Equations for the PSRK method

For a pure component, the Predictive Soave-Redlich-Kwong (PSRK) method uses the SRK equation of state:

We obtain the ai and bi properties from the critical temperature (Tc) and pressure (Pc) of the pure component (i):

where

ai(T) is the alpha formulation for component i

For the alpha formulation, the PSRK method uses the Mathias and Copeman[8] expression, which improves the description of pure component vapor pressures for polar components.

where

c1, c2, and c3 are the SRK-specific constants from the ALPHA data bank that you use in your Fluid

By default, any Fluid that uses the PSRK method as the system method automatically includes the system PSRKALPH data bank. If you want to use a custom ALPHA data bank instead of the PSRKALPH data bank, the software uses the alpha formulation that you define in your custom ALPHA data bank instead of the Mathias-Copeman expression. Because the PSRK method requires that the alpha formulation use the Mathias-Copeman expression, we recommend that you use Form 9 for all components in your custom ALPHA data banks. Otherwise, we cannot guarantee the results when you use the PSRK method.

If the software cannot find data for a component in any of the ALPHA data banks in your Fluid Type, it uses the standard SRK formulation for the alpha formulation:

where

w is the accentric factor for the component

Mixing rules

For mixtures, we use the Modified Huron-Vidal (MHV1) mixing rules to calculate the bulk a and b parameters of the equation of state:

where

g0E is the excess Gibbs energy

xi is the mole fraction of component i

b is a parameter with a value of one or zero based on your selections in the Fluid Editor

The b parameter allows you to include or exclude the combinatorial term, which is similar to the Flory-Huggins equation. Typically, the results for asymmetric mixtures improve when you exclude the combinatorial term. You use the Flory-Huggins like term in MHV1 mixing rule list in the Equilibrium Options section of the Fluid Editor to select whether to include (b = 1) or exclude (b = 0) the combinatorial term.

We use the following equation to calculate the excess Gibbs free energy from the activity coefficient at standard conditions, g0,i:

In the Fluid Editor, you can choose between the UNIQUAC Functional-group Activity Coefficient (UNIFAC) formulation and the Non-Random Two-Liquid (NRTL) formulation for the activity coefficient. You use the Excess Gibbs Energy Method list in the Equilibrium Options section of the Fluid Editor to select the desired formulation.

If you select the UNIFAC formulation, the software uses a slightly modified version of the original UNIFAC method. That is, we calculate the necessary activity coefficients by using the original UNIFAC method, except that we extend the exponential term for amk in the tmk calculation to allow a temperature dependency according to the following equation:

Note: This is the same temperature-dependent function used in the Dortmund UNIFAC method.

See UNIFAC — UNIQUAC Functional-group Activity Coefficient method for more details on the UNIFAC method and equations.

Because the UNIFAC formulation is based on group contributions to predict binary interactions between molecules, you cannot ignore the combinatorial term. That is, the b parameter is always one. Therefore, when you select the UNIFAC formulation, the Flory-Huggins like term in MHV1 mixing rule list is not available in the Fluid Editor.

If you select the NRTL formulation, the software uses the standard NRTL method to calculate the activity coefficients:

where

aij, Aij, Bij, Cij, Dij, Eij, and Fij are binary interaction parameters that come from the NRTL databank that you're using in your fluid

See NRTL — Non-random two-liquid method for more details on the NRTL method.