Ind. Eng. Chem. Process Des. Dev. 1904, 2 3 , 391-400 Qmxm
8 , = -(group surface area fraction)
5
39 1
methylpentane, 590-35-2; 2,2,4-trimethylpentane, 540-84-1; benzene, 71-43-2; cyclohexane, 110-82-7.
Qnxn
Literature Cited
i
Xm=
Cvmti)xj j
(group fraction)
Nomenclature T = temperature, K x = liquid composition, mole fraction Registry No. Ethanol, 64-17-5; amyl alcohol, 71-41-0; decane, 124-18-5;pentane, 109-66-0;2-methylpentane, 107-83-5; 2,2-di-
Fredenslund, Aa.: Jones, R. L.: Prausnitz, J. M. AIChE J. 1975, 21, 1086. Leeper, S. A,: Wankat, P. C. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 331. Magnussen, T.; Rasmussen, P.: Fredenslund, Aa. Ind. Eng . Chem. Process Des. Dev. 1981, 20, 331. Magnussen, T. Instlt. For Kemitch., DTH, Denmark 1980, MANIOO1. Nakaguchl, G. M.; Keller, J. L. DOE ALO EY-76-C-04-3683-31, July 1979. Othmer, D. F.: Ratcliffe, R. L. Ind. Eng. Chem. 1943, 35, 789. Othmer, D. F.: Trueger, E. Trans. AIChE 1941, 37, 597.
Received for review December 15, 1982 Revised manuscript received June 3, 1983 Accepted July 3, 1983
Prediction of Enthalpies of Mixing with Group Contribution Models: Primary Parameters Wllliam Rupp, Steve Hetrel, Ignatlus Ojinl, and Dlmltrlos Tasslos" New Jersey Institute of Technology, Newark, New Jersey 07102
The modlfied UNIFAC model of Skjold-Jorgensen et al. has been successfully used in the correlation and prediction of enthalpies of mixing. With nineteen pairs of primary parameters, and in the temperature range 0-100 OC,typical prediction errors of 5 1 5 % are obtained. Higher errors (10-30%) are observed for systems containing hydrogen-bonded compounds.
Introduction Knowledge of enthalpies of mixing is important in several chemical engineering applications (distillation, heat exchangers, etc.). Since experimental data are limited, several studies have attempted to predict enthalpies of mixing by one of two approaches: from vapor-liquid equilibrium data (see, for example, Nicolaides and Eckert (1978b) and Nagata and Yamada (1972)), or group contribution techniques, an area studied mostly by Ratcliff and his co-workers (Nguyen and Ratcliff (1974);Si" and Vera (2979)). Group contribution techniques calculate interactions among molecules in terms of the interaction between the functional groups of the molecules. For example, the mixture 1-butanol and n-heptane would consist of the groups OH, CH2, and CH3. Interaction parameters correlated from this binary mixture could then be used to predict any other mixture containing the same groups, for example the ternary: n-heptane + 1-propanol + 1-octanol. Hence information for a limited number of systems can be extended to a large number of mixtures. As a result, of the two aforementioned approaches, the group contribution one is the more promising for the prediction of heats of mixing. Two group contribution models, both developed for the estimation of phase equilibrium, are considered in this study: the AGSM model of Derr and Deal (1969), as adopted for enthalpies of mixing by Ratcliff and his co-
workers, and the UNIFAC model of Fredenslund et al. (1975). The AGSM model has been used in the prediction of heats of mixing for binary and ternary liquid mixtures. Lai et al. (1978), for example, successfully predicted mixtures containing alkanes, chloroalkanes, and alcohols. Primary parameters (CH2/OH,CH2/C1),Le., parameters obtained from mixtures containing only two groups, were correlated from alcohol/alkane and chloroalkane/alkane data. Secondary parameters (Cl/OH), i.e., parameters obtained from mixtures containing three groups and using the appropriate primary parameters, were generated from alcohol/chloroalkane binaries. In addition, Doan-Nguyen et al. (1977) obtained good results for binary and ternary systems involving alkanes, ketones, alcohols, nitriles, and amines. The UNIFAC model was considered for the prediction of enthalpies of mixing by Fredenslund et al. (1977). They concluded that the use of temperature-independent parameters, while giving good vapor-liquid equilibrium predictions, failed to provide accurate predictions of heats of mixing. Typical results differed from the experimental values by a factor of 2. Nagata and Ohta (1978) used temperature-dependent parameters to successfully predict mixtures of alkanes with alcohols, ketones, esters, and ethers. Recently, Skjold-Jorgensen et al. (1980) modified the UNIFAC model by developing-through the simultaneow correlation of vapor-liquid equilibriumand enthalpy of mixing data-a generalized temperature dependency for
0196-4305/84/1123-0391$01.50/00 1984 American Chemical Society
392
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 I
I
I
I
lo'
1
i
co'
0
4 0
0
0
0
A A
A
A
20
8
-4
12
16
20
Nc
Figure 3. Effect of alkane chain length on correlation and prediction error for benzene + n-alkane data at 25 and 50 "C (Nc = number of carbon atoms): (0) data at 25 "C; (A)data at 50 "C. I
I
I
0
I
I
The Group Contribution Models Enthalpies of mixing, AHM,can be calculated from the excess Gibbs free energy, GE,by the use of the following thermodynamic relationship
2
P
Figure 1. Performance of eq 12 with the UNIFAC model: (0) type I systems; (A)type I1 systems; ( 0 )overall error.
600
The GEexpression for all models contains two terms: the combinatorial and residual. The first reflects the number of groups (AGSM) or their size and shape (UNIF'AC). This term does not appear, however, in the expression for the enthalpy of mixing since it drops out in the differentiation with respect to temperature. The second term reflects interactions between the groups in the solution, and it is evaluated from the Wilson equation for AGSM and from the UNIQUAC equation for the UNIFAC model. Use of these two models in conjunction with eq 1yields the following expressions for the enthalpy of mixing
W -J
?
40C
-3
I.
I Q
200
AHM =
(2)
0
xNki(Hk - H k i * ) k
where xi = liquid mole fraction of component i, = partial molar excess enthalpy of component i, Nki = number of groups of type k in component i, Hk = excess enthalpy of group k, and Hki* = group excess enthalpy of group k in a reference solution containing only molecules of type i. For the AGSM model
the interaction parameters. It was applied, however, to a limited number of systems. The first phase of this study deals with the evaluation of three models: AGSM, UNIFAC with temperature dependent parameters, and the UNIFAC as modified by Skjold-Jorgensen et al. (1980), on the basis of their ability to correlate and predict enthalpies of mixing for a selected set of binary systems. In the second phase, primary parameter values for a large number of group pairs are determined for the best model.
(4)
Table I. Selected Tvpe I and Type I1 Systems Used in Evaluating the Optimum Exponent, p , in Eq 11 and 12 system type t, "C data points reference nitroethane + 2,2-dimethylbutane nitroet hane + 2,2-dimethylbutane 1-octanol + n-heptane 1-octanol + n-heptane benzene + n-octane benzene + n-octane n-butylamine + n-heptane n-butylamine + n-heptane
I I I I I1 I1 I1 I1
(3)
a
Figure 2. Comparison of experimental and predicted heats of experimental; mixing for 1-chlorobutane + n-octane at 25 "C: (0) (-) predicted.
30 40 30 55 25 50 25 45
10 4 18 10 18 18 8 6
Handa e t al. (1977) Handa e t al. (1977) Savini e t al. (1965a) Nguyen and Ratcliff (1975a) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (1974b) Letcher and Bayles (1971) Letcher and Bayles (1971)
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 393 Table 11. Systems Used in the Evaluation of the Interaction Parameters and the Corresponding Errors system
t, "C
data points
SJ
n-butylamine + n-heptane n-hexylamine + n-hexane n-butylamine + n-hexane diethylamine + n-heptane dibutylamine + n-hexane triethylamine + n-hexane triethylamine + n-heptane 1-chlorobutane + n-hexane 2-chlorobutane + n-hexane 1-chlorohexane + n-octane 1-chloropentane + n-heptane 1-chlorobutane + n-nonane dichloromethane t n-heptane dichloromethane + n-hexane chloroform + n-heptane chloroform + n-hexane carbon tetrachloride + isooctane carbon tetrachloride + n-hexadecane carbon tetrachloride + n-heptane carbon tetrachloride + n-hexane benzene + isooctane benzene + n-hexadecane benzene + n-pentane benzene + n-decane benzene + n-docosane benzene + n-tetradecane methanol + n-hexane methanol + n-hexane methanol + n-heptane ethanol + n-hexane n-butanol + n-nonane n-pentanol + 2,2-dimethylbutane 2-propanol + n-heptane 2-methyl-2-propanol + n-hexane 1-heptene + n-heptane 1-octene + n-heptane 1-octene + n-heptane 1,5-hexadiene + n-hexane 1,5-hexadiene + n-hexane 1,6-heptadiene + n-heptane 1,7-octadiene + n-octane 1,3,5-hexatriene + n-hexane n-propanone + n-pentane n-propanone + n-pentane n-butanone + n-pentane n-butanone + n-pentane n-butanone + n-heptane n-butanone + n-heptane 3-pentanone + n-pentane 3-pentanone + n-pentane 4-heptanone + n-pentane 4-heptanone + n-nonane 6-undecanone + n-heptane 6-undecanone + n-heptane methyl butyl ketone + n-hexane 3-pentanone + n-pentane acetone + 2-pentanone n-propanal + n-heptane n-butanal + n-heptane methyl acetate + n-hexane n-propyl acetate + n-hexane ethyl acetate + n-dodecane n-butyl acetate + n-hexane acetic acid + n-heptane n-propanoic acid + n-heptane acetic acid + n-hexane n-propanoic acid + n-heptane 1-n-hexyne + n-hexane 3-n-hexyne + n-hexane
45 30 25 45 30 30 45 35 35 25 25 25 25 25 25 25 30 40 40 20 25 25 25 50 50 50 40 50 60 45 55 25 60 45 25 25 50 25 15 15 15 15 40 0 40 0 80 40 40 0 0 40 40 80 30 25 30 25 25 45 25 25 25 25 35 25 25 25 25
6 19 10 19 19 19 19 10 10 19 19 19 11 12 10 9 13 12 12 10 8 11 11 14 10 13 14 13 16 14 10 10 14 6 9 8 4 9 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 12 19 3 9 11 13 17 20 18 17 15 14 14 19 19
6.3 7.0 13.5 15.5 1.4 3.0 7.5 3.1 11.2 3.5 0.7 3.6 2.9 4.6 0.9 1.8 5.4 9.8 7.0 7.5 2.1 3.8 7.3 0.7 3.6 2.0 5.3 3.5 4.8 13.4 15.6 12.3 24.0 28.7 14.0 10.9 1.1 2.7 1.7 1.2 7.7 3.6 2.8 15.2 0.5 21.3 20.1 0.3 12.8 9.8 23.0 15.9 7.4 36.5 13.6 8.3 7.0 19.0 10.9 11.1 3.5 3.9 5.4 23.7 17.1 29.5 19.3 5.4 9.8
aPmax 102.5 53.8 187.8 140.2 4.2 3.0 10.4 31.4 69.5 17.6 4.0 28.9 53.9 55.7 13.9 16.8 24.0 51.5 31 .O 31.9 30.1 63.3 64.4 17.8 61.3 24.8 52.8 54.2 117.6 227.3 291.9 141.4 335.1 377.2 10.8 4.4 0.5 13.6 5.2 4.6 17.7 23.9 42.9 209.2 6.4 230.1 291.9 3.9 120.9 86.1 142.4 148.0 36.1 200.6 167.2 89.5 8.7 356.7 126.8 192.4 37.6 80.5 96.5 206.8 86.3 135.3 99.2 43.7 54.4
reference Letcher and Bayles (1971) Velasco e t al. (1978) Murakami and Fujishiro (1966) Letcher and Bayles (1971) Velasco e t al. (1978) Velasco e t al. (1978) Letcher and Bayles (1971) Lai e t al. (1978) Lai e t al. (1978) Paz Andrade e t al. (1979) Paz Andrade e t al. (1979) Doan-Nguyen e t al. (1978) Bissell e t al. (1971) Bissell e t al. (1971) Bissell e t al. (1971) Bissell e t al. (1971) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Lundberg (1964) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (1974b) Diaz Pena and Menduina (1974b) Diaz Pena and Menduina (1974b) Savini e t al. (196513) Savini e t al. (196513) Savini e t al. (1965b) Savini e t al. (1965a) Nguyen and Ratcliff (1975a) Nguyen and Ratcliff (1975b) Van Nes e t al. (1967a) Brown e t al. (1969) Woycicki (1975) Grolier (1975) Grolier (1975) Woycicki (1980) Woycicki (1980) Woycicki (1980) Woycicki (1980) Woycicki (1980) Suhnel e t al. (1979) Suhnel e t al. (1979) Suhnel et al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) DeTorre et al. (1980) Kiyohara e t al. (1979) Ramalho e t al. (1971) Marongiu and Kehiaian (1974a) Marongiu and Kehiaian (1974b) Nagata e t al. (1975) Grolier (1974a) Grolier e t al. (1974) Grolier e t al. (1974) Nagata et al. (1975) Nagata e t al. (1975) Nagata et al. (1975) Nagata e t al. (1975) Woycicki and Rhensius (1979) Woycicki and Rhensius (1979)
394
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
Table I1 (Continued) system 1-n-heptyne + n-heptane n-butyl ether + n-hexane diethoxymethane + n-heptane 1,2-dimethoxyethane + n-hexane triethoxymethane + n-heptane acetonitrile + n-heptane acetonitrile + n-hexane 2-nitropropane + n-hexane 2-nitropropane + isooctane nitroethane + n-hexane nitroe thane + 3-methylpen tane nitroethane + 3-methylpentane
t , “C 25 25 25 30 25 45 25 25 25 50 30 40
data points
SJ
19 12 23 10 7 14 4 11 15 14 7 3
3.7 10.6 5.3 3.5 5.9 5.2 10.4 14.2 5.2 7.1 15.6 12.1
reference
AHM”
23.2 11.5 37.7 74 .O 45.5 71.3 55.1 183.4 111.6 136.2 371.2 260.0
where Xk is the mole fraction of group k in the mixture
Woycicki and Rhensius (1979) Murakami and Fujishiro (1966) Meser (1977) DeTorre e t ai. (1980) Olschwong and Rey (1975) Palmer and Smith (1972) Murakami and Fujishiro (1966) Hsu and Clever (1975) Hsu and Clever (1975) Nicolaides and Ecker (1978a) Handa e t al. (1977) Handa e t al. (1977)
I400
CXiNki
Xk =
i
CCxiNki
(5)
1200
A
k i
A
and Hki* is calculated from eq 4 using the group fraction of group k in pure component i. The group interaction parameters, c k j and bkj, are related by bkj
a = -Ckj
-
-I W
(6)
aT
A
IO00
’ 0
0
800
0
? 2
%
For the UNIFAC model
600
400
200
0
0
where Qk = area parameter for group k and 0, = area fraction of group m
n
Vmn
=
a Z $ m n
(10)
U,, = measure of the energy of interaction between groups m and n. In this study we propose to use the following temperature dependency for the parameters c k j and $ ,, AkjT’
04
0.2
0.6
Figure 4. Comparison of experimental and predicted heats of mixing of n-hexane with 1-butanol, 2-butanol, and 2-methyl-2propanol at 45 “C: (0) 1-butanol, experimental; (-1 predicted; (A) 2-butanol, experimental; (-) predicted; (0)2-methy1-2-propano1, experimental; (-) predicted.
80
-
60
-
? Y
40
-
0
0
0 0
-k Bkj 20
O0
0
0
I00
800 Mawnum
The value of 0,for each model, is evaluated from the correlation and prediction of the enthalpy of mixing data for a selected set of binary systems. The results with the best value of 0for each model will
IO
0.8
MOLE FRACTION OF ALCOHOL
0
1200
1600
2000
AHM (J/mole)
Figure 5. Average absolute percent error as a function of the maximum heats of mixing for systems containing cyclic compounds.
be compared to those obtained, for the same binary systems, by the modified UNIFAC model proposed by
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 395 Table 111. Group Classification and Q Values main group
sub group
Qk
example
CH, CH; CH, CH, ACH OH CH,OH CNH, CNH, CNH , CNH CNH CNH (C),N (C),N
CHI CH CH C ACH OH CH,OH CH,NH, CH,NH, CHNH, CH ,NH CH,NH CHNH CH,N CH ,N
0.848 0.540 0.228 0.000 0.400 1.200 1.432 1.544 1.236 0.924 1.244 0.936 0.624 0.940 0.632 0.720 0.728 1.988 1.684 1.448 2.410 2.184 2.910 1.176 0.867 0.676 0.988 1.488 1.180 0.948 1.728 1.420 1.088 0.780 0.468 1.100 1.724 1.416 1.224 1.532 1.868 1.560 1.248 1.088 0.784
ethane: 2 C H , butane: 2 CH,, 2 CH, 2-methylpentane: 3 CH,, 2 CH,, 1 CH 2,2-dimethylbutane: 4 CH,, 1 CH,, 1 C benzene: 6 ACH 2-butanol: 2 CH,, 1 CH,, 1 CH, 1 OH methanol: 1CH,OH methylamine: 1 CH,NH, n-butylamine: 1 CH,, 2 CH,, 1 CH,NH, isopropylamine: 2 CH,, 1 CHNH, dimethylamine: 1 CH,, 1CH,NH diethylamine: 2 CH,, 1 CH,, 1 CH,NH diisopropylamine: 4 CH,, 1 CH, 1 CHNH trimethylamine: 2 CH,, 1CH,N triethylamine: 3 CH,, 2 CH,, 1 CH,N l-chlorobutane: 1 CH,, 3 CH,, 1 C1-1 2-chlorobutane: 2 CH,, 1 CH,, 1 CH, 1 C1-2 dichloromethane: 1 CH,Cl, 1,l-dichloroethane: 1 CH,, 1 CHCl, 2,2-dichloropropane: 2 CH,, 1 CC1, chloroform: 1 CHCl, l,l,l-trichloroethane: 1 CH,, 1 CC1, carbon tetrachloride: 1CCl, l-hexene: 1 CH,, 3 CH,, 1CH,=CH 2-hexene: 2 CH,, 2 CH,, 1CH=CH 2-methyl-2-butene: 3 CH,, 1 CH=C 2-methyl-l-butene: 2 CH,, 1 CH,, 1 CH,=C 2-butanone: 1CH,, 1 CH,, 1CH,CO 3-pentanone: 2 CH,, 1 CH,, 1 CH,CO acetaldehyde: 1 CH,, 1 CHO butyl acetate: 1 CH,, 3 CH,, 1 CH,COO butyl propanoate: 2 CH,, 3 CH,, 1 CH,COO dimethyl ether: 1 CH,, 1 CH,O diethyl ether: 2 CH,, 1 CH,, 1CH,O diisopropyl ether: 4 CH,, 1 CH, 1 CHO tetrahydrofuran: 3 CH,, 1 FCH,O acetonitrile: 1 CH,CN propionitrile: 1 CH,, 1 CH,CN acetic acid: 1 CH,, 1 COOH formic acid: 1HCOOH nitromethane: 1 CH,NO, 1-nitropropane: 3 CH,, 1CH,, 1 CH,NO, 2-nitropropane: 2 CH,, 1 CHNO, l-hexyne: 1 CH,, 3 CH,, 1 H C S 3-hexyne: 2 CH,, 2 CH,, 1 C=C
c1 c1
c1-1
c1-2 CH,C1, CHCl , cc1, CHCl, c c 1, cc1, CH,=CH CH=CH CH=C CH,=C CH,CO CH,CO CHO CH,COO CH,COO CH ,O CH ,O CHO FCH,O CH ,CN CH,CN COOH HCOOH CH,NO, CH,NO, CHNO , HCS
CCl , cc1, CCl, CCl , CCl ,
cc1, c =c c =c c =c c =c
CH,CO CH,CO CHO COOC COOC CH,O CH,O CH,O CH,O CCN CCN COOH COOH CNO, CNO, CNO, C=C
c-c
c=c
Table IV. Group Interaction Parameters,
-CH, with G r o w G group G
CH, /G
G/CH,
s
c=c CH,CO co oc
7.67 52.25 44.98 21.92 68.87 80.05 51.53 394.40 81.31 50.02 22.65 74.52 26.60 15.27 2.75 12.09 106.88 20.22 323.39
-1.47 12.35 3114.10 14.99 4.54 3.01 6.75 12.89 -5.88 8.16 66.91 -5.70 -0.39 -2.78 1.79 1.90 -19.35 17.25 49.15
7.1 11.0 5.6 6.3 6.4 9.6 6.3 4.5 8.8 8.4 5.2 3.8 3.8 1.3 7.4 3.2 14.5 22.4 17.6
CH,O CCN CNO,
c-c
CH,OH CNH, CNH (C),N
c1 CCl, cc1;
cc1, ACH CHO COOH OH
Skjold-Jorgensen et al. (1980). They suggest that the parameter ,,$, eq 9, can be written as
and that the coordination number Z be made a function of temperature Z(T) = 35.2 - 0.12721‘+ 0.00014P
(14)
while a”,, is temperature independent. The numerical constants in eq 14 were obtained by a simultaneous fit of vapor-liquid equilibrium data for six binaries and AHM data for three binaries. The systems involved were hydrocarbons and ethers, and the temperature range was 25 to 129 O C . It should be noticed that the temperature dependency of the parameters described by eq 11and 12 is not the only one possible. For example, Nguyen and Ratcliff (1974) used temperature dependent parameters for the CH2/0H pair with the AGSM model that contained five adjustable constants. They were revised later by Lai et al. (1978) so that only four constants were involved. For the same group pair, and with the UNIFAC model, Nagata and Ohta (1978) used an expression involving six adjustable constants. Considering the large number of experimental @ data for n-alcoholsln-alkanes this approach may be justified. In the typical case, however, the available data are limited and eq 11and 12 were considered in this study. Comparison of the Models In developing the data base for the comparison of the
396
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
Table V. Prediction Results system n-propylamine + n-hexane n-butylamine + n-heptane diethylamine + n-heptane diethylamine + n-hexane triethylamine + n-heptane tri-n-dodecylamine + n-octane triethylamine + n-hexane tributylamine + n-octane triethylamine + n-octane 1-chloropentane + n-hexane 1-chloropentane + n-octane 1-chlorohexane + n-hexane 1-chlorohexane + n-heptane 1-chlorohexadecane + n-dodecane 1-chlorohexadecane + n-hexadecane tert-butyl chloride + n-hexane 1-chlorobutane + n-octane 1-chlorobutane + n-dodecane 1-chlorobutane + n-hexadecane 1-chlorododecane + n-octane 1-chlorododecane + n-dodecane 1-chlorododecane + n-hexadecane 1-chlorohexadecane + n-octane tert-butyl chloride + n-octane tert-butyl chloride + n-dodecane tert-butyl chloride + n-hexadecane 1-chlorooctane n-octane 2-chlorobutane + n-hexane 2-chlorobutane + n-octane 1-chlorobutane + n-hexane 1-chlorooctane + n-hexane carbon tetrachloride + n-nonane carbon tetrachloride + n-decane carbon tetrachloride + n-dodecane carbon tetrachloride + n-hexane carbon tetrachloride + n-heptane carbon tetrachloride + n-hexadecane carbon tetrachloride + n-hexadecane carbon tetrachloride + isooctane carbon tetrachloride + isooctane carbon tetrachloride + n-octane carbon tetrachloride + n-octane carbon tetrachloride + n-octane carbon tetrachloride + n-hexane carbon tetrachloride + n-heptane carbon tetrachloride + n-heptane carbon tetrachloride + n-hexane benzene + n-heptane benzene + n-heptane benzene + isooctane benzene + n-hexane benzene + 2-methylpentane benzene + 3-methylpentane benzene + 2,2-dimethylbutane benzene + 2,3-dimethylbutane benzene + n-octane benzene + n-undecane benzene + n-dodecane benzene + n-tetradecane benzene + n-pen tadecane benzene + n-heptadecane benzene + n-hexane benzene + n-octane benzene + n-dodecane benzene + n-hexadecane benzene + n-octadecane benzene + eicosane methanol + n-hexane methanol + n-pentane methanol + n-butane methanol + n-propane propanol + n-hexane 1-butanol + n-hexane
data t, "C points 30 25 25 30 25 30 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 20 30 20 40 30 40 20 30 30 20 40 50 25 50 25 25 25 25 25 25 25 25 25 25 25 50 50 50 50 50 50 45 25 25 25 45 45
19 6 8 19 7 11 19 18 19 14 15 14 15 15 15 12 13 10 11 13 13 11 13 12 13 14 19 19 19 19 19 21 21 21 10 10 8 8 9 14 8 13 11 10 8 6 12 4 8 4 10 15 11 10 10 21 11 10 10 10 11 13 13 15 16 11 13 17 23 23 25 8 7
SJ
5.4 3.5 14.7 20.9 40.5 90.0 2.2 15.5 13.1 2.9 2.5 5.1 4.3 2.3 16.4 5.9 10.7 3.9 2.9 8.7 21.6 13.9 27.3 4.2 4.7 15.7 3.2 6.9 5.8 2.6 1.4 1.8 1.6 3.6 10.2 7.9 19.3 15.8 2.8 7.9 4.9 7.6 5.7 9.5 6.0 5.8 9.5 2.5 2.6 1.1 2.3 0.9 1.8 2.4 2.5 3.2 4.3 3.2 0.6 1.4 3.6 2.8 2.3 0.7 2.3 2.8 2.3 4.4 17.0 16.1 40.3 12.3 10.4
AHM"
82.1 96.6 142.8 139.3 23.4 73.7 2.3 6.7 14.8 23.4 19.7 32.3 25.5 6.3 37.3 38.2 50.9 48.3 34.5 17.2 41.2 33.7 76.0 42.1 50.7 168.0 16.1 42.9 42.2 18.4 6.5 13.5 11.4 43.3 37.5 37.9 129.9 91.3 17.1 36.9 22.4 30.1 25.8 33.1 22.6 26.2 32.2 22.1 32.0 17.5 21.0 23.0 30.8 28.2 40.7 38.2 48.5 35.0 14.8 15.4 60.9 25.0 26.7 11.1 49.6 55.9 45.7 52.5 111.9 112.6 164.3 159.0 129.9
reference Letcher and Bavles (1971) Letcher and Bayles i1971) Letcher and Bayles (1971) Velasco e t al. (1978) Letcher and Bayles (1971) Grauer and Kertes (1973) Budoo and Philippe (1978) Budoo and Philippe (1978) Budoo and Philippe (1978) Paz Andrade and Bravo (1977) Paz Andrade and Bravo (1977) Paz Andrade and Bravo (1977) Paz Andrade and Bravo (1977) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Valero e t al. (1980) Doan-Nguyen e t al. (1978) Doan-Nguyen e t al. (1978) Doan-Nguyen e t al. (1978) Doan-Nguyen e t al. (1978) Doan-Nguyen e t al. (1978) Grolier and Inglese (1975) Grolier and Inglese (1975) Grolier and Inglese (197 5) Bissell e t al. (1971) Bissell e t al. (1971) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Harsted and Thomsen (1974) Lundberg (1964) Lundberg (1964) Lundberg (1964) Paz Andrade (1973) Paz Andrade (1973) Paz Andrade (1973) Paz Andrade (1973) Paz Andrade (1973) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (1974a) Diaz Pena and Menduina (197413) Diaz Pena and Menduina (1974b) Diaz Pena and Menduina (1974b) Diaz Pena and Menduina (197413) Diaz Pena and Menduina (1974b) Diaz Pena and Menduina (1974b) Savini e t al. (1965b) Collins et al. (1980) McFall e t al. (1981) Post e t al. (1981) Brown e t al. (1964) Brown e t al. (1964)
-
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984 397 Table V (Continued) data t , " ~points
system 1-pentanol + n-hexane 1-hexanol + n-hexane 1-octanol + n-hexane ethanol + n-heptane ethanol + n-heptane ethanol + n-heptane ethanol + n-heptane ethanol + n-heptane ethanol + n-heptane ethanol + n-heptane ethanol + n-decane 1-propanol + n-decane 1-butanol + n-decane 1-pentanol + n-decane 1-hexanol + n-decane 1-heptanol + n-decane 1-octanol + n-decane 1-pentanol + n-hexane 1-pentanol + n-heptane 1-pentanol + n-octane 1-pentanol + n-nonane 1-pentanol + n-tetradecane 1-pentanol + n-pentane 1-pentanol + n-butane 2-methyl-1-propanol + n-hexane 2-methyl-1-propanol + n-hexane 2-butanol + n-hexane 2-butanol + n-hexane 2 -methyl-2-propanol + n-hexane 2-propanol + n-heptane 2-propanol + n-heptane 1-hexene + n-hexane 1-octene + n-hexane 1,3-hexadiene + n-hexane 1,3-hexadiene + n-hexane 1,6-heptadiene + n-heptane 1,3,5-hexatriene + n-hexane 1-heptene + n-heptane 2-butanone + n-pentane n-propanone + n-nonane 4-heptanone + n-pentane acetone + n-hexane methyl ethyl ketone + 2-octanone methyl acetate + n-octane acetic acid + n-heptane 1,l-dimethoxyethane + n-heptane diethoxymethane + n-decane 2,2-diethoxypropane + n-heptane nitroethane + 2,2-dimethylbutane
45 45 45 10 20 25 30 45 60 75 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 45 25 45 27 30 45 25 25 15 25 25 25 25 25 40 40 30 40 25 35 25 25 25 30
18 7 7 14 12 12 16 13 15 14 19 18 18 17 19 19 19 10 12 13 18 13 16 17 10 10 6 6 8 20 21 9 10 2 9 10 9 9 19 1 1 7 3 21 14 32 38 32 10
models, it became apparent from preliminary calculations that it would be convenient to classify binary systems into two types: type I heats of mixing increase as temperature increases; type I 1 heats of mixing decrease as temperature increases. These calculations indicated that the values of p that gave good results for type I systems gave poor results for type I1 systems. The reverse was also true. To arrive at an optimum value for p we adopted the following procedure: (a) Select two type I and two type I1 systems, each at two temperatures, presented in Table I. (b) Correlate the heats of mixing data at the lower temperature using values of p from -2 to +2 in intervals of 0.5 excluding p = 0. ( c ) Predict the heats of mixing at the higher temperature. In practical applications it is often desirable to extrapolate the heats of mixing data to higher temperatures. (d) Calculate the average cumulative prediction error S, L
S, = C S j / L J
(15)
SJ
20.5 15.7 18.2 17.6 19.0 16.2 18.5 16.6 15.1 11.4 17.0 16.7 20.1 21.9 20.3 18.6 19.9 15.4 20.5 24.6 19.5 33.3 11.9 11.0 22.0 17.5 33.3 25.2 35.1 31.7 28.1 3.8 44.2 23.3 25.0 2.0 5.1 14.0 6.0 6.6 29.9 10.3 17.4 3.3 23.4 22.1 10.6 5.0 16.0
AH^^^
reference
189.7 199.4 204.7 87.3 140.8 162.0 189.2 258.2 287.9 248.3 284.3 200.4 183.2 184.6 207.7 196.9 207.3 128.3 146.9 165.6 184.5 273.4 89.7 81.4 221.9 271.9 440.7 499.3 463.1 313.6 349.5 5.1 12.9 61.4 63.4 5.5 33.5 10.8 92.0 134.2 209.1 240.0 28.3 81.3 197.5 193.7 86.7 24.2 438.9
Savini e t al. (1965a) Brown e t al. (1964) Brown e t al. (1964) Van Hess e t al. (1967b) Ramalho and Ruel (1968) Ramalho and Ruel (1968) Ramalho and Ruel (1968) Van Hess e t al. (1967b) Van Hess e t al. (196713) Van Hess e t al. (1967b) Christensen e t al. (1979a) Christensen e t al. (1979a) Christensen e t al. (1979a) Christensen e t al. (1979a) Christensen e t al. (1979a) Christensen e t al. (1979a) Christensen e t al. (1979a) Nguyen and Ratcliff (1975b) Ramalho and Ruel (1968) Ramalho and Ruel (1968) Christensen e t al. (1979b) Ramalho and Ruel (1968) Collins e t al. (1980) McFall e t al. (1981) Brown e t al. (1969) Brown e t al. (1969) Brown e t al. (1969) Brown e t al. (1969) Brown e t al. (1969) Van Ness e t al. (1967a) Van Ness e t al. (1967a) Woycicki (1975) Karbalai Ghassemi and Grolier (1976) Woycicki (1980) Woycicki (1980) Woycicki (1980) Woycicki (1980) Woycicki (1975) Kiyohara e t al. (1979) Suhnel e t al. (1979) Suhnel e t al. (1979) Srinivasan e t al. (1978) Ramalho e t al. (1971) Grolier e t al. (1974) Nagata e t al. (1975) Meyer (1977) Meyer (1977) Meyer (1977) Handa e t al. (1977)
where L is the number of systems and SJ is the average absolute percent error for system J
where M is the number of experimental point for system J and subscripts exptl and calcd indicate experimental and calculated, respectively. A plot of Sc vs. p is shown in Figure 1 for the UNIFAC model and it suggests that positive exponents favor type I systems and negative ones type I1 systems. On the basis of the cumulative error, p = 0.5 gives the best results with an average absolute error of 7.7%. Attempts to improve the results for p = + L O by using different starting values in the regression subrouting failed. The performance of the AGSM model was erratic and the results are not shown. Use of the Z(T) expression gave an error of 5.0% and it will be used in the second phase of this study. In addition, this expression requires the evaluation of only
398
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
Table VI. Multiplicity of Parameters initial Darameters 0.1, 0.1 0.1, +200.0 0.1, -200.0 +200.0, 0.1 +200.0, +200.0 1.200.0, -200.0 -200.0, 0.1 -200.0, +200.0 -200.0, -200.0
final Darameters 12.09, 1.89 14.24, 1624.10 12.08, 1.89 665.60, 14.50 516.80, 312.20 516.60, 312.30 12.08, 1.89 14.23, 1452.50 12.09, 1.89
S.7
set
3.2 3.2 3.2 6.9 50.9 50.9 3.2 3.1 3.2
A B A C
D D A E A
two parameters per pair of groups, which is extremely important in view of the problem of multiplicity of roots and data availability. Results and Disdussion Primary parameters, i.e., parameters for CH2with several groups G (CHi/G and G/CH2), were evaluated by regression of the data presented in Table 11, which also includes the obtained average absolute percent error for each system (SJ). For best parameter values, all available data were used with the exception of those reserved for prediction purposes. The group classification and Q values, presented in Table 111, were used along with the following minimization function
where V is the number of data points. The obtained values of the interaction parameters are presented in Table IV along with the correspondingvalues of the overall absolute percent error (S)
Prediction results are given in Table V and typical ones are shown in Figure 2 for the system 1-chlorobutane + n-octane. To demonstrate the size of the error, the max- AHMddI) for each system imum error AHM, (lAHMexpptl is included in Tables I1 and V. The regression of the experimental data was carried out with a modification of the subroutine of Fredenslund et al. (1977). As shown in Table VI, different starting values for the interaction parameters may lead to different final values and different quality of correlation. To ensure that all reasonable sets of final parameters were found, a grid covering the range +200 to -200 in intervals of 200 was used (Table VI). In case of similar results, the pair with the smallest in absolute value parameters was used. An important test of a group contribution model is the correlation and/or prediction of isomeric compounds. A major advantage of the UNIFAC model over the AGSM
is that it takes into account the surface area Q through which groups interact with each other. Consider, for example, the case of n-pentane and neopentane (tetramethylmethane). The AGSM model does not differentiate between them, since it only considers the total number of groups present. On the other hand, UNIFAC treats the first as consisting of two CH3 and three CH2 groups and the second as one C and four CH3 groups. While the interaction parameters between them and a group G are the same, the area parameters Q are very different (Table 111). Hence the UNIFAC model can, in principle at least, take into account the structural difference between isomers. This is demonstrated by the results in Tables I1 and V where the performance of systems containing isomeric compounds is, in general, similar to that of the others. The effect of the size of one of the components of the mixture on the performance of the UNIFAC model is demonstrated in Figure 3 for the systems benzeneln-alkanes. Good results are obtained up to C22H48.But if the large molecule contains the group G, the effect may be significant as suggested by the system tri-n-dodecylamineln-octane when the error is 90%. The difference between predicted and experimental enthalpies of mixing is small, however, as seen in Table V. In general, the UNIFAC model underpredicts systems of alkanes with another molecule containing a large number of CH2groups. It appears, therefore, that the model tends to overemphasize the athermal conditions approached in mixtures of alkanes with a large molecule as the number of CH2 groups in the later increases. This is not a serious problem, however, as the actual enthalpies of mixing for such systems are rather low. The results for systems containing the hydrogen-bonded alcohols, organic acids, and amines are reasonably good considering that no separate treatment of the chemical effects is involved. The performance for isomeric alcohols is somewhat poorer as demonstrated in Figure 4 where experimental and predicted enthalpies of mixing for the three butanols with a common solvent are presented. While the predicted values are similar, the experimental ones are quite different. As expected, the variation in functional groups in these alcohols cannot account for the large difference in chemical effects among primary, secondary, and tertiary butanols. This also explains the failure to obtain improved results by varying the Q value of the OH group or by using separate functional groups for primary and secondary alcohols (Fredenslund et al., 1975). Systems containing cyclic compounds were not used in the data base, for their inclusion gave erratic results (Rupp, 1982). Attempts to obtain improved results by varying the Q values for cyclo CH2 were not successful. Caution should, therefore, be exercised in using the reported parameter values for systems containing cyclic compounds for, as shown in Table VII, large percent errors may occur.
Table VII. Prediction Results for Systems Containing Cyclic Compounds system
t, "C
nitroethane + cyclohexane oxane + cyclopentane octene + cyclohexane n-butanal + cyclohexane methanol + cyclohexane ethyl ethanoate + cyclohexane 1-pentanol + cyclohexane ethyl butyl ketone + cyclohexane 2-chlorobutane + cyclohexane benzene + ethylcyclohexane
25 25 25 25 25 25 25 30 30 25
data points 9 9
8 8 13 19 11 12 10 9
SJ
AH^,,,
11.2 48.2 85.2 13.0 17.4 35.8 51.6 44.9 13.1 15.5
246.0 159.8 121.8 164.2 151.8 251.5 163.7 348.2 58.7 67.2
reference Clever and Hsu (1975) Inglese et al. (1980) Grolier (1974b) Marongiu and Kehiaian ( 1 9 7 4 ~ ) Touhara et al. (1975) Grolier (1973) Gonzalez Posa e t al. (1972) DeTorre e t ai. (1980) Polo e t al. (1976) Cabani and Ceccanti (1973)
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
It is worth noticing that the maximum error is typically within the range of enthalpies of mixing for alkanescycloalkanes. For example, the maximum enthalpy of mixing for the system n-hexane/cyclohexane at 25 "C is 221 J/mol (Marsh, 1973). The problem is not a serious one, however, for decreasing percent errors are observed as the size of the enthalpy of mixing increases. This is demonstrated in Figure 5, where the average absolute percent error is plotted against the maximum observed enthalpy of mixing for the systems in Table VII. Conclusions Of the three group contribution models for the correlation and prediction of enthalpies of mixing: AGSM, UNIFAC with temperature dependent parameters, and the modified UNIFAC of Skjold-Jorgensen et al. (1980), the latter is simpler and gives the best results. Primary parameters are given for CH2 with nineteen groups. Reliable prediction results are obtained with typical errors of 5-15%, except for systems containing hydrogen-bonded compounds where somewhat larger errors (15-30%) occur. The model can be used in the temperature range 0 to 100 OC. Nomenclature a,, = UNIFAC parameter, eq 9 a,' = modified UNIFAC parameter,
temperature independent, eq 13 Akj, B , = See eq 11 bkj, ckj = AGSM parameters C,, D,, = see eq 12 D = minimization function, eq 17 G = group, other than CH2 GE = excess Gibbs free energy Hk = excess enthalpy of group k Hki* = excess enthalpy of group k in a reference solution containing only molecules of type i AHi = partial molar excess enthalpy of component i A H M = excess enthalpy AHM,, = maximum absolute difference in J/mol between experimental and calculated excess enthalpy L = number of systems; see eq 15 MJ = number of data points for system J Nki= number of groups of type k in component i P = pressure Qk = area parameter of group k R = gas constant S, = average cumulative prediction error; see eq 15 SJ = average absolute percent error for system J; see eq 16 S = average correlation error; see eq 18 t = temperature, "C T = absolute temperature, K U,, = measure of the energy of interaction between groups m and n V = total number of experimental data points; see eq 17 and 18 x = liquid phase mole fraction Xk = liquid phase group fraction 2 = lattice coordination number Greek Symbols /3 = see eq 11 and 12 8, = area fraction of group m J.,,, J.,, = UNIFAC group interaction parameters
Subscripts calcd = calculated exptl = experimental i = component i j , k , m, n = group j , k , m, n
399
Superscript * = reference state
Literature Cited Bisseii, T. G.; Okafor, 0. E.; Williamson, A. G. J . Chem. Thermodyn. 1071, 3, 393. Brown, I.; Fock, W.; Smith, F. Aust. J. Chem. 1084, 77, 1106. Brown, I.; Fock, W.; Smith, F. J. Chem. Thermodyn. 1080, 7 , 273. Budoo, B.; Philippe, R. J . Chem. Thermodyn. 1078, 70, 1147. Cabani, S.;Ceccanti, N. J . Chem. Thermodyn. 1073, 5 , 5 . Christensen, J. J.; Izatt, R. M.; Stitt, B. D.; Hanks, R. W. J . Chem. Thermodyn. 1070a, 7 7 , 261. Christensen, J. J.; Izatt, R. M.; Stm, B. D.; Hanks, R. W.; Williamson, K. D. J. Chem. Thermodyn . 1070b, 7 7 , 1029. Clever, H. L.; Hsu, K. Y. "International Data Series, Selected Data Mixtures", Series A, 1975; p 167. Collins, S.G.; Christensen, J. J.; Izatt. R. M.; Hanks, R. W. J . Chem. Thermodyn. 1080, 72, 609. Derr, E. L.; Deal, C. H. I. Chem. E . Symp. Ser. No. 32 1080, 3,40. DeTorre, A.; Veiasco, 1.; 0th S.;Gutierrez Losa, C. J . Chem. Thermodyn. 1080, 72,87. Daz Pena, M.; Menduina, C. J . Chem. Thermodyn. 1074a, 6 , 387. Diaz Pena, M.; Menduina, C. J . Chem. Thermodyn. 1074b. 6 , 1097. Doan-Nguyen, T. H.; Vera, J. H.; Ratcliff, 0. A. 27th Canadian Chemical Engineering Conference, Calgary, Alberta, 1977. Doan-Nguyen, T. H.; Vera, J. H.; Ratcliff, 0. A. J. Chem. Eng. Data 1078, 23, 218. Fredenslund, Aa.; Jones, R. L.; Prausnitr, J. M. AIChE J. 1075, 27, 1086. Fredensiund, Aa.; Gmehiing, J.; Rasmussen, P. "Vapor-LiquM Equilibria Using UNIFAC"; Elsevier: Amsterdam, 1977. Gonzalez Posa, C.; Nunez, I.; Villar, E. J . Chem. Thermodyn. 1072, 4 , 275. Grauer, F.; Kertes. A. S. J . Chem. Eng. Data 1073, 76,405. Groiier, J. P. E. Int. Data Ser. Sel. Data Mixtures 1075, 111. Groiier, J. P. E. Int. Data Ser. Sel. Data Mlxtures 1074a. 17. Grolier, J. P. E. Int. Data Ser. Sel. Data Mixtures 1974b, 222. Groiier, J. P. E. Int. Data Ser. Sel. Data Mlxtures 1975, 43. Viallard. A. J . Chem. Thermodyn. 1074, 6 , 895. Groiier, J. P. E.; Ballet, 0.; Groiier, J. P. E.; Inglese, A. Int. Data Ser. Sel. Data Mixtures, Ser. A 1075, 72. Handa, Y. P.; Knobier, C. M.; Scott, R. L. J . Chem. Thermodyn. 1077, 9 , 451. Harsted, 6. S.;Thomsen, E. S.J . Chem. Thermodyn. 1974, 6 , 557. Hsu, K. Y.; Clever, H. L. J. Chem. Eng. Data 1075, 20,268. Ingiese, A.; Wilheim, E.; Groiier, J. P. E.; Kehiaian, H. V. J. Chem. Thermodyn. 1080, 72, 1049. Karbaiai Ghassemi, M. H.; Groiier. J. P. E. Int. Data Ser. Sel. Data Mixtures, Ser. A 1078, 66. Kiyohara, 0.; Handa, Y. P.; Benson, G. C. J . Chem. Thermodyn. 1070, 7 7 , 453. Lai, T. T.; Doan-Nguygen, T. H.; Vera, J. H.; Ratcliff, G. A. Can. J . Chem. Ena. 1078. 358. ., 56. . ... Letchir, T M.; Bayles, J. W. J. Chem. Eng. Data 1071, 76,266. Lundberg, 0. W. J . Chem. Eng. Data 1084, 9 , 193. Maronglu, B.; Kehiaian, H. V. Int. Data Ser. Sel. Data Mixtures, Ser. A 1074, 58. Marsh, K. N. Int. Data Ser. Sel. Data Mixtures, Ser. A 1073, 1. McFali, T. A.; Post, M. E.; Collins, S. G.; Christensen, J. J.; Izatt, R. M. J. Chem. Thermodyn. 1081. 73,41. Meyer, R. J. Int. Data Ser. Sel. Data Mlxtures, Ser. A 1077, 140. Murakami, S.;Fujishiro, R. Bull. Chem. SOC.Jpn. 1988, 3 9 , 720. Yamada, T. Ind. Eng. Chem. Process Des. D e v . 1072, 7 1 , 574. Nagata, I.; Nagashima, M.; Kazuma, K.; Nakogawa, M. J. Chem. Eng. Jpn. Nagata, I.; 1075, 4, 261. Nagata, I.;Ohta, T. Chem. Eng. Scl. 1078, 33, 177. Nguyen, T. H.; Ratcliff, 0. A. Can. J . Chem. Eng. 1074, 52, 641. Nguyen, T. H.; Ratcliff. 0. A. J. Chem. Eng. Data 1075a, 20, 252. Nguyen, T. H.; Ratcliff, G. A. J . Chem. Eng. Data 1075b, 2 0 , 256. Nicoiaides, G. L.; Eckert, C. A. J. Chem. Eng. Data 1078a, 23, 152. Nicolaides, G. L.; Eckert, C. A. Ind. Eng. Chem. Fundam. 1978b, 17, 331. Olschwong, D.; Rey, J. Int. Data Ser. Sel. Data Mlxtures, Ser. A 1075, 194. Palmer, D. A.; Smith, B. D. J . Chem. Eng. Data 1072, 17, 71. Paz-Andrade, M. I. Int. Data Ser. Sel. Data Mixtures, Ser. A 1073, 100. Paz-Andrade, M. I.;Bravo, R. Int. Data Ser. Sel. Data Mlxtures, Ser. A 1977, 71. Paz-Andrade, M. I.; Bravo, R.; Garcia, M.; Groiier, J. P. E.; Kehiaian, H. V. J. Chim. Phys. 1070, 76, 51. Polo, C.; Otin, S.;Gutierrez Losa, C.; Gracia, M. Int. Data Ser. Sel. Data Mixtures, Ser. A 1078, 143. Post, M. E.; McFali, T. A.; Christensen, J. J.; Izatt, R. M. J . Chem. Thermodyn. 1081, 13, 77. Ramalho, R. S.; Ruei, M. Can. J . Chem. Eng. 1088, 46, 456. Ramalho, R. S.;Tillie, J. L.; Kaliaguine, S. Can. J. Chem. Eng. 1071, 49, 830. Rupp, W., W. M.S. Thesis, New Jersey Institute of Technology, Newark, NJ, 1982. Savini, C. G.; Winterhaher, D. R.; Van Ness, H. C. J. Chem. Eng. Data 1965a .- - - -, 10 . - , 168 . - -. Savini, C. G.; Winterhaiter, D. R.; Van Ness, H. C. J. chem. Eng. Data I085b. 70. 171. Siman, J.'E.; Vera, J. H. Can. J. Chem. Eng. 1070, 5 7 , 355. SkjoldJorgensen. S.; Rasmussen, P.; Fredenslund, Aa. Chem. Eng. Sci. 1080, 35, 2389.
.
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Srinivasan, D.; Lakshmanan, C. M.; Degaleesan, T. E.; Laddha, G. S. Ind. Chem. Manuf. 1978, 16, 30. Suhnel. Von K.; Messow, U.; Salomon, M. Z . Phys. Chem. (Leiprig) 1979, 260, 142. Touhara, H.; Ikeda, M.; Nakanishi, K.; Watanabe, N. J . Chem. Thermodyn. 1975, 7, 887. Valero, J.; Gracia, M.; Gutierrez Losa, C. J . Chem. Thermodyn. 1980. 72, 621. Van Ness, H. C.;Soczek, C. A.; Peloquin, G. L.; Machado, R . L. J . Chem. Eng. Data 1987a, 12, 217. Van Ness, H. C.; Soczek, C. A.; Kochar. N. K. J . Chem. Eng. Data 1967b. 12, 346.
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Received for review July 8, 1982 Accepted June 16, 1983
Some Aspects of Process Design of Liquid-Liquid Reactors T. V. Vasudevan and Man Mohan Sharma' Department of Chemical Technology, Universtiy of Bombay, Matunga, Bombay-400 0 19, India
Some aspects of the process design of liquid-liquid reactors where extraction is accompanied by fast reaction in the immediate vicinity of the interface have been considered. In a large number of cases of practical relevance analytical expressions can be deriied to obtain the pertinent design parameter. In the case of mechanically agitated contactors, operated batchwise, it can be shown that even a 10% excess of the reactant can bring down the batch time very substantially. The height of packed columns, for different controlling regimes, c a n be calculated analytically. Even in the case of plate columns the number of plates can be calculated analytically.
Introduction A variety of industrially important reactions, such as nitration, sulfonation, alkylation, reduction, etc., involve two liquid phases. In some cases where a choice can be exercised, the liquid-liquid mode of operation may be preferred over gas-liquid operation, due to the possibilities of obtaining much higher values of interfacial area in the former case. Consider the removal of COS from a C3 stream where both gas-liquid and liquid-liquid modes of operation can be considered; some advantages may be realized by adopting the liquid-liquid mode of operation (Sharma, 1983). The design of liquid-liquid reactors has received very limited attention and this paper will consider some aspects of process design of such reactors. Some aspects of the process design of gas-liquid reactors have been considered by Juvekar and Sharma (1977), and their paper may be considered as background information. Depending on the circumstances, the reaction can be carried out in the following modes of operation: batch, "semi-batch", and continuous. Mechanically agitated contactors are used for batch and "semi-batch" operations and spray columns, packed columns, plate columns, multistage mechanically agitated contactors, centrifugal extractors, etc., are usually used for continuous operation. The important design parameter is the time of reaction for a specified level of conversion in the case of batch and "semi-batch" operations and volume/height of reactor for the continuous mode of operation. A variety of cases of possible practical relevance have been considered and analytical expressions are given for most of the cases; in some cases numerical solutions are required. Some typical cases reported in Table I will be considered. Equations for design parameters are derived based on the assumption that the reaction is isothermal. This assumption is well justified because of the ease of heat re0196-4305/84/1123-0400$01.50/0
Table I. Design of Liquid-Liquid Reactors case no.
statement
( i ) The concentration of solute in the dispersed phase is low so that there is no change in the dispersed phase flow rate and hence in the holdup and effective interfacial area. (ii) The molar volumes of reactant and product (soluble in the dispersed phase) are equal so that there is no change in the dispersed phase flow rate and hence in the holdup and effective interfacial area; there is no resistance in the dispersed phase. (iii) The dispersed phase is pure and the product is insoluble in the dispersed phase; time/height required for complete disappearance of droplets to be calculated.
moval in liquid-liquid reactors, and hence possibilities of maintaining isothermal conditions exist.
Batch Reactors In the design of batch reactors all the cases mentioned in Table I and subcases a and b mentioned in Table I1 have been considered. The analytical expressions for the different cases considered are given in Table 111. We assume that: (i) both the liquid phases are completely backmixed; (ii) the physical properties of liquids remain unchanged during the operation; and (iii) temperature remains constant throughout the period of operation. Consideringcase (i) of Table I with subcase (a) of Table 11, the material balance at any time can be written as
= NAaV
0 1984
American Chemical Society
