Interfacial Tension Correlations

Overview

Interfacial tension (IFT) is the force acting at the interface between two immiscible fluids. In petroleum engineering, gas-oil interfacial tension is important for:

• Multiphase flow — affects flow pattern transitions in pipes
• Wellbore hydraulics — influences bubble size and slip velocity
• Enhanced oil recovery — critical parameter for miscibility and displacement
• Separator design — impacts droplet coalescence and separation efficiency

This document covers empirical correlations for estimating gas-oil interfacial tension from fluid properties.

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Theory

Physical Significance

Interfacial tension arises from imbalanced intermolecular forces at fluid interfaces. For gas-oil systems:

• Decreases with pressure — approaching zero at critical conditions
• Decreases with temperature — higher molecular mobility reduces surface forces
• Depends on composition — lighter components reduce IFT
• Affects capillary forces — determines fluid distribution in porous media

Typical Values

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Correlations

Baker-Swerdloff (1956) - Gas-Oil Interfacial Tension

The Baker-Swerdloff correlation estimates gas-oil interfacial tension as a function of temperature, pressure, and oil gravity. It is widely used in multiphase flow correlations (Beggs-Brill, Hagedorn-Brown) for flow pattern determination and liquid holdup calculations.

Base Interfacial Tensions

Calculate base values at 68°F and 100°F:

$$\sigma_{68} = 39 - 0.2571 \times \text{API}$$

$$\sigma_{100} = 37.5 - 0.2571 \times \text{API}$$

Where:

• $\sigma_{68}$ = gas-oil interfacial tension at 68°F, dyne/cm
• $\sigma_{100}$ = gas-oil interfacial tension at 100°F, dyne/cm
• API = oil gravity, °API

Temperature-Dependent Dead Oil Interfacial Tension

The dead oil interfacial tension varies with temperature:

At T < 68°F:

$$\sigma_{od} = \sigma_{68}$$

At 68°F ≤ T ≤ 100°F:

$$\sigma_{od} = \sigma_{68} + \frac{(T - 68) \times (\sigma_{100} - \sigma_{68})}{(100 - 68)}$$

At T > 100°F:

$$\sigma_{od} = \sigma_{100}$$

Where:

• $\sigma_{od}$ = dead oil (gas-free) interfacial tension, dyne/cm
• $T$ = temperature, °F

Pressure Correction

The pressure correction reduces interfacial tension as pressure increases:

$$\sigma_{go} = \sigma_{od} \times (1 - 0.024 \times P^{0.45})$$

Where:

• $\sigma_{go}$ = gas-oil interfacial tension at pressure P, dyne/cm
• $P$ = pressure, psia

Miscibility Constraint

As pressure approaches the miscibility pressure, interfacial tension approaches zero. To avoid numerical issues in flow calculations, a minimum value of 1 dyne/cm is enforced:

$$\text{if } \sigma_{go} < 1, \text{ then } \sigma_{go} = 1 \text{ dyne/cm}$$

This constraint prevents unrealistic predictions near critical conditions while maintaining numerical stability in multiphase flow models.

Application Range

• Temperature: Validated for typical reservoir temperatures (68-280°F)
• Pressure: Valid from atmospheric to near-miscibility conditions
• Oil Gravity: Applicable to conventional oils (15-50°API)

Physical Behavior

The correlation captures key physical trends:

• Lighter oils (higher API) have lower IFT
• Higher temperature reduces IFT (increased molecular mobility)
• Higher pressure reduces IFT (approaching critical state)
• Near-miscibility IFT approaches zero

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Baker-Swerdloff (1956) - Gas-Water Interfacial Tension

The Baker-Swerdloff gas-water correlation provides interfacial tension for gas-water systems, useful in gas well loading calculations and multiphase flow with water production.

Base Interfacial Tensions

Calculate base values at 74°F and 280°F:

$$\sigma_{74} = 75 - 1.108 \times P^{0.349}$$

$$\sigma_{280} = 53 - 0.1048 \times P^{0.637}$$

Where:

• $\sigma_{74}$ = gas-water interfacial tension at 74°F, dyne/cm
• $\sigma_{280}$ = gas-water interfacial tension at 280°F, dyne/cm
• $P$ = pressure, psia

Temperature-Dependent Interfacial Tension

The gas-water interfacial tension varies with temperature:

At T < 74°F:

$$\sigma_{gw} = \sigma_{74}$$

At 74°F ≤ T ≤ 280°F:

$$\sigma_{gw} = \sigma_{74} + \frac{(T - 74) \times (\sigma_{280} - \sigma_{74})}{(280 - 74)}$$

At T > 280°F:

$$\sigma_{gw} = \sigma_{280}$$

Where:

• $\sigma_{gw}$ = gas-water interfacial tension, dyne/cm
• $T$ = temperature, °F

Application Range

• Temperature: 74-280°F (typical reservoir/wellbore conditions)
• Pressure: Atmospheric to high pressure gas wells

Physical Behavior

The correlation shows:

• Pressure effect is built into base values (pressure-dependent at reference temperatures)
• Higher temperature reduces IFT (linear interpolation between reference points)
• Gas-water IFT is generally higher than gas-oil IFT (stronger water intermolecular forces)

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Abdul-Majeed Gas-Oil IFT (1997)

The Abdul-Majeed correlation provides an alternative method for estimating gas-oil interfacial tension based on temperature and solution gas-oil ratio.

Dead Oil Surface Tension:

$$\sigma_{do} = (1.17013 - 1.694 \times 10^{-3} \cdot T) \cdot (38.085 - 0.259 \cdot \gamma_{API})$$

Live Oil Interfacial Tension:

$$\sigma_{go} = \sigma_{do} \cdot (0.056379 + 0.94362 \cdot e^{-3.8491 \times 10^{-3} \cdot R_s})$$

where:

• σ_go = gas-oil interfacial tension, dyne/cm
• σ_do = dead oil surface tension at temperature T, dyne/cm
• T = temperature, °F
• γ_API = oil gravity, °API
• R_s = solution gas-oil ratio, scf/STB
• Result range: 0 < σ_go ≤ 40 dyne/cm

The correlation uses an exponential reduction factor that decreases interfacial tension as dissolved gas content increases, similar to Baker-Swerdloff but with temperature-dependent dead oil properties.

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Applicability and Limitations

When to Use Baker-Swerdloff Gas-Oil

✅ Recommended:

• Multiphase flow calculations (Beggs-Brill, Hagedorn-Brown)
• Flow pattern determination in pipelines
• Liquid holdup estimation
• General wellbore hydraulics
• Screening studies without measured IFT data

❌ Not Recommended:

• Near-critical conditions (use parachor method or measured data)
• Enhanced oil recovery studies (requires more accurate IFT)
• Surfactant-altered systems
• CO₂ flooding (different correlation needed)

When to Use Baker-Swerdloff Gas-Water

✅ Recommended:

• Gas well liquid loading predictions
• Critical velocity calculations (Turner model)
• Gas-water flow in pipelines
• Produced water handling

❌ Not Recommended:

• High-salinity brines (may need correction)
• Systems with surfactants or chemicals

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Related Topics

• Gas Properties — Gas density and viscosity
• Oil Viscosity — Oil viscosity correlations
• Pipe Flow Overview — Multiphase flow correlations
• Beggs-Brill Correlation — Uses IFT in flow pattern maps

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References

1. Baker, O. and Swerdloff, W. (1955). "Calculation of Surface Tension 3—Calculating parachor Values." Oil Gas J. (5 December 1955): 141.

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.

3. Beggs, H.D. and Brill, J.P. (1973). "A Study of Two-Phase Flow in Inclined Pipes." Journal of Petroleum Technology, May 1973, 607-617.

   • References Baker-Swerdloff for surface tension in flow pattern maps

4. Abdul-Majeed, G.H. — Gas-oil interfacial tension correlation (details to be confirmed).

Related Reading

For background on interfacial tension in petroleum systems:

• McCain, W.D. (1990). Properties of Petroleum Fluids. PennWell Publishing.
• Ahmed, T. (2019). Reservoir Engineering Handbook. Gulf Professional Publishing.
• Dandekar, A.Y. (2013). Petroleum Reservoir Rock and Fluid Properties. CRC Press.
• Economides, M.J. et al. (1994). Petroleum Production Systems. Prentice Hall.