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Development of Surrogates for Aviation Jet Fuels
Seyed Ali Nasseri
A thesis submitted in conformity with the requirementsfor the degree of Master of Applied ScienceGraduate Department of Aerospace Studies
University of Toronto
Copyright c 2013 by Seyed Ali Nasseri
Development of Surrogates for Aviation Jet Fuels
Seyed Ali Nasseri
Master of Applied Science
Graduate Department of Aerospace Studies
University of Toronto
Surrogate fuels are mixtures of pure hydrocarbons that mimic specific properties of a real
fuel. The use of a small number of pure compounds in their formulation ensures that
chemical composition is well controlled, helping increase reproducibility of experiments
and reduce the computational cost associated with numerical modeling.
In this work, surrogate mixtures were developed for Jet A fuel based on correlations
between fuel properties (cetane number, smoke point, threshold sooting index (TSI),
density, viscosity, boiling point and freezing point) and the nuclear magnetic resonance
(NMR) spectra of the fuel as a measure of the fuels chemical composition. Comparison
of the chemical composition and target fuel properties of the surrogate fuels developed
in this work to a Jet A fuel sample and other surrogate fuels proposed in the litera-
ture revealed the superiority of these surrogate fuels in mimicking the fuel properties of
There are a number of people without whom this thesis might not have been written,
and to whom I am greatly indebted. I must first express my gratitude towards my su-
pervisor, Professor Omer L. Gulder, who trusted me with this project and provided me
with the opportunity to develop my research skills. I would also like to express my very
great appreciation to Professor Gottlieb for acting as my secondary thesis examiner and
providing detailed comments on my work.
I would like to thank the University of Toronto Institute for Aerospace Studies for pro-
viding me with a productive environment to work in. This work would not have been
possible without the support of all UTIAS staff members and professors who helped me
in my personal and professional growth during the course of my studies at UTIAS. I
would like to offer my special thanks to the student members of the combustion and
propulsion group who helped create an efficient, highly productive and collaborative re-
Finally, I want to thank my parents and siblings for instilling in me confidence and a
drive for pursuing my masters degree.
List of Figures vii
List of Tables viii
1 Motivation 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Limitations of Real Fuels for Research Applications . . . . . . . . . . . . 1
1.3 Overcoming the Limitations of Real Fuels for Research Purposes . . . . . 3
1.4 Classification of Surrogate Mixtures . . . . . . . . . . . . . . . . . . . . . 4
1.5 General Procedure for Surrogate Fuel Formulation . . . . . . . . . . . . . 5
1.6 Fuel Properties Targeted in Surrogate Fuel Formulation . . . . . . . . . . 6
1.7 A Review of Surrogate Fuel Development Activities . . . . . . . . . . . . 8
1.8 Objectives of the Current Research Work . . . . . . . . . . . . . . . . . . 10
2 Target Fuel Properties 12
2.1 Typical Aerospace Fuel Properties and Standards . . . . . . . . . . . . . 12
2.2 Properties of the Jet A Sample . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Temperature Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Properties of the Target Fuel . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Regression Analysis Procedure 17
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Regression Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.1 Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . . 18
3.2.2 Nonlinear Regression Analysis . . . . . . . . . . . . . . . . . . . . 18
3.3 Regression Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.1 Coefficient of Determination (R2 Value) . . . . . . . . . . . . . . 20
3.3.2 Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.3 Predicted Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.4 Root Mean Square Error . . . . . . . . . . . . . . . . . . . . . . . 21
4 Correlation Development for Fuel Parameters 22
4.1 Chemical Structure and Nuclear Magnetic Resonance (NMR) Spectroscopy 22
4.1.1 Chemical Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.2 Nuclear Magnetic Resonance (NMR) Spectroscopy . . . . . . . . 23
4.1.3 Identifying Chemical Characteristics of Compounds and Mixtures
Using NMR Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Cetane Number (CN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.1 Ignition Quality and the Cetane Number . . . . . . . . . . . . . . 27
4.2.2 Cetane Number Measurement . . . . . . . . . . . . . . . . . . . . 28
4.2.3 Sources of Cetane Number Data . . . . . . . . . . . . . . . . . . . 29
4.2.4 Correlations Development for Cetane Number . . . . . . . . . . . 30
4.2.5 Correlation of Cetane Number with NMR Spectrum . . . . . . . . 31
4.3 Sooting Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.2 Effect of Chemical Structure on Sooting Tendency . . . . . . . . . 35
4.3.3 Sooting Tendency Indices . . . . . . . . . . . . . . . . . . . . . . 37
4.3.4 Correlations Developed for Sooting Tendency . . . . . . . . . . . 41
4.3.5 Correlation Development Between Sooting Tendency and Proton
NMR Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Thermophysical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4.2 Density Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4.3 Boiling Point Correlations . . . . . . . . . . . . . . . . . . . . . . 50
4.4.4 Freezing Point Correlations . . . . . . . . . . . . . . . . . . . . . 53
4.4.5 Dynamic Viscosity Correlations . . . . . . . . . . . . . . . . . . . 54
5 Application of the Correlations to Jet Fuel and Its Surrogates 57
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 NMR Spectrum of Jet Fuel and Its Surrogates . . . . . . . . . . . . . . . 57
5.3 Properties of Jet Fuel and Its Surrogates . . . . . . . . . . . . . . . . . . 58
6 Surrogate Mixture Development 62
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2 Mixture Formulation Algorithm . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.1 Solution Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2.2 Algorithm Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.2.3 Definition of Different Cases . . . . . . . . . . . . . . . . . . . . . 65
6.3 Mixture Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7 Conclusion 72
List of Tables
1.1 Chemical compositions of some of the surrogate fuels proposed for jet fuel. 11
2.1 Chemical composition of Kerosene, JP-8 and Jet A. . . . . . . . . . . . . 13
2.2 Properties of aviation jet fuels cited in different sources. . . . . . . . . . . 14
2.3 Aviation jet fuel specifications and statistical data. . . . . . . . . . . . . 14
2.4 Target values for mixture properties. . . . . . . . . . . . . . . . . . . . . 16
4.1 Ranges of chemical shifts and their corresponding functional groups. . . . 26
4.2 Statistical properties of some of the correlations proposed for CN. . . . . 32
4.3 Statistical properties of the regression models developed for CN. . . . . . 33
4.4 Correlations proposed for sooting tendency indices. . . . . . . . . . . . . 41
4.5 Statistical properties of the regression models developed for smoke point. 43
4.6 Statistical properties of the regression models developed for TSI. . . . . . 45
4.7 List of some of the QSPRs proposed for thermophysical properties of interest. 48
4.8 Statistical properties of the regression models developed for density. . . . 49
4.9 Statistical properties of the regression models developed for boiling point. 51
4.10 Statistical properties of the regression models developed for freezing point. 53
4.11 Statistical properties of the regression models developed for viscosity. . . 55
5.1 NMR spectra of the Jet A sample and several jet fuel surrogates. . . . . 59
5.2 Application of the correlations to jet fuel sample and its surrogates. . . . 60
5.3 Properties of jet fuel surrogate fuels calculated using mixture rules. . . . 61
6.1 Chemical composition of jet fuel surrogates developed in this work. . . . 70
6.2 NMR spectra of the proposed aviation jet fuel surrogates and Jet A fuel. 71
6.3 Properties of Jet A and surrogate fuels developed in this work. . . . . . . 71
7.1 Chemical composition of the best surrogate fuels developed in this work. 73
A.1 Coefficients for linear correlations presented in Chapter 4. . . . . . . . . . 75
A.2 Coefficients for artificial neural network models presented in Chapter 4. . 76
List of Figures
4.1 Complete proton NMR spectrum of the Jet A fuel. . . . . . . . . . . . . 24
4.2 Cetane number regression results. . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Cetane number regression results compared to several proposed correlations. 34
4.4 Regression analysis results for smoke point. . . . . . . . . . . . . . . . . . 43
4.5 Diffusion flame TSI regression analysis results. . . . . . . . . . . . . . . . 45
4.5 Diffusion flame TSI regression analysis results. . . . . . . . . . . . . . . . 46
4.6 Comparison of diffusion flame TSI regression results to correlations pro-
posed in the literature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.7 Density regression results. . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.8 Boiling point regression analysis results. . . . . . . . . . . . . . . . . . . 52
4.9 Comparison of the ANN4 boiling point model to correlations proposed in
the literature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.10 Freezing point regression analysis results. . . . . . . . . . . . . . . . . . . 54
4.11 Dynamic viscosity regression analysis results. . . . . . . . . . . . . . . . . 56
6.1 Algorithm used for surrogate mixture formulation. . . . . . . . . . . . . . 66
6.2 Definitions of cases for surrogate mixture formulation. . . . . . . . . . . . 67
A.1 The ANN as depicted by the MATLAB documentation. . . . . . . . . . . 74
Surrogate fuels are chemical mixtures developed using pure compounds as a replacement
for real fuels for research, modeling and simulation purposes. They are blended to mimic
specific properties of the real fuel. In this chapter, methods for surrogate fuel formulation
will be reviewed and some of the results from previous research on this topic will be
1.2 Limitations of Real Fuels for Research Applica-
Understanding the detailed chemistry, combustion behavior and flow properties of con-
ventional and alternative fuels is of grave importance in the efficient utilization of these
fuels in combustion and propulsion systems. However, the chemistry of these real fuels
is extremely complicated, limiting the amount of insight that can be gained by directly
using them in combustion studies. Not only do they typically contain many different
chemical species, but their composition varies depending on the source of the crude oil
and the refining process.
Most transportation fuels are complex mixtures of thousands of hydrocarbons includ-
ing linear and branched alkanes, cycloalkanes, alkenes and aromatics [1, 2]. Additives
might also be added in low concentrations to such fuels to improve performance and fuel
stability. For instance, the main component of jet fuels is kerosene with major species
including straight chain and branched chain alkanes (35-45 % volume), cycloalkanes (30-
35% volume), aromatics (one and two ring, 20-25% volume) and alkenes (less than 5%
Chapter 1. Motivation 2
volume) . Jet fuel additives include naphtas which are added to jet fuels to improve
their performance. JP-8, one of the military variant of jet fuels, is often prepared by
splash blending from base Jet A stock at the end-user tank and includes icing inhibitors,
corrosion/lubricity enhancers, and anti-static additives.
The physical properties of a fuel (such as vapor pressure and flash point) and its com-
bustion properties (such as octane or cetane numbers and smoke point) are dependent
on the composition of the fuel. The fuel composition itself is greatly variable, depending
on manufacturer, feedstock origins, season, and economic factors that are imposed by
the refinery [1, 3, 4]. This variability in composition of the fuel is a hurdle to conducting
meaningful combustion studies using real fuels.
Fortunately, several means have been developed to overcome the problem of variable
composition and its effect on combustion studies. For some fuels, such as gasoline, refer-
ence mixtures have been developed as consensus standards which scientists and engineers
can use in their experiments. For example, a commonly used surrogate for gasoline fuels
contains iso-octane and n-heptane . The availability of such standard mixtures ensures
that all experiments are conducted using a well-understood fuel. Unfortunately, there are
no set of consensus standard mixtures for jet fuels. Reasons for this include the diversity
of testing protocols for gas turbine fuels and the unavailability of a knowledge base (such
as detailed kinetic mechanisms) for some of the components of real jet fuels.
In the past, many important trends in gas turbine combustor aerodynamics could be
established using gaseous propane as the fuel . However, the need for simulating com-
plex properties of the fuel such as emissions, flame stability and combustor durability
plus the need to improve key emerging propulsion technologies make such simple models
less robust for modern applications. Hence, more robust models need to be developed
based on mixtures of hydrocarbons.
The variable composition of fuels also affects computational modeling. Not only are real
fuels complex to model, but the models developed for one batch of fuel can not be used
for another batch due to the variability in chemical composition. Validation of such com-
putational models also requires experimental data using the real fuel.
These issues can be resolved by using standardized fuels. The use of standardized fuels
for modeling and experimentation increases experimental reproducibility and model gen-
erality. Moreover, the same standard fuel can be tested in different experimental settings,
geographical locations and using different analysis techniques.
Some might argue that standard mixtures may be developed using refinery streams.
Even if such standardized fuels are blended from refinery streams and stored for later
use, there is only a finite volume of them available, and they could chemically deteriorate
Chapter 1. Motivation 3
over time . It is practically impossible to recreate exactly the same mixture with the
same chemical composition from refinery streams. Furthermore, to reduce the need for
experimental testing and optimization of engines, acceptable modeling capability for fuels
is necessary. Due to the large number hydrocarbons in fuels from refinery streams, use of
such fuels in simulations is impractical. In addition to the change in composition of such
fuels, kinetic models for such fuels are unavailable since all the fundamental data needed
for development of such a model (e.g., chemical kinetic rate constants, reaction paths,
thermodynamic parameters) are not available and interactions between fuel components
are not well understood . The high computational cost in terms of CPU and memory
usage required for a fully detailed chemical kinetic descriptions of hydrocarbon oxidation,
tracking of hundreds of chemical species and thousands of reaction steps is an additional
factor prohibiting the use of real fuels in CFD simulations [6, 8]. Hence, reproducible
standardized fuels blended from pure compounds are the only viable way to overcome all
1.3 Overcoming the Limitations of Real Fuels for Re-
A solution to the problems outlined in the previous section is the use of surrogate fuels. It
is generally agreed in both experimental and numerical settings that the most important
traits of fuels can be effectively reproduced by simpler fuel surrogates containing a limited
number of components of high purity [1, 2, 3, 4, 6, 9, 10, 11]. This approach controls and
monitors fuel composition accurately, allowing for well-controlled fundamental modeling
and experimental studies in combustion. The smaller number of fuel components involved
means that experiments with these surrogates are more reproducible, facilitating deeper
insights into combustion processes. In addition to providing a model fuel for studying
the effect of fuel properties and chemical composition on combustor performance, the
compositional control afforded by a surrogate fuel is attractive for the development and
verification of computational codes for combustor design. Obviously, such surrogates are
not replacements for the real fuel for engine verification purposes and may only be used
for modeling and design purposes.
An inherent limitation of using surrogate mixtures is that they are often developed for
modeling specific properties of the fuel or specific combustion processes and ,hence, lack
generality. For example, a mixture developed to represent thermophysical parameters
Chapter 1. Motivation 4
might not be the best mixture to model the sooting behavior of the fuel. Moreover, large
kinetic models for surrogates might still contain thousands of species and reactions. Such
models can usually only be used for simulating simple homogeneous systems and must
be reduced for multidimensional engine applications . It has also been suggested that
properties relying on trace amounts of specific compounds might not be modeled with the
required precision by surrogate fuels. For example, thermal stability and emissions are
affected by trace amounts of polar compounds (such as sulphur containing compounds)
and metal content of the fuel  which are usually not included in surrogate fuels.
1.4 Classification of Surrogate Mixtures
Surrogate fuels can be classified either based on the properties they can model or based
on the number of components used in their formulation. Surrogate fuels are usually
classified into two groups based on the properties they model:
Physical surrogate fuels.Mixtures which are used to mimic physical properties of the fuel such as density,
viscosity and volatility.
Chemical surrogates.Such surrogate fuels are formulated to have the same chemical compositions and
average molecular mass as the fuel. Such mixtures should be composed of species
with the same chemical class as the main components of the fuel . Theoretically,
they should have chemical properties similar to the fuel under study.
The type of surrogate fuel developed and the parameters considered in creating the sur-
rogate fuel depend on its application. For instance, thermophysical properties such as
density, viscosity, thermal conductivity and specific heat are more important in heat
transfer analysis, while for analyzing phase changes and phase behavior, boiling point
and distillation curve become important. While surrogate fuels are often formulated
based on the ability of a particular mixture to reproduce specific properties of the fuel,
there is usually a desire to develop surrogate fuels that have secondary physical and
chemical properties similar to the finished fuel.
The number of components used in formulating the surrogate varies based on the appli-
cation of the surrogate. Single component surrogates have been used to analyze com-
bustion efficiency . Two-component surrogate fuels have been able to predict many
combustion properties of jet fuels. Such surrogate fuels are usually made of a long chain
Chapter 1. Motivation 5
aliphatic compound (usually n-decane or n-dodecane) and a cyclic compound (trimethyl-
benzene, propylbenzene, methylcyclohexane, decalin and 1-methylnaphthalene) . For
chemistry dependent or more detailed modeling of chemical or physical properties, more
components are added. Specific number of components have been suggested in the litera-
ture for modeling some combustion processes . The exact number of species needed to
model all aspects of combustion is not yet known ; however, most proposed surrogate
fuels have 4-14 components  and 3-10 components have been suggested to suffice for
most applications . In most cases, a compromise is reached between the degree to
which specific combustion properties are simulated and the number of components used
in the mixture.
1.5 General Procedure for Surrogate Fuel Formula-
Different procedures have been proposed for formulating surrogate fuels [10, 15, 16, 12].
Taking into account such proposed procedures, the following general steps need to be
1. Chemical analysis of the parent fuel to identify chemical composition.
2. Choosing the aspect of combustion the surrogate fuel is supposed to model.
3. Developing a methodology for surrogate fuel formulation, for example hydrogen to
carbon ratio matching.
4. Construction of a list of tentative species for use in the surrogate fuel formulation
which represent the various families of hydrocarbons available in the parent fuel.
5. Blending the components selected based on the methodology to match fuel compo-
sition (10-15 hydrocarbons maximum).
6. Comparing the physical and chemical properties of the surrogate with the parent
fuel and iterating until an acceptable degree of similarity is reached.
The fourth step above requires the creation of a database of tentative species for use in
surrogate fuel formulation. The following guidelines have been proposed to assess the
suitability of chemical species for use in surrogate fuel formulation for jet fuels [10, 15, 16]:
Chapter 1. Motivation 6
Feasibility and availability of experimental data.Chemical kinetic mechanisms should be available for the species used in the sur-
rogate fuel. Priority should be given to compounds for which the most abundant
and reliable experimental data are available.
Simplicity.Species with low number of carbons should be used. Typical guidelines are normal
alkanes with less than 12 carbons, mono-cyclic alkanes with less than 8 carbons
and simple aromatics.
Similarity.In most cases, the component should have some similarity with the fuel being
modeled in terms of target properties.
Availability and low cost.
1.6 Fuel Properties Targeted in Surrogate Fuel For-
One reason for the large variation in surrogate fuel composition is the wide variety of
jet fuel applications, and the sensitivity of these applications to mixture composition. In
order to determine the best composition for a surrogate fuel, the purpose for developing
the surrogate fuel needs to be specified first. Parameters that need to be predicted ac-
curately (target parameters) need to be identified, along with accuracy levels for each of
these parameters. Different research groups have used different parameters in developing
surrogate fuels. Such parameters have included chemical composition, distillation curve
properties, ignition quality, sooting tendency and many different thermophysical proper-
One of the primary steps in surrogate fuel development is quantifying chemical com-
position. Different measures of the chemistry of the fuel have been used in developing
surrogate fuels. Fuel properties stem from the chemistry of the fuel and strong correla-
tions have been observed between specific chemical species and properties of the fuel. For
instance, soot and other pollutant formation strongly depend on the amount of aromatic
rings and unsaturated compounds present in the fuel. As a result, many surrogate fuel
formulation procedures have some measure of chemistry as one of their target parameters.
Measures of chemical composition may include:
Chapter 1. Motivation 7
Hydrogen to carbon ratio which is a measure of the degree of saturation of the fuel.It affects local mixing phenomena in terms of the stoichiometry, flame speed, flame
temperature, and heat of combustion [2, 4, 17].
Chemical composition of the fuel measured using spectroscopic techniques.
Since the aim of developing surrogate fuels is modeling combustion phenomena, com-
bustion properties have also been used as targets in surrogate fuel formulation. These
include ignition quality which affects engine startability and operations, and sooting ten-
dency which affects engine emissions, flame propagation and combustion chamber life.
Thermophysical properties affect fluid flow and the formation of the air/fuel mixture.
Thus, they have also been used as target parameters for surrogate fuel formulation, spe-
cially for heavy fuels such as jet fuels. Thermophysical properties used for surrogate fuel
Density which affects the atomization and mixing processes in propulsion systems.It has been shown that many thermophysical properties of petroleum products (such
as specific heat capacity, latent heat of vaporization, and thermal conductivity) are
closely related to fuel density and can be accurately estimated using it. It should
be noted that density is known to be less sensitive to fuel composition .
Fuels heating value or enthalpy of combustion [1, 14].
Volatility (distillation properties, vapor pressures, or boiling point) which affectspre-combustion processes in combustion chambers  and provides valuable insight
into the performance of engines .
Viscosity  which affects pre-combustion processes in combustion chambers withshort propellant residence times and high efficiency requirements . Viscosity is
highly sensitive to both chemical composition and temperature .
Thermal stability .
Surface tension which affects fuel atomization and mixing .
Molecular mass (indirectly linked to distillation curve) [2, 17].
Diffusion coefficients .
Chapter 1. Motivation 8
Speed of sound which may be used for measuring fuel levels in aircraft fuel tanks.This property is slightly sensitive to fuel composition .
It should be emphasized that many of the targeted properties might be interrelated.
For instance, increased aromatic content in the fuel may lead to higher emissions .
Moreover, many of these properties such as density, heat release, volatility, viscosity and
thermal stability are regulated by fuel specifications.
1.7 A Review of Surrogate Fuel Development Activ-
Many surrogate fuels have been developed based on different applications and number
of components. There are currently active working groups for developing experimental
databases and surrogate models for modeling jet, diesel, and gasoline fuels. A good exam-
ple of such collaborative work is the Fuels for Advanced Combustion Engines (FACE)
Some of the previous research in this area focused on surrogate fuels with applications
in modeling jet fuel pool fires. Violi et al.  developed a surrogate fuel for pool fire
modeling by matching sooting properties and boiling point distribution of the actual fuel.
Eddings et al.  used relatively inexpensive components with known chemical kinetics
which were representative of the main classes of hydrocarbons present in jet fuels to
develop surrogate fuels with less than 10 components which matched the volatility, flash
point, sooting tendency, heat of combustion and flame characteristics of Jet A/JP-8 pool
Surrogate fuels have also been used for modeling specific combustion characteristics of
fuels. Aksit et al.  developed binary mixtures of alkanes and mono-aromatic com-
pounds to mimic the sooting propensity of kerosene and used this for detailed kinetic
modeling in CFD simulations. Hernandez et al.  developed a diesel fuel surrogate
for improving ignition modeling capability in HCCI engines by merging n-heptane and
toluene kinetic mechanisms.
Researchers have also focused on targeting specific fuel properties and using empirical
equations, mixture rules and equations of state in surrogate fuel formulation. Androulakis
et al.  developed a numerical algorithm based on integer programming that facilitates
the definition of model diesel fuels from well-characterized chemical streams while mini-
mizing the number of components. They focused on volatility range, ignition character-
istics (octane or cetane number), elemental composition (sulfur and nitrogen), molecular
Chapter 1. Motivation 9
composition (aromatics and alkenes) and vapor pressure as target properties and used
parameters such as the distillation curve, normal alkane content, iso-alkane content, one-
ring cycloalkane content, two-ring cycloalkane content, multi-ring cycloalkane content,
one-ring aromatic content, two-ring aromatic content, cetane number, threshold sooting
index (TSI) and density in their procedure. Huber et al.  used a procedure based
on experimental data for density, speed of sound, viscosity and thermal conductivity
along with an advanced distillation curve to develop surrogates for two rocket propel-
lants (RP-1 and RP-2). They also used advanced distillation curve measurements to
improve the volatility characteristics of a surrogate model to better represent thermo-
dynamic properties (density, sound speed, and boiling point) and transport properties
(thermal conductivity and viscosity) of the target fuel . In a separate work, they
used an equation of state in developing a surrogate fuel model to represent the volatility
behavior (distillation curve) of a synthetic paraffinic aviation fuel derived from biomass
. Bruno et al.  used an equation of state and a viscosity and thermal con-
ductivity surface for each pure surrogate fuel component to develop surrogate fuels for
jet fuel. Slavinskaya et al.  developed a surrogate fuel which closely matched the
boiling-point curve and two-phase diagram of Jet A and had similar physical properties.
Properties such as combustion enthalpy, formation enthalpy, molar mass, approximate
formula, sooting tendency index, critical point, chemical composition, carbon to hydro-
gen (C/H) ratio, flow reactor concentration histories, flame speeds and ignition delays
were compared in their work. Anand et al.  developed surrogate models for nine fuels
for the advanced combustion engines using computer simulations of distillation profiles.
They focused on matching specific gravity, lower heating value, hydrogen to carbon ratio
(H/C), cetane number, and cetane index of the fuels.
As fuel chemistry is inherently responsible for all other fuel properties, many researchers
have focused on matching the chemistry of the fuel using different spectroscopic tech-
niques. Natelson et al.  developed surrogates for jet and diesel fuels using three
components so that they could capture the three major hydrocarbon classes (alkane, cy-
cloalkane, and aromatic) found at significant levels in jet and diesel fuels, and maintain a
small number of components for computational modeling. Zhang et al.  developed a
surrogate fuel for JP-8 by matching its chemical composition measured using C-13 nuclear
magnetic resonance (NMR) spectroscopy. Huber et al.  developed a five component
surrogate for JP-900 using only information obtained from a gas chromatography-mass
spectrometry (GC-MS) analysis of the fuel and an advanced distillation curve.
A review of these surrogates shows that reference and model components selected to de-
fine surrogate fuels for jet fuel include normal alkanes (such as heptane, decane, dodecane,
Chapter 1. Motivation 10
tetradecane and hexadecane), branched alkanes (such as isooctane and isocetane), cy-
cloalkanes (such as methylcyclohexane), aromatics (such as toluene, xylenes and methyl-
naphthalene), multi-ring compounds (such as tetralin and Decalin), and alkenes (such as
A list of some of the Jet A and JP-8 surrogate fuels, for which data relevant to this
project was available, is summarized in Table 1.1. These surrogates will be analyzed
later in this work. It should be noted that some of the promising surrogate fuels such as
those proposed in reference  were not included in Table 1.1 due to unavailability of
NMR spectra for their components.
1.8 Objectives of the Current Research Work
After analyzing the target parameters used by different research groups, the following
parameters were chosen as target parameters which should be mimicked by the surrogate
fuel developed in this research project:
Thermophysical properties including density, dynamic viscosity, initial boiling point,maximum freezing point.
Sooting tendency (through smoke point or other sooting tendency indices).
Ignition quality (represented by cetane number).
Chemical composition as measured through proton NMR spectra with hydrogen tocarbon ratio (H/C) and molecular mass as auxiliary parameters.
Obviously, such a surrogate fuel will be classified as both physical and chemical. The aim
of this work was to use the minimum number of compounds possible to formulate the
surrogate fuel. Due to the dependance of all fuel properties on the chemical composition
of the fuel, correlations were developed between the chemical composition of the fuel
and its thermophysical properties, sooting tendency and ignition quality parameters.
This simplifies the mixture analysis as it transforms the mixture formulation into a
mathematical problem and makes chemical composition the only fuel parameter included
in mixture formulation.
Chapter 1. Motivation 11
Table 1.1: Chemical compositions of some of the surrogate fuels proposed for jet fuel.
Name Target Fuel Component Type Vol. % Ref.
1 Modified Aachen Surrogate Jet A/JP-8n-dodecane Normal Alkane 80
1,2,4-trimethylbenzene Aromatic 20
2 Aksit Kerosenen-decane Normal Alkane 70
propylbenzene Aromatic 30
3 Eddings JP-8
n-octane Normal Alkane 3.5
n-dodecane Normal Alkane 40n-hexadecane Normal Alkane 5
decalin Cycloalkane 35xylenes Aromatic 8.5tetralin Aromatic 8
4 Aachen Surrogate Kerosenen-decane Normal Alkane 80
1,2,4-trimethylbenzene Aromatic 20
5 Slavinskaya Jet A
n-dodecane Normal Alkane 20
n-hexadecane Normal Alkane 32
iso-octane Branched alkane 13propylcyclohexane Cycloalkane 10
1-methylnaphtalene Aromatic 25
6 Violi JP-8
n-dodecane Normal Alkane 30
n-tetradecane Normal Alkane 20isooctane Branched alkane 10
methylcyclohexane Cycloalkane 20m-xylene Aromatic 15tetralin Aromatic 5
7 Drexel S-5 JP-8
n-dodecane Normal Alkane 26
[26, 27]iso-cetane Branched alkane 36
methylcyclohexane Cycloalkane 14decalin Cycloalkane 6
-methylnaphthalene Aromatic 18
8 Schultz JP-8
n-octane Normal Alkane 15
n-dodecane Normal Alkane 20n-tetradecane Normal Alkane 15n-hexadecane Normal Alkane 10
iso-octane Branched alkane 5methylcylcohexane Cycloalkane 5
cyclooctane Cycloalkane 5xylene Aromatic 5
butylbenzene Aromatic 5tetramethylbenzene Aromatic 5-methylnaphthalene Aromatic 5
tetralin Aromatic 5
9 Montgomery JP-8
n-octane Normal Alkane 22.6
n-dodecane Normal Alkane 34.7
methylcyclohexane Cycloalkane 16.7butylbenzene Aromatic 16
10 Humer JP-8n-dodecane Normal Alkane 60
methylcyclohexane Cycloalkane 20xylene Aromatic 20
11 JP-8 surrogate (TSI = 22) JP-8n-dodecane Normal Alkane 54
[31, 32]iso-octane Branched Alkane 181,3,5-trimethylbenzene Aromatic 28
12 Kahandawala JP-8n-heptane Normal Alkane 80
toluene Aromatic 20
Target Fuel Properties
As mentioned in Chapter 1, target values need to be identified for the target fuel parame-
ters to initiate choosing fuel components and formulating mixtures which mimic the fuel.
It is reasonable to use the assumption of an average fuel in surrogate mixture formulation
. In this chapter, the properties of aviation jet fuel are summarized based on statis-
tical fuel data and data sheets of a Jet A fuel sample available at the Combustion and
Propulsion Group. This information is used to reach target values for fuel properties.
2.1 Typical Aerospace Fuel Properties and Standards
There are several propellants currently in use by the aerospace industry. These include
Jet A (Jet A-1 in Europe), JP-8 (military equivalent of Jet A with an additive package),
Jet B (enhanced cold-weather performance) and RP-1. Recently, several new fuels such
as JP-800, JP-900, Si-3 and S-8 have also been developed. All these fuels are composed
of hundreds of aliphatic and aromatic hydrocarbons. The main component of aviation
jet fuels is kerosene .
Aviation turbine fuels are not defined by composition, molecular structure, or purity.
Instead, their characteristics are limited by boundary conditions imposed based on fun-
damental or empirical inspection tests based on solutions to past engine or aircraft prob-
lems . The individual properties of the fuel can be divided rather arbitrarily into bulk
and trace properties [34, 35]. Bulk properties are those that are affected by significant
compositional changes (more than 5% by volume of the total fuel). Trace properties tend
to respond to changes less than 1% by volume or even 1 ppm or less. Energy content,
combustion characteristics, distillation range, density and fluidity depend on bulk fuel
composition while lubricity, stability, corrosivity, cleanliness and electric conductivity
depend on trace amounts of species. Based on this definition, the properties of our in-
Chapter 2. Target Fuel Properties 13
Table 2.1: Chemical composition of Kerosene, JP-8 and Jet A (values are volumetricpercentages).
Hydrocarbon Type Kerosene  Kerosene Jet A (World
survey average)[7, 13]
Straight Chain andBranched Chain
Alkanes35-45 50-65 58.78 60 60
Cycloalkanes 30-35 20-30 21.22 20 20Aromatics 20-25 10-20 19.94 18 15-20Alkenes 0-5 - 0.06 2 -
terest are bulk properties and the compositional accuracy of our interest is about 5% by
Aviation jet fuels are kerosene fuels, with a typical boiling range of 160-260 C. Aviation
jet fuel specifications (Jet A, Jet A-1, JP-8) control the 10% point of the distillation
(< 205C) and the final boiling point (< 300C) . JP-8 is Jet A fuel mixed with a
military additive package that includes an icing inhibitor (1000-1500 ppm), corrosion in-
hibitor/ lubricity enhancer (20 ppm), and a static dissipater additive (5 ppm) . Based
on Table 6.1 which shows the typical compositions of Kerosene, Jet A, Jet A-1 and JP-8
fuels, the assumption of an average jet fuel seems to be reasonable for surrogate mixtures
developed in this work as compositional changes seem to be less than 5% by volume.
Gas chromatography reveals that JP-8 components have 5-35 carbons . The n-
paraffins typically range from n-octane (n-C8) to n-hexadecane (n-C16), with maximum
concentrations from n-decane (n-C10) to n-dodecane (n-C12). These criteria can be used
in assessing chemical similarity of surrogate mixtures to aviation jet fuels and in choosing
suitable components for surrogate mixtures.
Some of the cited properties of aviation jet fuel for different samples are summarized in
Table 2.2. Evidently, the small compositional changes mentioned earlier lead to large
variations in jet fuel properties. Aviation jet fuel specifications also impose limits on
several properties of the fuel. Unfortunately, the specifications can vary and depend on
the country where the fuel is produces or used. Table 2.3 summarizes civil aviation jet
fuel specifications for the US fuel manufacturers and an international checklist, along
with statistical data of Jet A samples from around the world. The international checklist
was developed to facilitate airport operations and takes into account requirements by
different agencies. Hence, it is a reasonable alternative to aviation jet fuel specifications.
It should be note that Canada uses Jet A-1 as specified in the CAN/CGSB-3.23 specifi-
cation , which has properties similar to other Jet A-1s. Test methods which are used
Chapter 2. Target Fuel Properties 14
Table 2.2: Properties of aviation jet fuels cited in different sources.
Parameter JP-8  JP-8  JP-8  Jet A/A-1 Jet A  Kerosene 
(average 1.9)1.91 1.92 1.91 1.9 1.9-2.1 (C9-C13)
MW (g/mol) 153 153 152 153 162 175 Density (kg/m3) 804 797 - - - 770-830
Aromatic Content (vol%) 20 - - - - 10-20
(average 44)45 - - - -
Threshold Soot Index (TSI)16-26
- - - - -
Average Formula C11H21 C11H21 C10.9H20.9 C11H21 C11.6H22 -Boiling Point (C) - 165-265 Average 204 170-300 Average 216 140-280
Maximum Freezing Point (C) - -51 --40 (Jet A),
-47 (Jet A-1)- -
Kinematic Viscosity (cSt) - 1.2 @ 40 C - - - 1.8 @ 15C 
Table 2.3: Aviation jet fuel specifications and statistical data.
Specifications [26, 34, 35, 38] Statistical Data Country United States International International Jet A Samples
Designation Jet A Jet A-1 Jet A
Specification ASTM D 1655International
ChecklistMin Max Mean Wt Mean
Aromatics (vol%), max 25 22 14.8 21.9 19.15 18.73Naphthalenes (vol%), max 3 1 2.73 2.15 1.9
Sulfur (mass%), max 0.3 0.0545 0.14 0.1142 0.1011Initial Boiling Point (C) Report Not ReportedFinal Boiling Point (C) 300 263.3 279.3 274.5 270Density (kg/m3), 15 C 775-840 775-830 811.9 816.6 815.6 815.9
Freezing Point (C), max 40 -47 -51 -44.8 -48.3 -47.4Kinematic Viscosity
(mm2/sec), max at 20 C8 4.1 5.916 4.53 4.34
Net Heat of combustion(MJ/kg), min
42.8 43.09 43.13 43.11 43.11
Smoke point (mm), min 18 20 19 22 20.8 19.92
in defining the requirements in Table 2.2 are outlined in references [35, 38]. Note that,
based on the statistical data summarized in Table 2.3, sometimes the fuels do not abide
to all specifications.
2.2 Properties of the Jet A Sample
A Jet A sample was acquired by the Combustion and Propulsion Group at UTIAS for
use in this work. Chemical composition of the target fuel is based on the properties of
this fuel, which will be outlined in Chapter 4. Information about other properties of the
Chapter 2. Target Fuel Properties 15
sample was acquired through the sample information sheet (Appendix A in ). This
sample had an initial boiling point of 161.5 C, a maximum freezing point of -54.5 C and
a density of 804.8 kg/m3 at 15 C. These are experimentally evaluated values that can
be used in the mixture analysis as properties of the target fuel. Unfortunately, the data
did not include molecular mass, viscosity, cetane number and sooting data of the sample.
All these parameters need to be determined prior to surrogate mixture formulation. The
correlations developed in Chapter 4 will be used for evaluation of the properties not
determined by the fuel data sheet.
2.3 Temperature Corrections
The density and dynamic viscosities used for correlation development in Chapter 4 were
evaluated at 298.15 K. Hence, the density and dynamic viscosity of aviation jet fuel had
to be corrected for temperature. The following correction is suggested for correcting
density for temperature changes over small temperature ranges :
1 + (T T0)(2.1)
Where 0 is the reference density at the reference temperature T0 and is the volumetric
temperature coefficients which has a value of 9.9 104 1/K for aviation jet fuel .The following equation was used for correcting dynamic viscosities :
ln() = A +B
The values of the constants A and B were evaluated based on aviation jet fuel viscosity
measurement data from reference  to be - 8.45 cP and 2489.9 cP/K respectively for
Jet A fuel.
2.4 Properties of the Target Fuel
Based on the properties of most aviation jet fuel samples outlined in this chapter, values
for target fuel properties were chosen, as summarized in Table 2.4. The target values
are used for matching surrogate fuel properties to the real fuel, while the target ranges
are used as constraints in developing surrogate mixtures and for validating correlations.
These target fuel properties are used alongside the proton NMR spectrum of the sample
(outlined in Chapter 4) for surrogate mixture formulation in Chapter 6. All temperature
Chapter 2. Target Fuel Properties 16
Table 2.4: Target values for mixture properties (Correlations used in this table are pre-sented in Chapter 4.).
Property Target Value Source Target Range SourceCetane Number 45 Correlations 32-57 JP-8 
Smoke Point (mm) 21 Jet A > 18 ASTM D 1655Diffusion Flame Threshold
Sooting Index (TSI)26 Correlations 16-26 JP-8 
Density (kg/L) 0.7969 Sample properties  0.7827-0.8483 Kerosene Boiling Point (K) 434 Sample properties  413-443 Table 2.2
Maximum Freezing Point (K) 218.65 Sample properties  215-233.15 Jet A and JP-8 Dynamic Viscosity(cP) 1.6 Correlations < 6.5 ASTM D1655Molecular Mass (g/mol) 153 JP-8 [26, 39] 153-175 Table 2.2
H/C 1.9 JP-8 and Jet A [36, 39] 1.84-2.1 JP-8 
dependent properties were evaluated at a temperature of 298.15 K. It should be noted
that the cetane number, threshold sooting index (TSI) and viscosity of the sample were
determined using correlations which will be presented in Chapter 4. In the case of the
smoke point, the value calculated using these correlations was outside the range of typical
values for aviation jet fuels and has not been used in the target fuel properties. The initial
boiling point of the jet fuel was used since correlations developed in Chapter 4 only apply
to initial boiling points and can not assess other boiling point values.
Regression Analysis Procedure
As mentioned in the previous chapter, it has been well established that all fuel properties
are a function of the chemical composition, degree of saturation (as identified using the
H/C ratio) and molecular mass . Hence, it is possible to correlate the NMR spectra
of compounds with their physical or chemical properties. In this chapter, some of the
essential knowledge for regressions analysis is presented, which will be used in the next
chapter for developing and assessing correlations.
3.2 Regression Analysis Methods
The performance of a regression method depends on the application, the availability
of data and the availability of knowledge regarding the final mathematical form of the
regression equation. In order to find the best methods to be used in our analysis, many of
the regression analysis methods available in commercial statistical software were applied
to the data sets developed for this project. Although the regression analysis could be
applied to data that have NMR spectra similar to the jet fuel (as has been done in
the case of diesel fuel ), data points outside those ranges were also included so that
the regression equations developed were general and could be used for different types of
compounds. This will help use these results in analyzing compounds and mixtures where
there are small shifts which are not found in a jet fuel. A drawback of this approach is
the larger root mean square error (RMSE) values.
Chapter 3. Regression Analysis Procedure 18
3.2.1 Multiple Linear Regression
Multiple linear regression (MLR) analysis was performed using different types of Ordinary
Least Squares (OLS) methods. The best results were obtained using the High Precision
OLS (HP OLS) algorithm implemented in the GRETL software package . Hence,
this specific package was chosen for developing MLRs. Overall, MLR results were less
accurate compared to nonlinear models and are only reported for comparison.
3.2.2 Nonlinear Regression Analysis
Nonlinear Least Squares Method
The least squares solver minimizes the sum squared error, but requires the mathematical
form of the regression equation as an input. This solver was used on the data sets using
different mathematical forms. Polynomials were fitted to the data using RAPIDMINER
 and MATLABs curve fitting tool . Custom models were also developed using
MATLAB based on the variation of the target property with different predictor param-
eters. Using the screening function in the JMP software package , models based on
complex predictors formed from mathematical manipulation of initial predictor param-
eters were developed and assessed. Due to the fact that the nonlinear equations had to
be supplied to the algorithm, the results did not achieve high enough R-squared values
when compared to other options such as ANNs (as outlined in the next section). Hence,
nonlinear least squares results will not be presented in this work.
Artificial Neural Network (ANN) Models
It has been suggested that when the nonlinear relationship between the target property
and regression parameters is not known, artificial neural networks are the best choice for
creating accurate regression models . The ANN simply minimizes the mean squared
error by changing the internal parameters of the mathematical transfer function defined
for the neurons forming the artificial neural network. This internal transfer function can
be thought of as a transformation of the data. After fitting, the ANNs internal transfer
function may be used as a regression equation.
The ANNs used for fitting are usually made of a hidden layer and an output layer. Several
functions can be used as the transfer function for the neurons. The standard ANN fitting
tool implemented in MATLAB uses a set of nonlinear neurons with a hyperbolic tangent
transfer function whose outputs are transformed by a linear transfer function to create
the final output of the network. In other words, the results will be a linear combination
Chapter 3. Regression Analysis Procedure 19
of several hyperbolic tangent functions. The algorithm finds values for the weights and
biases applied to the inputs of each neuron and the outputs of the hidden layer.
By default, the MATLAB ANN fitting algorithm breaks down the data set into three
distinct sets in a random manner. One set is the training set, which is used in developing
the regression equation. The two other sets, called the verification set and the test set
are used to check for over-fitting. ANNs are prone to over-fitting the data and using
separate parts of the data for verification and testing purposes helps reduce the chance
of overfitting occurring. Although there are other methods by which to break the data
set down into three separate sets, this random approach reduces the bias. In all cases ran
during this work, 80% of the data was used as the training set, 10% as the verification set
and 10% as the test set. The algorithm automatically outputs the R-value (correlation
coefficient) for the regression in each set. The best regressions reach higher R-values,
near 1. The approach chosen in this project was to check the R-value in the three sets so
that they were within comparable ranges of each other (usually 0.1). The number ofhidden neurons was changed from 1 to the maximum possible and all regression results
that fitted this requirement were saved. The best regression was chosen from the set of
saved regression results based on comparison of total R-squared and RMSE values.
The number of coefficients in the model was calculated using:
ncoefficients = (npredictors + 3)nhidden + 1 (3.1)
In which ncoefficients is the number of coefficients in the model, npredictors is the number of
predictor parameters used and nhidden is the number of hidden neurons used in the model.
ncoefficients is important in assessing the model, as it should not exceed the number of
experimental data points available in the training set. The number of maximum hidden
neurons was calculated using equation 3.1 and the regressions were developed starting
with 1 hidden neuron and reaching the maximum number of hidden neurons. Due to
the random nature of breaking down the data set into three sets and the optimization
procedure, the results of consecutive regression analysis are different. The algorithm was
run many times (at least 20 times for each number of hidden neurons), so that the best
reliable results were achieved. The outputs of the regression analysis using the MATLAB
ANN fitting tool have the following mathematical form (using matrix notation):
f(Xk1) = W1n tanh(wnkXk1 + bn1) +B (3.2)
Where k is the number of predictor parameters (inputs), n is the number of neurons
used by the ANN, w is the input layer weight, b is the input bias, W is the hidden
Chapter 3. Regression Analysis Procedure 20
layer weight and B is the hidden layer bias. The ANN fitting tool in MATLAB requires
the number of hidden neurons to be input by the operator. In the IBM SPSS package
, this parameter is automatically tuned. Moreover, this software package uses other
transfer functions such as hyperbolic sine for both the hidden and output layers. Using
different transfer functions (as tested with the software packages STATISTICA  and
IBM SPSS) proved no major improvements in the results compared to the MATLAB
standard model. As a result, only the results from the standard model in MATLAB are
reported in Chapter 4.
3.3 Regression Diagnostics
There are no generic criteria for assessing regression results as such criteria generally
depend on the specific algorithm. The main criteria for choosing regression models in
this work were the highest R2 value and the lowest Root Mean Square Error (RMSE).
Regression equations developed using ANNs might over fit the data, as mentioned earlier.
Although precautionary measures were taken to prevent this, there was no way to make
sure over fitting did not occur. Some of the diagnostic measures used in this project are
summarized in the next subsections. There are also many other statistical parameters for
assessing regression models; however, as such measures are not common among engineers,
they were not used in this work.
3.3.1 Coefficient of Determination (R2 Value)
This regression diagnostic parameter is mainly used in assessing least squares results as
they focus on minimizing the errors used in calculating this parameter. It can also be
used to compare results obtained using ANNs, but should be used with caution when
comparing different methods (linear models to artificial neural networks). As the R or
R2 increases towards one, the regression results become more reliable. However, there
is no specific threshold that marks an acceptable regression result. In most cases, an R
value of 0.9 and higher is considered acceptable for ANN analysis and an R2 value of
more than 0.9 for linear regression analysis. The results reported here have the highest
attainable R2 values. The R2 values attained are compared to values published in the
literature to ease assessing the regression results.
Chapter 3. Regression Analysis Procedure 21
The least squares method requires that the residuals (difference between the predicted
values and actual values) form a normal distribution around zero. As a result, the average
of the residuals should be near zero and the standard deviation of the residuals should
be preferably within the error range of the experimental method. This requirement is
generally accepted for other regression methods as well. The histogram of the residuals
or a Normal Quartile Quartile plot (qqplot) can be used to check for normality.
The residuals should also be independent of the predicted and predictor values. To
check this, residuals can be plotted against the predictor, expected and predicted values.
The plot should show no special geometric feature. All the MLR results presented in
this report were checked for these requirements. For the ANNs, more than 50% of the
residuals were normal, the rest being at the lower range of the spectrum (helping reduce
the total RMSE value). As ANN regression does not require that residuals be normally
distributed, this aspect will not affect the result. In this case, only the mean and standard
deviations were checked.
3.3.3 Predicted Results
The mean and standard deviation of predicted values and the actual sample should be
the same. This is equivalent to the mean of the residuals being negligible. The plot of
predicted versus actual results was also used to assess the regression results, as it is the
best method of assessing the fitness of the regression model.
3.3.4 Root Mean Square Error
The root mean square error shows the general level of error seen when using a regression
equation. If the regression results met all other requirements, the most accurate regres-
sion model (the one with the lowest RMSE) was chosen. It should be noted that ANNs
all had lower RMSE values compared to their linear counterparts.
RMSE values depend on the units used. It is common practice to normalize these values
by the average experimental value of the parameter being predicted in the data set or
the difference between the maximum and minimum values in the data set. In this work,
normalization with respect to the latter will be used.
Correlation Development for Fuel
4.1 Chemical Structure and Nuclear Magnetic Res-
onance (NMR) Spectroscopy
4.1.1 Chemical Structure
Physical and chemical properties of a compound arise due to its chemical structure. Many
different parameters can be used to account for the chemical structure of a compound or
The type of atoms the molecule is made of and their relative numbers such ascarbon to hydrogen or oxygen to nitrogen ratios.
Bonding and bond strength.
Composition of mixtures as reported through mass percentage, volume percentageor molar percentage.
Many methods have been used to quantify the chemical structure of compounds and mix-
tures. These include gas chromatography-mass spectrometry (GC-MS), nuclear magnetic
resonance (NMR) spectroscopy, liquid chromatography (LC) and infrared (IR) spec-
troscopy. Each of these methods reveals pieces of information about the chemical struc-
ture and environment of the compound or mixture. In this work, proton nuclear magnetic
resonance(NMR) spectroscopy is used as a measure of the chemical structure of the fuel.
This method reveals many details about the chemical structure and environment of a
Chapter 4. Correlation Development for Fuel Parameters 23
mixture. Moreover, facilities for measuring the NMR spectra of compounds are available
at the University of Toronto.
4.1.2 Nuclear Magnetic Resonance (NMR) Spectroscopy
One of the most powerful methods for predicting the structure of hydrocarbons is nuclear
magnetic resonance (NMR) spectroscopy . NMR spectroscopy is based on the inher-
ent magnetic properties of the nucleus of different atoms. Magnetic nuclei are stimulated
by a magnetic field and their response in terms of the resonance frequency of the emitted
electromagnetic radiation is measured. Usually the frequency is Fourier transformed and
reported as a shift relative to a standard (tetramethylsilane (TMS) is usually assigned a
chemical shift of zero as the standard). A solvent is usually used in preparing mixtures
for the analysis and it slightly affects the chemical shifts observed. All isotopes that
contain an odd number of protons and neutrons have a nonzero spin and are possible
targets for NMR spectroscopy. In hydrocarbons, H-1 (proton) and C-13 can be used.
Specific ranges of chemical shifts have been correlated with specific functional groups in
chemical compounds. The spectrum output of NMR spectroscopy reveals the following
information about a compound:
The different types of chemical environments present in the molecule as identifiedby the different shift values.
The relative numbers of the nuclei in each environment as identified by the areaunder each shift.
The electronic environment of the different types of nuclei as identified by thelocation of the shift (up field or down field) in the shift range.
The number of neighbors each nuclei has as identified by the splitting of the shifts.
4.1.3 Identifying Chemical Characteristics of Compounds and
Mixtures Using NMR Spectra
A Jet A sample from the combustion and propulsion group was analyzed by the NMR
services at the University of Toronto. The result of this analysis is depicted in Figure
4.1. The NMR test sample was prepared at the University of Toronto NMR facilities by
mixing equal parts of Jet A and CDCl3 (400 L of each). The sample was placed in a 5
mm 8 inch tube for one dimensional proton NMR acquisition using a Bruker Avance
Chapter 4. Correlation Development for Fuel Parameters 24
III 400 spectrometer. The spectrum was acquired at 25 C over a 6410.3 Hz (16 ppm)
spectral window with a 1 s recycle delay.
0 1 2 3 4 5 6 7 8
(ppm)Figure 4.1: Complete proton NMR spectrum of the Jet A fuel from the combustion andpropulsion group. The horizontal axis shows the chemical shift and the vertical axis theintensity of each peak.
To use the information from the NMR spectrum, the spectrum was discretized into
several regions, each corresponding to a specific chemical environment. These regions
are summarized in Table 4.1. These proton NMR shift ranges were developed based
consensuses on the ranges of chemical shifts that correspond to different functional groups
[55, 56, 57, 58, 59, 60] and the Jet A NMR spectrum. In the following chapters, each
chemical range shift will be denoted using the letter P and a number corresponding
to the number assigned to each range in Table 4.1. It should be noted that, as most
CH3 shifts had a chemical shift less than 1 and most CH and CH2 shifts above 1, the
Chapter 4. Correlation Development for Fuel Parameters 25
general chemical shift group identified in most references as 0.5-1.6 was broken into two
categories. Moreover, this corresponded well to the two shifts seen in the Jet A NMR
spectrum between 0.5-1.6.
In breaking down the shift ranges, functional groups which are not found in the Jet A
were also taken into account. This was mainly due to the fact that databases used for
correlation development might have included compounds with similar shifts. Moreover,
although these groups are not found in aviation jet fuel, other functional groups can have
similar chemical shift values. It should also be noted that the NMR shift ranges outlined
in Table 4.1 are the most detailed version used in this work. Whenever possible, ranges
with similar group functionalities (overlapping functional groups) were lumped together
to simplify the regression analysis.
As mentioned earlier, the height of each shift shows the number of hydrogens contributing
to that shift. As a result, the area under two regions of the NMR spectrum can be used
to compare the relative number of protons in the two group functionality. As the area
under the curve is arbitrary, normalization of all area calculations will lead to values that
can be compared between different spectra.
AP1 + AP2 + AP3 + ...+ APn = 1 (4.1)
Where A denotes the area under the range of chemical shifts corresponding to the sub-
script, as outlines in Table 4.1. Values normalized in this way show the percentage of
protons in each range of chemical shifts, which can be used as a measure of chemical
Chapter 4. Correlation Development for Fuel Parameters 26
Table 4.1: Ranges of chemical shifts and their corresponding functional groups [55, 56,57, 58, 59, 60].
Min. Max. Proton Environments
1 0 1 Methyl (CH3), Tert-butyl ((CH3)3)2 1 1.6 Alkanes, CH2 , Amino (R NH2)
3 1.6 2Allylic (CH2 = CHCH2), benzylic (C6H5CH2),Hydroxylic, amino (R NH2), Alcohol, Amine
4 2 2.2
Benzylic (Ar-C-H), Acetylenic (C C H), Esters(HC-COOR), Acids(HC-COOH), carbonyl compounds
(HC C = O), iodides (HC-I), bromides (HC-Br),hydroxylic (ROH), amino (R NH2)
5 2.2 2.7
Benzylic (Ar-C-H), Acetylenic (C C H),Acids(HC-COOH), carbonyl compounds
(HC C = O), iodides (HC-I), bromides (HC-Br),hydroxylic (R-OH), amino (R NH2)
6 2.7 3Benzylic (Ar-C-H), Acetylenic (C C H ), iodides(HC-I), bromides (HC-Br), hydroxylic (R-OH), amino
7 3 3.5Iodides (HC-I), bromides (HC-Br), chlorides(HC-Cl),
Ethers (HC-OR), hydroxylic (R-OH), amino (R NH2)
8 3.5 4Alcohols (HC-OH), Ethers (HC-OR ), hydroxylic
(R-OH), amino (R NH2)
9 4 4.5
Fluorides (HC-F), iodides (HC-I), bromides (HC-Br),chlorides(HC-Cl), hydroxylic (R-OH), Ethers
(HC-OR), Alcohols (HC-OH), esters(R-COO-CH),phenolic(Ar-OH), amino (R NH2)
10 4.5 6Alkene, phenolic(Ar-OH), vinylic(C = C H),
Aromatic (Ar-H), amino (R NH2)
11 6 6.5Alkene, phenolic(Ar-OH), Aromatic (Ar-H), amino
(R NH2)12 6.5 8.5 Aromatic (Ar-H)13 8.5 10.5 Aldehydic (R-CHO)14 10.5 13 Carboxylic (R-COOH)15 13 15 -16 15 17 Enolic (C = C OH)
Chapter 4. Correlation Development for Fuel Parameters 27
4.2 Cetane Number (CN)
4.2.1 Ignition Quality and the Cetane Number
As mentioned in Chapter 1, ignition quality was chosen as one of the fuel properties
modeled using the surrogate fuel. Ignition quality is determined from the ignition pro-
cess. The injected fuel in an engine is first evaporated, leading to the physical delay in
ignition. Factors affecting evaporation include fuel properties (density, viscosity, surface
tension, specific heat, enthalpy of vaporization, vapor pressure, vapor diffusivity), air
properties (temperature, density, velocity and turbulence) and spray properties (atom-
ization, penetration and shape) . For ignition to occur, the fuel should be heated so
that radicals form which can initiate the oxidation process. The rate of radical formation
is responsible for the chemical delay in ignition. Ignition will only be initiated when a
specific amount of radicals have formed.
The efficiency of the complete ignition process is quantified using the cetane number.
The cetane number (CN) is a measure of the ignition quality of diesel fuels. It is used
to quantify the ignition quality of middle distillates in diesel engines by measuring their
self-ignition delay, the time between injection and combustion . It takes into account
all delay effects such as spray formation, heating, vaporization, mixing and chemical
induction times . Of course, ignition delay is also dependant on engine type and op-
erating conditions. In the absence of a parameter to quantify ignition quality of jet fuel,
cetane number has been used extensively with jet fuels as a measure of ignition quality
due to the the similarities between jet and diesel fuels.
Cetane number is generally dependent on the chemical composition of the fuel and can
affect engine startability, noise level and exhaust emissions . Fuels with low cetane
numbers generally lead to hard starting, tough operation, more noise and higher emis-
sions of particulate matter and NOx . Particulate emissions is less affected by cetane
number compared to NOx formation [51, 66, 67, 68]. Cetane number has an inverse re-
lationship with octane number (ON), meaning a compound with a higher ON typically
has a lower CN .
The first proposed rating scheme for ignition quality was the cetene (ketene) rating.
Since cetene was hard to prepare, the higher reference value was later replaced with n-
hexadecane (cetane, hence the name change to cetane number) with a cetane number of
100. The lower reference was changed to 2,2,4,4,6,8,8- heptamethylnonane, assigned a
cetane number of 15. It has been suggested that cetane number of a mixture has a linear
relationship with the cetane number of its components, although this is not always true
Chapter 4. Correlation Development for Fuel Parameters 28
Empirical equations used for predicting cetane number are called cetane indices (CIs)
[70, 71, 72]. For convenience, most refineries rely on ASTM approved CIs which are
non-engine predictive equations for cetane number. Such indices are updated based on
the crude properties and composition. They generally relate to the mid-boiling point of
the fuel and the API gravity . Many of the CIs can not be used with fuels contain-
ing cetane number improvers and are not applicable to vegetable oils, diesel fuel blends
containing alcohols, synthetic fuels derived from oil sands or oil shales .
The cetane number of a compound depends on its molecular structure . Based on
experimental data, it has been deduced that normal alkanes have higher cetane numbers
than branched alkanes. Cyclo-alkanes and aromatics generally reduce cetane number,
unless they have an n-alkane group attached [63, 67]. A linear relationship between the
chain length and CN for compounds with 8-16 carbon atoms has been proposed for dif-
ferent classes of hydrocarbons [68, 73]. This shows that one of the primary factors in CN
determination is carbon chain length. Another suggested factor is the ratio of primary
to secondary C-H bonds in a molecule .
4.2.2 Cetane Number Measurement
The most accepted methods for measuring CN are the ASTM D613 (engine test) 
and the ASTM D6890 (IQT measurements) . Overall, it has been suggested in the
literature that due to the simplicity of IQT tests and its higher accuracy and reproducibil-
ity, this test should replace the engine test. Unfortunately, only a few pure compounds
have been tested using the IQT procedure which reduces the usefulness of these data.
Of course, there have also been many alternative experimental methods developed for
measuring CN or ignition delay, such as the combustion bomb experiment . Such
methods have not been widely used.
ASTM D613 is the more prominent standard for CN measurement. It is based on the
measurement of the ignition delay in a standard CFR test engine built by the Waukesha
company . Other standardization agencies have similar tests with engines manufac-
tured by the country of origin of the standard. This method has several limitations. It
requires a large volume of fuel sample of high purity (about 1 L), takes typically long to
test (approximately a few hours) and has a high reproducibility error (3-5 CN numbers)
[63, 61, 77] (Note that the ASTM standard cites a reproducibility error of 0.8 .).
Despite all its flaws, ASTM D613 measurements and test facilities are widely available.
Chapter 4. Correlation Development for Fuel Parameters 29
Ignition Quality Tester (IQT)
IQT is an alternative method developed by Southwest Research Institute (SwRI). It
requires a Constant Volume Combustion Apparatus (CVCA) which is developed by Ad-
vanced Engine Technology Ltd. This method measures the ignition delay which is corre-
lated with the cetane number. Details of this method are available in references [79, 80].
CN measured using this method is called the derived cetane cumber (DCN). IQT mea-
surements require a smaller sample volume (less than 50 mL , although 100 ml has
also been cited as the sample size .) and a much shorter time (less than 10 min).
This testing method operates based on the ASTM D6890 standard  and has a repro-
ductivity error of 1 to 2 cetane numbers . It has been mainly used for measurements
of CN of middle distillates and alternative fuels. Despite the availability of test facilities,
reported values of IQT measurements are rare compared to the ASTM D613 method.
4.2.3 Sources of Cetane Number Data
In order to develop correlations between CN and fuel chemistry, a CN database was
developed. Most CN data for this database were acquired from reference . These
data were measured or calculated using the following methods:
Cetene rating.As previously mentioned, cetene ratings had been used before the CN rating was
established. Cetene ratings can be transformed to CNs using a correlation .
Blend CN.In some cases, measurements were not available for pure compounds and instead
blends of compounds with a specific composition were tested. In such cases, the
CN of the pure compound was wstimated from the blend cetane number. Such
data are of high uncertainty and are based on the assumption that the CN of the
blended mixture has a linear relationship with the CNs of its components. It is
suggested that large errors might exist for blend CNs .
Cetane numbers based on ignition delay correlations.These are cetane numbers which were calculated based on the ignition delay calcu-
lated for a special fuel using correlations developed between CN and ignition delay.
IQT measurements were considered separately, due to their higher accuracy and
Chapter 4. Correlation Development for Fuel Parameters 30
Derived CNs based on IQT measurement.
CNs based on Octane Number correlations.
Various sources were used in the creation of the CN database [61, 62, 68, 69, 70, 81, 82,
83, 84, 85, 86, 87, 88]. There were a lot of overlap between data in these sources and
several issues existed with the numbers acquired including:
In many cases, duplicate data did not agree. Fluctuations of 5 to 10 cetane num-bers (and even higher) were noticed. When small fluctuations existed in the data,
average values were used.
There was not enough information on the purity of the compounds used in themeasurements, specially in older sets of data.
There is no standard for extending the Cetane Rating to below zero and over 100.
In some cases, the method used to measure CN was not stated by the source.
4.2.4 Correlations Development for Cetane Number
Correlations between the CN and other properties of fuels have been developed in order
to make CN prediction simpler. These correlations are either based on thermophysical
properties or the chemical structure of the fuel.
Physical properties are a good indicator of chemical structure for many hydrocarbon
compounds. As a result, they may be used for correlating a chemical phenomenon (igni-
tion) with a compound. Physical properties typically correlated with CN include aniline
point, density, mid-boiling point, viscosity, heat of vaporization and heat of combustion.
Density and aniline point are somehow indicators of the composition of the mixture,
while boiling point and viscosity are indicators of molecular size and mass .
Obviously, thermophysical properties stem from fuel chemistry. As a result, there has
been an increased interest in correlating different fuel characteristics directly with the
fuel chemical structure. It has been suggested that due to the changes in most cetane
indices, an index based on compositional analysis might be better predictor of CN com-
pared to indices based on physical properties . This requires the characterization of
different classes of hydrocarbons available in the fuel. Different spectroscopic methods
may be used for such correlation development, creating a field called chemometrics .
Such models have been proposed based on NMR and IR spectra, liquid chromatography
Chapter 4. Correlation Development for Fuel Parameters 31
and gas chromatography-mass spectrometry (GC-MS) [51, 77]. They have reached ac-
ceptable results but extrapolation of these models is not reasonable since most of them
are based on linear assumptions and special functional forms. Moreover, such models
are application specific, focusing on special fuels and need to be updated. Another prob-
lem with such methods is that an overlap between the spectra of different hydrocarbon
species might exist which causes confusion in interpretation . It should be noted that
analytical methods based on topological indices have also been used to develop prediction
models for cetane number [90, 91].
A review of quantitative structure-property relationships (QSPRs) for cetane number
shows that most CN QSPRs have an R2 value in the range 0.79 to 0.97 . Reviewing
previous QSPRs developed for CN also reveals that as the range of CN values to which the
correlations is applicable increases, the R2 value decreases and the RMSE increases .
The statistical properties of some of the correlations developed for CN are summarized
in Table 4.2. As evident from this table, several simple linear and nonlinear correlations
for CN have been published with correlation coefficients of 0.9 to 0.99. However, in most
cases the correlation equations were solved and tested by the same data set which, with
a limited and insufficiently diverse data set, may lead to an overly optimistic assessment
of the correlation. Moreover, they mainly focus on special fuels or classes of compounds,
helping them achieve better regression statistics at the expense of generality. The R2
and RMSE values in Table 4.2 will be used as references in assessing the suitability of
CN correlations developed in this work.
4.2.5 Correlation of Cetane Number with NMR Spectrum
As previously mentioned, a database of CN data and NMR spectra of compounds was
created. Initial regression studies using all the CN data revealed that the difference in
experimental methods used to acquire the data created large errors for regression anal-
ysis. The best regression results were achieved when only the ASTM D613 data were
used. This was reasonable, since the ASTM D613 is the standard method of testing
and many of the pure compound properties were measured using this method. It should
also be noted that only hydrocarbons were used in regression analysis, since our focus
is on the aviation jet fuel which is primarily composed of carbon and hydrogen. The
properties of the data set used in the regression analysis along with the statistics of the
results obtained using high precision MLR and ANNs are summarized in Table 4.3.
All linear regression models met the requirements for the normality of residuals and their
independence from predicted and predictor values. They also had R2 values higher than
Chapter 4. Correlation Development for Fuel Parameters 32
Table 4.2: Statistical properties of some of the correlations proposed for CN (MLRdenotes Multiple Linear Regression, MNR denotes Multiple Nonlinear Regression andANN denotes Artificial Neural Network).
Predictor Range Data Set Size R2 RMSE Method Source1 Proton NMR 20-75 67 fuel mixtures diesel 0.992 1.11 MNR 
2 Proton NMR -10-100140 diesel fuels, pure
hydrocarbons andhydrocarbon blends
0.99 2.4 % MNR 
3 Proton NMR 48-55 (IQT) - 0.998 - MLR 4 Proton NMR 48-56 60 diesel fuels 0.97 (training) - MLR 5 Proton NMR 48-56 60 diesel fuels 0.91 (training) - ANN 6 Proton NMR + HPLC 43-64 53 diesel fuels and gas oils 0.692 2.11 MLR 7 C-13 NMR 13-57 93 hydrocarbon mixtures 0.98 2.0 - 8 C-13 NMR 40-71 21 diesel fuels 0.92 2.5 MLR 9 C-13 NMR 27.1-64.5 46 diesel fuels 0.95 2.8 MLR 10 C-13 NMR 31.2-68.4 46 diesel fuels 0.93 2.9 MLR 11 C-13 NMR 25.6-80.8 46 diesel fuels 0.94 4.1 MLR 8 C-13 NMR 37-72 81 diesel fuels 0.94 2.4 MLR 
8C-13 NMR and two points
on distillation curve37-72 81 diesel fuels 0.95 2.2 MLR 
12 C-13 NMR + HPLC 31.2-68.4 (CI) 27 diesel fuels 0.92 2.7 MLR 13 C-13 NMR + HPLC 40-71 21 diesel fuels 0.92 2.4 MLR 14 C-13 NMR + HPLC 27.1-64.5 46 diesel fuels 0.95 2.8 MLR 15 C-13 NMR + HPLC 31.2-68.4 46 diesel fuels 0.94 2.8 MLR 16 C-13 NMR + HPLC 25.6-80.8 46 diesel fuels 0.95 4.1 MLR 17 GC + HPLC 31.2-68.4 (CI) 27 diesel fuels 0.88 3.5 MLR 18 LC and GC-MS 30.9-56.8 69 diesel fuels 0.94 - ANN 19 LC and GC-MS 30.9-56.8 69 diesel fuels 0.75 - MLR 
20 - 10-110paraffins, isoparaffins, and
cycloparaffins0.89 - ANN 
21 - -10-90 olefins and aromatics 0.89 - ANN 22 Topological indices 10-110 alkanes and cycloalkanes 0.99998 (training) - - [90, 91]23 Compositional lumps 20-60 (IQT) 203 diesel fuels - 1.25 - 24 Chemical Structure 10-90 isoparrafins 0.97 - ANN 
25 Molecular descriptors -hydrocarbons likely to be
present in deisel fuel0.886-0.978(training)
2-7.1 (training) MLR 
26 Aniline point 10-70 3400 diesel fuels 0.89 2.0 Functional Fitting 
27Distillation properties and
density10-70 1531 diesel fuels 0.9 1.9 Functional Fitting 
density and aniline point10-70 - 0.92 1.7 Functional Fitting 
29 Physical properties 30.9-56.8 120 diesel fuels 0.86 1.62 ANN 
0.8. The actual values when plotted against predicted values , as illustrated in Figure
4.2, show that the linear models can have large errors in the range of CN of aviation jet
fuel (30-60). Moreover, normalized RMSE values are 9-10 %, which is higher than most
values cited in the literature.
To reach better regression results, artificial neural network (ANN) models were developed
for the CN data. These models all have R2 values higher than 0.9. RMSE values have
been approximately halved compared to the linear models and have reached values that
are near the experimental error of the ASTM D 613 standard which is less than 5 numbers
in CN . Comparing the normalized RMSE values to those found in the literature,
we see that they are only slightly higher than those observed in Table 4.2. This can be
justified by the varying chemistry used in developing the correlations. The correlations
developed here cover a wider range of CN values, as this is required in analyzing mixtures
made from different chemical compounds. The results show a really good fit to available
Chapter 4. Correlation Development for Fuel Parameters 33
data in the region of CN = 30-60, which is the range of typical aviation jet fuel cetane
Note that in both the MLR and ANN correlations, the importance of molecular mass
(MM) is apparent. The addition of molecular mass reduces the RMSE values dramat-
ically. This is physically acceptable, since ignition requires evaporation, which is de-
pendant on molecular mass. The fit acquired using different MLR and ANN models is
compared in Figure 4.2, plotting predicted values against actual values. It is apparent
that ANNs have better accuracy in predicting the cetane number. For the coefficients
and mathematical form of the regression results, please consult Appendix A.
The models developed in this work (MLR 1, MLR 4, ANN 1 and ANN 4 models) are
compared to several other models proposed for CN prediction in Figure 4.3. The ANN
models show comparable accuracy relative to the previous regression results develop and
seem to be acceptable tools for CN prediction.
Table 4.3: Statistical properties of the regression models developed for CN.
Properties of the data set used for regression analysisExperimental method ASTM D 613 Number of compounds 53
Atoms C, H Mean 46.96Range of values -20 to 110 Standard deviation (SD) 35.18
Multiple Linear RegressionNam