Prediction of phase equilibrium in systems containing alcohols, acids, ethers, esters and water with UNIFAC Panayiotis Tsavas, Epaminondas Voutsas*, Kostis Magoulas and Dimitrios Tassios Thermodynamics and Transport Phenomena Laboratory, School of Chemical Engineering, National Technical University of Athens, 9, Heroon Polytechniou Str., Zographou Campus, 15780 Athens, Greece

Keywords: vapour-liquid equilibria, liquid-liquid equilibria, solid-liquid equilibria, UNIFAC.

Abstract Mixtures involving sugars, sugar esters, alcohols, acids, esters, ethers and water are of interest in the

food and beverage industries as well as in enzymatic esterifications. As a part of a study to develop a

UNIFAC model suitable for phase equilibrium calculations in such mixtures, two commonly used

UNIFAC models - the Lyngby and the Dortmund versions- are evaluated in the prediction of phase

equilibria in systems involving these classes of compounds except sugars and sugar esters, using an

extended phase equilibria database.

For systems with low water concentrations and for non-aqueous ones both models provide satisfactory

results, while with increasing water concentrations the results become poorer. In terms of overall

performance the Lyngby model performs better and it will be extended to include sugars and sugar

esters in the next part of this study.

* Corresponding author: Tel. +30 210 7723137; FAX: +30 210 7723155; E-mail: evoutsas@chemeng.ntua.gr

1. Introduction

Aqueous sugar solutions in the presence of alcohols, acids, esters and ethers are very

important in the food and beverage industry [1]. Furthermore, sugar solutions in non-aqueous

media, such as t-alcohols, are becoming important in enzymatic esterification reactions [2], [3],

[4], especially those involving the production of sugar fatty acid esters that are non-ionic,

biodegradable surfactants of high commercial significance.

The kinds of phase equilibria that are of interest here include vapour-liquid, liquid-liquid and

solid-liquid ones and there is no study that addresses prediction for this type of systems. On

the one hand there are studies presenting overall results. Lohman and Gmehling [5] using a

data base of about 4500 binary azeotropic data points and 7400 binary excess enthalpy data

sets have shown that the UNIFAC-Dortmund [6] model performs better than the original

UNIFAC [7] and the UNIFAC-Lyngby [8] ones. In addition, the UNIFAC Consortium [9] has

made a comparison between original UNIFAC and UNIFAC-Dortmund using 3300

isothermal/isobaric VLE data sets and concluded that UNIFAC-Dortmund represents a slight

improvement over original UNIFAC. Also, using a data base consisting of 12600 infinite dilution

activity coefficient data points, of mainly non-aqueous mixtures, they concluded that the

UNIFAC-Dortmund gives slightly better results than the original UNIFAC and the UNIFAC-

Lyngby. Finally, to the best of our knowledge, for solid-liquid equilibria a comprehensive

comparison has not been made.

On the other hand, there are few studies that address systems which are of interest here.

Voutsas and Tassios [10] compared various UNIFAC models in the prediction of infinite dilution

activity coefficients using an extensive data base of binary non-aqueous and aqueous mixtures.

They concluded that, for non-aqueous mixtures the UNIFAC-Dortmund gives the best results,

while for aqueous ones all UNIFAC models fail. The same conclusion for aqueous mixtures

was also derived by Zhang et al. [11].

Kuramochi et al. [12] examined the accuracy of various UNIFAC models in the prediction of

octanol-water partition coefficients (Kow) of common chemicals such as hydrocarbons,

alcohols, ethers, esters etc., as well as biochemicals such as amino acids, their derivatives and

sugars. They concluded that in the case of common chemicals all UNIFAC models could fairly

predict Kow except for hydrocarbons, with the UNIFAC-Lyngby model giving the best results,

while in the case of biochemicals none of the models was sufficient to predict Kow values.

Sancho et al. [13] concluded that original UNIFAC gives poor infinite dilution activity coefficient

predictions of food aroma compounds in water, while Voutsas et al. [14] examining similar

systems concluded that the UNIFAC-Kow model [15] is a useful model for this kind of

application. Also, UNIFAC has been applied for the thermodynamic modelling of enzymatic

esterification reactions of alcohols with acids in different organic solvents. Successful results

have been demonstrated for such reactions, e.g. prediction of water activities and solvent

screening for maximum conversion [16], [17].

In this study we intend to evaluate the performance of two commonly used UNIFAC models,

UNIFAC-Lyngby and UNIFAC-Dortmund ones, in the prediction of phase equilibrium in

mixtures containing compounds typically involved in food and beverage industry applications as

well as in enzymatic reactions of sugars except sugars and sugar derivatives. To this purpose it

is used an extensive database of phase equilibrium data: vapor-liquid equilibrium (VLE), infinite

dilution activity coefficients (γ∞), liquid-liquid equilibrium (LLE) and solid-liquid equilibrium (SLE)

in mixtures containing alcohols, acids, esters, ethers and water. The complete data base is

presented in the Appendix.

2. The models considered

The most successful activity coefficient models for phase equilibria predictions are UNIFAC [7]

and modified UNIFAC [6], [8], [18]. In these models a molecule is described as a sum of

independent functional groups, and a mixture is considered to be a mixture of these functional

groups. The activity coefficient of a molecule in a mixture is then obtained from the sum of

activity coefficients of the constituent groups in the mixture. Such group contribution methods

greatly reduce the number of parameters needed in describing a variety of mixtures.

The activity coefficient (γ) in UNIFAC is calculated as the sum of two terms:

Ri

Cii γlnγlnγln += (1)

The combinatorial term (lnγiC), which is a function of the mole fraction, the group volume (Rk)

and group area (Qk) parameters, accounts approximately for the entropic effects, while the

residual term (lnγiR), which is a function of the mole fraction, the temperature, the group area

parameters and the pair group interaction parameters, describes the energetic interactions

between the different groups. It should be noted that the Lyngby model uses Bondi’s values

[19] for the R and Q parameters of the groups, which have a certain physical meaning as they

represent volume and surface area of the structural groups, while in the Dortmund model these

parameters are taken as adjustable to get a higher flexibility. However, free adjusting of these

values with a combinatorial expression that includes the Staverman-Guggenheim part may lead

to unreasonable results [20].

In view of previous published results, mentioned in the introduction section, on the performance

of the various UNIFAC models in phase equilibrium predictions we decided to evaluate in this

work the Lyngby and Dortmund UNIFAC versions. These two models use improved

combinatorial terms over the original UNIFAC model as well as residual ones by utilizing

temperature dependent interaction parameters. In the UNIFAC-Lyngby these parameters have

been estimated from VLE and heats of mixing data and in the UNIFAC-Dortmund from VLE,

LLE, SLE, heats of mixing and infinite dilution activity coefficient data. Details on the models

can be found in their original publications.

3. Results and Discussion

3.1. Prediction of Vapor-Liquid Equilibrium (VLE)

VLE calculations were performed using the so-called γ-φ approach where activity coefficients

are used to describe the real behavior of the liquid phase, while fugacity coefficients (φ) are

used to account for the non-ideality of the vapor phase:

( )isi

siii

vii POYPφγxPφy = (2)

Activity coefficients were predicted from UNIFAC. Fugacity coefficients were obtained from the

virial equation of state truncated after the second term with pure and cross virial coefficients

predicted from the Tsonopoulos’ correlations [21], except for the systems containing acids

where virial coefficients were predicted from the Hayden-O’ Connel correlations [22]. The

Poynting correction (POY) was calculated from the following expression:

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

RTPPV

expPOYsii

i (3)

where Vi is the average molar volume of pure liquid i at temperature T from Pis to the system

pressure P. Pure compound vapor pressures (Ps) were obtained from DIPPR [23] andvolumes

from the Rackett equation [24].

Table 1 presents prediction results for binary systems, while Table 2 for ternary systems.

Both models provide similar and satisfactory binary VLE predictions, considering the degree of

nonideality of the systems considered. Poor results are obtained, however, for the water/2-

methyl-2-butanol system with the Dortmund model, which is an important system considering

that this alcohol is one of the most suitable solvents for enzymatic esterification reactions of

sugars with fatty acids [4], [25], [26]. Excluding the isotherms for this system, the overall

absolute percent error in bubble point pressure prediction obtained by the Dortmund model is

4.9% as compared to 3.0% for the Lyngby model. The average absolute deviation in vapour

phase mole fraction is below 0.02 for both models.

From the results presented in Table 2 it is concluded that the two models give successful VLE

predictions for ternary systems. The deviations are below 1% in temperature and 0.04 in

vapour phase mole fraction for isobaric systems, and about 6% in pressure and 0.015 in

vapour phase mole fraction for isothermal ones.

3.2. Prediction of infinite dilution activity coefficients

Table 3 presents the summary of the overall results for binary activity infinite dilution activity

coefficients prediction. Satisfactory results are obtained by both models for non-aqueous

systems, but poorer ones for aqueous systems, especially for water in diols where both models

gives very poor results, with the Dortmund model to give the highest errors.

The most important systems for esterification reactions are those involving the infinite dilution

activity coefficients of water because these reactions carried out at very low water activities. In

such cases, except when a diol is the solvent, the results are considered satisfactory, taking

into account the high uncertainty involved in the experimental data for aqueous mixtures [11].

Finally, since no γ∞ values for water in multi-component systems are available, we examined

water activity predictions, at low water concentrations, in ternary systems. Very satisfactory

predictions results are obtained by both models as suggested by the typical results presented

in Figure 1.

3.3. Prediction of Liquid-Liquid Equilibrium (LLE)

LLE calculations were performed using the isoactivity criterion:

( ) ( )IIiiI

iiIIi

Ii γxγxaa =⇒= (4)

where the activity coefficients in the two liquid phases (I and II) were predicted from UNIFAC.

Typical binary LLE predictions for aqueous systems with alcohols and esters are shown

graphically in Figures 2, 3 and 4 respectively, while prediction of solubilities of some fatty acid

esters in water are shown in Figure 5.

Both models give poor results for alcohols as Figure 2 indicates. The Lyngby model predicts

the correct temperature dependency for t-pentanol but not for 1-pentanol while the opposite is

the case for the Dortmund one. The Dortmund model gives qualitatively the correct trend of

mutual solubilities for the two alcohols in water, i.e. 1-pentanol is less soluble in water than t-

pentanol, while the Lyngby model predicts the opposite. The same picture with 1-pentanol and

tert-pentanol is observed for 1-butanol and tert-butanol.

Better results are obtained for aqueous systems of ethers and esters as indicated by Figures 3

and 4 respectively. In general, typical solubility predictions are off by a factor of 2 and this is

also the case with long chain esters in water where both models strongly overestimate the fatty

acid ester solubility, especially the Lyngby one, by a factor of 2 to 3 (Figure 5).

Typical prediction results for ternary aqueous systems containing acids, along with alcohols or

with esters are presented in Figures 6, 7, 8 and 9. The Lyngby model gives better results,

which however tend to become poorer when a large acid is involved as suggested by Figure 7.

For aqueous ether/ alcohol ternary systems the Lyngby model gives good results as Figure 10

indicates, while poor results are obtained by both models for aqueous ether / acid systems

(Figure 11).

Finally, for the single available non-aqueous system: ethanediol/acetic acid/ethyl acetate,

presented in Figure 12, the Lyngby model gives rather poor results while the Dortmund one

cannot be applied since interaction parameters for the ethanediol group and the COOH one are

not available.

The relatively poor overall performance of the two models in LLE predictions as compared to

the VLE ones is expected: the systems are very non ideal and in addition, both models were

not developed with emphasis to LLE calculations, although in the database used for fitting the

parameters of the Dortmund model LLE information has been included. To this purpose we

investigated the use of the LLE-UNIFAC [27] , which has been especially developed for LLE

calculations. Surprisingly, no improvement over the other two UNIFAC models is obtained as

indicated by the results presented in Figures 2, 5, 7 and 11.

3.4. Prediction of Solid-Liquid Equilibrium (SLE)

Solubility data of fatty acids in ethanol and in ethanol/water mixtures are the only pertinent SLE

data available. Solubility predictions were carried out using the following expression:

⎟⎟⎠

⎞⎜⎜⎝

⎛−−=⋅

m

fus

TT1

RTH∆

)γxln( (5)

where the activity coefficient of the solute is predicted from UNIFAC. The required melting point

temperature (Tm) and heat of fusion (∆Hfus) data for the compounds involved in this work are

presented in Table 4.

The predicted solubilities of fatty acids in ethanol, presented in Figure 13, are in very good

agreement with the experimental data. However, in the ternary mixtures of fatty acid with

ethanol and water, Figures 14 and 15, both models cannot predict the strong effect of water on

fatty acid’s solubility at the higher temperatures where the fatty acid concentration is high.

Figure 16 presents prediction of SLE in quaternary mixtures containing two fatty acids, ethanol

and water. The results are qualitatively correct but they are not quantitatively satisfactory,

which is more pronounced at low fatty acid concentrations where significant underestimation is

observed especially by the Dortmund model. It is shown that fairly good predictions are

obtained by both models especially at the higher water concentrations, with the Lyngby model

yielding the best overall results.

Fortunately, the poor performance of the UNIFAC models in predicting the effect of water in the

fatty acid solubility in alcohol – water mixtures is not important in the enzymatic esterification of

sugars with fatty acids. In this case, water is continuously removed to increase conversion

using enzymes with very low optimum water activity. Thus, the important factor is the solubility

of the fatty acid in the alcohol which is predicted satisfactorily as shown in Figure 13.

4. Conclusions

Mixtures involving sugars, sugar esters, alcohols, acids, esters, ethers and water are of interest

in the food and beverage industries as well as in enzymatic esterifications. In this study, which

is a part of an ongoing project aiming to the development of a UNIFAC model suitable for such

mixtures, two commonly used UNIFAC models - the Lyngby and the Dortmund versions - are

evaluated in the prediction of phase equilibria of systems involving these kinds of compounds

except sugars and sugar esters.

The Lyngby and Dortmund UNIFAC models were evaluated in an extended database using:

over 1200 experimental VLE data from over 30 systems, experimental LLE data for over 40

binary and ternary mixtures, over 300 experimental activity coefficients at infinite dilution and

about 100 SLE experimental data.

For VLE in dilute aqueous systems – such as those encountered in the food and beverage

industry – both models give poor results and the UNIFAC Kow model should be used, as

demonstrated by the study of Voutsas et al. [14]. For systems with low water concentrations –

such as those encountered in the enzymatic reactions in non-aqueous solvents – the results

can be considered satisfactory by both models. For LLE in aqueous systems, the Lyngby

model performs better than Dortmund one, but the predicted solubilities are typically off by a

factor of 2 – 3 and the same applies for solubilities of solid fatty acid ester in water. In the case

of non-aqueous systems the phase equilibrium predictions can be considered satisfactory at

least for group contribution models.

On the basis of these results the Lyngby model will be extended to include sugars and sugar

esters in the next part of this study.

Nomenclature

a: activity

P: pressure

Ps: vapour pressure

POY: Poynting correction (Eq. 3)

Qk: group volume parameter

R: gas constant

Rk: group area parameter

T: temperature

Tm: melting point temperature

V: molar volume of pure liquid (Eq. 2)

x: mole fraction in the liquid phase

y: mole fraction in the vapor phase

Greek symbols

γ: activity coefficient

∆Hfus: heat of fusion

φ: fugacity coefficient

Superscripts

C: combinatorial (Eq. 1)

R: residual (Eq. 1)

s: saturated

v: vapor

∞: infinite dilution

Subscripts

i: component i

Table symbols

calc: calculated value

exp: experimental value

min: minimum

max: maximum

N: number of data points per system

∆P%: average absolute percent error in bubble pressure

∆T%: average absolute percent error in bubble temperature

∆y: average absolute error in vapor phase composition

References

[1] Watanabe T., Sucrose Fatty acid Esters: Past, Present and Future, Foods Food Ingredients

Journal of Japan, 180 (1999) 18-25

[2] Coulon D., Ismail, A., Girardin M., Rovel B, Ghoul M. J., Biotechnology, 51 (1996) 115-121

[3] Tsuzuki W., Kitamura Y., Suzuki T., Kobayashi S., Biotechnology Bioengineering, 64 (1999)

267-271

[4] Degn P., Pedersen L., Zimmermann W., Biotechnology Letters, 21 (1999) 275 –280.

[5] Lohman and Gmehling J. Chem. Eng. Japan, 34 (2001) 43-54.

[6] Gmehling J., Li J. and Shiller M., Ind. Eng. Chem. Res., 32 (1993) 178-193

[7] Fredenslund Aa., Jones, R. L.; Prausnnitz, J. M.; Group-Contribution Estimation of Activity

Coefficients in Nonideal Liquid Mixtures, ALChE J., 1975, 21, 1086

[8] Larsen B.L., Rasmussen P. and Fredenslund Aa., Ind. Eng. Chem. Res., 26 (1987) 2274-

2286

[9] http://www.uni-oldenburg.de/tchemie/Consortium/Model_Comparison.html

[10] Voutsas E. C., Tassios D., Ind. Eng. Chem. Res., 35, 1996, 1438-1445.

[11] Zhang S., Toshihiko H., Hongo M., Kojima K., Fluid Phase Equilibria, 144 (1998) 97-112

[12] Kuramochi et al., FPE, 144 (1998) 87-95.

[13] Sancho et al., J. of Food Engineering, 34 (1997) 145-158.

[14] Voutsas E. C., Andreou C. I., Thedorou D. G., Tassios D. P., Journal of Food Engineering

and Physical Properties, 66 (2001) 447-452.

[15] Wienke G., Gmehling J., Toxicological and Environmental Chemistry, 65 (1998) 57-86

[16] Halling P. J. , Biotechnology Bioengineering, 35 (1990) 691-701

[17] H. Stamatis; E. C. Voutsas; C. Delimitsou; F. N. Kolisis and D. Tassios, Biocatalysis

Biotransformation, 18 (1999) 259-269

[18] Weidlich, U. and Gmehling, J., 1987. A Modified UNIFAC Model. 1. Prediction of VLE, hE,

and γ∞. Ind. Eng. Chem. Res., 26: 1372-1381.

[19] Bondi A., Physical Properties of Molecular Crystals, Liquids and Glasses, 1968, Willey, N.

York

[20] Abildskov J., Gani R., Rasmussen P., O’ Connell J. P., Fluid Phase Equilibria 181 (2001)

163-186

[21] Tsonopoulos C., AlChE Journal, 20 (2) (1974) 263-272

[22] Fredenslund Aa., Gmehling J., Rasmussen P., Vapor-Liquid Equilibria using UNIFAC,

Elsevier Amsterdam-Oxford-N. York, 1977

[23] Daubert T. E., Danner R. P. Data Compilation tables of properties of Pure Compounds.

Design Institute for Physical Property Data; American Institute of Chemical Engineering.

1994, 13, 91

[24] Rackett H. G., J. Chem. Data, 15 (1970)

[25] Chamoleau F., Coulon D., Girardin M., Ghoul M., J. Mol. Catal. B: Enzymatic, 11 (2001)

949-954

[26] Flores M. F., Naraghi K., Engasser J. M., Halling P. J., Biotechnol. Bioeng., submitted

[27] Magnussen T., Rasmussen P. and Fredenslund Aa., Ind. Eng. Chem. Processes Des. Dev.,

20 (1981) 331-339.

[28] Kojima K., Zhang S., Hiaki T., Fluid Phase Equilibria 131 (1997) 145-179.

[29] Garriga R., Sánchez F., Pérez P., Gracia M., Fluid Phase Equil., 138 (1997) 131-144

[30] Fischer K., Shulgin I., Rarey J., Gmehling J.. Fluid Phase Equilibria, 120 (1996)143-165

[31] Gmehling J., Onken U., Vapor-Liquid Equilibrium Data Collection, DECHEMA Chemistry

Data Series, DECHEMA: Frankfurt 1986, Vol. I, Parts 1-5.

[32] Lee M. J., Hsiao C.C., Lin H. m., Fluid Phase Equilibria, 137 (1997) 193-207

[33] Sherman S. R., Eckert C. A., Scott L. S., Chemical Engineering And Processing 35 (1996)

363-371

[34] Krähenbuhl M. A., Munoz L., J. Chem. Eng. Data, 46 (2001) 120-124

[35] Darwish N. A., Al-Khateib A. A., Fluid Phase Equil., 126 (1996) 105-113

[36] Pierotti, G.J., Deak, C.H., Derr E.L., Ind. Eng. Chem., 51 (1959) 95

[37] Tiegs D., Gmehling J., Medina A., Soares M., Bastos J., Alessi P., Kikic I., Activity

Coefficients at Infinite Dilution, DECHEMA Chemistry Data Series, DECHEMA: Frankfurt

1986, Vol. IX, Parts 1 and 2.

[38] Fukuchi K., Miyoshi K., Watanabe T., Yonezawa S., Arai Y., Fluid Phase Equilibria., 156

(1999) 197-206

[39] Delcros S., Grollier J. P., Dohnal V., Fenclová D., Chemical Engineering Science, 50

(18) (1995) 2957-2962

[40] Α. M. Peres, E. A. Macedo, Entropie, 202/203 (1997) 1-5

[41] Α. M. Peres, E. A. Macedo, Carboh. Res., 36 (1997) 135-151

[42] Chen L.-J., Pai H.-Y., Fluid Phase Equilibria, 155 (1999) 99-105

[43] Sorensen J. M, Arlt W. Liquid-Liquid Equilibrium Data Collection, DECHEMA Chemistry

Data Series, DECHEMA: Frankfurt 1979, Vol. V, Parts 1, 2 and 3.

[44] Krop H. B., Martin J. M. van Velzen, Parsons J. R., Govers H. A. J., Chemosphere, 34

(1997) 107-119

[45] Maeda K., Yamada S., Hirota S., Fluid Phase Equilibria, 130 (1997) 281-294

[46] Acre A. J., Martinez-Ageitos J., Rodil E., Rodriquez O., Soto A. Fluid Phase Equilibria, 170

(2000) 113-123

[47] Maeda K., Kashimoto T., Fukui K., Hirota S., Fluid Phase Equilibria, 162 (1999) 193-209

[48] Solimo H., Bonatt C., Zurita J., Gramajo de Goz M., Fluid Phase Equilibria, 137 (1997) 163-

172

[49] Prochazka J., Heyberger A. Chemical Engineering Science 51 (1996) 893-903

Table 1. Prediction results for binary VLE systems

System T (K) Na Pmin PmaxDortmund UNIFAC

Lyngby UNIFAC

Dortmund UNIFAC

Lyngby UNIFAC Ref

acetic acid(1)-ethyl acetate(2) 315 7 39 - 194 1,86 0,81 0,82 0,75 31acetic acid(1)-ethyl acetate(2) 333 9 128 - 401 4,60 3,07 0,55 1,04 31

di-n-propyl ether(1)-1 propanol(2) 278 15 5 - 22 4,38 4,00 0,99 1,01 29di-n-propyl ether(1)-1 propanol(2) 288 15 11 - 38 4,69 4,20 0,86 0,71 29di-n-propyl ether(1)-1 propanol(2) 293 15 15 - 50 4,56 4,01 6,47 6,23 29di-n-propyl ether(1)-1 propanol(2) 298 15 21 - 65 4,32 3,72 0,90 0,63 29di-n-propyl ether(1)-1 propanol(2) 303 15 29 - 83 4,35 3,70 1,08 0,79 29di-n-propyl ether(1)-1 propanol(2) 308 15 39 - 105 4,01 3,31 1,12 0,82 29di-n-propyl ether(1)-1 propanol(2) 313 15 53 - 132 3,82 3,07 1,24 0,92 29di-n-propyl ether(1)-1 propanol(2) 323 15 92 - 203 3,03 2,16 1,25 0,85 29di-n-propyl ether(1)-2 propanol(2) 278 15 11 - 25 4,36 2,06 2,50 1,59 29di-n-propyl ether(1)-2 propanol(2) 288 15 23 - 45 4,91 2,55 2,53 1,68 29di-n-propyl ether(1)-2 propanol(2) 293 15 32 - 59 5,06 2,59 2,54 1,66 29di-n-propyl ether(1)-2 propanol(2) 298 15 44 - 77 5,03 2,63 2,47 1,62 29di-n-propyl ether(1)-2 propanol(2) 303 15 59 - 99 5,16 2,67 2,47 1,58 29di-n-propyl ether(1)-2 propanol(2) 308 15 79 - 126 5,06 2,59 2,24 1,49 29di-n-propyl ether(1)-2 propanol(2) 313 15 105 - 160 4,86 2,35 2,31 1,33 29di-n-propyl ether(1)-2 propanol(2) 323 15 177 - 251 4,18 1,66 2,23 1,09 29

ethyl acetate(1)-water(2) 313 8 56 - 191 1,63 1,29 1,49 1,24 31ethyl acetate(1)-water(2) 328 8 119 - 352 1,98 1,39 1,69 1,26 31ethyl acetate(1)-water(2) 343 9 234 - 610 1,77 1,03 1,28 1,00 31

methyl acetate(1)-ethanol(2) 323 8 241 - 570 8,17 7,95 1,40 1,46 31methyl acetate(1)-ethanol(2) 333 8 370 - 810 7,73 7,17 2,64 2,60 31methyl acetate(1)-ethanol(2) 343 8 580 - 1132 2,64 1,90 1,67 1,41 31

methyl propanoate(1)-ethanol(2) 298 16 67 - 101 4,78 1,60 1,74 1,00 31MTBE (1)-ethyl acetate(2) 353 11 950 - 1563 8,44 2,65 2,51 0,64 32MTBE (1)-ethyl acetate(2) 363 11 1289 - 2052 8,72 3,76 2,33 0,70 32MTBE (1)-ethyl acetate(2) 373 11 1706 - 2643 8,59 4,56 2,17 0,74 32

MTBE (1)-methyl acetate(2) 363 11 2192 - 2351 8,25 4,16 3,02 1,26 32MTBE (1)-methyl acetate(2) 373 11 2830 - 3038 7,99 4,95 2,90 1,35 32MTBE(1)-methyl acetate(2) 353 11 1673 - 1784 8,20 3,16 2,92 1,18 32propyl acetate(1)-water(2) 353 9 355 - 686 5,02 3,83 3,23 3,03 31

water(1)-2 methyl 2 butanol(2) 283 81 6 - 13 17,18 4,72 - - 30water(1)-2 methyl 2 butanol(2) 303 94 23 - 47 14,33 7,96 - - 30water(1)-2 methyl 2 butanol(2) 328 71 101 - 185 12,91 7,54 - - 30water(1)-2 methyl 2 butanol(2) 343 92 208 - 372 4,51 5,76 - - 30

water(1)-ethanol(2) 298 14 24 - 59 1,54 1,00 0,45 0,88 31water(1)-ethanol(2) 348 7 289 - 668 1,33 0,96 1,54 1,38 31

Overall 755 8,08 4,56 2,01 1,38

ISOBARIC DATA

System P(mmHg) N Tmin TmaxDortmund UNIFAC

Lyngby UNIFAC

Dortmund UNIFAC

Lyngby UNIFAC Ref

3 pentenoic acid(1)-methyl-3-pentenoate(2) 100 14 351 - 403,7 3,25 4,02 - - 333 pentenoic acid(1)-methyl-3-pentenoate(2) 270 14 377 - 429,5 5,63 6,63 - - 333 pentenoic acid(1)-methyl-3-pentenoate(2) 669 7 406 - 407,8 6,16 6,88 - - 33

3 pentenoic acid(1)-water(2) 100 10 325 - 404,8 1,55 2,03 - - 333 pentenoic acid(1)-water(2) 270 12 346 - 431,3 1,74 2,59 - - 33butyric acid(1)-n-butanol(2) 200 16 358 - 397,6 2,10 1,92 1,15 0,92 34butyric acid(1)-n-butanol(2) 400 12 374 - 416,6 2,16 2,77 2,00 1,37 34

diethyl ether(1)-acetic acid(2) 390 9 291 - 371 0,89 0,81 1,66 1,61 31diethyl ether(1)-acetic acid(2) 488 9 298 - 377,6 0,59 0,66 1,30 1,31 31diethyl ether(1)-acetic acid(2) 597 9 301 - 383,4 0,49 0,66 1,04 1,03 31ethyl acetate(1)-n-butanol(2) 529 15 340 - 381,1 0,09 0,12 0,81 0,39 35ethyl acetate(1)-n-butanol(2) 705 16 348 - 388,8 0,12 0,15 0,39 0,70 35

ethyl acetate(1)-water(2) 760 10 347 - 372 0,65 0,46 5,36 5,10 31methyl acetate(1)-ethanol(2) 760 9 331 - 347,7 0,05 0,09 0,51 0,81 31

propionic acid(1)-n-butanol(2) 760 17 392 - 413,9 0,78 1,37 1,78 2,89 31propionic acid(1)-water(2) 760 18 372 - 401,1 1,50 1,70 3,20 1,20 31

water(1)-ethanol(2) 760 19 349 - 372,1 0,18 0,22 1,77 2,29 31Overall 216 1,55 1,85 1,74 1,61

a: number of data pointsb,d: average absolute percent error defined as and

c: average absolute deviation defined as

ISOTHERMAL DATA

∆T% dT range (K) 100*∆Y1 c

100*∆Y1 c∆P% bP range (mmHg)

∑−

=∆N

i iPiPcalc

iPP exp

exp%

∑ −=∆ )exp( calciyiyNy 100100

∑−

=∆N

i iTiTcalc

iTT exp

exp%

Table 2. Prediction results for ternary VLE systemsISOBARIC DATA

System P(mmHg) N Tmin TmaxDortmund UNIFAC

Lyngby UNIFAC

Dortmund UNIFAC

Lyngby UNIFAC

Dortmund UNIFAC

Lyngby UNIFAC Ref

acetic acid(1)-methyl propionate(2)-water(3) 760 18 348 - 391 1,83 1,97 3,27 3,57 4,82 6,30 331ethanol(1) - water(2) - ethyl acetate(3) 760 22 352 - 367 0,18 0,24 1,34 1,78 2,34 2,29 31ethanol(1) - water(2) - butyl acetate(3) 760 20 352 - 363 0,2 0,32 5,4 4,81 4,70 3,93 31

ethanol(1) - water(2) - isopentyl acetate(3) 760 26 352 - 361 0,16 0,26 1,31 1,22 0,90 0,90 31diethyl ether(1) - ethanol(2) - water(3) 760 25 316 - 354 0,76 0,97 6,88 7,87 4,17 4,68 31

Overall 111 0,58 0,70 3,63 3,86 3,24 3,45

ISOTHERMAL DATA

System T(K) N Pmin PmaxDortmund UNIFAC

Lyngby UNIFAC

Dortmund UNIFAC

Lyngby UNIFAC

Dortmund UNIFAC

Lyngby UNIFAC Ref

ethanol(1) - water(2) - ethyl acetate(3) 333 27 252 - 486 6,59 6,65 1,92 1,47 2,64 2,2 31ethanol(1) - water(2) - isopentyl acetate(3) 323 26 380 - 557 6,62 6,79 1,81 1,1 1,25 1,11 31ethanol(1) - water(2) - isopentyl acetate(3) 333 24 267 - 343 3,59 4,34 1,67 1,14 1,19 1,07 31ethanol(1) - water(2) - isopentyl acetate(3) 343 26 173 - 252 6,28 6,92 1,35 1,11 1,03 0,97 31

Overall 103 5,82 6,22 1,69 1,21 1,54 1,35

P range (mmHg) 100*∆Y2 100*∆Y1

∆T% 100*∆Y2 100*∆Y1

∆P%

T range (K)

Table 3. Prediction results for infinite dilution activity coefficients

Solvent Solute N Tmin Tmax Dortmund UNIFAC Lyngby UNIFAC Ref.Alcohols Water 37 288 - 383 18,9 31,7 28, 36Water Alcohols 37 293 - 373 60,9 68,8 28Water Diols 18 297 - 348 565,07 282,0 28Acids Alcohols 17 344 - 413 23,8 8,5 37Esters Alcohols 16 313 - 394 9,1 29,1 37

Alcohols Esters 26 308 - -373 25 17,8 37Alcohols Ethers 27 283 - 373 21 13,4 38, 39Ethers Alcohols 18 296 - 348 15,1 12,0 37, 38, 39Water Ethers 16 298 - 298 103,7 75,1 28Water Acids 7 298 - 303 60,7 75,6 28Acids Water 4 340 - 373 23,3 3,9 28, 36Water Esters 24 298 - 308 29,8 47,7 28Esters Water 13 288 - 373 26 13,4 28Acids Esters 32 344 - 416 11,3 9,1 37Esters Acids 4 313 - 374 13,3 35,9 37

296 63,54 47,1

T range (K)

Overall

Average Absolute Error in γ∞

Table 4. Physical properties of fatty acids used with UNIFAC models

Tm (K) ∆Hfus (J / mol) Ref.lauric acid 316,8 36600 45

myristic acid 327 45000 45palmitic acid 335,2 54000 45

Figure Captions

Figure 1. Prediction of water activity at low water concentration -water mole fraction lower than 0.2- for the ethanol/water/isopentyl acetate mixture. Experimental data [31]

Figure 2. Prediction of LLE for water / 1-pentanol and water / t-pentanol mixture. Experimental data from [42]

Figure 3. Prediction of LLE for tert-butyl methyl ether / water mixture. Experimental data from [43]

Figure 4. Prediction of LLE for propyl acetate / water mixture. Experimental data from [43]

Figure 5. Solubility of fatty acid esters in water. Experimental data from [44]

Figure 6. Prediction of LLE for the propenoic acid / 1-hexanol / water mixture. Experimental data from [43]

Figure 7. Prediction of LLE in myristic acid / ethanol / water mixture. Experimental data from [45]

Figure 8. Prediction of LLE in acetic acid / ethyl pentanoate / water mixture. Experimental data from [43]

Figure 9. Prediction of LLE in butanoic acid / ethyl butanoate / water mixture. Experimental data from [43]

Figure 10. Prediction of LLE in di-isopropyl ether / 2-propanol / water mixture. Experimental data from [46]

Figure 11. Prediction of LLE in di-isopropyl ether / acetic acid / water mixture. Experimental data from [43]

Figure 12. Prediction of LLE in 1,2 ethanediol / acetic acid / ethyl acetate mixture. Experimental data from [43]

Figure 13. Prediction of fatty acid solubility in ethanol. Experimental data from [45], [47]

Figure 14. Prediction of lauric acid solubility in ethanol / water mixtures. Experimental data from [45]

Figure 15. Prediction of myristic acid solubility in ethanol / water mixtures. Experimental data from [45]

Figure 16. Total fatty acid solubility in lauric acid / myristic acid / ethanol / water mixtures. Experimental data from [47]

Figure 1. Prediction of water activity at low water concentration (water mole fraction lower than 0.2) for the ethanol/water/isopentyl acetate mixture. Experimental data

from [31]

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

experimental water activity

pred

icte

d w

ater

act

ivity

Dortmund UNIFAC

Lyngby UNIFAC

Figure 2. Prediction of LLE for water / 1-pentanol and water / t-pentanol mixture. a) alcohol ich phase; b) water rich phase. Experimental data from [42]

0

10

20

30

40

50

60

70

80

90

100

0.00 0.20 0.40 0.60 0.80

X water

t (o C

)

(a)

0.90 0.92 0.94 0.96 0.98 1.00

X water

1-pentanol, experimentalt-pentanol, experimentalDortmund UNIFAC (1-pentanol)Dortmund UNIFAC (t-pentanol)Lyngby UNIFAC (1-pentanol)Lyngby UNIFAC (t-pentanol)LLE UNIFAC (1-pentanol)LLE UNIFAC (t-pentanol)

(b)

Figure 3. Prediction of LLE for tert-butyl methyl ether / water mixture. a)ether rich phase; b)water rich phase. Experimental data from [43]

0

5

10

15

20

25

30

0.00 0.05 0.10 0.15 0.20

Xwater

T (o C

)

(a)

0.90 0.92 0.94 0.96 0.98 1.00

Xwater

Exp. dataDortmund UNIFAC

Lyngby UNIFAC

(b)

Figure 4. Prediction of LLE for propyl acetate / water mixture. Experimental data from [43]

0

5

10

15

20

25

30

35

40

0.00 0.05 0.10 0.15 0.20

X water

T (o C

)

(a)

0.90 0.92 0.94 0.96 0.98 1.00

X water

Exp. dataDortmund UNIFACLyngby UNIFAC

(b)

Figure 5. Solubility of fatty acid esters in water at 298 K. Experimental data from [44]

1

24

35 7

6

-1.5E+01

-1.0E+01

-5.0E+00

0.0E+00-1.5E+01-1.0E+01-5.0E+000.0E+00

log experimental solubility

log

pred

icte

d so

lubi

lity

Dortmund UNIFAC

Lyngby UNIFAC

LLE UNIFAC

Solubility is expressed in mole f ti1. methyl laureate2. ethyl laureate3. propyl laureate4. methyl myristate5. butyl laureate6. methyl stearate7. methyl palmitate

Figure 6. Prediction of LLE for the propenoic acid / 1-hexanol / water mixture at 303.15 K. Experimental data from [43]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

X water

X ac

id

Exp. data

Dortmund UNIFAC

Lyngby UNIFAC

Figure 7. Prediction of LLE in myristic acid / ethanol / water mixture. Experimental data from [45]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0X acid

X et

hano

l

T=313KT=323KDortmund UNIFACLyngby UNIFACLLE UNIFAC

The predicted by the models curves at different temperatures can not be distinguised

Figure 8. Prediction of LLE in acetic acid / ethyl pentanoate / water mixture at 293 K. Experimental data from [43]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

X water

X ac

id

Exp. data

Dortmund UNIFAC

Lyngby UNIFAC

Figure 9. Prediction of LLE in butanoic acid / ethyl butanoate / water mixture at 293 K. Experimental data from [43]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

X water

X ac

id

Exp. data

Dortmund UNIFAC

Lyngby UNIFAC

Figure 10. Prediction of LLE in di-isopropyl ether / 2-propanol / water mixture 298 K. Experimental data from [46]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

X water

X al

coho

l

T=298KT=308KT=318KDortmund UNIFACLyngby UNIFAC

298K

318K

318K

298K

Figure 11. Prediction of LLE in di-isopropyl ether / acetic acid / water mixture 298 K. Experimental data from [43]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

X water

X ac

id

Exp. dataDortmund UNIFACLyngby UNIFACLLE UNIFAC

Figure 12. Prediction of LLE in 1,2 ethanediol / acetic acid / ethyl acetate mixture 298 K. Experimental data from [43]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.0 0.2 0.4 0.6 0.8 1.0

X alcohol

X ac

id

Exp. data

Lyngby UNIFAC

Dortmund UNIFAC cannot be applied

Figure 13. Prediction of fatty acid solubility in ethanol. Experimental data from [45], [47]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

293.15 303.15 313.15 323.15 333.15 343.15

Temperature (K)

Solu

bilit

y of

aci

d (m

ole

frac

tion)

Myristic acid

Lauric acid

Palmitic acid

Dortmund UNIFAC

Lyngby UNIFAC

Figure 14. Prediction of lauric acid solubility in ethanol / water mixtures. Experimental data from [45]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

water mole fraction in acid-free solvent

fatty

aci

d m

ole

frac

tion

T=298KT=303KT=308KT=313KDortmund UNIFACLyngby UNIFAC

After the end point of the solubility curves LLE is predicted by the models.

Figure 15. Prediction of myristic acid solubility in ethanol / water mixtures. Experimental data from [45]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

water mole fraction in acid-free solvent

fatty

aci

d m

ole

frac

tion

T=293K

T=303K

T=313K

T=323K

Dortmund UNIFAC

Lygby UNIFAC

After the end point of the solubility curves LLE is predicted by the models.

Figure 16. Total fatty acid solubility in lauric acid / myristic acid / ethanol / water mixtures. Experimental

data from [47]

270

280

290

300

310

320

330

0.0 0.2 0.4 0.6 0.8 1.0

XFA

T (K

)

Xa: 0.1

Xa: 0.2

Dortmund UNIFAC

Lyngby UNIFAC

Xl=0.2

270

280

290

300

310

320

330

0.0 0.2 0.4 0.6 0.8 1.0

XFA

T (K

)

Xa: 0.1

Xa: 0.2

Dortmund UNIFAC

Lyngby UNIFAC

Xl=0.5

270

280

290

300

310

320

330

0.0 0.2 0.4 0.6 0.8 1.0

XFA

Tem

pera

ture

(K)

Xa: 0.1

Xa: 0.2

Dortmund UNIFAC

Lyngby UNIFAC

Xl=0.8

270

280

290

300

310

320

330

0.0 0.2 0.4 0.6 0.8 1.0

XFA

T (K

)

Xa: 0.2

Xa: 0.3

Dortmund UNIFAC

Lyngby UNIFAC

Xl=0.0

Xa: water mole fraction in acid free base

Xl: mole fraction of lauric acid in solvent free base

XFA: total mole fraction of fatty acids

APPENDIX: Data base

A. Binary VLE data

ISOTHERMAL DATA N Tmin Tmax Pmin Pmax Ref water Ethanol 21 298 - 348 24 - 668 [31] methyl acetate Ethanol 24 323 - 333 241 - 1132 [31] methyl propanoate Ethanol 16 298 - 67 - 101 [31] oleic acid Ethanol 12 318 - 14 - 173 [31] di-n-propyl ether 1-propanol 120 278 - 323 5 - 203 [29] di-n-propyl ether 2-propanol 120 278 - 323 11 - 251 [29] water t-pentanol 338 283 - 343 6 - 372 [31] ethyl acetate Water 25 313 - 343 56 - 610 [31] propyl acetate Water 9 353 - 355 - 686 [31] acetic acid ethyl acetate 16 315 - 333 39 - 401 [31] MTBE methyl acetate 33 353 - 373 1673 - 3038 [32] MTBE ethyl acetate 33 353 - 373 950 - 2643 [32] Overall 804 ISOBARIC DATA N Tmin Tmax Pmin Pmax Ref 3 pentenoic acid methyl-3-pentenoate 35 351 - 430 100 - 669 [33] 3 pentenoic acid water 23 325 - 431 100 - 270 [33] butyric acid n-butanol 28 358 - 417 200 - 400 [34] diethyl ether acetic acid 27 291 - 383 390 - 597 [31] ethyl acetate n-butanol 31 340 - 389 400 - 705 [35] Water ethanol 19 349 - 372 760 - 760 [31] propionic acid water 18 372 - 401 760 - 760 [31] propionic acid n-butanol 17 392 - 414 760 - 760 [31] methyl acetate ethanol 9 331 - 348 760 - 760 [31] ethyl acetate water 10 347 - 372 760 - 760 [31] 228

B. Ternary VLE data

ISOBARIC DATA N Tmin Tmax Pmin Pmax Ref Ethanol water ethyl acetate 22 352 - 367 760 - 760 [31] Ethanol water butyl acetate 20 352 - 363 760 - 760 [31] Ethanol water isopentyl acetate 26 352 - 361 760 - 760 [31] diethyl ether ethanol water 25 316 - 354 760 - 760 [31] acetic acid methyl propionate water 18 348 - 391 760 - 760 [31] Overall 111 ISOTHERMAL DATA N Tmin Tmax Pmin Pmax Ref

Ethanol water ethyl acetate 27 333 - 333 252 - 486 [31] ethanol water isopentyl acetate 76 323 343 173 - 557 [31] Overall 103

C. Binary LLE data

System T range (K) Ref.

water (1) / 1-butanol (2) 298-398 [43] water (1) / 1-pentanol (2) 283-353 [42] water (1) / 2-methyl-2butanol (2) 283-353 [42] acetic acid ethyl ester (1) / 1,2 ethanediol (2) 298, 304 [43] propionic acid ethyl ester (1) / 1,2 ethanediol (2) 304 [43] diisopropyl ether (1) / water (2) 293-333 [43] sec butyl methyl ether (1) / water (2) 273-298 [43] methyl tertiary butyl ether (1) / water (2) 273-298 [43] 2-methyl propionic acid (1) / water (2) 278-298 [43] isopropyl butanoate (1) / water (2) 283-306 [43] butyl butanoate (1)/ water (2) 293-308 [43] propyl acetate (1) / water (2) 293-308 [43] methyl laureate(1) / water (2) 298 [44] ethyl laureate(1) / water (2) 298 [44] propyl laureate(1) / water (2) 298 [44] butyl laureate(1) / water (2) 298 [44] methyl myristate(1) / water (2) 298 [44] methyl palmitate(1) / water (2) 298 [44] methyl stearate(1) / water (2) 298 [44]

D. Binary SLE data

System T range (K) Ref.

lauric acid (1) / ethanol(3) 286-327 [45] myristic acid (1) / ethanol(3) 286-327 [45] palmitic acid (1) / ethanol(3) 286-327 [45]

E. Ternary SLE data

System T range (K) Ref.

lauric acid (1) / ethanol(2) /water (3) 298-323 [45] myristic acid (1) / ethanol(2) /water(3) 298-323 [45] palmitic acid (1) / ethanol(2) /water(3) 298-333 [45] lauric acid (1)/ myristic acid(2) / ethanol(3) /water(4) 298-323 [47]

F. Ternary LLE data

System T range (K) Ref. acetic acid(1) / 1-butanol(2) / water(3) 298 [43] propenoic acid(1) / 1-hexanol(2) / water (3) 303 [43] propionic acid(1) / 1-butanol(2) / water(3) 298 [48] lauric acid(1) / ethanol(2) /water (3) 298-313 [45] myristic acid(1) / ethanol(2) /water(3) 298-313 [45] palmitic acid(1) / ethanol(2) /water(3) 298-313 [45] lauric acid(1)/ myristic acid(2) / ethanol(3) /water(4) 298-313 [47] acetic acid(1) / ethyl acetate(2) / water(3) 303-323 [43] acetic acid(1) / ethyl pentanoate(2) / water(3) 293 [43] propionic acid(1) / ethyl acetate(2) / water(3) 293, 323 [43] butanoic acid(1) / ethyl acetate(2) / water(3) 293 [43] butanoic acid(1) / ethyl butanoate(2) / water(3) 299 [43] acetic acid(1) / isobutyl acetate(2) / water(3) 293 [49] acetic acid(1) / ethyl acetate(2) / 1,2 ethanediol(3) 298 [43] ethyl acetate(1) / water(2) / ethanol(3) 273 [43] ethyl acetate(1) / water(2) / 2-butanol(3) 273 [43] ethyl acetate(1) / water(2) / 1-butanol(3) 293 [43] ethyl acetate(1) / water(2) / 1-propanol 2 methyl(3) 293 [43] dibutyl ether(1) / water(2) / 1-butanol(3) 293 [43] diisopropyl ether(1) / water(2) / 2-propanol(3) 298 [43] diisopropyl ether(1) / water(2) / isopropyl alcohol(3) 298-318 [46] diethyl ether(1) / water(2) / acetic acid(3) 292, 298 [43] dibutyl ether(1) / water(2) / acetic acid(3) 298 [43] diisopropyl ether(1) / water(2) / acetic acid(3) 298 [43] diisopropyl ether(1) / water(2) / propenoic acid(3) 298 [43]

G. Infinite dilution activity coefficients data (For References see in Table 3) Solvent Solute Tmin Tmax

ethyl acetate ethanol 313 - 373 dibutyl ether ethanol 298 - 298

methyl tertiary butl ether ethanol 323 - 323 dioctyl ether ethanol 296 - 323

hexadecanoic acid ethanol 344 - 395 heptanedioic acid ethanol 385 - 385 octadecanoic acid ethanol 354 - 413

octadecanoic acid ethyl ester ethanol 335 - 394 dipropyl ether 1-propanol 348 - 348

diisopropyl ether 1-propanol 333 - 333 dioctyl ether 1-propanol 296 - 323

MTBE 1-propanol 323 - 323 hexadecanoic acid 1-propanol 344 - 395 heptanedioic acid 1-propanol 385 - 385 octadecanoic acid 1-propanol 354 - 413

octadecanoic acid ethyl ester 1-propanol 335 - 394 water 1-propanol 293 - 373

dioctyl ether 1-butanol 296 - 323 heptanedioic acid 1-butanol 385 - 385

octadecanoic acid ethyl ester 1-butanol 335 - 394 water 1-pentanol 298 - 298 water 2-pentanol 298 - 363 water t-pentanol 298 - 298 water 1-hexanol 298 - 298 water 1-nonanol 298 - 298 water 1-decanol 298 - 298 water 1-dodecanol 298 - 298 water 1-tetradecanol 298 - 298 water 1-hexadecanol 298 - 298 water 1-octadecanol 298 - 298 water 1,2 butanediol 299 - 348 water 1,2 ethanediol 297 - 348 water 1,2 propanediol 297 - 348

ethyl acetate acetic acid 313 - 373 water butyric acid 298 - 298 water pentanoic acid 298 - 298 water hexanoic acid 298 - 298 water heptanoic acid 303 - 303 water decanoic acid 298 - 298 water dodecanoic acid 298 - 298 water tetradecanoic acid 298 - 298

1,6 hexanediol methyl acetate 334 - 354 1-dodecanol methyl acetate 308 - 333

decanedioic acid methyl acetate 416 - 416 hexadecanoic acid methyl acetate 344 - 395 heptanedioic acid methyl acetate 385 - 385 octadecanoic acid methyl acetate 354 - 413

ethanol ethyl acetate 313 - 373 1,6 hexanediol ethyl acetate 334 - 354 1-dodecanol ethyl acetate 308 - 333

decanedioic acid ethyl acetate 416 - 416 hexadecanoic acid ethyl acetate 344 - 395 heptanedioic acid ethyl acetate 385 - 385 octadecanoic acid ethyl acetate 354 - 413

Solvent Solute Tmin Tmax

water ethyl acetate 298 - 298 1,6 hexanediol propyl acetate 334 - 354 1-dodecanol propyl acetate 316 - 333

decanedioic acid propyl acetate 416 - 416 hexadecanoic acid propyl acetate 344 - 395 heptanedioic acid propyl acetate 385 - 385 octadecanoic acid propyl acetate 354 - 413

water propyl acetate 298 - 308 water isopropyl acetate 298 - 308

1-dodecanol butyl acetate 316 - 333 decanedioic acid butyl acetate 416 - 416 heptanedioic acid butyl acetate 385 - 385 octadecanoic acid butyl acetate 354 - 413

water pentyl acetate 298 - 298 water butyl acetate 298 - 308 water isopentyl acetate 298 - 298 water isopropyl butyrate 298 - 298 water hexyl acetate 298 - 298 water propyl propanoate 298 - 298 water butyl pentanoate 298 - 298

1-octanol diethyl ether 283 - 303 1-decanol diethyl ether 316 - 333

water ethyl propyl ether 298 - 298 water isobutyl methyl ether 298 - 298 water methyl butyl ether 298 - 298 water methyl propyl ether 298 - 298

ethanol dipropyl ether 343 - 343 2-propanol dipropyl ether 348 - 348

water dipropyl ether 298 - 298 1-octanol diisopropyl ether 283 - 303 1-decanol diisopropyl ether 283 - 303

1-dodecanol diisopropyl ether 303 - 303 water diisopropyl ether 298 - 298

ethanol butyl ethyl ether 343 - 343 ethanol dibutyl ether 343 - 343

2-propanol dibutyl ether 348 - 348 1-butanol dibutyl ether 373 - 373

water dibutyl ether 298 - 298 water isopropyl propyl ether 298 - 298

1-octanol methyl tertiary butyl ether 283 - 303 1-decanol methyl tertiary butyl ether 283 - 303

1-dodecanol methyl tertiary butyl ether 303 - 303 water methyl tertiary butyl ether 298 - 298

1-butanol water 308 - 383 1-decanol water 298 - 373 1-octanol water 298 - 373

1-propanol water 373 - 373 2-propanol water 288 - 373 acetic acid water 340 - 373

butyl acetate water 318 - 318 ethanol water 298 - 373

ethyl acetate water 288 - 373 iso-butyl alcohol water 323 - 379 tert-butyl alcohol water 323 - 323