STATISTICAL ANALYSIS OF THE RELATIONSHIP BETWEEN CERTAIN PROPERTIES OF OIL

G. G. Blagopoluchnaya, N. M. Smolyaninova, A. F. Fedorov

(Presented by the scientific-methodological seminar of the organic departments of the Faculty of Chemical Technology)

The expansion of the area of application of oil as a raw material for petrochemistry and for the production of a wide range of fuels and oils leads to an increase in the number of indices used in assessing oil quality and serving as the basis for designing technological processes. This is associated with carrying out a large number of lengthy, labor-intensive, costly studies. A more complete description of oil properties is needed already at the stage of exploration of oil fields, with respect to the various directions of its use. However, the inclusion of a large number of indices in the set of oil analyses leads to excessive complication and increased cost of exploration and research work, as well as to longer periods for carrying it out.

In the present work an attempt has been made, using methods of mathematical statistics, to investigate the interrelationships among certain properties of oil and to select a comparatively small set of indices by means of which, with accuracy sufficient for practical purposes, oil can be characterized as a raw material for the principal directions of its use.

The main difficulty in a quantitative study of indices of oil properties is the complex simultaneous influence of a large number of factors that are not subject to control. From the point of view of mathematics, such a process may be regarded as random and assessed from the standpoint of probabilistic-statistical theories. The problem posed is solved with the aid of correlation and regression analyses of experimental data [3].

In the present work an attempt has been made to study linear correlation dependences among ten main physicochemical characteristics of oils: specific gravity \((d^{20}_{4})\), molecular weight \((M)\), viscosity \((\gamma_{20})\), Conradson carbon residue \((K)\), pour point of the oil \((T_{\text{solid.}})\), content of total sulfur \((S_{\text{tot.}})\), paraffin \((P)\), resin-asphaltene substances \((SA)\), and yields of fractions up to 200 and 300°C.

The initial data for establishing the form and closeness of the relationship among the indicated indices of the physicochemical characteristics of oil were materials from studies of eastern oils, borrowed from [1, 2], and data from analyses of Tomsk oils obtained in the Laboratory for the Comprehensive Utilization of Peat of TPI. In processing the results of laboratory analyses, it was assumed that changes in the characteristics of oil, as in most other biological objects—

... (we regard oil as a biological object, since we are adherents of the theory of the organic origin of oil), and, with a sufficiently large sample of initial data [3], follow a normal distribution. In order to test this assumption, i.e., whether it may be considered that the deviations of the observed frequencies from those that follow the law of normal distribution arose from random quantities, theoretical normal frequencies were calculated for the principal indices.

Testing the initial data by Pearson’s criterion [4] gave satisfactory results. In the statistical analysis of oil properties, their means, standard deviations, coefficients of paired, partial, and multiple correlation, regression coefficients, and their standard deviations were calculated on the “Mir-1” electronic digital computer. The existence, closeness, and direction of the relationship between the indices of the physicochemical characteristics of oil were established from the magnitude and sign of the correlation coefficients [5], whose matrix is presented in Table 1.

Using the function

\[ Z=\frac{1}{2}\ln \frac{1+r}{1-r}, \tag{4} \]

proposed by Fisher, it was determined for what sample size a correlation coefficient of a given magnitude would be reliable at the required probability threshold of error-free forecasts [4, Table XII]. Equations of rectilinear regression were compiled for those characteristics for which significant paired correlation coefficients were obtained that sufficiently characterized a linear relationship \((r>0.5)\), Table 1.

Table 1

Matrix of correlation coefficients

It is known that, as the specific gravity of oil increases, its molecular mass, the content of resin-asphaltene substances in it, and its coking capacity increase [6, 7]. The pour point of oil is determined mainly by its paraffin content [6, 7]. In the present work an attempt is made to represent these dependences analytically.

On the basis of an analysis of the matrix of correlation coefficients, and of the complexity and accuracy of methods for determining the indices of the physicochemical characteristics of oil, the arguments of the regression equations were selected for calculating molecular mass, the content of resin-asphaltene substances, and paraffin. Calculation of the coefficients of the regression equation and analysis of the obtained equations of relationship (Appendix) were carried out by means of multiple correlation analysis [5] on an electronic digital computer...

Appendix

LINEAR REGRESSION EQUATIONS

I. Determination of the molecular weight \((M)\) of oil:

1)
\[ M=-923+1352.85d_4^{20}+5.3K; \]
\[ W=0.88;\quad Gd_4^{20}=161.868; \]
\[ R_{Md,\ K}=0.7;\quad GK=2.041; \]
\[ R_{MK,\ d_4^{20}}=0.3;\quad N=74. \]

2)
\[ M=-1169.33+1661.46d_4^{20}; \]
\[ Gd_4^{20}=114.442;\quad N=74. \]

II. Determination of the paraffin content \((P)\) in oil:

\[ P=4.95+0.69T_{\text{solid.}}; \]
\[ GT_{\text{solid.}}=0.0101;\quad N=130. \]

III. Determination of resinous-asphaltene substances in oil \((SA)\):

1)
\[ SA=-27.96+36.5d_4^{20}+2.4K; \]
\[ W=0.935;\quad Gd_4^{20}=13.805; \]
\[ R_{CAd_4^{20},\ K}=0.3;\quad GK=0.207; \]
\[ R_{CAK,\ d_4^{20}}=0.78;\quad N=89. \]

2)
\[ SA=1.29+2.56K+1.55S_{\text{tot}}; \]
\[ W=0.92;\quad GK=0.228; \]
\[ R_{CAK,\ S_{\text{tot}}}=0.73;\quad GS_{\text{tot}}=0.536; \]
\[ R_{CA,\ S_{\text{tot}}\ K}=0.3;\quad N=112; \]

3)
\[ SA=4.4+2.3K-0.005M; \]
\[ W=0.68;\quad GK=0.277; \]
\[ R_{CAK,\ M}=-0.65;\quad GM=0.0105; \]
\[ R_{CAM,\ K}=-0.49;\quad N=100. \]

4)
\[ SA=1.16+3K; \]
\[ GK=0.127; \]
\[ N=112, \]

where

\[ N \text{ — sample size;} \]
\[ W \text{ — coefficient of multiple correlation;} \]
\[ R \text{ — coefficient of partial correlation;} \]
\[ G \text{ — root-mean-square deviation of the regression coefficients.} \]

“Mir-1.” Verification of the compiled equations of straight-line regression by Rao’s criterion [8] and on oil samples whose data were not included in the calculations gave satisfactory results.

REFERENCES

1. New Oils of the Eastern Regions of the USSR. Reference book. Edited by S. N. Pavlova and Z. V. Driatskaya. Moscow, “Khimiya,” 1967.

2. Oils of the Eastern Regions of the USSR. Reference book. Edited by S. N. Pavlova and Z. V. Driatskaya. Moscow, “Khimiya,” 1962.

3. Aivazyan S. A. Statistical Studies of Dependencies. Moscow, “Metallurgiya,” 1968.

4. Plokhinskii N. A. Biometrics. Novosibirsk, NGU Publishing House, 1970.

5. Silich V. A., Shepelina M. M. Collected volume “Cybernetics and Higher Educational Institutions,” 4, 164, Tomsk, TSU Publishing House, 1971.

6. Rybak B. M. Analysis of Oil and Petroleum Products. Moscow, Gostoptekhizdat, 1962.

7. Nametkin S. S. Chemistry of Oil. Moscow, Publishing House of the Academy of Sciences of the USSR, 1955.

8. Rao S. R. Linear Statistical Methods and Their Application. Moscow, “Nauka,” 1968.