Published on *PNG 520: Phase Behavior of Natural Gas and Condensate Fluids* (https://www.e-education.psu.edu/png520)

Surface tension is a measure of the surface free energy of liquids, i.e., the extent of energy stored at the surface of liquids. Although it is also known as interfacial force or interfacial tension, the name *surface tension* is usually used in systems where the liquid is in contact with gas.

Qualitatively, it is described as the force acting on the surface of a liquid that tends to minimize the area of its surface, resulting in liquids forming droplets with spherical shape, for instance. Quantitatively, since its dimension is of force over length (lbf/ft in English units), it is expressed as the force (in lbf) required to break a film of 1 ft of length. Equivalently, it may be restated as being the amount of surface energy (in lbf-ft) per square feet.

Katz *et al.* (1959) presented the Macleod-Sudgen equation for surface tension ($\sigma $) calculations in dynes/cm for hydrocarbon mixtures:

$${\sigma}^{1/4}={\displaystyle \sum _{i=1}^{n}Pc{h}_{i}}\left[\frac{{\rho}_{i}}{62.4(M{W}_{l})}{x}_{i}-\frac{{\rho}_{g}}{62.4(M{W}_{g})}{y}_{i}\right]$$

where:

Pch_{i} = Parachor of component “i”,

x_{i} = mole fraction of component “i” in the liquid phase,

y_{i} = mole fraction of component “i” in the gas phase.

In order to express surface tension in field units (lbf/ft), multiply the surface tension in (dynes/cm) by 6.852177x10^{-3}. The parachor is a temperature independent parameter that is calculated experimentally. Parachors for pure substances have been presented by Weinaug and Katz (1943) and are listed in Table 18.1.

Component | Parachor |
---|---|

CO_{2} |
78.0 |

N_{2} |
41.0 |

C_{1} |
77.0 |

C_{2} |
108.0 |

C_{3} |
150.3 |

iC_{4} |
181.5 |

nC_{4} |
189.9 |

iC_{5} |
225.0 |

nC_{5} |
231.5 |

nC_{6} |
271.0 |

nC_{7} |
312.5 |

nC_{8} |
351.5 |

Weinaug and Katz (1943) also presented the following empirical relationship for the parachor of hydrocarbons in terms of their molecular weight:

$$Pc{h}_{i}=-4.6148734+2.558855M{W}_{i}+3.404065\cdot {10}^{-4}M{W}_{i}^{2}+\frac{3.767396\cdot {10}^{3}}{M{W}_{i}}$$

- This correlation may be used for pseudo-components or for those hydrocarbons not shown in Table 18.1.