Experimental Data of Citric Acid Extraction from Aqueous Solution with

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Experimental Data of Citric Acid Extraction from Aqueous Solution with 1‑Decanol by Using Liquid−Liquid Equilibrium Fattaneh Moradi Estalkhzir, Hamid Ramezanipour Penchah, Hossein Ghanadzadeh Gilani,* and Hadieh Mikayilzadeh

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Department of Chemical Engineering, University of Guilan, 41335 Rasht, Iran

ABSTRACT: In this study, experimental tie-line data for the ternary system containing water, citric acid, and 1-decanol were measured at various temperatures (298.2, 308.2, 318.2, and 328.2 K) and atmospheric pressure (101.3 ± 0.4 kPa). The reliability and consistency of the liquid−liquid equilibrium experimental data were evaluated by the Othmer−Tobias and Hand equations. The distribution coefficients and separation factor of this system for solvent capability were calculated. The maximum of separation factor for 1-decanol as solvent was obtained as 4.25 at 298.2 K and decreases with increasing temperature and citric acid concentration. Finally, by using the genetic algorithm method, interaction parameters of the NRTL thermodynamic model were measured for these experimental data. The values of the parameters of this model were evaluated with the root-mean-square deviation (rmsd) method. The average rmsd value between the experimental and calculated mass fraction was 0.1984% for the NRTL model. The rmsd values demonstrate that the NRTL model is suitable for description of phase behavior and can be applied to this system. extraction of citric acid. Uslu6 in 2008 studied citric acid extraction in 2-octanol and 2-propanol solutions containing TOMAC. Ju et al.11 in 2013 investigated the solvent extraction of citric acid from fermentation broth and reported the LLE data. In this research, 1-decanol, a straight chain alcohol that is insoluble in water, was investigated as a solvent for the separation of citric acid from aqueous solution. To the best of our knowledge and literature review, use of 1-decanol as a solvent for the extraction of citric acid from aqueous solution has not been reported in available articles. Correlating the experimental data of LLE on activity thermodynamic models and estimation of the adjustable parameters of the activity coefficient have been presented in different optimization methods.12−15 Recently, new optimization methods have been presented on the basis of the global optimization methods.13,16 Many authors have demonstrated that the results obtained by the genetic algorithm (GA) technique were better than other methods.17,18 In this method, the activity coefficient parameters can be obtained by

1. INTRODUCTION Carboxylic acids are produced by industrial and organic methods and used as raw materials to produce chemicals and organic solvents. Citric acid is one of the most widely used carboxylic acids which has many applications in chemical, food, etc., industries.1,2 Citric acid is an organic acid with high molecular weight that contains both hydroxyl and carboxyl groups in its molecule and has a high solubility in water.3 Separation and purification of water from such organic compounds is an important challenge in industries which usually is impossible with prevalent methods such as distillation due to formation of azeotrope mixtures.4,5 Nowadays, extraction with solvent (LLE) is a low cost and suitable method for separation of organic compounds from water.4 Many different solvents (mainly amine) have been reported in publications for the recovery of citric acid from aqueous solution by LLE.6−10 Lintomen et al.9,10 studied the liquid−liquid equilibrium of citric acid in water with alcohol as solvent at 298.15 K and estimated the interaction parameters of the NRTL and UNIQUAC thermodynamic models. Nikhade and Pangarkar8 in 2005 studied the extraction of citric acid from aqueous solutions in the alamine 336−cyclohexanone system, and physical and chemical equilibria have been determined for the © XXXX American Chemical Society

Received: December 31, 2017 Accepted: August 8, 2018

A

DOI: 10.1021/acs.jced.7b01135 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Provenance and Purity of the Materials component

IUPAC name

chemical formula

mass fraction purity

purity analysis method

source

citric acid 1-decanol water

2-hydroxypropane-1,2,3-tricarboxylic acid decan-1-ol water

C6H8O7 C10H22O H2O

>0.99 >0.99 deionized and redistilled

acid−base titration gas chromatograph conductometry

Merck Merck

compounds are shown in Table 2. The standard uncertainties for the refractive index and density are 0.0002 and 1 kg·m−3, respectively. Deionized and redistilled water was used in all of the experiments. 2.2. Methods. To obtain equilibrium tie-line data, six ternary mixtures (feed) with determined mass fraction are transferred to six similar glass cells with a volume of 50 cm3 and agitated with a magnetic stirrer for 2 h. Each glass cell contains a magnet for stirring, and all of them are placed in a chamber with a temperature controller. The temperature was estimated to have a precision within ±0.1 K that was checked by a digital thermometer (Lutron TM-917). After accomplishing the stirring time, the solution is left in a stationary state for 4 h. Preliminary experiments showed that these times are enough to reach equilibrium. After the complete phase separation into two liquid phases that become clear and transparent with a well-defined interface, sampling from each phase is performed by a glass syringe. After separation, samples of both phases were carefully weighed and analyzed to determine their compositions. The sample weighing was carried out with an AND electronic analytical balance (model HR-200) with an accuracy of ±0.0001. All measurements were taken at least three times, and the averages of the results are reported. All of the methods and experiments used in this study are similar in our previous publications.25−28 Figure 1 shows the main parts of the LLE process. 2.3. Analysis. The concentration of acid (mass fraction) in both phases was carried out by titration using NaOH. The concentration of water (mass fraction) was measured by the Karl Fischer method using a Metrohm-870 KF titrino plus titrator and refractive index measurements in the organic phase and the aqueous phase, respectively. An Abbe refractometer (model CETI) and DA210 (Kyoto electronic) density meter are used for measuring refractive indices at T = 298.2, 308.2, 318.2, and 328.2 K and density at T = 298.2 K, respectively.

Table 2. Experimental and Literature Values for the Refractive Index (nD) and Density (ρ) of the Components at T = 298.2 K and P = 101.3 kPaa ρ (kg·m−3)

nD component

exp.

lit.

exp.

lit.

citric acid 1-decanol water

1.356 1.4346 1.3324

1.3598b 22 1.434523 1.332224

1085.86 826.86 997.09

1085.8b 22 826.5323 997.04822

Standard uncertainties u are u(nD) = 0.0002, u(ρ) = 1 kg·m−3, u(T) = 0.1 K, u(P) = 0.4 kPa, and u(w) = 0.0001. bThe concentration of the aqueous solution of citric acid is 20.0 wt %. a

inserting experimental data into a thermodynamic model and fitting it with a suitable method. These parameters can predict all of the important properties of the system. Many investigations have reported thermodynamic interaction parameters at different temperatures.14,19 In this work, experimental tieline data for the system containing water, citric acid, and 1-decanol were obtained at different temperatures and correlated on the nonrandom two liquid (NRTL)20 thermodynamic model by use of the GA. All of the obtained parameters are evaluated with the method by Marcilla et al.,21 and the results show that the obtained binary parameters were consistent with experimental data. Finally, the experimental and calculated mass fractions for all components were plotted on triangular coordinates.

2. MATERIALS AND METHODS 2.1. Materials. 1-Decanol and citric acid were obtained from Merck Company with a purity higher than 0.99 in mass fraction stated and were used without any purification. The provenance and purity of the materials are listed in Table 1. Refractive indices were used for the purity of materials. The experimental and literature refractive index and density of the

Figure 1. Main parts of the LLE process. B



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Table 3. Experimental Refractive Index for the System (Water + Citric Acid + 1-Decanol) at Different Temperatures and P = 101.3 kPaa w(water)

w(citric acid)

0.9975 0.8911 0.7843 0.6813 0.5808 0.4808 0.3733 0.2484

0.0000 0.0990 0.1961 0.2920 0.3872 0.4808 0.5818 0.7019

0.9938 0.8878 0.7814 0.6788 0.5787 0.4790 0.3574 0.2418

0.0000 0.0986 0.1954 0.2909 0.3858 0.4790 0.5932 0.7062

0.9901 0.8845 0.7786 0.6763 0.5766 0.4773 0.3786 0.2461

0.0000 0.0983 0.1946 0.2899 0.3844 0.4773 0.5703 0.6973

0.9864 0.8813 0.7758 0.6739 0.5746 0.4756 0.3611 0.2441

0.0000 0.0979 0.1939 0.2888 0.3831 0.4756 0.5830 0.6961

w(1-decanol)

nD

T = 298.2 K 0.0025 0.0099 0.0196 0.0268 0.0319 0.0385 0.0448 0.0497

1.33545 1.34548 1.35888 1.37352 1.38698 1.39899 1.41218 1.42812

0.0062 0.0136 0.0232 0.0303 0.0354 0.0419 0.0494 0.0520

1.33463 1.34458 1.35728 1.37153 1.38368 1.39713 1.41101 1.42531

0.0099 0.0172 0.0268 0.0338 0.0389 0.0453 0.0511 0.0566

1.33317 1.34362 1.35487 1.36951 1.38199 1.39679 1.40713 1.42371

0.0136 0.0208 0.0303 0.0373 0.0424 0.0488 0.0559 0.0598

1.33224 1.34212 1.35321 1.36727 1.38091 1.39476 1.40744 1.42143

T = 308.2 K

T = 318.2 K

Figure 2. Flowchart of the genetic algorithm.

and temperatures were presented in Table 3. Equations for refractive index (nD) as a function of water mass fraction and correlation coefficient (R2) for the system containing water− citric acid−1-decanol at T = 298.2, 308.2, 318.2, and 328.2 K and atmospheric pressure were given in Table 4. 2.4. Genetic Algorithm. In this study, the genetic algorithm was applied for optimization of a fitness function similar to a method by Vatani et al.15 and contains five steps: (1) Initial population: Random production of a population that contains many chromosomes (each chromosome is a solution of problem). (2) Accuracy: evaluation of function accuracy for each chromosome in the population. (3) Production of a new population: production of a new population with accomplishment of the following steps: (3.1) Selection: parent chromosome selection from the previous population with respect to the fitness function. (3.2) Crossover: accomplishment of crossover and production of a new population. (3.3) Mutation: location of the produced child in the chromosome. (3.4) Accepting: putting the new child in the old population. (4) Replace: replacing of the old population with the new population and using that in the following step. (5) If the optimum condition is achieved, the procedure is terminated; otherwise, it continues with step 2.17 The GA procedure used in this work is summarized in Figure 2. 2.5. LLE Modeling. The relation between the mole fraction xi and the activity coefficient γi between phases I and II under equilibrium conditions is as follows29 (eqs 2 and 3)

T = 328.2 K

a

Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.4 kPa, u(nD) = 0.003, and u(w) = 0.001.

Table 4. Refractive Index (n) as a Function of Water (w11) in the Aqueous Phase and Various Temperatures for the System (Water, Citric Acid, 1-Decanol)a T (K) 298.2 303.2 308.2 318.2

refractive index equation nD nD nD nD

= = = =

−0.1262w11 −0.1231w11 −0.1246w11 −0.1238w11

+ + + +

1.4594 1.4551 1.4544 1.4518

R2 0.998 0.998 0.997 0.997

a

Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.4 kPa, u(nD) = 0.003, and u(w) = 0.001.

The mass fraction of other components can be calculated by determining the mass fraction of water and acid in both phases according to the following equation. n

∑ wi = 1 i=1

(xiγi)I = (xiγi)II

(2)

K i = xi I/xiII = γi II/γi I

(3)

where Ki is the distribution ratio of component i. The NRTL30 model (eq 4) was used to correlate the experimental LLE data. For this model, the activity coefficient γi is given by

(1)

Experimental refractive index data for the system (water + citric acid + 1-decanol) at different component mass fractions C



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Table 5. Experimental Tie-Lines for the System (Water + Citric Acid + 1-Decanol) at Different Temperatures and P = 101.3 kPaa aqueous phase mass fraction w1(water)

w2(CA)

organic phase mass fraction w3(1-decanol)

w1(water)

w2(CA)

w3(1-decanol)

0.0330 0.0360 0.0380 0.0406 0.0440 0.0470

0.0310 0.0553 0.0727 0.0991 0.1264 0.1405

0.9360 0.9087 0.8893 0.8603 0.8296 0.8125

0.0363 0.0396 0.0418 0.0447 0.0484 0.0517

0.0296 0.0522 0.0695 0.0931 0.1217 0.1374

0.9341 0.9082 0.8887 0.8622 0.8299 0.8109

0.0399 0.0436 0.0460 0.0491 0.0532 0.0569

0.0269 0.0497 0.0638 0.0869 0.1159 0.1296

0.9332 0.9068 0.8903 0.8639 0.8308 0.8135

0.0434 0.0458 0.0483 0.0516 0.0560 0.0598

0.0234 0.0443 0.0550 0.0811 0.1054 0.1223

0.9332 0.9099 0.8967 0.8673 0.8386 0.8179

T = 298.2 K 0.7993 0.6839 0.6060 0.4845 0.3782 0.3409

0.1770 0.2882 0.3607 0.4763 0.5749 0.6052

0.0237 0.0280 0.0333 0.0393 0.0469 0.0539

0.7826 0.6555 0.5708 0.4631 0.3543 0.3092

0.1891 0.3114 0.3900 0.4909 0.5908 0.6276

0.0283 0.0330 0.0392 0.0460 0.0549 0.0632

0.7706 0.6269 0.5547 0.4337 0.3360 0.2927

0.1976 0.3367 0.4025 0.5166 0.6050 0.6394

0.0319 0.0364 0.0428 0.0497 0.0590 0.0679

0.7577 0.5958 0.5378 0.4026 0.3171 0.2757

0.2064 0.3641 0.4154 0.5437 0.6196 0.6480

0.0359 0.0401 0.0468 0.0537 0.0633 0.0763

T = 308.2 K

T = 318.2 K

T = 328.2 K

a

Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.4 kPa, and u(w) = 0.004. m

Table 6. Experimental Distribution Coefficients of Water and Citric Acid (D1, D2) and Separation Factor (S) at T = 298.2, 308.2, 318.2, and 328.2 K and Atmospheric Pressure T (K)

D2

D1

S

298.2

0.1755 0.1918 0.2014 0.2081 0.2199 0.2322 0.1563 0.1675 0.1783 0.1898 0.2060 0.2189 0.1360 0.1475 0.1584 0.1683 0.1916 0.2027 0.1134 0.1217 0.1324 0.1492 0.1701 0.1887

0.0413 0.0526 0.0627 0.0838 0.1163 0.1379 0.0464 0.0604 0.0732 0.0964 0.1366 0.1672 0.0518 0.0695 0.0829 0.1133 0.1584 0.1943 0.0573 0.0768 0.0899 0.1282 0.1765 0.2168

4.2501 3.6429 3.2125 2.4828 1.8904 1.6846 3.3696 2.7725 2.4350 1.9676 1.5081 1.3089 2.6249 2.1231 1.9106 1.4855 1.2093 1.0435 1.9793 1.5834 1.4735 1.1631 0.9640 0.8706

308.2

318.2

328.2

ln γi =

∑ j = 1 τijGjixj m

∑l = 1 Glixl

m

+

∑ j=1

ÄÅ ÉÑ m ÅÅ ∑r = 1 τrjGrjxr ÑÑÑ ÅÅ ÑÑ ÅÅτij − m m Ñ ∑l = 1 Gljxl ÑÑÑ ∑l = 1 Gljxl ÅÅÅ Ç Ö Gijxj

(4)

In the NRTL model, a relation exists between adjustable parameters and energy differences (eq 5) τij =

gij − gjj

=

RT

Aij T

,

Gij = exp( −αijτij)

(5)

where, in eq 7, Aii = Ajj = 0, Aij ≠ Aji, and αij = αji. By calculation of γi in each phase with appropriate interaction parameters, the mole fractions of each component in each phase can be calculated by minimizing the appropriate objective function (eq 6). The obtained data are compared with each other by using the root-mean-square deviation (rmsd) in eq 7 t

F=

p

c

∑ ∑ ∑ (xijkexp − xijkcal)2 i=1 j=1 k=1

ÄÅ ÉÑ1/2 ÅÅ t p c ÑÑ ÅÅ Ñ exp cal 2 − xijk rmsd = ÅÅÅ∑ ∑ ∑ (xijk ) /6t ÑÑÑÑ ÅÅ ÑÑ ÅÅÇ i = 1 j = 1 k = 1 ÑÑÖ

(6)

(7)

where t, p, and c are the number of tie-lines, phases, and components, respectively. D



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Figure 3. Plot of the separation factor (S) of citric acid versus the mass fraction of the acid in the aqueous phase: (black) T = 298.2 K, (red) T = 308.2 K, (green) T = 318.2 K, (blue) T = 328.2 K.

Figure 4. Plot of the distribution coefficient (D2) of citric acid versus the mass fraction of the acid in the aqueous phase: (black) T = 298.2 K, (red) T = 308.2 K, (green) T = 318.2 K, (blue) T = 328.2 K.

3. RESULT AND DISCUSSION 3.1. LLE Data. The experimental tie-line data for the ternary system containing water, citric acid, and 1-decanol were obtained at T = 298.2, 308.2, 318.2, and 328.2 K and atmospheric pressure. The experimental data are shown in Table 5. In order to evaluate the ability of a solvent for the separation of citric acid from aqueous solution, distribution coefficients for water (D1) and citric acid (D2) and the separation factor (S) were determined from the LLE tie-line data. Equations 8, 9. and 10 are applied to calculate these factors D1 = w13/w11

(8)

D2 = w23/w21

(9)

S = D2 /D1

Table 7. Comparison between the Separation Factor (S) and Distribution Coefficients (D1, D2) of Citric Acid for Various Ternary Systems at 298.2 K and Atmospheric Pressure system 1-butanol

2-butanol

1-decanol

(10)

where w13 and w23 are the mass fraction of water and citric acid in the organic phase, respectively, and w11 and w21 are the mass

acid conc. in feed phase

D1

D2

S

0.0255 0.0433 0.0517 0.0109 0.0204 0.0355 0.1110 0.2005 0.2720

0.2390 0.2506 0.2512 0.4538 0.4780 0.5644 0.0413 0.0526 0.0627

0.3730 0.3663 0.3415 0.7239 0.7120 0.7469 0.1755 0.1918 0.2014

1.5606 1.4615 1.3591 1.5948 1.4895 1.3234 4.2501 3.6429 3.2125

literature 10

10

this study

fraction of water and citric acid in the aqueous phase, respectively. The experimental distribution coefficients and separation E



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factor are listed in Table 6. The values in the table show that the solvent has a relatively good ability for the extraction process of citric acid from its aqueous mixture. Figure 3 and Figure 4 show the variation of the separation factor (S) and distribution coefficient (D2) of the acid, respectively, versus the mass fraction of citric acid in the aqueous phase. When the separation factor (Figure 3) is greater than 1, the separation process is possible; it decreases with increasing concentration of the acid in the organic phase. As seen from Figure 4 at all temperatures, the distribution coefficients are suitable. In order to compare the ability of this solvent with other solvents, the values of the distribution coefficients and separation factor are presented in Table 7. According to this table, the separation factor decreases by increasing the concentration of acid in the feed. It can be seen that, under the same conditions, 1-decanol is better than 1-butanol and 2-butanol for separation of citric acid in ternary systems. 3.2. Correlation of Tie-Lines. Compatibility of experimental data and tie-lines, used as a measure of the reliability of experimental data, for the ternary system (water + citric acid + 1-decanol) has been evaluated by the Othmer−Tobias (eq 11)31 and Hand (eq 12) equations.32 For this ternary system, Othmer−Tobias and Hand plots were presented in Figures 5 and 6, at different temperatures. The linear regression coefficients of experimental data and the Othmer−Tobias and Hand equations at various temperatures are presented in Table 8

Figure 5. Othmer−Tobias plots of the ternary system (water + citric acid + 1-decanol) at various temperatures: (○) T = 298.2, (□) T = 308.2, (△) T = 318.2, (◇) T = 328.2 K.

ij 1 − w33 yz i y zz = A + B lnjjj 1 − w11 zzz lnjjj jj w zz j w33 zz 11 { k k {

(11)

ij w yz ij w yz lnjjj 21 zzz = C + D lnjjj 23 zzz jw z j w33 z k 11 { { k

where w33 and w23 are the mass fraction of solvent and citric acid in the organic phase, respectively, and w11 and w21 are the mass fraction of water and citric acid in the aqueous phase, respectively. Othmer−Tobias and Hand plots for the system containing water, citric acid, and 1-decanol at different temperatures and atmospheric pressure are shown in Figures 5 and 6, respectively. The correlation factor (R2) for the Othmer− Tobias and Hand equations in Table 8 is approximately close to unity, which indicates the consistency of LLE data. 3.3. Modeling. In this study, the genetic algorithm was used to estimate parameters of the LLE system containing water, citric acid, and 1-decanol. Interaction parameters and rmsd for different temperatures are calculated by the GA for the NRTL model and are listed in Table 9. The obtained parameters from the GA were evaluated and tested by the method of Marcilla et al.21, and it was observed that these parameters are thermodynamically correct and consistent with experimental LLE data. It should be noted that the mixing energy of the Gibbs in each phase is minimized by these

Figure 6. Hand plots of the ternary system (water + citric acid + 1-decanol) at various temperature: (○) T = 298.2, (□) T = 308.2, (△) T = 318.2, (◇) T = 328.2 K.

Table 8. Othmer−Tobias and Hand Equation Constants for the Ternary System at Various Temperatures correlation

T (K)

A

B

R2

Othmer−Tobias

298.2 308.2 318.2 328.2 298.2 308.2 318.2 328.2

0.5857 0.5716 0.5555 0.5392 0.7747 0.7810 0.7927 0.8212

−1.8551 −1.9201 −1.9753 −2.0630 −2.1706 −2.2981 −2.4316 −2.6091

0.9988 0.9999 0.9991 0.9936 0.9931 0.9964 0.9976 0.9994

Hand

(12)

Table 9. Binary Interaction Parameters of the NRTL Model for the System Water + Citric Acid + 1-Decanol F

temperature

RMSD

298.2

0.0018455

0.0001226

308.2

0.001505

8.15 × 10−5

318.2

0.00194204

0.00013577

Aij 1−2 1−3 2−3 1−2 1−3 2−3 1−2

1116.49432 1552.29933 500.99872 1174.13182 1546.49354 500.728 1300.48626 F

αij

Aji 2−1 3−1 3−2 2−1 3−1 3−2 2−1

−535.391 341.1145 145.228 −545.525 418.0807 256.7499 −587.884

1−2 1−3 2−3 1−2 1−3 2−3 1−2

0.302512 0.301371 0.319969 0.343863 0.324988 0.350827 0.347949



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Table 9. continued temperature

328.2

RMSD

0.00264548

F

0.00025194

Aij 1−3 2−3 1−2 1−3 2−3

αij

Aji

1522.44425 518.5379 1478.5292 1499.5636 524.446375

3−1 3−2 2−1 3−1 3−2

477.8986 399.6138 −655.312 551.1517 525.0445

1−3 2−3 1−2 1−3 2−3

0.347238 0.425523 0.345627 0.363593 0.413562

Figure 7. Effect of temperature on NRTL binary interaction parameters.

Figure 8. Ternary phase diagram for the ternary system at T = 298.2 K: (blue (black ○) solubility data points.

parameters, and all of the experimental tie-lines are in the minimum amount of mixture Gibbs energy; therefore, these interaction parameters are coherent with the experimental data. The effect of temperature on binary interaction parameters for the NRTL model is shown in Figure 7. In this figure, there

▲)

experimental points, (red ■) NRTL calculated points, and

is a linear dependency between interaction parameters in terms of temperature. The experimental LLE ternary phase diagram for the system (water + citric acid + 1-decanol) and NRTL calculated data are shown in Figures 8−11. As can be seen from these figures, the G



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▲)



▲)


Distribution coefficients and separation factors for this system were calculated. The amount of separation factor showed that organic solvent has the ability to extract citric acid from aqueous solutions. For this system, the separation factor exhibits larger values at T = 298.2 K. Among the substances that have been used as solvents for the extraction of citric acid from ternary aqueous solution, 1-decanol has a higher separation coefficient. Therefore, it can be a suitable solvent for

calculated mass fractions for all temperatures are in good agreement with the experimental mass fraction and show that NRTL model can be used to describe this ternary system.

■

CONCLUSION In this study, experimental liquid−liquid equilibrium data for the ternary system (water + citric acid + 1-decanol) were acquired at T = 298.2, 308.2, 318.2, and 328.2 K and P = 101.3 ± 0.4 kPa. H



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T a D S

separating citric acid from aqueous solution. The NRTL model was used to correlate the experimental data. Correlation of the experimental data on the activity thermodynamic model was accomplished by the genetic algorithm, and optimized interaction parameters were obtained at different temperatures. The obtained rmsd values demonstrate that the NRTL is a suitable model and can be applied to LLE data, and they also show that the GA technique is a good method for obtaining the thermodynamic interaction parameters.

■

▲)


temperature interaction parameter distribution coefficient separation factor

Greek Letters

γ activity coefficient τ adjustable interaction parameter α NRTL nonrandomness factor Superscripts

I phase (aqueous) II phase (organic)

AUTHOR INFORMATION

Corresponding Author

Subscripts

*Phone: +981333690274. Fax: +981333690278. E-mail: [email protected].

i j k 1 2 3

ORCID

Hamid Ramezanipour Penchah: 0000-0003-4206-7978 Notes

The authors declare no competing financial interest.

■

■

NOMENCLATURE nD refractive index R2 correlation coefficient w mass fraction x mole fraction K distribution ratio exp experimental cal calculated t Number of tie-lines p Number of phases c Number of components F Objective function rmsd root-mean-square deviation NRTL nonrandom two liquid g energy parameter characteristic A interaction parameter

component/tie-line component/phase component water citric acid 1-decanol

REFERENCES

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Experimental Data of Citric Acid Extraction from Aqueous Solution with

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