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# Interfacial tension

Interfacial or surface tension exists when two phases are present. These phases can be gas/oil, oil/water, or gas/water. Interfacial tension is the force that holds the surface of a particular phase together and is normally measured in dynes/cm. The surface tension between gas and crude oil ranges from near zero to approximately 34 dynes/cm. It is a function of pressure, temperature, and the composition of each phase.

## Approaches to determine gas/oil surface tension

Two forms of correlations for calculating gas/oil surface tension have been developed.

- The first form is a pseudocompositional black oil approach. Two components, gas and oil, are identified, and techniques used with compositional models are used to calculate surface tension.

- The second approach uses empirical correlations to determine surface tension.

Black oil correlations may provide less than accurate results because of the simplified characterization of the crude oil. Generally, the heavy end components of a crude oil may be made of asphaltic and surface active materials that have a measurable effect on surface tension.

With the compositional approach, surface tension is determined from the following equation proposed by Weinaug and Katz. ^{[1]}

where the density terms are defined with units of g/cm^{3}. *P*_{i} is the parachor of each component. This property is a characteristic of pure components and is determined from surface tension measurements where the density of the gas and liquid phases are known. **Fig. 1 ^{[2]}** provides a relationship between parachors and molecular weight.

## Models to calculate surface tension

In 1973, Ramey^{[3]} proposed a pseudocompositional method for calculating surface tension. The two components are oil and gas. Gas is free to dissolve in the oil phase, and oil is free to vaporize in the gas phase, which makes this method more versatile than the other methods discussed in this chapter. The Weinaug-Katz equation is modified as

where the oil mole fraction in the oil phase is defined as

and the gas mole fraction in oil is

The mole fraction of oil and gas in the as phase is

and

The traditional assumption used with the black oil approach is that the oil vaporized in the gas phase, *r*_{v}, is zero. In this instance, *y*_{o} = 0 and *y*_{g} = 1, which simplifies **Eqs. 5** and **6**.

The average molecular weights of the oil and gas phases are defined as

and

Liquid and gas densities are defined with units of g/cm^{3}:

and

Whitson and Brulé^{[4]} suggested the following parachor equations, which reproduce the graphical methods suggested by Ramey:

and

In 1989, Asheim^{[5]} presented another pseudocompositional correlation for surface tension. With the assumption that no oil vaporizes into the gas phase, the resulting equation is

where the gas formation volume factor (FVF), *B*_{g}, is defined as

Asheim proposed the following equations to calculate the parachors for the oil and gas phases.

While this method appears different from that proposed by Ramey, it is identical for the Ramey case in which no oil vaporizes into the gas phase. This method differs from Ramey’s method only by the definition of the oil and gas parachors.

The Baker and Swerdloff ^{[6]}^{[7]} method was published in 1955. It was presented in the form of graphs for estimating gas/oil surface tension (**Fig. 2**).

Equations to calculate the dead oil surface tension at 68 and 100°F are

and

Beggs^{[8]} suggests that for temperatures greater than 100°F, the value calculated for 100°F should be used. Similarly, if the temperature is less than 68°F, the value calculated for 68°F should be used. For intermediate temperatures, surface tension is derived by linear interpolation as described by

At pressures greater than atmospheric pressure, gas is dissolved in the oil, which reduces surface tension. Baker and Swerdloff provided the graphical correction factor shown in **Fig. 3**, which can be reproduced mathematically by

The live oil surface tension is then derived from

In 2000, Abdul-Majeed^{[9]} presented an update to Baker and Swerdloff’s correlation. Surface tension data from 18 crude oils covering the temperature range 60 to 130°F was used to derive **Eq. 22**, which **Fig. 4** shows graphically.

Data acquired from 42 crude oil/gas systems was used to develop the live oil correction factor. These data, shown graphically in **Fig. 5**, can be represented by

As with the Baker and Swerdloff method, the live oil surface tension is given by **Eq. 21**. **Table 1** shows the statistics provided by Abdul-Majeed comparing the results of the proposed method with the Baker and Swerdloff method. **Fig. 6** shows a comparison of the four methods for calculating interfacial tension.

## Water-hydrocarbon surface tension

The surface tension of a water-hydrocarbon system varies from approximately 72 dynes/cm for water/gas systems to 20 to 40 dynes/cm for water/oil systems at atmospheric conditions. In 1973, Ramey^{[3]} published methods to evaluate the surface tension of water-hydrocarbon mixtures. Unfortunately, this work was for liquid hydrocarbons and did not extend into the gas-phase region. A later publication by Firoozabadi and Ramey^{[10]} provided a more generalized correlation suitable for use with gas and liquid hydrocarbons. Surface tension data from pure components ranging from n-dodecane to methane were plotted as shown in **Fig. 7**. The surface tension function used for the *y*-axis is

while the density difference between the water and hydrocarbon phase is plotted on the *x*-axis. The data in **Fig. 7** can be represented by

**Fig. 7 – Generalized correlation for water/hydrocarbon surface tension. [This material is being used with permission from the Petroleum Society. The author thanks the Petroleum Society for the use of this material and reminds the recipients that no other copies may be made without the expressed written consent of the Petroleum Society. Firoozabadi, A. and Ramey, H.J.: “Surface Tension of Water-Hydrocarbon Systems at Reservoir Conditions,”***Journal of Canadian Petroleum Technology*(May-June 1988) 41.]

Solving for surface tension, the relationship becomes

This equation requires that the pseudocritical temperature of the oil and gas phases be calculated to evaluate reduced temperature. Riazi’s^{[11]} relationship for liquid hydrocarbons can be modified to yield

Sutton’s^{[12]} equation for pseudocritical temperature can be used for the gas phase:

When the pressure increases and gas dissolves into the oil phase, the composition of that phase changes. The pseudocritical temperature of the mixture can be evaluated by calculating the mole fraction of each component present in the oil. For the oil component, we have

while the gas mole fraction in oil is

The pseudocritical temperature of the mixture is then the mole fraction weighted average pseudocritical temperature of each component:

This work serves as a guide for estimating the surface tension between water and hydrocarbons. Firoozabadi and Ramey recommended that a single point measurement for oil water systems be obtained so that the curve in **Fig. 7** could be appropriately adjusted. **Fig. 8** shows an example of results for oil/water and gas/water systems derived from this method.

For methane-brine systems, Standing^{[4]} has indicated that the surface tension will increase according to **Fig. 9**. The relationship in **Fig. 9** can be approximated by

## Nomenclature

## References

- ↑ Weinaug, C.F. and Katz, D.L. 1943. Surface Tensions of Methane-Propane Mixtures. Ind. Eng. Chem. 35 (2): 239-246. http://dx.doi.org/10.1021/ie50398a028
- ↑
^{2.0}^{2.1}Katz, D.L., Monroe, R.R., and Trainer, R.P. 1943. Surface tension of crude oils containing dissolved gases. AIME Technical Publication 1624, American Institute of Mining and Metallurgical Engineers, New York, 285–294. - ↑
^{3.0}^{3.1}Ramey, H.J. Jr. 1973. Correlations of Surface and Interfacial Tensions of Reservoir Fluids. Paper SPE-4429-MS available from SPE, Richardson, Texas. - ↑
^{4.0}^{4.1}^{4.2}Whitson, C.H. and Brulé, M.R. 2000. Phase Behavior, No. 20, Chap. 3. Richardson, Texas: Henry L. Doherty Monograph Series, Society of Petroleum Engineers. - ↑ Asheim, H. 1989. Extension of the Black-Oil Model To Predict Interfacial Tension. Paper SPE-19383-MS available from SPE, Richardson, Texas.
- ↑ Baker, O. and Swerdloff, W. 1955. Calculation of Surface Tension 3—Calculating parachor Values. Oil Gas J. (5 December 1955): 141.
- ↑
^{7.0}^{7.1}^{7.2}Baker, O. and Swerdloff, W. 1956. Calculation of Surface Tension 6—Finding Surface Tension of Hydrocarbon Liquids. Oil Gas J. (2 January 1956): 125. - ↑ Bradley, H.B. 1987. Petroleum Engineering Handbook. Richardson, Texas: SPE.
- ↑ Abdul-Majeed, G.H. and Abu Al-Soof, N.B. 2000. Estimation of gas–oil surface tension. J. Pet. Sci. Eng. 27 (3–4): 197-200. http://dx.doi.org/10.1016/S0920-4105(00)00058-9
- ↑ Firoozabadi, A. and Ramey Jr., H.J. 1988. Surface Tension of Water-Hydrocarbon Systems at Reservoir Conditions. J Can Pet Technol 27 (May–June): 41–48.
- ↑ Riazi, M.R. and Daubert, T.E. 1980. Simplify Property Predictions. Hydrocarb. Process. 59 (3): 115–116.
- ↑ Sutton, R.P.: "Compressibility Factors for High-Molecular-Weight Reservoir Gases," paper SPE 14265 presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22–25 September.

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