UNIFAC

Vapor-liquid equilibrium with saddle azeotrope
calculated with UNIFAC at P = 1 atm. The red lines are vapor compositions, the blue lines the composition of the liquid.

UNIFAC (abbreviation for uni versal Quasi Chemical F unctional Group A ctivity C oefficients) is a method for the estimation of activity coefficients , which in the process technology and the technical chemistry is often used.

UNIFAC is derived from UNIQUAC . UNIQUAC uses substance-specific parameters that have to be determined from experimentally determined data. These parameters are predicted in UNIFAC so that measured data is no longer required.

Principles

UNIFAC is a group contribution method based on the principle of mixing structural groups . This is in contrast to the normal way of looking at the mixture of molecules . The groups are usually functional groups , for example alcohol or carbonyl groups, but also smaller molecular fragments such as individual atoms, but these small fragments are always considered taking their chemical environment into account. A few smaller molecules (such as water ) are fully defined as a separate group.

Group contribution method principle

Example of a group assignment in UNIFAC

The principle of the group contribution methods essentially consists in the fact that only the properties of a few dozen structural groups need to be known, instead of the properties of a few million substances being required for the calculation of substance mixture properties. With these few structural groups as building blocks, a very large number of molecules can be constructed.

UNIFAC group contributions

UNIFAC uses two types of group contributions to predict:

• Additive contributions that are assigned to very small groups ( subgroups ). These are group volumes and group surfaces .
• Interaction parameters between larger groups that comprise several similar subgroups.

The group volumes and surfaces are based on approximate van der Waals surfaces and volumes and are therefore constants in the model that have a physico-chemical background.

The interaction parameters are adapted to experimental activity coefficients as well as to phase equilibrium data, from which activity coefficients can be derived, with non-linear optimization methods. The interaction parameters are thus determined exclusively empirically .

Current parameterization

UNIFAC parameter matrix (last published version)

The UNIFAC model allows the prediction of activity coefficients in mixtures with alkanes , alkenes , alkynes , alcohols , aromatics , esters , ethers , amines , carboxylic acids , organic fluorides , organic chlorides , organic bromides , organic iodides , thiols , sulfones , water , furfural , Thiophenes , pyridines , morpholine , isocyanates , silanes , siloxanes , amides and organic nitrates .

For these functional groups there are interaction parameters with at least one of the other groups. However, not all combinations are fully parameterized, for example an activity coefficient of a mixture of 3-methylthiophene and n-hexane can be calculated, but a prediction of an activity coefficient in a mixture of thiophene with 3-hexene fails due to missing parameters.

UNIFAC cannot be used to calculate activity coefficients in mixtures containing salts or, more generally, electrolytes or polymers . However, there are extensions to the UNIFAC model described here for these two substance classes.

Equations

Detailed formulations can be found in the original article or in textbooks.

The calculation of the activity coefficient is done additively using two terms:

${\displaystyle \ln \gamma _{i}=\ln \gamma _{i}^{C}+\ln \gamma _{i}^{R}}$

Combinatorial part

γ ^C is called the combinatorial part and is calculated from van der Waals surfaces (F) and volumes (V) as well as mole fractions (x).

${\displaystyle \ln \gamma _{i}^{C}=1-V_{i}+\ln V_{i}-5q_{i}\left(1-{{V_{i}} \over {F_{i}}}+\ln {{V_{i}} \over {F_{i}}}\right)}$

With

${\displaystyle V_{i}={{r_{i}} \over {\sum _{j}{r_{j}x_{j}}}}}$

${\displaystyle F_{i}={{q_{i}} \over {\sum _{j}{q_{j}x_{j}}}}}$

In addition to the mole fractions, van der Waals surfaces q _i and volumes r _{i of} the molecules are required. These can be determined from tabulated values ​​for the groups (group surface Q _k and group volume R _k ).

${\displaystyle q_{i}=\sum {\nu _{k}^{(i)}Q_{k}}}$

${\displaystyle r_{i}=\sum {\nu _{k}^{(i)}R_{k}}}$

ν _k ⁽ⁱ⁾ is the frequency of group k in molecule i.

Remainder

γ ^R is referred to as the remainder and is ultimately calculated from adapted interaction parameters.

The remainder is calculated from the group activity _coefficient Γ _k .

${\displaystyle \ln \gamma _{i}^{R}=\sum _{k}{\nu _{k}^{(i)}\left(\ln \Gamma _{k}-\ln \Gamma _{k}^{(i)}\right)}}$

The group activity _coefficients in the mixture Γ _k and in the pure substance Γ _k ⁽ⁱ⁾ are determined by the relationship

${\displaystyle \ln \Gamma _{k}=Q_{k}\left[1-\ln \left(\sum _{m}{\Theta _{m}\Psi _{mk}}\right)-\sum _{m}{{\Theta _{m}\Psi _{km}} \over {\sum _{n}{\Theta _{n}\Psi _{nm}}}}\right]}$

calculated.

Θ is the surface area

${\displaystyle \Theta _{m}={{Q_{m}X_{m}} \over {\sum _{m}{Q_{m}X_{m}}}}}$

and X the group mole fraction.

${\displaystyle X_{m}={{\sum _{j}{\nu _{m}^{(j)}x_{j}}} \over {\sum _{j}\sum _{m}{\nu _{n}^{(j)}x_{j}}}}}$

The parameter ψ contains the adjustable parameters of the UNIFAC model.

${\displaystyle \Psi _{nm}=\exp {\frac {-a_{nm}}{T}}}$with a _nm as the interaction parameter between the groups.

Sample calculation

The pictures show the vapor-liquid equilibrium of the mixture of toluene and methanol. The red lines show the data calculated with (mod.) UNIFAC. For this system the calculation shows a very good agreement with the experimentally determined data.

history

UNIFAC was developed in the 1970s, with the focus at the beginning being solely on the prediction of vapor-liquid equilibria of mixtures of simple, essentially organic substances and mixtures of water. Since activity coefficients for a large number of mixtures were required for the development of the model, the construction of a fact database (the Dortmund database ) was started, which still exists today, albeit in a greatly expanded and modified form.

Since activity coefficients also allow solid-liquid equilibria (solubility of solids in liquids) and liquid-liquid equilibria (see miscibility gap ) to be calculated using simple thermodynamic relationships , the UNIFAC model was also increasingly used for calculation in the 1980s these phase equilibria are used. The model weaknesses of the original model that emerged in the process led, on the one hand, to the development of specially parameterized models for the calculation of liquid-liquid equilibria ( UNIFAC-LLE ) and later to a model for the estimation of octanol-water distribution coefficients . On the other hand, the model itself has been expanded, e.g. by temperature-dependent interaction parameters:

${\displaystyle \psi =\exp \left({{\frac {-a_{nm}}{T}}+{\frac {-b_{nm}\cdot T}{T}}+{\frac {-c_{nm}\cdot T^{2}}{T}}}\right)}$

These extended models are known as modified UNIFAC models.

meaning

UNIFAC (especially the newer versions) is the most frequently used method today for estimating substance mixture data. The predictions are used, for example, in process simulation , the predominant method today for designing and optimizing chemical processes, plants and entire factories . UNIFAC is also used in process synthesis, in which, in very general terms, substances with specific properties are sought for specific tasks. This task can, for example, be that of an entrainer for azeotrope or extractive rectification .

Current developments

UNIFAC is used and further developed in a number of research groups. Current developments (selection) aim at

• the calculation of electrolyte- containing mixtures
• the estimation of viscosities
• the integration of UNIFAC in mixing rules for equations of state ( PSRK )
• the prediction of UNIFAC interaction parameters
• the extension of the UNIFAC model to special groups of substances
• the derivation of the UNIFAC model for the prediction of enthalpies of vaporization and excess enthalpies: group contribution models UNIVAP & EBGCM
• the revision of interaction parameters for existing groups and the addition of interaction parameters for new functional groups in order to improve the applicability and the quality of the UNIFAC model ( UNIFAC consortium ).

literature

1. ↑ A. Fredenslund, RL Jones, JM Prausnitz: Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. In: AIChE J. 21 (6), 1975, pp. 1086-1099.
2. ↑ Å. Fredenslund, J. Gmehling, P. Rasmussen: Vapor-Liquid Equilibria Using UNIFAC - A Group Contribution Method. Elsevier, Amsterdam 1977.
3. ^ A. Bondi: van der Waals Volumes and Radii. In: J.Phys.Chem. 68 (3), 1964, pp. 441-451.
4. ^ R. Wittig, J. Lohmann, J. Gmehling: Vapor-Liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension. In: Ind.Eng.Chem.Res. 42 (1), 2003, pp. 183-188.
5. ↑ J. Gmehling, B. Kolbe: Thermodynamik. 2nd Edition. VCH-Verlag, Weinheim 1992.
6. ^ J. Vidal: Thermodynamique. Méthodes appliquées au raffinage et au Génie Chimique. Editions Technip, 1997.
7. ↑ Gudrun Wienke: Measurement and precalculation of n-octanol / water distribution coefficients. PhD thesis. Univ. Oldenburg, 1993, pp. 1-172.
8. ↑ U. Weidlich, J. Gmehling: A Modified UNIFAC Model. 1. Prediction of VLE, ​​hE, and γ ^∞ . In: Ind.Eng.Chem.Res. 26 (7), 1987, pp. 1372-1381.
9. ↑ H.-M. Polka: Experimental determination and calculation of vapor-liquid equilibria for systems with strong electrolytes. PhD thesis. Univ. Oldenburg, 1993, pp. 1-144.
10. ^ Y. Gaston-Bonhomme, P. Petrino, JL Chevalier: UNIFAC-VISCO Group Contribution Method for Predicting Kinematic Viscosity: Extension and Temperature Dependence. In: Chem.Eng.Sci. 49 (11), 1994, pp. 1799-1806.
11. ↑ T. Holderbaum: The pre-calculation of vapor-liquid equilibria with a group contribution state equation. In: progress report. VDI series 3, 243, 1991, pp. 1-154.
12. ↑ HE Gonzàlez, J. Abildskov, R. Gani, P. Rousseaux, B. Le Bert: A method for prediction of UNIFAC group interaction parameters. In: AIChE J. 53, 2007, pp. 1620-1633.
13. ^ Y. Zhang, X. Zhang, W. Zhang, H. Qu, W. Wang: Prediction of Solid-Liquid Equilibrium to Synthetic Nitro-Musk by using UNIFAC Group-Contribution Method. In: Huaxue-gongcheng. 33 (5), 2005, pp. 69-71.
14. ↑ P. Ulbig: Group contribution models UNIVAP & EBGCM. Development of the group contribution models UNIVAP and EBGCM for the prediction of thermodynamic quantities and determination of the model parameters using evolutionary algorithms. Hannemann-Verlag, 1996, ISBN 3-920088-70-0 .

Web links

Commons : UNIFAC  - collection of pictures, videos and audio files

• UNIFAC industrial consortium at the Carl von Ossietzky University of Oldenburg
• Calculation of activity coefficients in some binary mixtures
• UNIFAC structure groups and parameters
• Structure groups for UNIFAC