DEVELOPMENT OF A MODEL FOR CETANE NUMBER
ESTIMATION BASED ON A PARAMETRIC CORRELATION OF
DIESEL USING NEAR-INFRARED SPECTROSCOPY
Thesis
By
ANDRÉS FELIPE CADENA ECHEVERRY
Submitted to the Office of Graduate Studies of Universidad de los Andes
In partial fulfillment of the requirements for the degree of CHEMICAL ENGINEERING
December 2014
Advisor
ROCÍO SIERRA, M.Sc, Ph.D.
UNIVERSIDAD DE LOS ANDES
FACULTAD DE INGENIERÍA
DEPARTAMENTO DE INGENIERÍA QUÍMICA
DEVELOPMENT OF A MODEL FOR CETANE NUMBER
ESTIMATION BASED ON A PARAMETRIC CORRELATION OF
DIESEL USING NEAR-INFRARED SPECTROSCOPY
Thesis
By
ANDRÉS FELIPE CADENA ECHEVERRY
Submitted to the Office of Graduate Studies of Universidad de los Andes
In partial fulfillment of the requirements for the degree of CHEMICAL ENGINEERING
Approved by:
Chair of Committee, Rocío Sierra Ramírez, Ph.D. Committee Members, Felipe Salcedo Galan, Ph.D.
Head of Department, Óscar Alberto Álvarez Solano, Ph.D.
December 2014
ABSTRACT
Development of a model for cetane number estimation based on a parametric correlation of diesel using Near-Infrared Spectroscopy.
(December, 2014)
Andrés Felipe Cadena Echeverry Universidad de los Andes Advisor: Rocío Sierra Ramírez, Ph.D.
This study intends to assess a cetane number estimation method for mixtures of diesel with lubricating oil and cetane number enhancers and diminish compounds. The correlation takes into account decisive physiochemical properties for diesel engine fuel formulation. The cetane number is a far-reaching feature to evaluate the fuel quality and its determination is often expensive and difficult. This study aims to establish a calibration curve of NIR data to create a multivariate model using PLS (partial least squares) that allows to predict cetane number. Current results of samples of petro-diesel and synthesized diesel at different percentage of blending show that the mixture of different chemical composition (v/v) allows a determination over a wide range of cetane number.
Keywords: Cetane number, diesel, synthetized diesel, NIR, Partial Least Squares.
RESUMEN
Desarrollo de un modelo para la estimación del número de cetano basado en una correlación para diesel usando Estetroscopia de Espectro Cercano
(Diciembre, 2014)
Andrés Felipe Cadena Echeverry Universidad de los Andes Asesora: Dra. Rocío Sierra Ramírez
El presente estudio busca evaluar un método de predicción por correlación matemática del número de cetano en mezclas de diésel con aceite lubricante de motor, basado en propiedades químicas que son decisivas en el diseño de combustibles para motores de inyección de diésel. El número de cetano es un indicador relevante para la calificación de combustibles y su determinación es generalmente compleja y costosa. Este estudio busca establecer una curva de calibración que permita, tras un análisis multivariado, predecir el número de cetano a través de espectrometría NIR, seguido de la aplicación de una regresión de mínimos cuadrados parciales (PLS, siglas en inglés) como técnica de calibración. Los resultados actuales muestran que las mezclas a diferentes porcentajes de composicion (v/v) en rangos amplios de número de cetano.
Palabras clave: Número de cetano, diésel, diésel sintetizado, NIR, Mínimos cuadrados parciales.
ACKNOWLEDGMENTS
I deeply thank my God Jehovah and my parents, Dora and Jorge as well as my sister Diana for always supporting my dreams, for giving me the confidence to reach them all and for all their help and wise words. Special thanks to Rocío Sierra and Daniel Sanchez for their suggestions and orientation during this entire project, also to Sandra Vanessa Camacho, without her help my life could never be as good as it is right now. Thanks to Alfredo Santamaria, Mauricio Gomez and Deicy Tique for all their wise suggestions and contributions in this project. To my friends Tatiana Valcárcel, Sara Jiménez, Tim Lang, Ana Botello, Diana Cortés and all those that accompanied me during this journey and for being part of my life during all these years.
TABLE OF CONTENTS
ABSTRACT ... I RESUMEN ... II ACKNOWLEDGMENTS ... III TABLE OF CONTENTS ...IV LIST OF FIGURES ...VI LIST OF TABLES ... VII
INTRODUCTION ... 1
1.1. IGNITIONPROCESS ... 2
1.2. CETANENUMBERSCALE ... 3
1.3. TESTENGINEASSEMBLY ... 4
1.4. THEIGNITIONQUALITYTEST(IQT) ... 5
1.5. OTHERBENCHTEST(IQT) ... 5
1.6. DIESELBLENDS ... 5
1.7. DATASOURCEOFPURECOMPOUNDS ... 6
1.8. DATAFORHYDROCARBONS ... 6
1.9. ASTMD4737CETANEMODEL ... 6
1.10. NIRANALYSIS ... 7
1.11. SPECTRADERIVATIVES ... 8
1.12. PARTIALLEASTSQUARESREGRESSION(PLS) ... 8
1.13. PRINCIPALCOMPONENTSANALYSIS(PCA) ... 9
1.14. CORRELATIONCOEFFICIENT ... 9
1.15. DISTANCES ... 9
OBJECTIVES ... 10
2.1.GENERALOBJECTIVE ... 10
2.2.SPECIFICOBJECTIVES ... 10
METHODOLOGY ... 11
3.1.PHYSICOCHEMICALFUELPROPERTIESCALCULATION ... 11
3.1.1. DENSITY AND SPECIFIC GRAVITY ... 11
3.1.3 DEVELOPMENT OF THE CETANE NUMBER MODEL ... 12
3.1.4 CALIBRATION CURVE ... 3
RESULTS AND DISCUSSION ... 5
4.1 BASIC PROPERTIES ... 5
4.2 ASTMD-4737CORRELATION ... 9
4.3 CALIBRATIONCURVE ... 11
CONCLUSIONS ... 25
FUTURE WORK AND RECOMMENDATIONS ... 26
REFERENCES ... 27
APPENDIX 1 ... 29
APPENDIX 2 ... 34
APPENDIX C ... 36
APPENDIX 4 ... 38
APPENDIX 5 ... 42
APPENDIX 6 ... 52
APPENDIX 7 ... 65
LIST OF FIGURES
Figure 1. n- hexadecene ... 1
Figure 2. Heptamethyl cetane ... 1
Figure 3. Overall compression ignition process ... 3
Figure 4. Schematic pure compound CN (Ghosh & Jaffe, 2006) ... 10
Figure 5. Cetane number profile for molecular lumps ... 15
Figure 6. Atomization profile petro-diese ... 16
Figure 7. Overall atomization profile of diesel samples ... 17
Figure 8. Petro diesel samples spectrogram ... 19
Figure 9. Cetane number of petro-diesel spectrogram ... 20
Figure 10. Low cetane number of synthesized diesel spectrogram ... 21
Figure 11. High cetane number of synthesized diesel spectrogram ... 22
Figure 12. Second derivate filter ... 23
Figure 13. Mathematic pre-treatment from "apply math" ... 24
Figure 14. 3D factor cluster and probability histogram ... 25
Figure 15. PLS VISION® ... 25
Figure 16. Cross validation ... 26
Figure 17. Calibration set: Calculated vs and Lab data / Residuals vs. lab... 27
Figure 18. Validation set: Calculated vs. lab data ... 27
Figure 19. Cross validation Unscrambler X ... 30
Figure 20. Unscrambler X™ PLS screenshot ... 30
Figure 21. Spectra data without filter ... 31
Figure 22. Scores graph factor 1 ... 31
Figure 23. Cross validation factor score ... 32
Figure 24. Calibration vs. reference (validation) ... 33
Figure 25. Predictive deviation ... 34
LIST OF TABLES
Table 1. ASTM D-4737 Temperature recovery constrains ... 7
Table 2. Measurement devices for blended diesel ... 11
Table 3.Sample identification ... 2
Table 4. Molecular β parameters for CN (Ghosh & Jaffe, 2006) ... 9
Table 5.Pure compound cetane number and description ... 3
Table 6. Basic properties of lubricating oil + petro-diesel ... 5
Table 7. Colombian diesel quality standards to mix with diesel fuels ... 6
Table 8. Overall sample physical properties ... 8
Table 9. ASTM D-4737 distillation temperatures ... 9
Table 10. Organic group spectra distribution ... 11
Table 11. Statistical cross validation results VISION® ... 18
CHAPTER 1 INTRODUCTION
The cetane number represents the measure of ignition delay and is a quality parameter for diesel fuels (mainly composed of paraffinic hydrocarbons or alkynes) which predicts engine performance. The increasing demand of diesel has led to a revolutionary attempt for new fuels and possible applications of cetane number (CN) enhancers. Due to limited crude reserves, brand new alternatives of diesel mixtures have been formulated, which are widely known as blends. For instance, used engine oil (properly cleansed), tranesterified biodiesel, and synthesized fuels have been used as diesel replacement in engine fuel; in this study pyrolitic oil of waste tires will be assess (Kyari, Cunliffe, & Williams, 2005). As with any commercial fuel, all these blends must satisfy quality standards and have specific combustion characteristics; due to this, it is necessary to determine the most appropriate composition of blended mixtures. The cetane number therefore has become the main variable since it serves as a parameter that measures the impact of the combustion process and the engine performance (Sivaramakrishnan & Ravikumar, 2012).
Diverse attempts to estimate physical and chemical attributes on diesel bulks have been designed. These include tests based on physicochemical properties, molecular composition by gas chromatography, NMR spectroscopy approaches for chemical groups’ identification and even correlation formulations for multiple diesel fuels. Cetane number
Figure 2. Heptamethyl cetane
is understood as a scalar measure that discloses two particular blends, namely n-cetane (n-hexadecene) graded with 100, and heptamethyl cetane with 0 but attributed to different chemical species (Figure 2). In terms of performance, an n-hexadecene possesses a good ignition delay behavior in comparison with heptamethyl cetane, which is very low.
1.1. IGNITION PROCESS
The combustion process for compression-ignition engines is triggered by air through the intake valve, this valve shuts down and a piston that reduces the volume of air, generating compression into the combustion chamber, followed by the injected spray of fuel, forming sprays droplets and vaporization of the hot air-fuel mixture that ignites. This case is different from gasoline engine combustion process, that does not use compression compartments and the ignition point is prevented, it is configuration is known as spark ignition (SI) engines. This engines use and ignition spark nozzle, different from auto-ignited diesel engine, where the energy is supplied through the reservoir compression (Van Basshuysen & Schäfer, 2002).
The role of physicochemical properties in the ignition process such as density, viscosity, combustion heat and flash point are variable that give evidence of the ignition delay phenomenon as presented in Figure 1. Thus, multiple models can be design based on cetane number as a predictive variable resulting of the previous physicochemical properties as mentioned in former studies by Yu, Uyehara, and Myers (1956). As mentioned before, the ignition process begins with an air intake into the combustion chamber and it is followed by a compression of the chamber (about a ratio 18:1), generating and increase in the temperature approximately 600C. Once fuel is sprayed into the chamber, the droplets are formed and vaporized. At its final stage vapor fuel mixes with the air giving the setting for combustion (Dermirbas, 2008). Diesel combustion reaction that takes place in an ignition chamber and some of the products obtained are carbon dioxide (CO2) resulting
from fuel combustion, carbon monoxide (CO) produced by uncompleted combustion, oxygen and nitrogen react at high temperature and pressures which leads to formation of nitrogen oxides (NOx), ozone is also likely to be produced due to the presence of
hydrocarbons (HC) and sulfur oxides due to oil and coal fuels, these last two are well known as meaningful pollutants (Dermirbas, 2008).
Figure 3. Overall compression ignition process (Murphy, Taylor & McCormick, 2004)
Figure 1 presents an overall description of the properties that are highly recommended to assess cetane number, however, a complete and throughout analysis is necessary to represent accurately CN.
1.2. CETANE NUMBER SCALE
Cetane number rating consists of a reference measure that relates two different hydrocarbons: 1-hexadecene and α-methylnaphthalene (Heptamethyl cetane), also known as isocetane. This rating shows that the ignition delay in diesel engines is homologous to octane number for gasoline. 1-hexadecene has a long-straight chain that oxidizes quite easily, while isocetane resist highly to oxidation due to its aromatic ring structure. This suggest that resistance to oxidation during combustion is highly related to ignition delay, and incidentally, to cetane numbers (Williams, Aries, Cutler, & Lidiard, 1990). Some experimental difficulties in working with this reactive forced the replacement of
α-methylnaphthalene for hepthamethylnonane, graded later with a CN of 15. Currently, there is not an accepted methodology that allows cetane numbers below zero or greater than a value of 100. Considering that the ASTM (American Society for Testing and Materials) protocol is to be followed in this work, the α-methylnaphthalene shall indicate the lowest rate of cetane number.
Cetane number rating indicates that at a high value, a better performance of the fuel in the ignition chamber will be obtained, as well as an easier starting of the engine, less noise and lower emissions. Hence, cetane number is also known as a good indicator of diesel quality (Dermirbas, 2008).
1.3. TEST ENGINE ASSEMBLY
The ATSM D613-13 Standard method test for Cetane Number of diesel fuel oil is for now the most accurate procedure to determinate CN of fuels, with a standard deviation of 2.8 cetane numbers. This procedure has in itself difficulties due to the application of a single ignition chamber test; it has been criticized its reproducibility by the ATSM and its dependence on differentiation between two similar samples (Murphy, Taylor, & McCormick, 2004). Williams et al., points out the fact that also a few locations exist to perform this test and the fact that is considerably expensive to asses a single sample. Some researchers have oriented their work on the cetane index instead of assessing cetane number, but this index has a limitation for blended fuels and pure components as well.
In the ASTM D 613 the cetane number of a fuel is determined through a comparison procedure between ignition delays standard known as CFR test engine, Cooperative Fuel Research, which uses blended references of know cetane number. The compression ration varies with an adjusted hand wheel to obtain a same ignition delay for a sample or regarding two blank reference fuels, this procedure allows an interpolation of cetane number based on the hand wheel value. The ASTM D 613 procedure represents a measure error that varies from 2.8 cetane numbers to 3.8 for samples with cetane number of 40, 4.8 for fuels with a cetane number level of 48 and of 4.8 cetane numbers for fuels with a cetane number level of 56 (Murphy, Taylor, & McCormick, 2004). There is a
common effort to improve the accuracy in the determination of cetane number based on varied approaches.
1.4. THE IGNITION QUALITY TEST (IQT)
The ignition quality tester assesses samples of fuel injected through a headed constant volume combustion chamber. Cetane number is measured as the time delayed between the injector lifts and the raise of pressure at is initial value, which decreases initially due to a cooling state from fuel evaporation and recovers. This method results in a correlation between the observed ignition delay and the cetane number of the fuel (Murphy, Taylor, & McCormick, 2004). The present method is recognized among the category of bench method to estimate cetane number.
1.5. OTHER BENCH TEST (IQT)
Other bench apparatus have been designed to estimate cetane number throughout different studies, for instance using constant volume bomb combustion, which lead to the design of IQT tests. Nevertheless, a bench apparatus results in expensive routine analysis. Most recently, research attempts to measure cetane number based on correlate cetane number algorithm with a meaningful accuracy Olson, Meckel, & Quillian, 1960; Murphy, Taylor, & McCormick, 2004).
1.6. DIESEL BLENDS
Blends are known as a mixture at volumetric relation of different liquid fuels and they are of common practice in the fuel industry. However, determination of cetane number for blended fuels is needed. According to Olsen6 et al., not only cetane number property of blended diesel samples may be estimated, but also remarked that blending diesel might generate uncertainty in cetane number amplification (Olson, Meckel, & Quillian, 1960; Murphy, Taylor, & McCormick, 2004). This study aims to comprehend the cetane number for both petro-diesel and synthesized diesel based mainly on functional
groups with known CN. The cetane index in some crude oil assays is often referred to as Cetane calculi.
1.7. DATA SOURCE OF PURE COMPOUNDS
The present study references several databases that have been reported as “handbooks” for cetane number. Some of the suggested handbooks as expressed by Murphy et al., list a total 299 pure compounds cetane number based on a recompilation of 40 authors and a classification regarding chemical compounds class. The compendium of cetane number data is essential for the application of cetane number correlations. Some data may not be presented or its use depends on the measurement method that suites better. Multiple issues with cetane number have been identified, for instance purity of compounds below a lever of purity of 98% or lower affect greatly as mentioned for the ASTM D 613.
1.8. DATA FOR HYDROCARBONS
Petro diesel data has been classified as good; however, multiple studies support the theory that outliers and some results disregard measurements with diesel fuel. Some researches affirm that such defies are associated to unusual ignition chemistry, it is possible that multiple compounds and impurities (mainly peroxides) present in petro diesel affect the measurement of cetane number. A gas chromatography is suggested to identify possible outliers present in samples.
1.9. ASTM D 4737 CETANE MODEL
Another method available for control quality is the use of cetane index (CI), which is an estimated number based on fuel density at 10%, 50% and 90% volumetric distillation recovery temperature. Cetane index is often used as an empirical equation for predicting the cetane number for non-additive compounds. The recovery vessel must be of 100 ± 1.0 mL and must have an inclination below 13°; also 100 mL of samples are fed to the batch distillation column following the ASTM D-86. An example of the recovery vessel is presented in the appendix 1 Figure A.1.2 and the distillation assemblage in appendix 1
Figure A.1.3. This protocol was applied to assess petro-diesel samples BD100 and BD90 (BD100 is 100% diesel and BD90 a blend of 10% lubricating oil + 90% of petro-diesel).
Table 1. ASTM D-4737 Temperature recovery constrains
(De la Paz, Rodríguez, Valentín, & Ramos, 2007) T 10, °C T 90, °C
Minimum Value 165 228
Maximum Value 287 376
Table 1 presents the ranges where protocol ASTM D-4737 works as a feasible and trustworthy approach to estimate cetane number for diesel fuels, any test run out of specified temperatures distillation goes out of the ASTM guaranteed measures and it is not reported in the present investigation. De la Paz et al., presents a compete new optimized version of the ASTM D 4737 as well a variety of correlation that can be easily applied for cetane number determination.
1.10. NIR ANALYSIS
Near-Infrared spectroscopy is a method that refers broadly to the electromagnetic spectrum on the microwave region, mainly applied in chemical structure analytical problems. Similar methods have been used for gas oil cetane number estimation due to the fact that NIR laser overcomes fluorescence and noise issues and data can be assigned to each spectrum (Williams, Aries, Cutler, & Lidiard, 1990). NIR spectroscopy is an analytical technique due to its robustness and tolerance in the detection for C-O, C-H, C-C and N-H chemical bounds, existent in fuel samples. Near infrared suggests a wavenumber range around 14,200-4000 cm-1, ideal zone in which most of the organic compounds are observed, far from the fingerprint region, where excessive vibrations, rotations and stretching is sensed on any sample, making though, a proper chemical bound detection (Åbo Akademi, 2009). Although the IR spectrum characterize for entire molecule detection, some groups of atoms might rise up bands at near frequency regardless of the structure of the rest of the molecule. Data lumped shall identify and permit by simple
inspection, a classification of the main groups that alter cetane number scale, this analysis looks to determine the chemical effects of atoms in oil-blended diesel.
1.11. SPECTRA DERIVATIVES
The application of derivative spectra is possible when attempts to remove overlapping peaks and a correct baseline. The derivate separates the peaks as known as first derivate. In the second derivate peaks alter to troughs, causing the first derivate to be zero. This former derivates magnifies the noise; therefore it is necessary to perform a smooth of data throughout the Savitzky-Golay smoothing procedure (Jørgensen, 2000).
1.12. PARTIAL LEAST SQUARES REGRESSION (PLS)
PLS regression is a statistical method that assesses combined features from component analysis and multiple regressions. It is mainly applied to mathematical predictive sets of dependent variables based on a large amount of independent variables (predictors). It was initially presented as an algorithm solver supported on eigenvectors, but in time rigged out as a statistical frame. The aim of PLS is to predict Y from X, where Y is a solution vector of dimension 𝑛𝑥𝑞 and X is a predictor vector of dimension 𝑛𝑥𝑝 (Abdi, 2003). PLS model assumes that a unique (target) response will be found by a linear decomposition of the matrix X and Y as presented by the Equation 1 and 2:
X= TPT+E (1) Y=UQT +F (2) Where:
T and U are 𝑛𝑥𝑝 matrixes from the p latent vectors of each variable.
P and Y are loading 𝑁𝑥𝑝 and 𝑀𝑥𝑝 matrixes, respectively.
E and F are residual 𝑛𝑥𝑁 and 𝑀𝑥𝑝 matrixes respectively of each variable.
PLS method is also supported by a non-linear iterative partial least square (NIPALS) that assess w and c weights as presented in the Equation 3.
Where 𝑐𝑜𝑣 𝑡, 𝑢 = 𝑡𝑇 expression is the covariance between the latent vector t and u. PLS algorithm begins with a random initialization over the u latent space vector, followed by 7 iteration loops until it converges (Rivera, 2012).
1.13. PRINCIPAL COMPONENTS ANALYSIS (PCA)
PCA analysis reduces the quantity of spectral data avoiding overfitting issues but without remove meaningful information. This analysis specifically uses projections to extract from a large number of variables to highly variability among samples. All new variables or principal components follow a linear combination of the original lump of data. PCA presents new axes, the fist axis correspond to data variability, the second choose the orthogonal of the first axe, this represents a distribution of data differentiation. The second variable is uncorrelated with the first one and the whole structure is established until a sufficient amount of data is explained with the new variables. This method permits an accurate projection of variable of interest (Jørgensen, 2000).
1.14. CORRELATION COEFFICIENT
The correlation for wavelengths can be applied for spectra contrast. This method depends on the spectra shape and not in its magnitude. The product correlation dots the two vectors representing the spectra. The correlation dots are presented by the constant, r, given by the Equation 4. This method is not suggested for identification purposes. The best results are represented by the second derivate spectra (Jørgensen, 2000).
𝑟 = 𝑥𝑖𝑦𝑖 𝑥𝑖2 𝑦
𝑖2
(4)
1.15. DISTANCES
Distances can inform the similarity of objects. The most common distance is the Euclidean distance. The object with the smallest distances indicates a link together with other object. The process ends when all objects are linked together (Jørgensen, 2000).
CHAPTER 2 OBJECTIVES
2.1. GENERAL OBJECTIVE
Obtain a cetane number predictive calibration curve using NIR-PLS as a function of a parametric correlation and estimate physicochemical properties of diesel samples: viscosity and density measured according to ASTM protocols.
2.2. SPECIFIC OBJECTIVES
- Determine the following physicochemical properties of diesel samples prepared within a wide range of cetane number: viscosity, density according to ASTM protocols.
- Develop a calibration curve based on Near-Infrared Spectroscopy analysis using PLS for cetane number estimation.
CHAPTER 3 METHODOLOGY
The following methodology assets main chemicals properties of petro-diesel obtained from a Mobil™ gas station nearby to the Universidad de los Andes in Colombia. Synthesized diesel blends samples were selected as the most representative compounds, considering its percentage of peak area after a gas chromatography analysis and mass spectrometry, as reported by Kyari et al., in his work “Characterization of Oils, Gases, and Char in Relation to the Pyrolysis of different brands of Scarp Automotive Tires”. One synthesized sample obtained of tire waste pyrolysis was assessed once cetane model was obtained. Each chemical properties used in this work was analyzed following ASTM standards protocols.
3.1. PHYSICOCHEMICAL FUEL PROPERTIES CALCULATION
Table 2 shows ASTM Standards for the assessment of the fuel properties as well as measurement apparatus for each variable of interest.
Table 2. Measurement devices for blended diesel
Properties Measurement apparatus ASTM Standard
Density
Specific Gravity Pycnometer
D70 D7371 Kinematic viscosity Brookfield viscometer D445 Cetane number Batch distillation column
Parametric equation
D86 D4737
3.1.1. DENSITY AND SPECIFIC GRAVITY
Density measurements are carried out in a Fisher Scientific Pycnometer designed to perform specific gravity measurements of a sample radio density. This apparatus is made of aluminum alloy and conformed of a circular lid. The cap is a threaded ring that screws down onto the cup, holds the lid in place and contains 11.5 mL of fluid, which produces highly accurate measurements. According to the ASTM D-70 and ASTM D-7371, a
calibration procedure must take place before testing fuel samples as to avoid any systematic error. Initially, the pycnometer was filled with deionized water and immersed inside the cold water reservoir at 0.1°C. This protocol is followed by the measurement of the fuel density at 15.56°C.
3.1.2 KINEMATIC VISCOSITY
Viscosity measurements are carried out in a Brookfield viscometer coupled with a thermic bath and temperature sensor. This apparatus is conformed of sample chamber temperature probe SC4-13RPA of a sample volume of 7.1 mL, a spindle type SC4-21 and a maximum of 200 RPM (0.93 RPS); as mention before, this viscometer is couple resistant to high temperatures (Max. 80°C). The sample chamber fits into a water jacket so that precise temperature control can be attained when the circulating temperature water bath is used. Kinematic viscosity at high temperature is key for fuel atomization (formation of small droplets inside the combustion chamber) in the engine chamber, therefore the lower viscosity and higher fluidity represents an easy pumping and atomization of the fuel. Viscosity is measured at 40°C and 200 RPM for standard measurements and through varied temperature range to assess fuel atomization.
3.1.3 DEVELOPMENT OF THE CETANE NUMBER MODEL
As stated previously, the cetane number (CN) is the measurement of ignition delay of a diesel engine. A fuel name abbreviation description has been formulated for blended diesel (BD) and synthesized blend diesel (BDS). Table 3 presents the identification given overall samples tested.
Table 3. Sample identification
Sample ID Sample ID
1 BD 90 7 BDS 05
2 BD 100 8 BDS 06
3 BDS 01 9 BDS 07
4 BDS 02 10 BDS 08
5 BDS 03 11 BDS 09
3.1.3.1DEVELOPMENT OF ASTM D-4737
Among the most commonly used protocols to measure cetane number is the ASTM D-4737 equation, which correlates the specific gravity and the T10, T50 and T90 points of
the boiling curve of cetane number for fuels, this is summarized in the Equation 5.
𝐶𝐼 = 45.2 + 0.089𝑇𝑁10+ 0.131 + 0.901𝐵𝑁 𝑇𝑁50+ 0.0523 − 0.42𝐵𝑁 𝑇𝑁90
+ 0.00049(𝑇𝑁102+ 𝑇𝑁902) + 107𝐵𝑁+ 60𝐵𝑁2 (5)
Where d represents the specific gravity at 60°F (15.5°C), TN10 represents the
temperature measured at 10% volumetric recovery minus 215, TN50 represents the
temperature measured at 50% volumetric recovery minus 260, TN90 represents the
temperature measured at 90% recovery minus 310, 𝐵𝑁 = 𝑒−3.5 𝑑−0.85 − 1 and 𝑇𝑖 is the
temperature (°C) at which a given volume fraction of the sample is distillated. This protocol has been implemented for the BD100 and BD90 samples.
3.1.3.2 MOLECULAR COMPOSITION MODEL OF CETANE NUMBER
As formulated by Ghosh et al., and with the support of ExxonMobil’s refineries, a molecular based model for predicting cetane number was designed, based on a linear combination of cetane number for pure species and integrated to blended fuels. The blend composition is explained in the present article.
The model presented for cetane number is based initially on a linear volumetric blend, since it applies molecular lumps parameters that evaluate the cetane number of a fuel correlation as shown in Equation 6. The present study base its calculation on linear regressions to estimate experimental cetane number; nevertheless, due that the application of β parameters that correspond to a derived, or methodology knows as a not actual calculated value by a ASTM engine, instead this measurement takes place by a nonlinear approach as presented in Figure 4 for a parametric cetane number correlation.
𝐶𝑁 = 𝑣𝑖𝐵𝑖𝐶𝑁 (6)
𝑖
Where 𝑣𝑖 is the volume fraction of the molecular specie 𝑖 present in the sample fuel. Ghosh et al., assumes that 𝐵𝑖𝐶𝑁 represented in the Equation 6, or blend value varies linearly with the diesel CN and that depends to the composition of the fuel as presented in the Equation 7.
𝐵𝑖𝐶𝑁 = 𝑎𝑖(0)+ 𝑎𝑖(1) (7)
𝐶𝑁 = 𝑎𝑖(0)+ 𝑎𝑖(1)𝐶𝑁
𝑖 (8)
Equation 8 shows two parameters that describe the model slope, 𝑎𝑖(1) and the intercept 𝑎𝑖(0), this parametric contribution leads to a variation of CN blend values.
Furthermore, the author defines molecular class β parameters that correlate slope and intercepts as presented on Table 4.
Table 4. Molecular β parameters for CN (Ghosh & Jaffe, 2006)
Molecule class Lumps β
n-paraffins nC5 to nC16 0.5212
i-paraffins iC5to iC25 7.3717
naphthenes cyclohexane to C10 naphthene
decalin to C4 decalins 0.0727
aromatics
benzene to C14aromatics, naphthalene to C13 naphthalenes,
tetralin to C15 tetralins
Ghosh presents a final rearranging correlation based on the β parameters and the CN for blended fuels as presented in Equation 9.
𝐶𝑁 = 𝑣𝑖 𝑖 𝐶𝑁𝑖 βi 𝑣𝑖 𝑖𝐶𝑁𝑖
(9)
Nine (9) pure compounds of cetane number known are presented in Table 5 and complete description of sample mixtures lumps are presented in the appendix 1 Table A.1.2.
Table 5. Pure compound cetane number and description
Compound Name Type 𝐶𝑁𝑖
1 Benzene Aromatic 0
2 Toluene Aromatics 18
3 n-octadecane n-paraffin 103 4 n-hexadecane n-paraffin 92 5 n-heptadecane n-paraffin 100 6 n-nonadecane n-paraffin 110 7 n-eicosane n-paraffin 110 8 Cyclohexane naphthene 17
9 Diesel - 46
3.1.4 CALIBRATION CURVE
Spectrograms were be determined using NIR spectroscopy overall the samples. The processed data structured the calibration curve. The calibration curve for 12 samples was generated based on a predictive correlation of cetane number, as described previously, for each sample type (petro-diesel or synthesized). The NIR spectrometer possesses a data library or manual storage setting that allows the cetane number estimation based on spectrograms of each sample. Spectra data was grouped and allow analysis using proven methods of PLS models (integrated in the NIR software) and other mathematical parameters to reduce error associated to the cetane number correlation. This calibration curve is carried out using the manufacturer independent software named VISION®. Near infrared spectroscopy went under the following conditions, wavenumber range 2200-1100 cm-1, resolution of 400 cm-1, and average of scans 3 per sample as to identify and reduce spectra noise. A FT-IR analysis was performed in order to identify functional groups that led to a higher cetane number of the sample BD90 in relation with BD100. All the
equations applied for the coefficients for statistical analysis are presented to evaluate both data location and variable response (CN) in the regression model.
Based on the statistical validation presented by Rivera et al., through the Equation 16, coefficients report accuracy can be validated for the expression as present from Equation 10 to 16.
𝑆𝑆𝑟𝑒𝑠 = (𝑦𝑖
𝑁
𝑖=1
− 𝑦 ) (10)𝑖
𝑆𝑆𝑡𝑜𝑡 = 𝑁𝑖=1(𝑦𝑖 − 𝑦 )𝑖 2 (11)
𝑆𝑆𝑟𝑒𝑔 = 𝑆𝑆𝑡𝑜𝑡 − 𝑆𝑆𝑟𝑒𝑠 (12)
𝐵𝐼𝐴𝑆 = 𝑁𝑖=1(𝑦𝑖−𝑦 )𝑖
𝑁 (13)
𝑆𝐸𝑃 = (
𝑁
𝑖=1 𝑦 − 𝑦𝑖 𝑖 − 𝐵𝐼𝐴𝑆)2
𝑁 − 1 (14)
𝑆𝐸𝑃2 ≈ 𝑅𝑀𝑆𝐸𝑃2− 𝐵𝐼𝐴𝑆2 (15)
𝑅𝑝𝑟𝑒𝑑𝑖𝑡𝑖𝑜𝑛2 = 1 −𝑃𝑅𝐸𝑆𝑆
CHAPTER 4
RESULTS AND DISCUSSION
4.1 Basic properties
The aim of this research is to assess cetane number based on chemical properties of overall the lumps considering each sample atomization in a diesel chamber and relate CN calculation with each sample spectrogram detected using near-IR spectroscopy data. Primarily experimental results for density and viscosity are shown in the Table 6.
Table 6. Basic properties of lubricating oil + petro-diesel
Table 6 shows density and viscosity of pure diesel (BD100) and oil enhanced diesel corresponding to the BD90 fuel based on ASTM protocols. Lower densities render easier spray injection through the engine nozzle, this spray injection is better in pure petro-diesel. Results reported indicate that enhanced fuel reduce engine performance. The diesel density and viscosity reported in the present study will reference as the maximum value allowed for the synthesized samples, this last relies in the fact that the samples BD90 and BD100 are accepted parameters for commercial fuels in Colombia.
The Colombian fuel regulations bestowed by the ministerio de ambiente, vivienda y desarrollo territorial (ministry of environment, housing and territorial development) resolution 1499 of 2011 defines the protocols and ranges of chemical properties within acceptance for fuel additives quality testing.
Properties Units ASTM Standard BD90 BD100
Density at 40°C kg/L D-70 0.851 0.860
Table 7. Colombian diesel quality standards to mix with diesel fuels (Ministerio de Minas y Energía, 2011)
Results reported shows an increase of the cetane number maximum of 23.7% in initial samples (BDS01) onward and a minimum of 3.4% regarding each cetane number intervals for the last samples tested. An ample report of cetane number is shown in appendix 1 as Table A.1.2. The presence of olefins in the molecular lump are not considered in this study since fuel crystallization can take place at low temperatures, even tough, it could add a higher increment on CN. The application of the model presented by Ghosh et al., through the use of β parameters and the application of the ASTM D-4737 display a cetane number profile of samples.
Figure 5. Cetane number profile for molecular lumps
Test Unit Specification Method
Density Min 0.780
at 15°C Max 0.820
Min 3.0
at 40°C Max 3.7
Kinematic
Viscosity mm2/s ASTM D455
Figure 5 shows that CN lineally measured trends to maximize the error for each sample, and after applications of parametric model this cetane number this error was corrected. As expressed by Ghosh et al., this model has an accuracy of 90% and guarantees the measurements taken and representative enough for the model, also the ASTM measurements reports values for petro-diesel samples with the same accuracy. Figure 6 shows the diesel BD90 and BD100 viscosity profile where it is clearly seen that a decrease in the viscosity as temperature increases, which is to be expected and contributes to fuel injection. Even though big differences in viscosity at lower temperatures are found, at higher temperature these fuels will be sprayed normally since its viscosity reaches closer levels to those found on commercial diesel and fuel atomization would take place properly. Atomization analysis rends an estimative if a mixture considered is certainly a feasible fuel.
Figure 7. Overall atomization profile of diesel samples
Table presents an general report of physical properties assessed. The densities of the samples reported in the present study are within the range established by the Colombian regulation. Bases on the law resolution presented in Colombian in which diesel fuel additives standards and values, results achieved of the samples show that at least not samples existing in this study might be used as cetane number enhancers. Synthesized samples with higher cetane number have major kinematic viscosity this last might be due to the friction between neighboring particles in a fuel conformed mainly of long chain hydrocarbons.
Table 8. Overall sample physical properties
Properties Units ASTM Standard BD 90 BD 100 BDS 1 BDS 2 BDS 3 BDS 4 BDS 5 BDS 6 BDS 7 BDS 8 BDS 9 BDS 10 Density at 40°C Specific Gravity Kinematic viscosity 40°C 1.204 0.793
1.539 2.163 2.158 3.129 3.752 0.793 0.804
0.803
0.669 0.778 - D7371 0.859 0.854
kg/L D70 0.851 0.860 0.830 0.812 0.809 0.811
0.613 0.896 0.816 0.822 0.836 0.837
0.815 0.829
0.799 0.800
0.809 0.831
D455
mm2/s 7.427 4.851
Figure shows the atomization profiles of the samples tested where it is clearly seen that a decrease in the kinematic viscosity of the samples while increasing the temperature, however, samples BDS05 and BDS06 outline at 60°C is qualified as an error since it goes in opposition to the general samples tendency. The atomization profile clearly contain information relating cetane number since a higher CN is a more demanding fuel while is sprayed inside the diesel nozzle, therefore samples with an increment in the CN might have higher kinematic viscosity. None of the samples studied overcome the petro-diesel threshold at 70°C besides the outline previously mentioned.
4.2 ASTM D-4737 Correlation
As for the samples BD100 and BD90 was used and Table 9 presents the cetane number as well the temperature obtained during the distillation. Appendix A.1.3 and A.1.4 show the distillation profiles for the petro-diesel samples.
Table 9. ASTM D-4737 distillation temperatures
Sample BD90 BD100 % Vol temp (°C) temp (°C)
10 228 222
50 296 294
90 355 348
𝐵𝑁 -0.0035 -0.0344
CN 52.6 47.4
Table shows CN for diesel fuels based on ASTM protocols and also their 𝐵𝑁
values that relate to physic properties such as density and specific gravity of the fuel tested. The same protocol was intended to be extrapolated to synthesized samples but its result was unfavorable, this last due to the 10% recovery temperature out of the minimum range tolerable (82°C below) based on the contains presented by de la Paz et al., a look of the results is presented in the appendix 1 Table A.1.2. This last result may be explained due to the presence of aromatics with lower boiling point in the mixture; however, mixtures were formulated regarding pure components cetane number and not based on the application of
the ASTM D4737 since these types of samples have not been included as measurable for the ASTM.
Figure 8. Petro diesel samples spectrogram
Spectra were recorded under the following conditions, wavenumber range 4000-400 cm-1, resolution of 400 cm-1, and average of scans 6. Spectrograms of two petro-diesel samples were obtained in attempt to detect chemical groups in the samples and correlate these groups with their due cetane number as shown in Figure 8. Cetane number values of each sample were obtained by using ASTM D-4737 correlation. These values varied from 47.4 to 52.6. Group identification was assessed following organic and inorganic chart reported by Robert M. Silverstein et al., in his book “spectrometric identification of organic compounds” and reported in Table 10. Mainly compounds considered in this study as samples are paraffins, aromatic and naphthenes. As to identify organic groups in the NIR spectra, the following wavelengths reference the path to follow depending on the groups of interest (Silverstein, Webster, & Kiemle, 2005). As quoted by Ickes et al., many studies have shown the implication of cetane number and a strong dependency in the presence of NOx in fuels, it reports that a higher cetane number when NOx concentrations
increases in diesel fuels; thus, following the results obtained and reported in Figure 8 explains why a major concentration of NOx is identified in 1460 nm, and SOx (1377 nm)
that conform the sample, this represents a higher cetane number in contrast with the sample BD100 (Ickes, Bohac, & Assanls, 2009).
Table 10. Organic group spectra distribution
4.3 CALIBRATION CURVE
Figure 9 show spectrograms overlapped, this fact represents a difficulty for the determination of the cetane number, however, through a through mathematic pre-treatment the present study is intended to separate co-linearity of any kind.
Figure 9. Cetane number of petro-diesel spectrogram
Group band Strech
Carbonyl C=O 1820-1660 cm-1
3300-2500 cm-1 1100-1300 cm-1
Alcohol OH 3600-3300 cm-1
Ketone C=O 1725-1705 cm-1
Aldehyde C-H 2850-2750 cm-1
Ester C-O-C 1300-1000 cm-1
Aromatic C=C 1650-1450 cm-1
Alkanes (Paraffins) C-H 3000 or 1650 cm-1 C-O
Each spectrum was assigned with a cetane value previously estimated; this last gives an understanding of chemical lumps or bulks and specific parameters attributing an effect in the correlation. Petro-diesel samples underwent cetane number calculation through ASTM protocols. While the constructions of the calibration curve some statistical factors reported that showed considerable errors were dismissed. As expected, fuels spectrograms follow the same configuration in absorbance vs. wavelength; however, as presented in Figure 10, samples with low rated cetane number differ widely from samples within 1620 through 2400 cm-1 range, this comportment due to variety chemical composition. Figure shows a narrower comportment in the spectra. Note that a high cetane spectrum presents a slightly negative absorbance, which means that the sample is brighter than the reference material (air) and for the rest of the spectrum absorbance is positive. The differences in the spectra are largely attributed to variation in the compounds fluorescence.
Figure 11. High cetane number of synthesized diesel spectrogram
Through the application of the software VISION®, some statistical and calibration features were performed in association with the diesel spectra. The first step involves subjecting spectra to a second derivate mathematic pre-treatment as to identify most varied component zones throughout near infrared spectrum. Second spectral derivate delimits interest group displayed as sharply perturbation all over the wavelength as presented in Figure 12. Note that Figure 12 displays second derivate for high cetane number samples where less perturbation is observed over C-H group band as well as for C=O bands, hence, it may be affirmed that alkanes composition predominate over aromatic in the samples. Bases on group identification functional groups were detected as function of the wavelength.
Figure 12. Second derivate filter
Each spectrum can thus be presented as a particular set of principal components after the second derivate. Likewise, the application of some mathematic procedures upon the spectrums was needed. One of these contemplates reduction of physic component effect (molecular size variation), separate spectra peaks that cause fluctuations in the absorbance and therefore reduce the complexity over the model (Rivera, 2012). The selection of the number of wavelengths to use in multi-linear regression models is an important factor in the model development. If few wavelengths are considered, a less precise model will be reached (ASTM, 2012). A baseline correction was applied to remove background noise and unnecessary peaks. The spectra and cetane number concentration data were later entered as parameter to Unscrambler™, this and further multivariable calibration have been supported by ASTM E1655, which guides into multivariable calibration procedures of infrared spectrometers commonly used to determine physical and chemical properties (Martens & Næs, 1992).
1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 -0,8334 -0,6766 -0,5198 -0,3630 -0,2062 -0,0493 0,1075 0,2643 0,4211 0,5779 0,7348 Wavelength In te n s it y 1830 Carbonyl group C=O 1626 Aromatic and Alkanes 1170 C-H
Figure 13. Mathematic pre-treatment from "apply math"
The application of the VISION® software feature “apply math” allows the performance of the spectra filter for first, second and third derivate. In this case, second derivate filter measures the curvature over the spectra data recollected, and the first derivate filter keeps wave intensity constant and peaks clearly defined allowing a better identification of the groups previously contemplate. Third derivate filter undergoes as a replacement over the first filter since this one is constrained by a maximum spectra slope that restrict spectra separation (Rivera, 2012). Figure 13 shows the application of the Mahalanobis Distance method followed by a PCA (principal component) analysis for a product (CN). All samples with a Mahalanobis distance that are not in the frame of the region of the population are flagged as outliers. The cetane number model presents a normal distribution of data shown in Figure 14.
Figure 14. 3D factor cluster and probability histogram
Partial least squares (PLS) algorithm applied used the spectral information of a range of wavelengths and eliminated co-linearity. PLS was performed by VISION® through the feature “regression method”. Light blue in the probability histogram flags validation samples since not one of the calibration samples was rejected by the Mahalanobis Distance method.
Figure 15. PLS VISION®
Additionally, a cross validation was performed to obtained better data adjustment and regression set. Cross validation setting allows samples differentiation between
validation and training samples (calibration samples). The PRESS value is calculated as the sum of squared residuals. The present studies applied 2 different validation samples: Jet fuel A-1 obtained from the Instituto Colombiano de Petróleo (ICP, for its acronym in Spanish) and a pyrolitic oil of waste tires sample.
Figure 16. Cross validation
In this case, cross validation analysis of samples reported a high standard error per validation in the case of factor 6 and factor 7 this due to mayor variability between calibration and validation samples. The factors that present the best R squared value and the lowest PRESS value that indicates a better cetane number prediction through the estimated function. Generally, a large difference between the PRESS values and ordinary residuals indicate points where fits data well, thus, factors 6 and 7 represent pretty well the model. Results reported in Table 11 identify the factors 2 and 5 as latent variables that reduce highly the prediction error. VISION® features suggests potential factor to remove.
Table 11. Statistical cross validation results VISION®
R2 Std. Error Calibration PRESS F-Value Std. Error x Validation
Factor 1 0.674 12.91 2308.0 20.72 13.87
Factor 2 0.740 12.19 2311.0 12.78 13.88
Factor 3 0.758 12.48 3951.0 8.344 18.15
Factor 4 0.829 11.21 8346.0 8.476 26.37
Factor 5 0.851 11.31 6017.0 6.836 22.39
Factor 6 0.923 8.925 22,8589.0 9.928 138.02
Factor 7 0.947 8.246 22,7258.0 10.23 137.62
A quantitative analysis was executed through VISION® to contrast the calibration data set and validation set processed. The error associated with the cetane number measurement is likely associated to widespread range reported at a high cetane number rating. Figure 17 and Figure 18 present the laboratory data deviation with respect to the predictive method developed.
Figure 17. Calibration set: Calculated vs and Lab data / Residuals vs. lab
Figure 18. Validation set: Calculated vs. lab data
If the model is correct and all its assumptions are appropriate and satisfied, the residuals plots should not follow any particular structure or plotting pattern. Since the residual plot have runs of positive and negative residuals indicated a positive. Also data
1,0 16,2 31,4 46,6 61,8 77,0 1,0 10,5 20,0 29,5 39,0 48,5 58,0 67,5 77,0
Calibration Set : Calculated vs Lab Data Calibration Set : Calculated vs Lab Data
1,0 8,5 16,0 23,5 31,0 38,5 46,0 53,5 61,0 68,5 76,0 -25,1 -20,3 -15,6 -10,9 -6,2 -1,5 3,2 7,9 12,6 17,3
Calibration Set : Residuals vs Lab Data
Calibration Set : Residuals vs Lab Data
1,0 16,2 31,4 46,6 61,8 77,0 1,0 10,5 20,0 29,5 39,0 48,5 58,0 67,5 77,0
Validation Set : Calculated vs Lab Data Validation Set : Calculated vs Lab Data
clustering over the regression line indicates a slightly a normal distribution of data. Jet fuel A-1 distillation profile was obtained from ICP at its volumetric percentage recovery and trough ASTM 4735 and the calibration curve a cetane number validation was performed. ASTM 4737 graded Jet Fuel A-1 with 42.72 and the calibration curve with 51.5 as its cetane number, this means an error of 17.05%. As for the pyrolitic oil of waste tire sample its cetane number was measured as reported in the appendix 3 as Figure A.3.1 and graded with a 37.7. Finally, the most representative statistical coefficients regarding the PLS regression were estimated.
Table 12. General statistical coefficients report
SS res 1674
SST 207.1
SS reg. -1674
r2 0.851
T test (correlation) 8.634
SE Calibration 11.07
Prediction error 139.5
BIAS -1.740E-06
BIAS Adjust 1.105
BIAS Adj. Std. Err 8.083
SEP possible 11.07
Predict. Std. Error 12.34 RM SE Calibration 3.327
RM SEP 11.82
ӯi average observed 34.80
Slope Adjust 1.013
Slope Adj. Std. Err 0.2080
MSE 0.0231
Table 12 presents a general review of statistical indicators, therefore, we could expect based on the model R2 to explain about 85.15% of the variability in predicting CN.
A 𝑅2prediction validates statistical coefficients reported in this study. Douglas Montgomery present in his book “Design and Analysis of Experiments” a computed approximation of PRESS based on R2:
The corresponding PRESS value for cetane number prediction is 30.83, this PRESS value display a low variability of statistical residual coefficients. An overall analysis of the model statistical criterion seems very satisfactory for the prediction of cetane number. The application a baseline correlation to remove background noise to the model seemed a correct approach for spectra data obtained experimentally. The mean squared error (MSE) indicates that the regression line adjust to data satisfactorily. The BIAS function parameter reported differenced the cetane number estimator (expected value) and the true value with a 1.105 cetane; this indicates the proper adjustment of the function to estimate cetane number bases on wavelength set of data. In general, the cetane number predictive model presents a good R2 what indicates trustworthiness and a well-adjusted model (Montgomery, 2005).
Preliminary evaluation of the model indicates a satisfactory regression and predictive information to cetane number, nevertheless, the present study attains the extraction of irrelevant information through the application of a third and fourth derivate with Unscrambler™. Fourth derivate analysis clears up and defines better spectra peaks which turns a useful mechanism when overlapping wavelength are perceived. Unscrambler™ integrates a Savitzky-Golay calculation method that allows a display the length of wavelength spectral segment expressed as a polynomial (Rivera, 2012).
Unscambler X™ corresponds to a external data coupled multivariated programm that is not integrated to the calibration curve, its application allows a understanding of the modeling background in the calibration procedure. Unsclambler allows to import data packagaes from varied sources, the present model contemplates two diferent matrixes: wavelengh spectral absorbance (12x700) predictors,X, matrix and cetane number matrix response, Y, (12x1) as shown in Figure 20.
Spectra set of data underwent PLS regression and a cross validation as previuosly performed in VISION®. Examination of wavelength spectra without filter is presents in Unscrambler X™ in Figure 21.
Figure 19. Cross validation Unscrambler X
Figure 20. Unscrambler X™ PLS screenshot
Unscrambler X™ presents a calibration score graphic as shown in Figure 22.
Figure 22. Scores graph factor 1
Calibration score reported in Figure 22 shows matrix X covariance regarding Y variance. Factor 1 represents the cetane number model covariance about 90% regarding overall wavelength absorbance of fuels sampling. The factor covariance properly indicates that about 630 wavelengths variables are being used through one latent variable (factor 1) to express X and Y covariance.
Figure 23 shows the cross validation covariance results per sample iteration, since one sample is removed at a time, to multiple assess are made to validate the model. A covariance clustered in middle of the graph indicates that cross validation is an appropriate approach to support the model since lower covariance was estimated between cetane number of samples.
Figure 24. Calibration vs. reference (validation)
Previous graphics flag calibration samples with blue and validation samples with red. Figure 24 shows that calibration and validation procedure performed through Unscrambler is satisfactory based on R2; nevertheless, the calibration curve indicated a higher valuation through first and second derivate of spectra data. Figure 25 shows the identification of lower cetane number samples as outliers. Clearly, outliers add a significant spectra error during variation assessment in the cetane number model, and the reason that explains these samples as outliers relies on the latent variable removed (factor 2 and 5) while the calibration procedure. However, Unscrambler X feature, PCA analysis, flagged factors 1 and 5 also for removal leaving the model with 3 factors. Remove lower cetane number samples would be a successful approach to improve cetane number
estimation, nevertheless, it goes in opposition to this study purposes previously mentioned to establish a scale within a wide range of cetane number. The cetane number model regression and prediction formulation are satisfactory.
Figure 25. Predictive deviation
Figure 26. Wavelength regression coefficients predominance
Figure 26 presents PLS coefficients profile overall the spectra wavelength after a PCA analysis, this graphic permit to affirm that main group detected in the second derivate are well represented through the model multivariable regression. Normality of cetane number set of data was proved through the nonparametric Kolmogorov–Smirnov test applied to evaluate set the data probability distribution in Unscrambler X.
CHAPTER 5 CONCLUSIONS
Near infrared spectroscopy data have shown a satisfactory correlation of cetane number (R2 0.85) and through PCA analysis in Unscrambler™ a lesser value (R2 0.71) using multivariable calibration and PLS regression. Samples applied in this model are somewhat limited, statistical validation shows a satisfactory representation of cetane number within a wide range and regression coefficients represents the main organic groups identified through FT-IR analysis and NIR spectroscopy. Additional sampling of varied cetane number would contribute to the model if the cetane number increment is defined closely among each sample. Likewise, chemical properties measured based on the ASTM assessed effectively that all samples applied in the model are in the tolerated range value to be a feasible fuel.
PCA analysis proves to be a successful approach to identify the most representative coefficients in the multivariate study. Chemical groups identified in the model are well represented by the partial least square regression which remarks the reliability of the model. A total of 12 samples were contemplated for the construction for the cetane number calibration curve within a grade of cetane number from 1 to 76, as maximum value reached through a parametric correlation. A validation of the calibration curve was performed for Jet fuel A-1 and a pyrolitic oil of waste tire sample graded with a cetane number of 51.5 ± 10 and 37.7 ± 10.
All samples underwent PLS, PCA, Cross validation analysis and a statistical analysis that included Standard Error of Prediction (SEP), Prediction error and a probability distribution test, to verify the model accuracy. While different kinds of diesel might be assessed, this method clearly offers potential robustness to predict fuels cetane number since it integrates fuels chemical composition and a well-defined predictive calibration curve.
CHAPTER 6
FUTURE WORK AND RECOMMENDATIONS
For future work it is recommended:
To define a narrower scale of cetane number among sampling (cetane grading proximity between two sample), since error is minimized.
To include more samples and conduct a larger number of replications, since the samples used in this study were few and all of them are classified as diesel fuel type 1but there is no diesel type 2 included in the calibration curve.
To perform a Levenberg-Marquadt minimization of parametric values to improve the predicted cetane number.
Make use of “MethodCN” in VISION® features to predict samples since this method includes all predictive and multivariable algorithms.
To validate samples error with ASTM D613 to determine the model deviation from commercial testers.
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APPENDIX 1
PETRO-DIESEL SAMPLES
Figure A.1.1. Fuel sampling
Figure A.1.3. Diesel distillation assemblage
Figure A.1.5. Distillation profile 90% diesel+10% lubricating oil
Table A.1.1. Jet fuel A-1 ICP sample distillation data
% Vol. recovery Temperature (°C)
0 154.6
10 181.4
20 191.1
30 198.7
40 206
50 213.4
60 220.3
70 227.4
80 235.3
90 246.2
100 266.3
Table A.1.2. Pure component CN of blended samples and lumps considered
Sample Blend Compound CN* Parameters Composition CN linear CN (number) CN parameters
1 BD90
Diesel
- -
0.10
52 - -
Lubricating
oil 0.90
2 BD100
Diesel
- -
1.00
48 - -
Lubricating
oil 0.00
3 BDS1
n-hexadecane 92 0.5212 0.03
4 3 1
Benzene 0 3.1967 0.90
Toluene 18 3.1967 0.03
cyclohexane 16.9 0.0727 0.05
4 BDS2
n-eicosane 110 7.3717 0.08
10 61 19
Benzene 0 3.1967 0.85
n-nonadecane 18 0.5212 0.03
cyclohexane 16.9 0.0727 0.05
5 BDS3
Benzene 0 3.1967 0.20
23 29 14
Cyclohexane 17 0.0727 0.30
Toluene 18 3.1967 0.40
n-heptadecane 100 0.5212 0.05
n-nonadecane 110 0.5212 0.05
6 BDS4
Benzene 0 3.1967 0.20
36 69 30
Cyclohexane 17 0.0727 0.18
Toluene 40 3.1967 0.48
n-hexadecane 92 0.5212 0.10