A Modified Unifac Model

178

Ind. Eng. Chem. Res. 1993,32, 178-193

A Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties Jurgen Gmehling,* Jiding Li,’ and M a r t i n Schiller Lehrstuhl fur Technische Chemie (FB9),Universitdt Oldenburg, Postfach 2503, 0-2900 Oldenburg, F.R.G.

Several years ago a modified UNIFAC (Dortmund, FRG) method was proposed, which shows various advantages when compared with the group contribution methods UNIFAC or ASOG; the latter are used worldwide for the synthesis and design of rectification processes. These advantages were reached by using a modified combinatorial part and by using a large data base to fit temperature-dependent group interaction parameters simultaneously to vapor-liquid equilibrium (VLE),liquid-liquid equilibrium (LLE),hE, and ymdata. The main advantages of the modified UNIFAC method are a better description of the temperature dependence and the real behavior in the dilute region and that it can be applied more reliably for systems involving molecules very different in size. T o increase the range of its applicability, the temperaturedependent group interaction parameters of the modified UNIFAC have been fitted for 45 main groups using phase equilibrium information (VLE,hE,ym, LLE)stored in the Dortmund Data Bank. A comprehensive comparison with the results of other group contribution methods confirms the high reliability of the modified UNIFAC (Dortmund) method. Introduction The synthesis and design of separation processes requires a reliable knowledge of the phase behavior cf the system to be separated. For the description of multicomponent non-electrolyte systems, gE-modelsor equations of state can be applied using binary data alone. Experimental data are however often missing. In such cases group contribution methods such as ASOG (Derr and Deal, 1969; Kojima and Tochigi, 1979)or UNIFAC (Fredenslund et al., 1975,1977)can be successfully applied. These methods are developed for the prediction of vapoAiquid equilibria (VLE),so that the required group interaction parameters were mainly fitted to experimental VLE data stored in the Dortmund Data Bank (Gmehling, 1985,1991).The actual parameters of these methods were published by Hansen et al. (1991)and Tochigi et al. (1990). With the help of these methods it is possible to obtain reliable results for vapor-liquid equilibria, including azeotropic points. However poor results are often obtained when these methods are used for the prediction of the activity coefficients at infinite dilution (7-1, heats of mixing (hE),or systems with components very different in size. This is not surprising because VLE data normally cover only the concentration range 5-95 mol 9%. Furthermore, compounds of similar size are usually considered, and with VLE data from different authors no reliable information about the temperature dependence (e.g., hE data) can be derived. But for design purposes (determination of the number of theoretical stages), reliable information on the real behavior in the very dilute region is particularly important. For example, for positive deviation from Raoult’s law, the greatest separation effort is required for the removal of the last traces of the high boiling component at the top of the column (smallest values for the difference cyl2 - 1). Following the Gibbs-Helmholtz relation, a good description of the hE-valuesallows the use of the parameters across a larger temperature range (lower or higher temperatures), e.g., to account for the real behavior during the calculation of solid-liquid equilibria. The use of thermodynamic mixture information from compounds very different in size (e.g., y”-values) will allow an improved de-

scription of the real behavior of these kinds of mixtures (e.g., the removal of solvents by physical absorption using high boiling solvents). Modified forms of the UNIFAC method by Weidlich and Gmehling (1987)and Larsen et al. (1987)were proposed in order to overcome the aforementioned weaknesses. Apart from a modified combinatorial part, these methods introduce temperature-dependent group interaction parameters which were fitted to a data base (VLE, hE) much larger than that for the original UNIFAC method. In the version developed in Dortmund by Weidlich and Gmehling (1987),ymvalues were also used for fitting the parameters. In a comprehensive comparison by Gmehling et al. (1990),the great advantages of the modified forms of the UNIFAC method have already been demonstrated; the Dortmund, FRG, version was superior to the modified UNIFAC method developed in Lyngby, Denmark, by Larsen et al. (1987),particularly because more reliable ymresults were obtained. Apart from more reliable results for industrial applications, a broad range of applicability is also important. The existing parameter matrix for the modified UNIFAC (Dortmund) method was therefore extended with the help of the Dortmund Data Bank (DDB) and the integrated fitting routines. The results were then checked with the aid of a large data base and thoroughly compared with the results of other group contribution methods. The Modified UNIFAC Model In the modified UNIFAC (Dortmund) model, as in the original UNIFAC model, the activity coefficient is the s u m of a combinatorial and a residual part: In yi = In yci + In -yRi (1) The combinatorial part was changed in an empirical way to make it possible to deal with compounds very different in size: In yci = 1 - V’i

+ In V:

( ; (2))

- 5qi 1 - - + In

(2)

The parameter V: can be calculated by using the relative van der Waals volumes Rk of the different groups.

+ Permanent address: Department of Chemical Engineering, Tsinghua University, Peking, China.

o ~ ~ ~ - ~ ~ ~ ~ ~ ~ ~ 0~ 1993 z ~American ~ z - Chemical o i ~ ~Society ~ o ~ . o o ~ o

(3)

Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 179

All other parameters are calculated in the same way as for the original UNIFAC model; i.e. ri vi = Cxjrj

(4)

= CYk(i)Rk

(4a)

for appr. 3050 compounds

References for each type of data XYX

i

Fi

Pure Component Properties

x*x = VLE, LLE HE.ACT GLE CPE AZD appr 7700 references

Data on Mixtures Number of Isotherms or Isobars

The residual part can be obtained by using the following relations: In yiR= Cuk(')(lnrk - In rk(i)) (6) k

Vapor-Liquid Equilibria ( V L E ) Liquid-Liquid Equilibria ( LLE ) Heats of Mixing ( HE ) Activity Coefficients at Infinite Dilution ( ACT ) Gas Solubilities ( GLE ) Excess Heat Capacities ( CPE ) Azeotropic Data ( AZD )

14300 5600

8000 28500 values 5250 630 28000 values

Figure 1. Present status of the Dortmund Data Bank.

whereby the group area fraction 8, and group mole fraction X, are given by the following equations: Qmxm e,,, = n

c

Qnxn V,%j

(9)

In comparison to the original UNIFAC method, only the van der Waals properties were changed slightly, at the same time temperature-dependent parameters were introduced to permit a better description of the real behavior (activity coefficients) as a function of temperature.

Data Base Used for Fitting the Group Interaction Parameters The generation of reliable group interaction parameters requires the use of a large data base for fitting the required parameters. The construction of a computerized data compilation (DDB) was started at the University of Dortmund as early as 1973. The intention was to use the vast amount of published phase equilibrium information for the development or improvement of group contribution methods. At first, mainly VLE data were stored in computer readable form together with the pure component properties (e.g., Antoine constants, critical data, van der Waals properties, structural information) required for phase equilibrium calculations. Later, liquid-liquid equilibrium data (LLE), heats of mixing (hE),gas solubilities, excess heat capacities (cpE), activity coefficients at infinite dilution (7-1, and azeotropic data were added. These additions were partly carried out in collaboration with the research groups of Prof. Aa. Fredenslund (Lyngby, Denmark), Prof. A. G. Medina (Porto, Portugal), Prof. I. Kikic and Prof. P. Alessi (Trieste, Italy), and Prof. H. Knapp (Berlin, FRG). The present status of the DDB (Gmehling, 1985,1991) is shown in Figure 1. To obtain information about the real mixture behavior at low temperatures, the construction of a data bank for solid-liquid equilibria (SLE) is in progress. A great part of the data (ca. 50%)has been published in an evaluated and unified form in the different volumes of the DECHEMA Chemistry Data Series (Gmehling et al., 1977,1984; Tiegs et al.,

1986; Serrensen, 1979) and has been integrated in process simulators by a large number of chemical and petrochemical companies. To complete the data base and to fill, at least partially, the existing gaps in the data base, more than 100 hE-data sets using isothermal flow calorimetry and ca. 1000 ymvalues using gas-liquid chromatography and ebulliometry have been measured; in the case of the hE-data in particular, data at temperatures different from 25 OC where most of the hE-data were obtained and data for compounds containing new main groups (e.g., CCl,, ...) were measured.

Fitting Procedure The temperature-dependent parameters for the modified UNIFAC (Dortmund) method were obtained, as far as the required experimental data for the different thermodynamic properties were available in the DDB, by fitting the parameters simultaneously to VLE, hE, and 7data. In a few cases LLE and cpE-datawere also used. The parameter fitting procedure is shown in Figure 2. Using the DDB, the selection of the desired pure component and mixture data is quite simple. The procedure will be discussed for the arbitrary example of fitting alcohol-ester parameters. With the decision as to what group pair (in this example, alcohol-esters) should be fitted and what additional groups are allowed (in this case, alkane groups), a program (CODSNT) runs through the pure component data file (STOFF) to find all the code numbers used in the DDB for the different alcohols and esters with the help of stored structural information. The selected code numbers are then stored in files (STL-files 1 and 2) and are used to search the different binary data sets and to store the appropriate mixture data in different files (VLE, ACT, HE, CPE, LLE). Afterward the complete VLE data (x, y, P, T ) or isothermal xy-data ( x , y, T given) are checked for thermodynamic consistency using the programs KONSlSRK and KONSSSRK, while for other incomplete VLE data a flexible Legendre polynomial is used to fit the data. The files are then checked for plausibility with the help of other programs (XXXMOD). After a good distribution (compounds, temperature) of the systems has been reached, the final data files are used to fit the parameters and Rk- and Qk-values, whereby the van der Waah properties Rk and Qkof the different subgroups have almost always been fitted using alkane systems, e.g., alcohol-alkanes, ester-alkanes, etc. The fitting procedure involves the use of consistent VLE data (reliable Px-, Tx-,

180 Ind. Eng. Chem. Res., Vol. 32,No. 1, 1993

NEMA input

I

I

Figure 2. Procedure used for fitting the required group interaction parameters of the modified UNIFAC (Dortmund) method.

and isothermal xy-data) together with other mixture information to minimize the following objective function: J'(anm,bnm,Cnm8h,Qk)

= CAVLE + CAY"+

CAhE+ CAcpE + CALLE = min (11)

In the case of VLE, depending on the data type (complete, incomplete, etc.), it was necessary to define different relative deviations which contribute to the objective function. The contribution of the different types of data to the objective function is given in Table I. The following relations were used for calculating vapor-liquid equilibria (yi, Ki, ...):

The real behavior of the vapor phase was taken into account by using the Soave-R.edlich-Kwong equation of state (klZ= 0.0). In the case of carboxylic acids, chemical theory was applied using the dimerization constants given in the DECHEMA Chemistry Data Series (part 5 ) (Gmehling et al., 1977). During the fitting procedure (program NEMA), it is possible to change the weighting factors for the different types of binary data. For fitting the parameters the Simplex-Nelder-Mead method by Nelder and Mead (1965) is first used to obtain good initial values for the method by Marquardt (1963). In all cases the fitting procedure was started with constant group interaction parameters (two parameters). When enough information about the temperature dependence was available (hE, vLE(T),y"(T), LLE(T)), linear temperature-dependent parameters were fitted (four parameters) using the constant parameters as initial values. In the case of very strong temperature dependence, the number of fitted parameters was increased to six (quadratic temperature dependence) when sufficient information about the temperature dependence was

available (hE(T),cpE,besides VLE(T), 7"(T),LLE(T)). In this case the linear temperature-dependent parameters served as initial values for the fitting procedure. AU fitted parameters were used subsequently for a thorough test of the predicted results. Besides the deviation from the experimental data, the results were compared with other group contribution methods. The comparison was simplified by using programs which were able to check the results not only for group combinations but also for the whole DDB. The comparison was supported by helpful printed tables and graphical representations. If unsatisfactory results were obtained, the fitting procedure was restarted with modified weighting factors. During the fitting procedure data points or systems often had to be excluded. For this job (fitting of group interaction parameters, comparison of the predicted results, etc.) the DDB is the ideal tool, since all the required information (mixture data, pure component properties such as Antoine constants, critical data, structural information, etc.) for checking the thermodynamic consistency or fitting the required group interaction parameters can directly be called from direct access files. Since about 95% of the published hE-valueswere measured within the temperature range 10-50 OC, the fitted temperature-dependent group interaction parameters can lead to erroneous results when used outside the temperature range of the data base (in most cases 20-125 "C). Apart from the comparison of the calculated results with the experimental data, the reliability of the predicted hE-valuesand activity coefficients at low (190 K)and high temperatures (500 K) were checked using typical binary systems for the group combination under consideration. The reliability of the temperature extrapolation can be judged from this information. For unreasonable results, i.e., when very high positive or negative values for hEor ym(near zero or very large) were obtained, the parameters were, in most cases,fitted again. Most of these parameters can now be used with confidence. For some group combinations (e.g. alkane-alcohols at low temperatures),

Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 181 Table I. Contribution of the Different Types of Data to the Objective Function data type thermodmamic information constant 1 VLE (VLE) x,, Y1, p 2 VLE (VLE) X , ? YIP T 3 VLE (VLE) XI, p 4 VLE (VLE) x,, T 5 VLE (VLE) x11 Y, 6 7- (ACT) Y -, 7 hE (HE) x,, he 8 cpE (CPE) X I , CPE 9 LLE (LLE) x ;, x ff, VLE (data types 1, 2): 7th

AVLE= 2nw k-1 E fIrl (gm VLE (data types 3, 4):

1

AvLE=--C

nw

(

- Yik,calc Ytk

>'

pk p+-:dc

g m

nWk=l

2

)

VLE (data type 5):

AVLE = -

nw

(

2nwk=lI-1

Kik - K t k , d c

gvLE

K,k

7- (data type 6):

hE (data type 7):

cpE(data type 8):

LLE (data type 9):"

In the case of LLE, activity coefficienta at ca. four different temperatures for every system were used in the fitting procedure. The required activity coefficients in the coexisting phases were obtained by fitting temperature-dependentNRTL or UNIQUAC parameters to the LLE data from different authors stored in the Dortmund Data Bank using the program LLEOPT2 by Meyer and Gmehling (1991).

however, it is dangerous to use the parameters in a temperature range outside 20-125 "C. In the future the parameters marked by "+!", "-!", or "&!" will be revised, but, first, hE-data in the temperature range 50-180 "C will be measured for these systems using isothermal flow calorimetry. This experimental work is in progress (Gmehling and Meents, 1992). In comparison to the original UNIF'AC method four new main groups (cyclic hydrocarbons, cyclic ethers, chloroform, formic acid) were added to obtain more reliable results for systems containing these components. Thus, for example with the cyclic hydrocarbon group, hE-values different from zero are obtained for systems containing alkanes and cycloalkanes; with the cyclic ether group resulta are improved for systems with compounds such as dioxane, 1,4-tetrahydrofuran, dioxolane, etc. The same is true for systems containing chloroform and formic acid. Using the same main group for chloroform and the CC13

Table 11. Data Base Used for Fitting the Group Interaction Parameters VLE hE (a) Alcohol-Ester Systems total no. of data seta 169 91 2926 1504 total no. of data pointa no. of consistent data seta 63 temperature range ("C) 25-193 25-75 C-atoms alcohol 2-5 2-10 C-atoms ester 3-9 3-6

20-150 2-22: 2-4' 4-26; 3-6'

(b) Ester-Carboxylic Acid 35 total no. of data seta total no. of data points 463 no. of consistent data seta 6 25-155 temperature range ("C) C-atoms ester 3-13 C-atoms carboxylic acid 2-12

40-143 4-18," 3-6' 2-18," 2-4'

7-

188

Systems 1 13 52 35 3 2

Solvent. Solute.

group, e.g., for l,l,l-trichloroethane, strong negative deviation from Raoult's law and large negative hE-valuesare predicted (for example, for systems with acetone). But because of the missing hydrogen bond, the system acetone-l,l,l-trichlorothanebehaves very differently when compared with the system acetone-chloroform. Thus in contrast to the system acetone-chloroform, the system acetone-l, 1,l-trichloroethane shows positive deviation from Raoult's law and positive hE-values. The group combinations which now have group interaction parameters are shown in Figure 3. In this figure black squares characterize combinations for which, apart from sufficient VLE data, enough hE- and 7"-data for different compounds (e.g., different alcohols, different esters) were also available across a large temperature range for fitting the required group interaction parameters. Shaded squares are used in the parameter matrix when the data base was not fully satisfactory. However, even in these cases at least the data base used to fit the original UNIFAC parameters was applied. Examples for black and shaded squares are given in Table I1 for the ester-alcohol systems (black squares) and for the main group combination eaters with carboxylic acids (shaded squares). From Table I1 it can be seen that for alcohol-ester mixtures more than 4500 experimental data points were available within the temperature range 20-193 "C and that at the same time very different alcohols (ethanol4ocosanol) and eaters (methyl acetate-bis(2-ethylhexyl) sebacate) were applied to fit the parameters, whereby, with the use of 7"-data, information about compounds very different in size is included. For estel-carboxylic acids the data base is much smaller. The van der Waals properties of the different subgroups together with the group assignments are given in Table III. All the group interaction parameters obtained are listed in Table IV. While in the first paper by Weidlich and Gmehling (1987) parameters for only 15 group combinations and 6 main groups were presented, the parameters for 45 main groups and 530 group pairs are now available. This means that the Rk-and Qpalues and group interaction parameters given in Tables I11 and IV allow the prediction of the phase behavior of a large number of non-electrolyte systems of interest for the chemical industry.

Rssults A comprehensive comparison of the results of the different group contribution methods was carried out by Schiller (1992) using all the information stored in the DDB. Since the number of main groups and available group

182 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 Table 111. Rk-and Qk-Parametersand Group Assignment for the Modified UNIFAC (Dortmund) Method sample group assignment main group subgroup no. Rk Qk 1 'CHz"

2 'C=C"

3 "ACH" 4 'ACCHz" 5 'OH" 6 'CH30H" 7 'H20" 8 'ACOH" 9 'CHzCO" 10 'CHO" 11 "CCOO" 12 "HCOO" 13 "CHzO" 14 'CNHz"

15 "CNH" 16 "(C)3N" 17 'ACNHZ" 18 'Pyridine" 19 "CCN" 20 'COOH" 21 "CCl" 22 "CClZ" 23 'CCl," 24 'CCl," 25 "ACCl" 26 "CN02" 27 'ACNOZ" 28 "CSZ" 29 'CH3SH" 30 'furfural" 31 'DOH" 32 'I" 33 "Br" 34 'C=C" 35 'DMSO" 36 'ACRY" 37 'ClCC" 38 'ACF" 39 'DMF" 40 'CFZ"

CH, CH; CH C CHz=CH CH=CH CHz=C CH=C

c=c

ACH AC ACCH3 ACCHZ ACCH OH (PI OH (s) OH (t) CHBOH HZO ACOH CH&O CHzCO CHO CH3CO0 CHZCOO HCOO CH30 CHZO CHO CH3NHz CHzNH2 CHNHz CNH, CH3NH CHzNH CHNH CH3N CHzN ACNHZ C5H5N C5H4N C5H3N CH3CN CHzCN COOH CHzCl CHCl CCl CHzClz CHClz CClZ CCl, CCl, ACCl CH3N02 CHzNOz CHNOz ACNOz CSZ CHBSH CHZSH furfural DOH I Br CH=C CEC DMSO acrylonitrile Cl(C=C) ACF DMF HCON(CH2)z CF3 CFZ CF

1 2 3 4 5 6 7 8 70 9 10 11 12 13 14 81 82 15 16 17 18 19 20 21 22 23 24 25 26 28 29 30 85 31 32 33 34 35 36 37 38 39 40 41 42 44 45 46 47 48 49 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 71 72

73 74 75 76

0.6325 0.6325 0.6325 0.6325 1.2832 1.2832 1.2832 1.2832 1.2832 0.3763 0.3763 0.9100 0.9100 0.9100 1.2302 1.0630 0.6895 0.8585 1.7334 1.0800 1.7048 1.7048 0.7173 1.2700 1.2700 1.9000 1.1434 1.1434 1.1434 1.6607 1.6607 1.6607 1.6607 1.3680 1.3680 1.3680 1.0746 1.0746 1.1849 2.5000 2.8882 3.2211 1.5575 1.5575 0.8000 0.9919 0.9919 0.9919 1.8000 1.8000 1.8000 2.6500 2.6180 0.5365 2.6440 2.5000 2.8870 0.4656 1.2400 1.2890 1.5350 1.2990 2.0880 1.0760 1.2090 0.9214 1.3030 3.6000 1.oooO 0.5229 0.8814 2 . m 2.3810 1.2840 1.2840 0.8215

1.0608 0.7081 0.3554 O.oo00 1.6016 1.2489 1.2489 0.8962 0.4582 0.4321 0.2113 0.9490 0.7962 0.3769 0.8927 0.8663 0.8345 0.9938 2.4561 0.9750 1.6700 1.5542 0.7710 1.6286 1.4228 1.8000 1.6022 1.2495 0.8968 1.6904 1.3377 0.9850 0.9850 1.4332 1.0805 0.7278 1.1760 0.8240 0.8067 2.1477 2.2496 2.5000 1.5193 1.1666 0.9215 1.3654 1.0127 0.6600 2.5000 2.1473 1.7946 2.3778 3.1836 0.3177 2.5000 2.3040 2.2410 0.3589 1.0680 1.7620 1.3160 1.2890 2.4000 0.9169 1.4000 1.3000 1.1320 2.6920 0.9200 0.7391 0.7269 2.0930 1.5220 1.2660 1.0980 0.5135

hexane octane 2-methylpropane neopentane 1-hexene 2-hexene 2-methyl-1-butene 2-methyl-2-butene 2,3-dimethyl-2-butene naphthalene styrene toluene ethylbenzene isopropylbenzene 1-propanol 2-propanol tert-butanol methanol water phenol 2-butanone 2-pentanone propionic aldhyde butyl acetate methyl propionate ethyl formate dimethyl ether diethyl ether diisopropyl ether methylamine ethylamine isopropylamine tert-butylamine dimethylamine diethylamine diisopropylamine trimethylamine triethylamine aniline pyridine 2-methylpyridine 2,3-dimethylpyridine acetonitrile propionitrile acetic acid 1-chlorobutane 2-chloropropane tert-butyl chloride dichloromethane 1,l-dichloroethane 2,2-dichloropropane l,l,l-trichloroethane tetrachloromethane chlorobenzene nitromethane 1-nitropropane 2-nitropropane nitrobenzene carbon disulfide methanethiol ethanethiol furfural 1,2-ethanediol ethyl iodide ethyl bromide 1-hexyne 2-hexyne dimethyl sulfoxide acrylonitrile trichloroethylene hexafluorobenzene NJ-dimethylformamide NJ-diethylformamide l,l,l-trifluoroethane perfluorohexane perfluoromethylcyclohexane

2 CH3,4 CHZ 2 CH3,6 CHZ 3 CH3,l CH 4 CHB, 1 C 1 CH3,3 CH2,l CHz=CH 2 CH3,2 CH2,l CH=CH 2 CH3,l CH2,l C H 2 4 2 CH3,l CH=C 4 CH3,l C=C 8 ACH, 2 AC 1 CHz=CH, 5 ACH, 1 AC 5 ACH, 1 ACCH3 1 CH3,5 ACH, 1 ACCHZ 2 CH3,5 ACH, 1 ACCH 2 CH3, 1 CH2, 1 OH (p) 2 CH3,l CH, 1 OH (9) 3 CH3, 1 C, 1 OH (t) 1 CH30H 1 HzO 5 ACH, 1 ACOH 1 CH3,l CH2,l CH3CO 2 CH3,l CHp, 1 CHzCO 1 CH3,l CHZ, 1 CHO 1 CH3,3 CHZ, 1 CH3COO 2 CH3,l CHZCOO 1 CHR, 1 CH,. 1 HCOO 1 CH,, 1 CHjO 2 CH3,l CHP, 1 CHZO 4 CH3,l CH, 1 CHO 1 CHBNHZ 1 CH3,l CHzNHz 2 CHe, 1 CHNH, 3 CH,, 1 CNHz 1 CHB, 1 CH3NH 2 CH3,l CH2,l CHzNH 4 CH3,l CH, 1 CHNH 2 CH3,l CH3N 3 CH3,2 CH2,l CHZN 5 ACH, 1 ACNHz 1 C5HSN 1 CH3,l C5H4N 2 CH3,l C5H3N 1 CH3CN 1 CH3,l CHZCN 1 CH3,l COOH 1 CH3, 2 CHz, 1 CH,Cl 2 CH3, 1 CHCl 3 CH3, 1 CCl 1 CHzClz 1 CH3, 1 CHClz 2 CH3, 1 CC12 1 CH,. 1 CCL 1 cci4' 5 ACH, 1 ACCl 1 CH,NO, 1 CH,, 1 6Hz, 1 CHZNOz 2 CH3,l CHNOz 5 ACH, 1 ACNO,

cs2

1 1CHSH 1 CH,, 1 CHzSH 1 furfural 1 DOH 1 CH3,l CHZ, 1 I 1 CH3, 1 CH,, 1 Br 1 CH3,3 CH2,l C H 4 2 CH3,2 CHZ, 1 C 4 1 DMSO 1 acrylonitrile 1 CH=C, 3 Cl(C=C)

6 ACF 1 DMF 2 CH3, 1 HCON(CHz)z 1 CH3, 1 CF3 2 CF,. 4 CFo 1 CF,; 5 CF;, 1 CF

Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 183 Table I11 (Continued) main group 41 'COO" 42 'c-CH," 43 'C-CHZO" 44 'HCOOH" 45 "CHC13"

subgroup

coo

c-CHZ C-CH c-c C-CHZOCH~ c-CHzO[WIi z C-[CH21120[C~211/2 HCOOd CHCl,

no. 77 78 79 80 27 83 84 43 50

sample group assignment

Rk

Qk

1.6000 0.7136 0.3479 0.3470 1.7023 1.4046 1.0413 0.8000 2.4500

0.9000 0.8635 0.1071 O.oo00 1.8784 1.4000 1.0116 1.2742 2.8912

methyl acrylate cyclohexane methylcyclohexane 1,l-dimethylcyclohexane tetrahydrofuran 1,3-dioxane 1,3,5-trioxane formic acid chloroform

1 CHq, 1 CH,=CH, 1 COO 6 c-CH, 1 CHS, 5 c-CH~,1 C-CH 2 CH3, 5 c-CH,, 1 c-C 2 c-CH~,1 c-CH~OCH~ 1 c-CH~,2 ~-CH20[CH2]1/2 3 c-[CH211 20[CHZ11/2 1 HCOOd 1 CHCI,

Figure 3. Present status of the modified UNIFAC (Dortmund) parameter matrix.

interaction parameters is very different for the group contribution methods studied (ASOG by Tochigi et al. (1990), UNIFAC by Hansen et al. (1991), modified UNIFAC (Dortmund) (thiswork), modified UNIFAC (Lyngby) by Larsen et al. (1987)), there is also a difference in the total number of systems which can be predicted by the different methods. With the original and the modified UNIFAC (Dortmund) method, more systems can be predicted than with the ASOG or modified UNIFAC (Lyngby) method. The results for binary systems are summarized in Tables V-VIII. In these tables the results are given for compounds with a limited number of different main groups; furthermore the comparison was limited to the number of systems which could be calculated with the modified UNIFAC (Lyngby) method proposed. Since more systems can be predicted with the original UNIFAC and the modified UNIFAC (Dortmund) methods, the tables also contain deviations for all the systems which could be predicted with these latter methods. Tables V and VI provide the results for VLE (P< 5000 mmHg, cpvi/cpSi = 1). While in Table V the results are shown only for the data seta which passed two thermodynamic consistency

tests (Gmehling et al., 1977), in Table VI the deviations in vapor-phase mole fraction, temperature, and pressure are given for all binary data sets (P< 5000 mmHg, p v i / & = 1). From these results it is concluded that modified UNIFAC (Dortmund) gives the best results. When compared with the original UNIFAC method, which today is used in most of the commercial process simulators for VLE, a clear improvement can be recognized. An improvement in Ay = 0.5 mol % (36%), AT = 0.3 K (33%), and hp of ca. 6 mmHg (45%) is obtained. Also when comparison is made with the modified UNIFAC (Lyngby) method, better results are predicted for all the mentioned quantities. That the absolute deviations presented in Table VI are much larger than those in Table V is due to the fact that all data were considered and all experimental errors are included in the deviations calculated. Table VI1 shows the deviation between experimental and predicted heats of mixing data. Besides the results for 4900 data sets for the UNIFAC method and the modified UNIFAC (Dortmund) method, the deviations are also given for all predictable data sets. It can be seen that improved results are obtained for the modified UNIFAC

184 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 Table IV. n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Modified UNIFAC (Dortmund) Group Interaction Parameters"

m 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 41 42 +! 43 44 -! 45 3 4

5 6 7 -! 8 9 10 11 12 13 -! 14 *! 15 t! 16 *! 17 18 *! 19 20 *! 21 22 23 &! 24 25 26 28 a! 30 33 34 35 36 37 38 39

on,

(K)

189.66 114.20 7.3390 2777.0 2409.4 1391.3 1381.0 433.60 875.85 98.656 508.40 233.10 -164.04 350.58 -175.70 958.74 -9.2805 593.07 1182.2 401.00 -233.66 -653.74 267.51 -1385.0 2345.0 2383.0 24.330 465.90 577.70 897.70 559.90 527.70 477.50 -547.50 1662.0 334.50 468.50 406.20 342.00 1312.0 -680.95 79.507 1935.7 164.25 174.10 117.30 2649.0 -628.07 778.30 1207.0 179.80 476.25 980.74 309.80 733.30 1857.0 224.80 165.30 2800.0 13.502 634.85 -2026.1 498.90 -44.958 -204.51 616.62 -56.690 417.60 46.060 470.40 -19.820 -44.760 -174.60 179.70 967.90 141.10 388.40

brim -0,2723 0.9330 X lo-' -0.4538 -4.6740 -3.0099 -3.6156 -0.9977 0.1473 0.0 1.9294 -0.6215 -0.3155 4.9683 0.6673 X 10-I 1.8570 -0.1484 1.9682 0.7335 -3.2647 -0.7277 1.2561 4.5311 -1.7109 15.890 -13.200 -2.693 1.5210 -0.8557 0.9384 0.0 -0,3564 -0.4990 -0.6581 3.4570 0.0 0.9102 X -1.0420 0.6525 -1.6790 -3.6430 4.0194 0.7089 0.0 -0.2683 -0.5886 -0.8552 -6.5080

1o.ooo 0.1482 -1.9550 0.6991 0.0 -2.4224 0.0 -2.5090 -8.6530 0.0 0.0 -10.720 0.0 0.0 8.1549 -1.4870 0.0 0.0 -2.1164 9.8050 0.8726 X 10-1 1.5450 0.0 0.5941 0.0 1.9600 0.0 -0.3862 X 10-1 -0.3025 0.0

c,,

(K-7

0.0

0.0 0.0 0.1551 X 0.0 0.1144 X low2 0.0 0.0 0.0 -0.3133 X lo-* 0.0 0.0

-0.1025 X 0.0 0.0 0.0 -0.1405 X 0.0 0.9198 X 0.0 0.0 -0.8735 X 0.3388 X -0.4831 X 0.2156 X 0.0 0.0 0.0

10-1

lo-' lo-' 10-1

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.6878 X lov2 -0,2098 X 0.0

0.0 0.0 0.0 0.4822 X -0.1497 X lo-' 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.1088 X 10-1 0.0 0.0 0.1339 X 10-1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

amn(K)

bmn

c,

-95.418 16.070 47.200 1606.0 82.593 -17.253 1987.0 199.00 256.21 632.22 238.50 -9.6540 326.04 207.26 205.65 2257.3 258.57 293.81 2017.7 -65.685 311.55 1302.6 -148.07 3264.0 -396.50 1744.0 72.120 -59.900 210.50 28.170 166.00 -62.080 -22.040 477.10 -291.90 3.2020 -160.30 151.00 -484.30 -314.60 1020.8 186.71 -21.230 -44.069 -157.20 -113.10 1566.0 -96.297 -1301.0 191.60 91.811 202.49 -582.82 -28.630 -844.30 498.80 -124.32 -131.50 3982.0 -13.317 -181.93 -347.50 -359.60 55.881 255.41 -663.45 215.50 452.20 70.880 -146.10 160.40 180.60 154.00 -113.80 -300.60 -139.50 -152.20

0.6171 X lo-' -0.2998 0.3575 -4.7460 -0.4857 0.8389 -4.6150 -0.8709

0.0

0.0

-3.3912 -0,5358 -0,3242X 10-1 -2.6348 -1.0916 -1.4436 -5.6676 -2.1156 -1.3979 -9.0933 0.7409 X 10-1 -1.1856 -8.4270 1.0927 -20.840 3.0920 -4.0820 -1.1260 -0.8313 X -1.0810 0.0 -0,7116 -0.3658 -0,1018 -2.1750 0.0

-0.6894 -0.1080 x 10-1 -0.9023 2.4670 1.2870 -6.0746 -1.3546 0.0 0.2778 X lo-' 0.6166 1.1720 -5.8090 0.6304 4.0720 0.4936 -0.7171 0.0 1.6732 0.0 2.9450 -5.1480 0.0 0.0 -19.720 0.0 0.0 1.2160 1.2380 0.0 0.0 2.3281 -1.5190 -1.9970 -1.0900 0.0 -0.5148 0.0 -1.3030 0.0 -0.9576 X 10-1 0.9076 0.0

(K-9

0.0 0.0

0.9181 x 0.0 0.9021 X 0.0 0.0 0.0 0.3928 x 0.0 0.0 0.3358 X 0.0 0.0 0.0 0.1574 X 0.0 0.1024 X 0.0 0.0 0.1442 X -0.2416 X 0.3317 X -0.6266 X 0.0 0.0

10-3

10-1

10-1 lo-* 10-1

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.1015 X 10-1 0.2402 x 0.0 0.0 0.0 0.0 0.5197 X -0.1800 x 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.1039 X 10-1 0.0 0.0 0.2783 X lo-' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 185 Table IV (Continued) n m 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

41 42 43 *! 45 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 A! 30 31 32 *! 33 35 37 38 39 41 42 43 44 +! 45 5 -! 6 7 8 9 10 11 12 *! 13 14 15 *! 16 17 18 19 20 21 22 23 24 25 26 27 28 30 31 32 33 35 37 38 39 41 42

4nm

(K)

-339.80 -78.190 -322.10 389.28 139.20 3972.0 1604.3 792.00 1356.0 146.20 -365.50 -274.54 170.50 -87.080 2036.0 139.67 -71.400 1044.7 1047.0 -17.440 69.561 73.046 133.66 66.214 269.0 595.20 134.10 746.90 3736.0 59.230 331.60 345.50 -82.280 -248.20 347.60 602.10 808.00 15.570 -126.20 33.344 -26.852 -1172.0 380.02 3989.0 436.21 1050.2 1375.0 1001.0 683.60 -242.50 78.940 -595.10 2977.0 1250.0 -2631.0 4000.0 -189.30 208.10 1352.5 -46.994 213.85 192.52 -106.20 -113.60 1358.0 -2345.0 2586.0 157.90 323.60 69.000 277.00 88.930 234.20 -172.20 403.30 2303.0 147.38

bnm

1.2970 0.1327 -0.2037 0.0 -0.6500 -13.160 -2.0299 -1.7260 -2.1180 -1.2370 1.8740 0.9149 -0.2393 X lo-' -0.1859 -8.7290 0.3769 X 10-1 0.7078 -1.7112 -5.5620 0.9437 1.8881 -0.2132 -0.4614 -0.6363 -1.7760 3.3090 -0.8156 0.0 -25.000 0.0 0.3778 0.0 0.5677 1.2140 -1.4300 -7.7980 -5.3310 0.8460 0.3860 -0.4849 -0.4421 10.106 -0.2333 -14.090 1.9094 -1.9939 -1.7020 -1.8710 -1.0200 2.7200 0.0 2.9780 -19.160 0.0 13.560 -16.680 1.8600 1.3330 0.0 0.3044 0.2000 -0.2536 0.6081 19.720 -9.9680 12.290 -9.5ooo 1.4080 -0.2739 0.4317 -0.5955 0.2236 -0,2311 0.2257 -0.3234 -6.3460 -0.4889

cnm

W-')

0.0 0.0 0.4517 X 0.0 0.0 0.1208 x 10-1 0.0 0.0 0.0 0.4237 X 0.0 0.0 0.0 0.0 0.8138 X 0.0 0.0 0.0 0.8771 X 0.0 0.0 0.0 0.0 0.0 0.2645 X -0.2844 x 10-1 0.1450 X lo-' 0.0 0.4593 X lo-' 0.0 0.0 0.0 0.0 0.0 0.0 0.1966 X 10-1 0.6077 X loe2 0.0 0.0 0.0 0.0 -0.1428 X lo-' 0.0 0.1530 X lo-' 0.0 0.0 0.0 0.2390 x 10-3 0.8690 x 10-3 -0.3449 x 10-2 0.0 0.0 0.3333 X lo-' 0.0 -0.7036 X 0.2112 x 10-1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2093 X lo-' 0.0 0.8819 X 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

4mn

(W

698.50 182.40 1182.6 -174.41 -45.330 3049.0 13.733 332.30 2340.0 -57.530 1011.0 622.73 108.30 179.00 -121.00 105.63 16.290 154.39 -590.00 111.80 613.32 -58.972 -142.20 -78.116 -305.50 1885.0 -330.00 36.450 574.60 -41.770 0.4086 -14.060 298.90 187.50 -345.60 1887.0 -1367.0 -4.2990 670.80 84.418 47.230 -1141.6 -201.52 2673.0 145.54 24.144 1825.0 -146.60 1963.0 1624.0 732.00 375.00 -45.440 -316.22 978.30 3969.0 214.20 170.10 29.747 113.07 -75.010 -38.939 107.80 -69.230 1014.0 1567.0 -1494.0 181.20 694.80 448.80 -156.70 178.60 -115.90 -13.150 -45.150 -736.80 -62.534

bmn

-2.1590 -0.3030

-5.oooo 0.0 0.4223 -12.770 -0.1177 1.1580 -5.0430 1.2120 -2.1670 -1.7605 -0.2620 0.5615 X lo-' -1.9010 -0.6067 -0.6022 1.2458 2.9160 -0.5959 -1.5950 0.1046 0.3966 0.6998 2.1200 -10.980 3.0660 0.0 -3.7020 0.0 -0.4601 0.0 -0.8374 -0.9020 1.5450 -8.7070 7.8830 -0.4298 -1.8070 0.4046 0.6404 8.6562 -0.6877 X lo-' -5.7650 -0.4880 1.6504 -3.7430 0.2419 2.6560 -9.4090 0.0 -1.5700 5.1410 0.0 -6.4810 8.4970 -1.2790 -0.8218 0.0 -0.5957 -0.4268 -0,1938 -0.6785 -0.7359 -4.7020 -2.6780 7.6790 -1.0810 -0.8527 -0.9919 0.1221 -0,7113 -0.2925 X 10-I 0.1763 X -0.5665 X 3.3320 0.1798

Cmn

W-')

0.0 0.0 0.3745 X 0.0 0.0 0.1435 X 10-1 0.0 0.0 0.0 -0.3715 X 0.0 0.0 0.0 0.0 0.6999 X lo-* 0.0 0.0 0.0 -0.4935 x 10-2 0.0 0.0 0.0 0.0 0.0 -0.3239 X 0.1661 X lo-' -0.5376 X 0.0 0.3682 X 0.0 0.0 0.0 0.0 0.0 0.0 0.7813 X -0.7754 x 10-2 0.0 0.0 0.0 0.0 -0.1544 X lo-' 0.0 -0.3320 X 0.0 0.0 0.0 0.1133 X -0,1355X 10-1 0.1338 X lo-' 0.0 0.0 -0.1420 X 10-1 0.0 0.7088 X -0.5945 x 10-2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.4381 X 0.0 -0.1225 X lo-' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

186 Ind. Eng. Chem. Res., Vol. 32, No.1, 1993 Table IV n 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7

(Continued) m

43 44 +! 45 6 7 8 9 10 -! 11 12 13 14 -! 15 -! 16 17 18 -! 19 20 -! 21 22 23 24 25 26 27 30 31 32 33 34 35 36 37 38 h! 39 41 42 43 45 7 8 f! 9 10 f! 11 12 13 14 -! 15 -! 16 -! 17 18 19 20 21 22 23 24 25 26 28 +! 29 +! 30 31 32 33 f! 35 f! 36 37 38 39 41 42 43 45 8 9 10 -!

(K) -26.486 -514.79 297.73 346.31 -801.90 83.910 -250.00 -281.40 973.80 235.90 1102.0 -923.70 -355.10 104.60 -1114.0 3979.0 123.50 -1295.0 238.10 -126.00 1314.8 925.60 1862.0 741.80 2100.0 738.40 499.80 838.80 699.70 -148.90 190.40 1117.0 439.40 848.60 1036.0 403.80 3856.0 401.89 -32.643 108.20 -867.00 86.439 -392.50 299.23 220.70 -87.480 -495.25 -1508.5 -1039.0 -2012.0 3153.0 97.973 -733.07 -16.521 -85.926 -139.58 -40.130 3000.0 374.20 -332.40 75.710 -369.80 33.190 180.50 28.950 -185.90 164.00 -43.880 -99.580 101.20 308.70 68.972 -308.7 -242.60 -2686.0 190.50 -1545.0

brim

a,,

-0,2952 4.9372 -0.2420 -2.4583 3.8240 -1.2620 2.8570 2.3790 -5.6330 -0.5874 -7.1760 2.4680 0.5800 -5.0140 5.9160 -19.790 0.8503 4.3634 -0.7077 0.1322 0.0 -2.0270 32.070 -2.0980 0.0 -1.7710 -2.4100 0.0 -1.7670 1.0340 -1.2000 -2.1960 0.0 0.0

-2.9950 -0.9346 -17.970 -0,4363 -0.1043X lo-' -0.9224 -1.2580 -0,4651 2.2560 -1.2702 -0.6402 -0,5522 1.0807 4.4917 5.6030 13.460 -13.320 -0.2867 2.3351 -0.2814 -0.2637 0.0 -0.6709X 10-I -11.810 -2.2120 4.4190 -0,3753 2.2030 -0.2074 0.3161 -0,3303 0.3906x lo-' 0.0 0.0 0.0 -1.0780 -1.1750 -0.4200 1.7454 0.2956 19.440 -3.6690 6.5120

cn, (K-9 0.0 0.0 0.0 0.2929X -0.7514X 0.0 -0,6022X -0,6668X 0.7690X 0.0 0.9698X 0.0 0.0 0.8854X lo-* -0.7126X 0.2691X lo-' -0.2478X

0.0 0.0 0.0 0.0 0.0

-0.9397x 10-2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.2083X loF1 -0,2004X 0.0 0.0 0.2998X lo-' 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.6551 X -0.2004x 10-1 0.1190x 10-1 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.2688X -0,7797x 10-2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.3350X -0.9006x 10-4 -0.2702X 10.' 0.8838X 0.0

a,

(K)

199.48 291.65 -248.30 -1218.2 1460.0 465.40 653.30 1590.0 310.40 839.60 1631.0 -75.630 -660.20 1876.0 1325.0 -1496.0 -46.000 1525.8 2177.0 2389.0 963.37 3139.0 3664.0 1091.0 316.60 616.50 -468.80 774.7 1439.0 1255.0 -452.30 1072.0 959.30 1253.0 -366.40 703.40 3246.0 -238.36 2985.8 -774.50 265.50 394.78 -158.40 294.76 444.70 475.20 -467.95 -278.09 39.330 251.20 1556.0 615.01 1075.5 1831.2 1904.4 893.38 2150.0 2955.0 1079.0 2645.0 1334.0 662.00 -3.4280 1965.0 648.80 145.00 135.90 2421.0 1235.0 -269.70 678.10 2540.7 952.24 4519.3 148.40 770.60 512.60

bmn

0.3370X 10-I -1.2039 0.2547 9.7928 -8.6730 -1.8410 -1.4120 -24.570 1.5380 -1.2150 -7.3620 -0,1511 1.7430 11.500 -6.2630 9.3530 4.4150 -4.9155 -4.3630 -4.5090 0.0 -5.9640 34.130 -1.2740 0.0 -0.1457 2.4210 0.0 -1.6730 -2.5380 1.9560 -1.2480 0.0 0.0 1.1290 -1.3830 -4.9370 5.oooo -6.2270 3.8720 -2.9050 -0.3605 -0,6469 0.3745 -0.6819X 10-1 0.1198 0.6574 -0.3989 -3.3540 -1.2740 -14.970 -0.9444 -3.4339 -2.9694 -2.7981 0.0

-2.8130 -6.3830 -1.7660 -9.1720 -1.8630 -1.9030 0.4830 -3.8580 0.8050 -0.6343 0.0 0.0 0.0

1.7320 -1.3350 -3.5236 -3.3287 -19.456 -2.7570 -0.5873 -2.1450

c,, (K-9 0.0

0.0 0.0 -0.1616X 0.1641X 0.0 0.9540X 0.6212X -0.4885 X 0.0 0.1176 X 0.0 0.0 0.9Ooox 0.7584x -0.1410X -0.8780X

10-I 10-I

lo-' lo-' 10-1 10-I

0.0 0.0

0.0 0.0 0.0 0.2987X 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.1143X -0.8186X 0.0 0.0 0.2283X 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.6714X 0.2214X 0.3041X 10-I 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.1238X 0.1177X lo-' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0

0.5360X lo-* 0.2598x lo-' 0.2329X -0.3252X 0.0

Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 187

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10

13 14 -! 15 -! 16 -! 17 18 -! 19 20 21 22 24 +! 25 26 30 31 33 35 -! 36 39 -! 41 42 43 44 -! 45 9 -! 11 -! 13 17 -! 18 -! 20 24 25 31 -! 42 10 11 12 13 15 16 17 18 19 20 21 22 -! 23 24 25 26 27 28 29 f! 30 -! 31 *! 32 A! 33 34 35 37 39 41 42 43 45 -! 11 12

13 20 21 a! 22 f! 29 f! 30 *! 32 f! 37 +! 39 a!

-675.50 -197.50 798.50 1524.0 274.50 158.40 732.20 -634.10 -1795.2 86.690 134.10 1008.0 -1895.0 -595.70 -123.80 372.50 822.20 117.00 419.80 -494.20 676.00 274.37 54.962 -804.28 509.30 -145.20 -212.90 -329.30 542.00 -1231.0 401.88 2356.0 555.50 -309.00 -749.40 197.60 -16.486 -83.570 3645.0 -47.970 -389.60 1732.0 513.30 -191.00 -109.51 -99.976 -18.695 810.17 -808.60 1297.0 -35.890 -169.60 419.90 2.7140 -986.00 478.50 346.60 -717.76 -62.430 -76.870 64.010 80.792 64.210 156.53 -62.857 -497.98 -208.40 -160.70 209.00 435.64 985.70 -111.50 -373.70 -742.70 114.30 -43.560 2371.0

3.6090 0.1766 -5.8690 -2.5310 -0,5905 0.5246 -0.6607 3.5900 12.708 1.5920 0.9495 -1.7950 9.3030 2.6340 3.8470 -0.9091 0.0 -0,6110 2.4360 2.8260 -0.9909 -0.5861 -2.5850 2.8280 -0.2900 -0.7380 0.0 0.0 -6.7920 4.9730 0.0 -3.3470 0.0 0.0 6.5890 0.0 -0.2792 0.0 -26.910 0.0 0.1944 -9.896 -1.0360 0.6835 0.9689 0.0 -0.5261 -3.2209 4.5640 -1.3650 -0.1009 2.9860 0.9772 X lo-' 0.0 3.8470 -1.1480 -0.7017 2.9431 -0.8977 0.5372 -1.0770 -3.7020 0.0 -0.7135 0.2898 0.7972 0.0 0.0

-0.6241 0.0

-2.9860 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.1032 X lo-' 0.0 0.2205 X 0.0 0.2019 X 0.00 -0.1546 X lo-' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.3001 x 10-3 0.8218 X 0.0 0.0 0.0 0.0 0.0 0.1655 X lo-' -0.6327 X lo-' 0.0 0.0 0.0 0.0

-0.1101 x 10-1 0.0 0.0 0.0 0.4757 X lo-' 0.0 0.1863 X 0.141 X lo-' 0.0 0.0 0.0 0.0 0.0 0.2144 X -0.7230 X lo-' -0.2253 X lo-' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.1159 0.0 0.0 0.0 0.2982 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

X

X

lo-'

322.30 140.70 -980.60 -851.00 -446.00 -131.00 -619.30 509.60 624.97 313.30 748.20 1282.0 591.60 882.60 501.40 -368.80 -17.990 -370.80 276.90 -121.80 808.40 1632.9 843.09 594.45 -523.80 -666.80 -224.40 -80.580 -131.10 608.20 281.08 2157.0 1554.0 191.70 1826.0 -93.080 33.415 101.30 695.80 119.50 2831.0 1460.0 -258.00 79.080 178.22 55.270 -218.94 -48.641 913.90 1375.0 -32.600 -328.10 315.30 64.410 277.00 -72.580 -182.00 319.69 -481.20 38.060 -153.40 1955.5 -148.30 498.92 80.038 945.14 389.70 226.60 235.70 -188.00 -888.30 473.30 -397.50 -214.80 293.50 945.60 -225.30

-1.3050 0.5679 X 10-I 3.6710 1.0340 -0.7738 -0.7957 1.9300 -1.9160 -4.6878 -0,5041 -1.3190 -2.8150 -3.0800 -2.6060 -1.9390 0.7775 0.0 0.1043 -0.9948 -0.6029 -2.9290 -2.8719 -2.6350 -2.2535 3.1580 1.9180 0.0 0.0 -0.9399 -6.2610 0.0

-3.7180 0.0 0.0

-1.0350 0.0 0.2191 0.0 -0.9619 0.0 -13.010 -13.730 0.5070 -0,3808 -0.9168 0.0 1.0749 -0.7950 -3.3060 2.4990 0.8470 X lo-' 0.3045 -0.5617 0.0 -1.3570 0.4909 0.7905 -1.4362 9.6040 -0.5189 3.1430 -1o.Ooo 0.0 -0,4400 x 10-1 -0.1012 -3.8168

0.0 0.0 -0.5908 0.0 0.2634 0.0 -0.3386 0.0 0.5237 0.0 0.0 0.0 0.0 0.0

X

X

lo-*

X

0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.3455 X 0.7040 X 0.0 0.0 0.0 0.0 0.0

0.4690 x 10-3 0.9693 X 0.0 0.0 0.0 0.0

-0.2210 x 10-2 0.0 0.0 0.0

-0,2462 X 0.0 0.1558 X 10-1 0.2917 X lo-' 0.0 0.0 0.0 0.0 0.0 0.3713 X 0.4963 X 0.6309 X lo-* 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.1139 0.0 0.0 0.0 0.4535

0.0 0.0

0.0

0.1314 0.0 3.4260 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0

X

0.0

X

X

10-1

188 Ind. Eng. Chem. Res., Vol. 32, No.1, 1993 Table IV (Continued) n m a,, (K) 10 42 *! 856.5 342.40 11 12 -! 11 13 195.30 11 15 3168.0 16 +! 11 152.80 11 17 -! -1355.0 -193.23 11 19 11 62.031 20 -49.339 21 11 168.17 11 22 *! -5.7100 11 24 11 25 -! 3351.0 9.2220 11 26 11 28 A! 861.10 80.690 11 30 11 -72.070 31 11 82.960 32 *! 11 -386.30 33 296.80 11 35 *! 11 -92.120 36 -! -201.40 11 37 -! 11 39 231.00 11 41 -! -338.80 42 11 296.88 -28.231 43 11 11 44 -! 745.40 11 45 &! -579.11 12 18 167.50 19 *! 92.210 12 12 24 *! -142.20 25 *! 1894.0 12 29 h! 12 161.80 745.40 12 37 *! 12 39 -! 580.30 42 i! 12 245.10 12 44 -! 489.15 12 45 -! 260.64 13 18 957.80 13 1987.0 19 521.48 13 20 21 -208.60 13 22 *! 492.90 13 23 -607.35 13 24 -425.40 13 25 974.00 13 26 &! 13 -305.10 28 ! 35.020 13 29 *! 102.60 13 513.70 30 13 32 +! 13 -104.80 37 -! -422.70 13 38 &! 155.70 13 42 251.40 13 43 -124.33 13 44 -! -454.92 13 45 -! 13 -515.93 15 +! 14 1517.0 14 16 -472.40 14 19 -4 12.38 24 t! 14 -65.760 25 *! 14 2553.0 29 14 -205.10 14 162.14 39 &! 42 14 444.60 43 *! 14 -143.07 15 16 402.60 15 19 242.20 15 24 -3.2800 15 25 &! 3888.0 15 38 &! -330.20 15 42 +! 154.50 15 43 -186.98 16 -473.00 22 f! 16 24 k! 215.90 16 25 -! 1622.0 16 38 &! -7.5320 16 39 965.00

bnm

-1.9Ooo 0.0 -9.75 -24.070 -1.0990 7.6830 0.4301 1.0567 0.0 -1.0536 -0.2724 -14.540 -0,3292 -1.6930 0.0 0.0 0.0 1.8920 -1.2640 0.9031 0.5487 0.0 1.8370 -1.1816 0.0 0.0 0.9455 0.0 0.0 0.5720 0.0 0.0 -0.6220 0.0

-0.8394 0.0

-1.2868 -5.7730 -8.0220 0.0

-0.2571 -6.4750 2.3467 0.9514 -1.3680 0.7063 1.7020 0.0 0.0 0.0 2.2300 -1.5780 -1.0210 -0.294 0.0 0.3835 -12.720 -0.2051 -0.4909 -0.3148 -11.900 0.0 0.0

-3.1420 0.0

-1.6140 0.0 0.0 -16.260 0.0 -0.9466 0.0 0.8883 -1.3990 -4.8120 -0.8077 0.0

c,,,,

(K-9

0.0 0.0 0.4051 X 10-1 0.4303 X 10-' 0.0 -0.1012 x 10-1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.1074 X 0.1065 X 0.0 0.2418 X 0.1806 x 0.0 0.0 -0,1983 X

lo-' lo-'

lo-' lo-'

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.2557 X 10-' 0.1058 X lo-' 0.6255 X 0.0 0.0 0.0 0.0 0.2975 X 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 -0.1856 0.0 0.0

X

lo-'

a,

(K)

1129.0 -251.70 824.20 3329.0 160.80 3499.0 139.55 59.594 48.852 -461.35 223.40 -788.60 -50.360 280.00 -136.30 69.250 11.620 248.30 -337.10 503.50 -320.00 -173.50 3.9240 323.18 36.948 -447.04 966.35 -14.230 -33.640 465.80 18.790 13.970 -479.10 -285.50 475.90 -441.01 -597.09 460.30 -588.80 -310.82 872.00 215.30 97.128 641.20 381.10 319.60 198.50 -210.10 -299.60 464.00 -326.40 -528.80 -86.600 561.14 310.75 1368.0 -1074.0 836.60 2412.2 333.90 3873.0 244.40 -112.76 -526.10 182.58 -639.90 -131.90 43.830 -868.80 904.10 528.30 295.07 406.80 -825.90 -94.870 35.160 -311.90

bmn

-0.4978 0.0 -6.m -13.780 0.8719 -22.960 -0.4367 -0.7120 0.0 1.8569 0.1237 1.6930 0.2448 X lo-' -0.9491 0.0 0.0 0.0 -1.1980 0.8843 -1.7920 1.0520 0.0 -1.1740 0.3626 0.0 0.0 -2.1861 0.0 0.0

-0.7730 0.0 0.0 0.8031 0.0 -0).1080 0.0 2.5295 -5.6870 1.4810 0.0 -2.9390 -2.4820 -0.6439 -1.4860 -5.6820 -1.3680 -1.4340 0.0 0.0 0.0 0.2400 2.8220 0.9724 -0.7058 0.0 -2.6254 9.oooO -5.2080 -10.495 -0,1415 -9.315 0.0 0.0

7.6850 0.0

2.5610 0.0 0.0

2.9480 0.0

-0.3991 0.0 -1.5240 3.1500 -9.6120 0.9723 X lo-' 0.0

cmn (K-') 0.0 0.0 0.8271 X lo-* 0.1193 X lo-' 0.0 0.3543 X lo-' 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.9776 x lo-* -0.2636 x 0.0 0.1269 X 0.2745 x 0.0 0.0 0.1675 X lo-' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0,1795 X lo-' 0.4801 X 0.9741 X 0.0 0.0 0.0 0.0

-0.1110 x 10" 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0

0.3722 x lo-' 0.0 0.0

Ind. Eng. Chem. Res., Vol. 32,No. 1, 1993 189

16 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 23 23 23 24

45 *! 18 -! 19 -! 21 a! 24 27 31 -! 39 -! 42 19 20 -! 22 *! 33 i! 37 38 42 43 i! 45 -! 21 22 24 25 26 28 i! 29 i! 31 *! 33 *! 34 i! 36 i! 37 39 *! 41 42 43 45 -! 21 22 24 25 i! 32 33 37 *! 39 42 *! 43 44 -! 45 22 23 24 25 *! 26 27 +! 28 i! 30 -! 33 37 42 43 -! 44 45 23 24 25 -! 26 *! 30 -! 32 i! 33 i! 35 i! 37 42 -! 43 45 24 t! 33 -! 37 i! 25

420.24 1489.0 393.90 582.10 3986.0 3770.0 1268.0 -391.90 1186.0 81.520 -502.21 -63.540 -623.80 50.527 196.00 173.70 -95.689 -29.855 176.50 -78.960 65.820 1283.0 117.53 468.80 -18.800 506.60 -211.20 11.650 267.10 61.960 396.60 -75.670 -128.30 -28.653 237.42 27.618 94.606 701.95 -1398.7 146.06 -18.328 -447.95 -421.21 1169.3 720.45 -65.631 508.72 70.790 592.40 16.340 3985.0 24.440 1248.0 295.90 666.00 128.80 280.00 -65.685 -325.77 530.30 207.12 187.43 46.290 3353.0 822.40 -174.60 132.70 -139.60 -178.30 160.70 34.133 108.83 7.3664 -323.17 599.82 325.81 -131.80

0.2632 -13.480 -4.703 -2.3300 -16.150 1.6860 -3.0420 0.0 -2.2810 0.0 1.0583 -0,4358 2.5670 -0.7980 -1.1780 -1.7780 -0.1720 -0.7479 -1.2370 0.0 -0.6265 3.3610 -0.4469 0.0 -0.3652 -1.2630 0.0 -1.2290 0.0 -0.4161 -1.8290 0.0 0.8538 -0.4815 -1.2928 0.0 0.0

-1.7576 0.0 0.0 0.0 1.5141 0.0 -3.0737 -1.5187 0.0 -1.4005 0.0 -4.2459 0.7287 X lo-' -15.700 -0.4713 -2.0400 0.0 0.0

-0,2077 0.0 0.7409 X lo-' 2.0412 0.0 -0.4396 -3.4460 -0.2115 -14.200 -2.0500 0.0 -0.1183 1.0220 0.7426 0.0 -0.3925 -0.8606 0.4046 1.1973 0.0 0.0 9.8020

0.0

0.2990 x 10-1 0.9003 X 0.3770 X 0.1635 X 10-1 0.0 0.0 0.0 -0.1336 X lo-* 0.0 0.0 0.0

0.0 0.0 0.0 0.1480 X 0.0 0.0 0.0 0.0 0.0

-0.2978 X 10-1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.2378 X 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.6905 X 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.6718 X 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.3582 X lo-'

-1035.8 245.80 2987.0 -338.0 2626.0 1.6550 -818.80 650.70 1851.0 31.100 -504.25 -92.490 243.20 -110.08 -474.50 32.270 173.18 -422.66 -368.70 14.760 357.60 2331.0 -128.21 434.80 41.540 11.720 362.60 -1428.0 -144.70 -19.100 -663.00 26.800 2402.0 56.754 -642.44 702.40 425.97 213.34 1Ooo.o 780.71 753.21 283.64 93.773 582.81 -140.77 -14.016 -386.93 -66.210 603.29 95.050 15.620 142.10 1295.0 -137.70 -390.60 -92.680 -207.30 401.00 70.075 17.052 -175.29 1468.9 46.030 368.60 -423.10 106.30 -23.810 96.400 -39.450 -135.90 193.77 -358.57 -1.6641 350.92 -364.76 -199.87 972.10

3.0786 -0.1692 -9.3360 3.3720 -10.590 -1.1640 3.2290 0.0 -4.4760 0.0 0.4034 0.2791 -1.4720 2.1903 2.1540 2.6840 -0.3557 x 10-1 1.8153 1.9920 0.0 0.7676 -9.2380 0.5035 0.0 0.6460 0.7004 0.0 7.6980 0.0 1.1950 2.6910 0.0 -10.300 0.8978 2.8574 0.0 0.0 2.1861 0.0 0.0 0.0 1.5491 0.0 1.4976 0.3090 0.0 2.3961 0.0 -3.9770 -0.2348 -1.0990 -0.1530 -4.2240 0.0

0.0 -0.1307 x 10-l 0.0 -0.7277 -1.1490 0.0 0.3275

-5.oooo 0.5388 x lo-' -1.7480 0.8154 0.0 -0.9204 X lo-' -0,7760 -0.8556 0.0 0.3179 x 10-l 1.3307 -0.3783 -1.3456 0.0 0.0

-6.8200

0.0 -0.6990 X 0.7147 X -0.3676 x 0.1466 X 10-l 0.0 0.0 0.0 0.5577 x 0.0 0.0 0.0 0.0

0.0 0.0

-0.3948 X 0.0 0.0

0.0 0.0 0.0 0.1158 X lo-' 0.0 0.0 0.0 0.0 0.0

0.0 0.0

0.0 0.0 0.0 0.1521 X 10-1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.6248 X 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.3701 X 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.9219 X lo-*

190 Ind. Eng.Chem. Res., Vol. 32, No. 1, 1993 Table IV (Continued) n m 24 26 f ! 27 f ! 24 28 24 30 -! 24 32 i! 24 33 24 35 f ! 24 36 f ! 24 37 24 38 24 39 i! 24 42 24 43 24 45 24 26 25 27 25 33 25 42 25 43 f ! 25 45 -! 25 27 -! 26 28 f ! 26 32 f ! 26 33 -! 26 34 26 37 26 39 i! 26 42 26 43 26 42 i! 27 32 i! 28 37 28 42 f ! 28 43 *! 28 45 28 35 i! 29 39 29 42 f ! 29 37 -! 30 42 30 44 f ! 30 35 a! 31 39 f ! 31 33 f ! 32 45 i! 32 35 i! 33 41 f ! 33 42 f ! 33 43 f ! 33 39 -! 34 39 i! 35 45 -! 35 37 36 41 -! 37 42 37 43 f ! 37 45 37 40 i! 38 42 38 43 f ! 38 42 39 43 39 44 -! 39 42 i! 40 42 41 43 42 45 i! 42 45 f ! 43

brim

anm (K)

441.50 3286.0 9.3620 750.20 49.510 203.20 325.20 902.00 220.60 197.40 512.70 -37.183 190.45 22.779 3986.0 518.50 -69.880 1352.0 96.855 -27.161 85.600 68.870 643.80 9.2580 -70.240 159.00 606.90 115.60 53.750 1804.0 212.40 -93.310 29.450 166.56 89.744 467.10 356.60 -255.30 -277.60 96.590 778.78 -228.40 373.80 -536.20 -47.772 -83.700 -378.10 -146.20 -186.40 1025.0 -2 13-80 -322.46 -74.880 -211.10 1026.0 321.62 185.82 -57.380 96.190 -22.572 141.20 53.871 -310.13 108.50 610.10 242.49 183.79 -523.96

-0.5353 0.0 1.0330 0.8165 0.6829 -1.3280 0.4405 0.0 0.3756 -0.4858 0.2702 X -0.4783 X 0.1272 X 0.4214 X 25.000 0.0 0.0 -3.7970 -1.2993 0.6110 0.0 3.2170 -0.7376 -0.1079

c,,

10-1 lo-'

10" 10-1

0.0 0.0 0.0

-0.5435 0.0 0.6361 -0.3692 -0.1286 -0.9194 -1.0407 -1.0122 0.0 0.0 0.3653 0.0 -0.7691 0.0 0.0 0.0 1.9950 -0.9201 X 0.1436 2.5600 0.2411 0.0 0.0 0.0 -0.2083 x 10-l 0.0 0.0

-7.4690 -4.9963 0.0 0.0

-0.4476 0.0

-0.8783 -0.6775 0.0 0.0

5.9600 -0.3832 X 10-l -0.1518 0.4945

(K-9

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.1114 X lo-' 0.1387 X 10-I 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

(K) -65.740 167.50 52.010 100.50 186.40 -1360.0 -60.890 -194.90 -134.40 -98.980 -168.40 60.780 -131.87 14.947 3638.0 -1713.0 981.50 2838.0 2991.9 4235.3 986.00 655.70 17.810 121.40 132.20 108.40 -340.90 531.00 -47.089 2500.0 200.60 319.40 92.400 1.0902 40.987 -360.00 -247.60 685.30 1168.0 846.70 -384.29 -47.810 -231.60 558.00 92.429 -116.70 13.780 498.10 265.42 -416.50 203.40 67.069 1004.0 516.50 -1189.0 713.90 -139.00 110.40 32.470 -7.5600 666.50 -54.260 -367.48 -69.940 835.20 20.834 -61.922 1414.0 ,a,

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

bmn

0.9670 X

Cmn

lo-'

0.0

-0.9095 -0,8269 -0.7294 7.4020 -0.6321 0.0 -0,3226 -0.2128 X lo-' -0.1230 0.2426 X lo-' -0,1420 X lo-' -0.1109 -14.250 0.0 0.0 -12.980 -9.3959 -16.954 0.0 -2.2030 -0.2245 0.5397 X 10-1 0.0 0.0 0.0 -0.2908 0.0

-3.8140 -0.2280 0.3419 X lo-' 1.1910 1.5927 1.1526 0.0 0.0 -1.0480 0.0 0.2545 0.0 0.0 0.0

-1.9240 0.1744 -0.6775 X lo-' -0.9360 -0.7754 0.0 0.0 0.0 0.2396 0.0 0.0 8.8650 -2.7759 0.0 0.0 -0.7141 X 10-1 0.0 -0.1555 1.0612 0.0 0.0

-2.6780 4.3472 -0.5944 x 10-1 -2.8776

(K-')

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-0.1285 0.9172 0.0 0.0

X X

lo-'

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

"The use of these modified UNIFAC interaction parameters (+!) at high temperatures, (-!) at low temperatures, (f!)at high and low temperatures can lead to erroneous results.

methods. While for the original UNIFAC method an absolute deviation of 324.6 J/mol and a relative deviation of 77.2% are obtained, with the present parameters a much better estimation of hE-data (102.9 J/mol, 28.5% relative deviation) is possible; this should provide (at least for a

limited temperature range) a more reliable description of the temperature dependence of the activity coefficients, and thus a more reliable prediction of the temperature dependence of azeotropic points and LLE. This should allow the prediction of the appearance of lower or upper

Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 191

=I

=I

=1

Figure 4. Experimental and predicted results for cyclic ether-alkane systems. VLE: (A) tetrahydrofuran (1)-n-hexane (2) at 760 mmHg; (B) 1,3-dioxolane (1)-n-heptane (2) at 70 OC; (C) 1,4-dioxane (1)-n-heptane (2) at 80 "C. hE: (D)tetrahydrofuran.(l)-n-hexane (2) at 30 OC; (E) 1,3-dioxolane(1)-n-heptane (2) at 25 OC; (F) 1,Cdioxane (1)-n-heptane at 25 "C. Lines and symbols: (-) modified UNIFAC (Dortmund) resulta; original UNIFAC results; (0,w ( ) experimental values. (a-)

Table V. Deviations between Experimental and Predicted Binary VLE Data (1730 Consistent Isothermal or Isobaric Data Sets)

AP group contribution method ASOG UNIFAC (2141 data seta) modified UNIFAC (Dortmund) (2130 data seta) modified UNIFAC (Lyngby)

Ay 0.0137 0.0135 0.0141 0.0087 0.0088 0.0117

A T (K) 1.03 0.93 1.06 0.62 0.68 0.80

(mmHg) 12.51 12.53 12.56 6.89 6.55 11.95

Table VI. Deviations between All Experimental and Predicted Binary VLE Data (Approximately 7000 Iaothermal or Isobaric Data Sets)

AP group contribution method ASOG UNIFAC (approximately 9OOO data sets) modified UNIFAC (Dortmund) (approximately 9OOO data seta) modified UNIFAC (Lyngby)

Ay 0.0219 0.0213 0.0224 0.0167 0.0172 0.0195

A T (K) 1.63 1.58 1.74 1.39 1.46 1.50

(mmHg) 14.56 14.75 15.00 9.36 9.28 13.43

Table VII. Deviations between Experimental and Predicted Binary Heats of Mixing Data (4900 Ieothermal Data Sets) ~ O U D contribution method AhE (J/mol) A h E d (%) 550.7 202.8 ASOG 324.6 77.2 UNIFAC 335.0 88.8 (6061 data seta) modified UNIFAC (Dortmund) 102.9 28.5 103.8 30.0 (5990 data seta) modified UNIFAC (Lyngby) 152.8 47.5 uErel

I(hEerpt

- hEcd/hEexpt,maxI X

100 (%).

critical solution temperatures. The results for activity coefficients at infinite dilution are listed in Table VIII. Since the values published by different authors are contradictory especially for strongly non-ideal systems (e.g., wateralkanes, water with higher esters, etc.), Table VI11 contains deviations only for binary systems with 7'-values < 100 or for all water-free systems. All ' 7 measured by liquid-liquid chromatography are excluded because the results are often very poor. As mentioned before, reliable values for 7' are of special importance for the design of separation processes and the

Table VIII. Deviations between Experimental and Predicted Activity Coefficients at Infinite Dilution (10000 Data Points (Coefficients with a n Asterisk Determined with 9900 Data Points)) ~ O U D contribution

method

ASOG UNIFAC (approximately 14000 data points) modified UNIFAC (Dortmund) (approximately 13600 data points) modified UNIFAC (Lyngby)

A V 1.30 1.42 2.09

AY-'nl (%) 26.69 26.03 28.15

AT-* 1.56 1.85

AY-reI*

26.69 25.82

0.82

13.92

0.99

13.35

1.06

15.56

1.53

21.72

1.68

21.15

(%)

< 100 without water selection of selective solvents for extractive distillation, extraction, or absorption. It can again be seen that with the parameters for the modified UNIFAC method presented in this paper much better results (approximatelya factor of 2 better) are obtained in comparison with the results given by the other group contribution methods. The resulta for ternary systems are presented in Tables IX and X. For VLE no consistency test was performed. Therefore all data seta (P < 50oO mmgHg, (pVi/& = 1) were used for the comparison. This means that the experimental error has a considerable influence on the calculated deviations. Also,a large number of systems show a large miscibility gap. Both factors lead to a similar error, as obtained for the case where all binary VLE data sets (Table VI) were used for the comparison. Apart from the deviations in y, T,and P or hE. Tables IX and X contain the number of data sets for which the examined group contribution method provided the lowest (+) and the largest deviations (-1. It can be concluded from the deviations and the number of data sets with a plus or minus sign that the best results are again obtained using the method presented in this paper. Because of the problems mentioned, the improvements obtained for VLE are not large, but prediction of hE-data shows considerable improvement (by a factor of 2-3). Figure 4 shows resulte for VLE and hE in the form of y-x- or h%-diagrams for different cyclic ethers with alkanes. These systems usually caused great problems for the original UNIFAC method, because for the cyclic ethers the same main group as for 7-

192 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 Table IX. Deviationr between Experimental and Predicted Ternary VLE Data (Approximately 660 Isothermal or Isobaric Data Sets) (516 data seta) (357 data seta) (187 data seta) AT (K) AP(mmHg) + AY group contribution method 106 156 1.24 86 86 20.64 26 73 0.0194 ASOG 65 191 1.28 88 128 24.39 40 59 0.0203 UNIFAC 202 74 106 60 15.43 68 20 1.09 modified UNIFAC (Dortmund) 0.0172 77 1.15 83 18.02 53 35 0.0181 143 95 modified UNIFAC (Lyngby)

+

+

sures and not to different activities. During this research work we attempted to improve the situation somewhat for the different alcohols (primary, secondary, tertiary) by introducing different Rk- and Qk-vduesfor different alcohol group. These systems show a very different LLE behavior with water. While there are miscibility gaps for 1-butanol, isobutanol, and 2-butanol, no miscibility gap is observed for tert-butanol. This means that the deviation from Raoult's law decreases on going from 1-butanol via isobutanol and 2-butanol to tert-butanol. The use of different main groups for the primary, secondary, and tertiary alcohols would be very helpful for describing the observed behavior. This would however involve a great increase in the number of required group interaction parameters, and the present limited data base does not allow a fit of the required parameters for three alcohol main groups with all the other main groups given in Table IV. Thus only different Rk- and €&-valueswere introduced to improve this situation. In Table XI the activity coefficients at infinite dilution for the different butanols in water are given in the temperature range 25-100 OC. For the m&ied UNIFAC method presented here, it can be seen that the highest 7"-values are obtained for 1-butanol and isobutanol, while the valuea for 2-butanol are smaller. The smallest value is obtained for tert-butanol. At the same time a maximum of the 7"-values is predicted in the temperature range given. This is in agreement with the experimental hE-values. For all butanol-water systems a miscibility gap is however still predicted using the parameters presented in Table IV.

Table X. Deviations between Experimental and Predicted bE-Data for Ternary Syrtemr (144 Isothermal Data Sets) AhE

(J/mol) 532.1 ASOG 312.5 UNIFAC modified UNIFAC (Dortmund) 106.7 154.8 modified UNIFAC (Lyngby) POUP

contribution method

&Ele?

(%)

+ -

82.7 34.9 13.3 23.5

4 93 12 46 82 2 46 3

- hEule)/hEerpt,mluI x 100 (%). aliphatic ethers was used. A great improvement of the results is obtained using a special main group, as in this work. As shown in Figure 4, all azeotropic points are &'rei

I(hEexpt

predicted with the desired accuracy. Furthermore, in agreement with the experimental findings, no miscibility gap is predicted for the system dioxolanen-heptane and much better agreement between experimental and predicted is obtained for heats of mixing.

Problems In the previous section the results for VLE, hE,and 7" of different group contribution methods were compared. It is concluded that the modified UNIFAC method presented in this paper provides the best predictions for these properties. Further results for VLE, LLE, hE, T", azeotropic data, and solid-liquid equilibria are given (Schiller, 1992; Schiller et al., 1992). The user should apply the method only in the temperature range for which experimental data were available. An extrapolation may be dangerous, especially because the greatest part of the hE-data, which following the Gibbs-Helmholtz relation provides the most important information about the temperature dependence, were measured only in the temperature range 25-50 OC. Furthermore the reader should remember that there are still weaknesses connected with the solution of groups concept when only a very limited number of adjustable parameters is fitted. For example it is very difficult with a limited number of parameters to account for isomeric effects. Of course new main groups can be included, which would improve the results, but even when the DDB is applied, the data base is still too small to account for isomeric effects, e.g., the behavior of isomeric hydrocarbons, alcohols, etc., or substitution effects (e.g., ortho, meta, or para substitution) in the case of the different benzene derivates. Fortunately, the different VLE behavior of isomers is often due to different vapor prss-

Conclusion The modified UNIFAC method presented here allows better predictions of the real behavior of non-electrolyte systems than do other group contribution methods. This was made possible by using a modifed combinatorial part, additional main groups, and temperature-dependent parameters in the UNIFAC model which were fitted to all the suitable phase equilibrium information stored in the Dortmund Data Bank. At the same time the large parameter set guarantees a large range of applicability. These advantages should allow a more reliable synthesis and design of separation processes, selection of solvents for extractive distillation or extraction, calculation of chemical equilibria, etc. When new experimental phase equilibrium data and especially hE-data at temperatures very different

Table XI. Activity Coefficientr at Infinite Dilution for Different Butanol-Water Systems modified modified modified UNIFAC UNIFAC UNIFAC temp ("C) ASOG UNIFAC (Dortmund) (Lyngby) ASOG UNIFAC (Dortmund) I-Butanol in Water Isobutanol in Water 54.1 41.9 25 45.7 30.2 30.8 54.2 41.9 50 46.5 47.9 43.0 40.5 31.7 48.0 43.0 75 47.4 43.1 42.2 48.2 32.7 43.2 42.2 100 49.0 39.4 40.0 53.1 34.1 39.4 40.0 25 50

75 100

30.8 31.7 32.7 34.1

2-Butanol in Water 54.2 36.2 48.0 36.9 43.2 36.0 39.4 33.9

30.0 40.2 47.8 52.7

17.1 18.0 18.8 19.9

tert-Butanol in Water 51.0 27.2 45.0 27.6 40.3 26.7 36.6 25.0

modified UNIFAC (Lyngby) 30.0 40.2 47.8 52.7 35.2 47.6 56.9 62.6

Ind. Eng. Chem. Res., Vol. 32, No. 1,1993 193 from 25 OC are available, some of the group interaction parameters should be revised and the existing modified UNIFAC parameter matrix should be extended. This would require the fitting of the group interaction parameters as well as the regular update of the Dortmund Data Bank and the measurement of required missing data. This kind of work is impossible without financial support from industry or government.

Acknowledgment The authors thank "Arbeitsgemeinschaft Industrieller Forschungavereinigungen (AIF)" for the financial support received for the development of the modified UNIFAC method and B. Meents and R. B6lts for technical assistance.

Nomenclature a, = UNIFAC group interaction parameter between groups n and m (K) b,, = UNIFAC group interaction parameter between groups nandm c,, = UNIFAC group interaction parameter between groups n and m (K-l) cpE = excess heat capacity [J/(mol K)] p i= standard fugacity of component i (kPa) F = objective function Fi= auriliaryproperty for component i (surface fraction/mole fraction) gi= weighting factor for the different types of data hE = molar excess enthalpy [J/moll Ki= K-factor for component i nw = number of data pointa in a data set qi = relative van der Waals surface area of component i Qk= relative van der Waals surface area of subgroup k ri = relative van der Waals volume of component i Rk = relative van der Waals volume of subgroup k T = absolute temperature (K) Vi = auriliary property for component i (volume fraction/mole fraction) V i= empirically modified Vi-value xi = mole fraction of component i in the liquid phase X, = group mole fraction of group m in the liquid phase yi = mole fraction of component i in the vapor phase Greek Symbols q2= separation factor rk = group activity coefficient of group k in the mixture = group activity coefficient of group k in the pure substance 7 ; = activity coefficient of component i ymi= activity coefficient of component i at infinite dilution 8, = surface fraction of group m in the liquid phase Y k ( j ) = number of structural groups of type k in molecule i (pvi = fugacity coefficient for component i in the vapor phase di= saturation fugacity coefficient for component i 9,, = UNIFAC group interaction parameter between groups nandm Indexes calc = calculated quantity C = combinatorial part expt = experimental quantity E = excess quantity

i = component i R = residual part = at infinite dilution

Supplementary Material Available: The parameters can be obtained on a diskette, at cost, from the authors. Literature Cited Derr, E. L.; Deal, C. H. Analytical Solutions of Groups. Correlation of Activity Coefficients through Structural Group Parameters. Znst. Chem. Eng. Symp. Ser. (London) 1969, No. 32, 340-61. Fredenslund, Aa.; Jones, R. L.; Prauanitz, J. M. Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mmtures. AZChE J. 1975,21,1086-1099. Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNZFAC; Elsevier: Amsterdam, 1977. Gmehling, J. Dortmund Data Bank-Basis for the Development of Prediction Methods. CODATA Bulletin 58; Pergamon Prese: Oxford, U.K., 1985; pp 56-64. Gmehling, J. Development of Thermodynamic Models with a View to the Synthesis and Design of Separation Proceseee. In Software Development in Chemistry 5; Gmehling, J., Ed.; Springer-Verb Berlin, 1991; pp 1-14. Gmehling, J.: Meents, B. Znt. Data Ser., Sel. Data Mixtures 1992, Ser. A; 14-213. Gmehlinn. J.: Onken. U.: Ark. W.: Grenzheueer. P.: Kolbe. B.: Rarev, J. R.; beidlich, U. VaporLLi&id Equilibrium Data Coilecti&; DECHEMA Chemistry Data Series, Vol. I, 16 Parts; DECHEMA: Frankfurt, 1977. Gmehling, J.; Christensen, C.; Holderbaum, Th.;Rasmussen, P.; Weidlich, U. Heats of Mixing Data Collection; DECHEMA Chemistry Data Series, Vol. 111,4 Parts; DECHEMA: Frankfurt, 1984. Gmehling, J.; Tiegs, D.; Knipp, U. A Comparison of the Predictive Capability of Different Group Contribution Methods. Fluid Phase Equilib. 1990,54,147-165; 1990,59,337-338 (correction). Hansen, H. K.; Rasmussen, P.; Fredenslund, Aa.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5. Revision and Extension. Znd. Eng. Chem. Res. 1991, 30, 2352-2355. Kojima, K.; Tochigi, K. Prediction of Vapor-Liquid Equilibria by the ASOG Method; Kodanaha-Elsevier: Tokyo, 1979. Lareen, B. L.; Rasmwen, P.; Fredenslund, A a A Modified W A C Group-Contribution Model for the Prediction of Phase Equilibria and Heats of Mixing. Znd. Eng. Chem. Res. 1987,26,2274-2286. Marquardt, D. W. An Algorithm for Least Square Estimation of Nonlinear Parameters. J. SOC.Znd. Appl. Math. 1963, 11,431. Meyer, Th.; Gmehling, J. Chem.-Zng.-Tech. 1991, 63,486-488. Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. Comput. J. 1965, 7, 308-313. Schiller, M. Ph.D. Dissertation, University of Dortmund, 1992 (submitted for publication). Schiller, M.; Li, J.; Gmehling, J. Znd. Eng. Chem. Res. 1992, manuscript in preparation. Ssrensen, J. M.; Arlt, W. Liquid-Liquid Equilibrium Data Collection; DECHEMA Chemistry Data Series, Vol. V, 3 Parts, DECHEMA Frankfurt, 1979-80. Tiegs, D.; Gmehliig, J.; Medina, A.; hares, M.; Baatos, J.; Alemi, P.; Kikic, I. Actiuity Coefficients a t Infinite Dilution; DECHEMA Chemistry Data Series, Vol. M,2 Parts; DECHEMA: Frankfurt, 1986. Tochigi, K.; Tiegs, D.; Gmehling, J.; Kojima, K. Determination of New ASOG Parameters. J. Chem. Eng. Jpn. 1990,23,453-463. Weidlich, U.; Gmehling, J. A Modified UNIFAC Model. 1. Prediction of VLE, he, and T-. Znd. Eng. Chem. Res. 1987, 26, 1372-1381. Received for review May 19, 1992 Revised manuscript received September 16, 1992 Accepted September 30,1992