ON THE DETERMINATION OF OCTANE AND CETANE NUMBERS BY A COMPUTATIONAL METHOD

G. G. Blagopoluchnaya, A. F. Fedorov, A. K. Maksimov

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

Previously proposed empirical equations [1, 2, 3] for calculating octane and cetane numbers have not come into wide use. More reliable and widespread remain the motor and research methods for determining octane numbers and the coincidence-of-flashes method for cetane numbers. These analyses require special, and moreover expensive, installations, a special room, and qualified maintenance, which creates certain difficulties for many scientific research organizations.

At the present time, a large amount of material has accumulated on the investigation of fuel-quality indices determined according to identical standardized methods [4, 5, 6, 7, 8], which creates the necessary prerequisites for their statistical processing with the aim of quantitatively expressing the regularities of the properties of petroleum products.

In recent years, correlation and regression methods have become widely used for studying interrelations among the properties of an object; in the field of petrochemistry and petroleum refining they are still applied very limitedly.

We set ourselves the task of studying the relationship of the octane number (o.n.) with the relative density \((\rho_4^{20})\) and the group hydrocarbon composition of gasolines (fraction 28—200°C); and of the cetane number (c.n.) with relative density \((\rho_4^{20})\), viscosity \((v_{20})\), pour point \((T_{\text{pour}})\) and flash point \((T_{\text{flash}})\), as well as sulfur content \((s)\) in various fractions of diesel fuels. The stated problem was solved by the method of linear multiple regression using the “MIR” electronic digital computer [9] and by the principal-components method on the “BESM-4” computer [10].

The closeness and direction of the relationship were established from the magnitude and sign of the pair-correlation coefficients \((r)\), presented in Tables 1, 2, 3, 4.

The reliability of the coefficients obtained was established by Student’s criterion by comparing them with the critical coefficients for the given sample size and confidence probability \(\alpha = 0.95\) [11].

In analyzing the matrix of correlation coefficients (Table 1), it was established that the closest relationship exists between the octane number and the content of naphthenic and paraffinic (P) hydrocarbons; a less close relationship—with the relative density of the gasoline (28—200°C);

Table 1

Matrix of pairwise correlation coefficients of gasoline quality indices
(fraction 28–200° C)

Note: The left part of the matrix contains the critical values of the correlation coefficients.

Table 2

Matrix of pairwise correlation coefficients of quality indices of diesel fuel
fraction 150–350° C

Note: All correlation coefficients greater than 0,20 are significant.

Table 3

Matrices of pairwise correlation coefficients of quality indices
of diesel fuel fraction 200–350° C

Note: All pairwise correlation coefficients greater than 0,21 are significant.

Table 4

Matrix of pair correlation coefficients of quality indices
of diesel fuel, fraction 240–350°C

Note. Correlation coefficients greater than 0.30 are significant.

However, density is an indirect indicator of chemical composition; its determination is simpler, more precise, and does not require much time or expense; consequently, it is expedient to select this index as an argument in the regression equation for calculating the octane number. In addition, the inadvisability of using the chemical hydrocarbon composition as arguments of the equation is indicated by the high correlation among the contents of aromatic, naphthenic, and paraffinic hydrocarbons, which is entirely inadmissible from the standpoint of mathematical statistics, since it leads to large errors in multiple-regression equations [12]. Similarly, by analyzing the matrices of correlation coefficients of diesel-fuel quality indices (Tables 2, 3, 4), the relative density of the corresponding fractions was selected as the argument of the regression equations for determining cetane numbers.

Linear regression equations for calculating octane and cetane numbers from relative density are presented in Table 5.

Since density possesses the property of additivity, we additionally investigated the relationships between the indices of detonation resistance, ignitability, and the relative density of the oil. No linear relationship was found between them (Tables 1, 2, 3, 4), but a close linear relationship exists between the densities of fuels and oil ($r$ 28–200°C = 0.48; $r$ 150–350°C = 0.5; $r$ 200–350°C = 0.7; $r$ 240–350°C = 0.78); therefore one may assume the presence of a nonlinear dependence of octane and cetane numbers on oil density.

For the indicated relationships, nonlinear models in the form of a second-degree polynomial were constructed; they are presented in Table 6.

The quality of approximation of the obtained regression equations was assessed by the Fisher ratio at confidence probability $\alpha = 0.95$ [12].

\[ F = \frac{s_y^2}{s_{\text{res}}^2}, \]

where $F$ is the Fisher ratio;
$S_y$ is the sample variance;
$S_{\text{res}}$ is the residual variance of the regression equation.

Table 5

Regression equations for calculating octane and cetane numbers
from the relative density of fuels

Table 6

Regression equations for calculating octane and cetane numbers
from the relative density of crude oil

The greater the calculated value exceeds the tabulated one, the more effective the equation. The error of the equations was determined by the formula [12]

\[ m_{\overline{y}_x}=\sigma_y \sqrt{\frac{1-r^2}{1-n}}, \]

where \(m_{\overline{y}_x}\) is the error of the equation;
\(n\) is the sample size.

A statistical evaluation of the regression equations showed the possibility of using them to calculate the octane and cetane numbers from the relative density of fuels and to predict them from the relative density of crude oils, since the latter expressions have a large residual variance compared with the former.

To check the regression equations obtained, thirty samples were taken for all four fuel fractions that were not included in the initial samples [8]. Comparison of the octane and cetane numbers determined under laboratory conditions and calculated from the equations gave satisfactory results. The mean absolute error of discrepancy between the calculated and experimental values of the cetane numbers, presented in Tables 5 and 6, is less than the absolute error permitted by GOST 3122-52.

REFERENCES

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2. N. G. Puchkov, Diesel Fuels. Moscow, Gostoptekhizdat, 1953.

3. B. V. Losikov, Petroleum Products. Handbook. Moscow, “Khimiya,” 1966.

4. Crude Oils of the Eastern Regions of the USSR. Reference book edited by S. N. Pavlova and Z. V. Driatskaya. Moscow, Gostoptekhizdat, 1953.

5. Crude Oils of the Eastern Regions of the USSR. Reference book edited by S. N. Pavlova and Z. V. Driatskaya. Moscow, Gostoрizdat, 1962.

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

7. E. A. Robinson, Crude Oils of the Tatar ASSR. Moscow, Publishing House of the Academy of Sciences of the USSR, 1960.

8. Crude Oils of the USSR. Handbook, Vol. 1. Crude Oils of the Northern Regions of the European Part of the USSR and the Urals. Moscow, “Khimiya,” 1971.

9. V. A. Silich, M. M. Shepelina. Program for constructing linear multiple regression. In: Cybernetics and the Higher Educational Institutions, issue 4. Tomsk, Tomsk State University Publishing House, 1971.

10. I. Petersen. Use of Statistical Data of Normal Operating Conditions of a Statistical Process to Construct Its Model. Moscow, IL, 1971.

11. N. A. Plokhinskii, Biometrics. Moscow, Moscow State University Press, 1970.

12. V. V. Kafarov, Methods of Cybernetics in Chemistry and Chemical Technology. Moscow, “Khimiya,” 1971.