**3.1. Acquisition database: Infrared radiation**

In the oil industry, signs of infrared radiation generated by sensors are associated with the prediction of the quality of distillates such as naphtha, gasoline, diesel and jet fuel (Kim, Cho; Park, 2000).

Contributions of Multivariate Statistics in Oil and Gas Industry 7

overlap. The broad spectral bands formed are difficult to interpret (Skoog; Holler; Crouch, 2007) due to the phenomenon of collinearity (Naes; Martens, 1984). The origin of this phenomenon is associated with the manner in which the infrared radiation interacts with

These input variables (radiation absorbed), called Xi are correlated, so are said collinear or multicollinear (NAES et al., 2002). To illustrate the collinearity, X is a dummy matrix aij with i rows and j in terms columns, where aij is the radiation absorption of three samples i (i = 1,

The columns of X are linearly dependent, so the variables column j1 and j2 are colinear, that is, when increases j1, j2 increases proportionally. This causes the determinant of X'X to be

<sup>T</sup> 14 28

Then, the det (X'X) = (14.56) - (28.28) = 0 and this according to Naes et. al (2002) means that there is a singular error matrix and that those erros are propagated when the dependent properties, Y, are determined by regression methods which are not based on the principal

However, the multivariate approaches such as Principal Component Regression (PCR) and PLS have been quite appropriate due to dimensionality reduction, which creates a new set of variables called principal components (Rajalahti; Kvalheim, 2011). So with data mining for Multivariate Analysis, it is possible to relate the physicochemical properties (quality characteristics) of products with the chemical composition of the sample reflected by the absorption spectra. So once modeled a property, just a sample is subjected to infrared

In this work were modeled properties of gasoline, diesel and jet fuel. For gasoline, the

According to Freitas (2012), kinematic viscosity of the diesel oil and jet fuel products is an important property in terms of its effect on power system and in fuel injection. Both high and low viscosities are undesirable since they can cause, among others, problems in fuel atomization. The formation of large and small droplets (low viscosity), can lead to a poor distribution of fuel and compromise the mixture air – fuel resulting in an incomplete

octane number and for diesel oil and jet fuel, the kinematic viscosity property.

combustion followed by loss power and greater fuel consumption.

28 56 

X X=

matter and can be demonstrated by Quantum Mechanics at work Pasquini (2003).

**X**

2, 3) at two wavelengths j (j = 1, 2).

zero, where X' is the transpose of matrix X.

components, such as the MLR.

radiation to predict their properties.

**3.1. Acquisition data base: Reference properties** 

Freitas et al. (2012) and Pasquini (2003) explain this instrumentation (Figure 1): the polychromatic radiation emitted by the source has a wavelength selected by a Michelson interferometer. The beam splitter has a refractive index such that approximately half of the radiation is directed to the fixed mirror and the other half is reflected, reaching the movable mirror and is therefore reflected by them. The optical path differences occur due the movement of the movable mirror that promotes wave interference.

An interferogram is obtained as a result of a graph of the signal intensity received by the detector versus the difference in optical path traveled by the beams. By calculating the Fourier Transform (FT) the interferogram can be written as a sum of sines and cosines (Tarumi et al, 2005) and in this case, happens to be called transmittance spectra, T (Forato; Filho; Colnago, 1997). Finally, the spectrum of transmittance, T, is converted to absorbance spectra, A, by co-logarithm of T (Suarez et al. May 2011). The absorbance can be interpreted as the amount of radiation that the sample absorbs and the transmittance, the fraction of radiation that the sample does not absorb. These phenomena occur depending on their chemical composition (Kramer; Small, 2007).

**Figure 1.** Scheme for technology acquisition database (Adapted from Pasquini, 2003)

The chemical bonds of the type carbon-hydrogen (CH), oxygen-hydrogen (OH) and nitrogen-hydrogen (NH), present in petroleum products (Pasquini; Bueno, 2007), are responsible for the absorption of infrared radiation, however, are not very intense and overlap. The broad spectral bands formed are difficult to interpret (Skoog; Holler; Crouch, 2007) due to the phenomenon of collinearity (Naes; Martens, 1984). The origin of this phenomenon is associated with the manner in which the infrared radiation interacts with matter and can be demonstrated by Quantum Mechanics at work Pasquini (2003).

6 Multivariate Analysis in Management, Engineering and the Sciences

**3.1. Acquisition database: Infrared radiation** 

chemical composition (Kramer; Small, 2007).

movement of the movable mirror that promotes wave interference.

**Figure 1.** Scheme for technology acquisition database (Adapted from Pasquini, 2003)

The chemical bonds of the type carbon-hydrogen (CH), oxygen-hydrogen (OH) and nitrogen-hydrogen (NH), present in petroleum products (Pasquini; Bueno, 2007), are responsible for the absorption of infrared radiation, however, are not very intense and

In the oil industry, signs of infrared radiation generated by sensors are associated with the prediction of the quality of distillates such as naphtha, gasoline, diesel and jet fuel (Kim,

Freitas et al. (2012) and Pasquini (2003) explain this instrumentation (Figure 1): the polychromatic radiation emitted by the source has a wavelength selected by a Michelson interferometer. The beam splitter has a refractive index such that approximately half of the radiation is directed to the fixed mirror and the other half is reflected, reaching the movable mirror and is therefore reflected by them. The optical path differences occur due the

An interferogram is obtained as a result of a graph of the signal intensity received by the detector versus the difference in optical path traveled by the beams. By calculating the Fourier Transform (FT) the interferogram can be written as a sum of sines and cosines (Tarumi et al, 2005) and in this case, happens to be called transmittance spectra, T (Forato; Filho; Colnago, 1997). Finally, the spectrum of transmittance, T, is converted to absorbance spectra, A, by co-logarithm of T (Suarez et al. May 2011). The absorbance can be interpreted as the amount of radiation that the sample absorbs and the transmittance, the fraction of radiation that the sample does not absorb. These phenomena occur depending on their

**3. Methods** 

Cho; Park, 2000).

These input variables (radiation absorbed), called Xi are correlated, so are said collinear or multicollinear (NAES et al., 2002). To illustrate the collinearity, X is a dummy matrix aij with i rows and j in terms columns, where aij is the radiation absorption of three samples i (i = 1, 2, 3) at two wavelengths j (j = 1, 2).

$$\mathbf{X} = \begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{bmatrix}$$

The columns of X are linearly dependent, so the variables column j1 and j2 are colinear, that is, when increases j1, j2 increases proportionally. This causes the determinant of X'X to be zero, where X' is the transpose of matrix X.

$$\mathbf{X}^{\top}\mathbf{X} = \begin{bmatrix} 14 & 28\\ 28 & 56 \end{bmatrix}$$

Then, the det (X'X) = (14.56) - (28.28) = 0 and this according to Naes et. al (2002) means that there is a singular error matrix and that those erros are propagated when the dependent properties, Y, are determined by regression methods which are not based on the principal components, such as the MLR.

However, the multivariate approaches such as Principal Component Regression (PCR) and PLS have been quite appropriate due to dimensionality reduction, which creates a new set of variables called principal components (Rajalahti; Kvalheim, 2011). So with data mining for Multivariate Analysis, it is possible to relate the physicochemical properties (quality characteristics) of products with the chemical composition of the sample reflected by the absorption spectra. So once modeled a property, just a sample is subjected to infrared radiation to predict their properties.

#### **3.1. Acquisition data base: Reference properties**

In this work were modeled properties of gasoline, diesel and jet fuel. For gasoline, the octane number and for diesel oil and jet fuel, the kinematic viscosity property.

According to Freitas (2012), kinematic viscosity of the diesel oil and jet fuel products is an important property in terms of its effect on power system and in fuel injection. Both high and low viscosities are undesirable since they can cause, among others, problems in fuel atomization. The formation of large and small droplets (low viscosity), can lead to a poor distribution of fuel and compromise the mixture air – fuel resulting in an incomplete combustion followed by loss power and greater fuel consumption.

The octane number of a gasoline is an important characteristic which is related to their ability to burn in spark-ignition engines. It is determined by comparing its tendency to detonate with the reference fuel with octane known under standard operating conditions.

When it comes to defining the octane required by engines, many countries use anti-knock index (I), defined by Equation 1:

$$\text{I} = \frac{\text{MON} + \text{RON}}{2} \tag{1}$$

Contributions of Multivariate Statistics in Oil and Gas Industry 9

**Variables RMSEP Correlation** 

Mean -3,10862E-17 StDev 1 N 25 AD 0,515 P-Value 0,174

Samples of gasoline, diesel and jet fuel, collected during 1 year, were subjected to laboratory tests, to determine the input variables, Xi, which are the infrared radiation absorbed, and the response variables, Yi, that are physicochemical properties. The physicochemical properties

The Table 1 summarizes the validation results of each model for products gasoline, diesel and jet fuel, where RMSEP (Root Mean Square Error of Prediction) corresponds to the standard deviation of the residuals (differences between measured and predicted values by the model). The Figures 3-6 illustrate that the residues of models follow normal distribution, since in all

**Latent**

**samples** 


**Stardadize Residuals**

Diesel Oil Viscosity (40ºC) 180 8 0.116 cSt 0.9368 Gasoline MON 350 6 0.22 0.8723 Gasoline RON 350 7 0.22 0.9891 Jet Fuel Viscosity (-20ºC) 279 7 0.01 cSt 0.8836

> **MON (Gasoline)** Normal

**4. Results and discussion** 

will be predicted by PLS models.

cases the p-value was greater than 0.05.

**Product Property Number of** 

**Table 1.** Summary of results of modeling and validation.

99

**Percent**

1

**Figure 3.** Normality Test for the property MON

where MON is the Motor Octane Number and RON is the Research Octane Number. The method MON measures the resistance to detonation when gasoline is being burned in the most demanding operating conditions and at higher rotations. The test is done in motors CFR (Cooperative Fuel Research), single-cylinder with variable compression ratio equipped with the necessary instrumentation in a stationary base, as shown in Figure 2.

**Figure 2.** CFR engine for MON octane (WAUKESHA, 2012)

The RON method evaluates the resistance of the gasoline to detonation under milder conditions and work in less rotation than that measured by octane number MON. The test is done in similar engines to those used for testing in MON octane.

It takes two hours and half to run the test MON and it is spent the same time for the test RON.
