Liquid-Vapor UNIFAC

Model description

This is the original and classic Liquid-Vapor UNIFAC model. In this model, the parameters are defined as: $$z = 10$$

$$d = 1$$

The temperature function $E_{jk}$ is defined with a single temperature constant $a_{jk}$ coefficient as follows:

$$E_{jk} = \text{exp} \left(- \frac{U_{jk}}{RT} \right) = \text{exp} \left(- \frac{a_{jk}}{T} \right)$$

Subgroups list

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

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

Using ugropy to retrieve UNIFAC subgroups

There is the possibility of using another library of our group ugropy to retrieve the UNIFAC 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 unifac, writers


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

fortran_code = writers.to_yaeos(groups, unifac)

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 UNIFACLV 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_unifac 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_unifac

! 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_unifac(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. Fredenslund, A., Jones, R. L., & Prausnitz, J. M. (1975). Group‐contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE Journal, 21(6), 1086–1099. https://doi.org/10.1002/aic.690210607
2. Skjold-Jorgensen, S., Kolbe, B., Gmehling, J., & Rasmussen, P. (1979). Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension. Industrial & Engineering Chemistry Process Design and Development, 18(4), 714–722. https://doi.org/10.1021/i260072a024
3. Gmehling, J., Rasmussen, P., & Fredenslund, A. (1982). Vapor-liquid equilibriums by UNIFAC group contribution. Revision and extension. 2. Industrial & Engineering Chemistry Process Design and Development, 21(1), 118–127. https://doi.org/10.1021/i200016a021
4. Macedo, E. A., Weidlich, U., Gmehling, J., & Rasmussen, P. (1983). Vapor-liquid equilibriums by UNIFAC group contribution. Revision and extension.
5. Industrial & Engineering Chemistry Process Design and Development, 22(4), 676–678. https://doi.org/10.1021/i200023a023
6. Tiegs, D., Rasmussen, P., Gmehling, J., & Fredenslund, A. (1987). Vapor-liquid equilibria by UNIFAC group contribution. 4. Revision and extension. Industrial & Engineering Chemistry Research, 26(1), 159–161. https://doi.org/10.1021/ie00061a030
7. Hansen, H. K., Rasmussen, P., Fredenslund, A., Schiller, M., & Gmehling, J. (1991). Vapor-liquid equilibria by UNIFAC group contribution. 5. Revision and extension. Industrial & Engineering Chemistry Research, 30 (10), 2352–2355. https://doi.org/10.1021/ie00058a017
8. Wittig, R., Lohmann, J., & Gmehling, J. (2003). Vapor−Liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension. Industrial & Engineering Chemistry Research, 42(1), 183–188. https://doi.org/10.1021/ie020506l