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Development of Surrogates for Aviation Jet Fuels by Seyed Ali Nasseri A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Aerospace Studies University of Toronto Copyright c 2013 by Seyed Ali Nasseri

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  • Development of Surrogates for Aviation Jet Fuels

    by

    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

  • Abstract

    Development of Surrogates for Aviation Jet Fuels

    Seyed Ali Nasseri

    Master of Applied Science

    Graduate Department of Aerospace Studies

    University of Toronto

    2013

    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

    interest.

    ii

  • Acknowledgements

    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-

    search environment.

    Finally, I want to thank my parents and siblings for instilling in me confidence and a

    drive for pursuing my masters degree.

    iii

  • Contents

    Contents vi

    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

    iv

  • 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

    v

  • 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

    Appendices 74

    Bibliography 80

    vi

  • 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

    vii

  • 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

    viii

  • Chapter 1

    Motivation

    1.1 Introduction

    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

    presented.

    1.2 Limitations of Real Fuels for Research Applica-

    tions

    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%

    1

  • Chapter 1. Motivation 2

    volume) [1]. 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 [2]. 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 [5]. 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 [6]. 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 [7]. 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

    these issues.

    1.3 Overcoming the Limitations of Real Fuels for Re-

    search Purposes

    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 [2]. 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 [10] 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 [12]. 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 [7]. 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) [12]. 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 [10]. The exact number of species needed to

    model all aspects of combustion is not yet known [7]; however, most proposed surrogate

    fuels have 4-14 components [13] and 3-10 components have been suggested to suffice for

    most applications [14]. 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-

    tion

    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

    followed:

    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-

    mulation

    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-

    ties.

    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].

    Aromatic content.

    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

    formulation include:

    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[4]. It should

    be noted that density is known to be less sensitive to fuel composition [18].

    Fuels heating value or enthalpy of combustion [1, 14].

    Volatility (distillation properties, vapor pressures, or boiling point) which affectspre-combustion processes in combustion chambers [14] and provides valuable insight

    into the performance of engines [4].

    Viscosity [1] which affects pre-combustion processes in combustion chambers withshort propellant residence times and high efficiency requirements [14]. Viscosity is

    highly sensitive to both chemical composition and temperature [3].

    Thermal stability [1].

    Surface tension which affects fuel atomization and mixing [14].

    Molecular mass (indirectly linked to distillation curve) [2, 17].

    Diffusion coefficients [6].

  • 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 [18].

    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 [19].

    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-

    ities

    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)

    initiative [4].

    Some of the previous research in this area focused on surrogate fuels with applications

    in modeling jet fuel pool fires. Violi et al. [15] developed a surrogate fuel for pool fire

    modeling by matching sooting properties and boiling point distribution of the actual fuel.

    Eddings et al. [9] 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

    fires.

    Surrogate fuels have also been used for modeling specific combustion characteristics of

    fuels. Aksit et al. [5] 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. [20] 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. [21] 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. [22] 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 [16]. 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

    [23]. Bruno et al. [18] 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. [14] 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. [4] 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. [13] 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. [24] developed a

    surrogate fuel for JP-8 by matching its chemical composition measured using C-13 nuclear

    magnetic resonance (NMR) spectroscopy. Huber et al. [25] 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

    1-pentene) [1].

    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 [16] 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

    [3]1,2,4-trimethylbenzene Aromatic 20

    2 Aksit Kerosenen-decane Normal Alkane 70

    [5]propylbenzene Aromatic 30

    3 Eddings JP-8

    n-octane Normal Alkane 3.5

    [9]

    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

    [12]1,2,4-trimethylbenzene Aromatic 20

    5 Slavinskaya Jet A

    n-dodecane Normal Alkane 20

    [14]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

    [15]

    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

    [28]

    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

    [29]n-dodecane Normal Alkane 34.7

    methylcyclohexane Cycloalkane 16.7butylbenzene Aromatic 16

    10 Humer JP-8n-dodecane Normal Alkane 60

    [30]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

    [33]toluene Aromatic 20

  • Chapter 2

    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

    [7]. 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 [1].

    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 [34]. 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-

    12

  • Chapter 2. Target Fuel Properties 13

    Table 2.1: Chemical composition of Kerosene, JP-8 and Jet A (values are volumetricpercentages).

    Hydrocarbon Type Kerosene [1] Kerosene [36]Jet A (World

    survey average)[7, 13]

    JP-8 (JetA/A-1)

    [10]JP-8 [33]

    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

    volume.

    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) [7]. 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) [3]. 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 [33]. 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 [37], 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 [39] JP-8 [26] JP-8 [36] Jet A/A-1[26] Jet A [36] Kerosene [36]

    H/C ratio1.84-2.07

    (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 [40]Density (kg/m3) 804 797 - - - 770-830

    Aromatic Content (vol%) 20 - - - - 10-20

    Cetane Number32-57

    (average 44)45 - - - -

    Threshold Soot Index (TSI)16-26

    (average18-22.1)

    - - - - -

    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 [5]

    Table 2.3: Aviation jet fuel specifications and statistical data.

    Specifications [26, 34, 35, 38] Statistical Data [41]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 [42]). 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 [43]:

    0=

    1

    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 [35].The following equation was used for correcting dynamic viscosities [44]:

    ln() = A +B

    T(2.2)

    The values of the constants A and B were evaluated based on aviation jet fuel viscosity

    measurement data from reference [45] 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 [39]

    Smoke Point (mm) 21 Jet A[41] > 18 ASTM D 1655Diffusion Flame Threshold

    Sooting Index (TSI)26 Correlations 16-26 JP-8 [39]

    Density (kg/L) 0.7969 Sample properties [42] 0.7827-0.8483 Kerosene [36]Boiling Point (K) 434 Sample properties [42] 413-443 Table 2.2

    Maximum Freezing Point (K) 218.65 Sample properties [42] 215-233.15 Jet A and JP-8 [26]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 [39]

    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.

  • Chapter 3

    Regression Analysis Procedure

    3.1 Introduction

    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 [46]), 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.

    17

  • 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 [47]. 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

    [48] and MATLABs curve fitting tool [49]. 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 [50], 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 [51]. 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

    [52], 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 [53] 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

    3.3.2 Residuals

    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.

  • Chapter 4

    Correlation Development for Fuel

    Parameters

    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

    mixture, including:

    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

    22

  • 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 [54]. 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

    0

    4

    8

    12

    16

    In

    tens

    ity

    (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

    composition.

  • 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].

    ProtonType No.

    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

    (R NH2)

    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) [61]. 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 [62]. It takes into account

    all delay effects such as spray formation, heating, vaporization, mixing and chemical

    induction times [63]. 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 [64]. Fuels with low cetane

    numbers generally lead to hard starting, tough operation, more noise and higher emis-

    sions of particulate matter and NOx [65]. 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 [69].

    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

    [61].

  • 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 [54]. 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 [70].

    The cetane number of a compound depends on its molecular structure [62]. 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 [73].

    4.2.2 Cetane Number Measurement

    The most accepted methods for measuring CN are the ASTM D613 (engine test) [74]

    and the ASTM D6890 (IQT measurements) [75]. 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 [76]. Such

    methods have not been widely used.

    ASTM D613

    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 [61]. 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 [78].).

    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 [77], although 100 ml has

    also been cited as the sample size [62].) and a much shorter time (less than 10 min).

    This testing method operates based on the ASTM D6890 standard [75] and has a repro-

    ductivity error of 1 to 2 cetane numbers [77]. 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 [61]. 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 [61].

    ASTM D613.

    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 [61].

    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

    reproducibility.

  • 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[61].

    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 [70].

    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 [89]. 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 [63].

    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 [89]. 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 [92]. 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 [93].

    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 [94]

    2 Proton NMR -10-100140 diesel fuels, pure

    hydrocarbons andhydrocarbon blends

    0.99 2.4 % MNR [46]

    3 Proton NMR 48-55 (IQT) - 0.998 - MLR [95]4 Proton NMR 48-56 60 diesel fuels 0.97 (training) - MLR [63]5 Proton NMR 48-56 60 diesel fuels 0.91 (training) - ANN [63]6 Proton NMR + HPLC 43-64 53 diesel fuels and gas oils 0.692 2.11 MLR [89]7 C-13 NMR 13-57 93 hydrocarbon mixtures 0.98 2.0 - [78]8 C-13 NMR 40-71 21 diesel fuels 0.92 2.5 MLR [93]9 C-13 NMR 27.1-64.5 46 diesel fuels 0.95 2.8 MLR [93]10 C-13 NMR 31.2-68.4 46 diesel fuels 0.93 2.9 MLR [93]11 C-13 NMR 25.6-80.8 46 diesel fuels 0.94 4.1 MLR [93]8 C-13 NMR 37-72 81 diesel fuels 0.94 2.4 MLR [96]

    8C-13 NMR and two points

    on distillation curve37-72 81 diesel fuels 0.95 2.2 MLR [96]

    12 C-13 NMR + HPLC 31.2-68.4 (CI) 27 diesel fuels 0.92 2.7 MLR [97]13 C-13 NMR + HPLC 40-71 21 diesel fuels 0.92 2.4 MLR [93]14 C-13 NMR + HPLC 27.1-64.5 46 diesel fuels 0.95 2.8 MLR [93]15 C-13 NMR + HPLC 31.2-68.4 46 diesel fuels 0.94 2.8 MLR [93]16 C-13 NMR + HPLC 25.6-80.8 46 diesel fuels 0.95 4.1 MLR [93]17 GC + HPLC 31.2-68.4 (CI) 27 diesel fuels 0.88 3.5 MLR [97]18 LC and GC-MS 30.9-56.8 69 diesel fuels 0.94 - ANN [51]19 LC and GC-MS 30.9-56.8 69 diesel fuels 0.75 - MLR [51]

    20 - 10-110paraffins, isoparaffins, and

    cycloparaffins0.89 - ANN [98]

    21 - -10-90 olefins and aromatics 0.89 - ANN [98]22 Topological indices 10-110 alkanes and cycloalkanes 0.99998 (training) - - [90, 91]23 Compositional lumps 20-60 (IQT) 203 diesel fuels - 1.25 - [77]24 Chemical Structure 10-90 isoparrafins 0.97 - ANN [99]

    25 Molecular descriptors -hydrocarbons likely to be

    present in deisel fuel0.886-0.978(training)

    2-7.1 (training) MLR [62]

    26 Aniline point 10-70 3400 diesel fuels 0.89 2.0 Functional Fitting [71]

    27Distillation properties and

    density10-70 1531 diesel fuels 0.9 1.9 Functional Fitting [71]

    28Distillation properties,

    density and aniline point10-70 - 0.92 1.7 Functional Fitting [71]

    29 Physical properties 30.9-56.8 120 diesel fuels 0.86 1.62 ANN [99]

    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 [61]. 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

    numbers.

    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