2.39. MedeA UNIFAC: Activity Coefficient Prediction Using UNIFAC

download:pdf

2.39.1. Key Benefits of MedeA UNIFAC

  • Determination of geometric descriptors for organic molecules
  • Evaluation of activity coefficients for binary mixtures based on Group contributions

2.39.2. Introduction

The UNIFAC method (UNIQUAC Functional-group Activity Coefficients) [1] is a group-contribution method for the prediction of activity coefficients in non-electrolyte liquid mixtures. UNIFAC uses the functional groups present in the molecules that make up the liquid mixture, to calculate the activity coefficients based on an extension of the quasi chemical theory of liquid mixtures (UNIQUAC). By using interactions for each of the functional groups present on the molecules, as well as some binary interaction coefficients, the activity of each of the solutions can be calculated. This information can be used to obtain information on liquid equilibria, which is useful in many thermodynamic calculations, such as chemical reactor design, and distillation calculations.

The UNIFAC model was first published in 1975 by Fredenslund, Jones and Prausnitz, a group of chemical engineering researchers from the University of California. Subsequently, they and other authors have published a wide range of UNIFAC papers, extending the capabilities of the model by the development of new or the revision of existing UNIFAC model parameters.

MedeA UNIFAC uses the original UNIFAC description and parameters, as published from 1975 to 2003 [1] [2] [3] [4] [5] [6] [7]. The method and the groups used are described in the rest of this section.

2.39.3. Method

In a multicomponent mixture, the UNIQUAC equation for the activity coefficient of (molecular) component i is:

(1)\[\ln {\gamma_{i}} = \ln {\gamma_{i}^{C}} + \ln {\gamma_{i}^{R}}\]

where

(2)\[\ln {\gamma_{i}^{C}} = \ln{\dfrac{\Phi_{i}}{x_{i}}} + \dfrac{z}{2} q_{i} \ln{\dfrac{\theta_{i}}{\Phi_{i}}} + l_{i} - \dfrac{\Phi_{i}}{x_{i}} \sum_{j}x_{j}l_{j}\]

and

(3)\[ \begin{align}\begin{aligned}\begin{split}\gamma_{i}^{R} = q_{i} \left[ 1 - \ln{\sum_{j} \theta_{j} \tau_{ji}} - \sum_{j} \left( \theta_{j} \tau_{ij} / \sum_{k} \theta_{k} \tau_{kj} \right) \right] \\\end{split}\\\begin{split}l_{i} = \dfrac{z}{2} (r_{i} - q_{i}) - (r_{i} - 1) \quad ; \quad z = 10 \\\end{split}\\\begin{split}\theta_{i} = \dfrac{q_{i}x_{i}}{\sum_{j}q_{j}x_{j}} \quad ; \quad \Phi_{i} = \dfrac{r_{i}x_{i}}{\sum_{j}r_{j}x_{j}} \\\end{split}\\\tau_{ji} = \exp{ - \left[ \dfrac{u_{ij} - u_{ii}}{RT} \right]}\end{aligned}\end{align} \]

where \(x_{i}\) is the mole fraction of component i, and the summations in equations (2) and (3) are over all components, including component i; \(\theta_{i}\) is the area fraction, and \(\Phi_{i}\) is the segment fraction which is similar to the volume fraction. Pure component parameters \(r_{i}\) and \(q_{i}\) are, respectively, measures of molecular van der Waals volumes and molecular surface areas.

Parameters \(r_{i}\) and \(q_{i}\) are calculated as the sum of the group volume and area parameters \(R_{k}\) and \(Q_{k}\), given in table Table 47:

(4)\[r_{i} = \sum_{k} \nu_{k} ^{i} R_{k} \quad and \quad q_{i} = \sum_{k} \nu_{k} ^{i} Q_{k}\]

where \(\nu_{k}^{i}\), always an integer, is the number of groups of type k in molecule i.

The residual part of the activity coefficient, Eq. (3), is replaced by the solution-of-groups concept. Instead of (3), we write:

(5)\[\ln{\gamma_{i}^{R}} = \sum_{k} \nu_{k}^{(i)} [\ln{\Gamma_{k}} - \ln{\Gamma_{k}^{(i)}}]\]

where \(\Gamma_{k}\) is the group residual activity coefficient, and \(\Gamma_{k}^{(i)}\) is the residual activity coefficient of group k in a reference solution containing only molecules of type i.

Note

In Eq. (5) the term \(\ln{\Gamma_{k}^{(i)}}\) is necessary to attain the normalization that activity coefficient \(\gamma_{i}\) becomes unity as \(x_{i} \rightarrow 1\).

The group activity coefficient \(\Gamma_{k}\) is found from an expression similar to Eq. (3):

(6)\[\ln{\Gamma_{k}} = Q_{k} \left[ 1 - \ln{\sum_{m}\Theta_{m}\Psi_{mk}} - \sum_{m} (\Theta_{m}\Psi_{km} / \sum_{n} \Theta_{n} \Psi_{nm}) \right]\]

Eq. (6) also holds for \(\ln{\Gamma_{k}^{(i)}}\). In Eq. (5), \(\Theta_{m}\) is the area fraction of group m, and the sums are overl all different groups. \(\Theta_{m}\) is calculated in a manner similar to that for \(\theta_{i}\):

(7)\[\Theta_{m} = \dfrac{Q_{m}X_{m}}{\sum_{n}Q_{n}X_{n}}\]

where \(X_{m}\) is the mole fraction of group m in the mixture.

The group interaction parameter \(\Phi_{mn}\) is given by:

(8)\[\Psi_{mn} = \exp{- \left [ \dfrac {U_{mn} - U_{nn}}{RT} \right] } = exp {- (\alpha_{mn}/T)}\]

where \(U_{mn}\) is a measure of the energy of interaction between groups m and n. The group-interaction parameters \(\alpha_{mn}\) (two parameters per binary mixture of groups) are the parameters that have been evaluated from experimental phase equilibrium data.

Note

\(\alpha_{mn}\) has units of degrees Kelvin and \(\alpha_{mn} \ne \alpha_{nm}\).

The UNIQUAC model also serves as the basis of the development of the group contribution method UNIFAC, where molecules are subdivided into functional groups. In fact, UNIQUAC is equal to UNIFAC for mixtures of molecules, which are not subdivided; e.g. the binary systems water-methanol, methanol-acryonitrile and formaldehyde-DMF.

2.39.4. UNIFAC groups

Table 47 Groups and subgrous used in MedeA UNIFAC
Group Subgroup Name Description
1      
  1A CH3 end group of hydrocarbon chain
  1B CH2 middle group in hydrocarbon chain
  1C CH middle group in hydrocarbon chain
  1D C middle C in hydrocarbon chain
2      
  2A CH2=CH2 α-olefins, CH2=CH group
  2B CH=CH olefin CH=CH group
  2C CH=C olefin CH=C group
  2D CH2=C α-olefins, CH2=C group
  2E C=C α-olefins, C=C group
3      
  3A ACH aromatic carbon group
  3B AC aromatic carbon with a branch
4      
  4A ACCH3 toluene group
  4B ACCH2 aromatic carbon - alkane group: general case
  4C ACCH aromatic carbon bonded to a CH group
5      
  5A OH OH in alcohols
6      
  6A CH3OH methanol
7      
  7A H2O water
8      
  8A ACOH aromatic carbon-alcohol group
9      
  9A CH3CO carbonyl group in ketones, includes nearest CH3
  9B CH2CO carbonyl group in ketones, includes nearest CH2
10      
  10A CHO aldehyde group
11      
  11A CH3COO ester group, including CH3 bonded with carbonyl C
  11B CH2COO ester group, including CH2 bonded with carbonyl C
12      
  12A HCOO formate group
       
13      
  13A CH3O O, in ethers, including nearest CH3
  13B CH2O O, in ethers, including nearest CH2
  13C CHO O, in ethers, including nearest CH
  13D THF tetrahydrofuran
14      
  14A CH3NH2 methylamine
  14B CH2NH2 primary amine group, includes nearest CH2
  14C CHNH2 primary amine group, includes nearest CH
15      
  15A CH3NH secondary amine group, includes nearest CH3
  15B CH2NH secondary amine group, includes nearest CH2
  15C CHNH secondary amine group, includes nearest CH
16      
  16A CH3N tetriary amine group, includes nearest CH3
  16B CH2N tertiary amine group, includes nearest CH2
17      
  17A ACNH2 aromatic carbon-amine group
18      
  18A C5H5N pyridine
  18B C5H4N pyrridine with 1 branch
  18C C5H3N pyrridine with 2 branches
19      
  19A CH3CN nitrile group, includes nearest CH3
  19B CH2CN nitrile group, includes nearest CH2
20      
  20A COOH carboxyl group
  20B HCOOH formic acid
21      
  21A CH2CL chlorine, includes nearest CH2 group
  21B CHCL chlorine, includes nearest CH group
  21C CCL chlorine, includes nearest C group
22      
  22A CH2CL2 CH2Cl2 group
  22B CHCL2 CHCl2 group
  22C CCL2 CCl2 group
23      
  23A CHCL3 chloroform
  23B CCL3 CCl3 group
24      
  24A CCL4 tetrachloro-methane
25      
  25A ACCL aromatic carbon-chloride group
26      
  26A CH3NO2 nitro group, includes nearest CH3
  26B CH2NO2 nitro group, includes nearest CH2
  26C CHNO2 nitro group, includes nearest CH
27      
  27A ACNO2 nitro group attached to an aromatic carbon
28      
  28A CS2 carbon disulfide
29      
  29A CH3SH methanethiol
  29B CH2SH thiol, includes nearest CH2 group
30      
  30A FURFURAL furfural
31      
  31A DOH two CH2OH groups
32      
  32A I iodine
33      
  33A Br bromine
34      
  34A CH=-C α-alkynes
  34B C=-C alkynes (triple bond not in α position)
35      
  35A DMSO dimethylsulfoxide
36      
  36A ACRY acrylonitrile
37      
  37A Cl(C=C) chloro-olefins, includes C=C group
38      
  38A ACF aromatic carbon-fluorine group
39      
  39A DMF dimethylformamide
  39B HCON(CH2)2  
40      
  40A CF3 CF3 group
  40B CF2 CF2 group
  40C CF CF group
41      
  41A COO ester group (recommended for acrylates and benzoates)
42      
  42A SIH3 methylsilane
  42B SIH2 silanes (only SiH2 group)
  42C SIH  
  42D SI  
43      
  43A SIH2O  
  43B SIHO  
  43C SIO  
44      
  44A NMP N-methylpyrrolidone
45      
  45A CCL3F trochlorofluoromethane
  45B CCL2F  
  45C HCCL2F  
  45D HCCLF  
  45E CCLF2  
  45F HCCLF2  
  45G CCLF3  
  45H CCL2F2  
46      
  46A CONH2  
  46B CONHCH3  
  46C CONHCH2  
  46D CON(CH3)2  
  46E CONCH3CH2  
  46F CON(CH2)2  
47      
  47A C2H5O2  
  47B C2H4O2  
48      
  48A CH3S sulfide, includes one nearest CH3 group
  48B CH2S sulfide, includes one nearest CH2 group
  48C CHS sulfide, includes one nearest CH group
49      
  49A MORPH morpholine
50      
  50A C4H4S thiophene
  50B C4H3S thiophene with 1 branch
  50C C4H2S thiophene with 2 branches
51      
  51A NCO  
55      
  55A (CH2)2SU  
  55B CH2CHSU  
84      
  84A IMIDAZOL  
85      
  85A BTI  

2.39.5. Activity coefficients calculation

MedeA UNIFAC is an interactive tool, providing an easy and quick calculation of activity coefficients of binary mixtures.

The UNIFAC GUI can be accessed through Tools >> UNIFAC. The two components can be added directly from MedeA or from a saved file and the activity coefficients are calculated for the binary mixture at either constant temperature or constant composition.

At constant temperature, a range of compositions can be explored, providing the lower and upper limits of the composition range (in molar fraction) and the composition increment.

At constant composition, a range of temperatures can be explored, providing the lower and upper limits of the temperature range (in Kelvin, Celsius or Fahrenheit) and the temperature increment.

The output comprises:

  • a table with data for temperature, composition and activity coefficients
  • csv and/or txt formated output of the table
  • a graph that can be viewed from within MedeA

For example, at a constant temperature, for a mixture of water and ethanol the MedeA UNIFAC GUI reports the table with all data on activity coefficients:

../../_images/water-ethanol-UNIFAC.png

A graph is available, showing the activity coefficients as a function of the molecular fraction:

../../_images/water-ethanol-UNIFAC-graph.png
[1](1, 2) A. Fredenslund, R. L. Jones, J. M. Prausnitz, “Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures”, AIChE Journal 21, p. 1086 (1975)
[2]S. Skjold-Jorgensen, B. Kolbe, J. Gmehling and P. Rasmussen, “Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension”, Ind. Eng. Chem. Process Des. Dev. 18, p. 714, (1979)
[3]J. Gmehling, P. Rasmussen and A. Fredenslund, “Vapor=Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension. 2”, Ind. Eng. Chem. Process Des. Dev. 21, p. 118 (1982)
[4]E. A. Macedo, U. Weidlich, J. Gmehling and P. Rasmussen, “Vapor-liquid equilibriums by UNIFAC group contribution. Revision and extension. 3”, Ind. Eng. Chem. Process Des. Dev. 2, p. 676 (1983)
[5]D. Tiegs, J. Gmehling, P. Rasmussen, A. Fredenslund, “Vapor-Liquid Equilibria by UNIFAC Group Contribution. 4. Revision and Extension”, Ind. Eng. Chem. Res. 26, p. 159 (1987)
[6]H. K. Hansen, P. Rasmussen, A. Fredenslund, M. Schiller, J. Gmehling, “Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5. Revision and Extension”, Ind. Eng. Chem. Res 30, p. 2352 (1991
[7]R. Wittig, J. Lohmann, J. Gmehling, “Vapor-Liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension”, Ind. Eng. Chem. Res. 42, p. 183 (2003)
download:pdf