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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/cm3. Pi 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 provides a relationship between parachors and molecular weight.

## Models to calculate surface tension

In 1973, Ramey 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 ....................(2)

where the oil mole fraction in the oil phase is defined as ....................(3)

and the gas mole fraction in oil is ....................(4)

The mole fraction of oil and gas in the as phase is ....................(5)

and ....................(6)

The traditional assumption used with the black oil approach is that the oil vaporized in the gas phase, rv, is zero. In this instance, yo = 0 and yg = 1, which simplifies Eqs. 5 and 6.

The average molecular weights of the oil and gas phases are defined as ....................(7)

and ....................(8)

Liquid and gas densities are defined with units of g/cm3: ....................(9)

and ....................(10)

Whitson and Brulé suggested the following parachor equations, which reproduce the graphical methods suggested by Ramey: ....................(11)

and ....................(12)

In 1989, Asheim presented another pseudocompositional correlation for surface tension. With the assumption that no oil vaporizes into the gas phase, the resulting equation is ....................(13)

where the gas formation volume factor (FVF), Bg, is defined as ....................(14)

Asheim proposed the following equations to calculate the parachors for the oil and gas phases. ....................(15) ....................(16)

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  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 ....................(17)

and ....................(18)

Beggs 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 ....................(19)

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 ....................(20)

The live oil surface tension is then derived from ....................(21)

In 2000, Abdul-Majeed 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. ....................(22)

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 ....................(23)

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 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 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 ....................(24)

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 ....................(25)

Solving for surface tension, the relationship becomes ....................(26)

This equation requires that the pseudocritical temperature of the oil and gas phases be calculated to evaluate reduced temperature. Riazi’s relationship for liquid hydrocarbons can be modified to yield ....................(27)

Sutton’s equation for pseudocritical temperature can be used for the gas phase: ....................(28)

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 ....................(29)

while the gas mole fraction in oil is ....................(30)

The pseudocritical temperature of the mixture is then the mole fraction weighted average pseudocritical temperature of each component: ....................(31)

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 has indicated that the surface tension will increase according to Fig. 9. The relationship in Fig. 9 can be approximated by ....................(32)

## Nomenclature

 Bg = gas FVF, ft3/scf Bo = oil FVF, bbl/STB Kw = Watson characterization factor, °R1/3 Mg = gas molecular weight, m, lbm/lbm mol Mgo = gas/oil mixture molecular weight, m, lbm/lbm mol Mo = oil molecular weight, m, lbm/lbm mol Mog = oil-gas mixture molecular weight, m, lbm/lbm mol p = pressure, m/Lt2, psia pb = bubblepoint pressure, m/Lt2, psia T = temperature, T, °F Tcg = gas pseudocritical temperature, T, °R Tcm = mixture pseudocritical temperature, T, °R Tco = oil pseudocritical temperature, T, °R Tr = reduced temperature, T Tsc = temperature at standard conditions, T, °F xg = gas "component" mole fraction in oil xo = oil "component" mole fraction in oil yg = gas "component" mole fraction in gas yo = oil "component" mole fraction in gas γg = gas specific gravity, air=1 γghc = gas specific gravity of hydrocarbon components in a gas mixture, air=1 γgs = separator gas specific gravity, air=1 γo = oil specific gravity Z = gas compressibility factor ρg = gas density, m/L3, lbm/ft3 ρo = oil density, m/L3, lbm/ft3 σgo = gas/oil surface tension, m/t2, dynes/cm σod = dead oil surface tension, m/t2, dynes/cm P = parachor Pg = gas parachor Pi = parachor of each component Po = oil parachor Rs = solution GOR, scf/STB psc = pressure at standard conditions, m/Lt2, psia ρh = hydrocarbon density, m/L3, g/cm3 = dead oil surface tension at 68°F, m/t2, dynes/cm σhw = hydrocarbon/water surface tension, m/t2, dynes/cm ρw = water density, m/L3, g/cm3 ρh = hydrocarbon density, m/L3, g/cm3 Csw = salt concentration in water, ppm rv = vaporized oil/gas ratio, STB/scf xi = component i mole fraction in oil phase yi = component i mole fraction in gas phase