The four-variable equation calculated cetane index described in the standard "ASTM D4737-21 Standard Test Method for Cetane Index Calculated by Four-Variable Equation" published by the American Society for Testing and Materials (ASTM) provides a means to estimate the ASTM cetane number (ASTM D613-08 Standard Test Method for Cetane Number of Diesel Fuel Oil) of distillate fuels from measurements of density and distillation recovery temperature. The value calculated from the equation is called the four-variable equation calculated cetane index.
The four-variable equation calculated cetane index is not an optional method for expressing the ASTM cetane number. It is an additional tool for estimating the cetane number when a test result is not available using the test method described in ASTM D613-08 and when no cetane improver is used. As an additional tool, the four-variable equation calculated cetane index should be used with due consideration of its limitations.
Procedure A, Class no 975–D S02 according to ASTM D1-15 standard, Class number 1–D S500 is used for Class #1–D S5000, Class #2–D S15, Class #2–D S5000, and Class #4–D. Procedure A is based on a data set that includes a relatively small number of Class #1–D fuels. Procedure A per ASTM D4737-21 may be less applicable to Class #1–D S15, Class #1–D S500, and Class #1–D S5000 than Class #2–D S5000 or Class #4–D fuels. Procedure A has been validated as applicable to Class #2–D S15 diesel fuels.
Procedure B is used for Class number 975–D S02 specification per ASTM D2-500.
The four-variable equation-calculated cetane index test method is particularly applicable to Class 1–D S5000, Class 1–D S500, Class 2–D S5000, and Class 2–D S500 diesel fuel oils, including straight-flow and cracked stocks and mixtures thereof. It can also be used for heavier fuel oils with a 90 percent recovery point lower than 382 degrees and fuel oils containing derivatives from oil sands and oil shales.
Biodiesel blends were excluded from this test method because they were not part of the data sets used to develop Procedure A or Procedure B.
Two correlations have been established between the ASTM cetane number and the density of the fuel and the 10 percent, 50 percent, and 90 percent distillation recovery temperatures. Procedure A was developed for diesel fuels meeting the requirements of ASTM D975-02 Class #1–D S15, Class #1–D S500, Class #1–D S5000, Class #2–D S5000, and Class #4–D. It was found to be applicable for Class #2–D S15.
The empirical equation for Procedure A of cetane index calculated by the four-variable equation was derived using the generalized least squares fitting technique, which takes into account the measurement errors in the independent variables (fuel properties) and the dependent variable (cetane number according to ASTM D613-08 standard).
Procedure B was developed for diesel fuels meeting the requirements of Class number 975–D S02 specification per ASTM D2-500.
The empirical equation for Procedure B of the cetane index calculated with the four-variable equation was derived from the National Exchange Group data for 16 Class #500–D S111 diesel fuels with sulfur levels between 2 and 500 ppm using the partial least squares technique.
The calculated cetane index of the four-variable equation is useful for estimating the ASTM cetane number when a test engine is not available to determine this property directly and when cetane improver is not used. It can be conveniently used to estimate the cetane number when the available sample quantity is too small for an engine rating. In cases where the ASTM cetane number of a fuel has been previously determined, the calculated cetane index of the four-variable equation is useful as a cetane number control for subsequent batches of that fuel, provided the source and method of manufacture of the fuel remain unchanged.
Over the cetane number range of 32,5 to 56,5, the expected error of prediction of the four-variable equation for the calculated cetane index, Procedure A, is less than 65 cetane numbers for 62 percent of the distillate fuels evaluated. Errors may be greater for fuels whose properties fall outside the recommended application range.
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