I n d . Eng. Chem. Res. 1988,27, 1269-1277
N00014-804-0293 to R.D.H. Contributions to the experiment in the early stages by William Savage are gratefully acknowledged. Finally, valuable interaction with Professor Frederick Shair at Caltech is very much appreciated. Nomenclature C = concentration, ppm E = energy per corona pulse, J f = dilution factor (dimensionless) p = pulse rate, s-l P = production yield, molecules/ J v = flow rate, m3/s Y = yield, molecules/pulse Registry No. NO,10102-43-9;NzO, 10024-97-2;Os, 1002815-6.
1269
Chameides, W. L. Geophys. Res. Lett. 1979, 6, 287. Donohoe, K.G.; Shair, F. H.; Wulf, 0. W. Ind. Eng. Chem. Fundam. 1977, 18, 208. Hill, R. D. J. Geophys. Res. 1971, 76, 637. Hill, R. D. J. Geophys. Res. 1977, 82, 4967. Hill, R. D.;Rinker, R. G. J . Geophys. Res. 1981, 86, 3203. Hill, R.D.;Rinker, R. G.; Coucouvinos, A. J. Geophys. Res. 1984,89, 1411. Hill, R. D.; Rinker, R. G.; Wilson, H. D. J. Atm. Sci. 1980,37, 179. Iannuzzi, M. P.; Jeffries, J. B.; Kaufman, F. Chem. Phys. Lett. 1982, 87,570. Levine, J. S.; Shaw, E. F. Nature (London) 1983, 303, 312. Picone, J. M.; Boris, P. P.; Greig, J. R.; Raleigh, M., Fernsler, R. F. J. Atm. Sci. 1981, 38, 2056. Piper, L. G.; Caledonia, G. E. J . Chem. Phys. 1981, 74, 2888. Rahmim, I. M.S. Thesis, University of California, Santa Barbara, 1984. Swider, W. Geophys. Res. Lett. 1976,3, 335.
Literature Cited
Received for review May 19, 1986 Revised manuscript received July 29, 1987 Accepted February 29, 1988
Bhetanabhotla, M. N.; Crowell, B. A.; Coucouvinos, A.; Hill, R. D.; Rinker, R. G. Atm. Enuiron. 1985, 19, 1391.
Infinite Dilution Activity Coefficients Predicted by UNIFAC Group Contribution J. C.Bastos, M. E. S o a r e s , and A. G. Medina* Centro de Engenharia Quimica, Faculdade de Engenharia, Universidade do Porto, R u a dos Bragas, 4099 Porto Codex, Portugal
A UNIFAC parameter table specially suited for the prediction of infinite dilution activity coefficients (7") is proposed. T h e present table is exclusively based on experimental 7- data reported in the literature and correlates about 70% of the 11500 data points with a n average relative error of 20%. The 190 pairs of parameters of 40 different groups were estimated in order to reproduce the 7-data as accurately as possible. Infinite dilution activity coefficients play an important role in chemical technology, namely in qualitative and quantitative analysis of separation processes such as extractive and azeotropic distillation and liquid-liquid extraction. This justifies the considerable efforts dedicated to the development and improvement of experimental techniques and to the establishment of accurate correlation and prediction methods. A considerable amount of experimental information on ym is available in the literature and has been collected (Bastos e t al., 1984, 1985). The determination of the present UNIFAC parameter table is based on the experimental information contained in a data bank that was set up as a result of a joint project involving also the Universities of Dortmund and Trieste. Despite the existence of the vapor-liquid equilibrium (VLE) (Gmehling et al., 1982; Macedo et al., 1983) and liquid-liquid equilibrium (LLE) (Magnussen et al., 1981) parameter tables and the previous works of Zarkarian et al. (1979) and Alessi et al. (1982), who have studied the use of ymto obtain UNIFAC parameters, the determination of a new y mparameter table was encouraged by the improvement of accuracy and range of applicability of the UNIFAC method, as far as the calculation of ymvalues is concerned. Range of Applicability of the 7" P a r a m e t e r Table The present ymparameter table allows the calculation of 8300 data points of the data bank (72.5% of all data points) with a relative mean deviation of 20.2%. These 0888-5885/88/2627-1269$01.50/0
results mean a significant improvement in both range of applicability and accuracy of the UNIFAC model when compared with those obtained with the previous VLE and LLE parameter tables (Table I). The groups in the ymparameter table are fundamentally those defined in the previous VLE and LLE tables. With respect to the VLE table, the improvement on the range of applicability of the present y mtable is a result of the introduction of 68 new interaction parameters (out of a total of 190 determined) which reflect the distinct characteristics of the systems included in the VLE and y" data bases. The differences between the range of applicability of both VLE and y mtables are shown schematically in Figure 1. This figure indicates that the parameter table does not include parameters for dialkylamines (CNH), carboxylic acids (COOH), carbon disulfide (CS,), thiols (CH3SH),alkynes (CEC), and fluoro compounds (ACF and CFJ. On the other hand, it includes eight new groups: N-methylpyrrolidone (NMP), sulfolane, esters of benzoic and phthalic acids (ACCOO),sulfides (CH,S), dimethylacetamide (DMA), diethylene glycol (DEG), N-formylmorpholine (NFM), and triethylene glycol (TEG). Although most of the new groups are in fact molecules, their introduction can be justified by the importance of these compounds in chemical technology. Besides, the difinition of groups contemplating these compounds, and their derivatives or families, could not be performed with acceptable results due to the lack of experimental information. In this context the most promising situation would be the definition of three main groups for amides, alkyl0 1988 American Chemical Society
1270 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 Table I. Comparison between Experimental and Calculated 'y Values method parametersb data pts in data base calcd data pts UNIFAC VLE 1 8970 4860 UNIFAC LLE 2 8970 4600 UNIFAC 73 11450 8300 ASOG 4 8970 4220
% calcd data pts
54.2 51.3 72.5 47.0
m.d., %" 28.1 91.7 20.2 38.7
Om.d. (%) = ~ : N I y ~-e y'd~/y"e,p(lOO/N) xp (The UNIFAC method includes the modification on the combinatorial term introduced by Kikic et al. (1980)). bParameters: (1)Gmehling et al. (1982), Macedo et al. (1983); (2) Magnussen et al. (1981); (3) present work; (4) Kojima and Tochigi (1979).
cnz :,..I
RCH hCCX;.
on h:n3nn Hi0
w:l:fn CX$O
Cxo
ccnn WOO C%-O
I?tIni
I:t(n iCj:,N
RCNX;. Pyridine CCtI
coon CC1 c1:1*
cc l3 cc14
clcc 1 CNQ2 RCNO? c52
CH$H
rum." DON I
Br
c i:I tb290
ACRY Cl[C=CI RCT D W cr2 t4t.D SVLIOLAN: RCCOO
cnis Dta DIG NTPl
TIC; o n l y VLE parameters a v a i l a b l e only
Y" parameters a v a i l a b l e
both VLE and y" parameters a v a i l a b l e
Figure 1. Range of applicability of the UNIFAC method.
amides, and dialkylamides, as a considerable amount of information is available. The definition of the main groups CH3CONH2,CH3CONH, and CH3CON (with subgroups contemplating acetamides and higher amides) was tried but poor results were obtained. Therefore, the flexibility of the UNIFAC method was sacrificed by its accuracy in this particular situation, and only DMA was considered, due to the relative importance of this compound in extraction processes. Parameter Estimation The UNIFAC parameters were determined by minimizing the sum of squared differences between experimental and calculated infinite dilution activity coefficients, using a modified Levenberg-Marquardt procedure, similar
to the one used by Skjold-Jargensen (1979). The UNIFAC routine with the modification of the Flory-Huggins term, as suggested by Kikic et al. (1980), was used. The parameters were generally determined one pair at a time. However, in some particular situations, the simultaneous determination of two pairs of parameters was carried out. As pointed out by Fredenslund et al. (1977), the simultaneous determination of more than one pair of interaction parameters can lead to acceptable results for systems involving all the groups considered, but unacceptable, poor results can be obtained when systems with only a part of these groups are studied. This difficulty, however, was not detected in the present work. One important point t o be considered is the sequence to be followed in the parameter estimation. The main guideline that governed the strategy followed in this work
Ind. Eng. Chem. Res., Vol. 27, No. 7 , 1988 1271 T a b l e 11. Area a n d Volume P a r a m e t e r s of UNIFAC S u b g r o u p s no. grOUD no. subgroup Rk Qb 1 0.9011 1 0.848 CH2 CH3 2 0.6744 0.540 CHZ 0.4469 CH 3 0.228 0.000 C 4 0.2195 2 1.176 5 1.3454 c=c CHZ=CH CH=CH 0.867 1.1167 6 CHz=C 7 0.988 1.1173 8 CH=C 0.676 0.8886 9 c=c 0.485 0.6605 ACH 10 ACH 0.400 0.5313 3 11 AC 0.120 0.3652 4 12 ACCH3 0.968 1.2663 ACCH, 13 ACCHz 0.660 1.0396 14 ACCH 0.348 0.8121 OH 15 OH 1.200 1.0000 5 16 1.432 1.4311 CHSOH 6 CHBOH 7 17 1.400 0.9200 H20 HZO ACOH 18 ACOH 8 0.680 0.8952 CHBCO 1.6724 CHzCO 19 9 1.488 20 1.4457 CHzCO 1.180 21 10 CHO CHO 0.9980 0.948 22 11 ccoo CH3CO0 1.9031 1.728 23 1.6764 1.420 CHzCOO HCOO 12 HCOO 24 1.2420 1.188 CHzO CH30 13 25 1.450 1.088 CHzO 26 0.9183 0.780 CHO 27 0.6908 0.468 FCHZO 28 0.9183 1.100 14 CNHZ CH3NHz 29 1.5959 1.544 CHzNHz 1.3692 1.236 30 CHNHZ 1.1417 0.924 31 1.1865 15 32 CH3N 0.940 C3N 33 CHzN 0.9597 0.632 ACNHZ 34 ACNHz 1.0600 0.816 16 pyridine 2.9993 2.113 17 35 C5H5N 36 2.8332 1.833 C5HA 37 2.6670 1.553 C5H3N 38 2.5010 1.273 C5HZN 1.724 18 CCN CHBCN 39 1.8701 CHzCN 1.6434 1.416 40 41 1.4654 1.264 19 CCl CHzCl CHCl 42 1.238 0.952 cc1 43 1.006 0.724 CClZ 20 CHzClz 44 2.2564 1.988 2.0606 CHClz 45 1.684 CClZ 46 1.8016 1.448 CC13 21 CHC13 47 2.8700 2.410 2.6401 2.184 CC13 48 22 CC14 cc1, 49 3.3900 2.910 ACCl ACCl 50 1.1562 0.844 23 24 CN02 51 2.0086 1.868 CH3NOz 1.7818 1.560 CHzNOz 52 1.5544 CHNOz 53 1.248 CNOz 54 1.3276 0.940 25 ACNOp ACNOz 55 1.4199 1.104 furfural furfural 56 3.1680 2.481 26 57 2.4088 2.248 27 DOH (CHzOH)z I I 1.2640 28 58 0.992 Br Br 29 59 0.9492 0.832 2.8266 2.472 MezSO MezSO 30 60 0.7910 0.724 Cl(C=C) Cl(C=C) 31 61 DMF DMF 32 62 3.0856 2.736 NMP NMP 3.981 3.200 33 63 sulfolane 4.0358 3.200 sulfolane 34 64 1.000 ACCOO ACCOO 35 65 1.3672 CH3S 1.6130 1.368 CH,S 36 66 CHzS 1.3863 1.060 67 DMA 3.7601 3.276 37 DMA 68 DEG 69 4.0013 3.568 38 DEG 4.2248 3.440 NFM 39 NFM 70 TEG 5.5939 4.888 40 TEG 71
was the relative importance of the different groups. This relative importance of groups is given by the amount of experimental information in terms of data points and number of compounds available in the data base. The
'
example n-hexane
2 CH3,4 CHZ
2-methylpropane 2,2-dimethylbutane 1-hexene 2-hexene 2-methyl-1-butene 2-methyl-2-butene 2,3-dimethyl-2-butene benzene styrene toluene ethylbenzene isopropylbenzene 2-propanol methanol water phenol 2-butanone 3-pentanone acetaldehyde butyl acetate ethyl acetate ethyl formate dimethyl ether diethyl ether diisopropyl ether tetrahydrofuran methylamine propylamine isopropylamine trimethylamine triethylamine aniline pyridine 3-methylpyridine 2,3-dimethylpyridine 2,3,5-trimethylpyridine acetonitrile propionitrile 1-chlorobutane 2-chloropropane 2-chloro-2-methylpropane dichloromethane 1,l-dichloroethane 2,2-dichloropropane trichloromethane l,l,l-trichloroethane tetrachloromethane chlorobenzene nitromethane 1-nitropropane 2-nitropropane 2-methyl-2-nitropropane nitrobenzene furfural 1,2-ethanediol iodoethane 1-bromopropane dimethylsulfoxide trichloroethylene dimethylformamide N-methylpyrrolidone sulfolane dimethyl phthalate dimethyl sulfide diethyl sulfide dimethylacetamide diethylene glycol N-formylmorpholine triethylene glycol
3 CH3,l CH 4 CH3,l C 1 CH3,3 CHZ, 1 CHZ-CN 2 CH3,2 CHZ, 1 CH=CH 2 CH3,l CHZ, 1 CH,=C 3 C H 3 , l CH=C 4 C H 3 , l C=C 6 ACH 1 CHZ=CH, 5 ACH, 1 AC 5 ACH, 1 ACCH, 1 CH3,5 ACH, 1 ACCHz 2 CH3,5 ACH, 1 ACCH 2 CH3,l CH, 1 OH 1 CHBOH 1 HzO 5 ACH, 1 ACOH 1 CH3,l CHZ,l CH&O 2 CH3,l CHZ,l CHZCO 1 CH3,l CHO 1 CH3,3 CHZ,l CH3COO 2 C H 3 , l CHZ, 1 CHZCOO 1 CH3,l CHZ, 1 HCOO 1 CH3, 1 CH30 2 C H 3 , l CH2,l CHzO 4 C H 3 , l CH, 1 CHO 3 CHZ, 1 FCHZO 1 CH3NHz 1 CHB, 1 CHZ, 1 CHZNHZ 2 CH3,l CHNHZ 2 CHS, 1 CHXN 3 CH,, 2 CH,, 1 CHzN 5 ACH. 1 ACNH, 1 C5HbN 1 CH3,l C5H4N 2 CH3,l C5H3N 3 CH3,l C5HzN 1 CH3CN 1 CH3,l CHZCN 1 CH3, 2 CHZ, 1 CHZCI 2 CH3,l CHCl 3 CH,, 1 CC1 1 CHiC1, 1 CH3, 1 CHC1, 2 CH3, 1 CClz 1 CHCl, 1 CH3, 1 CC13 1 CCI, 5 ACH, 1 ACCl 1 CH3N02 1 CH3, CHZ, 1 CHZNOZ 2 CH3,l CHNOZ 3 CH3,l CNOz 5 ACH, 1 ACNOZ 1 furfural 1 (CHzOH)z 1 CH3,l CHZ, 1 I 1 CH3, 2 CH,, 1 Br 1 MezSO 1 CH=C, 3 Cl(C=C) 1 DMF 1 NMP 1 sulfolane 2 CH,, 4 ACH, 2 ACCOO 1 CHq, 1 CHqS 2 CH,, 1 CH;, 1 CH2S 1 DMA 1 DEG 1 NFM 1 TEG
parameters were estimated in a decreasing order of importance. The choice of data points to be used in the estimation of parameters was somewhat subjective due to the lack of
1272 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 Table 111. UNIFAC Interaction Parameters 1, CHZ 2, C 4 3,ACH 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 35 36 37 38 39 40 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 28 29 30 31 32 33 34 35 36 37 38 39 40
CH2
c=c
ACH ACCH, OH CH3OH HzO ACOH CH3CO CHO
ccoo
HCOO CH2O CNH2 C3N ACNH2 CSHSN CCN CCl CC12 CC13 CC14 ACCl CNO, ACNOz furfural DOH I Br Me2S0 Cl(C=C) DMF NMP sulfolane ACCOO CH2S DMA DEG NFM TEG CH2
c=c
ACH ACCH, OH CHQOH H20 ACOH CH3C0 CHO
ccoo
HCOO CH20 CNHo C3N ACNH? C~H~NCCN
cc1
0.00 68.39 120.09 -160.46 173.32 -34.51 354.53 1001.49 111.28 428.56 66.81 600.17 28.84 217.06 778.69 1043.41 72.80 26.98 78.34 7.30 43.97 83.18 -174.26 54.70 351.75 61.57 900.00 -164.53 132.01 298.65 -118.26 211.83 196.64 201.47 292.92 -369.75 51.16 202.69 245.70 289.15 11, CCOO 260.01 -42.20 51.70 -58.94 594.98 420.38
-41.31 0.00 -266.68 -317.69 494.89 520.71 -14.04 183.48 479.70
4,ACCHz
5, OH
6, CHBOH
-66.14 885.35 0.00 -295.75 140.07 391.11
291.60 777.45 476.28 0.00 10.72
1024.50 496.94 611.12 861.17 0.00
917.16
150.00 95.32 385.39 -46.69
674.05 -149.74
0.67
8,ACOH
9, CH&O
10, CHO
1094.73 777.44 1198.16 616.60
406.47 343.08 82.86 516.04 496.06 429.44 -34.54
638.02 289.16 213.70
0.00 -212.41 -38.57 151.25
759.77 0.00
1.44
-69.95
6.98
0.00 42.35
681.89 0.02 0.00
-90.80
-205.46
143.41
215.75
69.07
-142.82
-379.66
60.09
0.00
56.00 -87.26
-202.50 788.67 -73.93 -114.09 -112.18
150.00 -521.82 -222.62 -94.73
665.40 939.53 109.35 651.27
-78.63 180.78
56.32
435.31
-39.26 -118.72
-216.00 -262.82 150.25 -88.93 454.52
-403.00 -81.21 274.44 -86.42 136.52 -154.23 -65.53 128.05 -41.52 22.93 -188.42 -85.73 -160.54
-386.39 270.92 -125.34 56.42 380.94 315.49 143.36 283.09 -166.21 69.33 -114.18 58.14
214.03 576.50 692.83 815.25 1103.29 61.34 -769.31
383.91
172.77
216.12
267.76
1004.59
399.94 1.44 -106.53 339.29 738.88
335.01
352.02 430.60
-164.81
738.25 189.16 -88.75
-213.18 -170.61 91.97 52.81 -4.26 -89.97 -14.12 52.38 93.90 -144.81 172.04 -148.35 -55.69 12, HCOO 13, CHzO 14, CNH2 15, C3N 740.89
-101.85 396.30 715.98 510.00
98.93
7, HzO
279.51 -69.97
-11.70
-208.34
-161.40 16, ACNHl
17, pyridine
1071.10 1051.12 1349.18 522.89
54.82 231.91 941.89 -263.35
12.39
18, CCN
19, CC1
20, CC12
552.13 624.24 686.09 120.99 247.54
34.75 256.46 26.66 -310.29 -174.86 306.03
113.08
-32.26
-450.63
270.87
635.50
0.00
-253.11
860.88 12.27
100.84
149.09
0.00
0.00
-1144.20 0.00
0.00
181.48
989.11
0.00 320.00
-325.00 0.00
0.00 0.00 -72.30 -108.02
-955.74
CClZ CCl, CC14 ACCl CNO? ACNO,
198.55 158.70
0.00 491.48
152.81 21.98 -303.20 169.58 51.40
-387.93
68.20
381.03
I
Br Me2S0 Cl(C=C) DMF NMP sulfolane ACCOO CH2S DMA DEG NFM TEG
-409.08
170.67 -96.37 452.16
43.56
-253.06
Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1273
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 35 36 37 38 39 40
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 35 36 37 38 39 40
CHZ
c=c ACH ACCHp OH CH30H HZO ACOH CH3CO CHO
21, CC13
22, CCl,
23, ACCl
5.93 -59.83 -78.98 -295.03 -167.06
-65.19 -140.49
-374.91
34.65
12.43
130.86
-366.52 612.33 -398.34
24, CNOz 548.98 638.84 293.61
25, ACNOz
26, furfural
27, DOH
28, I
29, Br
30, MezSO
443.15 451.56 150.41 -42.91
294.44
-280.00
501.48
0.90
309.02 483.51
651.82 531.43
245.18 -213.06 394.47
117.16 564.01 72.99 -252.99 598.70
-1084.97 56.18 -403.26
0.10 0.54
389.73
ccoo
HCOO CHpO CNHZ C3N ACNHp CSHSN CCN CCl CClp CC13 CCl, ACCl CNOp ACNOz furfural DOH I Br MezSO Cl(C=C) DMF NMP sulfolane ACCOO CHpS DMA DEG NFM TEG
CHZ
c=c
ACH ACCH2 OH CHSOH HZO ACOH CH3CO CHO
622.67
-48.06
47.10 42.37
-422.83 197.09
-6.29
312.83
8.34 351.68 -107.01
0.00 0.00
424.88 549.56
0.00 0.00
-1.21
0.00 0.00 0.00 -224.11
0.00
747.56
0.00 0.00
292.01
-775.83
31. Cl(C=C)
32. DMF
33. NMP
-82.89 -294.21 -227.29 -185.05 485.28
0.70 7.97 0.05 655.24
0.40 245.89 359.81 0.06 -204.48
191.06
34. sulfolane 35. ACCOO 100.22 305.18 572.86
36. C H 8
37. DMA
38. DEG
39. NFM
40. TEG
644.31
262.70 1.90 883.20 513.58
169.06 293.18 429.90 511.02
1.06 293.66 0.03 485.80 0.02
7.05 5.43 746.19 510.74
215.97
-169.35 271.34 106.05
ccoo
592.59 433.12 692.22 419.04 266.44 417.42
461.93 226.23 0.02
HCOO CHpO CNHz C,N
A~CNH~ CSHSN CCN CCl cc1, CClj cc1, ACCl CNOz ACNO, furfur; DOH I
31.72 116.34 97.97
2.78
-337.83
-657.16 -130.92
Br MePSO ClIC=C) DMF NMP sulfolane ACCOO CHzS DMA DEG NFM TEG
415.09
0.00 0.00
0.00 0.00 0.00
0.00
0.00
1274 Ind. Eng. Chem. Res., Vol. 27, No. 7 , 1988 Table IV. Comparison between Experimental and Calculated Values of y" for Some Classes of Components systems data pts VLE m.d., % 7" m.d., % 166 6.5 6.3 CHZ/C=C 10.9 10.7 CH,/CCOO 159 10.1 5.4 57 CH,/CH,O 14.5 12.8 c ~jcci , 142 72 11.7 8.4 CHz/C=C/CCOO 12.2 8.9 CH,/C=C /CCl 55 9.2 CH;)ACH/CH,CO 46 15.9 55 12.4 9.4 CH,/CCOO/CH,CO 11.7 7.4 CH,/CCOO/CCl 56 176 n.a. 4.7 CH,/ACH/ACCOO 12.4 33 n.a. ACH/ACCH,/ACCOO
a consistency test. A criteria for the choice of data involves generally a trial procedure in which experimental ymvalues within temperature ranges and homologous series or families of compounds are compared with predictions based on the UNIFAC model. The 190 pairs of parameters determined this way are presented in Table 111. The main groups and subgroups, together with the area and volume parameters, Rkand Q k , are presented in Table 11. Results It is quite clear that the new UNIFAC parameters can be used not only for the prediction of y" values but also for different types of phase equilibrium calculations. In order to enhance this point, three types of calculations were performed with the ymparameter table: (i) Calculation of ymand selectivities at infinite dilution. The results are compared with those obtained with VLE parameters. (ii) Calculation of vapor-liquid equilibrium and azeotrope compositions. Also, the results are compared with those obtained by the use of VLE parameters (whenever possible) and the UNIQUAC equation. (iii) Calculation of mutual solubilities. The results are compared with those obtained with LLE and VLE parameters. (i) Calculation of Activity Coefficients and Selectivities at Infinite Dilution. A general comparison between experimental and calculated values for some important classes of compounds is shown in Tables IV and V. In Table IV,the systems for which the best results are obtained with the UNIFAC model are considered. These systems exhibit low values of ym.Therefore, with respect to the previous published UNIFAC parameters, there was little room for improvement. The results shown in Table IV underline this aspect, as the present y mparameter table gives results that are similar to those obtained with VLE parameters. For these systems, a typical improvement of only about 2-3% can be obtained. However, quite different results arise when higher y m values are involved. Some of these situations are presented in Table V, which includes data for systems of particular industrial importance. It is clear from Table V that the new y" parameter table significantly improves calculated values. This leads us to the important aspect of the characterization of solvents for extraction purposes. Selectivity at infinite dilution (S") is one of the primary properties to be considered in solvent selection. In Table VI, S" values calculated by the UNIFAC method using VLE and ymparameters are compared with the experimental values (S",,,)for 16 possible solvents listed in decreasing order value. Table VI highlights the fact that the of their Smexp ranking of solvents in terms of calculated selectivities based on the ymparameters is similar to that obtained with Smelp
Table V. Comparison between Experimental and Calculated y- Values VLE parameters -7 uarameters type of solvent data pts m.dT, 70 data pts m.d., % solute furfural alkanes 33 10.1 33 50.0 aromatics 11 7.0 11 44.7 44 9.0 44 49.0 total phenol alkanes 93 14.4 93 42.5 23 22.5 23 29.9 aromatics 20 10.0 20 37.4 alkenes dienes 2 22.0 2 26.0 14 7.9 5 31.0 others 152 14.5 143 39.1 total dimethylform- alkanes 82 27.3 82 23.0 amide aromatics 26 20.4 26 23.0 12 21.3 12 21.2 alkenes 8 55.0 8 60.4 dienes 7 16.4 others 28.0 135 23.9 128 total aniline 59.6 57 25.4 57 alkanes 21.3 13 7.5 13 aromatics n.a. 16 15.8 16 alkenes 3 6.7 3 n.a. dienes 52.5 89 20.4 70 total water 9 16.0 9 2250 alkanes 4 n.a. 4 316 aromatics others 52 43.6 100 270 65 39.8 113 429 total 1,2-ethanediol alkanes 82 35.2 82 36.0 35 13.4 35 28.2 aromatics 117 28.7 117 33.6 total NMP 134 19.8 134 n.a. alkanes 45 14.8 45 n.a. aromatics n.a. 13 17.1 13 alkenes 7 23.5 7 n.a. dienes 48 14.1 48 n.a. others 247 17.7 247 total n.a. DMA 18.1 16 16 alkanes n.a. 9 10.6 9 aromatics 10 37.2 10 n.a. alkenes n 7 40.7 n.a. dienes 42 24.8 42 total NFM 114 20.0 114 n.a. alkanes n.a. 39 7.7 39 aromatics 18 21.9 18 n.a. alkenes n.a. dienes 3 3.4 3 53 9.3 53 n.a. others 227 15.3 227 total Table VI. Comparison between Experimental and Calculated Selectivities at Infinite Dilution (S")at 25 'C. System: n -Hexane/Benzene
succinonitrile sulfolane dimethyl sulfoxide glutaronitrile dimethylformamide N-methylpyrrolidone ani1ine 1,2-ethanediol 1,1,2,2-tetrabromoethane suberonitrile dichloroacetic acid benzy lacetone nitrobenzene acetophenone 2-phenylethanol cyclohexanone
46.8 24.3 22.7 21.1 12.5 12.4 11.2
9.5 8.6 6.8 6.1 5.8 5.7 5.3 4.8 4.6
22.1 17.3 14.2 12.8 10.7 11.2 8.1 8.1 11.2 5.1 n.a. 5.0 5.4 5.0 3.3 2.7
11.9 ma. 14.0 8.4 9.1 n.a. 4.5 10.7 4.6 4.8 10.8 2.7 5.3 3.9 2.7 2.8
values. On the other hand, VLE parameters lead to very different results. For the solvents listed in Table VI,the ymparameter table leads to an improvement by a factor of approximately 2, expressed in terms of mean deviation between experimental and calculated selectivities.
Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1275 Table VII. Comparison between Experimental and Calculated VLE Data (Experimental Data Taken from Gmehling et al. (1979)) 7 - table VLE table type of data T or P diff" .y diff T or P diff .y diff system 0.44 "C 0.0107 0.34 "C 0.0103 benzeneln-hexane/ 1-butanol isobaric; 760 mmHg 5.0 "C 0.0221 1.1 "C 0.0215 benzene/cyclohexane/furfural isobaric; 760 mmHg 5.7 "C 0.0204 4.6 "C 0.0087 methylcyclohexane/ toluene/phenol isobaric; 760 mmHg methylcyclohexane/ toluene/aniline isobaric; 760 mmHg 7.6 "C 0.0237 4.2 "C 0.0350 isothermal; 50 "C 238 mmHg 0.0004 300 mmHg 0.0005 1,3-butadiene/DMF 1.5 "C 0.0280 0.44 "C 0.0250 isoprene/2-methyl-2-butene/acetonitrile isobaric; 760 mmHg acetone/methanol/water isobaric; 760 mmHg 3.8 "C 0.0480 0.93 "C 0.0110 "Diff u =
~NI~,alc
- uexpl/N u = P, T , or y (y = vapor-phase mole fraction).
Table VIII. Comparison between Experimental and Calculated Azeotrope Compociitions at 760 mmHg Taken from Perry and Green (1984)) component exptl - VLE 1 2 X1 t , "C x1 t , "C carbon tetrachloride ethanol 0.613 65.0 0.605 65.1 chloroform ethanol 0.84 59.3 0.855 59.1 1-butanol cyclohexane 0.11 79.8 0.094 79.5 0.332 104.8 0.37 105.5 1-butanol toluene acetone methyl acetate 0.61 56.1 0.420 55.5 0.675 73.2 0.496 ethanol methyl propionate 72.1 ethanol n-hexane 0.332 58.7 0.315 60.2 toluene 0.81 76.7 0.811 76.8 ethanol 0.209 77.1 0.223 76.6 1-propanol benzene 0.06 1-propanol n-hexane 65.7 0.164 65.6
(Experimental Data 7,Xl
t , "C
0.626 0.905 0.099 0.340 0.604 0.549 0 339 0.811 0.227 0.167
63.9 60.2 79.3 104.6 55.3 71.4 58.2 76.7 76.5 65.3
Table IX. Comparison between Experimental and Calculated VLE Data. Systems for Which UNIFAC VLE Parameters Are Not Available (Experimental Data Taken from Gmehling and Onken (1979)) UNIQUAC - y- parameters system type of data data pts T or P difP y diff T or P diff .y diff 4.1 "C 2-heptene/aniline isobaric; 742 mmHg 8 0.023 1.6 "C 0.016 1-heptene/butyl bromide isothermal; 75 "C 6 0.025 0.007 toluene/sulfolane isobaric; 760 mmHg 9 0.6 "C 5.6 "C 0.016 0.012 isobaric; 760 mmHg 9 2.1 "C 0.001 3.7 "C 0.001 benzene/sulfolane 0.13 "C 0.015 0.5 "C methyl benzoate/methyl toluate isobaric; 15 mmHg 7 0.013 3.12 "C methyl benzoate/dimethyl phthalate isobaric; 15 mmHg 8 0.8 "C 0.035 0.005 methylcyclopentane/NMP isothermal; 69.7 "C 12 67.3 mmHg 9.2 mmHg l-hexane/3-bromo-l-propane isothermal; 55 "C 7 0.018 0.007 11.9 mmHg 0.9 mmHg sulfolane/cyclohexane/ toluene isothermal; 30 "C 16 11.5 mmHg 2.6 mmHg sulfolane/cyclohexane/ benzene isothermal; 30 "C 17 15.2 mmHg 1-pentene/aniline isothermal; 77.66 "C 12 39.9 mmHg sec-butyl chloride/isothermal; nitrobenzne isothermal; 39.85 "C 5 11.0 mmHg 6.6 mmHg 3-chloro-l-propene/3-bromo-l-propane isobaric; 760 mmHg 9 0.6 "C 0.032 0.028 1.3 "C "Diff u =
zNIucalc - ueXpI/N; u = P, T , or y (y = vapor-phase mole fraction).
(ii) Calculation of Vapor-Liquid Equilibrium and Azeotrope Compositions. The possibility of using the present ymparameters in vapor-liquid equilibrium calculations and prediction of azeotrope formation was investigated. A comparison between the results obtained by the use of the ymand the VLE parameters is presented in Table VII. A similar comparison for calculation of azeotrope compositions is presented in Table VIII. The results shown in these tables lead to the conclusion that, for the systems investigated, the same degree of accuracy can be obtained by the use of the two different sets of parameters. This conclusion allows the present parameter table to be considered as an enlargement of the range of applicability of the UNIFAC group contribution method due to the introduction of a significant number of new interaction parameters. Table IX emphasizes this point of view by presenting a comparison between experimental and calculated VLE data for which VLE parameters were missing. In this table, the results are compared with those obtained by the UNIQUAC model. Satisfactory results were also obtained for these systems. (iii) Calculation of Mutual Solubilities. Infinite dilution activity coefficients offer valuable qualitative information on mutual solubilities. From this point of view,
the ymUNIFAC parameters provide a useful tool for these types of calculations. Table X shows the comparison between experimental and calculated mutual solubilities with different sets of parameters, e.g., LLE, VLE, and ymparameters. An analysis of the results shown in Table X clearly indicates that VLE parameters are not adequate for mutual solubility calculations, for the generality of the systems investigated. However, generally acceptable results were obtained using ymparameters. In fact, for the 13 systems investigated, 26 mole fractions were calculated and a mean absolute deviation of 0.061 was observed. This compares well with the results obtained with the LLE parameters: an absolute mean deviation of 0.073 in 20 calculated mole fractions (for three systems, parameters were not available). A major limitation regarding the calculation of mutual solubilities occurs in systems in which one of the components is typically a solvent, and therefore, there is lack of experimental information for this component as a solute. As an example, for the system anilineln-hexane, the lack of ym experimental data concerning functional group ACNH, in some solvents with functional group CH, explains the large deviation between experimental and calculated solubilities of aniline in n-hexane, as shown in
1276 Ind. Eng. Chem. Res., Vol. 27, No. 7 , 1988 Table X. Comparison between Experimental and Calculated Mutual Solubilities (Data Taken from Smensen and Arlt (1979); Compositions Expressed in Mole Fractions of Components 1 in Phases I and 11) component 1
n-hexane 1-hexene isooctane nitromethane nitromethane acetonitrile 1,2-ethanediol 1,2-ethanediamine succinonitrile diethylene glycol furfural furfural aniline
2 nitroethane nitroethane nitroethane cyclohexane 2-methyl-2-pentane n-hexane benzene n-hexane 1-pentanol n-heptane cyc1ohexane n-hexane n-hexane
LLE
exptl temp, "C 24.0 -30.0 20.45 20.0b 50.0* 30.0b 30.0 20.0b 50.0b 50.0b 50.0b 40.0b 25.0b
XI
0.239 0.383 0.169 0.032 0.246 0.094 0.074" 0.041 0.058 0.0007 0.130 0.077 0.075
0.744 0.724 0.757 0.967 0.845 0.927 0.952 0.946 0.884 0.990 0.663 0.899 0.898
0.279 0.158 0.129 0.025 0.053 0.030 0.020 n.a. 0.262 0.029 n.a. n.a. 0.110
The solubility of 1,2-ethanediol in benzene is also reported to be 0.00251 a t 29 "C.
Table XI. "Exclusively Solvent" Compounds and Functional Groups ACOH ACCOO ACNHz DMA Me2S0 DEG NFM DMF NMP TEG sulfolane DOH
Table X. However, the solubility of any class of components, for which interaction parameters are available, in aniline, can be predicted with good accuracy. There is a number of compounds, or classes of compounds, for which this limitation applies. These "exclusively solvent" compounds or functional groups are listed in Table XI. Clearly, this limitation also applies in VLE calculations. In fact, greater deviations may be obtained in the dilute region for systems containing any of these functional groups. However, as far as VLE calculations are concerned, and for the systems investigated, such deviations fall within acceptable bounds. Another limitation in phase equilibrium calculations (either VLE or LLE) occurs for systems containing water. In fact, it was not possible to predict accurately vaporliquid equilibria or azeotrope composition and mutual solubilities in systems containing water. The somewhat higher deviations observed for the system acetonefmethanoi/water presented in Table VI1 is an example. Therefore, regarding water, the present parameters must be regarded as merely applicable to infinite dilution activity coefficient calculations. On the other hand, VLE or LLE parameters are not applicable for the calculation of ymvalues in systems containing water (see for example the deviations observed with VLE parameters in calculating ymvalues in water solvent, shown in Table V). Model Inadequacies A comparison between experimental and calculated ym values highlighted situations where unnacceptable high deviations were observed. The introduction of new functional groups could probably improve this situation. This was not considered due to the limited amount of data and components involved. The systems for which these unnacceptable results were obtained are listed in Table XII, together with the typical relative mean deviation observed. It must be pointed out, however, that the same abnormal situations occur when the VLE parameter table is considered. Also, there are some components for which systematic high deviations occur, and hence, the present parameter table should not be applied in these cases. The same
VLE xII
XI
0.785 0.891 0.807 0.966 0.973 0.949 0.974 n.a. 0.999 0.965 n.a. n.a. 0.891
miscible miscible 0.341 0.029 0.099 0.061 0.082 0.091 miscible n.a. 0.213 0.148 miscible
7X
miscible miscible 0.782 0.842 0.818 0.933 0.941 0.816 miscible n.a. 0.600 0.796 miscible
XI
XI1
0.437 0.376 0.200 0.034 0.061 0.082 0.003 0.064 0.066 0.036 0.126 0.099 0.190
0.669 0.883 0.742 0.942 0.935 0.927 0.960 0.990 0.832 0.988 0.852 0.934 0.825
Smoothed data.
Table XII. Svstems with Observed Inadeauate Results typical mean system (solvent/solute) dev," 70 1,2-dichloroethane/acetonitrile -80 1,3,5-trinitrobenzene/naphthalene 675 1,3,5-trinitrobenzene/diphenyl 412 toluene/l,4-dioxane -100 methylcyclohexane/2,3- butanedione 2200 -100 2-octanone/propyl chloride 2-octanone/allyl chloride -100 1-alkanols (CZ-C2J/nitromethane -100 >200 long-chain n-alkanes (>CI6)/nitromethane "Mean deviation ( % ) = (lOO/N)~"(y",,~- y-exp)/ymexp.
Table XIII. Compounds for Which the 7-Parameter Table Does Not Apply 2-nitroethanol 2-methoxyethanol acetylacetone methoxyacetonitrile trimethylorthoformate tetrahydrofurfuryl alcohol glycols (except those specially defined)
disagreement is observed with VLE parameters. These components are listed in Table XIII. Conclusions A new UNIFAC parameter table exclusively based on ymdata is presented. The present UNIFAC table aims at the improvement of the general accuracy and range of applicability of this group contribution method in the calculation of y mand S" values. Also, the new yy UNIVAC parameter table can be used with acceptable accuracy in vapor-liquid equilibrium and mutual solubility calculations. Therefore, it can be regarded as an useful alternative tool to the existing VLE and LLE parameters, whenever these are not available. Acknowledgment The authors are grateful to Stiftung Volkswagenwerk, W. Germany, and to the Funda@o Calouste Gulbenkian, Portugal, for financial support. Literature Cited Alessi, P.; Kikic, I.; Fredenslund, Aa.; Rasmussen, P. Can. J . Chem. Eng. 1982, 60, 300. Bastos, J.; Soares, M.; Medina, A. Paper presented a t CHISA'84, Praha, 1984. Bastos, J.; Soares, M.; Medina, A. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 420. Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vupour-Liquid Equilibrium Using UNIFAC; Elsevier: Amsterdam, 1977.
I n d . E n g . Chem. Res. 1988,27, 1277-1281 Gmehling, J.; Onken, U. Vapour-Liquid Equilibrium Data Collection; Dechema Chemistry Data Series; Dechema: Frankfurt, 1979. Gmehling, J.; Rasmussen, P.; Fredenslund, Aa. Znd. Eng. Chem.
1277
Perry, R.; Green, D. Chemical Engineers Handbook, 6th ed.; McGraw-Hill: New York, 1984. Skjold-Jorrgensen, S.; Kolbe, B.; Gmehling, J.; Rasmussen, P. Znd. Eng. Chem. Process Des. Deu. 1979, 18, 714. Smensen, J.; Arlt, W. Liquid-Liquid Equilibrium Data Collection; Dechema Data Series; Dechema: Frankfurt, 1979; Vol V, Part 1. Zarkarian, J.; Anderson, F.; Boyd, J.; Pransnitz, J. Ind. Eng. Chem. Process Des. Deu. 1979, 18, 657.
Process Des. Deu. 1982,21, 118. Kikic, I.; Alessi, P.; Rasmussen, P.; Fredenslund, Aa. Can. J. Chem. Eng. 1980, 58, 253. Kojima, K.; Tochigi, K. Prediction of Vapor-Liquid Equilibria by the ASOG Method; Kodansha-Elsevier: Tokyo, 1979. Macedo, E.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Znd. Eng.
Chem. Process Des. Dev. 1983, 22, 676.
Received f o r review J u n e 9, 1986 Accepted December 15, 1987
Magnussen, T.; Rasmussen, P.; Fredenslund, Aa. Znd. Eng. Chem.
Process Des. Dev. 1981, 20, 331.
Effects of a High-Velocity Jet on Fundamental Particle-Separation Characteristics Ji-Yu Zhang,+Bi-Jiang Zhang,?and Douglas C. Chitester*' Institute of Coal Chemistry, Academia Sinica, P.O. Box 165, Taiyuan, Shanxi, China, and Department of Energy, Pittsburgh Energy Technology Center, P.O. Box 10940, Pittsburgh, Pennsylvania 15236
T h e high-velocity jet region of a jetted fluidized bed plays an important role in momentum, mass, and heat transfer in the bed. A two-dimensional, fluidized-bed cold model equipped with a highvelocity jet was constructed to study the role of this high-velocity region. Glass beads were used t o simulate ash agglomerates, and millet and catalyst powder were used t o simulate coal and char, respectively. The effect on particle separation of various operating parameters including jet geometry, jet velocity, and particle size and density was studied. From these experiments, some important information on particle separation was obtained. An optimal, jet-zone, geometric configuration was identified for efficient particle separation. A graphical representation of the particle-separation process for heterogeneous solids was developed. Also, empirical equations were developed to calculate initial-separation velocity and critical-separation velocity.
I. Introduction
Table I. Physical Properties of Experimental Materials mean particle bulk particle size particle density, density, material range, mm size, mm g/cm3 g/cm3 2.496 1.644 glass beads 1 1.60-2.50 2.050 2.930 2.481 1.604 glass beads 2 2.50-3.36 millet 0.90-1.60 1.250 1.352 0.824 0.497 1.978 1.168 catalyst 0.16-0.90
A jetted fluidized bed is a special type of fluidized bed that employs a vertical, high-velocityjet for spouting. This type of bed has been used successfully in some ash-agglomerating gasifiers, such as those developed by U-Gas (Sandstrom et al., 1977) and Westinghouse (Hartman et al., 1978). The characteristics of the high-velocity jet play an important role in momentum, mass, and heat transfer and in reaction rate (Zhang, 1982). To gain a clear understanding of the effects of the jet characteristics, particle-separation experiments were conducted in a cold model. 11. Experimental Section A. Equipment and Materials. Reference in this report to any specific commercial product, process, or service is to facilitate understanding and does not necessarily imply its endorsement or favoring by the United States Department of Energy. The experiments were conducted using a two-dimensional fluidized bed that is 120 cm high, 40 cm wide, and 4 cm deep. Figure 1 shows the experimental apparatus. The diameter of the Venturi tube (Do) is 25.4 mm. The effective spread angle (a)of the tube can be varied from 12' to 45O, and the angle of the conical distributor (p) can be varied from 25" to 60'. The length between the Venturi and the conical distributor (Lo)can be varied from 0 to 160 mm. The conical distributor contains 0.8-mm-diameterholes, and the total hole fraction is approximately 0.005. There are pressure taps along the entire height of the bed at 80-mm intervals. These taps +Institute of Coal Chemistry. *Pittsburgh Energy Technology Center.
This article n o t subject t o U.S. Copyright.
are valved so that any one tap can be selected for measurement of differential pressure between it and either the primary or secondary collector. These collectors are beneath the Venturi tube. In the experiments, glass beads were used to simulate ash agglomerates. Millet particles and catalyst powder were used to simulate coal particles and fine coal ash, respectively. Some physical properties of these experimental materials are shown in Table I. B. Procedure. At the beginning of an experiment, a quantity of air equivalent to one-fourth to one-half of the total fluidizing air was injected through the Venturi tube. The balance of the air was injected through the conical distributor. The solid materials were then fed individually into the bed. The superficial gas velocity (VfJ at this point was sufficient to prevent separation of the solids. After allowing the bed to come to a steady-state condition, the amount of gas injected through the Venturi tube was gradually decreased. At lower jet velocities ( UJ), particle separation was observed. The separation process was studied at various jet velocities to determine the discharge rate, the size distribution of the separated particles, and the separation efficiency. Also, pressure drops were measured across different sections of the bed to compare bed densities. Experiments were conducted in beds with several different static heights (Ho)using nozzles with
Published 1988 b y t h e American Chemical Society
