GENERALIZED EQUATION PREDICTS VAPOR PRESSURE OF HYDROCARBONS

M. Edalat, R. B. Bozar-JomehriSharif University of Technology Teheran
G. A. MansooriUniversity of Illinois at Chicago

One of the most important physical properties of hydrocarbons needed by practicing engineers in the oil and gas industries is vapor pressure.1-5 But until now, no reliable equation could predict hydrocarbon vapor pressures accurately, with only one set of generalized parameters.

A new equation addresses this critical industry need. The accuracy of this generalized equation for predicting 1,106 vapor pressure data points for 94 different fluids has been successfully tested.

This testing has demonstrated that the simple equation performs better than the other vapor pressure equations for all data points tested.

The equation also requires only critical pressure, critical temperature, and acentric factor.

It should be noted that several equations for vapor pressures exist in the literature. 6-9

The Antoine equation (Equation 1) is the oldest and simplest of such equations (see Equations and Nomenclature)."

Equation 1 contains the constants A, B, and C, which must be obtained by fitting the equation to the experimental vapor pressure data of every hydrocarbon separately. As a result, the use of this equation for all hydrocarbons requires a large data bank for the equation coefficients.

On the other hand, an equation developed by Wagner is a bit more generalized (Equation 2)." In Wagner's equation, a, b, c, and d are characteristic constants for the fluid under study, and PI is the vapor (saturation) pressure. If parameters a, b, c, and d are available for a pure hydrocarbon, the equation predicts vapor pressures within the acceptable accuracy down to a reduced temperature (see Nomenclature) of 0.5.

The simple generalized equation presented here accurately estimates vapor pressure of hydrocarbons, nonhydrocarbons, and polar fluids, using only the critical properties (Pc and Tc) and acentric factor (w).

The equation has been successfully tested for a variety of fluids and can be readily used in the oil and gas industry.

GENERALIZED EQUATION

To develop a generalized vapor pressure equation with a simple form, applicable to wide ranges of temperature and a variety of fluids, the authors propose the use of Equation 2, but with its parameters defined as functions of w.

The result of this is Equation 3.

Based on coefficient data of Equation 2 - available for 73 compounds - and applying a regression method by considering Pitzer's definition of acentric factor (Equation 4), the parameters of Equation 3 can be defined by Equations 5-8.12

Equation 3, together with Equations 5-8, constitute the new generalized, accurate correlation for vapor pressure.

The applicability of this equation has been tested for a variety of fluids.

EQUATION COMPARABILITY

The results of calculations indicate that Equations 3, 5, 6, 7, and 8 can predict vapor pressures of hydrocarbons, nonhydrocarbons, and polar fluids more accurately than the other vapor pressure equations available in the literature without the need for information about any additional parameters.

Table 1 compares vapor pressures of pure liquids, as predicted by the Ambrose and Patel (AP) equation, the Lee-Kessler (LK) equation, and Equation 3.1311 -The new equation predicts vapor pressure more accurately than the AP interpolative method. The prediction of the new equation is also superior to the LK equation for all hydrocarbons and other substances, excluding alcohols.

Also reported in Table 1 are the overall average percentage errors of the present and other equations for all 94 substances, tested with a total of 1,106 vapor pressure data points." '

This comparison shows that, overall, the new equation predicts vapor pressure more accurately than the other equations.

It should be pointed out that the application of the other vapor pressure equations requires knowledge of the coefficients of those equations for every individual substance. The new equation, however, does not require such knowledge, and is accurate and suitable for engineering design calculations.

ACKNOWLEDGMENT

This research is supported in part by GRI Contract 5090-260-2020.

REFERENCES

1. Edmister, W.C., and Lee, B.I., Applied Hydrocarbon Thermodynamics, Vol. 1, Gulf Publishing Co., Houston, 1986.

2. Whitson, C.H., "Effect of Physical Properties Estimation on Equation-of-State Predictions," SPE Journal, December 1984, pp. 685-96.

3. Hall, K.R., and Yarborough, L., "A new equation of state for Z-factor calculations," OGJ, June 18, 1973, pp. 82-92.

4. Sutton, R.P., and Farshad, F.F., "Evaluation of Empirically Derived PVT Properties for Gulf of Mexico Crude Oils," SPE Paper 13172, Proceedings of the 59th Annual SPE Technical Conference, Houston, 1984.

5. Campbell, J.M., Gas Conditioning and Processing, Campbell Petroleum Series, Vol. 1, Norman, Okla., 1960.

6. Gupta, P.A., and Daubert, D.E., "New Corresponding States Model for Vapor Pressure of Non-Hydrocarbon Fluids," Ind. & Eng. Chemical Process Design Develop., Vol. 24, 1985, pp. 674-77.

7. Miller, D.G., "Graphical Method for Determining a Non-linear Constant in Vapor Pressure Equations," Ind. Eng. Chem. Found., Vol. 2, 1963, pp. 68-73.

8. Thek, R.E., and Stiel, L.I., "A New Reduced Vapor Pressure Equation," AlChE J., Vol. 12, 1966, pp. 599-602.

9. Gomez-Nieto, M., and Thodos, G., "A New Vapor Pressure Equation and its Application to Normal Alkanes," Ind. & Eng. Chem. Found., Vol. 16, 19,-,, pp. 254-59.

10. Antoine, C., Compt. rend., Vol. 107, 1988, pp. 681-85.

11. Wagner, W., "New Vapor Pressure Measurement for Argon and Nitrogen and a New Method for Establishing Rational Vapor Pressure Equations," Cryogenics, Vol. 13, 1973, pp. 470-82.

12. McGarry, J., "Correlation and Prediction of the Vapor Pressures of Pure Liquids over Large Pressure Ranges," Ind. Eng. Chem. Process Design Develop., Vol. ??, 1983, pp. 313-22.

13. Ambrose, D., and Patel, N.C., "The Correlation and Estimation of Vapor Pressures," J. Chem. Thermodynamics, Vol. 16, 1984, pp. 459-68.

14. Lee, B.I., and Kesler, M.G., "A Generalized Thermodynamics Correlation Based on Three-Parameter Corresponding States," AlChE J., Vol. 21, 1975, p. 510.

15. Boublik, T., Fried, V., and Hala, E., The vapor pressure of pure substance, 3rd ed., Elsevier, Amsterdam, 1987.

BOOK

Saudi Arabia and the Gulf War, by Nasser Ibrahim Rashid and Esber Ibrahim Shaheen. Published by International Institute of Technology Inc., 830 Wall St., Joplin, Mo., 64801. 564 pp., $39.95.

Here is the story of the recent Gulf War from the viewpoint of Saudi Arabia. It includes events leading up to the conflict and the role played by Saudi Arabia in the war. The book provides a fresh look at the war as seen from the perspective of a Gulf ally which had both its civilians and military directly involved.