Correlation of Surface and Interfacial Tension of Light Hydrocarbons in the Critical Region
Authors: Hough E.W. , Stegemeier G.L. 
Published: December 2007

Abstract
Empirical equations for surface tension of propane and normal butane as functions of reduced temperature are obtained from experimental data. Another correlation relating surface tension to enthalpy of vaporization is given for these two compounds. In addition, new parachor numbers are calculated for the normal paraffin hydrocarbons. These numbers are utilized for the calculation of interfacial tension of two-component systems as functions of pressure and temperature, using a modified form of Weinaug-Katz equation. The experimental data for two binary systems are approximated by the correlation. From these results it is found that the inter facial tension in the high-pressure region remains extremely low at large pressure decrements below the critical pressure. Thus, it appears that condensate systems may have flow characteristics almost like single-phase conditions even though the pressure is within the two-phase region. Experimental data have shown that interfacial tension divided by density difference approaches zero as the critical pressure is approached. A calculation of wetting-phase saturations indicates that the saturation gradient at the two-phase contact becomes increasingly abrupt as the critical pressure is approached.

Discussion
Prediction of the surface and interfacial tension of the light hydrocarbons and of two-component hydrocarbon mixtures at various temperatures and pressures may be made if other physical properties are known. Extensive experimental work on single-component and binary systems is the basis for the correlations outlined in this paper. Interfacial tension is defined as the specific surface-free energy between two phases of unlike fractional composition, while surface tension is defined as the specific surface-free energy between two phases of the same fractional composition. The usual definitions relating interfacial tension to a liquid-liquid interface and surface tension to a gas-liquid interface are not clearly defined when the critical region is included, and there is no sharp distinction between a gas and a liquid phase. Interfacial tension is probably the most important single force that makes one-half to one-third of the total oil actually in place in a reservoir rock unrecoverable by conventional gas-drive or waterflood methods. A rough estimate of this figure for the United States is 100 billion bbl. Interfacial tension presently is used by petroleum engineers in the estimation of saturation gradients at the gas-oil contact and at the oil-water contact. The data in this paper should prove useful for estimates of reserves involving gas-oil contacts. Relative permeability undoubtedly is influenced by interfacial tension, for sufficiently small values. These data should be useful in determining how small the values are. In addition, these data should eventually add to our fundamental knowledge of surfaces. At the critical point, all surface excesses approach zero and the thickness becomes very large.

SINGLE-COMPONENT SYSTEMS
It has been observed that the following relationships are good approximations to the physical properties of propane and n-butane.
For propane,
For n-butane,
Guggenheim's values for these constants, not specifically for hydrocarbons, are
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