Liquid - liquid equilibrium for the quaternary reaction system water + sec-butyl alcohol + sec-butyl acetate + acetic acid

Fluid Phase Equilibria 432 (2017) 70e75

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Liquid - liquid equilibrium for the quaternary reaction system water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid Ling Li, Ting Zeng, Xiaoda Wang, Changshen Ye, Ting Qiu, Zhixian Huang* School of Chemical Engineering, Fuzhou University, Fuzhou, 350116, Fujian, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 July 2016 Received in revised form 20 October 2016 Accepted 22 October 2016 Available online 24 October 2016

There is a reversible reaction (sec-butyl acetate þ water ⇔ sec-butyl alcohol þ acetic acid) catalyzed by acetic acid in the quaternary system water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid. In this work, the liquid-liquid equilibrium (LLE) data for this quaternary system were determined at 303.15e333.15 K at atmosphere pressure. The LLE model of this quaternary reaction system was established with consideration of the chemical equilibrium of the reversible reaction. The measured LLE data were used to correlate the binary interaction parameters of the NRTL and UNIQUAC models. The NRTL model is more suitable than UNIQUAC model for describing the LLE of this quaternary reaction system. © 2016 Elsevier B.V. All rights reserved.

Keywords: LLE Quaternary reaction system Sec-butyl acetate NRTL model UNIQUAC model

1. Introduction The separation of acetic acid from aqueous solutions is extremely important in industry. Azeotropic distillation and extraction distillation were often used to separate the solution of acetic acid-water in industry. And the entrainers were mainly isopropyl acetate, butyl acetate, isobutyl acetate, ethyl acetate, benzene [1e4], and so on. As an isomer of isobutyl acetate, sec-butyl acetate has the same water carrying capacity as isobutyl acetate. But it has larger water carrying capacity than isopropyl acetate and ethyl acetate. Sec-butyl acetate was produced by the addition reaction of acetic acid and 1-butene or 2-butene from liquefied petroleum gas, which has been developed on a scale of 400 000 tons/ year by Hunan Zhongchuang Chemical Co., Ltd. since 2006. This production route exhibits high selectivity and low raw material costs, and thereby significantly reduces the cost of sec-butyl acetate. We did hydrolysis experiment of n-butyl acetate, isobutyl acetate and sec-butyl acetate which catalyzed by acetic acid at the same condition. The Hydrolysis rates were 25.01%, 21.90% and 13.3% respectively. The prices are 7850 yuan, 12000 yuan, 6000 yuan per ton respectively. The LD50 are 10768 mg/kg, 15400 mg/kg, 13400 mg/kg respectively. So it has more stable chemical property

* Corresponding author. E-mail address: [email protected] (Z. Huang). http://dx.doi.org/10.1016/j.fluid.2016.10.027 0378-3812/© 2016 Elsevier B.V. All rights reserved.

and low price and toxicity. So the basic research of sec-butyl acetate has attracted more attention. But sec-butyl acetate as entrainer has not been reported. Up to now, the determination of the ternary LLE data for this system has been carried out. The experimental LLE date for the ternary system water þ sec-butyl acetate þ acetic acid was measured by Hu et al. [5] at 298.15 K, 303.15 K, 308.15 K and 313.15 K. The NRTL and UNIQUAC models were applied to fit the experimental data for the ternary system. In addition, the LLE date for the two ternary systems water þ butyl acetate þ acetic acid and water þ isobutyl acetate þ acetic acid were determined by Wang et al. [6] at 304.15 K, 332.15 K and 366.15 K, and the experimental data were used to estimate the LLE interaction parameters in the NRTL model. However, the LLE data for the quaternary system water þ secbutyl alcohol þ sec-butyl acetate þ acetic acid have not been reported in literature. In this quaternary system, there is a reversible reaction between sec-butyl acetate þ water and sec-butyl alcohol þ acetic acid, where acetic acid acts not only as catalyst but also as reactant. There exist both chemical reaction equilibrium between hydrolysis reaction and esterification and liquid liquid equilibrium in this quaternary system water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid. In the determination of the experimental data, it is not only to achieve the chemical equilibrium but also the liquid-liquid equilibrium. In the mathematical model of this phase equilibrium with reaction the liquid-liquid

L. Li et al. / Fluid Phase Equilibria 432 (2017) 70e75

equilibrium and the reaction equilibrium should be both considered. Due to the effect of this reversible reaction, the LLE for this quaternary system is more complicated than other systems without chemical reaction. In presented paper, the LLE date for the quaternary reaction system of water þ sec-butyl alcohol þ sec-butyl acetate þ acetic were determined. Additionally, the LLE model for this system was established by considering the hydrolysis of secbutyl acetate catalyzed by acetic acid. Finally, the experimental data were correlated with the NTRL and UNIQUAC models.

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Table 2 Densities r, refractive indexes nD of pure compounds at P ¼ 101.3 kPa.

r(g/cm3)

Compound

Lit. water(298.15 K) acetic acid(298.15 K) sec-butyl acetate(293.15 K) sec-butyl alcohol(298.15 K)

0.9970 1.0437 0.8720 0.8080

[7,8] [8] [8] [8]

nD Exp.

Lit.

Exp

0.9970 1.0446 0.8710 0.8040

1.3325 1.3698 1.3894 1.3969

[8] [8] [8] [7]

1.3320 1.3703 1.3876 1.3962

The measurement uncertainties for r, nD and T are u(r) ¼ ±0.001 g cm3, u(nD) ¼ ±0.0002 and u(T) ¼ ±0.01 K, respectively.

2. Experimental 2.1. Materials In this paper, all the chemicals were high purity grade. Sec-butyl acetate was distilled in a glass column in order to eliminate the organic impurities. The sources of the materials, purification methods, and final purities were listed in Table 1. The refractive indexes of these pure components were measured by a WAY refractometer with uncertainty of ±0.0002. The densities of the pure liquids were measured by an densimeter(Anton Paar DMA-58) with uncertainty of ±0.0001 g cm3. The experimental values of these properties at P¼101.3 kPa were compared with their counterparts in literature, as shown in Table 2.

5

2

3 6

4 7

1

2.2. Sample analysis Sec-butyl alcohol and sec-butyl acetate were determined by a Gas Chromatograph (GC-2010, Japan Shimadzu) equipped with a flame ionization detector (FID) and a free fatty acid phase (FFAP) column (30 m  0.32 mm  0.25 mm), and their compositions were analyzed by internal standard method with isopropanol as internal standard substance. Nitrogen was used as carrier gas at the flowrate of 3.0 mL/min. The temperatures of the injection port and the detector were held at 520.15 K and 550.15 K, respectively. The column temperature was first kept at 323.15 K for 1 min, then increasing at the rate of 15 K/min to 423.15 K, finally keeping at 423.15 K for 1 min. The chromatographic peaks for all the organics involved in the experiment could be completely separated with this analysis method. The concentration of acetic acid was determined by acid base titration with sodium hydroxide (NaOH) as basic titrant and phenolphthalein as indicator. The water content was tested by Switzerland Metrohm 756Karl-Fischer Coulometer with uncertainty of ±0.0001mass fraction. 2.3. Apparatus and procedure The reaction equilibrium constant for the hydrolysis of sec-butyl acetate was measured by the apparatus shown in Fig. 1. The reaction was carried out in a 500 mL three-neck flask at atmosphere pressure. The temperature inside the three neck flask was controlled by a thermostatic oil bath with uncertainty of ±0.5 K. This thermostatic oil bath could provide a rotating magnetic field. By means of this magnetic field, a cylindrical magnet was put into the three-neck flask to stir the liquid to ensure the uniform distribution of temperature and reactant concentration. A condenser

Fig. 1. Apparatus to measure reaction equilibrium constant. 1. thermostatic oil bath; 2. thermometer; 3. sampling (or feeding) hole; 4. reactor (three neck flask); 5. condenser pipe; 6. thermocouple; 7. magnet stirrer.

was placed above the three-neck flask to avoid the volatilization of the reactants. Prior to experiment, sec-butyl acetate and acetic acid were charged into the three-neck flask, and heated to desired temperature by the thermostatic oil bath. In the following, the water preheated to the same temperature was added into the three-neck flask. Meanwhile, this moment was taken as the initial moment of reaction. During the process of reaction, sample was taken through the sampling site every minutes to monitor the reactant concentration in the reactor. The sample composition was analyzed by the method in section 2.2. When the concentration of each reactant in the reactor was almost unchanged, the reversible reaction was considered to arrive its chemical equilibrium. The most widely used equilibrium still method was employed to measure the LLE data in this paper. The schematic of the experimental apparatus is shown in Fig. 2. The temperature in the liquidliquid cell was controlled by the concatenation of a thermostatic water bath (DBK-501A, Shanghai Laboratory Instrument Works Co.Ltd) and a cooling water bath (DC-3006, Shanghai Hengping Instrument and Meter Factory). The uncertainty of this

Table 1 .Mass fraction purities of chemical samples. Compound

Source

Initial mass fraction

Purification method

Final mass fraction

Analysis method

acetic acid sec-butyl acetate sec-butyl alcohol

Sinopharm Chemical Reagent Co., Ltd Hunan Zhongchuang Chemical Co., Ltd. Sinopharm Chemical Reagent Co., Ltd

0.998 0.987 0.998

none distillation none

0.998 0.997 0.998

acid base titration GCa GCa

a

GC: gas chromatography.

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L. Li et al. / Fluid Phase Equilibria 432 (2017) 70e75

5

1 4

3 2

Fig. 2. Apparatus to measure LLE data. 1 liquid-liquid equilibrium cell; 2 magnetic stirrer; 3 thermostatic water bath; 4 cooling water bath; 5 condenser.

temperature-controlling system is ±0.01 K. Before the experiment, about 25 mL of mixture sample was put into the equilibrium cell. The concentration of each chemical was adjusted to ensure the liquid-liquid phase separation. The mixture in the equilibrium cell was vigorously stirred for at least 4 h, and then left to settle for at least 12 h. Finally, a sample of each phase was drown out by a dropping pipette. The composition of each chemical in the sample was analyzed by the method in Section 2.2.

Fig. 3. Correlation of reaction equilibrium constant and temperature.

water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid with reversible reaction were determined at 303.15, 308.15, 313.15, 318.15, 323.15 K and 333.15 K at P¼101.3 kPa, as shown in Table 3.

3. Results and discussion

3.2. Thermodynamic model of LLE with reversible reaction

3.1. Experimental data

If the liquid-liquid phase equilibrium was established, the two phases are equal not only in temperature and pressure but also in fugacity coefficient of each component [9]:

3.1.1. Reaction equilibrium constant for hydrolysis reaction of secbutyl acetate The ternary system sec-butyl acetate þ water þ acetate acid is partially miscible. In order to avoid the liquid-liquid separation of the reaction system, the initial concentration of each chemical was chosen by referring to the LLE data for the ternary system water þ sec-butyl acetate þ acetic acid measured by Hu et al. [5]. The equilibrium constant Ke for hydrolysis reaction of sec-butyl acetate was measured at five different temperatures (348, 353, 358, 363 and 368 K). The effect of temperature on Ke is shown in Fig. 3. The increase of temperature with Ke indicates that the hydrolysis of sec-butyl acetate is an endothermic reaction. Generally, there is a linear relationship between lnKe and 1/T:


A þB Ke ¼ exp T

(1)

Here, both A and B are the parameters of Eq. (1). The experimental data in Fig. 3 were used to correlate the two coefficients of Eq. (1) by the least square method: A ¼ 728.21; B ¼ 0.9485. The correlation coefficient for Eq. (2) is 0.985. The chemical equilibrium constant Ke for hydrolysis reaction of sec-butyl acetate catalyzed by acetic acid was calculated with the following equation:

728:21  0:9485 In Ke ¼  T

(2)

3.1.2. LLE data for the quaternary system The experimental LLE data for the quaternary system

xIi gIi ¼ xIIi gIIi

(3)

Here, xІi , xІІ i are the mole fractions of component i in each phase of the LLE system, respectively. Correspondingly, gІi , gІi І are the fugacity coefficients of component i, which could be calculated by the NRTL [10,11] or UNIQUAC [12] model. The superscripts I and II indicate organic phase and water phase, respectively. Additionally, the sum of morality of each component must satisfy the normalization equation in the each phase of the system: 4 X

ðxi ÞI ¼ 1

(4)

ðxi ÞII ¼ 1

(5)

i¼1

4 X i¼1

For the LLE of the quaternary system water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid, there is a reversible reaction between sec-butyl acetate þ water and sec-butyl alcohol þ acetic acid due to the catalysis of acetic acid. As a result, the chemical equilibrium of this reversible reaction should be taken into consideration when constructing the LLE model of this quaternary system. Obviously, once the LLE was established, the reversible reaction had reached its chemical equilibrium. Therefore, the chemical equilibrium constant Ke for each phase of the LLE system with reversible reaction must be equal to each other:

L. Li et al. / Fluid Phase Equilibria 432 (2017) 70e75

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Table 3 LLE data for the system water(1) þ sec-butyl alcohol(2) þ sec-butyl acetate(3) þ acetic acid(4) at P ¼ 101.3 kPa. T/K

No.

303.15

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

308.15

313.15

318.15

323.15

333.15

Organic phase

Aqueous phase

xI1

xI2

xI3

xI4

xII1

xII2

xII3

xII4

0.2078 0.4503 0.0979 0.5233 0.2654 0.4941 0.4413 0.0324 0.4978 0.594 0.5886 0.4419 0.4917 0.5022 0.4385 0.4635 0.5395 0.6144 0.5250 0.5436 0.5581 0.8348 0.6107 0.5244 0.4640 0.4662 0.3454 0.3408 0.5313 0.4839 0.5166 0.4198 0.5557 0.5433 0.5382 0.5670 0.4137 0.5409 0.4767 0.5604 0.4423 0.5184 0.3556 0.5856 0.3423 0.4715 0.4948 0.4690

0.1881 0.0602 0.1645 0.0477 0.1092 0.0452 0.0868 0.0941 0.2107 0.1587 0.2232 0.2094 0.2497 0.1972 0.1123 0.1105 0.2401 0.2357 0.2546 0.2880 0.2686 0.1029 0.2706 0.1707 0.2574 0.2177 0.2280 0.2031 0.2449 0.0986 0.2473 0.0974 0.3454 0.1001 0.2186 0.2908 0.2456 0.0737 0.2242 0.2113 0.1704 0.0664 0.1949 0.0442 0.1818 0.1383 0.0529 0.1454

0.4773 0.3304 0.6202 0.3125 0.3962 0.2648 0.3278 0.6179 0.1421 0.1075 0.1178 0.1068 0.1296 0.1428 0.2052 0.1395 0.1013 0.0527 0.0830 0.0702 0.0767 0.0239 0.0378 0.1978 0.1580 0.1582 0.2677 0.3158 0.1100 0.2232 0.1148 0.2876 0.0526 0.175 0.1210 0.0754 0.1985 0.1885 0.1819 0.1108 0.2893 0.2503 0.3499 0.1482 0.3785 0.2390 0.2075 0.2460

0.1267 0.1591 0.1173 0.1165 0.2292 0.1958 0.1442 0.2557 0.1525 0.1075 0.1178 0.1068 0.1296 0.1594 0.2052 0.2332 0.1191 0.0972 0.1087 0.0982 0.1037 0.0399 0.0896 0.1068 0.1206 0.1578 0.1588 0.1404 0.1138 0.1943 0.1213 0.1952 0.0463 0.1816 0.1222 0.0668 0.1422 0.1969 0.1171 0.1174 0.0980 0.1649 0.0997 0.2220 0.0975 0.1512 0.2448 0.1396

0.9514 0.9146 0.9588 0.9315 0.9002 0.8779 0.9246 0.9115 0.9032 0.9408 0.9041 0.9476 0.9205 0.9162 0.8866 0.8720 0.9211 0.9334 0.9311 0.9307 0.9367 0.9297 0.9388 0.9298 0.9334 0.9085 0.9300 0.9378 0.9269 0.8842 0.9318 0.8939 0.9543 0.8850 0.9239 0.9478 0.9303 0.8647 0.9387 0.9254 0.9527 0.9001 0.9559 0.7980 0.9580 0.9208 0.8252 0.9271

0.0108 0.0054 0.0082 0.0056 0.0089 0.0064 0.0079 0.0034 0.0219 0.0159 0.0377 0.0148 0.0273 0.0192 0.0136 0.0116 0.0287 0.0316 0.0258 0.0358 0.0247 0.0347 0.0270 0.0247 0.0216 0.0232 0.0156 0.0130 0.0265 0.0132 0.0251 0.0102 0.0299 0.0149 0.0226 0.0272 0.0184 0.0128 0.0172 0.0236 0.0106 0.0078 0.0100 0.0163 0.0088 0.0119 0.0120 0.0114

0.0019 0.0049 0.0017 0.0027 0.0046 0.0068 0.0027 0.0023 0.0058 0.0021 0.0039 0.0018 0.0031 0.0037 0.0059 0.0076 0.0028 0.0020 0.0021 0.0019 0.0019 0.0017 0.0014 0.0031 0.0025 0.0034 0.0026 0.0027 0.0028 0.0068 0.0025 0.0058 0.0008 0.0063 0.0025 0.0013 0.0024 0.0082 0.0018 0.0025 0.0015 0.0043 0.0015 0.0235 0.0015 0.0028 0.0149 0.0026

0.0358 0.0752 0.0314 0.0602 0.0863 0.1088 0.0648 0.0828 0.0635 0.0412 0.0542 0.0358 0.0490 0.0612 0.0939 0.1087 0.0474 0.0363 0.0410 0.0316 0.0368 0.0294 0.0328 0.0424 0.0425 0.0649 0.0518 0.0465 0.0437 0.0958 0.0407 0.0901 0.015 0.0939 0.0509 0.0237 0.0488 0.1142 0.0422 0.0485 0.0353 0.0877 0.0326 0.1622 0.0317 0.0644 0.1479 0.0588

The measurement uncertainties for T and x are u(T) ¼ ±0.01 K and u(x) ¼ ±0.0002, respectively.

Ke¼

Ke¼

Y Y

gIi xIi

vi

gIIi xIIi

vi

ði ¼ 1; 2; 3; 4Þ

ði ¼ 1; 2; 3; 4Þ

(6)

(7)

3.3. Correlation of LLE data The experimental LLE data for the quaternary system water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid were correlated with NRTL and UNIQUAC models. The binary interaction parameters of these two models were obtained by minimizing the following objective function F through the simplex method [9]:

2 !2 I;exp N X n X x  xI;cal ik 4 ik F ¼ min þ xI;exp k¼1 i¼1 ik

II;exp

xik

 xII;cal ik

xI;exp ik

!2 3 5

(8)

Where i and k are the numbers of components and sets of experimental data, respectively, while superscript exp and cal respect the experimental and calculated values, respectively. The correlated binary interaction parameters of the NRTL and UNIQUAC models are listed in Tables 4 and 5, respectively. It should be pointed out that the non-randomness parameters of the NRTL model were set as 0.3 to simply the optimizing calculation. 3.4. Prediction The NRTL and UNIQUAC models can be used to calculate the LLE data on the basis of the correlated binary interaction parameters.

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L. Li et al. / Fluid Phase Equilibria 432 (2017) 70e75

Table 4 Parameters of the NRTL model for the LLE system water(1) þ sec-butyl alcohol(2) þ sec-butyl acetate(3) þ acetic acid(4). T/K

Model parameters/(J mol1)

303.15

Dg12 ¼ 8957.42 Dg13 ¼ 18322.13 Dg14 ¼ 1165.16 Dg12 ¼ 10396.75 Dg13 ¼ 17900.77 Dg14 ¼ 844.691 Dg12 ¼ 9660.40 Dg13 ¼ 17525.49 Dg14 ¼ 3487.05 Dg12 ¼ 7979.81 Dg13 ¼ 14458.71 Dg14 ¼ 2982.21 Dg12 ¼ 8053.53 Dg13 ¼ 17648.30 Dg14 ¼ 803.111 Dg12 ¼ 6656.17 Dg13 ¼ 20043.89 Dg14 ¼ 2499.52

308.15

313.15

318.15

323.15

333.15

Dg21 ¼ 811.342 Dg31 ¼ 18076.74 Dg41 ¼ 8163.25 Dg21 ¼ 2156.50 Dg31 ¼ 20999.41 Dg41 ¼ 5444.02 Dg21 ¼ 20998.16 Dg31 ¼ 174.908 Dg41 ¼ 4948.51 Dg21 ¼ 2068.39 Dg31 ¼ 8478.43 Dg41 ¼ 8755.30 Dg21 ¼ 798.621 Dg31 ¼ 8556.24 Dg41 ¼ 14789.29 Dg21 ¼ 789.514 Dg31 ¼ 8750.20 Dg41 ¼ 15234.68

Dg23 ¼ 1707.38 Dg24 ¼ 20959.37 Dg34 ¼ 896.392 Dg23 ¼ 1207.48 Dg24 ¼ 8057.64 Dg34 ¼ 4464.99 Dg23 ¼ 3423.16 Dg24 ¼ 2161.24 Dg34 ¼ 2308.71 Dg23 ¼ 5886.27 Dg24 ¼ 4167.06 Dg34 ¼ 4760.49 Dg23 ¼ 546.330 Dg24 ¼ 7344.26 Dg34 ¼ 1821.83 Dg23 ¼ 3637.94 Dg24 ¼ 1106.44 Dg34 ¼ 1631.82

Dg32 ¼ 15391.82 Dg42 ¼ 915.872 Dg43 ¼ 2764.21 Dg32 ¼ 9712.77 Dg42 ¼ 15151.35 Dg43 ¼ 2005.55 Dg32 ¼ 6424.80 Dg42 ¼ 2647.81 Dg43 ¼ 4882.78 Dg32 ¼ 396.247 Dg42 ¼ 2028.69 Dg43 ¼ 2035.73 Dg32 ¼ 9411.70 Dg42 ¼ 12796.06 Dg43 ¼ 1956.77 Dg32 ¼ 1716.41 Dg42 ¼ 587.626 Dg43 ¼ 217.870

Table 5 Parameters of the UNIQUAC model for the LLE system water(1) þ sec-butyl alcohol(2) þ sec-butyl acetate(3) þ acetic acid(4). T/K

Model parameters/(J mol1)

303.15

DU12 ¼ 1605.56 DU13 ¼ 519.693 DU14 ¼ 255.300 DU12 ¼ 258.458 DU13 ¼ 2953.93 DU14 ¼ 5015.01 DU12 ¼ 699.556 DU13 ¼ 4411.05 DU14 ¼ 3313.36 DU12 ¼ 268.156 DU13 ¼ 1818.96 DU14 ¼ 2266.65 DU12 ¼ 603.857 DU13 ¼ 2608.53 DU14 ¼ 3714.52 DU12 ¼ 842.272 DU13 ¼ 1730.28 DU14 ¼ 2787.90

308.15

313.15

318.15

323.15

333.15

DU21 ¼ 80.096 DU31 ¼ 19133.08 DU41 ¼ 19972.24 DU21 ¼ 14978.93 DU31 ¼ 137.400 DU41 ¼ 5142.07 DU21 ¼ 2171.98 DU31 ¼ 935.551 DU41 ¼ 5173.45 DU21 ¼ 7723.87 DU31 ¼ 3648.23 DU41 ¼ 2351.70 DU21 ¼ 2129.38 DU31 ¼ 1067.00 DU41 ¼ 19985.33 DU21 ¼ 3027.32 DU31 ¼ 3388.98 DU41 ¼ 19819.08

Fig. 4. The relationship between experiment values xexp and calculated values xcal by the NRTL model.

DU23 ¼ 2603.51 DU24 ¼ 2056.19 DU34 ¼ 286.050 DU23 ¼ 2119.38 DU24 ¼ 6092.92 DU34 ¼ 134.368 DU23 ¼ 813.819 DU24 ¼ 2578.56 DU34 ¼ 3390.17 DU23 ¼ 1049.29 DU24 ¼ 19999.04 DU34 ¼ 2072.75 DU23 ¼ 49.3267 DU24 ¼ 3397.48 DU34 ¼ 19935.91 DU23 ¼ 19997.19 DU24 ¼ 19807.33 DU34 ¼ 19673.69

DU32 ¼ 1891.51 DU42 ¼ 19988.14 DU43 ¼ 18201.75 DU32 ¼ 15469.60 DU42 ¼ 2452.67 DU43 ¼ 593.276 DU32 ¼ 2155.85 DU42 ¼ 63.4043 DU43 ¼ 7256.22 DU32 ¼ 1200.24 DU42 ¼ 1751.35 DU43 ¼ 19982.47 DU32 ¼ 1023.47 DU42 ¼ 2830.83 DU43 ¼ 1421.91 DU32 ¼ 2292.30 DU42 ¼ 1533.59 DU43 ¼ 1547.60

Fig. 5. The relationship between experiment values xexp and calculated values xcal by the UNIQUAC model.

L. Li et al. / Fluid Phase Equilibria 432 (2017) 70e75

The relationship between experiment values xexp and calculated values xcal were shown in Fig. 4 and Fig. 5. For the NRTL model the average relative deviations of each component are 7.28%, 6.59%, 9.77%, 5.62% for water, sec-butyl alcohol, sec-butyl acetate and acetic acid respectively in organic phase. And values are 0.77%, 12.66%, 8.92%, 9.26% respectively in water phase. For the UNIQUAC model the average relative deviations of each component are 10.97%, 12.54%, 21.71%, 8.17% for water, sec-butyl alcohol, sec-butyl acetate and acetic acid respectively in organic phase. And values are 0.84%, 16.76%, 16.15%, 9.92% respectively in water phase. It suggests that NRTL model is more suitable than UNIQUAC model to describe the LLE for the quaternary system water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid at the temperature from 303.15 K to 333.15 K. 4. Conclusion The LLE data for the quaternary systems water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid at the temperature range of 303.15 Ke333.15 K were measured. The LLE thermodynamic model of the quaternary system was established with consideration of the chemical equilibrium of the reversible reaction in this system. The binary interaction parameters of the NRTL and UNIQUAC models were correlated with the LLE data by the Simplex Method. The correlated binary interaction parameters were used to predict the LLE data. The small deviation between the predicted and experimental values indicates that both these two models are

75

suitable for describing the LLE of the quaternary systems water þ sec-butyl alcohol þ sec-butyl acetate þ acetic acid. Acknowledgements We acknowledge the financial support for this work from the National Natural Science Foundation of China (Nos. 21576053 and 91534106), the Science Foundation for Distinguished Young Scholars of Fujian (No. 2014J06004), the Natural Science Foundation of Fujian Province (No. 2016J01689), the International S&T Cooperation Program of China (No. 2013DFR90540), the Key Project of Fujian Provincial Department of Science and Technology (No. 2014Y0066). References [1] H.J. Huang, I.L. Chien, J. Chin, Ins. Chem. Eng. 39 (2008) 503e517. [2] S.J. Wang, D.S.H. Wong, J. Process Contr. 23 (2013) 78e88. [3] I.L. Chien, H.P. Huang, T.K. Gau, C.H. Wang, Ind. Eng. Chem. Res. 44 (2005) 3510e3521. [4] S.J. Li, Ind. Eng. Chem. Res. 48 (2009) 6358e6362. [5] S. Hu, Q.L. Chen, B.J. Zhang, Y.L. Liang, X.N. Gao, Fluid Phase Equilib. 293 (2010) 73e78. [6] L.J. Wang, Y.W. Cheng, X.J. Xiao, X. Li, J. Chem. Eng. Data 52 (2007) 1255e1257. [7] N.L. Chen, Chem. Ind. Press, 2008. [8] G.J Liu, L.X. Ma, S.G. Xiang, Chem Ind Press, 2002. [9] J.M. Smith, H.C. Van Ness, M.M. Abbott, McGraw - Hill, NewYork, 2005. [10] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135e144. [11] R.L. Scott, J. Chem. Phys. 25 (1956) 193. [12] D.S. Abrams, J.M. Prausnitz, AIChE J. 1 (1975) 116e128.