UNIFAC group parameters for the interaction between CH2 and CF2 (c) and CH2 and CF3 were obtained using experimental liquid-liquid equilibrium
data for hydrocarbon - perfluorodecaline (PFD) and hydrocarbon - perfluoromethylcyclohexane (PFMCH) systems.
Some difficulties were experienced on the use of the UNIFAC method with those particular systems, namely the group parameters dependence on
the length of the hydrocarbon chain.
Attempts were made to correlate UNIFAC parameters with the number of carbon atoms and temperature and the results compared with those obtained with NRTL equations

Gil, M. G. Bernardo

Soares, Luís J. S.

Universidade do Minho: RepositoriUM

t). re, •ms) 1114) 04/1 "SOME DIFFICULTIES ON THE APPLICATION OF THE UNIFAC HODEL FOR THE PREDICTION OF LIQUID-LIQUID EQUILIBRIUM COMPOSITIONS" M. G. BERNARDO GIL*; L.J.S. SOARES** *C.P.Q.U.T.L.-IST-1096 LISBOA CODEX **UNIVERSIDADE DO MINHO- L.PACO-4719 BRAGA CODEX ABSTRACT UNIFAC group parameters for the interactiOn between CH2 and CF2 (c) and CH2 .and CF3 were obtai ned using experimental liquid-liquid equilibrium data for hydrocarbon - perj1uorodecaline (PFD) and hydrocarbon - perfluoromethyZcyclohexane (PFMCH) systems. Some difficulties were experienced on the use of the UNIFAC method with those particular sy!!_ terns, name ly the group parameters dependence on the Length of the hydrocarbon chain. Attempts were made to correlate UNIFAC pa-rameters with the number of carbon atoms and tem-perature and the results compared with those obtai ned with NRTL equations. INTRODUCTION One of the· basic assumptions of the "cortri bution of groups" method is that the interactions between molecules can be obtained adding the cont~ but ion of a 11 the interactions between the molecu-les functional groups. Therefore the properties of a liquid mixture depend both on the interaction between groups and the size and shape of those groups . The relatively small number of functional groups that need to be considered, when compared with the number of mixtures of industrial interest makes any contribution method attractive particu-larly in a preliminary study of a project : once the group interaction and size parameters are ob-tained we are able to predict activity coeffic~s and phase equilibrium data for a particular mixt~ re without any experimental results. UNIFAC is one of such methods, combining the solution of groups concept with the UNIQUACm£ del. The calculation of the molecular activity co~ fficients is separated into two parts: a combina~ rial part, essentially due to differences in size ... / ... 04/2 and shape of the molecules in the mixture, and a residual part essentially due to energetic intera. ctions. Fredenslund et al (1975, 1977), Jorgensen et al (1979), Gmehling et al (1982), Macedo et al (1983) ·present values of interaction parameters s table for vapor-liquid equilibrium data calculat;. ons, and Magnussen et al (1981) published a diff~ rent set of values adequate to the calculation of liquid-liquid equilibrium data. Perfluorocarbon/hydrocarbon systems are particularly adequate for the assessment of any co rrelating equation becaus.e ternary and quaternary mixtures change 5\ll'i fty from \Ype to type of equ il i briump~ ttern o9er a small temperature range. The experi-mental liquid-liquid equilibrium data of Bernardo--Gil (1984 a, b, 1985), Packer (1979) and Soares ( 1972) and vapor-liquid equilibrium data of Packe (1970) and Soares (1972) were used in the present study. CALCULATION PROCEDURES . METYODS USING A SYSTEM OF NON-LINEAR EQUATIONS Combining the thermodynamic condition of equilibrium (1) with the stoichiometric relation (2) yields a system of N non-linear equations: .tn (yil xil) - .tn ( Y i 2 x i 2) 0 i = 1 ,N (1) N E Xij = J= 1 ,2 ( 2) i=l y 1j and xij being the activity coefficient and com . METHODS USING AN OBJECTIVE FVNCTION UNJFAC parameters were also obtained corr~ lating all available mutual solubility data for ' I PFD/n-alkanes, and PFMCH/n-alkanes, assuming tern~ rature dependent parameters (equation 4) and using a Nelder-Mead minimization procedure coupled vtith one of the following objective functions: ~1 N !' x. 2 2 E 1: [in (~) - i n (- 1-) ] k=l i=l yi2 Xil ( 5) a .era. sen al S SIJi ati. ffe. of e y co ary 1111P! position of component i in phase j. Selecting an activity coefficient - composition relationship (3}, such as A being the adjustable parameters and T the tem-L perature, it is possible to solve the system of N non-linear equations. A Newton-Raphson technique was used to determine both the parameters, from mu tual solubility data, and the predicted equil ibri-um compositions for a binary or multicomponent mi~ ture, once the correlating equation parameters ~ were known. ri- Having calculated the parameters from.. the rdo- experimental data for a given binary mixture, they ~s were then correlated with the temperature through: ;Jeer mt AK = c + d.T ( 4) 04/3 M N 2 2 F2 = E E ~ ( xcal - xexp ] " iJ'Ic iJ' Ic k=l i=l J•l (6) with 3M> L, M being the available number of tie--line data, N the number of components and L the number of parameters. The objective function F2 yi elds better a-greement between experimental and calculated comp£ sit ions, but requires a much longer computing ti~ So F 1 was used at the initial stages of the mini-mization procedure changinq later to F . 2. APPLICATION TO PERFLUOROCARBON/HYDROCARBON MIXTURES th For PFD/n-alkane mixtures the interaction parameters between the groups cH 3, CH 2, cF 2(c) and CF(c) must be taken in account. Considering : (7) 0 (8) (9) ( 10) • 04/4 the interaction parameters aCH ICF (c) and aCF (c)ICH can be obtained from mutual solubility data for any 2 2 2 2 PFDin-alkane system. For PFMCHin-alkane mixturesthe interaction parameters between the groups CH3, CH 2, CF 2(c), CF(c) and CF3 must be accounted for. Considering the previous results and: 0 ( 11) ( 12) (13) the interaction parameters aCH ICF and aCF /CH can be obtained from mutual solubility data for anyPFMOf 2 3 3 2 In-alkane mixture. Having calculated the parameters it should be possible to predict the mutual solubility data for any other PFDin-alkane. The analysis of PFDihydrocarbon and PFMCHihydrocarbon equilibrium data revealed however significant differences between the group interaction parameters obtained from €Xperimental dab determined for each system. The following alternative approaches were then used to overcome this problem and the results were compared in terms of the root man square diviations (RMSD) between predicted and experimental compositirns a) simultaneous correlation of all available mutual solubility data for PFDialkanes, allowing for the temperature dependence of the interaction parameters; b) analysis of the parameter dependence on the number of carbon atoms of the alkane (Nc) and the temperature (T): (14) with Aij' Bij and Cij temperature dependent. Using the calculated parameters, together with those recommended by Jorgensen et al (1979) for CH 2=CHICH 2 and PFD 1 PFMCHin-alkane mutual solubility data, the group interaction parameters for CH2=CH/ ICF 2(c) and CH 2=CH/CF 3 were calculated. Recommended parameters were published elsewere (Bernardo-Gil and Soares 1984, 1985 ) . c) 1) 2) 3) !re ioos: for te I) 1/ RESULTS For comparative purposes the calculated RMSD values for binary mixtures are included in TA BLE 1, together with those obtained using: . the NRTL and UNIQUAC equations; _ cH 2/CF 2 and CF 2/ CH 2 parameters recommen ded by Gmehling et al (1982). 04/5 According to Shapovalov and Yurkin (1983) the assumption of aCH /CH = aCH /CH = 0 leads to 2 3 3 2 the hypothesis, contradictory to the experiment, of athermal hydrocarbon mixtures. On that basis they recommended the use of non-zero interaction parameters between groups CH 3 and CH 2, calculated from hydrocarbon-hydrocarbon phase equilibrium da-ta. All the calculations were rev10rked on that ba-sis (TABLE l) but the initial problem was not over come: experimental data for each perfluorocarbon/ hydrocarbon binary leads to a different set of group interaction parameters. TABLE 2 presents some results for multi-component systems, using UNIFAC model and, forco!!! parative purposes, RMSD values obtained with the NRTL and UNIQUAC equations are also included Bernardo-Gil and Soares, 1984 a, b; 1985 ). Experimental vapor-liquid equilibrium da-ta were determined by Packer (1970), for n-hepta-ne/PFO, 1-heptene/PFO, PFMCH/n-heptane and PFMCH/ /1-heptene at 700 rrffi-lg and Soares ( 1972) for PFI"CH/n-hexane and PFMCH/1-hexene at 700 rmflg and 55°C • RMSO values between experimental and calc~ lated vapor composition (Y), temperature (T) and • pressure (P), for UN!FAC model ... / ... CONCLUSIONS The conclusions can be SUITJllarized as fo]~: l, The RMSD values, between experimental and calcu lated compositions, are, in general, much lar-ger for the UNIFAC model than for the NRTL and UNI~UAC equations; 2. There is no set of interaction parameters that can, with accuracy, represent all the binary systems considered; 3. The simultaneous correlation of the available binary mutual solubility is not recoiTJllended, al though the parameters so ca 1 cu l a ted all ow, in some particular cases, a better agreement bet-ween predicted and experimental vapor-liquid equilibrium data; 4. The correlation of group interaction parameters with the number of carbon atomd of the hydroca! bon improves significantly the prediction of bi nary and multicomponent data ; 5. The parameters obtained from liquid-liquid equl librium data do not represent vapor-liquid equl librium data accurately; 6. The larger deviations found with UNIFAC for PFIY /alkene and PFMCH/alkene mixtures were expec-ted : CH 2=CH/CF 3 and CH 2=CH/CF 2(c) interactions were the last to be accounted for, using the values previously assumed for all the other groups. 04/6 TABLE 1: RMSD (. 103) vaLues for per fLuorocarbon/hydrocarbon binary mixtures using NRTL , UNIQUAC an, UNIFAC parame ters. UNIFAC EQUATION --SYSTn1 PFDin-hexane PFDin-heptane PFDin-octane PFDin-nonane PFD/1-hexene PFDI1-heptene POCHin-hexane FfM:H;h-hepta ne FFMCHin-octane fHICH;h- nona ne FfMCH11-hexene FfM:H/1-heptene NRTL EQUATION 13.4 7.9 6.0 10.0 6.7 5.6 3. 7 10.9 8.3 8.3 7.4 6.3 UNIQUAC EQUATION 7.4 9.6 13. 1 7.8 6.0 7.7 4.0 12.3 6.9 5.7 6.0 10.0 SI~1UL T. CORREL. 37.3III 29.2 21 , 4 IV 42.0 25.4v 22.6 45.9v 39.7 I I I 36.4II 78.6I 36.4v 33. 7I a .. =f(N) lJ c 7.8 12.2 45.3 8.4 34.0 111 36.8 11 18.2 16. 1 45.3 36.1 32.0VI 83 .4~II I Gmeh 1 i ng PAR. r I<U~1 t.ACH. BTif."S1, et a1. a = 01 ShaPQi 58.8 11 42.4IV 83.2IV 60.0IV 40.6IV 49.6IV 56.2 111 CH3/CH2 and YL -7.5 11.3 12. 1 I 3.5 4.0 5.8 10.3 5.0 16. 18. 12, 4. 4. 1 7.8 13.9 SA I I- VIII . 1 - 8 tie lines (close to C.S.T.) are not included in the calculation . TABLE 2: RMSD ( . 1 o3) vaLues for some ternC11'y and quaternary PFD / hydrocarbons and PFMCH !hydrocarbons systems. SYSTDI PFD/1-heptenel n-hexane PFD/1-heptenel n-heptane PFD/1-heptenel n-heptanel In-hexane PFMCH/1 - hepteneln-hexane PFMCH/1-hepteneln-heptane PFMCH/1-heptene/n-heptanel In -hexane TEMP. 15 25 15 25 15 25 15 25 15 25 15 TYPE I I I II I I I I I I I I I II II NRTL EQUATION 5.8 7.0 1.4 3.9 10.4 11.6 14.3 15.4 5.2 9.8 12. 1 II - number of tie-lines not included in the calculation. * -convergence was only found for M ~ 3 tie-lines. UNIQUAC EQUATION 9.2 8.6 1 . 5 3.9 17. 1 13.0 17.2 32.1 4.4 13.9 18.0 UNIFAC . EQUATION S 111\JLT. CORREL. 18.7 43.3 19.2 13.0 35.2 27.3 66.8 4 7.4 26.2 44.4 * 16.1 15.5 1.8 4,0 25.4 15.2 31.3 50.0 30. 4!1 41.4 20.0 '·· ... 04/8 are compared with those obtained with the NRTL and UNIQUAC parameters determined from vapor-l~id equilibrium data (VLE) and from liquid-liquid equi librium data (LLE) (TABLE 3). ACKNOWLEDGMENTS The authors want to express their grati-tude to Instituto Nacional de lnvestigacao Cientl fica, that through the CQPA (Universidade do ~1int-o) and C.P.Q. (Universidade Tecnica de Lisboa), su-pport this work. The computing facilities offered by the Centro de Informatica (I.S.T.) are also gratefully acknowledged. REFERENCES Bernardo-Gil, M.G. and Soares, L.J.S., 1984 a, 7Q Encontro de Quimica, C0-13, Lisboa . Bernardo-Gil, M.G. and Soares, L.J.S., 1984 b, CHISA'84, 485, Praga. Bernardo-Gil, M.G. and Soares, L.J.S., 1985 to be published. Fredenslund, A., Jones, R.L. and Pransnitz, J.M. l975~IChE J., Il_, 1086. Fredenslund, A., .Gmehl ing, J., and Rasmussen, P. 1977, "Vapour-liquid equilibria using UNIFAC", Elsevier, Amsterdam. Gmehling, J., Rasmussen, P. and Fredenslund, A., 1982, Ind. Eng. Chern. Proc. Des. Dev., ~. 118. Jorgensen, S.S., Kolbe, B., Gmehling, J. and Rasmussen, P., 1979, Ind. Eng. Chern. Proc. Des. Dev., ~. 714. Macedo, E.A., Weidlich, U., Gmehling, J. and Rasmussen, P., 1983, Ind. Eng. Chern. Proc. Des. Dev., 22. 676. Magnussen, T., Rasmussen, P. and Fredenslund, A. 1981, Ind. Eng. Chern. Proc. Des. De., 20, 331. Packer, L.G., 1970, Ph. D. Thesis, University of Birmingham. Shapovalov, M.P. and Yurkin, V. G., 1983, J. Apll. Chern. (USSR), 56 2631. Soares, L.J.S., 1972, Ph.D. Thesis, Univ.Birminghalll 

Some difficulties on the application of the UNIFAC model for the prediction of liquid-liquid equilibrium compositions

t). 
re, 
•ms) 
1114) 
04/1 
"SOME DIFFICULTIES ON THE APPLICATION OF THE UNIFAC HODEL FOR 
THE PREDICTION OF LIQUID-LIQUID EQUILIBRIUM COMPOSITIONS" 
M. G. BERNARDO GIL*; L.J.S. SOARES** 
*C.P.Q.U.T.L.-IST-1096 LISBOA CODEX 
**UNIVERSIDADE DO MINHO- L.PACO-
4719 BRAGA CODEX 
ABSTRACT 
UNIFAC group parameters for the interactiOn 
between CH2 and CF2 (c) and CH2 .and CF3 were obtai 
ned using experimental liquid-liquid equilibrium 
data for hydrocarbon - perj1uorodecaline (PFD) and 
hydrocarbon - perfluoromethyZcyclohexane (PFMCH) 
systems. 
Some difficulties were experienced on the 
use of the UNIFAC method with those particular sy!!_ 
terns, name ly the group parameters dependence on 
the Length of the hydrocarbon chain. 
Attempts were made to correlate UNIFAC pa-
rameters with the number of carbon atoms and tem-
perature and the results compared with those obtai 
ned with NRTL equations. 
INTRODUCTION 
One of the· basic assumptions of the "cortri 
bution of groups" method is that the interactions 
between molecules can be obtained adding the cont~ 
but ion of a 11 the interactions between the molecu-
les functional groups. Therefore the properties of 
a liquid mixture depend both on the interaction 
between groups and the size and shape of those 
groups . 
The relatively small number of functional 
groups that need to be considered, when compared 
with the number of mixtures of industrial interest 
makes any contribution method attractive particu-
larly in a preliminary study of a project : once 
the group interaction and size parameters are ob-
tained we are able to predict activity coeffic~s 
and phase equilibrium data for a particular mixt~ 
re without any experimental results. 
UNIFAC is one of such methods, combining 
the solution of groups concept with the UNIQUACm£ 
del. The calculation of the molecular activity co~ 
fficients is separated into two parts: a combina~ 
rial part, essentially due to differences in size 
... / ... 
04/2 
and shape of the molecules in the mixture, and a 
residual part essentially due to energetic intera. 
ctions. 
Fredenslund et al (1975, 1977), Jorgensen 
et al (1979), Gmehling et al (1982), Macedo et al 
(1983) ·present values of interaction parameters s 
table for vapor-liquid equilibrium data calculat;. 
ons, and Magnussen et al (1981) published a diff~ 
rent set of values adequate to the calculation of 
liquid-liquid equilibrium data. 
Perfluorocarbon/hydrocarbon systems are 
particularly adequate for the assessment of any co 
rrelating equation becaus.e ternary and quaternary 
mixtures change 5\ll'i fty from \Ype to type of equ il i briump~ 
ttern o9er a small temperature range. The experi-
mental liquid-liquid equilibrium data of Bernardo-
-Gil (1984 a, b, 1985), Packer (1979) and Soares 
( 1972) and vapor-liquid equilibrium data of Packe 
(1970) and Soares (1972) were used in the present 
study. 
CALCULATION PROCEDURES 
. METYODS USING A SYSTEM OF NON-LINEAR EQUATIONS 
Combining the thermodynamic condition of 
equilibrium (1) with the stoichiometric relation 
(2) yields a system of N non-linear equations: 
.tn (yil xil) - .tn ( Y i 2 x i 2) 0 i = 1 ,N (1) 
N 
E Xij = J= 1 ,2 
( 2) 
i=l 
y 1j and xij being the activity coefficient and com 
. METHODS USING AN OBJECTIVE FVNCTION 
UNJFAC parameters were also obtained corr~ 
lating all available mutual solubility data for ' 
I 
PFD/n-alkanes, and PFMCH/n-alkanes, assuming tern~ 
rature dependent parameters (equation 4) and using 
a Nelder-Mead minimization procedure coupled vtith 
one of the following objective functions: 
~1 N !' x. 2 2 
E 1: [in (~) - i n (- 1-) ] 
k=l i=l yi2 Xil 
( 5) 
a 
.era. 
sen 
al 
S SIJi 
ati. 
ffe. 
of 
e 
y co 
ary 
1111P! 
position of component i in phase j. Selecting an 
activity coefficient - composition relationship 
(3}, such as 
A being the adjustable parameters and T the tem-
L 
perature, it is possible to solve the system of N 
non-linear equations. A Newton-Raphson technique 
was used to determine both the parameters, from mu 
tual solubility data, and the predicted equil ibri-
um compositions for a binary or multicomponent mi~ 
ture, once the correlating equation parameters ~ 
were known. 
ri- Having calculated the parameters from.. the 
rdo- experimental data for a given binary mixture, they 
~s were then correlated with the temperature through: 
;Jeer 
mt AK = c + d.T ( 4) 
04/3 
M N 2 2 
F2 = E E ~ ( xcal - xexp ] 
" iJ'Ic iJ' Ic k=l i=l J•l 
(6) 
with 3M> L, M being the available number of tie-
-line data, N the number of components and L the 
number of parameters. 
The objective function F2 yi elds better a-
greement between experimental and calculated comp£ 
sit ions, but requires a much longer computing ti~ 
So F 1 was used at the initial stages of the mini-
mization procedure changinq later to F . 2. 
APPLICATION TO PERFLUOROCARBON/HYDROCARBON MIXTURES 
th 
For PFD/n-alkane mixtures the interaction parameters between the groups cH 3, CH 2, cF 2(c) and CF(c) 
must be taken in account. Considering : 
(7) 
0 (8) 
(9) 
( 10) 
• 
04/4 
the interaction parameters aCH ICF (c) and aCF (c)ICH can be obtained from mutual solubility data for any 
2 2 2 2 
PFDin-alkane system. 
For PFMCHin-alkane mixturesthe interaction parameters between the groups CH3, CH 2, CF 2(c), CF(c) 
and CF3 must be accounted for. Considering the previous results and: 
0 ( 11) 
( 12) 
(13) 
the interaction parameters aCH ICF and aCF /CH can be obtained from mutual solubility data for anyPFMOf 
2 3 3 2 
In-alkane mixture. 
Having calculated the parameters it should be possible to predict the mutual solubility data for 
any other PFDin-alkane. The analysis of PFDihydrocarbon and PFMCHihydrocarbon equilibrium data revealed 
however significant differences between the group interaction parameters obtained from €Xperimental dab 
determined for each system. 
The following alternative approaches were then used to overcome this problem and the results were 
compared in terms of the root man square diviations (RMSD) between predicted and experimental compositirns 
a) simultaneous correlation of all available mutual solubility data for PFDialkanes, allowing for 
the temperature dependence of the interaction parameters; 
b) analysis of the parameter dependence on the number of carbon atoms of the alkane (Nc) and the 
temperature (T): 
(14) 
with Aij' Bij and Cij temperature dependent. 
Using the calculated parameters, together with those recommended by Jorgensen et al (1979) for 
CH 2=CHICH 2 and PFD 1 PFMCHin-alkane mutual solubility data, the group interaction parameters for CH2=CH/ 
ICF 2(c) and CH 2=CH/CF 3 were calculated. 
Recommended parameters were published elsewere (Bernardo-Gil and Soares 1984, 1985 ) . 
c) 
1) 
2) 
3) 
!re 
ioos: 
for 
te 
I) 
1/ 
RESULTS 
For comparative purposes the calculated 
RMSD values for binary mixtures are included in TA 
BLE 1, together with those obtained using: 
. the NRTL and UNIQUAC equations; 
_ cH
2
/CF
2 
and CF 2/ CH 2 parameters recommen 
ded by Gmehling et al (1982). 
04/5 
According to Shapovalov and Yurkin (1983) 
the assumption of aCH /CH = aCH /CH = 0 leads to 
2 3 3 2 
the hypothesis, contradictory to the experiment, 
of athermal hydrocarbon mixtures. On that basis 
they recommended the use of non-zero interaction 
parameters between groups CH 3 and CH 2, calculated 
from hydrocarbon-hydrocarbon phase equilibrium da-
ta. All the calculations were rev10rked on that ba-
sis (TABLE l) but the initial problem was not over 
come: experimental data for each perfluorocarbon/ 
hydrocarbon binary leads to a different set of 
group interaction parameters. 
TABLE 2 presents some results for multi-
component systems, using UNIFAC model and, forco!!! 
parative purposes, RMSD values obtained with the 
NRTL and UNIQUAC equations are also included 
Bernardo-Gil and Soares, 1984 a, b; 1985 ). 
Experimental vapor-liquid equilibrium da-
ta were determined by Packer (1970), for n-hepta-
ne/PFO, 1-heptene/PFO, PFMCH/n-heptane and PFMCH/ 
/1-heptene at 700 rrffi-lg and Soares ( 1972) for 
PFI"CH/n-hexane and PFMCH/1-hexene at 700 rmflg and 
55°C • RMSO values between experimental and calc~ 
lated vapor composition (Y), temperature (T) and 
• pressure (P), for UN!FAC model ... / ... 
CONCLUSIONS 
The conclusions can be SUITJllarized as fo]~: 
l, The RMSD values, between experimental and calcu 
lated compositions, are, in general, much lar-
ger for the UNIFAC model than for the NRTL and 
UNI~UAC equations; 
2. There is no set of interaction parameters that 
can, with accuracy, represent all the binary 
systems considered; 
3. The simultaneous correlation of the available 
binary mutual solubility is not recoiTJllended, al 
though the parameters so ca 1 cu l a ted all ow, in 
some particular cases, a better agreement bet-
ween predicted and experimental vapor-liquid 
equilibrium data; 
4. The correlation of group interaction parameters 
with the number of carbon atomd of the hydroca! 
bon improves significantly the prediction of bi 
nary and multicomponent data ; 
5. The parameters obtained from liquid-liquid equl 
librium data do not represent vapor-liquid equl 
librium data accurately; 
6. The larger deviations found with UNIFAC for PFIY 
/alkene and PFMCH/alkene mixtures were expec-
ted : 
CH 2=CH/CF 3 and CH 2=CH/CF 2(c) interactions were 
the last to be accounted for, using the values 
previously assumed for all the other groups. 
04/6 
TABLE 1: RMSD (. 103) vaLues for per fLuorocarbon/hydrocarbon binary mixtures using NRTL , UNIQUAC an, 
UNIFAC parame ters. 
UNIFAC EQUATION --
SYSTn1 
PFDin-hexane 
PFDin-heptane 
PFDin-octane 
PFDin-nonane 
PFD/1-hexene 
PFDI1-heptene 
POCHin-hexane 
FfM:H;h-hepta ne 
FFMCHin-octane 
fHICH;h- nona ne 
FfMCH11-hexene 
FfM:H/1-heptene 
NRTL 
EQUATION 
13.4 
7.9 
6.0 
10.0 
6.7 
5.6 
3. 7 
10.9 
8.3 
8.3 
7.4 
6.3 
UNIQUAC 
EQUATION 
7.4 
9.6 
13. 1 
7.8 
6.0 
7.7 
4.0 
12.3 
6.9 
5.7 
6.0 
10.0 
SI~1UL T. 
CORREL. 
37.3III 
29.2 
21 , 4 IV 
42.0 
25.4v 
22.6 
45.9v 
39.7 I I I 
36.4II 
78.6I 
36.4v 
33. 7I 
a .. =f(N) 
lJ c 
7.8 
12.2 
45.3 
8.4 
34.0 111 
36.8 11 
18.2 
16. 1 
45.3 
36.1 
32.0VI 
83 .4~II I 
Gmeh 1 i ng PAR. r I<U~1 t.ACH. BTif."S1, 
et a1. a = 01 ShaPQi 
58.8 11 
42.4IV 
83.2IV 
60.0IV 
40.6IV 
49.6IV 
56.2 111 
CH3/CH2 and YL -7.5 
11.3 
12. 1 I 
3.5 
4.0 
5.8 
10.3 
5.0 
16. 
18. 
12, 
4. 
4. 1 
7.8 
13.9 
SA 
I 
I- VIII . 1 - 8 tie lines (close to C.S.T.) are not included in the calculation . 
TABLE 2: RMSD ( . 1 o3) vaLues for some ternC11'y and quaternary PFD / hydrocarbons and PFMCH !hydrocarbons 
systems. 
SYSTDI 
PFD/1-heptenel n-hexane 
PFD/1-heptenel n-heptane 
PFD/1-heptenel n-heptanel 
In-hexane 
PFMCH/1 - hepteneln-hexane 
PFMCH/1-hepteneln-heptane 
PFMCH/1-heptene/n-heptanel 
In -hexane 
TEMP. 
15 
25 
15 
25 
15 
25 
15 
25 
15 
25 
15 
TYPE 
I I 
I 
II 
I I 
I I I 
I I 
I I 
II 
II 
NRTL 
EQUATION 
5.8 
7.0 
1.4 
3.9 
10.4 
11.6 
14.3 
15.4 
5.2 
9.8 
12. 1 
II - number of tie-lines not included in the calculation. 
* -convergence was only found for M ~ 3 tie-lines. 
UNIQUAC 
EQUATION 
9.2 
8.6 
1 . 5 
3.9 
17. 1 
13.0 
17.2 
32.1 
4.4 
13.9 
18.0 
UNIFAC . EQUATION 
S 111\JLT. 
CORREL. 
18.7 
43.3 
19.2 
13.0 
35.2 
27.3 
66.8 
4 7.4 
26.2 
44.4 
* 
16.1 
15.5 
1.8 
4,0 
25.4 
15.2 
31.3 
50.0 
30. 4!1 
41.4 
20.0 
'·· 
... 
04/8 
are compared with those obtained with the NRTL 
and UNIQUAC parameters determined from vapor-l~id 
equilibrium data (VLE) and from liquid-liquid equi 
librium data (LLE) (TABLE 3). 
ACKNOWLEDGMENTS 
The authors want to express their grati-
tude to Instituto Nacional de lnvestigacao Cientl 
fica, that through the CQPA (Universidade do ~1int-o) 
and C.P.Q. (Universidade Tecnica de Lisboa), su-
pport this work. 
The computing facilities offered by the 
Centro de Informatica (I.S.T.) are also gratefully 
acknowledged. 
REFERENCES 
Bernardo-Gil, M.G. and Soares, L.J.S., 1984 a, 
7Q Encontro de Quimica, C0-13, Lisboa . 
Bernardo-Gil, M.G. and Soares, L.J.S., 1984 b, 
CHISA'84, 485, Praga. 
Bernardo-Gil, M.G. and Soares, L.J.S., 1985 to 
be published. 
Fredenslund, A., Jones, R.L. and Pransnitz, J.M. 
l975~IChE J., Il_, 1086. 
Fredenslund, A., .Gmehl ing, J., and Rasmussen, P. 
1977, "Vapour-liquid equilibria using UNIFAC", 
Elsevier, Amsterdam. 
Gmehling, J., Rasmussen, P. and Fredenslund, A., 
1982, Ind. Eng. Chern. Proc. Des. Dev., ~. 118. 
Jorgensen, S.S., Kolbe, B., Gmehling, J. and 
Rasmussen, P., 1979, Ind. Eng. Chern. Proc. Des. 
Dev., ~. 714. 
Macedo, E.A., Weidlich, U., Gmehling, J. and 
Rasmussen, P., 1983, Ind. Eng. Chern. Proc. Des. 
Dev., 22. 676. 
Magnussen, T., Rasmussen, P. and Fredenslund, A. 
1981, Ind. Eng. Chern. Proc. Des. De., 20, 331. 
Packer, L.G., 1970, Ph. D. Thesis, University of 
Birmingham. 
Shapovalov, M.P. and Yurkin, V. G., 1983, J. 
Apll. Chern. (USSR), 56 2631. 
Soares, L.J.S., 1972, Ph.D. Thesis, Univ.Birminghalll 


English

http://repositorium.sdum.uminho.pt/bitstream/1822/26384/1/CHEMPOR85_BernardoGil.pdf

Some difficulties on the application of the UNIFAC model for the prediction of liquid-liquid equilibrium compositions

Abstract

Similar works

Full text

Available Versions

Universidade do Minho: RepositoriUM

Universidade do Minho: RepositoriUM

Universidade do Minho: RepositoriUM