Dortmund modified UNIFAC model

Model description

This is the Dortmund modified UNIFAC model. In this model, the parameters are defined as:

$$z = \frac{3}{4}$$

$$d = 1$$

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/PublishedParametersUNIFACDO.html

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

Using ugropy to retrieve UNIFAC-Dortmund subgroups

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


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

fortran_code = writers.to_yaeos(groups, dortmund)

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 = [78]
molecules(3)%number_of_groups = [6]

Examples

Here is an example of a fully instantiated UNIFAC-Dortmund 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_dortmund 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_dortmund

! 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_dortmund(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. Weidlich, U., & Gmehling, J. (1987). A modified UNIFAC model. 1. Prediction of VLE, hE, and .gamma..infin. Industrial & Engineering Chemistry Research, 26(7), 1372-1381. https://doi.org/10.1021/ie00067a018
2. Gmehling, J., Li, J., & Schiller, M. (1993). A modified UNIFAC model. 2. Present parameter matrix and results for different thermodynamic properties. Industrial & Engineering Chemistry Research, 32(1), 178-193. https://doi.org/10.1021/ie00013a024
3. Gmehling, J., Lohmann, J., Jakob, A., Li, J., & Joh, R. (1998). A Modified UNIFAC (Dortmund) Model. 3. Revision and Extension. Industrial & Engineering Chemistry Research, 37(12), 4876-4882. https://doi.org/10.1021/ie980347z
4. Lohmann, J., & Gmehling, J. (2001). Modified UNIFAC (Dortmund). Reliable Model for the Development of Thermal Separation Processes. JOURNAL OF CHEMICAL ENGINEERING OF JAPAN, 34(1), 43-54. https://doi.org/10.1252/jcej.34.43
5. Lohmann, J., Joh, R., & Gmehling, J. (2001). From UNIFAC to Modified UNIFAC (Dortmund). Industrial & Engineering Chemistry Research, 40(3), 957-964. https://doi.org/10.1021/ie0005710
6. Wittig, R., Lohmann, J., Joh, R., Horstmann, S., & Gmehling, J. (2001). Vapor−Liquid Equilibria and Enthalpies of Mixing in a Temperature Range from 298.15 to 413.15 K for the Further Development of Modified UNIFAC (Dortmund). Industrial & Engineering Chemistry Research, 40(24), 5831-5838. https://doi.org/10.1021/ie010444j
7. Gmehling, J., Wittig, R., Lohmann, J., & Joh, R. (2002). A Modified UNIFAC (Dortmund) Model. 4. Revision and Extension. Industrial & Engineering Chemistry Research, 41(6), 1678-1688. https://doi.org/10.1021/ie0108043
8. Wittig, R., Lohmann, J., & Gmehling, J. (2003). Prediction of phase equilibria and excess properties for systems with sulfones. AIChE Journal, 49(2), 530-537. https://doi.org/10.1002/aic.690490223
9. Jakob, A., Grensemann, H., Lohmann, J., & Gmehling, J. (2006). Further Development of Modified UNIFAC (Dortmund): Revision and Extension 5. Industrial & Engineering Chemistry Research, 45(23), 7924-7933. https://doi.org/10.1021/ie060355c
10. Hector, T., & Gmehling, J. (2014). Present status of the modified UNIFAC model for the prediction of phase equilibria and excess enthalpies for systems with ionic liquids. Fluid Phase Equilibria, 371, 82-92. https://doi.org/10.1016/j.fluid.2014.03.006
11. Constantinescu, D., & Gmehling, J. (2016). Further Development of Modified UNIFAC (Dortmund): Revision and Extension 6. Journal of Chemical & Engineering Data, 61(8), 2738-2748. https://doi.org/10.1021/acs.jced.6b00136