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In order to calculate the fugacity of a species in the vapor phase an equation of state must

be used. However, there are two distinct methods for calculating the fugacity of a

species in the liquid phase. An activity coefficient model or an equation of state can be

applied. (2)

The activity coefficient model can be used for liquid mixtures of all species. The activity

coefficient model does not incorporate the density of the liquid and does not do a good

job of describing an expanded liquid that occurs near the vapor liquid critical point of the

mixture. Problems can also occur when using two different models for the liquid phase

and the vapor phase. For example, when using an activity coefficient model for the

liquid phase and an equation of state for the vapor phase the properties of the two phases

may not become identical. When this occurs the vapor liquid critical region behavior is

predicted incorrectly. (2)

When using an identical equation of state to calculate vapor and liquid phase properties

good phase equilibrium predictions can be made over a wide range of temperatures and

pressures. These equations also do very well predicting conditions at the critical region.

Not only can the phase compositions be predicted from an equation of state but other

physical properties can be predicted as well. Some of the properties that can be predicted

using an equation of state are densities and enthalpies. However, this is only possible for

hydrocarbon mixtures, inorganic gases, and a few other materials. (2)

The most common method is to use an equation of state to predict vapor phase

compositions and properties and using an activity coefficient model to predict liquid

phase compositions and properties. This way insures that the physical properties for both

the liquid phase and the vapor phase can be calculated with reasonable accuracy.

**Equations of State **

The mathematical relationship between pressure, temperature, volume and composition is

called the equation of state. Most equations of state are pressure explicit. (3)

Thermodynamic properties can be predicted over a wide temperature and pressure range,

including the critical region, by equations of state. When molecules are relatively small

and nonpolar, they have been proven to be effective for vapor-liquid equilibrium

calculations. However, the equations of state tend to be inaccurate for strongly hydrogen-

bonding mixtures or substances with more complex molecular structure. (4,5) Many of

the equations of state give similar results in estimating the vapor-liquid equilibrium.

Bubble point pressure estimations of hydrocarbons and gases have been found to be

within five percent and estimations based on binary interaction parameters have been

within about 15 % accuracy. (4) In general, the variations in accuracy between the

equations of state are subtle. One equation might be best for a narrow range of

applications, while another equation might be more appropriate for another range of

applications. (4)

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