Ind. Eng. Chem. Res. 1990,29, 1578
1578
p250c = crude oil mixture density at 25 "C, g/cm3 Subscripts
i = component i mix = liquid mixture, average p = at pressure P 0 = at atmospheric pressure Superscript -
= crude oil mixture, average
Literature Cited Al-Besharah, J. M.; Akashah, S. A.; Mumford, C. J. The Effect of Temperature and Pressure on the Viscosities of Crude Oils and their Mixtures. Ind. Eng. Chem. Res. 1989, 28, 213. ASTM. 1982 Annual Book of ASTM Standards; ASTM: Philadelphia, PA, 1982; Part 23, p 23:208. Irving, J. B. Viscosities of Binary Liquid Mixtures: The Effectiveness of Mixture Equations. NEL Report 631; National Engineering Laboratory: Glasgow, 1977. Khan, M. A. B.; Mehrotra, A. K.; Svrcek, W. Y. Viscosity Models for Gas-Free Athabasca Bitumen. J. Can. Pet. Technol. 1984,23 (3),
Mehrotra, A. K. Development of Mixing Rules for Predicting the Viscosity of Bitumen and Its Fractions Blended with Toluene. Can. J . Chem. Eng. 1990, in press. Mehrotra, A. K.; Svrcek, W. Y. Viscosity of Compressed Athabasca Bitumen. Can. J . Chem. Eng. 1986, 64, 844. Mehrotra, A. K.; Svrcek, W. Y. Viscosity of Compressed Cold Lake Bitumen. Can. J. Chem. Eng. 1987,65,672. Mehrotra, A. K.; Eastick, R. R.; Svrcek, W. Y. Viscosity of Cold Lake Bitumen and Its Fractions. Can. J. Chem. Eng. 1989,67, 1004. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977; p 435. Svrcek, W. Y.; Mehrotra, A. K. One Parameter Correlation for Bitumen Viscosity. Chem. Eng. Res. Des. 1988, 66, 323. Walther, C. The Evaluation of Viscosity Data. Erdol Teer 1931, 7, 382.
Ani1 K. Mehrotra Department of Chemical and Petroleum Engineering The University of Calgary Calgary, Alberta, Canada T2N IN4 Received for review December 26, 1989 Accepted April 4, 1990
4:.
CORRESPONDENCE Comments on "The Effect of Temperature and Pressure on the Viscosities of Crude Oils and Their Mixtures" Sir: It has been suggested that eq 10 in our paper (Al-Besharah et al., 1989), used as an approximation for liquids with densities that do not differ widely, = CxiPi where x refers to the weight fraction, is dimensionally incorrect. An alternative mixing rule, proposed by Handley (1989), which assumes that component volumes are additive, is Pmix
-1- - c-x , Pmix
PI
However, the deviations between the mixture densities calculated via these two equations are very small: temperature 25 "C 30 "C 40 "C 50 "C
av % deviation -0.14% -0.15% -0.16% -0.16%
calculated by eq 10 were very low (
