New equations predict boiling point from viscosity, gravity

José Vicente Gomez
Maraven S.A. Punto Fijo, Venezuela

• Equations [58119 bytes]

Although somewhat complex, the equations easily can be programmed into a personal computer or hand-held calculator.

The algorithm makes use of a single nonlinear equation with one unknown variable (boiling point), which requires numerical solution. A convenient correlation generates starting values for mean average boiling point (MeABP) that are accurate enough to allow convergence in three or fewer iterations.

Background

When it comes to characterizing petroleum fractions, distillation curves are the most common source of data. They allow calculation of the average boiling points of the cuts. These values then can be plugged into correlations for predicting molar mass, pseudocritical properties, and characterization factors (Fig. 1a [43161 bytes]).

In the absence of distillation data, further characterization of a stream cannot proceed unless a good estimate of its average boiling point is somehow obtained. The lack of distillation curves usually is faced when dealing with heavy products, but this sometimes happens with lighter fractions also.

One feasible approach for characterizing fractions with unknown distillation curves is suggested by API. This technique is shown in graphical form in Fig. 1b [43161 bytes].¹

Here, the kinematic viscosities at standard temperatures (100 and 210° F.) and the specific gravity at 60° F. are used as alternative characterization parameters. (Kinematic viscosities at 100° F. and 210° F. are referred to as, respectively, V100 and V210)

In the API method, the Riazi-Daubert correlation is used to calculate the fraction's molar mass from its viscosity and specific gravity.^{1 2} Then, molar mass and specific gravity are used to read MeABP from the API nomograph.¹ Finally, the remaining properties are obtained from predictive models based on boiling point and specific gravity.^3-7

While the scheme in Fig. 1b is not the only possible approach, it is one of the few feasible choices for an engineer with limited data and time.⁸ Yet for all its simplicity, it has an important drawback: it cannot be set up for a computer program because finding the boiling point involves a graphical interpretation step.

Furthermore, as will be seen later, the accuracy of boiling points from the API nomograph for heavier fractions leaves something to be desired. Hence, it would be useful to mathematically circumvent the use of the API nomograph. If this is accomplished, determining boiling points from viscosity and gravity data would be amenable to computer programming.

Abbott, et al., and Twu have developed well-known mathematical methods for predicting V100 and V210 from normal boiling point and specific gravity.^9-11 It can be argued, therefore, that those models could be solved backwards to find boiling point by a trial-and-error procedure.

In practice, however, this author has found that such an approach usually is misleading. Those methods use separate correlations to calculate V100 and V210, and backwards calculations tend to yield two boiling points that are inconsistent with each other.

Obviously, the goal of the calculation is to arrive at a single, reliable value for boiling point.

New approach

The graphical step in the scheme described previously hinges on molar mass, which is determined via a viscosity and gravity-based correlation. For this calculation, the Riazi-Daubert method is preferred over the one by Hirschler due to its superior accuracy.^{1 6 12}

In contrast with the scheme in Fig. 1b, molar mass in Fig. 1a is obtained via equations based on boiling point and specific gravity. It was thus an intuitive approach to match the Riazi-Daubert viscosity/gravity correlation to one of the boiling point/gravity equations available in the open literature and through private sources.^{1 8-23} The resulting expression could be then mathematically solved for boiling point.

This raised the question, however, of which of the boiling point/gravity equations would yield the best match.

The author's initial trials for lighter fractions showed that readings from the API nomograph were best reproduced when matching the Riazi-Daubert correlation to that of Rao-Bardon.^{1 6 23} After running data for heavy fractions, however, it became evident that the match had its flaws.

Although boiling points from the matched equations were consistent with those from the API nomograph, the predicted values always overestimated the boiling point relative to the reported values.

In a trial of one heavy fraction, for example, the Rao-Bardon and Riazi-Daubert equations predicted a boiling point of 1,174° F. and the API nomograph predicted 1,185° F. The reported value was 1,054° F.

The reason for such high deviations has to do with the accuracy of the molar mass data from which the API nomograph was originally derived.

Recent data demonstrate that stocks with normal boiling points of 800° F. and higher have greater molar masses than was estimated during the 1930s, when the data bases for the API nomograph were developed.²⁴ Refinements in laboratory methods and awareness of the effect of asphaltenes content on a fraction's molar mass have been responsible for these changes.

It is the asphaltenes that are regarded as largely responsible for the physical and rheological properties of petroleum residue, bitumens, and asphalts.²⁵

For the sake of accuracy, the desired boiling point prediction method had to closely reproduce the API nomograph portion for lighter cuts and the new data for heavier ones.

The best overall results were obtained when matching three previous methods.^{1 6 11}

Matching these correlations produced the functions shown in Equations 1 and 3, which predict boiling points for, respectively, heavy and light fractions (Equations, Nomenclature).

Because it is here assumed that V100, V210, and specific gravity (SG) are known, the only unknown variable in the equations is the normal boiling point (BP). Equations 1 and 3 are nonlinear in BP and have to be numerically solved. The Newton-Raphson technique has been found to be satisfactory for this purpose.

Equations 2 and 4 give the first derivative of F(BP), which is required by the Newton-Raphson procedure. Although the equations admittedly appear bulky, they can be programmed easily into a personal computer or hand-held calculator.

Finally, to provide starting values for BP in order to run the Newton-Raphson routine, the author proposed Equation 5. Estimates returned by this equation are accurate enough to allow convergence in three or fewer iterations.

The calculations

Routine data input comprises V100, V210, SG, and e (the allowed error for convergence). Since one decimal figure is usually considered sufficiently accurate for molar mass, a value of 0.05 is suggested for e.

Fig. 2 [47200 bytes] shows the flowchart for the calculation routine.26

First, BPstart is estimated by Equation 5, then, Equations 1 and 2 are solved for heavy fractions (BPi >/- 1,110° R.). Likewise, Equations 3 and 4 are solved for light fractions (BPi < 1,110° r). iterations continue until the criterion for convergence is met.

Table 1 [6627 bytes] shows a calculation for the boiling point of one vacuum distillate. In this case, only two iterations were needed to reach convergence.

Riazi and Daubert originally evaluated their viscosity/gravity correlation with data fitting the following ranges:⁶

• M, 200-800 lb/lb-mole

• V100, 2-18,000 cSt

• V210, 1-180 cSt

• SG, 0.82-1.08.

Nevertheless, the routine predicts reasonably well beyond those limits, as is shown in Table 2 [45091 bytes].

To illustrate the ability of the routine to estimate average boiling points of even extra-heavy, viscous products, data for Zuata and Boscan crude oils and for two Athabasca bitumens are included.²⁵

Although full-range distillation data are not available for comparison purposes, the estimated boiling points of the bitumens are in good agreement with one partially simulated distillation curve for Athabasca bitumen, and with boiling points derived from the molecular formulae calculations of Speight.^{25 27}

As can be seen from Table 2, estimates from the new method match well with those from the API nomograph for cuts with normal boiling points below 800° F. (1,260° R.). Beyond this range, the API nomograph largely overpredicts boiling points, with respect to reported ones.

The normal boiling points estimated by the routine are obtained indirectly, rather than from distillation data. For this reason, it is impossible to strictly define the type of boiling point found (volume average, molar average, mean average, etc.).

Based on comparisons of actual-vs.-predicted boiling points of lighter fractions (for which complete distillation curves are available), the author concludes that mean average boiling points best fit the ones predicted by the new method.

This view is consistent with other authors' observations that molar mass (the cornerstone property of this method) is best correlated by the mean average boiling point.^{9 28 29}

When estimating normal boiling points of heavier stocks it is necessary to bear in mind, of course, that such values are theoretical, as at atmospheric pressure cracking would occur before those temperatures were reached.

Upon testing the routine against 107 fractions from the author's data base, average and maximum deviations were, respectively, about 1% and 5%.

Viscosity estimation

The present routine requires the kinematic viscosities at standard temperature of 100° F. and 210° F. to be provided. Should V100 or V210 values not be readily available, the following are useful tips for their estimation:

1. When either V100 or V210 is unknown, the missing viscosity can be roughly estimated from Equation 6.

2. When the only available viscosities are at two temperatures other than 100° F. and 210° F., V100 and V210 can be computed by solving the ASTM viscosity equation (Equation 7).³⁰

Acknowledgment

The author is indebted to Dr. James G. Speight, chief executive officer and managing director of Western Research Institute in Laramie, Wyo., for the insight and data generously provided for this article.

References

1. API Technical Data Book, Petroleum Refining, 9th rev., pp. 2-32, Procedures 2B2.1 and 2B2.3, Fig. 2B6.1, March 1988.

2. Riazi, M.R., Daubert, T.E., OGJ, Dec. 28, 1987, pp. 110-12.

3. Kesler, M.G., and Lee, B.I., Hydrocarbon Processing, March 1976, pp. 153-58.

4. Riazi, M.R., and Daubert, T.E., Hydrocarbon Processing, March 1980, pp. 115-16.

5. Twu, C.H., Fluid Phase Equilibria, Vol. 16, 1984, pp. 137-50.

6. Riazi, M.R., and Daubert, T.E., Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986, pp. 1,009-15.

7. Riazi, M.R., and Daubert, T.E., Ind. Eng. Chem. Process Des. Dev., Vol. 26, No. 4, 1987, pp. 755-59.

8. Gomez, J.V., OGJ, July 13, 1992, pp. 49-52.

9. Abbott, M.M., Kaufmann, T.G., and Domash, L., Canadian Journal of Chem. Eng., Vol. 49, 1971, p. 379.

10. Twu, C.H., Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985, pp. 1,287-93.

11. Twu, C.H., AIChE Journal, 32, 1986, pp. 2,091-94.

12 Hirschler, A.E., Journal of the Institute of Petroleum, Vol. 32, No. 267, 1946, p. 153.

13. Mair, B.J., and Willingham, C.B., Ind. Eng. Chemistry, Vol. 28, 1936, p. 1,452.

14. Smith, R.L., and Watson, K.M., Ind. Eng. Chemistry, Vol. 29, 1937, p. 1,408.

15. Hersh, R.E., Fenske, M.R., Booser, E.R., and Koch, E.F., Journal of Inst. of Petr., Vol. 36, No. 322, 1950, p. 624.

16. Nokay, R., Chemical Engineering, Vol. 66, 1959, pp. 147-48.

17. Cavett, R.H., "Physical Data for Distillation Calculations: Vapor-Liquid Equilibria," 27th midyear API meeting, Refining Div., Vol. 42, No. 111, pp. 351-66, 1962.

18. Hariu, O., and Sage, R.C., Hydrocarbon Processing, April 1969, p. 143.

19. Mathur, B.C., Ibrahim, S.H., and Kuloor, N.R., Chemical Engineering, Vol. 76, 1969, pp. 182-84.

20. Massachusetts Institute of Technology, "Computer-Aided Industrial Process Design," U.S. DOE, Contract E(49-18)-2295, Task Order No. 9, Aspen Project, 2nd annual report, June 1, 1977 through May 30, 1978.

21. Brule, M.R., Lin, C.T., Lee, L.L., and Starling, K.E., AIChE Journal, Vol. 28, 1982, pp. 616-25.

22. API Technical Data Book, Petroleum Refining, Vol. 1, 4th ed., Procedure 2B2.1, 1983.

23. Rao, V.K., and Bardon, M.F., Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985, pp. 498-500.

24. Winn, F.W., Petroleum Refiner, February 1957, pp. 157-59.

25. Speight, J.G., The Chemistry and Technology of Petroleum, 2nd ed., Chs. 8 and 11, Marcel Dekker Inc., 1991.

26. Sandler, H.J., and Luckiewicz, E.T., Practical Process Engineering, McGraw-Hill Inc., 1987, p. 33.

27. Speight, J.G., private communications to the author, June-October 1995.

28. Huggins, P., OGJ, Nov. 30, 1987, pp. 38-45.

29. Maxwell, J.B., Data Book on Hydrocarbons., Ch. 2, Van Nostrand Co., 1975.

30. ASTM Standard D341.

31. GPSA, Engineering Data Book, 10th ed., Vol. 2, pp. 23-51, Figs. 23-45, 1987.

The Author