Linear regression determines crude properties at variable boiling points

Robert E. Maples
Maples & Associates Tulsa

• Examples of linear regression [44,979 bytes]

Crude assays nearly always include a true boiling point (TBP) distillation, which consists of crude properties given at discrete boiling points. However, an engineer is often interested in blends with different boiling ranges than those reported.

Using regression analysis, an engineer can get the information that crude assays do not provide.

In crude assays, a TBP distillation provides properties of discrete crude fractions obtained by batch distillation of the crude. Consecutive fractions are blended together to obtain larger fractions of boiling ranges approximating those commonly obtained by plant distillation. Examples of reported blend properties are sulfur content, octane number, freeze point, and gravity.

Over the years, various companies have developed their own equipment and procedures to perform TBP distillations. Many companies use the ASTM-approved method D-2892, also known as "15/5." It uses a column with 15 theoretical plates and a 5:1 reflux ratio. The distillation is conducted at atmospheric pressure (with temperatures corrected to a pressure of 760 mm Hg) to a temperature of 400° C. (752° F.). The residue is then distilled at reduced pressure to as high as 600° C. (1,112° F.) (equivalent atmospheric temperature). A discontinuity usually results in plots of the data where the change in operating pressure occurs. It is thought that a smooth curve through the data better represents the actual crude.

Linear regression

An engineer is often interested in blends with different boiling point ranges than those reported in the crude assays because they simulate seasonal variations in refinery operation that satisfy different product slates. Also, the ranges are used to explore other operating scenarios.

Plots of TBP distillation data have the form of a "flattened S" with two points of inflection. Several equations have been used to fit these data. The equations are usually forms of the Gompertz equation. However, the volume percent distilled (the dependent variable) data from a TBP distillation can be fitted satisfactorily to a simpler third order polynomial of the temperature (the independent variable) by linear regression.

Linear regression allows an engineer to determine the yields and properties of any fraction of crude. The accompanying box shows the results of regression analysis for Arab Light crude and Norwegian Oseberg crude.

Figs. 1a, 1b, and 1c [162,336 bytes] graphically compare the assay data and the regression analysis for Norwegian Oseberg crude. Having calculated the starting and ending volume percents (V) corresponding to the chosen cut temperatures (T), the volume mid-percent (M) for the cut can be calculated. A correlation between volume mid-percent (the independent variable) and properties of TBP cuts or blends (the dependent variables, such as gravity and sulfur content) can be made by simple linear regression. Results are sometimes unsatisfactory because reported data on some properties, such as sulfur content, may be too few for satisfactory simulation.