714
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension
'
Steen Skjold-J$rgensen,' Barbel Kolbe,2 Jurgen Gmehling,* * and Peter Rasmussen"
Instituttet for Kemiteknik, The Technical University of Denmark, DK-2800 Lyngby, Denmark, and Lehrstuhl Technische Chemie 6, University of Dortmund, 46 Dortmund 50, West Germany
The UNIFAC group contribution method for estimating liquid phase activity coefficients is widely used for phase equilibrium calculations. The accuracy and the range of applicability of the method is determined by the available number of reliable group parameters. New parameters are reported for eight different groups not previously covered by UNIFAC, and some of the previously published parameters have been revised based on new experimental vapor-liquid equilibrium data. The definition of the alcohol group has been modified making UNIFAC easier to use and more reliable for alcohol containing mixtures.
Introduction The UNIFAC group contribution method is a reliable and fast method for predicting liquid phase activity coefficients in nonelectrolyte mixtures at low to moderate pressures and temperatures between 300 and 425 K. It has become a valuable tool in phase equilibrium calculations for systems for which little or no experimental information is available. The UNIFAC method was developed in 1975 by Fredenslund et d. (1975). The method has later been revised, the range of its applicability has been extended, and detailed descriptions of the method have been presented (Fredenslund et al., 1977a,b). It is the aim of this work to report further extensions and revisions of the UNIFAC parameter tables. UNIFAC Parameters The UNIFAC group contribution method is based on the solution of groups concept. The groups are structural units such as CH,, OH, and others which when added form the parent molecules. Instead of considering a liquid mixture as a solution of molecules, the mixture is considered as a solution of groups. The activity coefficients are then determined by the properties of the groups rather than by those of the molecules. A review on group contribution methods for prediction of activity coefficients is given by Rasmussen and Fredenslund (1978). The activity coefficients are calculated from two terms: a combinatorial part essentially due to differences in size and shape of the molecules and a residual part due to energetic interactions between the groups. The fundamental equations are presented in the Appendix. Three types of group parameters are needed: group volume parameters ( R J , group surface area parameters ( Q k ) , and group interaction parameters (arnnand an,,,). The indices k , m, and n represent different groups. The group interaction parameters am,, and an,,, published by Fredenslund et al. (1977a,b) were mainly estimated from experimental vapor-liquid equilibrium data available from the literature up to the end of 1975. The procedures for testing the data and for estimating the parameters are described in detail by Fredenslund et al. (1977a). Lack of reliable experimental data has pre'Technical University of Denmark. *University of Dortmund. 0019-7882/79/1118-0714$01 .OO/O
vented the estimation of some interaction parameters, and some are based on relatively few data points. As new data become available it is possible to calculate some of the missing parameters and to revise some of the parameters based on limited information. One might consider to include liquid-liquid equilibrium data and heat of mixing data in the estimation of group parameters. Our experience has shown, however, that if a high priority is placed on the correct representation of vapor-liquid equilibria, the parameters should as far as possible be based on vapor-liquid equilibrium data. Simultaneous correlation of vapor-liquid, liquid-liquid, and heat of mixing data is being extensively studied at the moment by our group and others.
New Parameters In this work we have revised and extended the UNIFAC group interaction parameter tables by including experimental vapor-liquid equilibrium data published until the middle of 1978. The literature data have been collected at the University of Dortmund and stored on magnetic tape as the Dortmund Data Bank (Gmehling et al., 1977). Table I presents a short supplementary list of group volume and group surface area parameters, Rk and Qk. Only new groups and groups for which the Rk and Qk values have been altered are included. Table I1 presents the new UNIFAC group interaction parameter table. Estimation of UNIFAC Parameters The group interaction parameters are estimated by minimization of the following objective functions i Fmin =
j
C C[ln ri(UNIFAC) - In yi(exper)]?
(1)
where yi(UN1FAC) and yi(exper) are the activity coefficients calculated respectively from the UNIFAC method and from the experimental vapor-liquid equilibrium data. The summations are to be taken over d l data points, j , and components, i. Fredenslund et al. (1977a,b) used the Nelder-Mead search method (Nelder and Mead, 1965) for the minimization. In this work we have used a modified Levenberg-Marquardt method from the IMSL program library. This method is much faster than the search method. When comparisons are made of the quality of fits between different sets of data we use a more convenient
0 1979 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
715
Table I. New Group Volume and Surface Area Parameters main group
sub group
“OH” “CC1”Q “(C),N”
OH
Qk
sample group assignment
Br
1.0000 1.0060 1.187 0.9598 1.242 1.264 0.9492
1.200 0.7 24 0.940 0.632 1.188 0.992 0.832
CH,SH furfural CAN C,HJ C,HJ (CH ,OH )Z CH,SH
1.877 3.168 2.9993 2.8332 2.667 2.4088 1.651
1.676 2.484 2.113 1.833 1.553 2.248 1.368
2-butanol: 2 CH,, 1 CH,, 1 CH, 1 OH 2-chloro-2-methylpropane: 3 CH,, 1 CC1 trimethylamine: 2 CH,, 1 CH,N triethylamine: 3 CH,, 2 CH,, 1 CH,N ethyl formate: 1 CH,, 1 CH,, 1 HCOO iodoethane: 1 CH,, 1 CH,, 1 I bromomethane: 1 CH,, 1 Br bromobenzene: 5 ACH, 1AC, 1 Br methanethiol: 1 CH,SH furfural: 1 furfural pyridine: 1 C,H,N 3-methylpyridine: 1 CH,, 1 C,H,N 2,3-dimethylpyridine: 2 CH,, 1 C,H,N 1,2-ethanediol: 1(CH,OH), ethanethiol: 1 CH,, 1CH,SH
Rk
CCl CH,N CH,N HCOO
“HCOO”
I
“pyridine” “DOH”
a In the publications by Fredenslund et al. there was a misprint in R k for “CC1”. The group interaction parameters were correct and have hence not been changed.
.
4
.
0.2 0
0.0
0.2
0.4
0.6
0.8
1.0
x1
Figure 1. Iodoethane(l)-ethanol(2) at 303.15 K. Experimental points: Smith and Engel (1929);predicted curve: parameters from Table 11.
Figure 2. Methanethiol(l)-acetnitrile(2) at 313.15 K. Experimental points: Eng (1977); predicted curve: parameters from Table 11.
function than Fmin.F,,, is thus independent of the total number of data points, nobs.
experimental vapor-liquid equilibrium data for aromatic iodides have been found. The parameters should therefore only be used to predict the properties of nonaromatic iodides. Figure 1 shows an x-y diagram indicating the quality of fit from the iodide parameters. Bromides. The available experimental vapor-liquid equilibrium data for mixtures containing alkyl or aromatic bromides are scarce. All information for the two types of compounds has therefore been combined to a general Br group. As a consequence, the predictions for mixtures containing the Br group may not be too accurate. Methanethiol. Figure 2 shows an x-y diagram for methanethiol-acetonitrile. It has not been possible to estimate common parameters which can be used with confidence for methanethiol, ethanethiol, and higher thiols. Very little reliable information can actually be found for mixtures with higher thiols and it has only been possible to estimate the interaction parameters between alkane and higher thiols. Glycols. The group interaction parameters between CHz and DOH and between OH and DOH are estimated at the same time based on infinite dilution activity coefficients of hydrocarbons dissolved in 1,2-ethanediol and from vapor-liquid equilibrium data for mixtures of alcohols and 1,2-ethanediol. Revised Parameters The old group interaction parameters have been revised when the new literature data included in DDB were of a higher quality than the old data or if the new data covered a wider temperature range. The parameters which have been changed are indicated by asterisks in Table 11.
(2)
It does not make much difference whether (1)or (2) is used as the objective function when the ratio ri(UNIFAC)/ yi(exper) is close to unity. New Groups Eight different new groups have been included: tertiary amines, formates, bromides, iodides, methanethiol, furfural, pyridine, and glycols. A few comments may be given to some of the groups. Tertiary Amines. A few interaction parameters based on a limited data base were already presented by Fredenslund et al. (1977a). It is difficult to obtain good results for mixtures with water. This may be due to the reaction (C)3N + H20 = (C)3NH+ + OH-
(3)
For triethylamine the dissociation constant is pKB = 2.99 a t 18 “C (HCP, 1974/75). Formates. The ester group COOC cannot be used for formates since the ester group includes a CH, or CH2group next to the COO group. A special HCOO group has therefore been introduced. Iodides. The group interaction parameters have been based on data for aliphatic iodides only. No reliable
716
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
Table 11. UNIFAC Group Interaction Parameters a,,, 1 CH 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
CH 2
c=c
ACH ACCH OH CH,OH !k&H CH,CO CHO COOC CH20 CNH, CNH ACNH, CCN COOH cc1 CCl,
cc1,
CCl, ACCl CNO, ACNO,
cs
2
(C),N HCOO I Br CH,SH CCOH furfural pyridine DOH
CH,
c=c
ACH ACCH, OH CH,OH X H CH,CO CHO COOC CH,O CNH, CNH ACNH CCN COOH
,
cc1
CCl, CCl, CCI, ACCl CNO,
I Br CH,SH CCOH furfural pyridine DOH
0 2520 - 11.12 -69.70 156.4 16.51 300.0* 311.0 26.76 505.7 114.8 83.36 -30.48 65.33 5339 24.8 2* 315.3 91.46 34.01 36.70 - 78.45 -141.3 -32.69 5541 - 52.65* - 83.98 90.49 128.0 -31.52 -7.481 -87.93 -25.31 - 101.6 140.0
K (rn Indicates the Row, n the Columnp 2
c=c - 200.0 0 -94.78 - 269.7 8694 - 52.39 692.7* ma. -82.92 n.a. n.a. 76.44 79.40 -41.32 n.a. 34.78* 349.2 - 24.36 -52.71 - 185.1 - 293.7 ma. -49.92 ma. 16.62 - 188.0
n.a. n.a. n.a. ma. 121.5 ma. n.a. n.a.
3 ACH 61.13 340.7 0 - 146.8 89.60 - 50.00 362.3 2043 140.1 n.a. 85.84 52.13 -44.85 -22.31 650.4 - 22.97 62.32 4.680 ma. 288.5 -4.700 -237.7 10.38 1825 21.50* - 223.9 n.a. 58.68 155.6 28.41 -64.13 157.3 31.87 221.4
4 ACCH,
5 OH
76.50 4102 167.0 0 25.82 -44.50 377.6 6245 365.8 n.a. -170.0 65.69 ma. 223.0 979.8* - 138.4 268.2 122.9 n.a. 33.61 134.7
986.5 693.9 636.1 803.2 0 249.1 -229.1 -533.0 164.5 -404.8$ 245.4 237.7 -164.0 - 150.0 529.0
3 75.5
-97.05 n.a. 40.68
n.a. ma. n.a. 291.1 n.a. -99.38 404.3 49.80 150.6
185.4
- 151.0 562.2 747.7 742.1 856.3 246.9 341.75 n.a. 823.5 28.60 191.2 501.3 721.9 461.69 n.a. 521.6 - 132.3 267.6
6 CH,OH
7 H2O
8 ACOH
9 CH,CO
10 CHO
697.2 1509 637.4 603.3 -137.1 0 289.6 (ma.) 108.7 - 340.2 249.6 339.7 -481.7 -500.4 (ma.) 157.8* 1020 529.0 669.9 649.1 860.1 (n.a.) 252.6 n.a. 914.2 (n.a.) 155.7 (ma.) (n.a.) 382.8 127.4 (ma.) -378.2 (n.a.)
1318 634.2* 903.8 5695.0 353.5 -181.0 0 - 540.6 472.5* 232.7*
2789 n.a. 1397.0 726.3 286.3 (n.a.) 442.0 0 n.a. n.a. 853.6 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. 1616 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. ma. 257.3 ma. -222.2 523.0
476.4 524.5 25.77 -52.10 84.00 23.39 - 195.4* n.a. 0 128.0 372.2 52.38 n.a. n.a. n.a. -287.5* - 297.8 286.3 423.2 552.1 372.0 n.a. - 142.6 n.a. 303.7* n.a. n.a. 138.0 - 142.6 160.6 48.16 317.5 ma. n.a.
677.0 n.a. n.a. n.a. 441.8f 306.4 -257.3* n.a. -37.36 0 n.a. n.a. ma. n.a. n.a. n.a. n.a.
10000*
-314.7’* - 330.4* -448.2+* -339.5 242.8 -66.17* 698.2 708.7 826.8 1201 920.4 417.9* 360.7 1081 - 598.8’ n.a. n.a. n.a. n.a. 60.81* 23.48 -332.9 n.a.
47.51
n.a. n.a. n.a. ma. n. a. n.a. n.a. n.a. n.a. n.a. ma. n.a. n.a. ma. ma. n.a.
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979 717 Table 11. (Continued)
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
CH,
c=c
ACH ACCH, OH CH,OH % !H CH,CO CHO COOC CH,O CNH, CNH ACNH, CCN COOH CCl CCl,
cc1; cc1,
ACCl CNO ACNO,
cs,
Br CH,SH CCOH furfural pyridine DOH
CHl
c=c
ACH ACCH, OH CH,OH H,O ACOH CH,CO CHO COOC CH,O CNH, CNH ACNH, CCN COOH
cc1 cc1, cc1;
cc11 ACCl CNO ACNO,
11 COOC
12 CH,O
13 CNH,
14 CNH
15 ACNH,
232.1 n.a. 5.994 5688 101.1 -10.72 14.42* - 713.2 - 213.7 n.a. 0 461.3 n.a. 136.0 n.a. -266.6* - 256.3 n.a. - 132.9 176.5 129.5 -246.3* n.a. ma. 243.8* n.a. - 261.1 21.92 n.a. n.a. 76.20 - 146.3 n.a. n.a.
251.5 289.3 32.14 213.1 28.06 - 180.6 540.5+* n.a. 5.202 n.a. -235.7 0 n.a. - 49.30 n.a. n.a. -338.5 225.4 - 197.7 - 20.93
391.5 396.0 161.7 n.a. 83.02 359.3 48.89* ma. n.a. n.a. n.a. n.a. 0 108.8 n.a. n.a. n.a. n.a. n.a. n.a. n.a. 203.5 n.a. n.a. n.a. n.a. ma. n.a. n.a. 106.7 110.8 ma. n.a. n.a.
255.7 273.6 122.8 - 49.29 42.70 266.0 168.0+* n.a. n.a. n.a. -73.50 141.7 63.72 0 n.a. n.a. n.a. n.a. ma. ma. 91.13 - 108.4 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. 188.3 n.a. ma. n.a.
1245 n.a. 668.2 764.7* -348.2 (ma.) 213.0 ma. n.a. n.a. n.a. n.a. ma. ma. 0 ma. ma. n.a. ma. ma. 1302 n.a. n.a. 5250 n.a. n.a. n.a. n.a. n.a. n.a. 412.0 n.a. n.a. 164.4
16 CCN
17 COOH
18 CCl
19 CCI,
cc1,
597.0* 405.9* 212.5 6096 6.71 2 36.23* 112.6 n.a. 481.7* n.a. 494.6* n.a. n.a. n.a. n.a. 0 n.a. n.a. n.a. 74.04 492.0 n.a. ma. n.a.
663.5 730.4 537.4 603.8 199.0 -289.5 - 14.09* n.a. 669.4 n.a. 660.2 664.6 n.a. n.a. ma. n.a. 0 326.4 1821 n.a. 689.0 n.a. ma. n.a. n.a. n.a. - 356.3 n.a. n.a. ma. 77.61 ma. n.a. ma.
35.93 99.61 - 18.81 -114.1 75.62 -38.32 325.4 ma. - 191.7
53.76 337.1 n.a. n.a. -112.1 - 102.5 370.4 n.a. - 284.0 ma. 108.9 137.8 ma. n.a. ma. n.a. - 183.4 108.3 0 0 17.97 n.a. n.a. ma. n.a. - 73.87 n.a. -40.82 ma. n.a. - 185.9 n.a. n.a. n.a.
24.9 4583 -231.9 -12.14 -98.12 - 139.4 353.7 n.a. -354.6 ma. - 209.7 - 154.3 ma. ma. n.a. - 15.62 n.a. 249.2 0 0 51.90 n.a. ma. n.a. -26.06* -352.9 n.a. 21.76 n.a. ma. -170.9 48.30 -114.7 n.a.
335.7
I Br CH,SH CCOH furfural pyridine DOH
ma. n.a. n.a. n.a. 125.7 ma. n.a. - 169.7 ma.
113.9
n.a. -94.49 n.a. 112.4* ma. n.a. 474.6 n.a. 63.71 70.00 n.a. n.a. n.a.
751.8
n.a. 301.1 n.a. n.a. n.a. n.a. 44.42 0 - 84.53 -157.1 11.80 n.a. n.a. n.a. - 73.09 n.a. n.a. n.a. 1169 -27.94 - 38.23 n.a. n.a. n.a.
20
718
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
Table 11. (Continued)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
CH,
c=c
ACH ACCH, OH CH,OH H,O ACOH CH,CO CHO COOC CH,O CNH, CNH ACNH, CCN COOH
cc1 CCl, cc1, cc1,
ACCl CNO, ACNO,
I Br CH,SH CCOH furfural pyridine DOH
21
22
23
24
CCL,
ACCl
CNO,
ACNO,
104.3 5831 3.000 - 141.3 143.1 -67.80 497.5 4894 -39.20
321.5
n.a. 538.2 -126.9
287.8
(ma.) 678.2
n.a. n.a. n.a.
CH 1
c=c
ACH ACCH, OH CHIOH H,O ACOH CH,CO CHO COOC CH ,O CNH , CNH ACNH, CCN COOH
cc1 CC1, cc1,
CC1” ACCl CNO, ACNO,
1
Br CH,SH CCOH furfural pyridine DOH
137.5
54.47
629.0*
47.67
n.a.
95.18
n.a.
68.81 4350
n.a. n.a. n.a. n.a. n.a. n.a.
n.a. ma. n.a. n.a. n.a. ma. ma. n.a.
475.8 0 794.4
490.9 - 154.5 0
n.a. n.a.
n.a. n.a. n.a. n.a. n.a.
71.23 8455 - 54.86 212.7 62.42 56.33 -30.10 0 - 255.4 - 34.68 514.6 -60.71 - 8.283
- 86.36
n.a.
n.a.
48.49 225.8
ma. 224.0
125.3
n.a.
n.a.
ma. ma. n.a. ma.
-98.66 - 133.2
n.a. n.a. (C),N
I
n.a. n.a. n.a.
n.a.
290.0
ma. n.a. ma.
206.6 658.8 90.49
n.a. -323.0
(n.a.) 304.0+
n.a. ma. ma. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. - 141.4
-293.7 -126.0 1088
n.a. n.a. n.a. 0 n.a. n.a. n.a. n.a. n.a. n.a. ma. n.a.
481.3 27
26
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
661.5 542.1 168.1 3629 61.119 75.14 220.6*
543.0
25
cs
2
153.6*
n.a.
76.30
194.9
52.07*
ma. n.a. n.a.
-9.450
399.5
n.a. n.a. n.a. n.a. n.a. n.a. n.a. -62.73
ma. ma. n.a. n.a. n.a. 534.7
n.a. ma. 0
ma. ma. n.a. n.a. n.a. n.a. n.a. n.a. ma. n.a.
477.0 -31.09 887.1
n.a. 216.1*
n.a. 183.0* 140.9*
ma. n.a. n.a. 230.9
n.a. 450.1 n.a. 116.6* 132.2 n.a.
n.a. n.a. 0 n.a. ma. n.a. ma. n.a. 73.52
n.a. ma. n.a.
28
29
30
I
Br
CH,SH
HCOO 741.4
335.8
479.5
184.4
n.a. n.a. n.a.
n.a.
n.a. - 13.59
193.1 193.4
313.5
-171.3 133.4
n.a. - 10.43 ma.
(ma.) n.a. n.a.
(n.a.) n.a. n.a.
n.a. n.a.
53.59
245.2
-46.28
n.a.
n.a. n.a. ma. n.a. n.a. n.a. ma. n.a.
n.a. n.a.
n.a. n.a. n.a. ma. 372.9
n.a. ma. ma. n.a. n.a. 312.5
n.a. ma. n.a. ma. n.a. ma. n.a. n.a. ma. 0 n.a. n. a. 239.8
n.a. ma. ma. n.a.
113.3
n.a.
148.3 - 149.5
n.a. n.a. n.a. n.a. n.a. n.a. 177.6 86.40 247.8
n.a. n.a. n.a. n.a. ma. ma. 0 n.a. n.a. n.a. n.a. n.a. ma.
14.758 37.84
-8.538 -70.14
n.a. n.a. 21.37
n.a.
-125.9
59.02
n.a. n.a.
n.a. ma. n.a. ma. ma. n. a. n.a. n.a.
41.94 -60.70 10.17
n.a. n.a. n.a. n.a. n. a. 0 n.a. n. a. n.a. n.a. n.a.
4.339
n.a. n.a. 0
ma. n.a. n.a. ma.
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
719
Table 11. (Continued) -
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
CH,
c=c
ACH ACCH, OH CH,OH H2O ACOH CH,CO CHO COOC CH,O CNH, CNH ACNH, CCN COOH
cc1 CCl, cc1,
CCI, ACCl CNO I ACNO, CS, (C),N HCOO I Br CH,SH CCOH furfural pyridine DOH
31
32
33
34
CCOH
furfural
pyridine
DOH
737.5 53 5.2 477.0 469.0
354.6
287.8
3025
n.a.
ma.
n.a.
-64.69 - 20.36 - 120.5
-4.449 52.80 170.0 580.5 459.0 -637.3
210.4 4975 -319.0
n. a. n.a. n.a. n. a. n.a. n.a. n.a.
n.a. ma. n.a. n.a. n.a. n.a.
134.3
n.a. n.a. n.a. n.a. n.a. ma. n.a.
n.a.
(n.a.)
-80.78 43.31* -455.4 129.2
-163.7
ma.
ma.
109.9 42.00 -217.2 -243.3 - 245.0
n.a. -17.59 368.6 601.6 491.1 570.7 134.1
n.a. n.a. 442.8
n.a. n. a. n.a. n.a. n.a. 0 n.a. n.a. n.a.
188.0
n.a. 202.3
n.a. ma. n.a. n.a. n.a. n.a. n.a. ma. -64.38 546.7
n.a. ma. ma. n. a. ma. n. a. n.a. n. a. n.a. n.a. 0
n.a. n.a.
(ma.) n.a. -538.6
125.3
n.a. n.a. n.a. 18.98
ma. n.a. n.a. n.a. n. a. n.a. n.a. ma. n.a. n.a. ma. n.a. 0 n.a.
139.8
n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. 0
a n.a. = not available; (n.a.) = not available CH,OH parameter; predictions may be obtained by means of the OH group; italicized numbers = n.a. eliminated; * = revised parameter; 9 = estimated from CH,OH data; = predictions not reliable in the whole concentration range. In addition t o the tabulated parameters one pair of parameters is available for higher thiols: +
Revisions regarding the alcohol and water groups are commented on below. Group Interactions with Water The CH2/H20group interaction parameters presented by Fredenslund et al. (1977a,b) were evaluated from mutual solubility data for alkanewater mixtures. Because of the very limited miscibility of such compounds, the group fractions of CH2in the water rich phase and of H20 in the hydrocarbon rich phase are small. This means that only narrow group fraction ranges have been covered. In most applications of the group interaction parameters, we experience a wide concentration range for the various groups. It has already been pointed out that group interaction parameters estimated from liquid-liquid equilibrium data are not reliable for vapor-liquid equilibrium predictions. New parameters for the C H 2 / H 2 0group interactions have therefore been determined from vapor-liquid equilibrium data for aqueous solutions of alcohols, ethers, and ketones. All other group interaction parameters which depend on the CH2/H20 interaction have been revised based on the new C H 2 / H 2 0parameters. The new parameters presented in Table I1 are generally more reliable than the previously published values except for mixtures of alkanes with water. For such mixtures one finds, as expected, better results with the “old’ parameters. New Group Definition for Alcohols Fredenslund et al. (1977a,b) defined the alcohol group as a rather large group containing two carbon atoms besides OH. With this large group it is possible to predict
the properties of many types of alcohols except methanol and it is possible to distinguish between many isomers. The group has five subgroups, and in addition it was found necessary to introduce special group interaction parameters for some ethanol-containing mixtures. In this work, the alcohol group has been redefined as a group containing OH only. Fredenslund et al. determined all Rk and Qk values from the van der Waals volumes and surface areas presented by Bondi (1968) and the large group was necessary to present all alcohols. We have determined the Rkand Qk values for OH empirically. They were fitted together with the group interaction parameters between CH2 and OH and H 2 0 and OH based on experimental data for alkane/alcohol and water/alcohol mixtures. These Rk and Qk values have been used in all subsequent estimations of group interaction parameters for the OH groups. Tables I and I1 present the Rk and Q k values and the group interaction parameters for alcohols both according to the “old” and to the “new” group definition. Methanol. The new OH group can be used to predict activity coefficients for methanol (1CH3, 1 OH). Methanol has, however, been retained as a special group because of the ready availability of experimental data for mixtures with methanol and for mixtures with higher alcohols. This also agrees with our experience that it is advantageous to treat the first number of a homologous series with special care. It is possible to estimate OH group interaction parameters from experimental data for mixtures with methanol and thus to extrapolate to mixtures with higher
720
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
Table 111. Comparison between Estimation of OH Parameters from CH,OH Data and from Using OH Parameters from Table I1 to Predict CH,OH Activity Coefficients type .. of system
comments
methanol-ester
methanol parameters: QCH,OH,COOC = -10.72, QCOOC,CH,OH = 249.6 methanol by means of OH parameters from Table 11: aOH,COOC = 101.1, aCOOC,OH = 245*4 parameter estimation; OH parameters from CH,OH data: QOH,COOC = - 8.93, aCOOC,OH = 292.4 H. A. by means of OH parameters from CH,OH data: aOH,COOC = -8.93, aCOOC,OH = 292*4 H. A. by means of OH parameters from Table 11: aOH.COOC = 101.1, aCOOC,OH = 245.4
methanol-ester
methanol-ester
H. A.-estera
H. A.-estera
a
Y 1o*l
0.6
2.62 0.4
10.0 0.2
2.62
7.31
6.85
H. A. = Higher Alcohols.
alcohols from data on mixtures with methanol. Table I11 shows an example of the various possibilities for using the parameters and data. This example and others where a comparison between various procedures is possible show that the prediction of activity coefficients of higher alcohols by means of OH parameters estimated from CH,OH activity coefficients is very successful and that the prediction of CH30H activity coefficients by means of OH parameters from higher alcohols is acceptable. The following interactions presented in Table I1 have been determined by means of methanol data: OH/CHO, OH/CN02, and OH/CH3SH. Results with the New Alcohol and Water Parameters Roekens and Verhoeye (1976) compare experimental and predicted azeotropic compositions and temperatures for alkane-alcohol mixtures. The UNIFAC predictions based on the old group definitions and parameters agree well with
0.2
0.0
0.4
0.6
0.8 XI
1.0
Figure 3. Hexane(l)-ethanol(2) at 333.15 K. Experimental points: Lindberg and Tassios (1971); predicted curve: parameters from Fredenslund et al. (1977a,b).
the experimental data. Table IV gives a comparison also to the predictions with the new OH parameters. The redefinition of the alcohol group has led to considerable improvements. Table IV also gives a comparison between experimental and predicted azeotropes for some binary water-alcohol mixtures. The values predicted by means of the new OH and H 2 0 parameters are at least as good as the values predicted from the old parameters. More predictions of azeotropes using the new parameter table are given by Magnussen et al. (1979). Experimental values for a number of ternary azeotropes are given by Morachevsky and Pukinsky (1978). Table V compares the experimental data and the predictions by UNIFAC. The agreement between experimental and predicted values is very good. It has to be noted that a comparison between the predicted azeotropic temperature and an experimental value is not possible since the temperature was not measured. The old parameters (even the special ethanol parameters) incorrectly predicted a phase splitting for the system hexane-ethanol at 333.15 K as shown on Figure 3. Figure 4 shows that the new OH parameters do not predict such a phase splitting.
Conclusion The UNIFAC group interaction parameter table has been revised and extended based on consistent vapor-
Table IV. Comparison between Azeotropes Predicted by Means of the New and the Old Parameters and the Experimental Values for Some Alcohol-Alkane and Water-Alcohol Mixtures at 1 atma predicted values (UNIFAC) exptl values system ethanol( 1)-pentane( 2 ) ethano I( 1)-hexane( 2) 1-propanol(1)-pentane( 2 ) 1-propanol(1)-hexane( 2) 1-butanol(1)-hexane( 2) 1-butanol(1)-heptane( 2 ) 1-pentanol(1)-heptane( 2 ) water( 1)-ethanol( 2 ) water( 1)-1-propanol( 2) water( 1)-2-propanol( 2) water( 1)-1-butanol( 2 ) water( 1)-2-butanol(2)
- xi,az, % 8.6 33.2 1.9 15.3 4.0 22.9 6.9 9.6 57.8 32.5 75.2 60.7
Taz, K 307.10 331.47 308.99 338.48 341.28 367.06 371.08 351.32 360.91 353.25 365.85 360.65
parameters from Table I1 x i . a z , ?h
8.9 33.7 0.3 16.1 2.9
23.0 6.7 10.4 57.9 31.0 77.4 63.1
Taz,
K
307.50 331.65 309.0 338.75 341.56 366.76 370.94 351.19 360.43 353.25 365.75 360.24
parameters from Fredenslund et al. (1977a) xi.azi %
8.8 35.6 no azeotrope 16.2 1.0 23.3 5.4 7.9 57.0 33.6 76.0 62.4
Taz, K 308.29 332.21
339.51 342.13 367.69 371.51 351.25b 360.48 352.50 365.44 358.68
The experimental values for alcohol-alkane: Roekens and Verhoeye ( 1 9 7 6 ) ; for water-alcohol: Azeotropic Data I11 (1973). Special ethanol-water parameters were used.
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979 721
Table V. Experimental and Predicted (UNIFAC) Ternary Azeotropes at Different Pressures. The Temperature Is the Predicted One Since No Experimental Temperatures Are Given by Morachevsky and Pukinsky (1978) UNIFAC predictions system acetonef lkmethanolf 2 h ~ h e x a n e.3) f, \
,
\
,
methyl acetate( 1)-methanol( 2)-n-hexane( 3)
ethyl acetate( 1)-ethanol( 2)-cyclohexane(3)
ethanol( 1)-MEK( 2)-cyclohexane( 3)
P,mmHg T , K 400 500 600 700 800 400 500 600 700 800 300 400 500 600 700 800 300 400 500 600 700 800
304.9 310.3 315.0 319.0 322.6 304.8 310.1 315.0 318.7 322.6 314.7 321.0 326.8 331.3 335.5 339.3 314.7 321.0 326.7 331.6 335.5 339.1
Figure 4. Hexane(1)-ethanol(2)at 333.15 K. Experimental points: Lindberg and Tassios (1971); predicted curve: parameters from Table 11.
liquid equilibrium data published before the middle of 1978. Some of the previous n.a.’s (not available parameters) have thus been eliminated, new groups have been added, and some parameters have been revised based on new experimental data. A new alcohol group has been defined. The group (OH) is much more flexible than the old one. With only one subgroup it is now possible to predict activity coefficients in mixtures containing alcohols with at least as great reliability as with the old alcohol group with its five subgroups and special ethanol parameters. This improvement has been attained through optimization of the group volume and surface area for the alcohol group. The new group is unfortunately not able to distinguish between isomers. These revisions and extensions of the parameter table have made the UNIFAC method more flexible, and its range of applicability and its accuracy have been increased.
Supplement A list of references used for the parameter estimation can be obtained from the authors. A supplement, UNIDIST, which shows the application of the new pa-
exptl values
X1
Xl
x3
0.386 0.360 0.336 0.317 0.299 0.332 0.320 0.308 0.298 0.288 0.165 0.146 0.129 0.117 0.106 0.096 0.299 0.324 0.348 0.367 0.385 0.401
0.214 0.240 0.264 0.284 0.302 0.296 0.311 0.326 0.337 0.348 0.319 0.340 0.360 0.375 0.390 0.403 0.158 0.137 0.117
0.400 0.400 0.400 0.399 0.399 0.372 0.369 0.366 0.365 0.364 0.516 0.514 0.511 0.508 0.504 0.501 0.543 0.539 0.535 0.532 0.528 0.525
0.101 0.087 0.074
Xl
XZ
x3
0.393 0.376 0.360 0.341 0.333 0.352 0.336 0.328 0.316 0.306 0.172 0.150 0.128 0.107 0.087 0.06 7 0.258 0.290 0.319 0.342 0.361 0.375
0.206 0.227 0.248 0.268 0.277 0.290 0.305 0.322 0.335 0.346 0.273 0.296 0.319 0.341 0.362 0.383 0.159 0.131 0.106 0.083 0.068 0.054
0.401 0,397 0.392 0.391 0.390 0.358 0.359 0.350 0.349 0.348 0.555 0.554 0.553 0.552 0.551 0.550 0.583 0.579 0.575 0.573 0.571 0.571
rameters for distillation calculations is also available from P. Rasmussen. Acknowledgment The authors thank Professor Aa. Fredenslund for his help to this work during many fruitful discussions. The authors further thank Bundesministerium fur Forschung und Technologie and Professor U. Onken for support of the project. Appendix The UNIFAC Model. Equations giving the activity coefficients as functions of composition and temperature are here stated very briefly. The model has a combinatorial contribution to the activity coefficients, essentially due to differences in size and shape of the molecules, and a residual contribution, essentially due to energetic interactions In yi = In yic + In yiR (14 comb. resid. I. Combinatorial Part. aJL
2
0,
aJ
In ylc = In - + -4, In - + 1, - 2Cxlll Xl 2 aJ‘ xi J
(2A)
Pure-component parameters ri and qi are, respectively, measures of molecular van der Waals volumes and molecular surface areas. They are calculated as the sum of the group volume and group area parameters, Rk and Q k ri = CVk(i)Rk;qi = C V k ( i ) Q k k
k
(44
where vk(i), always an integer, is the number of groups of type k in molecule i. Group parameters Rk and Q k are normally obtained from van der Waals group volumes and surface areas, vk and Ak, given by Bondi (1968)
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Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
11. Residual Part. In
7iR =
Cvk(i)[lnr k - In
rkci)]
k
(64
r k is the group residual activity coefficient, and r k C i ) is the residual activity coefficient of group k in a reference solution containing only molecules of type i.
CV,(i)Xi
6, = -.Q m x r n
'
EQ,X,'x"'= n
i
vk(i'x i
Equations 7A-9A also hold for In r k ( i ) , except that the group composition variable, Ok, is now the group fraction of group k in pure fluid i. Literature Cited
(84
k
X , is the fraction of group m in the mixture.
Parameter anm characterizes the interaction between groups n and m. For each group-group interaction, there are two parameters: unm # umn. No ternary (or higher) parameters are needed to describe multicomponent equilibria.
Azeotropic Data 111, Adv. Cbem. Ser., No. I16 (1973). Bondi, A., "Physical Properties of Molecular Crystals, Liquids, and Glasses", Wiley, New York, N.Y., 1968. Eng, W. W. Y., M.S. Thesis,Department of Chemical Engineering, Brgham Young University, Provo, Utah, 1977. Fredenslund, Aa., Jones, R. L., Prausnitz. J. M., AICbE J., 21, 1086 (1975). Fredenslund, Aa., Gmehling, J., Rasmussen, P., "Vapor-Liquid Equilibria Using UNIFAC", Elsevier, Amsterdam, 1977a. Fredenslund, Aa., Gmehling, J., Michelsen, M. L., Rasmussen, P., PrausnRz, J. M., Ind. Eng. Chem. Process Des. Dev., 16, 450 (1977b). Gmehling, J., Onken, U., "Vapor-Liquid Equilibrium Data Collection", DECHEMA Chemistry Data Series, Vol. 1, Part 1 (1977), Part 2a (1977), Part 2b (1978) (together with W. Arlt). HCP 1974175. "Handbook of Chemistry and Physics", 55th ed, p 0-128, 1974- 1975. Lindberg, G. W., Tassios, D., J . Cbem. Eng. Data, 16, 52 (1971). Magnussen, T., Michelsen, M. L., Fredenslund, Aa., International Symposlum on Distillation, London, April, 1979. Morachevsky, A. G., Pukinsky, J. B., Leningrad State University, USSR, private communication, 1978. Nelder, J. A., Mead, R., Comput. J., 7, 308 (1965). Rasmussen, P.. Fredenslund, Aa., Sep. Purif. Methods, 7(2), 147 (1978). Roekens. E. J. L., Verhoeye, L. A. J., J . Appl. Cbem. Biotecbnol., 26, 595 (1976). Smith, C. P., Engel, E. W., J . Am. Cbem. Soc., 51, 2660 (1929).
Receiued for reuieu December 12, 1978 Accepted May 23, 1979
Viscosity Measurements of Non-Newtonian Slurry Suspensions Using Rotating Viscometers Subhas K. Sikdar" and Fernando Or6 Occidental Research Corporation, Irvine, California 927 13
Non-Newtonian suspension viscosities of slurries were characterized by the shear thinning index method using a Brookfield viscometer. I t is demonstrated that the slurry viscosities at a given shear rate depend on the volume fraction of solid, temperature, and the particle size distribution of the suspended phase. Correlations between viscosities and the variables were developed in the laminar shear rates regime. Various concentrations of calcium sulfate suspended in phosphoric acid were considered.
Introduction Slurry suspensions in industrial processes frequently require rheological characterization for flow equipment design. A knowledge of the rheology of such suspensions contributes also to a better understanding of underlying mechanisms of momentum and mass transfer processes. Present work demonstrates that slurry viscosities of calcium sulfate in phosphoric acid can be correlated with solid concentration, temperature, shear rate, and particle size. For engineering purposes, where a direct measurement is not feasible, such relationships would be of value. Also demonstrated is that the shear thinning index (STI) method of Rosen (1972), which proved useful for polymer melts and solutions, is also applicable to slurry suspensions. Brookfield viscometry was applied to phosphate slurries containing 5-35% by weight of solid and at temperatures between 35 and 85 "C. Size distribution of calcium sulfate particles was determined by a Coulter Counter. Theoretical Background An important factor determining the non-Newtonian slurry viscosity is the volume fraction of solid in the slurry. 0019-7882/79/1118-0722$01 .OO/O
The slurries, however, tend to be Newtonian for low solid concentrations (Jeffrey and Acrivos, 1976; Jinescu, 1974). Volume fraction of solid has the strongest influence on the apparent viscosity of slurries (Jeffrey and Acrivos, 1976; Thomas, 1965; Ting and Luebbers, 1957; Sikdar and Or6, 1977). Other factors, which may also affect slurry viscosities, are the shape and size distribution of suspended particles, surface properties, electrical charges, and the nature of the flow fields. Jeffrey and Acrivos (1976) discussed that for particles considerably larger than colloidal dimensions, nonhydrodynamic forces arising from Brownian motion, electrical double layer and van der Waals attraction are negligible. It is apparent that for a given slurry the contributions from these nonhydrodynamic factors are small over a large range of solid concentrations. Ting and Leubbers (1957) and Sikdar and Or6 (1977) showed that slurry viscosities could be correlated fairly well with the volume fraction of solid. Each slurry was assigned a characteristic constant which is dependent on temperature and size distribution of the suspended phase. Deviation from Newtonian behavior was not analyzed in either of these works. 0 1979 American Chemical Society
