In
order to accomplish this goal, both GC-MS and high resolution time-of-flight mass
spectrometry (ToF-MS) were utilized and results were compared. Atmospheric pressure
chemical ionization (APCI) was selected as it allows for improved detection of higher
mass PAHs and oxygenated compounds that are either not sufficiently volatile or are
obscured by more abundant substances when GC-MS analyses are performed [5]. After
promising compounds were annotated, kinetic rate constants were determined in order
to quantify the rate of decay and formation of the selected compounds. While previous

243

reports have described kinetic rate constants for the decay of compounds, little work has
been done to determine rate constants for the compounds formed by photooxidation of
petroleum products. Knowing the rates of formation and decay for compounds could be
used to link precursors to oxygenated products.
4.2 Materials and Methods
4.2.1 Collection of Diesel Fuel
Refined petroleum products, such as diesel fuel have not been widely studied for
photooxidation. Refined products are simpler than crude oil and have fewer compounds
that contain heteroatoms, which will affect the photooxidation. Diesel fuel was chosen as
an illustrative refined product because of its wide range of compounds compared to other
refined products. Diesel fuel was collected from a local service station in East Lansing,
MI in July 2010 and stored at 3 ˚C in acid washed amber bottles until used.
4.2.2 Irradiation of Diesel Fuel
In order to irradiate the samples, a solar simulator with a commercially available
xenon arc lamp was modified (Figure 4-1). The light source was a 300 W xenon arc lamp
housing (Model SP66902-4000, Newport Corporation, Stratford, CT), with two 2-inch
diameter plano-convex condenser lenses (f/# = 2), an ozone-free xenon lamp (model
6258, Newport Corporation) and power supply (model 69911, Newport Corporation). A
2-inch plano-convex lens (f/# = 2) in a lens holder was placed on the condenser assembly
of the lamp housing to focus the light. A 2-inch beam turner (model 66246, Newport
Corporation) was used to redirect the light at a 90° angle, towards the sample. A second
2-inch plano-convex lens (f/# = 2) in a lens holder was placed approximately 28 cm from

244

the source, using a filter holder as a spacer. The sample was a total distance of 49.3 cm
away from the source. The sample was placed in a petri dish, which fit into a watercooled, aluminum block, located inside a clear Plexiglas box. A recirculating water bath
was used to maintain a constant 21 °C in the petri dish. A metal plate covered the top of
the box to prevent extraneous light from reaching the sample. A hole (diameter = 2 in) in
the box and metal was positioned directly above the sample. Two bandpass filters (model
FSQ-KG2, Newport Corporation) covered the hole and helped to remove unwanted
regions of the spectrum (discussed below). High-purity air was flowed into the box (~270
mL min-1) allowing for a continuous supply of oxygen.
In the selection and testing of the solar simulator, there were several important
considerations including the temporal stability of the light source, the spatial uniformity of
the beam, the similarity of the spectrum of the source relative to that of the sun, and the
irradiance of the source. The temporal variation was reported by the manufacturer as <
5%. This was verified by taking periodic measurements using a thermopile (model 407A,
Newport Corporation) and finding no measurable difference in the irradiance of the
source. The intensities were measured 49.3 cm from the source. A 5.5 cm grid was used
to evenly collect intensity measurements across the irradiated area, allowing the
measurement of uniformity over the area of the petri dishes which contained the samples
during irradiation (Figure 4-2). The intensity was measured at nine equally spaced points
and the uniformity (U) was calculated using the maximum (Imax) and minimum (Imin)
intensities.

245

Figure 4-1. A diagram depicted the solar simulator used for irradiation. A commercially
available xenon light source was utilized along with several plano-convex lens to
homogenize the beam. A beam turner redirected the beam from the source to the sample.
The sample was placed on an aluminum block, connected to a circulating water bath to
maintain constant temperature. The sample and block were housed inside a Plexiglas
box with a hole in the top to allow light to pass. Two filters (KG2) were placed over the
hole to reduce the infrared light reaching the sample. A ray tracing is shown as the red
dashed line.

246




U   I max I min  100
 I max  I min 

Equation 4-1

The spectral uniformity was monitored and was 5.0% (± 0.8) over the course of the
experiment.
The desired spectrum of the light source should closely match that of the sun at
the Earth’s surface, which will allow for simulation of solar photooxidation in the
environment. Light from the sun contains x-ray through infrared radiation, however, much
of that light is absorbed before reaching the Earth’s surface [6].

X-ray and UVC

wavelengths (from 100 – 280 nm) are absorbed by ozone, while much of the infrared light
is absorbed by water, oxygen, and carbon dioxide [6].
A typical spectrum of sunlight, based on ASTM G-173-03 (National Renewable
Energy Laboratory, SMARTS v. 2.9.2 [7]), is shown in Figure 4-3a (dotted black line). A
spectrum of the xenon light source (Figure 4-3a, dashed blue line) was obtained using a
spectrophotometer (Fluorolog 3, Jobin Yvon Horiba, Kyoto, Japan). The xenon arc lamp
provided a continuum source, and its emission extends to wavelengths shorter than 280
nm and has several large peaks in the infrared region. Light with wavelengths shorter
than 280 nm will deposit more energy per photon (115 kcal/mol at 250 nm versus 95
kcal/mol at 300 nm) than is experienced at the Earth’s surface, which could lead to
environmentally atypical photoreactions and has been a weakness in previous studies
[8]. Energy in the infrared region (32 kcal/mol at 900 nm) is too low to induce electronic
excitation in petroleum constituents, but can heat the water and sample, and such heating

247

1.63 cm
1.63 cm

5.5 cm
Figure 4-2. A diagram showing how uniformity was measured. The irradiated sample
was contained in a petri dish (dashed line, diameter ~5.5 cm). Intensity measurements
were taken at the points where the grid lines intersect.

248

could increase evaporation. In the environment, this heat would be easily dissipated into
the surrounding, but in the experimental setup this heating could make maintaining
constant temperature challenging. Two bandpass KG2 filters were used to remove the
light of wavelengths shorter than 280 nm and 95% of the light with wavelengths longer
than 800 nm, including the large peaks in the infrared region. The spectrum of the xenon
source with the KG2 filters in place is also shown in Figure 4-3a (solid red line) and is in
agreement with the sun spectrum. Between 280 – 330 nm, which is the region most likely
to cause photochemical reactions, the spectrum of light delivered to the sample by the
solar simulator closely agrees with the spectrum of the sun. The normalized abundance
from the solar simulator is higher from 330 – 450 nm, while the abundance in sun’s
spectrum is higher at wavelengths greater than 550 nm. In order to provide direct
comparisons between the xenon source and the sun, a portable spectrometer was used
(USB4000, Ocean Optics, Dunedin, Florida). The resulting spectra are shown in Figure
4-3b. The solar simulator and sun are again in good agreement, except for the increased
abundance between 350 – 450 nm for the solar simulator. This spectrometer had a short
wavelength cutoff at 350 nm so shorter wavelengths could not be evaluated.
Last, the spectral irradiance of the source was measure and compared to that of
the sun. Using a thermopile, the irradiance of the source was 0.69 W (304 mW/cm2)
without the KG2 filters and 0.1 W (44 mW/cm2) with the KG2 filters in place. This
demonstrates the large contribution from the infrared region being removed by the filters.
The irradiance of the sun was measured as 0.2 W (88 mW/cm2) using the same

249

a

b

Figure 4-3. A spectrum of the sun [7] (black dotted line) compared to the spectrum of a
xenon light source (dashed blue line) and the xenon light source with 2 KG2 filters (solid
red line) (a). The same spectra are shown in b, but all were collected using the same
spectrometer. The spectra were normalized to the average intensity between 500 – 550
nm. The spectral irradiance of the sun and the xenon source with the 2 KG2 filters is
shown in part c.

250

Figure 4-3 cont’d

c

251

thermopile (measured July 12, 2014 at 1500 hrs in East Lansing, MI, USA). This is
consistent with literature values of approximately 97 mW/cm2 for irradiation at the Earth’s
surface [7]. With the two KG2 filters in place, the irradiance of the sun was 0.5 W (22
mW/cm2). The spectral irradiance was calculated using the spectra and thermopile
measurements. The fraction of the total signal in the spectra was determined at each
wavelength, for the sun and the xenon source with the KG2 filters in place. The total
irradiance, measured using the thermopile, was multiplied by the fraction at each
wavelength to calculate the spectral irradiance (Figure 4-3c). The irradiance of the sun
and solar simulator were approximately equal from 280 – 330 nm. The solar simulator
had an approximately 1.5 times higher irradiance from approximately 330 – 400 nm.
Above 400 nm the irradiance of the sun was higher. However, this region of the spectrum
is expected to induce fewer photochemical reactions. This demonstrates that the solar
simulator is approximately equivalent to the irradiance of the sun over the region that is
likely to cause photochemical reactions.
A thin film of diesel fuel (1.0 mL, ~0.5 mm) on distilled water (10 mL) was irradiated
in glass petri dishes (60 mm ID x 15 mm). The irradiance of the source was measured
as 0.1 W (corresponding to ~44 mW/cm2), measured using a thermopile. A circulating
water bath maintained nearly constant temperature (~21 °C). Samples were irradiated
in triplicate for at 7 different lengths of time (0 – 10 h).
4.2.3 Sample Extraction
After irradiation, the diesel residues were extracted from the petri dish. Prior to
extraction, 1 mL of cyclohexane containing 8.4 *10-3 M quinoline-d7 was added as a
reference standard and as a lock mass for mass spectrometric analysis. Cyclohexane
252

was selected as the solvent was it was more amenable to the MS analysis than
dichloromethane used previously.

The diesel/water/cyclohexane mixture was

quantitatively transferred to a separatory funnel.

The petri dish was rinsed with

approximately 1 mL of cyclohexane, which was then quantitatively transferred to the
separatory funnel. The water layer and interface were removed, then the cyclohexane
layer was transferred to a 10.0 mL volumetric flask, which was filled to the line with
cyclohexane. The extract was further diluted (1:50) and transferred to an autosampler
vial for GC-MS and MS analysis.
4.2.4 Selection of an Internal Standard
Selection of an appropriate internal standard for this work was challenging. Ideally,
the internal standard should be added to the fuel prior to irradiation, meaning that the
internal standard must be resistant to photooxidation. Saturated hydrocarbons, such as
normal alkanes, are resistant to photooxidation, however, they are not efficiently ionized
by APCI. For analysis by APCI, an unsaturated hydrocarbon or a compound containing
a heteroatom is necessary. These compounds likely undergo photooxidation, so they
must be added after the irradiation experiment. In order to differentiate the internal
standard from a native compound, a deuterated analogue is desirable. Many deuterated
PAHs, such as phenanthrene-d10, were found to have masses that correspond to
compounds already in the fuel.

Naphthalene-d8 did not have a compound with a

corresponding mass, but naphthalene was not efficiently ionized, and was not observed
using APCI.
Deuterated quinoline was selected as an internal standard because it ionized
effectively by APCI and has a mass that does not correspond to a compound already in
253

diesel. However, quinoline can adsorb onto tubing and surfaces in the MS instrument.
Initial studies indicated that analyzing pyridine before each analysis could minimize these
effects. However, during the analysis of the irradiated samples, the signal from quinlined7 was highly variable, even within replicate analyses, indicating that quinline-d7 was not
appropriate internal standard. In this work, quinline-d7 was used as a lock mass for the
ToF-MS.
For normalization, m/z 199.1487 was used, because it remained relatively constant
over the 10 hour irradiation. The mass was assigned an elemental formula of C15H19
(M+H+) and had 7 double bond equivalences (DBE). This compound is consistent with
naphthalene with five methylene groups. Prior to normalization, many compounds with 7
DBE were unchanged after irradiation for 10 hours. The GC-MS experiment also showed
no change for the alkyl naphthalene, which indicates that it may be more resistant to
photooxidation than other PAHs.
4.2.5 Gas Chromatography-Mass Spectrometry
The gas chromatography-mass spectrometry analysis was performed using a gas
chromatograph (model 7890N, Agilent Technologies, Santa Clara, CA) with an automatic
liquid sampler (model 7693, Agilent Technologies) coupled to a mass spectrometer
(model 5975, Agilent Technologies). Ultra-high-purity helium was flowed (1 mL/min)
through a capillary column containing a 100% poly(dimethylsiloxane) stationary phase
(HP-1MS, 30 m x 0.25 mm x 0.25 μm, Agilent Technologies). The diesel extract was
injected (1 µL) using a pulsed (15 psi for 0.25 min) split (50:1) injection at 280 °C. The
initial GC oven temperature was 50 °C and was ramped at 5 °C/min-1 to 280 °C where
the temperature was held for 4 min. The transfer line temperature was 300 °C. The
254

quadrupole mass analyzer employed electron ionization (70 eV) and scanned mass-tocharge ratios (m/z) from 40 – 550 at a rate of 2.91 scans/s.
4.2.6 Time of Flight-Mass Spectrometry
Mass spectrometry experiments were conducted using a LCT Premier (Waters
Corporation, Milford, MA) time-of-flight mass spectrometer (TOF-MS). The diluted diesel
samples (10 µL) were introduced using flow injection analysis with hexanes pumped at
0.5 mL/min for 2 min. The sample was ionized using atmospheric pressure chemical
ionization (APCI) in positive ion mode with the corona current at 20 µA. The capillary
voltage was 1000 V and the sample cone voltage was 10 V. The probe and source
temperatures were 500 °C and 100 °C, respectively. The cone gas flow was 40 mL/min
and the desolvation gas flow was 350 mL/min. The mass analyzer was operated in “Wmode”, which yields mass resolution of about 9000 (m/m, full width, half maximum) and
scanned m/z 90 – m/z 1000, with data acquisition in centroid mode using extended
dynamic range acquisition.
4.3 Results
4.3.1 Visual Observations and Mass Change of Diesel Residue
Irradiation resulted in visible changes in the diesel fuel. Prior to irradiation, the
diesel a light yellow and was not turbid. After 1 h of irradiation, the fuel became darker
yellow. After 3 h, a precipitate was observed at the water/fuel interface, and the turbidity
increased through 10 h. For one analysis, the weight was recorded to determine the
change in mass of the fuel and mass of precipitate formed during irradiation (Section
4.3.7). Prior to irradiation, 1 mL of diesel fuel (0.906 g) was placed into a petri dish

255

(without water). The fuel was irradiated for 10 h and weighed (0.8222 g; 90.7% of the
original mass). To determine the mass of precipitate formed, the liquid diesel was
extracted using pentane, then the precipitate was dried under nitrogen, and the residual
was weighed (0.0371 g). For the fuel sample, nearly 5% (by mass) had formed a
precipitate after 10 h of irradiation.

The precipitate was insoluble in hexane,

dichloromethane, and water, but was soluble in methanol, acetone, and acetonitrile,
suggesting that the precipitate had an increased polarity, which would be consistent with
increased oxygen content. This demonstrated that photooxidation is a more substantial
source of mass loss from the liquid than previously thought and results in considerable
chemical change in the fuel. The formation of a precipitate after photooxidation has not
been widely reported in the literature, except for a few laboratory experiments. Larson et
al. [9] reported the formation of a precipitate in diesel fuel after less than 12 h of irradiation
and King et al. [10] reported the formation of a solid layer in crude oil within 6 h irradiation.
The precipitate is likely not observed in the environment due to the physical mixing that
occurs from wave action and wind.
4.3.2 Gas Chromatography-Mass Spectrometry of Diesel Residue
Example total ion chromatograms (TIC) of diesel fuel irradiated from 0 – 10 h (Figure
4-4a) show a progressive decrease in the most volatile compounds, similar to that
observed for evaporation. The same decrease is observed for the dark control (Figure
4-4a), indicating that there was no detectible change due to photooxidation, based on the
TIC. The chromatograms were normalized to the peak height of nonadecane from m/z
57 to correct for variation in extraction and analysis. Nonadecane has a low volatility and
normal alkanes have been shown to be resistant to photooxidation, so this peak was

256

expected to be unchanged during the experiment. The aliphatic compounds, which
dominate the GC-MS TIC, are resistant to photooxidation and previous studies have
shown that the changes in the fuel due to photooxidation are not observed in the GC-MS
chromatogram [11-13]. However, the decrease of some GC-amiable PAHs, such as
fluorene and phenanthrene, were hypothesized to change during irradiation. Extracted
ion chromatograms (EICs) were employed to look for specific classes of compounds
which may be present at a low abundance and not observed in the TIC. The EIC of m/z
216 (Figure 4-4b) shows a decrease in abundance of two peaks (corresponding to
isomers of methylpyrene) over the 10 h irradiation. A corresponding decrease was not
observed in the dark control, indicated that the loss was due to photooxidation. A
complete list of compound monitored by GC-MS is shown in Table 4-1. The oxidized
products were not expected to be observed by GC-MS, because they would be present
in low abundance and the addition of an oxygen would decrease volatility.
The most volatile normal alkanes in diesel (C8 – C10) completely evaporated which
was consistent with the dark control. The fraction remaining after 10 hours of irradiation
was not significantly different from the dark control for the larger normal alkanes (C12 –
C20). However, a statistically significant (α = 0.05) decrease in abundance was observed
for most other selected compounds, compared with the dark control, indicating
accelerated evaporation or photooxidation. It is hard to differentiate which process is
occurring. For the more volatile compounds, accelerated evaporation due to irradiation
the likely process. For substituted PAHs and less volatile compounds, the losses are
likely due to photooxidation. These changes were quantified in Section 4.3.6.

257

Figure 4-4. Total ion chromatograms (a) and extracted ion chromatograms (b) of m/z 216
of diesel fuel irradiated for 0 – 10 h as well as a 10 h dark control. In the total ion
chromatogram the even numbered normal alkanes are labeled for reference. The peaks
at 34.39 min and 34.77 min correspond to methyl pyrenes.

258

Table 4-1. A list of compounds monitored by the GC-MS experiment. For each
compound the mass-to-charge (m/z) ratio for the extracted ion chromatogram, the
retention time (tR), retention index (IT), the observed rate constant (kobs), and a predicted
rate constant (kpre) for evaporation available from Chapter 3.
Compound

m/z
of
EIC

tR
(min)

IT

kobs
(h-1)

Uncertainty

kpre
(h-1) a

Toluene

91

3.137

768

1.211

0.067

0.379

Octane

57

3.686

800

0.572

0.020

0.274

Ethyl benzene

91

4.443

844

0.419

0.014

0.175

m/p-Xylene

91

4.593

853

0.340

0.011

0.160

o-Xylene

91

4.997

876

0.274

0.009

0.126

Nonane

57

5.413

900

0.170

0.006

0.098

Propyl
benzene

91

6.285

938

0.138

0.006

0.067

Ethyl methyl
benzene
isomer

105

6.458

945

0.118

0.005

0.062

1,3,5-Trimethyl
benzene

105

6.637

953

0.091

0.005

0.057

Ethyl Methyl
benzene
isomer

105

6.857

963

0.099

0.005

0.052

1,2,4-Trimethyl
benzene

105

7.209

978

0.078

0.004

0.044

Methyl propyl
benzene
isomer

105

7.648

997

0.069

0.004

0.037

Decane

57

7.723

1000

0.045

0.003

0.035

1,2,3-Trimethyl
benzene

105

7.862

1005

0.058

0.004

0.034

259

Table 4-1 cont'd

Compound

m/z
of
EIC

tR
(min)

IT

kobs
(h-1)

Uncertainty

kpre
(h-1) a

Indane

117

8.121

1015

0.070

0.005

0.030

105

8.682

1036

0.037

0.004

0.024

105

8.763

1039

0.035

0.004

0.024

105

9.051

1050

0.032

0.003

0.021

Alkyl indane
isomer

117

9.473

1066

0.049

0.004

0.018

Diethyl
benzene
isomer

105

10.027

1087

0.019

0.004

0.015

Undecane

57

10.362

1100

0.007

0.003

0.013

Methyl decalin
isomer

117

10.876

1119

0.028

0.004

0.011

Alkyl indane
isomer

117

11.130

1128

0.023

0.003

0.010

1,2,3,4Tetrahydronaphthalene

91

11.373

1137

0.011

0.003

0.009

Naphthalene

128

11.852

1155

0.007

0.004

0.007

Methyl tetralin
isomer

91

12.875

1192

0.010

0.004

0.005

Dodecane

57

13.094

1200

n/cb

n/c

0.000

Alkyl indane
isomer

117

13.406

1212

0.012

0.004

0.000

Methyl propyl
benzene
isomer
Methyl propyl
benzene
isomer
Methyl propyl
benzene
isomer

260

Table 4-1 cont'd

Compound

m/z
of
EIC

tR
(min)

IT

kobs
(h-1)

Uncertainty

kpre
(h-1) a

Alkyl indane
isomer

145

13.625

1220

0.020

0.003

0.000

Alkyl tetralin
isomer

117

14.197

1241

0.015

0.003

0.000

Alkyl decalin
isomer

165

14.469

1251

n/c

n/c

0.000

Alkyl tetralin
isomer

117

15.641

1295

0.006

0.003

0.000

Tridecane

57

15.768

1300

n/c

n/c

0.000

Alkyl tetralin
isomer

145

15.826

1302

0.022

0.004

0.000

Alkyl biphenyl
isomer

179

16.553

1331

n/c

n/c

0.000

Alkyl tetralin
isomer

132

16.623

1333

0.014

0.004

0.000

Alkyl tetralin
isomer

145

17.483

1367

0.018

0.003

0.000

Alkyl tetralin
isomer

145

17.541

1369

0.026

0.004

0.000

Dimethyl
naphthalene
isomer

128

18.015

1387

n/c

n/c

0.000

Tetradecane

57

18.338

1400

n/c

n/c

0.000

Alkyl tetralin
isomer

132

18.754

1417

0.013

0.003

0.000

Alkyl tetralin
isomer

132

18.823

1420

0.014

0.003

0.000

Alkyl tetralin
isomer

132

18.916

1424

0.016

0.003

0.000

261

Table 4-1 cont'd

Compound

m/z
of
EIC

tR
(min)

IT

kobs
(h-1)

Uncertainty

kpre
(h-1) a

Alkyl biphenyl
isomer

165

19.58

1451

n/c

n/c

0.000

Pentadecane

57

20.781

1500

n/c

n/c

0.000

Fluorene

165

21.751

1542

0.011

0.003

0.000

Alkyl biphenyl
isomer

165

22.000

1552

0.020

0.003

0.000

Hexadecane

57

23.108

1600

n/c

n/c

0.000

Methyl fluorene
isomer

165

24.367

1657

0.014

0.003

0.000

Methyl fluorene
isomer

165

24.494

1663

0.035

0.004

0.000

Alkyl biphenyl
isomer

179

24.783

1676

0.059

0.003

0.000

Heptadecane

57

25.315

1700

n/c

n/c

0.000

Phenanthrene

178

25.904

1728

n/c

n/c

0.000

179

26.857

1773

0.033

0.003

0.000

179

26.972

1779

0.034

0.003

0.000

179

27.099

1785

0.045

0.003

0.000

Octadecane

57

27.417

1800

n/c

n/c

0.000

Alkyl hopanes
isomer

192

28.306

1844

0.006

0.002

0.000

Dimethyl
fluorene
isomer
Dimethyl
fluorene
isomer
Dimethyl
fluorene
isomer

262

Table 4-1 cont'd

Compound

m/z
of
EIC

tR
(min)

IT

kobs
(h-1)

Uncertainty

kpre
(h-1) a

Alkyl hopanes
isomer

192

28.393

1849

0.004

0.002

0.000

Alkyl hopanes
isomer

192

28.739

1866

0.009

0.003

0.000

Alkyl hopanes
isomer

192

28.837

1871

0.006

0.002

0.000

Nonadecane

57

29.421

1900

n/c

n/c

0.000

Eicosane

57

31.332

2000

n/c

n/c

0.000

Pyrene

202

32.181

2047

0.174

0.005

0.000

Heneicosane

57

33.157

2100

n/c

n/c

0.000

Alkyl pyrene
isomer

216

34.388

2170

0.218

0.014

0.000

Alkyl pyrene
isomer

216

34.774

2192

0.243

0.010

0.000

a. Model obtained in Chapter 3
b. n/c = kobs< 0.002 h-1, which was not significantly different from 0.0 (α = 0.05)

263

1.40x105

Abundance

a

0.00 *0.00
100

0

1
Retention Time (min)

34000
100

2

211.15

b

Relative Abundance

197.13 225.16

185.13

237.17
239.18
251.16

171.12
*

265.20
295.25
338.35

0
100

200

300
m/z

400

500

Figure 4-5. The output from mass spectrometry analysis of diesel fuel. An example TIC
chromatogram (a) is representative of all chromatograms indicating the region over which
the spectra were averaged (red line). The mass spectrum prior to irradiation (b) and after
irradiation for 10 h (c) and the 10 hour dark control (d) are also shown. Quinoline-d7 (*)
was used at the lock mass. The formulas for each mass is in Table 4-2 and Table 4-3.

264

Figure 4-5 cont’d

Relative Abundance

100
23000

175.11 189.13
199.15

c

213.16
215.14
223.11
229.16

159.12

237.13

145.10

255.21

*

311.27

0
100

200

28000
100

185.13

500

d

225.16

237.17
239.18
251.16

171.12

265.20
295.25

*

0
100

400

211.15
197.13

Relative Abundance

300
m/z

338.35

200

300
m/z

265

400

500

4.3.3 Determination of Elemental Formulas by High Resolution Mass Spectrometry
The high resolution mass spectrometry (HR-MS) analyses used flow injection
analysis, resulting in a total ion chromatogram with a single peak (Figure 4-5a). To obtain
the mass spectrum, 12 spectra from 0.09 to 0.20 min were averaged (MassLynx, Waters
Corporation). A lock mass of m/z 137.1091 Da corresponding to quinoline-d7, was used
to correct for mass drift. Only masses between m/z 100 – m/z 500 were evaluated as
spectra did not have meaningful ions greater than m/z 500. The threshold was set at 2%
of the base peak.
The MS analysis of the fuel sample yielded hundreds of masses (Figure 4-5b and
c). Elemental formulas were assigned using MassLynx, with element ranges of C (1 –
500), H (1 – 1000), N (0 – 4), O (0 – 4), and S (0 – 4). Even using a mass error of less
than 3 mDa, the Elemental Composition algorithm of MassLynx frequently reported
multiple possible formulas. Because diesel fuel is a refined petroleum product, many of
the compounds containing heteroatoms typically found in crude oil would not be present
in the fuel before irradiation. Moreover, diesel fuel goes through additional refining to
create ultra-low sulfur diesel (<15 ppm sulfur) [14]. Therefore, it is unlikely that these
heteroatoms are present at high abundance, except for oxygen after photooxidation.
Elemental formulas were then assigned using C (1 – 500), H (1 – 1000), and O (0 – 4)
with a mass error of 10 mDa.

This allowed the assignment of one or two elemental

compositions to most compounds. The typical mass error was 3 – 7 mDa, but was as
high 20 mDa in some cases.
A list of masses and elemental compositions were exported to Excel (2013,
Microsoft Corporation, Redmond, WA). In cases where two elemental formulas were
266

possible, each were evaluated based on the mass error and whether that formula was
present in other replicates. Masses for which an elemental formula did not match within
the 10 mDa error window were omitted. This allowed for the assignment of a single
elemental formula for each mass. This resulted in over 850 elemental formulas, ranging
from 8 – 49 carbons, 7 – 59 hydrogens, 0 – 4 and oxygens, with 0 – 30 double bond
equivalences (rings or double bonds).
In the mass spectrum of diesel prior to irradiation (Figure 4-5b), Over 99% of the
elemental formulas suggest the compounds contain only carbons and hydrogens.
Clusters of peaks separated by approximately 2 Da are observed.

These regions

correspond to compounds that have the same number of carbons, but differ by 2
hydrogen atoms, or 1 double bond equivalent (DBE).

Each of these clusters are

separated by approximately 14 Da, corresponding to differences of a CH2 group as
expected from alkyl homologs. This repeating pattern is common in the MS of petroleum
products [15, 16]. A similar pattern, but with different masses, was observed in the
spectrum of diesel fuel after 10 h of irradiation (Figure 4-5c).

After irradiation, the

dominant masses that were observed still have varying DBE and CH2 groups, but now
contain at least one oxygen atom. These new masses were not observed in the dark
control (Figure 4-5d), indicating that they were formed by photooxidation. Quantification
of the changes in abundance for specific masses will be discussed in Section 4.3.6.
4.3.4 Kendrick Mass Defect
In the analysis of petroleum products, the Kendrick mass defect (KMD) is
commonly applied to simplify the interpretation of high resolution MS data [17]. The KMD
is calculated from the Kendrick mass (mK), which rescales the exact monoisotopic mass
267

(mE) so that the mass of CH2 is set to equal exactly 14, rather than the IUPAC mass scale,
based upon the atomic mass of 12C equaling exactly 12 [18] (Equation 4-2).
mK  mE *

14.00000
14.01565

Equation 4-2

The KMD is calculated as difference between the Kendrick mass and the nominal mass
(mN), as shown in Equation 4-3.

KMD  mK  mN

Equation 4-3

Using the Kendrick mass defect, compounds with the same double bond equivalency
(DBE) and heteroatoms will have the same mass defect [18]. When the nominal mass is
plotted against the Kendrick mass defect, compounds with the same DBE and
heteroatom, but different numbers of methyl groups will appear as horizontal lines
allowing for the rapid determination of structurally related compounds [18].
Using the elemental formulas determined in Section 4.3.3, Kendrick mass defects
were calculated using Equation 4-2 and Equation 4-3. The Kendrick mass was plotted
against the Kendrick mass defect to identify structurally related compounds (Figure 4-6a).
On this plot, compounds with the same Kendrick mass defect, (i.e. differing by a
methylene group) form a straight horizontal line, 14 Da apart. In Figure 4-6a, only
hydrocarbons are present, so the Kendrick mass defect corresponds to differences in
DBE. Compounds with the same number of carbons, form diagonal lines, with points that
differ by 2 Da, indicating differences in the number of hydrogen atoms.

268

Figure 4-6. The Kendrick mass defect versus the nominal mass for an unirradiated diesel
sample (a). Compounds in a horizontal row have the same double bond equivalence
(DBE) and differ by 14 Da, indicating a difference in one methylene group. Compounds
in a diagonal line, indicate the same number of carbon atoms, and differ by 2 Da,
indicating a difference in 2 hydrogen atoms. The Kendrick mass defect versus the
nominal mass for the unirradiated diesel fuel (large red circles) overlaid with the 10 hour
dark control (small black circles) (b), and the 10 hour irradiated sample (small black
diamonds) (c).

269

Figure 4-6 cont’d

270

The plot of the Kendrick mass defect versus the nominal mass for diesel fuel
irradiated for 10 hours and the corresponding dark control were compared to the plot of
the unirradiated diesel sample (Figure 4-6 b and c). In the unirradiated sample (larger
red circles), 228 elemental formulas were assigned, only two of which contained an
oxygen. In the 10 hour dark control (smaller black circles), 228 elemental formulas were
also assigned (Figure 4-6b). In this case, two different elemental formulas contained
oxygen. When overlaid, all but 10 formulas from each sample agree. This demonstrates
that the unirradiated sample and dark control are similar and newly formed compounds
can be attributed to photooxidation. By comparison, the diesel sample irradiated for 10
hour contained 574 elemental formulas, or about 2.5 times as many as in the untreated
fuel. In the plot of the Kendrick mass defect versus nominal mass (Figure 4-6c), a large
number of new elemental formulas are present in the irradiated sample (black diamonds).
In addition to the large number of newly formed compounds, approximately 58
compounds (about 25% of the original diesel constituents) were no longer present,
suggesting complete degradation from photooxidation or evaporation. This demonstrates
that even over a relatively short period of time, there are substantial changes due to
photooxidation.
4.3.5 Principal Component Analysis
In order to determine which masses were changing during the irradiation, principal
component analysis (PCA) was performed (Pirouette v. 4.0, Infometrix, Bothell, WA).
PCA organizes sample data based on the greatest sources of variance and has two main
outputs, scores plots and loadings plots (Figure 4-7). The scores plot shows a visual

271

PC2 (3.3%)

3.0E+00

0.0E+00

-3.0E+00
-3.0E+00

0.0E+00
PC1 (89.7%)

211.15

0.4

197.13

PC1 Loadings

0.3
0.2

3.0E+00

225.16
239.18
251.16

183.12

0.1
0.0
-0.1
-0.2
-0.3
100

161.10

229.16

215.14
175.11
189.13 203.14

200

m/z

300

400

Figure 4-7. The PCA scores plot (a) and loadings plot (b) for samples irradiated for 0 h
(), 1 h (■), 2 h (♦), 4 h (▲), 6 h (+),8 (▼), and 10 h ( ).

272

relationship between samples; samples that are positioned close together are more
chemically similar than those positioned further apart.

The PCA in this work was

performed using the abundances (peak heights) for each exact mass, based on the
elemental formulas discussed in Section 4.3.3, after normalizing abundances to m/z
199.1487. The scores plot (Figure 4-7a) shows the first principal component (PC1)
accounts for 89.7% of the variance and the second principal component (PC2) accounts
for 3.2% of the variance. Because PC1 accounts for such a large amount of the variance,
most of the chemical differences are accounted for on this PC. The unirradiated diesel
samples are positioned positively on PC1. As irradiation time increased, the diesel
samples were positioned progressively more negative until 10 h, which are positioned the
most negatively on PC1. This demonstrates that PC1 is accounting for difference in
irradiation time.
The loadings plots show which variables are influencing the positioning of the
samples on the scores plot. The loadings plot for PC1, which is the loadings versus the
m/z, is shown in Figure 4-7b. The masses that are most abundant in the unirradiated fuel
(Figure 4-5b) are loading positively on PC1, while the masses that are most abundant
after 10 h of irradiation (Figure 4-5c) are loading negatively on PC1. Therefore, on the
PC1 loadings plot, the masses that are loading positive correspond to compounds that
are decaying, while masses that are loading negatively likely correspond to compounds
that are forming during irradiation.
PCA results demonstrated several important points. First, PCA was useful in
demonstrating differences in sample composition as a function of irradiation time.
Experimental replicates are clustered close together, indicating that the irradiation

273

experiments were reproducible. Second, PCA was useful in identifying characteristic
masses corresponding to compounds that were undergoing formation or decay.
Compounds that loaded positively were hydrocarbons that decayed in abundance during
photooxidation while compounds that loaded negatively were oxygenated compounds
that formed during irradiation.
4.3.6 Determination of Photooxidation Rate Constants
In order to quantify the rate of change from both the GC-MS and HR-MS
experiments, kinetic rate constants were determined. In the GC-MS experiment, peak
abundances were normalized to nonadecane and in the HR-MS experiments the peak
abundances were normalized to m/z 199.1487, which had 7 DBE, equivalent to a
naphthalene with 5 methylene groups.
Decay or formation curves (Figure 4-8) were plotted for individual compounds by
plotting the normalized abundance versus time.

Kinetic rate constants were then

determined by nonlinear regression (TableCurve 2D, version 5.01, Jandel Scientific, San
Rafael, CA).

Zeroth- and first-order kinetics were considered, based on previous

research [8, 9, 19]. A zeroth-order rate constant results in a reaction that is independent
of concentration. This may occur when the reactant is at a low concentration or is being
replenished by another reaction. Zeroth order kinetics could also arise when light serves
as the limiting reactant [20]. A first-order rate constant results in a reaction that is directly
proportional to the concentration of the reactant.

Also possible are pseudo-first-order

reactions in which the reaction is dependent upon the concentration of two

274

a

b

Figure 4-8. Decay and formation curves for various compounds. The regression equation
is shown and the first order rate constant is underlined. From the GC-MS analysis: methyl
pyrene (a) (retention time 34.77 min, y = 0.033 * exp (-0.243 * t)). From the HR-MS
analysis: C16H19 (b) (m/z: 211.15, y = 1.840 * exp (-0.205 * t)), C13H17O1 (c) (m/z: 189.13,
y = 6.291 * exp (-0.0165 * t)), C18H21O2 (d) (m/z: 269.15, y = 0.097 * exp (-0.045 * t)).

275

Figure 4-8 cont’d

c

d

276

reactants. However, one reactant is at a much higher concentration and can be thought
of as constant, so that the kinetics can be thought of as first-order. The first-order
formation of a compound is the inverse of the first-order decay of a precursor, even when
the identity of the precursor is unknown. Previous reports suggested that the decay due
to photooxidation was likely first-order or pseudo-first-order [21-23], while other
investigations have suggested formation was zeroth-order [24]. It is likely that the kinetics
of photooxidation of diesel fuel and other complex petroleum products are not simple, and
depend on the concentrations of the compound as well as the sensitizer. However, the
total abundance of all sensitizers may be large compared to the abundance of any single
compound, allowing pseudo-first-order kinetic equations to provide an accurate depiction
of the rate constants.
4.3.6.1 Kinetic

Rate

Constants

Determined

from

Gas

Chromatography-Mass

Spectrometry
Using the GC-MS chromatographic data, 61 compounds were quantified and
decay curves were generated. An example decay curve for methyl pyrene (retention time:
34.77 min, from Figure 4-4b) is shown in Figure 4-8a. A decrease in abundance over
time was observed for 41 of the 61 compounds, and first-order rate constants were
determined for each. The experimental rate constants were compared with rate constants
predicted for evaporation alone, using a model based on the retention index of the
compound on a nonpolar stationary phase and temperature (Chapter 3).

The

temperature of the water was 21 °C and retention indices were calculated from the GCMS experiment.

Surprisingly, the experimental rate constants determined during

photooxidation (0.004 – 1.211 h-1) were nearly twice as large as the rate constants

277

predicted by the evaporation model (0.000 – 0.379 h-1) for the compounds expected to
evaporate (with retention indices greater than about 1200).
It is unlikely that the increase in the rate constant is due to photooxidation, because
a similar increase was observed for all compound classes, including the normal alkanes,
which are not expected to decay by photooxidation owing to their lower reactivity relative
to alkyl aromatics toward free radicals [11, 12]. This increase in the disappearance rates
is likely to result from increased deposition of energy deposited into the molecules during
irradiation that results in warming rather than electronic excitation. This observation
demonstrates the interconnection between weathering processes; even though the
compounds are not being degraded by photooxidation, increased rates of evaporation
are observed.
Other compounds that were not expected to evaporate, decreased in abundance
over the 10 h irradiation experiment due to photooxidation.

The compounds that

underwent photooxidation were typically larger and alkyl substituted PAHs, however,
compounds that were provisionally identified as alkyl indanes and tetralins also were
oxidized.

Naphthalene, methyl naphthalene, phenanthrene, and alkyl biphenyl

compounds did not undergo photooxidation over the course of this experiment as judged
by their minimal changes in abundances. For the compounds that did oxidize, those with
more alkyl substituents had a higher rate constant. This is consistent with results reported
by Prince et al. who observed more degradation due to photooxidation in compounds with
more aromatic rings and more alkyl substitutions, consistent with the notion that electrondonating groups add to the photo-reactivity of benzene rings [12]. In addition, structural
isomers that were more retained than other isomers, based on retention index (IT), also

278

often had an increased rate constant. For example, the rate constant for pyrene (IT =
2047, k = 0.174 h-1) was lower than that of methyl pyrene (IT = 2170, k = 0.218 h-1). The
rate constant for the methyl pyrene was lower than the rate constant for the more retained
structural isomer (IT = 2192, k = 0.243 h-1). A similar trend is observed for fluorene (IT =
1542, k = 0.011 h-1) and the methyl fluorenes (IT = 1657, k = 0.014 h-1 and IT = 1663, k =
0.036 h-1) and dimethyl fluorenes (IT = 1773, k = 0.033 h-1 and IT = 1779, k = 0.034 h-1
and IT = 1785, k = 0.045 h-1). Identification of additional isomers would help to elucidate
additional underlying patterns however, this identification was not feasible given the small
sample size, the complexity of the sample, and the relatively low abundance of many of
the isomers.
4.3.6.2 Kinetic Rate Constants Determined from High Resolution Mass Spectrometry
In the HR-MS experiments, over 850 unique masses were identified in the
photooxidized diesel, however, many were only present in a few samples. Only masses
that were present in at least 27 of the 63 total analyses (equivalent data collected at three
time points) were considered for the rate determination, resulting in 201 masses.
Changes in abundance were observed for 121 of the 201 masses, for which rate
constants were determined using either decay (kd, n = 67) or formation (kf, n = 54) curves.
An example decay curve of m/z 211.15 (C16H19) and example formation curves of m/z
189.13 (C13H17O1) and m/z 269.15 (C18H21O2) at shown in Figure 4-8 b – d respectively.
All of the newly formed compounds suggest the presence of at least one oxygen atom.
There do not appear to be any high molecular weight ions (m/z > 300) that does not
contain oxygen, suggesting dimerization is not occurring.

279

All of the determined rate constants were considered first-order or pseudo-firstorder. Rate constants ranged from 0.003 – 0.210 h-1 for decay, 0.000 – 0.221 h-1 for
formation of a compound containing one oxygen atom, and 0.017 – 1.173 h-1 for formation
of a compound containing two oxygen atoms. A complete list of the rate for decay and
formation are in Table 4-2 and Table 4-3, respectively. Some formation rate constants
appeared to be zeroth-order and could not be reasonably fit to a first-order formation
equation (n = 25). The zeroth-order formation is consistent with observations by Larson
et al. [24], however, it is possible these formations are first-order, but only a small portion
of the formation curve is seen over the 10 hour experiments. The zeroth-order rate
constants for all formed compounds that form are also available on Table S3. The
uncertainty measurement in kf was as high as 0.13, larger than many of the first-order
rate constants for formation, supporting that the compounds may not form by zerothorder. In addition, a reaction involving singlet oxygen or free radicals would likely not
result in zeroth-order kinetics, as the rate constant is dependent on concentration [25].
These compounds were excluded from further consideration, however many of the trends
discussed below for the first-order rate constant for formation were also observed when
using the zeroth-order rate constants. Of note, there were also three hydrocarbons that
were shown to grow during irradiation. These hydrocarbons are related with differing alkyl
substitution. These hydrocarbons are like a rearrangement of an oxygenated compound,
with a loss of water, occurring during ionization. These compounds also showed zerothorder formation and were excluded from further consideration.

280

Table 4-2. The exact mass, the number of carbon atoms (C), the number of hydrogen
atoms (H), the number of oxygen atoms (O), the double bond equivalence (DBE), the
Kendrick mass defect (KMD), the rate constant for decay (kd), and the uncertainty in the
rate constant for compounds identified using mass spectrometry.
Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

163.149

12

19

0

4

-0.0335

n/ca

n/c

177.164

13

21

0

4

-0.0335

n/c

n/c

191.18

14

23

0

4

-0.0335

n/c

n/c

205.196

15

25

0

4

-0.0335

0.100

0.009

219.211

16

27

0

4

-0.0335

0.113

0.008

233.227

17

29

0

4

-0.0335

0.117

0.008

247.243

18

31

0

4

-0.0335

0.112

0.009

261.258

19

33

0

4

-0.0335

0.104

0.010

275.274

20

35

0

4

-0.0335

0.091

0.010

289.29

21

37

0

4

-0.0335

0.080

0.010

303.305

22

39

0

4

-0.0335

n/c

n/c

317.321

23

41

0

4

-0.0335

n/c

n/c

119.086

9

11

0

5

-0.0469

0.096

0.013

133.102

10

13

0

5

-0.0469

0.094

0.010

281

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

147.117

11

15

0

5

-0.0469

0.105

0.009

161.133

12

17

0

5

-0.0469

0.153

0.008

175.149

13

19

0

5

-0.0469

0.196

0.009

189.164

14

21

0

5

-0.0469

0.205

0.010

203.18

15

23

0

5

-0.0469

0.197

0.010

217.196

16

25

0

5

-0.0469

0.206

0.014

231.211

17

27

0

5

-0.0469

0.186

0.009

245.227

18

29

0

5

-0.0469

0.185

0.009

259.243

19

31

0

5

-0.0469

0.171

0.010

273.258

20

33

0

5

-0.0469

0.158

0.011

287.274

21

35

0

5

-0.0469

0.153

0.012

301.29

22

37

0

5

-0.0469

0.129

0.011

315.305

23

39

0

5

-0.0469

0.084

0.013

329.321

24

41

0

5

-0.0469

0.074

0.014

131.086

10

11

0

6

-0.0603

n/c

n/c

282

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

145.102

11

13

0

6

-0.0603

n/c

n/c

159.117

12

15

0

6

-0.0603

n/c

n/c

173.133

13

17

0

6

-0.0603

n/c

n/c

187.149

14

19

0

6

-0.0603

n/c

n/c

201.164

15

21

0

6

-0.0603

0.044

0.003

215.18

16

23

0

6

-0.0603

0.078

0.003

229.196

17

25

0

6

-0.0603

0.074

0.003

243.211

18

27

0

6

-0.0603

0.050

0.003

257.227

19

29

0

6

-0.0603

0.033

0.004

271.243

20

31

0

6

-0.0603

0.026

0.004

285.258

21

33

0

6

-0.0603

0.018

0.005

299.274

22

35

0

6

-0.0603

0.019

0.005

313.29

23

37

0

6

-0.0603

n/c

n/c

327.305

24

39

0

6

-0.0603

n/c

n/c

341.321

25

41

0

6

-0.0603

n/c

n/c

283

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

355.336

26

43

0

6

-0.0603

n/c

n/c

129.07

10

9

0

7

-0.0737

n/c

n/c

143.086

11

11

0

7

-0.0737

n/c

n/c

157.102

12

13

0

7

-0.0737

n/c

n/c

171.117

13

15

0

7

-0.0737

0.058

0.005

185.133

14

17

0

7

-0.0737

0.038

0.003

199.149

15

19

0

7

-0.0737

n/c

n/c

213.164

16

21

0

7

-0.0737

n/c

n/c

227.18

17

23

0

7

-0.0737

n/c

n/c

241.196

18

25

0

7

-0.0737

n/c

n/c

255.211

19

27

0

7

-0.0737

n/c

n/c

269.227

20

29

0

7

-0.0737

n/c

n/c

283.243

21

31

0

7

-0.0737

n/c

n/c

297.258

22

33

0

7

-0.0737

n/c

n/c

311.274

23

35

0

7

-0.0737

n/c

n/c

284

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

325.29

24

37

0

7

-0.0737

n/c

n/c

339.305

25

39

0

7

-0.0737

n/c

n/c

353.321

26

41

0

7

-0.0737

n/c

n/c

141.07

11

9

0

8

-0.0871

n/c

n/c

155.086

12

11

0

8

-0.0871

0.046

0.011

169.102

13

13

0

8

-0.0871

0.073

0.008

183.117

14

15

0

8

-0.0871

0.136

0.008

197.133

15

17

0

8

-0.0871

0.184

0.007

211.149

16

19

0

8

-0.0871

0.205

0.007

225.164

17

21

0

8

-0.0871

0.210

0.007

239.18

18

23

0

8

-0.0871

0.172

0.006

253.196

19

25

0

8

-0.0871

0.124

0.006

267.211

20

27

0

8

-0.0871

0.099

0.006

281.227

21

29

0

8

-0.0871

0.080

0.005

295.243

22

31

0

8

-0.0871

0.099

0.006

285

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

309.258

23

33

0

8

-0.0871

0.041

0.004

323.274

24

35

0

8

-0.0871

0.040

0.005

337.29

25

37

0

8

-0.0871

0.018

0.004

351.305

26

39

0

8

-0.0871

n/c

n/c

365.321

27

41

0

8

-0.0871

n/c

n/c

153.07

12

9

0

9

-0.1005

n/c

n/c

167.086

13

11

0

9

-0.1005

n/c

n/c

181.102

14

13

0

9

-0.1005

n/c

n/c

195.117

15

15

0

9

-0.1005

n/c

n/c

209.133

16

17

0

9

-0.1005

0.072

0.004

223.149

17

19

0

9

-0.1005

0.158

0.006

237.164

18

21

0

9

-0.1005

0.190

0.007

251.18

19

23

0

9

-0.1005

0.184

0.007

265.196

20

25

0

9

-0.1005

0.162

0.008

279.211

21

27

0

9

-0.1005

0.131

0.006

286

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

293.227

22

29

0

9

-0.1005

0.104

0.006

307.243

23

31

0

9

-0.1005

0.069

0.004

321.258

24

33

0

9

-0.1005

0.062

0.005

335.274

25

35

0

9

-0.1005

0.050

0.005

349.29

26

37

0

9

-0.1005

0.041

0.005

363.305

27

39

0

9

-0.1005

n/c

n/c

221.133

17

17

0

10

-0.1139

n/c

n/c

235.149

18

19

0

10

-0.1139

0.052

0.005

249.164

19

21

0

10

-0.1139

0.065

0.006

263.18

20

23

0

10

-0.1139

0.056

0.007

277.196

21

25

0

10

-0.1139

0.047

0.007

291.211

22

27

0

10

-0.1139

0.046

0.006

305.227

23

29

0

10

-0.1139

0.040

0.005

319.243

24

31

0

10

-0.1139

n/c

n/c

333.258

25

33

0

10

-0.1139

n/c

n/c

287

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

347.274

26

35

0

10

-0.1139

n/c

n/c

219.117

17

15

0

11

-0.1273

n/c

n/c

233.133

18

17

0

11

-0.1273

0.112

0.015

247.149

19

19

0

11

-0.1273

0.077

0.009

261.164

20

21

0

11

-0.1273

n/c

n/c

275.18

21

23

0

11

-0.1273

n/c

n/c

289.196

22

25

0

11

-0.1273

n/c

n/c

303.211

23

27

0

11

-0.1273

n/c

n/c

317.227

24

29

0

11

-0.1273

n/c

n/c

331.243

25

31

0

11

-0.1273

n/c

n/c

345.258

26

33

0

11

-0.1273

n/c

n/c

217.102

17

13

0

12

-0.1407

0.097

0.014

231.117

18

15

0

12

-0.1407

n/c

n/c

245.133

19

17

0

12

-0.1407

n/c

n/c

259.149

20

19

0

12

-0.1407

n/c

n/c

288

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

273.164

21

21

0

12

-0.1407

n/c

n/c

287.18

22

23

0

12

-0.1407

n/c

n/c

301.196

23

25

0

12

-0.1407

n/c

n/c

315.211

24

27

0

12

-0.1407

n/c

n/c

329.227

25

29

0

12

-0.1407

n/c

n/c

343.243

26

31

0

12

-0.1407

n/c

n/c

357.258

27

33

0

12

-0.1407

n/c

n/c

285.164

22

21

0

13

-0.1541

n/c

n/c

299.18

23

23

0

13

-0.1541

n/c

n/c

313.196

24

25

0

13

-0.1541

n/c

n/c

327.211

25

27

0

13

-0.1541

n/c

n/c

341.227

26

29

0

13

-0.1541

n/c

n/c

355.243

27

31

0

13

-0.1541

n/c

n/c

311.18

24

23

0

14

-0.1675

n/c

n/c

325.196

25

25

0

14

-0.1675

n/c

n/c

289

Table 4-2 cont’d

Mass

C

H

O

DBE

KMD

kd
(h-1)

Uncertainty

339.211

26

27

0

14

-0.1675

n/c

n/c

353.227

27

29

0

14

-0.1675

n/c

n/c

367.243

28

31

0

14

-0.1675

n/c

n/c

a. n/c = kobs< 0.002 h-1, which was not significantly different from 0 (α = 0.05)

290

Table 4-3. The exact mass, the number of carbon atoms (C), the number of hydrogen
atoms (H), the number of oxygen atoms (O), the double bond equivalence (DBE), the
Kendrick mass defect (KMD), the first (1st) and zeroth (0th) rate constant for formation (kf),
and the uncertainty in the rate constant for compounds identified using mass
spectrometry.
Mass

C

H

O DBE

KMD

kf 1st
(h-1)

Uncertainty

kf 0th
(h-1)

Uncertainty

165.07

13

9

0

10

-0.114

0.958

0.153

0.003

0.0002

179.086 14 11

0

10

-0.114

0.647

0.119

0.005

0.0003

193.102 15 13

0

10

-0.114

0.758

0.138

0.012

0.0009

147.081 10 11

1

6

-0.083

0.000

0.036

0.008

0.0004

161.097 11 13

1

6

-0.083

0.028

0.026

0.043

0.0019

175.112 12 15

1

6

-0.083

0.033

0.020

0.092

0.0031

189.128 13 17

1

6

-0.083

0.017

0.015

0.097

0.0024

203.144 14 19

1

6

-0.083

0.000

0.017

0.073

0.0016

217.159 15 21

1

6

-0.083

0.000

0.027

0.051

0.0017

231.175 16 23

1

6

-0.083

0.000

0.030

0.037

0.0013

245.191 17 25

1

6

-0.083

0.000

0.030

0.030

0.0011

259.206 18 27

1

6

-0.083

0.000

0.028

0.025

0.0008

273.222 19 29

1

6

-0.083

0.000

0.029

0.020

0.0006

287.237 20 31

1

6

-0.083

0.000

0.031

0.015

0.0005

291

Table 4-3 cont’d

O DBE

KMD

kf 1st
(h-1)

Uncertainty

kf 0th
(h-1)

Uncertainty

159.081 11 11

1

7

-0.097

0.000

0.031

0.005

0.0002

173.097 12 13

1

7

-0.097

0.000

0.024

0.012

0.0005

187.112 13 15

1

7

-0.097

0.000

0.019

0.033

0.0011

201.128 14 17

1

7

-0.097

0.000

0.015

0.065

0.0016

215.144 15 19

1

7

-0.097

0.000

0.013

0.079

0.0014

229.159 16 21

1

7

-0.097

0.000

0.021

0.068

0.0018

243.175 17 23

1

7

-0.097

0.000

0.032

0.046

0.0017

257.191 18 25

1

7

-0.097

0.000

0.049

0.031

0.0017

183.081 13 11

1

9

-0.123

0.002

0.029

0.010

0.0005

197.097 14 13

1

9

-0.123

0.064

0.021

0.035

0.0013

211.112 15 15

1

9

-0.123

0.142

0.018

0.052

0.0019

225.128 16 17

1

9

-0.123

0.221

0.024

0.041

0.0020

239.144 17 19

1

9

-0.123

0.111

0.027

0.028

0.0013

253.159 18 21

1

9

-0.123

0.000

0.037

0.016

0.0008

195.081 14 11

1

10

-0.137

0.000

0.023

0.017

0.0005

Mass

C

H

292

Table 4-3 cont’d

O DBE

KMD

kf 1st
(h-1)

Uncertainty

kf 0th
(h-1)

Uncertainty

209.097 15 13

1

10

-0.137

0.017

0.013

0.047

0.0010

223.112 16 15

1

10

-0.137

0.055

0.012

0.063

0.0014

237.128 17 17

1

10

-0.137

0.101

0.015

0.048

0.0014

251.144 18 19

1

10

-0.137

0.104

0.016

0.029

0.0009

265.159 19 21

1

10

-0.137

0.038

0.021

0.019

0.0007

235.112 17 15

1

11

-0.150

0.002

0.001

0.011

0.0006

249.128 18 17

1

11

-0.150

0.074

0.021

0.013

0.0005

263.144 19 19

1

11

-0.150

0.045

0.024

0.012

0.0004

203.107 13 15

2

7

-0.120

0.013

0.043

0.014

0.0009

201.092 13 13

2

8

-0.133

0.000

0.035

0.006

0.0003

215.107 14 15

2

8

-0.133

0.070

0.034

0.011

0.0006

229.123 15 17

2

8

-0.133

0.215

0.035

0.015

0.0008

243.139 16 19

2

8

-0.133

0.909

0.095

0.014

0.0017

257.154 17 21

2

8

-0.133

1.173

0.130

0.011

0.0017

271.17

2

8

-0.133

1.045

0.121

0.010

0.0014

Mass

C

H

18 23

293

Table 4-3 cont’d

O DBE

KMD

kf 1st
(h-1)

Uncertainty

kf 0th
(h-1)

Uncertainty

213.092 14 13

2

9

-0.146

0.000

0.023

0.008

0.0002

227.107 15 15

2

9

-0.146

0.063

0.022

0.013

0.0005

241.123 16 17

2

9

-0.146

0.065

0.065

0.014

0.0005

255.139 17 19

2

9

-0.146

0.131

0.022

0.011

0.0005

269.154 18 21

2

9

-0.146

0.405

0.029

0.009

0.0006

283.17

19 23

2

9

-0.146

0.427

0.042

0.007

0.0006

239.107 16 15

2

10

-0.160

0.000

0.030

0.012

0.0005

253.123 17 17

2

10

-0.160

0.129

0.026

0.010

0.0005

267.139 18 19

2

10

-0.160

0.141

0.024

0.008

0.0004

281.154 19 21

2

10

-0.160

0.017

0.032

0.006

0.0003

Mass

C

H

294

The compounds that decayed and formed were organized by KMD, so that the rate
constant for compounds with the same DBE but varying alkyl substitution could be
evaluated. As observed in the GC-MS experiment, for a compound with the same DBE,
more alkyl substitution resulted in an increase in the rate constant. As alkyl substitution
continues, the rate constant then decreases (Figure 4-9a).

This decrease was not

observed in the GC-MS experiment because the compounds with sufficient alkyl
substitution were not amenable to GC-MS analysis. The increase in the rate constant
could be due to the alkyl groups donating additional electrons to the ring or the addition
of benzylic hydrogen presenting more reactive sites, which would be consistent with
photooxidation with free radicals. Electron donating groups, such as additional alkyl
groups, enhance free radical reactions.

Reactions with free radicals often proceed

through abstraction of hydrogen atoms, and making alkyl PAHs attractive candidates for
free radical oxidation [26]. It has been proposed that alkyl olefins, such has a dimethyl
indene, would initiate a free radical reaction [24]. However, other authors suggested that
the initiator required for free radical mechanisms is not present in petroleum, but it could
be formed from reactions with singlet oxygen [27, 28].
More extensive alkyl substitution resulted in a decrease in photooxidation rate
constants. Steric effects and decreases in the number of benzylic hydrogens may explain
the resulting decrease in the rate constant for larger homologs. Most compounds with
DBE greater than 11 showed no decay over the 10 hour of irradiation, which is consistent

295

a

b

Figure 4-9. The rate constant for decay (a) and formation (b) of selected compounds
versus the mass of the compound. Compounds are classified based on the number of
double bond equivalences (4: red, 5: orange, 6: yellow, 7: light green, 8: dark green, 9:
light blue, 10: dark blue, 11: purple) and number of oxygens (0: , 1: ▲, 2: ■).

296

with results reported for crude oil [29]. Large PAHs typically have large gaps between
the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital
(HOMO). A large HOMO-LUMO gap has been shown to result in decreased reactivity,
because it is energetically unfavorable to remove electrons from a low HOMO and add
electrons to a high HOMO [30, 31].

Addition of alkyl substitution reduces the HOMO-

LUMO gap, also helping to explain the increased reactivity with alkyl substitution [31].
Many of the PAHs with DBE greater than 11 were detected at very low abundances, which
also made quantification of changes challenging.
The formation rate constants showed a similar increase then decrease with
additional alkyl substitution (Figure 4-9b).

The rate constants for decay maximized

between m/z 150 – m/z 250, while the rate constants for formation maximized between
m/z 175 – m/z 275, a mass difference consistent with the addition of an oxygen. The
compounds that contained two oxygen atoms typically had higher rate constants for
formation than those that only contained one oxygen atom. This could be a result of the
mechanism of photooxidation. The reaction with singlet oxygen typically results in the
addition of two oxygen atoms, forming a quinone, peroxide, or hydroperoxide, each of
which contain two oxygen atoms [8, 26, 32]. The peroxides can then further react, forming
an alcohol or other stable oxygen-containing species. Many of the compounds containing
two oxygen atoms reached a constant abundance after the first few hours (Figure 4-8d).
This indicates that either the reactant(s) have been depleted or that another reaction is
occurring and the species containing 2 oxygen atoms are only intermediates that achieve
steady-state concentrations. The formation curves for several compounds containing one
oxygen show a delayed onset of formation (up to 4 hours), indicating that it may be formed

297

from an intermediate. There were also several compounds containing 3 or 4 oxygen
atoms, but were only present at the latest time points. These were excluded from the rate
determination, but suggest that additional oxidation is occurring.
4.3.7 Analysis of Precipitate formed during Irradiation of Diesel Fuel
The precipitate that was formed during irradiation was analyzed using infrared
spectroscopy to identify functional groups and mass spectrometry to determine an
elemental formula. Fourier transform infrared spectroscopy attenuated total reflectance
(Spectrum One, Perkin Elmer, Waltham, MA) allowed for the analysis of the solid
precipitate without any additional sample preparation. The instrument acquired four
scans at a resolution of 4 cm-1, from 4000 – 650 cm-1. The resulting spectrum (Figure
4-10) indicates oxygenated compounds.

There was a broad peak at 3400 cm-1,

consistent with O-H stretch, a large peak at 1703 cm-1, consistent with a carbonyl stretch,
and a peak at 1262 cm-1, consistent with a C-O stretch. There is also several peaks
around 2929 cm-1, which are consistent with alkyl stretches. These peaks indicates that
the precipitate contains hydrocarbons with oxygen functional groups, which would be
expected from photooxidation.
The precipitate was also dissolved in acetonitrile for MS analysis. Flow injection
analysis was used, with methanol as the mobile phase instead of hexane. There were
over 620 masses observed in the precipitate (Figure 4-11). Many of the masses observed

298

Figure 4-10. An infrared spectrum of the precipitate formed from diesel after 10 hours of
irradiation. Several peaks are labeled for reference.

299

Relative Abundance

100
6000

189.13
175.11
233.12

261.12
159.12
289.15

x
417.18

0
200

400

m/z

600

800

Figure 4-11. The mass spectrum of the precipitate formed from diesel fuel after 10 h of
irradiation. The peak marked with “x” at 391.28 is from a phthalate and is present in the
blank. It was used as a lock mass in this analysis.

300

in the precipitate were also observed in the 10 hour irradiated diesel sample. A number
of additional masses were observed, many of which contain 3 or more oxygen atoms.
The same masses being present in both the fuel and the precipitate suggest that the
precipitate is made up of weakly-bonded clusters of oxygenated compounds that dissolve
in solution rather than large dimerized compounds.
Several small studies were designed to try to determine the origin of the
precipitate. In one experiment, ascorbic acid (Columbus Chemical Industries, Columbus,
WI) was added to water (0.8 g/mL) as a free radical scavenger. Peroxides are likely
formed in the water layer which could lead to reactions at the oil water interface. Diesel
fuel (1 mL) was added on top of the water with ascorbic acid (10mL) and irradiated for 8
hours. In another study, the water layer was completely omitted and 1 mL of diesel fuel
was irradiated. In both cases, the precipitate formed as in previous experiments. In
addition the mass spectra of the extracted fuel residue in both case contained the same
masses at similar abundances to that observed in normal 8 hour irradiation of diesel on
distilled water. This demonstrates that the water layer does not significantly influence the
rate of photooxidation. However, natural waters which contain additional sensitizers
could result in an increased rate of photooxidation.
In another study, diesel fuel was diluted 5-fold by hexadecane. For irradiation, 5
mL of diesel fuel (thickness = 19mm) was places on 10 mL of distilled water. In this case,
the number of compounds from diesel fuel are the same, but at a lower concentration.
After 8 hours of irradiation, the fuel became a darker yellow and was slightly turbid, but
the precipitate was not formed. The mass spectrum of the extracted diesel fuel was
compered to spectra irradiated for 0 – 10 hours. The ratio of masses present in the

301

spectrum of the diluted diesel fuel was similar to that of non-diluted diesel fuel irradiated
for 2 – 4 hours.

This demonstrates that the rate of photooxidation is affected by

concentration of the reactants, indicating that the rate constants for photooxidation are
not zeroth-order.

This could also suggest a free-radical mechanism, because free

radicals have very short lifetimes to react. In a dilute solution, free-radicals would not
encounter as many compounds to react with as in the undiluted sample.
Diesel fuel (100 mL) was redistilled using rotary evaporation, to remove nonvolatile
and heteroatom containing compounds. In addition, distillation should have removed any
antioxidants or other additives. Approximately 90% of the diesel was recovered after
rotary evaporation. The residuum was a dark brown, and likely contained the sulfur and
nitrogen containing compounds.

In an additional step to remove additives and

heteroatom containing compounds, 5 mL of the redistilled diesel was filtered through a
C18 sep-pak cartridge (Waters Associates, Milford, MA). This filtration should remove the
volatile polar compounds (antioxidants or other additives) that were distilled. The distilled
and filtered diesel fuel was analyzed by GC-MS and APCI-ToF-MS. The TIC from the
GC-MS experiment showed no identifiable difference between the fuels.

This was

expected because the compounds removed by distillation and filtration are likely not
amenable to GC-MS. The APCI-ToF-MS spectra also did not show any differences
between the two fuels. This is likely to the relatively low abundance of the compounds
that were removed. The distilled and filtered fuel was also exposed to irradiation for 5
hours. A precipitate was observed at the end of the experiment. The APCI-ToF-MS
spectra of the irradiated diesel samples both with and without distillation and filtration

302

were also similar. This indicates that the polar and heavy molecular weight compounds
likely had little effect on the photooxidation experiment.
The photooxidation of kerosene, which contains more volatile hydrocarbons and
fewer PAHs than diesel fuel, was also investigated. The PAHs are the compounds
undergoing photooxidation and likely resulting in the precipitate. There are fewer PAHs
in kerosene which would making the characterization more straight-forward.

The

kerosene was evaporated by 50% to reduce the volatility and minimize risk of ignition
during the experiment. This also resulted in an increased concentration the less volatile
compounds, such as PAHs. Kerosene (1 mL) on water (10 mL) was irradiated for 5 hours.
Kerosene is a clear liquid and no color change was observed, however, there was a small
amount of turbidity after irradiation. The mass spectra of kerosene prior to irradiation
contained fewer masses than the mass spectrum for diesel fuel, indicating that there are
fewer PAHs in the kerosene. The mass spectrum of kerosene after irradiation did not
suggest the formation of new compounds or decay of existing compounds. However,
only limited information can be taken from this experiment as no replicate analyses were
performed. It did show that photooxidation of kerosene is sufficiently slow that kerosene
would not be well suited for the photooxidation experiments.

It also demonstrated the

variability in photooxidation between different petroleum products.
4.4 Discussion and Conclusions
This work has demonstrated the significance of photooxidation in the weathering
of petroleum products. While photooxidation may not account for significant mass loss
(it may actually add mass, because the oxidized products are heavier), it does lead to the
formation of oxidized products that are often more toxic and water-soluble than the parent
303

compound. In addition, the results from this work suggest that photooxidation occurs
much faster than discussed previously. In this work, a color change in the fuel was
observed within an hour, and a precipitate formed after 3 hours. Using high resolution
mass spectrometry, the diesel samples that were irradiated for 10 hours showed the
formation of over 300 new compounds. For these experiments, there were not any
photosensitizers added to the water, as there would be in the environment, though the
possibility that dissolved CO2 could be converted to peroxycarbonate and associated
radicals cannot be discounted. The photosensitizers present in natural waters would
likely lead to additional reactions, with the potential for formation of more compounds and
an increase in reaction rates.

Diesel fuel and other refined products often contain

antioxidants (10-25 ppm) added to help prevent degradation of the fuel prior to use [14].
While these antioxidants were not observed during the analysis, they were likely present
and could also affect the rates of degradation.
Even though substantial chemical changes were occurring, few differences due to
photooxidation were observed by GC-MS. Using EICs, PAHs such as fluorene and
methyl pyrene, were shown to decrease over the course of 10 hours, but no oxidized
products were seen. GC-MS is useful in analyzing volatile, nonpolar compounds, but was
not effective for analyzing polar oxygenated compounds. Using high resolution mass
spectrometry with APCI, the less volatile and oxygenated compounds were detected.
APCI allows for a soft ionization of moderately polar compounds including PAHs and
oxygenated compounds. This makes APCI an appropriate ionization method for the
analysis of petroleum and for monitoring photooxidation.

When coupled to a high

resolution mass spectrometer, unique elemental formulas can often be assigned. This

304

demonstrates the need for complementary instrumental techniques to account for the
physical and chemical changes that occur during wreathing of petroleum.
The rate constants determined using GC-MS and HR-MS also provided
complementary data regarding the rate and mechanism at which the oxidized compounds
form. GC-MS allowed for the separation of isomers, demonstrating structural isomers
have different rates at which photooxidation occurs. One of the limitations of using the
flow injection analysis is that there is no separation of structural isomers. Previous
research has shown that different isomers can have nearly a 2-fold difference in their rate
constants [23]. In the HR-MS experiment, multiple isomers, each of which react at
different rates, could be contributing apparent rate constant. This makes determination
of the rate constant challenging and does not allow for a direct comparison of rate
constants determined using GC-MS and HR-MS experiments or from the decay and
formation of compounds. The GC-MS data also showed that for the decay of a series of
compounds, increased alkyl substitution resulted in an increase in the first-order rate
constant. A similar trend was observed in the MS data, where an increase in alkyl
substitution (with the same KMD) resulted in an increase the photooxidation rate
constants. Without chromatographic separation of isomers, it is challenging to assess
the number or type of alkyl substitutions, but the rate constants maximized for
substitutions between 4 and 8 methylene groups.
In this work, abundances were normalized prior to determination of the rate
constant. By normalizing, all calculated concentrations are relative, but for environmental
applications, it may be necessary to obtain absolute concentrations. This is challenging
using many ionization methods in mass spectrometry unless authentic standards are

305

available for all compounds of interest. The signal from each compound is dependent on
the ionization efficiency of that compound. In APCI, the oxygenated compound was found
to ionize more efficiently than pure hydrocarbon PAHs. For example, at equal molar
concentrations, phenanthraquinone resulted in a 50 time larger signal than phenanthrene.
Similarly, larger PAHs also ionized more efficiently. Pyrene resulted in a 10 times higher
signal than that of phenanthrene at equal molar concentrations. For quantification by
mass spectrometry, often deuterated or isotopically labeled analogues are required. In a
complex mixture such as petroleum, it is impossible to use analogues of every compound.
However, specific compounds of interest can be quantified, then the rate constants
determined by this approach could be utilized to determine a final concentration.
Exact reaction mechanisms explaining photooxidation of petroleum are still
elusive, but it is likely that both singlet oxygen and free radicals are involved in the
photooxidation of crude oil and the significance of each process depends on the starting
material and the sensitizers in the environment [8, 24, 26]. A recent study by Correa et
al. showed that diesel fuel was more effective at generating singlet oxygen during
irradiation than crude oil [33]. Therefore, singlet oxygen reactions may account for more
photodegradation in refined petroleum products, as opposed to crude oil. It is also
possible that singlet oxygen is the initiating step in a free radical chain reaction.
Determination of the rates of decay and formation due to photooxidation is further
complicated by the multiple mechanisms are occurring simultaneously and likely some of
the same products are formed by different mechanisms. Miller and Olejnik demonstrated
a synergic effect in photodegradation when PAHs are added together [34]. This further
complicates the understanding of photooxidation because the pathways and rates may

306

be highly sample dependent. There are also other mechanisms have been suggested
involving electron transfer and the formation of ions at the oil water interface leading to
heterogeneous solutions, further complicating mechanistic studies [35, 36].
In conclusion, this work has demonstrated that photooxidation is a significant
weathering process for refined petroleum products, such as diesel fuel. This work also
proposed a large number of kinetic rate constants determined using GC-MS and APCIMS as a tool to help quantify the rates of weathering. A large number of oxygenated
compounds were formed in a shorter period of time than previously thought. Utilizing
complementary analytical techniques, capable of monitoring volatile nonpolar (GC-MS)
and nonvolatile, moderately polar molecules (APCI-MS), provided a more complete
picture of the changes in the fuel during weathering. This work has also demonstrated
the importance of understanding the interdependence of weathering process, such as the
increased evaporation resulting from irradiation during photooxidation. Last, the kinetic
information on the formation and decay would be useful for developing a model to predict
changes in petroleum products due to photooxidation. However, in order to develop the
models, work is still needed to understand the mechanism by which photooxidation
occurs.

307

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311

5. Conclusions and Future Works
5.1 Evaporation
5.1.1 Conclusions
When a petroleum release occurs, it is critical to have accurate fate and transport
models in order to assess potential impacts and guide remediation. Evaporation is one
of the most significant sources of mass loss during a petroleum spill and evaporative loss
can alter many physical properties of the fuel. Therefore the ability to predict evaporation
is a critical aspect of oil spill models. Many current evaporation models require a physical
property, such as vapor pressure, which are not readily available for most oils. Therefore,
an estimation of the physical properties are required. Moreover, the physical property
can change over time, complicating the estimation. In this work, a model was developed
to predict the evaporation rate constant for an individual compound, based on the
retention index of that compound on a nonpolar stationary phase and the temperature.
The first-order rate constant was used to determine a fraction remaining for an individual
compound. The total fraction remaining of the fuel was then determined using the sum
of the fraction remaining of each individual compound. This predictive model was in good
agreement with other evaporation models (percent difference = 4%) as well as
experimental measurements (percent difference = 2%).
Current predictive models for evaporation result in a percent evaporated for the
total fuel, however, this model also includes the ability to predict the fraction remaining of
individual compounds. This provides powerful new tools, not available from other models.
Using the fraction remaining of individual compounds, this model can be used to predict

312

the distribution of compound abundances in a fuel at a given time (i.e. create a
chromatographic profile), determine the length of time over which the evaporation has
occurred, and determine the time it would take for a fuel or an individual compound to
reach a specific fraction remaining, which are tools not typically available in oil spill
modeling. The prediction of a chromatogram allows users to compare the weathered fuel
directly to the neat fuel for identification and forensic purposes. The evaporation time can
be estimated using a chromatogram of the evaporated fuel and predicted chromatograms
from the model.

The predicted chromatograms can be iteratively compared to the

evaporated sample. The evaporation time corresponds to the predicted chromatogram
that is most similar to the evaporated sample. In this work, the similarity was compared
using Pearson product moment correlation coefficients. Currently, the length of time over
which evaporation has occurred is estimated using peak ratios of several volatile
compounds compared to a nonvolatile compound. The evaporation model developed in
this work uses the entire chromatogram, leading to a more accurate determination of
evaporation time.
Most evaporation models allow iterative calculations to predict the time it would
take to reach a specific fraction remaining or percent evaporated for the fuel. The
evaporation model in this work can predict this time for the fuel as well as for individual
compounds. This allows for additional assessment of the individual toxic compounds,
such as benzene, which could pose additional risks to first responders or marine life. This
demonstrates the increased versatility of the kinetic evaporation model developed in this
work compared to existing evaporation models.

313

Enhanced models provide a more

accurate and detailed assessment to guide decision making, risk assessment, and
remediation.
5.1.2 Limitations
There are a few additional investigations that must be addressed before wide
implementation of this model for oil spill fate determination. First, the only variable
changed in this work was temperature, however, some research suggests that wind
speed, thickness of the film, and surface area may also influence the rate of evaporation
[1]. Jones demonstrated using three different predictive models that varying wind speed
resulted in an approximately 10% difference in the amount of crude oil evaporated in 48
hours and varying initial thicknesses resulted in an approximately 20% difference. While
the influence of these variables are still debated, they require investigation prior to
implementation.
Second, in this work the model was developed and validated using fuels with
containing different chemical constituents, but with a moderately similar distribution of
compounds. The fuels were a complex mixture (more than 100 compounds in each fuel)
with boiling points for the majority of the compounds ranging from approximately 100 °C
to over 400 °C. However, there are other environmentally relevant fuel samples that have
a different distribution of compound abundances and boiling points.

For example,

gasoline is considerably more volatile than diesel fuel, containing compounds with boiling
points lower than 80 °C. As a result, in the GC-MS analysis, several compounds elute
prior to typical solvent delays, meaning that these compounds would not be included in
the calculation of the fraction remaining of the total fuel, predicting less evaporation than
actually occurred. In a similar manner, oils with low volatility (e.g. bunker C or crude oil)
314

which are not amenable to GC-MS analysis, would also not be included in the total fraction
remaining calculation, resulting in predicting more evaporation than actually occurred. In
some cases, more than 75% of the compounds in oil would not be sufficiently volatile for
GC-MS analysis [2]. Therefore, further investigation of these petroleum products are
necessary to determine how to correct the total fraction remaining for compounds not
observed in the GC-MS analysis.

However, the use of the model to predict the fraction

remaining of an individual compound is unaffected by the problem, as long as a retention
index can be determined.
Last, this model has not been applied to simple mixtures or pure liquids. For pure
liquids, evaporation proceeds linearly with time, indicating zeroth order kinetics [3, 4]. As
the mixture becomes more complex, the evaporation kinetics becomes first order. First
order kinetics arise because a compound is evaporated, the mole fraction will decrease,
resulting in a decrease in the vapor pressure, based on Raoult’s Law. However, the
methodologies developed in this work could be used to assess evaporation rate and
develop new models if necessary.
5.1.3 Future Directions
In addition to addressing the limitations discussed above, there are numerous
applications of the methodologies discussed in this work both in environmental and
forensic applications.
Additional weathering processes could be modeled using similar methodologies to
those developed in this work. Arey et al. demonstrated that aqueous solubilities and
octanol-water partition coefficients could be determined for diesel fuel hydrocarbons using

315

a column with a mid-polarity stationary phase (50% phenyl polysilphenylene-siloxane) in
two dimensional gas chromatography [5]. A model to predict dissolution of compounds
from the oil into water could be developed. The hydrocarbon compounds likely to undergo
dissolution are the small molecules such as benzene. These compounds frequently are
toxic, and determining their fate is critical in effective remediation.
The model developed in this work could have significant implications in the
analysis of fire debris. In a forensic laboratory, the detection of an accelerant in fire debris
analysis is typically performed using GC-MS. The fire debris is extracted, analyzed, and
the resulting chromatogram is compared to reference standards of known fuels [6].
Because burning also leads to the loss of volatile compounds, evaporated standards of
the fuels are also used. Typically, these evaporated standards are prepared at several
evaporation levels (e.g. 0%, 50%, 75%, 90%) by an analyst in the lab. Preparing and
analyzing a large number of standards is very time consuming.

By applying the

evaporation model, the predicted evaporated chromatogram could be determined from
the neat fuel, without the need for evaporating and analyzing the sample, saving time and
money.
Another application of this work would be for improved training for explosive
detection canines, where the vapor pressure and rate of decomposition are critical
aspects of detection. Canines use multiple volatile organic compounds released from an
explosive to locate it [7]. When developing training aids for the dogs, it is important to
have reproducible vapor-time profiles for each explosive to ensure proper training. The
vapor-time profile is related to the vapor pressure of the compounds that compose the
explosive.

However, the vapor profile is constantly changing due to environmental

316

transport [8]. Target compounds are often from similar classes, which should allow for
the development of a model, using the same methodologies applied in this work, capable
of predicting the vapor profile for new compounds and monitoring temporal changes in
the profile. This would allow for better real-time understanding of the vapors to which the
canines are exposed, leading to a better understanding canine scent training and the
development of better and more representative training aids.
5.2 Photooxidation
5.2.1 Conclusions
The photooxidation study highlighted the need for a better understanding of
photooxidation as well as the interdependence of weathering processes. Some research
suggests that photooxidation is not a significant source of weathering, however, this work
showed the formation of hundreds of oxygenated compounds after only 10 hours
irradiation of light similar to the sun and without the sensitizers that would be present in
natural waters. The new formed oxygenated products have increased toxicity and water
solubility. This poses an increased risk to sea life and humans, because the toxins are
often bioaccumulated in fish which are ingested by humans.

Visual and chemical

changes in the diesel fuel were observed, even after the first hour of irradiation, far faster
than previously believed [9].

This work highlights the critical need to understand

photooxidation because of the early onset at which these toxic compounds form.
The kinetic rate constants determined for photooxidation were useful in assessing
rates of change in comparing weathering. In the photooxidation experiments, a large
number of first-order kinetic rate constants never previously discussed in the literature,

317

were calculated for compounds quantified using gas chromatography-mass spectrometry
(GC-MS) and atmospheric pressure chemical ionization-time of flight-mass spectrometry
(APCI-ToF-MS). In the GC-MS experiment, there was an observed decrease in the
volatile compounds, as would be expected due to evaporation. However, when compared
to predicted evaporation rate constants (Chapter 3), many of the compounds decayed
nearly twice as fast as expected. While this could be explained by photooxidation for
some compounds, this phenomenon was observed for a range of compounds, including
normal alkanes, which are less reactive toward photooxidation. Therefore, the increased
rate of evaporation was likely due to the increased energy deposition from the light
source.

In the APCI-ToF-MS experiment, the rate constants for structurally related

compounds increased with greater alkyl substitution, until 4 – 8 methylene units, then
decreased. Larger PAHs, with more than 11 double bond equivalences, were shown to
not change over the 10 hours of irradiation. Kinetic rate constants provide valuable
information which allows for the comparisons of rates of change for various weathering
processes and could be useful in predictive models and determining mechanism of
reaction.
5.2.2 Limitations
The development of a predictive model for the photooxidation of petroleum is a
challenging task. Most photooxidation proceeds through sensitizers. The sensitizers in
the environment can vary greatly between locations. Moreover, the sensitizers in the fuel
can vary depending on the composition of the oil. The sensitizers can change over the
course of the spill depending on other weathering processes and remediation. Also
complicating the development of the model is the changing intensity and spectrum of the

318

light. Diurnal and seasonal variations change the intensity of the sunlight the surface film
of oil changes the intensity and the spectrum of light, complicating model development
[9]. To date, no one has developed a predictive model for photooxidation incorporating
all of these variables.
One of the major challenges in understanding photooxidation comes from the lack
of a comprehensive analytical tool for the analysis of petroleum. Prior to oxidation, many
of the compounds in oil are hydrocarbons. The smaller, more volatile compounds can be
analyzed by GC-MS, while larger less volatile compounds cannot. High resolution mass
spectrometry techniques have been applied in the analysis of petroleum, typically using
electrospray ionization (ESI) [10, 11]. Ionization, which is necessary for analysis by MS,
exhibits a dependence on the molecule being analyzed. ESI works well to ionize polar
compounds, typically those containing one or more heteroatoms, but does not ionize
hydrocarbon PAHs unless exceptional steps are taken [12]. Intermediate ionization
methods, such as atmospheric pressure chemical ionization and atmospheric pressure
photoionization ionize PAHs as well as compounds containing heteroatoms, but still do
not ionize saturated or mostly saturated hydrocarbons (normal alkanes, hopanes, etc.).
This work also demonstrated that APCI can be used to effectively ionize PAHs and the
resulting oxidized products for high resolution MS analysis. Therefore, APCI provides
ionization for a larger range of compounds and would be useful to monitor oxidative
processes (photooxidation and biodegradation) in petroleum products.
An additional limitation in this work was the lack of a chromatographic separation
prior to high resolution MS analysis. Large molecules often form a number of isomers,
which could not be differentiated by single-stage MS because they have the same

319

elemental formula and molecular mass. Plata et al. showed that two PAH structural
isomers had an approximate two-fold difference in the apparent rate constant for
photooxidation [13]. In the MS experiment performed in this work, all isomers would be
accounted for in the same mass, preventing the determination of individual rate constants.
For additional experiments, differentiation of isomers would be an important consideration
in obtaining accurate rate constants.
5.2.3 Future Directions
Very little is known about the mechanisms and processes associated with
photooxidation and experiments often lead to conflicting conclusions.

These

contradicting views arise from the highly variable experimental conditions, including
different light sources, oil samples, and environmental matrices.

Tightly regulated

laboratory experiments, where a single variable is changed, would allow for a better
understanding of the role each variable plays in photooxidation, which would be
necessary for model development.
One area that might provide particularly useful additional insight is the effect of
environmental sensitizer.

Most research agrees that indirect photolysis via

photosensitizers is occurring in oil, however, it is not clear whether the effect is only from
sensitizers in the fuel or whether sensitizers found in the environment also play a role in
photooxidation. This research has demonstrated that the photosensitizers in the diesel
fuel were sufficient to lead to photooxidation. Sensitizers, including dissolved organic
matter, nitrates, or iron could be placed into water to determine if the rate of
photooxidation is increased or if new oxygenated compounds are formed [14].

If

sensitizers in the water did not lead to increased photooxidation, future experiments and
320

models could be simplified because only the composition of the fuel would affect the
photooxidation.
Another challenge in understanding photooxidation during an environmental
release is that photooxidation and biodegradation are occurring simultaneously, so it is
difficult to separate the result of each process. Moreover, other weathering processes
including evaporation and emulsification are occurring and leading to additional confusion
in the results. Laboratory experiments of photooxidation and microbial degradation could
be conducted, where conditions are tightly controlled and affects from other weathering
processes could be minimized.

During an experiment, evaporation would be difficult to

stop, however, the evaporation model developed in this work could be utilized to account
for and even correct for evaporative losses. This would allow for experiments which
evaluated only photooxidation or microbial degradation. Once there is an understanding
of the individual compounds that are formed from each process, multiple weathering
processes could be tested simultaneously. In this work, photooxidation significantly
increased the rate of evaporation, demonstrating the interdependence of weathering.
Previous microbial degradation studies also suggest that the sunlight and the presence
of oxidized products can greatly affect the ability of microbes to breakdown the fuel also
indicating an interdependence of weathering processes [15]. By understanding individual
weathering process and the linkage between weathering processes, better fate and
transport models can be developed. Enhanced and more accurate models will provide a
better impact assessment, thus helping to guide spill response and remediation.

321

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