Equations for the Grayson-Streed method

The Grayson-Streed method is based on a heterogeneous, asymmetric approach, in which the distribution coefficient, Ki, is calculated as follows:

where the three factors are calculated by using a different model:

• The pure liquid fugacity coefficient, jiL*, is calculated by using a specific corresponding states method.

• The liquid activity coefficient, gi, is calculated by using the regular solution model

• The vapor phase fugacity coefficient, jiV, is computed from the Redlich-Kwong (RK) cubic equation of state.

Fugacity coefficient of pure liquid

The fugacity coefficient of pure liquid, jiL*, is calculated with a Curl-Pitzer corresponding state correlation, that is, in terms of the reduced temperature, reduced pressure, and the acentric factor:

where

w is the acentric factor

When the component at hand is hydrogen or methane, the acentric factor is zero.

The first term on the right-hand side of the equation represents the fugacity coefficient of "simple fluids".The second term is a correction accounting for departure of the properties of real fluids from those of "simple fluids."

The quantity ji(0) depends only on reduced temperature and reduced pressure. It was fitted with the following function by Chao and Seader2:

where

Tr and Pr are the reduced temperature and pressure of the component at hand

Coefficients for this equation were determined by Grayson and Streed1 and they are presented in Table 1.

The quantity ji(1) similarly depends only on reduced temperature and reduced pressure and was fitted by Chao and Seader2:

Activity coefficient from regular solution theory

The liquid activity coefficient, gi, is calculated from the Hildebrand equation, assuming a "regular" liquid solution (no excess volume and no excess entropy).

where

Vi is the molar volume of component i

di is the solubility parameter of component i

is the solubility parameter for the solution

The solubility parameter is calculated as follows:

The quantity fi is the volume fraction, that is, the ratio of the molar volume of component i to the weighted molar volume of the mixture.

Fugacity coefficient in a vapor phase

The software calculates the fugacity coefficients by using the same equations from the Redlich-Kwong equation of state. The Redlich-Kwong equation of state is a specific case of the General two-parameter equation of state in which u = 0 and w = 1 to get the following equation:

Enthalpy and entropy calculations

This method uses the Curl-Pitzer equation of state to calculate the enthalpy and entropy for all phases. See CP — Curl-Pitzer method for more information.

Vapor density calculations

This method uses the Soave-Redlich-Kwong equation of state to calculate the density of the vapor phase. See SRK — Soave-Redlich-Kwong equation of state for more information.