Correlation for Fitting Multicomponent Vapor-Liquid Equilibria Data and Prediction of Azeotropic Behavior


Al-Khwarizmi 

Engineering   

Journal 

Al-Khwarizmi Engineering Journal, Vol. 4,  No. 4, PP 9-25 (2008) 

 

 

Extraction of Phenol From Industrial Water Using Different Solvents 
 

Mahmoud Omar Abdullah*, Khalid Farhod Al-Jiboury**  

and Bushra Yaseen*** 
*Chemical Engineering Department/ Al-Nahrain University 

 **Chemical Engineering Department/ University of Technology 

 ***Chemical Engineering Department/ Al-Mustanserya University 
 

(Received  7 October  2007; Accepted  11 Septerber 2008) 

 

 

Abstract 
 

The analysis and efficiency of phenol extraction from the industrial water using different solvents, were 

investigated. To our knowledge, the experimental information available in the literature for liquid-liquid equilibria of 

ternary mixtures containing the pair phenol-water is limited. Therefore the purpose of the present investigation is to 

generate the data for the water-phenol with different solvents to aid the correlation of liquid-liquid equilibria, including 

phase diagrams, distribution coefficients of phenol, tie-lines data and selectivity of the solvents for the aqueous phenol 

system. 

 The ternary equilibrium diagrams and tie-lines data for systems containing Water-Phenol-Benzene, Water-Phenol-

Chloroform, Water-Phenol-iso-Butyl Acetate, Water-Phenol-Butanol, Water-Phenol-Ethyl Methyl Keton and Water-

Phenol-Toluene, were determined at 303 K and atmospheric pressure. 
 The capacity and selectivity of these organic solvents in each of these systems were determined from the tie-lines 

data. The capacity of the isobutyle acetate was found to be the highest among the other solvents, and its selectivity was 

also the highest. Similar results also were obtained for the ethyl methyl keton but gave less capacity and selectivity as 

compared to the isobutyle acetate. It can be concluded that both isobutyle acetate and ethyl methyl keton are good 

solvents for extraction of phenol from industrial water. 

 The liquid-liquid equilibrium data of ternary systems were correlated to the NRTL, UNIQUAC and UNIFAC 

models of activity coefficient to determine their adjustable parameters. The standard deviations from experimental 

compositions were calculated. Results show that the correlation may be greatly improved by applying the NRTL model 

with the regression criteria based on minimizing the experimental and calculating distribution coefficients SK to give an 

average value of the root mean square deviation about 1.436 % and in terms of the average errors in the distribution 

ratio for all tie-lines about 10.776 %. 

 
Keywords: Liquid -Liquid Equilibria, Extraction of Phenol, Activity Coefficient. 

 

 

1. Introduction: 
 
 Phenol is an example of a highly toxic 

chemical substance. The maximum amount 

sanctioned by the World Health Organization in 
drinking water is 0.001 mg/L., Macedo and 

Soares (1996). This component is found in large 

quantities in the effluents of different 

petrochemical factories and is regularly released 
into the rivers. Therefore there is great need for 

elimination phenol from the water, on the other 

hand, phenol constitutes a valuable component in 
the production of various chemicals and could be 

reclaimed from the water to great advantage. 

 The separation process most widely used in 

the industry is the extraction with solvents. To 

design new equipment or to simulate the 
performance of existing units, it is important to 

have access to liquid-liquid equilibrium data. 

 Solvent extraction is a major unit operation 
based entirely on limited liquid miscibility and the 

distribution of solute between two liquid phases. 

In the design of a separation process and indeed 
whenever solvents are used in chemical 

technology it is unconditionally necessary to 

know from data or from calculation, the 

composition of the two phases in equilibrium. 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 

 

 10 

 For many types of mixture containing for 
example strongly polar molecules, it is necessary 

to use activity coefficient and hence expression 

for the excess Gibbs function G
E
 for the 

calculation of liquid phase fugasities, Hull and 
Kronberg (2006). 

 The aim of this research is to obtain the 

necessary liquid-liquid equilibrium data for the 
extraction of phenol from water. Phase 

equilibrium data of the ternary systems water-

phenol-organic compounds were generated 

including phase equilibrium diagrams, distribution 
coefficients of phenol, tie-lines data and 

selectivity of the solvent. Tie-lines of two phase 

conjugate layers were determined by use of cross-
section method and the accuracy of experimental 

tie-line data for the ternary was checked for six 

different solvents. 
 The NRTL, UNIQUAC and UNIFAC models 

were used to correlate the experimental data 

obtained for the ternary systems under study. The 

results showed whether the above model is fitted 
or not to the systems under consideration. A 

computerized procedure for predicting or 

representing multicomponent liquid-liquid phase 
equilibrium was developed by using the 

combination of optimization theory and 

thermodynamic. 
 The systems studied in this investigation were 

Water-Phenol-Benzene, Water-Phenol-

Chloroform, Water-Phenol-Isobutyle Acetate, 

Water-Phenol-Butanol, Water-Phenol-Butanone 
and Water-Phenol-Toluene. 

 

 

2. Experimental Work Chemicals: 

 
 The chemicals used was supplied from local 
markets. The selection of the six solvents is based 

on the available solvents in the local market 

which is considered to be controlling factor in this 
study. In spite of that the solubility parameters of 

the six selected solvents is within the range of 

10.4 – 8.9. These chemicals were presented in 
Table 1 with their purities. Physical properties 

such as density of these materials used in this 

study were measured experimentally by measure 
the refractive index and compared with values in 

the literature (Frances, 1963; Fredenslund and 

Rasmussen, 1985; Jone and Theodore, 1986). 

 
 

 

 
 

3. Refractive Index Measurement: 
 

 The refractive index was determined by a 

refractometer of the specification ABBE, the 
precision of the refractive indices was 0.0002 

units. Refractive indices for the samples of liquid 

were measured and the values presented were the 

average values of at least three independent 
readings for each sample. The samples were 

thermostated by circulating water from a constant 

temperature bath through the refractometer. The 
constant temperature at which the measurements 

were taken was 30 
o
C and atmospheric pressure. 

 
 

4. Experimental Apparatus: 
 
 The experimental work was carried out using 

Erlenmeyer flask with a stopper to prevent 

evaporation with a capillary inserted into the 
stopper, whilst maintaining a constant agitation by 

means of a magnetic stirrer. The flask has jacket 

through which water from a Haake thermostat 

bath was circulated. Temperature was measured 
by means of a precision thermometer, with an 

accuracy of ± 0.1 
o
C. The apparatus shown 

diagrammatically in figure 1. 
 

 

 
 

Fig.1. Cloud Point Titrator for Liquid-Liquid 

Equilibria. 
 

 
 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 
 

 11 

5. Experimental Procedure: 
 

 The procedure involves operating the 

apparatus at steady state in order to predict the 
properties of liquid-liquid equilibria for ternary 

systems. 

 
6. Determination of The Binodal Curves; 
 

 The binodal curves of the ternary systems 

were determined by the method of titration as 

described by (Alders, 1959). The solvent 3 was 

added to the mixture of water 1 and phenol 2 in 
the sample bottle inside the constant temperature 

water-jacket. As soon as the cloud point was 

reached, phenol 2 was then added to make the 
liquid homogenous again. The procedure was 

repeated a number of times, and the successive 

cloud points were connected up to produce the 
binodal curve. The maximum error of binodal 

points determination was ± 0.2 %.  

 

 

Table 1  

Physical Properties of Chemicals Used at 303 K. 

Component M. wt. 
Density Refractive index Boiling point 

o
C 

Purity % Supplier 
Exp. Lit. Exp. Lit. 

Benzene 78.114 0.8683 0.8685 1.496 1.4962 80.1 99 % BDH 

Butanol 74.12 0.8053 0.8057 1.3970 1.3971 117.7 99.5 % BDH 

Butanone 72.11 0.7941 0.7941 1.3770 1.3773 79.6 99.5 % BDH 

Chloroform 119.38 1.4693 1.4706 1.4400 1.4401 61.2 99 % BDH 

Iso-butyl acetate 116.16 0.8621 0.8599 1.3880 1.3880 117.5 99 % BDH 

Toluene 92.14 0.8575 0.8577 1.4930 1.4935 110.6 99 % BDH 

Water 18.015 0.9951 0.9956 1.3340 1.3342 100.0 99.5 % BDH 

Phenol 94.113 1.588 1.587 1.5423 1.5395 181.8 99.5 % Merck 

 

 

7. Determination of the Tie Lines: 
 

 The determination was carried out using a 

double-walled similar to that described by 
(Novak, 1987). The separating funnels containing 

heterogeneous mixture of three components were 

placed in a thermostat bath. Temperature was 

controlled within an accuracy of ± 0.01 
o
C by 

using a temperature regulator as shown in fig.2. 

The prepared heterogeneous mixtures were 

shaken for at least 20 min., equilibration of the 
two phases took place in a thermostatted double-

walled separating funnels (250 ml) over a period 

of 20 hr. After equilibrium had been reached, the 
refractive index of one of the separated phases 

was measured. The composition of the tie-lines 

was calculated numerically from the calibration 

data by polynomial regression analysis. The third 
order polynomial was the best approximation 

(stand. dev. = 1.5*10-4) of the relation between 

refractive index and composition. 
 

 

 

 

 
Fig.2.  Thermostatted Separating Funnel for 

Determining Tie-Lines 1-Separating Funnel, 

2-Thermostatting Mantle, 3-Thermometer 

Holder, 4-Stop Cock.  

 

 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 

 

 12 

 To determine the tie-lines of the two 
conjugate layers, ternary two phase systems were 

analyzed by the so-called cross-section method 

reported by (Radecki and Grzyboski, 1975). This 

method consists of plotting the refractive index of 
a mixture against concentration of one of the 

components at a constant ratio of the remaining 

two components. 
 

 

8. Results and Discussion Tie-Line Data: 

 
 The tie-line data between the two conjugate 
phases were obtained from the cross-section 
method. The liquid-liquid equilibrium data (tie-

line data) obtained experimentally for the series of 

the ternary systems water-phenol-benzene, water-
phenol-chloroform, water-phenol-isobutyl acetate, 

water-phenol-butanol, water-phenol-butanone and 

water-phenol-toluene at 30
o
C were plotted in 

figures 3 to 8, the data of (Macedo and Soreas, 

1996) for the system water-phenol-benzene was 

plotted in figure 3 for comparison only. 

 The tie-lines data were used to determine the 
selectivity (Ki) and distribution coefficients (Sij) 

for the systems under investigation according to 

the following relationships: 
 

)1..(.
e phasen raffination of i iConcentrat

phasen extract ion of i iConcentrat
K i

  

)2...(
K
K

S
j

i
ij

     

 The subscript (i) is referred to phenol 
component and (j) is referred to water component 

one. 

 A simple graph of distribution curve for 

phenol compound between the two immiscible 
phases were obtained by plotting the 

concentration of phenol compound in organic 

phase against its concentration in the aqueous 
phase, and presented in figure 9. This type of 

diagram could be compared to a Y-X plot for the 

presentation of vapor-liquid equilibrium data, and 
the deviation of each curve from the Y-X line is a 

measure of the selectivity of solvent. As the 

deviation increases the selectivity of the solvent 

increases. 
 

 

 

 
Fig. 3.   Experimental Liquid-Liquid Equilibrium 

of Ternary System Water-Phenol-Benzene. 

 

 

 

 
Fig. 4.  Experimental Liquid-Liquid Equilibrium 

of Ternary System Water-Phenol- Chloroform.    
 

 

 
Fig. 5.  Experimental Liquid-Liquid Equilibrium 

of Ternary System Water-Phenol-Isobutyl Acetate. 

 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 
 

 13 

 
Fig.6.  Experimental Liquid-Liquid Equilibrium of 

Ternary System Water-Phenol-Butanol. 
 
 

 

 
Fig.7.  Experimental Liquid-Liquid Equilibrium of 

Ternary System Water-Phenol-Butanone. 

 
 

 

 
Fig.8.  Experimental Liquid-Liquid Equilibrium  of 

Ternary System Water-Phenol-TOLUENE. 

 

 
Fig.9. Distribution Coefficient of Phenol Between 

Water Layer and Solvent Layer at 303 K. 

 

 

 
Fig.10. Othmer-Tobias Correlation for Water-

Phenol-Solvent at 303 K. 

 
 

9. Evaluation of the Consistency of the 

Experimental Tie-Lines: 
 

 The accuracy of the experimental data for the 

six ternary systems at 30 
o
C was checked by 

plotting in figures 10 and 11, the Othmer-Tobias 

correlation (Othmer and Tobias, 1942): 

 
 

)3...(            
1

log  
1

log  n
X
-X

m
X
-X

SS

SS

WW

WW

                



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 

 

 14 

 Figures 10 and 11 can be useful to check 
whether experimental data have a regular or not. 

This can help to identify some tie-lines with high 

random errors. 

 
 

 
Fig. 11.  Othmer-Tobias Correlation for Water-

Phenol-Solvent at 303 K. 

 
 

 Figures 3 to 8 show the equilibrium diagrams 
of the systems water-phenol-organic solvent 
(benzene, chloroform, isobutyle acetate, butanol, 

butanone (MEK) and toluene). The six solvents 

are totally miscible with phenol. For butanol 

system the two phase area is small. A small area 
has the disadvantage that the purity of the extract 

is low and that, more over, only mixtures of 

limited concentrations can be extracted (Alders, 
1959). Thus it follows for figure 6 that with 

butanol as extractive solvent at 303 K, no 

mixtures can be separated that contain more than 

40 % of phenol. For benzene the area under the 
binodal curve is large and for figure 3 it can be 

seen that mixtures of 70 % phenol can be 

extracted with benzene. In figures 4, 5, 7 and 8 the 
same conclusions can be reached for the other 

solvents. Figure 9 verifies this result. It shows the 

distribution curves of benzene, chloroform, 
isobutyle acetate, butanol, butanone and toluene. 

The distribution coefficient of phenol was higher 

towards isobutyle acetate and butanone than for 

the other solvents. 
 Also, the liquid-liquid equilibrium data 

presented were plotted in figure 10 in the form of 

separation factor (S) versus the equilibrium 
distribution ratio of phenol (K), in the range of 

concentration under observation. This study 

showed that, for all the solvents considered, the 
organic ester and keton emerge as the most 

indicated for the separation of phenol from water. 

Although isobutyle acetate and MEK have similar 

distribution curve. The boiling point and specific 
gravity of MEK differ greatly from those of 

phenol, and so MEK is a more suitable solvent for 

phenol. 
 

 

 
Fig.12. Separation Factor Versus Equilibrium 

distribution Ratio for Extraction of Phenol From 

Water With Solvents at 303 K. 

 

 

10. Correlation Methods Estimation of 

Parameters: 
 

 The NRTL equation (Renon and Prausnitz, 

1968), the UNIQUAC equation (Anderson and 
Prausnitz, 1978) and the UNIFAC equation 

(Fredenslund and Prausnitz, 1982) were used to 

correlate the experimental phase equilibrium data. 
Binary parameters were calculated using the 

maximum likelihood procedure for the 

minimization of the following objective functions 

 

)4(...  

2

1 1

ln-ln1 
 












































k

M

K

N

i
γ

γ

x
x

F II
i

I

i
I

i

II

i

                     
 

  )5...(     
1 1

2

1

2
-ˆ2 

  



M

k

N

i j

ijkjk xxF i

                                  

 The calculation begins using the objective 
function F1 and when the parameters are near 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 
 

 15 

optimum value the calculation continues with the 

objective function F2. For ternary mixtures nine 
parameters for the NRTL equation must be fitted, 

six parameters for the UNIQUAC equation and 

the predictive method for UNIFAC equation for 
describing a ternary data set. 

 This procedure gives a set of parameters 

shown in tables 2 and 3 
 

 

11. Calculation of Tie-Lines: 
 

 The above mentioned procedure for estimated 

– parameters were employed to calculate the tie-

lines. Computation started from the heterogeneous 
mixture: 

 

)6...(
2


 xx

Z

II

i

I

i

i

                                                        
The computation of tie-lines was based on the 

algorithm published by (Null, 1970) 

Figures 13, 14, 15, 16, 17 and 18 represent NRTL 
models correlation with two regression criteria for 

the systems under study. 

 A good representation was obtained in figures 
13, 15, 16, 17 and 18 for the two regression 

criteria Sa, Sk and the residuals to the 

experimental data were low but residuals to the 

distribution coefficients was better for the 

regression criteria Sk than the regression criteria 

Sa for all the systems. 
 For chloroform system, the NRTL model 

represents the correlation with the regression 

criteria Sk only and give a good residuals for both 
the experimental data and the distribution 

coefficients. 

 Figures 19, 20, 21, 22, 23 and 24 represent the 
UNIQUAQ modeling to the ternary system under 

study. For all the systems the residuals were 

higher for the experimental data and the 

distribution coefficient, and representation was 
better for the NRTL model than the UNIQUAC 

model. 

 For all the systems above it can be seen that, 
at low concentration of the solute both the NRTL 

model and UNIQUAC model fit the experimental 

data. But at high concentrations the deviation 

from experimental are obvious. 
 Figures 25, 26, 27, 28, 29 and 30 represent 

UNIFAC models correlation for the systems 

under study. In figures 25, 26, 27, 28, 29 and 30 
the residuals were higher for the experimental 

data, and representation was better for both the 

NRTL model and UNIQUAC model than the 
UNIFAC model. 

 For Butanol system, the UNIFAC model 

gives good residuals for both the experimental 

data and the distribution coefficients than the 
UNIQUAC model. 

 
Table 2 

NRTL Correlation Parameters for Ternary System in kJ/mol at 303 K. 

Solvent i-j Aij Aji ij 

Benzene 

1-2 

1-3 

2-3 

1267.83346 

1595.76351 

-265.14854 

-125.07542 

1108.3348 

858.27337 

0.21906 

0.31233 

0.42423 

Chloroform 

1-2 

1-3 

2-3 

1084.83814 

2024.50135 

116.82185 

154.68756 

473.8733 

263.54813 

0.5169 

0.19131 

0.60211 

iso butyl acetate 

1-2 

1-3 

2-3 

1552.05204 

1973.83952 

2190.65119 

136.07517 

651.2274 

20.7399 

0.5743 

0.28968 

0.67227 

Butanol 

1-2 

1-3 

2-3 

1244.98256 

2193.96024 

782.10278 

119.92193 

501.96555 

379.55085 

0.53109 

0.34753 

0.69905 

MEK 

1-2 

1-3 

2-3 

1527.03582 

3037.4255 

2299.1531 

-448.7063 

148.9289 

-2185.0569 

0.16978 

0.21666 

0.06204 

Toluene 

1-2 

1-3 

2-3 

1370.2677 

1376.6916 

-476.4699 

-208.4991 

822.2341 

1533.0258 

0.2116 

0.2566 

0.2385 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 

 

 16 

Table 3 

Uniquac Correlation Parameters for Ternary System in kJ/mol at 303 K. 

Solvent i-j Bij Bji 

Benzene 
1-2 
1-3 

2-3 

-7.1734 
220.908 

-53.1383 

164.64 
514.0597 

91.1305 

Chloroform 

1-2 

1-3 

2-3 

52.6238 

643.2392 

81.6293 

345.7274 

425.8234 

78.7847 

iso butyl acetate 

1-2 

1-3 

2-3 

267.108 

158.795 

2141.241 

322.71 

1106.435 

-282.265 

Butanol 

1-2 

1-3 

2-3 

90.3247 

2514.7869 

827.905 

80.0523 

473.0648 

-270.6094 

MEK 
1-2 
1-3 

2-3 

93.4385 
949.4014 

1543.2946 

396.148 
546.9067 

423.9119 

Toluene 

1-2 

1-3 

2-3 

-103.013 

47.108 

-246.023 

375.872 

1139.4387 

904.198 

 
 
 

Table 4  

Classical and Statistical Regression Criteria. 


 








M N

II

ik

II

ik

I

ik

I

ik

k i

γxγxS a
1 1

2

-          …(7) 

 

2

1 1

-


 



















M N

II

ik

I

ik

II

ik

I

ik

k i aa

aa
S a                  …(8) 

 
2

1 1

lnln -

kk i

M N

I

i

II

i

I

i

II

i

γ

γ

x

x
S k 

  














































       …(9) 

 

 

 

 

 

 

 

 
Fig. 13.  Representation of the Ternary System 

Water-Phenol-Benzene by NRTL Model With 

Parameters Obtained From LLE  Data at 303 K. 

 

 

 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 
 

 17 

 
Fig.14.  Representation of the Ternary System 

Water-Phenol-Chloroform by NRTL Model With 

Parameters Obtained from  LLE  Data at 303 K. 

 

 

 
Fig.15. Representation of the Ternary System 

Water-Phenol-Isobutyle Acetate by  NRTL Model 

With Parameters Obtained from LLE  Data at 303 

K. 

 

 

 

 
 
Fig.16. Representation of the Ternary System 

Water-Phenol-Butanol by NRTL Model with 

Parameters Obtained From LLE  Data at 303 K. 

 

 
 

 

Fig.17. Representation of the Ternary System 

Water-Phenol-MEK by NRTL Model With 

Parameters Obtained From LLE  Data at 303 K. 

 

 

 
 

Fig.18. Representation of the Ternary System 

Water-Phenol-Toluene by NRTL Model With 

Parameters Obtained From LLE  Data at 303 K. 

 

 

 

 
Fig.19. Representation of the Ternary System 

Water-Phenol-Benzene by UNIQUAC Model with 

Parameters Obtained From LLE  Data at 303 K. 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 

 

 18 

 
Fig.20. Representation of the Ternary System                 

Water–Phenol-Chloroform by UNIQUAC Model 

with Parameters Obtained From LLE  Data at 

303K. 

 

 
Fig.21. Representation of the Ternary System                

Water-Phenol-Isobutyle Acetate by UNIQUAC 

Model with Parameters Obtained From LLE Data 

at 303 K. 

 

 

 
Fig.22. Representation of the Ternary System 

Water-Phenol-Butanol by UNIQUAC Model with 

Parameters Obtained From LLE  Data at 303 K. 

 

 

 

 
Fig.23. Representation of the Ternary System 

Water-Phenol-MEK by UNIQUAC Model with 

Parameters Obtained From LLE  Data at 303 K. 

 

 

 
Fig.24. Representation of the Ternary System 

Water-Phenol-Toluene by UNIQUAC Model with 

Parameters Obtained From LLE  Data at 303 K. 

 

 

 

 

 
Fig.25. Representation of the Ternary System 

Water-Phenol-Benzene by UNIFAC  Model with 

Parameters Obtained From  LLE Data at 303 K. 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 
 

 19 

 

 
 

Fig.26. Representation of the Ternary System                 

Water-Phenol-Chloroform by UNIFAC                 

Model with Parameters Obtained from                 

LLE Data at 303 K. 

 

 

 
Fig.27. Representation of the Ternary System 

Water-Phenol-Isobutyle Acetate by UNIFAC Model 

with Parameters Obtained From LLE Data at 
303K. 
 

 

 
Fig.28. Representation of the Ternary System 

Water-Phenol-Butanol by UNIFAC Model with 

Parameters Obtained From  LLE Data at 303 K. 
 

 

 
Fig.29. Representation of the Ternary System 

Water-Phenol-MEK by UNIFAC Model with 

Parameters Obtained from  LLE Data at 303 K. 

 

 

 
Fig.30. Representation of the Ternary System 

Water-Phenol-Toluene by UNIFAC Model with 

Parameters Obtained From  LLE Data at 303K. 

 

 
 

12. Correlation: 
 
 In liquid extraction studies experimental 

results obtained for low solute concentrations are 

most important. Table 5 shows the root mean 
square deviation between the experimental and 

calculated values for the tie-lines, as calculated 

from the formula 

)10...(min

2
1

1 1 1

2

6ˆ100 
















  









   

k

k

N

j

I

i

Mijk
x

ijk
xFRMSD

         

 

and the average error in the distribution ratio for 

all tie-lines 
 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 

 

 20 

)11...(

2
1

2

-ˆ100 






























 

k

kkk
Mββββ

                       
 
  

 

 

Table 5 

Residuals for the six ternary Liquid-liquid equilibrium data set correlated by NRTL, UNIQUAC and UNIFAC 

at 303 K. 

Data Set No. Residuals 
NRTL UNIQUAC UNIFAC 

Sa Sk Sa Sa’ Sk Sk 

1 
F 0.342 1.4704 1.092 1.73 1.859 1.4996 

 117.98 15.284 96.84 17.38 16.165 19.318 

2 
F 0.432 0.7267 1.021 0.405 0.501 0.5649 

 65.76 12.645 97.787 15.359 15.757 19.106 

3 
F 0.543 1.788 0.7411 2.697 1.287 2.445 

 32.944 9.005 68.856 29.725 31.369 21.054 

4 
F 0.2496 0.9316 0.412 2.729 2.731 2.482 

 13.975 1.9572 152.02 5.608 5.608 8.803 

5 
F 1.122 1.867 1.058 2.475 2.058 2.703 

 73.989 4.75 51.828 14.146 19.201 14.948 

6 
F 1.234 1.832 1.949 2.308 1.93 2.843 

 129.28 1.54 172.92 6.173 9.895 46.86 

Average 
F 0.9775 1.436 1.045 2.057 1.727 2.089 

 73.634 1.13 106.71 14.732 16.332 21.685 

 

 

 
 An analysis of table 5, shows that for all data 

sets the binodal curves are well reproduced by the 

regression criteria Sa for both models NRTL and 

UNIQUAC model but give a high residuals of the 
phenol distribution ratios for almost all the system 

as indicated by the residual . The overall fit 
measured by F is worse when both Sa’ and Sk 

were applied to UNIQUAC model but a large 

improvement in the values of  is obtained as 
compared with the results of the regression 

criteria Sa. Using the UNIFAC equation, the 

correlation residuals does not improve the results. 

The NRTL models results using the regression 
criteria Sk can be more accurate than the 

UNIQUAC equation and give good improvement 

in F and the values of . Table 5 verifies the 

results of the above figures. The disagreement 

between the experimental and calculated results, 

expressed in terms of solute distribution ratios, is 

more easily visualized in figures 31, 32, 33, 34, 35 
and 36. 

 Figure 31, shows the experimental phenol 

distribution ratio at 30 
o
C together with those 

calculated by using the NRTL (Sa and Sk, which 

gave the best NRTL results), UNIQUAC (Sa, Sa’ 

and Sk) and UNIFAC (Sk). The NRTL results can 

be seen to be more accurate with the objective 
function Sk than the other models with the 

different objective function. The results for the 

other five systems, figures 32, 33, 34, 35 and 36 
are similar to that of figure 31. 

 

 

 
 

 

 
 

 

 

 

 
 

 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 
 

 21 

 
 

Fig.31. Experimental and Calculated Distribution 

Ratio of Water-Phenol- Benzene at 303 K. 

 

 

 

 
Fig.32. Experimental and Calculated Distribution 

Ratio of Water-Phenol-Chloroform at 303 K. 

 

 

 

 

 

 

 

 

 

 

 

 

 
Fig.33. Experimental and Calculated Distribution 

Ratio of Water-Phenol-Isobutyle Acetate at 303K. 

 

 
 

 

 
Fig.34. Experimental and Calculated Distribution 

Ratio of Water-Phenol- Butanol at 303 K. 

 
 

 

 

 

 

 

 

 

 

 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 

 

 22 

 
 
Fig.35. Experimental and Calculated Distribution 

Ratio of Water-Phenol- MEK at 303 K. 

 

 

 
Fig.36. Experimental and Calculated Distribution 

Ratio of Water-Phenol-Toluene at 303 K. 

 

 
Table 6  

Fitting Accuracy of Ternary LLE Data 

No. 

NRTL UNIQUAC UNIFAC 

Sa Sk Sa Sa’ Sk Sk 

x x x x x x 

I II I II I II I II I II I II 

1 15.1 16.9 18.8 1.66 13.8 16.3 23.8 2.01 4.8 7.20 28.4 1.98 

2 0.76 0.76 9.76 0.64 11.8 6.51 5.28 0.83 22.1 1.25 7.52 0.98 

3 6.51 1.06 22.1 0.47 8.93 12.1 35.3 1.01 17.1 1.53 32.6 1.27 

4 3.15 0.62 11.7 0.39 3.49 4.28 36.8 0.76 36.8 0.78 32.7 0.48 

5 5.55 14.2 24.2 2.11 13.2 5.33 48.3 1.38 27.3 0.72 38.1 2.12 

6 7.13 0.56 22.0 0.41 9.63 13.2 33.2 1.54 29.1 1.79 25.6 2.16 

Av. 7.49 6.69 18.1 0.95 10.2 29.2 30.5 1.25 22.8 2.13 27.5 1.53 

 

 

 

13. Comparison of Fitting Accuracy: 

 
 The fitting accuracy of six set of ternary LLE 
data applying NRTL with two regression criteria, 

UNIQUAC with three regression criteria and 
UNIFAC with one regression criteria are listed in 

Table 6, it can be seen from the table that 

correlation is improved by applying the NRTL 

model with regression criteria Sk . 
 

 

 

 

14. Conclusions: 

 
1. Of the six solvents used to extract phenol 

from an aqueous phenol solution, both 

iso-butyle acetate and Etyl methyl keton 
have the highest selectivity and capacity 

because the iso-butyle acetate hydrogen 

bonds and ethyl methyl keton hydrogen 

bond preferentially with phenol. And due 
to the greatest differences between the 

boiling point and specific gravity of the 

ethyl methyl keton and those of phenol. It 
is therefore considered an excellent 



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 
 

 23 

solvent for extracting phenol from 

phenol-water solutions. 
2. The consistency of experimental tie-line 

data for the ternary system water-phenol-

solvent at 30 
o
C was confirmed for six 

different solvents, and the data can then 

be used to calculate the values of the 

parameters and the tie-lines in the NRTL, 
UNIQUAC and UNIFAC models. 

3. The NRTL model for the activity 
coefficients of ternary liquid systems 

gives a good representation of liquid-
liquid equilibria for the systems under 

study. This fact helps for calculations 

required in the design of extraction unit to 
reach the optimum use of the solvent. 

4. The root mean-square deviation F 
between the calculated and the 

experimental tie-lines lays within the 
range of 1.867-0.726 for the NRTL model 

for the objective function F2 and in terms 

of the error  the range is lays within 
15.284-9.005. 

5. The NRTL equation gives F values 
slightly lower than those of the 
UNIQUAC equation but the difference is 

not significant it is 1.2-1.1 times larger 

than the NRTL model. 

6. The NRTL equation gives the best  
results, in which case it proves to be more 

accurate than the UNIQUAC equation at 

all objective functions, it is 1.5 times 
larger than the NRTL model. 

7. The UNIFAC equation gives F values 
slightly lower than those of the 
UNIQUAC equation for the system 

containing an alcohol component but the 

difference is not significant. 

 
 

15. Nomenclature Abbreviations: 
 

LLE Liquid – Liquid Equilibrium 

MEK Methyl Ethyl Keton (Butanone) 

NRTL Non-Random Two Liquid 

Activity Coefficient model 

RMSD Root mean square deviation 

UNIFAC UNIQUAC Functional Group 

Activity Coefficients model 

UNIQUAC Universal Quasi-Chemical 
Activity Coefficient model 

 

   

16. Symbols: 
 

ai Activity of component i 

F1 Objective function no. 1 

F2 Objective function no. 2 

G
E
 Excess Gibbs function 

Ki Selectivity 

m slope of the line 

M No. of experimental points 

M.wt. Molecular weight 

n Intersect of the line 

Sa Classical regression criteria 

SK Statistical regression criteria 

Sij Distribution coefficient 

x
I

i
  

mole fraction of component i in the I 

phase 

x
II

i
 

mole fraction of component i in the II 
phase 

Xss mole fraction of solvent in the solvent 

phase 

Xww mole fraction of water in the water 

phase 

Zi number of mole of component i in the 
system 

 

17. Greek Litters: 
 

 Average error 

 Activity coefficient 

 

18. Superscript: 
 

E Excess Property 

I Phase I 

II Phase II 

^  Experimental value 

i component i 

j component j 

ss solvent in the solvent phase 

ww water in the water phase 

 

 

  



Mahmoud Omar Abdullah                                     Al-Khwarizmi Engineering Journal, Vol.4, No.4, PP 9-25 (2008) 
 

 

 24 

19. References: 
 

[1] Alders, L., “Liquid-Liquid Extraction” 2nd 
ed., Elsevier publishing Co., 1959 

[2] Anderson, T. F. and Prausnitz, J., M., Ind. 
Eng. Process Des. and Dev., 17, 1978. 

[3] Francis, A. W., “Liquid-Liquid Equilibrium” 
Interscience publishers, NewYork, 1963. 

[4] Fredenslund Aa. and Rasmussen P., “vapor-
liquid equilibria using UNIFAC a group 

contribution method, Elsevier, Amsterdam, 
1977 

[5] Fredenslund Aa. and Rasmussen P., Fluid 
phase equilibria, 24, 115-150, 1985. 

[6] Hull, A. and Kronberg B., J. Chem. Eng. 
Data, 51, 202-208, 2006 

[7] John A. R., William B. and Theodore K., 
“Organic solvents”, 1986. 

[8] Macedo E. A. and Soares M. E.,Fluid Phase 
equilibria, 26, 36-42, 1996. 

[9] Novak J. P., Matous J. and Pick J., “Liquid-
liquid Equilibria”, Elsevier, Amsterdam, 

1987. 

[10] Null H. R., Phase equilibrium in process 
design, 1970. 

[11] Othmer D. F., Ind. Eng. Chem., 38, 11-19, 
1942. 

[12] Radecki A. and Grzyboski J., J. Chemical 
and Engineering data, 20, 2, 1975. 

[13] Renon H. and Prausnitz M., AIChE Journal, 
14, 1, 1968. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 (2008 )25-9، صفحة 4، العذد 4       هجلة الخىارسهي الهنذسية الوجلذ                                                                                  د عوزوهحن
 
 

 25 

 

 استخالص الفينىل هن الوياه الصناعية باستخذام هذيبات هختلفة
 

*** بشزي ياسين**                خالذ فزهىد*هحوىد عوز
جايعح انُهشٍَ    / لسى انهُذسح انكًُُاوَح *

انجايعح انركُىنىجُح / لسى انهُذسح انكًُُاوَح      **

انجايعح انًسرُصشَح / لسى انهُذسح انكًُُاوَح     ***

 

 

 

الخالصة 

تحسة انًعهىياخ انعًهُح انًحذودج انًرىفشج فٍ . ذى ذحهُم و دساسح كفاءج اسرخالص انفُُىل يٍ انًُاِ انصُاعُح تاسرخذاو يزَثاخ يخرهفح

سائم نألَظًح انثالثُح وانرٍ ذحىٌ عهً انثُائٍ انًاء و انفُُىل ،فاٌ انهذف يٍ هزِ انذساسح هى – انُششاخ وانًجالخ انعهًُح نرىاصٌ سائم 

انسائم ألَظًح انًاء و انفُُىل يع انًزَثاخ انًخرهفح تضًُها يخطظ – يعشفح تُاَاخ انرىاصٌ نألطىاس نغشض إَجاد عاللاخ ذىاصٌ انسائم 

. األطىاس ، يعايم انرىصَع نهفُُىل وتُاَاخ خطىط انرىاصٌ واَرمائُح افضم يزَة نهفُُىل

اَضوتُىذاَم اسُرُد ، -فُُىل-كهىسوفىسو ، ياء-فُُىل-تُضٍَ ، ياء-فُُىل-ياء: ذى إَجاد تُاَاخ يخططاخ انرىاصٌ نألَظًح انثالثُح انرانُح 

.  كهفٍ وضغظ جىٌ واحذ 303ذهىٍَ عُذ دسجح حشاسج -فُُىل-اثُم يثُم كُرىٌ و ياء-فُُىل-تُىذاَىل ، ياء-فُُىل-ياء

نمذ وجذ اٌ سعح . ذى حساب سعح واَرمائُح كم يٍ هزِ انًزَثاخ انعضىَح نكم يٍ األَظًح انًزكىسج أعالِ يٍ تُاَاخ ذىاصٌ األطىاس 

كًا إٌ اَرمائُح انًزَة اعالِ هٍ األعهً ، تًُُا كاَد سعح و اَرمائُح يزَة . األَضوتُىذاَم اسُرُد هٍ األعهً يماسَح يع انًزَثاخ األخشي

ًَكٍ انمىل اٌ كم يٍ يزَة األَضوتُىذاَم اسُرُد و يزَة . االثُم يثُم كُرىٌ الم يٍ انًزَة أعالِ واألعهً يماسَح يع انًزَثاخ األخشي 

. االثُم يثُم كُرىٌ يٍ انًزَثاخ االَرمائُح انجُذج وًَكٍ اسرخذايهى فٍ اسرخالص يادج انفُُىل يٍ انًُاِ انصُاعُح 

 نًعايم انفعانُح ، ورنك نًعشفح NRTL, UNIQUAC and UNIFACذى ذطثُك انُرائج انعًهُح نألَظًح انثالثُح عهً يعادالخ 

 NRTLذى حساب انرشاكُض انًرىلعح حسة ذهك انًعادالخ و يماسَرها يع انُرائج انعًهُح ووجذ اٌ يعادنح . انًعايالخ انثُائُح نرهك انًعادالخ 

يع انذوال انشَاضُح نرمهُم َرائج انفشق تٍُ انمُى انُظشَح و انعًهُح نًعايم انرىصَع َعطٍ افضم انُرائج حُث إٌ يعذل انخطأ فٍ يخطظ لاتهُح 

 % . 10.776ويعذل انخطأ فٍ َسثح انرىصَع تحذود  % 1.436راتح تحذود اإل