Predictive Soave-Redlich-Kwong (PSRK) UNIFAC

Model description

This is the Predictive Soave-Redlich-Kwong (PSRK) UNIFAC model. In this model, the parameters are defined as:

$$z = 10$$

$$d = 1$$

The temperature function $E_{jk}$ is defined with a quadratic temperature function as follows:

$$E_{jk} = \text{exp} \left(- \frac{U_{jk}}{RT} \right) = \text{exp} \left(- \frac{a_{jk} + b_{jk} T + c_{jk} T^2}{T} \right)$$

Subgroups list

The list of the functional groups and its interaction parameters could be accessed on the DDBST web page: https://www.ddbst.com/psrk.html

We reproduce here the list of functional groups. To instantiate a UNIFAC-PSRK model you must define which functional groups are used in a molecule by the Subgroup Number column.

Using ugropy to retrieve UNIFAC-PSRK subgroups

There is the possibility of using another library of our group ugropy to retrieve the UNIFAC-PSRK subgroups and not suffer the pain of typing the subgroup numbers and parameters by hand. The next Python snippet shows how you can use it.

from ugropy import psrk, writers


names = ["water", "toluene", "acetone"]
groups = [psrk.get_groups(n).subgroups for n in names]

fortran_code = writers.to_yaeos(groups, psrk)

print(fortran_code)

And you will obtain:

use yaeos__models_ge_group_contribution_unifac, only: Groups

type(Groups) :: molecules(3)

molecules(1)%groups_ids = [16]
molecules(1)%number_of_groups = [1]

molecules(2)%groups_ids = [9, 11]
molecules(2)%number_of_groups = [5, 1]

molecules(3)%groups_ids = [1, 18]
molecules(3)%number_of_groups = [1, 1]

Examples

Here is an example of a fully instantiated UNIFAC-PSRK model. Please check the Gibbs Excess Models section in the user documentation to learn all the things you can do with this model.

Notice that here we are using the setup_psrk function to instantiate the model.

Calculating activity coefficients

We can instantiate a UNIFAC model with a mixture ethanol-water and evaluate the logarithm of activity coefficients of the model for a 0.5 mole fraction of each, and a temperature of 298.0 K.

use yaeos__constants, only: pr
use yaeos__models_ge_group_contribution_unifac, only: Groups, UNIFAC, setup_psrk

! Variables declarations
type(UNIFAC) :: model
type(Groups) :: molecules(2)
real(pr) :: ln_gammas(2)

! Variables instances
! Ethanol definition [CH3, CH2, OH]
molecules(1)%groups_ids = [1, 2, 14] ! Subgroups ids
molecules(1)%number_of_groups = [1, 1, 1] ! Subgroups occurrences

! Water definition [H2O]
molecules(2)%groups_ids = [16]
molecules(2)%number_of_groups = [1]

! Model setup
model = setup_psrk(molecules)

! Calculate ln_gammas
call model%ln_activity_coefficient([0.5_pr, 0.5_pr], 298.0_pr, ln_gammas)

print *, ln_gammas

References

1. Holderbaum T., “Die Vorausberechnung von Dampf-Flüssig-Gleichgewichten mit einer Gruppenbeitragszustandsgleichung”, Thesis, Universität Dortmund, 1990
2. Holderbaum T., Gmehling J., “PSRK: Eine Zustandsgleichung zur Vorhersage von Dampf/Flüssig- Gleichgewichten bei mittleren und hohen Drücken.”, Chem.Ing.Tech. CIT, 63(1), 57-59, 1991
3. Holderbaum T., Gmehling J., “PSRK: A Group-Contribution Equation of State based on UNIFAC”, Fluid Phase Equilib., 70, 251-265, 1991
4. Fischer K., “Die PSRK-Methode: Eine Zustandgleichung unter Verwendung des UNIFAC-Gruppenbeitragsmodells”, Thesis, C.-v.-O. Universität Oldenburg, 1993
5. Fischer K., Gmehling J., “Further Development, Status and Results of the PSRK Method for the Prediction of Vapor-Liquid Equilibria and Gas Solubilities”, Fluid Phase Equilib., 112, 1-22, 1995
6. Fischer K., Gmehling J., “Further Development, Status and Results of the PSRK Method for the Prediction of Vapor-Liquid Equilibria and Gas Solubilities”, Fluid Phase Equilib., 121, 185-206, 1996
7. Gmehling J., Li J., Fischer K., “Further development of the PSRK model for the prediction of gas solubilities and vapor-liquid-equilibria at low and high pressures”, Fluid Phase Equilib., 141, 113-127, 1997
8. Horstmann S., Fischer K., Gmehling J., “PSRK group contribution equation of state: revision and extension III”, Fluid Phase Equilib., 167, 173-186, 2000
9. Horstmann S., “Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung”, Thesis, C.-v.-O. Universität Oldenburg, 2000
10. Horstmann S., Jabloniec A., Krafczyk J., Fischer K., Gmehling J., “PSRK Group Contribution Equation of State: Comprehensive Revision and Extension IV, Including Critical Constants and a-Function Parameters for 1000 Components”, Fluid Phase Equilib., 227(2), 157-164, 2005