cyclohexane) by extractive distillation

J. Chem. Thermodynamics 144 (2020) 106070

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Entrainers selection and vapour-liquid equilibrium measurements for separating azeotropic mixtures (ethanol + n-hexane/cyclohexane) by extractive distillation Yi Zhang a, Zhaojie Wang a, Xin Xu a, Jun Gao a,⇑, Dongmei Xu a, Lianzheng Zhang a, Yinglong Wang b a b

College of Chemical and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China College of Chemical Engineering, Qingdao University of Science and Technology, Qingdao 266042, China

a r t i c l e

i n f o

Article history: Received 10 January 2020 Received in revised form 23 January 2020 Accepted 26 January 2020 Available online 30 January 2020 Keywords: Vapour-liquid equilibrium Extractive distillation Ethanol n-Hexane Cyclohexane

a b s t r a c t For synthesis of ethyl propionate with ethanol and propionic acid as raw materials, n-hexane and cyclohexane are usually used as water-carrying agents. However, ethanol can form the minimum boiling azeotropic mixtures with n-hexane and cyclohexane. For separating the binary azeotropic mixtures (ethanol + n-hexane) and (ethanol + cyclohexane) by extractive distillation, in this work, the suitable entrainers were explored by selectivity and relative volatility, and the influence of the selected entrainers on the azeotropic system phase behaviour was analyzed. Based on the selection results, butyl propanoate and butyl butanoate were adopted as the entainers. The vapour-liquid equilibrium (VLE) data for the four binary mixtures (n-hexane + butyl propanoate), (n-hexane + butyl butanoate), (cyclohexane + butyl propanoate) and (cyclohexane + butyl butanoate) were investigated. Furthermore, the VLE data was validated using the van Ness and Herington tests. Also, the experimental data was fitted by the Wilson, UNIQUAC and NRTL models. The binary interaction parameters were optimized for the separation process design and simulation. Ó 2020 Elsevier Ltd.

1. Introduction Ethyl propionate is a useful chemical and benign solvent [1], which is applied in chemical industry. For preparation of ethyl propionate with ethanol and propionic acid as raw materials, the produced water is removed by n-hexane or cyclohexane as watercarrying agent [2]. However, ethanol can form azeotropic mixtures with n-hexane and cyclohexane at the azeotropic temperatures of 332.15 K and 337.65 K and 101.3 kPa, respectively, where the azeotropic composition in mole fraction for (ethanol + n-hexane) is 0.3842: 0.6158 and that for (ethanol + cyclohexane) is 0.4345: 0.5655 [3]. It is difficult to recover the water-carrying agents by conventional distillation. Therefore, extractive distillation (ED) [4–6] is considered to separate the azeotropic mixtures (ethanol + n-hexane) and (ethanol + cyclohexane). For extractive distillation, the selection of entrainers is of importance. Luyben et al. [7] presented a solvent screening procedure on the basis of binary VLE diagrams, equivolatility and univolatility. Momoh [8] selected the entrainers by calculating the selectivity at infinite dilution; Kossack et al. [9] based on the ⇑ Corresponding author. E-mail address: [email protected] (J. Gao). https://doi.org/10.1016/j.jct.2020.106070 0021-9614/Ó 2020 Elsevier Ltd.

computer-aided molecular design to screen the suitable entrainers. In this work, based on selectivity at infinite dilution, relative volatility and x-y diagrams of the azeotropic systems with the addition of entrainers, the entrainers butyl propanoate and butyl butanoate were determined for separating n-hexane and cyclohexane from the azeotropic mixtures. To design and simulation the ED process for separation of the mixtures (ethanol + n-hexane) and (ethanol + cyclohexane), the VLE data contained ethanol, n-hexane cyclohexane and entrainers are required. Up to now, Sinor et al. [10] studied the binary vapour-liquid phase behaviour for (ethanol + n-hexane) at p = 101.3 kPa. The results showed that ethanol and n-hexane can form a minimum boiling azeotrope and the mixture deviates greatly from ideal liquid phase behaviour. Vittal Prasad [11] explored the vapour-liquid phase behaviour for (ethanol + nhexane) under 95 kPa. The results indicated that the Wilson model was capable of correlating the measured VLE data. Hongo and Tsuji et al. [12] investigated the binary VLE data of the mixture (nhexane + ethanol) and the measured values were fitted well by the thermodynamic models. Also, the binary VLE data of the mixture (ethanol + n-hexane) was investigated at near-critical temperatures by Seo et al. [13] and the measured data was correlated by the PRSV equation [14] with the WS mixing rules [15]. For the bin-

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Y. Zhang et al. / J. Chem. Thermodynamics 144 (2020) 106070

ary mixture (ethanol + cyclohexane), the VLE data was measured by Reddy et al. [16] at (40.00, 69.81, 97.72 and 150.0) kPa, and the determined value was also fitted using the Wilson, UNIQUAC and NRTL models. Joseph et al. [17] measured the binary VLE data for (ethanol + cyclohexane) under 40 kPa and the reported VLE data were consistent with those reported in the literature [18– 19]. Also, Zhao [20] and Li [3] investigated the VLE data of the system (ethanol + cyclohexane) at atmospheric pressure. Besides, González [21] determined the VLE data for (ethanol + butyl propanoate) and (ethanol + butyl butanoate). The measured VLE data was thermodynamically consistent and exhibited positive deviations from ideal behaviour. Lladosa et al. [22] explored the vapour-liquid phase behaviour for (ethanol + butyl propanoate). However, by retrieving the NIST database, the VLE data of the mixtures (n-hexane + butyl propanoate), (n-hexane + butyl butanoate), (cyclohexane + butyl propanoate) and (cyclohexane + butyl butanoate) have not been reported. In this study, based on selectivity at infinite dilution, relative volatility and x-y diagrams of the azeotropic systems with the addition of entrainers, butyl propanoate and butyl butanoate were determined as the entrainers for separating the azeotropes by extractive distillation. Moreover, the binary VLE data of the four systems (n-hexane + butyl propanoate), (n-hexane + butyl butanoate), (cyclohexane + butyl propanoate) and (cyclohexane + butyl butanoate) was measured at p = 101.3 kPa. The Wilson [23], UNIQUAC [24] and NRTL [25] models were adopted to fit the experimental data. In addition, the binary interaction parameters of the three models were determined. 2. Entrainer selection 2.1. Selectivity Generally, the selectivity at infinite dilution (S1 12 ) can be adopted as an important parameter to evaluate the effect of the entrainers and shown as follows [26,27]:

S1 12 ¼

c1 1 c1 2

Fig. 1. From Fig. 1, for the systems (ethanol + n-hexane) and (ethanol + cyclohexane), the order of the values of selectivity at infinite dilution is as follows: butyl butanoate > butyl propanoate > propyl propionate. The values of selectivity for butyl propanoate and butyl butanoate are larger than propyl propionate. 2.2. Relative volatility To select the suitable entrainers, the relative volatility (a12) of n-hexane to ethanol and ethanol to cyclohexane were explored, which is defined as follows [31,32]:

a12 ¼

y1 =x1 y2 =x2

ð2Þ

The relative volatility diagrams of systems (n-hexane + ethanol) and (ethanol + cyclohexane) are presented in Fig. 2. From Fig. 2, the calculated a12 values for the mixture n-hexane (1) + ethanol (2) with the added entrainers are less than 1 and for the mixture ethanol (1) + cyclohexane (2) are greater than 1. Meanwhile, the calculated values of a12 with butyl propanoate and butyl butanoate show larger deviations from the unity than those with propyl propionate. 2.3. Effect of entrainers The x-y plots for (n-hexane + ethanol) and (ethanol + cyclohex ane) with the three different entrainers are shown in Fig. 3. As seen from Fig. 3, both the azeotropic points for the two systems are eliminated by adding the entrainers. For the mixtures of (n-hexane + ethanol) and (ethanol + cyclohexane) with butyl propanoate and butyl butanoate as the entrainers show larger deviations from the x-y diagonal than with propyl propionate. Therefore, based on the results selectivity in definite dilution, relative volatility and effect of the entrainers, butyl butanoate and butyl propanoate were selected as the entrainers for separating the mixture of (n-hexane + ethanol) and (ethanol + cyclohexane).

ð1Þ

In this work, the infinite dilution activity coefficient was calculated by the COSMO-SAC model [28–30]. The values of selectivity at infinite dilution for the different entrainers are presented in

3. Experimental 3.1. Chemicals All the chemicals butyl propanoate, butyl butanoate n-hexane and cyclohexane were analytical grade. The information of the chemicals is listed in Table 1. The purity of the chemicals was validated by gas chromatograph. The chemicals were used directly. Meanwhile, the boiling temperature for the chemicals was measured and compared to those from the literatures [21,22,33–37], which is summarized in Table 1. 3.2. Apparatus and procedures The binary VLE data for the four mixtures (n-hexane + butyl propanoate), (n-hexane + butyl butanoate), (cyclohexane + butyl propanoate) and (cyclohexane + butyl butanoate) was determined in a Rose-Williams still. When the temperature of the binary mixture was stable for 50 min [38,39], the system reached to the equilibrium state. Then, the samples were taken out and analysed [40]. The detailed information of the measurements was reported in the literatures [41–43]. 3.3. Analysis

Fig. 1. Selectivity at infinite dilution calculated by the COSMO-SAC model at T = 298.15 K.

The GC (Lunan SP6890) with a TCD was employed to measure the vapour and liquid compositions. The Porapak Q column was

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Y. Zhang et al. / J. Chem. Thermodynamics 144 (2020) 106070

Fig. 2. Relative volatility vs. x1 plot: (a) -j-, the reference values [3] for n-hexane (1) + ethanol (2); (b) -j-, the reference values [3] for ethanol (1) + cyclohexane (2); and , calculated values by the UNIFAC model with the entrainers propyl propionate, butyl propanoate and butyl butanoate.

Fig. 3. Influence on VLE for (a) n-hexane (1) + ethanol (2) and (b) ethanol (1) + cyclohexane (2) calculated by the UNIFAC model with the different entrainers: propionate; , butyl propanoate; , butyl butanoate; - - -, reference values [3] without entrainer.

,

, propyl

Table 1 Detailed information of the chemicals. Name

a b

CAS

Suppliers

Mass

Tb/Kb

fraction

exp

lit 341.88 341.94 353.85 353.75 418.26 418.69 438.15 438.32

n-hexane

110–54-3

Tianjin Kemiou Chemical Reagent Co., Ltd.

0.995

341.75

cyclohexane

110-82-7

Tian jin Fuyu Fine Chemical Co., Ltd.

0.995

353.62

butyl propanoate

590-01-2

Aladdin reagent Shanghai Co., Ltd.

0.990

418.57

butyl butanoate

109-21-7

Shanghai Macklin Biochemical Co., Ltd.

0.990

438.29

Analysis method [33] [34] [35] [36] [21] [22] [21] [37]

,

GCa GCa GCa GCa

Gas chromatograph. The experimental pressure for the measurement of boiling temperature is 101.3 kPa, the standard uncertainties u of p and T are u(p) = 0.35 kPa, u(T) = 0.35 K.

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Y. Zhang et al. / J. Chem. Thermodynamics 144 (2020) 106070

4.3. Thermodynamic consistency

Table 2 The analysis conditions for the gas chromatography. Name

Characteristic

Description

Column

Type Specification Type Pressure Temperature Temperature Type Temperature

Packing column Porapak Q (3 mm  2 m) Hydrogen 0.18 MPa 453.15 K 393.15 K Thermal conductivity detector (TCD) 463.15 K

Carrier gas Injector Column Detector

For validating the measured VLE data consistency, the Herington [45,46] and van Ness methods [47,48] were applied. The Herington test is expressed as follows:




A  B

D ¼ 100

A þ B


ð5Þ




T max  T min

J ¼ 150


T min

ð6Þ

used and the carrier gas was high purity hydrogen. The gas flow rate and the column inlet pressure were kept at 25 mL/min and 0.18 MPa, respectively. The GC operating conditions is summarized in Table 2.

where A and B donate the areas of ln(c1/c2) vs. x above and below the abscissa axis; Tmax and Tmin are the highest and lowest boiling temperatures. If the jD  J j value is not more than 10, the measured VLE data is regarded as thermodynamically consistent. The van Ness test can be expressed as follows:

4. Results discussion

Dy ¼

N 1 X 100jyexp  ycal i j i N ði¼1Þ

ð7Þ

Dp ¼

N 1 X 100jpexp  pcal i j i N ði¼1Þ

ð8Þ

4.1. Experimental results The experimental VLE data of the systems (n-hexane + butyl propanoate), (n-hexane + butyl butanoate), (cyclohexane + butyl propanoate) and (cyclohexane + butyl butanoate) was determined under 101.3 kPa. The measured VLE values are summarized in Tables 3–6 and plotted in Fig. 4. 4.2. VLE calculation

where the superscripts ‘‘cal” and ‘‘exp” are the calculated and experimental values; N is the data point number. For this test, Dy and Dp should be less than 1. The test results of jD  J j;Dy and Dp are summarized in Table 8. As seen form Table 8, the results demonstrate that the experimental VLE data is thermodynamic consistency.

At atmospheric pressure, the VLE expression can be presented as:

4.4. VLE data regression

py ci ¼ s i pi xi

ð3Þ

where xi, and yi stand for the liquid and vapour phase compositions; psi represents the pure component vapour pressure and can be obtained by the extended Antoine equation. The extended Antoine equation is expressed in the following equation and the constant values are given in Table 7.

C 2i lnðpsi =kPaÞ ¼ C 1i þ þ C 4i ðT=KÞ þ C 5i lnðT=KÞ T=K þ C 3i

The measured VLE data was fitted using the Wilson, UNIQUAC and NRTL equations. For the UNIQUAC model, the values of the structural volume and area parameters r and q of the components are presented in Table 9. The objective function is given as follows [49–50]: 2 3 !    exp  exp cal 2 exp cal 2 cal 2 XN pexp  pcal 2 T  T x  x y  y i i i i 4 i 5 F¼ þ i þ i þ i i

rp

rT

rx

ry

ð9Þ

where r is the standard deviation; p, T refer to equilibrium pressure and temperature, respectively.

C 7i

þ C 6i ðT=KÞ C 8i 6 T=K 6 C 9i

Table 3 Experimental isobaric VLE data (liquid mole fraction x1, vapour phase mole fraction y1) for the binary system of n-hexane (1) + butyl propanoate (2) and activity coefficient (c) at 101.3 kPa.a

a

T/K

x1

y1

c1

c2

341.75 346.16 350.25 355.43 360.53 365.26 370.74 375.48 380.87 385.99 390.56 398.38 401.28 405.95 409.29 416.59 418.57

1.0000 0.8656 0.7518 0.6323 0.5351 0.4559 0.3781 0.3190 0.2591 0.2090 0.1691 0.1091 0.0888 0.0594 0.0398 0.0035 0.0000

1.0000 0.9874 0.9744 0.9546 0.9325 0.9050 0.8672 0.8265 0.7708 0.7076 0.6418 0.5052 0.4456 0.3393 0.2551 0.0446 0.0000

– 1.0004 1.0060 1.0086 1.0097 1.0117 1.0122 1.0136 1.0186 1.0256 1.0336 1.0573 1.0752 1.1072 1.1580 1.9828 –

– 1.2162 1.1170 1.0714 1.0210 1.0164 1.0059 1.0058 1.0049 1.0046 1.0035 1.0021 1.0019 1.0017 1.0007 1.0002 –

Standard uncertainties u of T, p, x and y are u(T) = 0.35 K, u(p) = 0.35 kPa, u(x) = 0.0057, u(y) = 0.0065.

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Y. Zhang et al. / J. Chem. Thermodynamics 144 (2020) 106070

Table 4 Experimental isobaric VLE data (liquid mole fraction x1, vapour phase mole fraction y1) for the binary system of n-hexane (1) + butyl butanoate (2) and activity coefficient (c) at 101.3 kPa.a

a

T/K

x1

y1

c1

c2

341.75 343.40 348.86 353.27 358.31 363.77 368.60 374.48 379.73 384.77 389.60 394.22 399.68 404.09 408.92 413.75 418.58 424.04 428.45 434.12 438.29

1.0000 0.9496 0.7968 0.6752 0.5710 0.4828 0.4143 0.3439 0.2921 0.2484 0.2123 0.1811 0.1488 0.1260 0.1028 0.0805 0.0600 0.0409 0.0254 0.0080 0.0000

1.0000 0.9977 0.9884 0.9806 0.9688 0.9529 0.9353 0.9103 0.8826 0.8501 0.8143 0.7739 0.7195 0.6715 0.6086 0.5349 0.4517 0.3485 0.2513 0.1112 0.0000

– 1.0024 1.0033 1.0323 1.0453 1.0490 1.0533 1.0619 1.0639 1.0671 1.0679 1.0706 1.0730 1.0749 1.0780 1.0951 1.1255 1.1440 1.2202 1.5406 –

– 1.3067 1.2673 1.0873 1.0629 1.0580 1.0550 1.0372 1.0319 1.0323 1.0284 1.0276 1.0225 1.0112 1.0083 1.0087 1.0076 1.0024 1.0017 1.0008 –

Standard uncertainties u of T, p, x and y are u(T) = 0.35 K, u(p) = 0.35 kPa, u(x) = 0.0063, u(y) = 0.0065.

Table 5 Experimental isobaric VLE data (liquid mole fraction x1, vapour phase mole fraction y1) for the binary system of cyclohexane (1) + butyl propanoate (2) and activity coefficient (c) at 101.3 kPa.a

a

T/K

x1

y1

c1

c2

353.62 355.21 359.24 363.27 367.20 371.14 375.44 379.20 383.59 388.24 392.18 396.48 401.13 405.16 409.19 413.21 418.57

1.0000 0.9633 0.8265 0.7002 0.5941 0.5040 0.4206 0.3587 0.2974 0.2403 0.1987 0.1576 0.1177 0.0871 0.0582 0.0315 0.0000

1.0000 0.9945 0.9693 0.9430 0.9142 0.8829 0.8437 0.8044 0.7529 0.6904 0.6291 0.5536 0.4635 0.3734 0.2747 0.1631 0.0000

– 0.9936 1.0024 1.0254 1.0494 1.0728 1.0958 1.1111 1.1225 1.1359 1.1387 1.1423 1.1513 1.1458 1.1554 1.1632 –

– 1.3128 1.3115 1.1976 1.1405 1.0955 1.0665 1.0519 1.0386 1.0256 1.0211 1.0162 1.0061 1.0028 0.9966 0.9953 –

Standard uncertainties u of T, p, x and y are u(T) = 0.35 K, u(p) = 0.35 kPa, u(x) = 0.0064, u(y) = 0.0066.

The correlated parameters of the activity coefficient models and the root-mean-square deviations (RMSDs) for the four mixtures are summarized in Table 10. As shown in Table 10, the maximum RMSDs of T and y1 are 0.33 K and 0.0111, which indicates the three activity coefficient models could be applied to fit the experimental VLE values. For comparison, the COSMO-UNIFAC model [51,52] was applied to predict the VLE data for the systems. As shown in Fig. 4, the predicted values by the COSMO-UNIFAC model show less deviations from the measured VLE data, which indicates the COSMO-UNIFAC model can provide better predictive VLE values for the systems.

5. Conclusions To separate the binary mixture (n-hexane + ethanol) and (ethanol + cyclohexane) by extractive distillation, the entrainers butyl propanoate and butyl butanoate were selected based on explorations of selectivity, relative volatility and the entrainer

effect on VLE phase behaviour. The isobaric VLE data of (nhexane + butyl propanoate), (cyclohexane + butyl propanoate), (n-hexane + butyl butanoate) and (cyclohexane + butyl butanoate) was determined. The van Ness and Herington tests were adopted to validate the experimental VLE data consistency. The test results indicated that all the VLE data were thermodynamic consistency. Besides, the determined VLE data were fitted by the Wilson, UNIQUAC and NRTL models. The maximum values of RMSD for the vapour phase mole fraction and temperature were 0.0111 and 0.33 K, which shows that the three models can fit the VLE data of the four mixtures. Meanwhile, the model interaction parameters were optimized, which is can be used for the separation process simulation and optimization.

CRediT authorship contribution statement Yi Zhang: Data curation, Writing - original draft. Zhaojie Wang: Data curation. Xin Xu: Validation. Jun Gao: Conceptualization,

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Fig. 4. T-x-y diagram for the four binary systems at 101.3 kPa: (a), n-hexane (1) + butyl propanoate (2); (b), cyclohexane (1) + butyl propanoate (2); (c), n-hexane (1) + butyl butanoate (2); (d), cyclohexane (1) + butyl butanoate (2); j, T-x, experimental values; d, T-y, experimental values; ––, calculated by the NRTL model; , calculated by the UNIQUAC model; , calculated the Wilson model; , predicted by the COSMO-UNIFAC model.

Table 6 Experimental isobaric VLE data (liquid mole fraction x1, vapour phase mole fraction y1) for the binary system of cyclohexane (1) + butyl butanoate (2) and activity coefficient (c) at 101.3 kPa.a

a

T/K

x1

y1

c1

c2

353.62 355.31 360.17 365.39 370.79 375.47 380.51 385.37 390.23 395.63 400.49 405.53 410.75 415.61 420.47 425.33 430.37 435.95 438.29

1.0000 0.9449 0.8057 0.6783 0.5591 0.4775 0.4043 0.3422 0.2894 0.2396 0.1993 0.1618 0.1275 0.0992 0.0730 0.0496 0.0265 0.0044 0.0000

1.0000 0.9957 0.9833 0.9657 0.9455 0.9231 0.8963 0.8648 0.8269 0.7806 0.7297 0.6676 0.5954 0.5190 0.4296 0.3311 0.2120 0.0637 0.0000

– 1.0111 1.0153 1.0211 1.0456 1.0552 1.0622 1.0719 1.0766 1.0804 1.0861 1.0938 1.1054 1.1178 1.1379 1.1711 1.2720 2.0705 –

– 1.2986 1.1606 1.1592 1.0824 1.0751 1.0523 1.0411 1.0396 1.0239 1.0201 1.0192 1.0130 1.0070 1.0059 1.0014 1.0010 1.0003 –

Standard uncertainties u of T, p, x and y are u(T) = 0.35 K, u(p) = 0.35 kPa, u(x) = 0.0063, u(y) = 0.0066.

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Y. Zhang et al. / J. Chem. Thermodynamics 144 (2020) 106070 Table 7 Constants of the extended Antoine equation.a Component n-hexane cyclohexane butyl propanoate butyl butanoate a

C1i 97.74 44.18 64.32 102.27

C

C3i

2i

6995.50 5226.40 7709.80 9384.00

0 0 0 0

C4i

C5i 12.70 4.2278 6.8418 12.77

0 0 0 0

C6i 1.24 7.76 6.36 7.47

   

5

10 1018 1018 106

C7i

C8i/K

C9i/K

2 6 6 2

177.83. 279.69 183.63 181.15

507.60 553.80 594.60 616.00

Taken from Aspen property databank [44].

Table 8 Results of the thermodynamic consistency. System

jD  J j

Dp

Dy

n-hexane + butyl propanoate cyclohexane + butyl propanoate n-hexane + butyl butanoate cyclohexane + butyl butanoate

9.1236 8.5057 4.7128 7.5874

0.0599 0.0398 0.0648 0.0449

0.4220 0.1793 0.2516 0.2645

Table 9 Parameters r and q of the components for the UNIQUAC model.a

a

Component

r

q

n-hexane cyclohexane butyl propanoate butyl butanoate

4.4997 4.0475 5.5017 6.1892

3.8560 3.2400 4.7360 5.2760

Taken from Aspen property databank [46].

Table 10 Regressed parameters of the NRTL, UNIQUAC and Wilson models and root-mean-square deviations (RMSDs) of the four binary systems. Model

Parameters aij

n-hexane + butyl propanoate NRTLc 1.0069 UNIQUACd 22.8461 e Wilson 5.2567 cyclohexane + butyl propanoate NRTL 2.40877 UNIQUAC 15.4914 Wilson 28.8676 n-hexane + butyl butanoate NRTL 7.2013 UNIQUAC 22.1958 Wilson 18.6067 cyclohexane + butyl butanoate NRTL 1.2449 UNIQUAC 23.3393 Wilson 3.4446 a

b c d e

RMSD aji

bij/K

bji/K

y1a

T/Kb

2.5559 8.87491 4.7252

378.76 2301.60 3324.19

661.69 2874.627 1470.15

0.0059 0.0111 0.0083

0.16 0.33 0.23

1.37311 5.9865 0.2915

959.52 1889.55 2450.11

478.48 1985.21 141.48

0.0025 0.0015 0.0024

0.09 0.08 0.09

0.34402 6.6371 0.1208

3077.27 2088.22 858.21

48.56 2100.55 251.78

0.0035 0.0041 0.0079

0.21 0.19 0.33

5.4162 10.1914 5.6900

515.29 2525.85 4210.22

1884.48 3430.68 1938.48

0.0038 0.0094 0.0070

0.13 0.32 0.23

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 PN ðyexp ycal Þ i i RMSDðy1 Þ ¼ . i¼1 N rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cal 2 PN ðT exp T i Þ i . RMSDðTÞ ¼ i¼1 N NRTL,sij ¼ aij þ bij =T, the value of alphaij was set at 0.3.   UNIQUAC,sij ¼ exp aij þ bij =T . Wilson, lnAij ¼ aij þ bij =T.

Methodology. Dongmei Xu: Formal analysis. Lianzheng Zhang: Visualization, Investigation. Yinglong Wang: Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement The authors are grateful to the financial support of the National Natural Science Foundation of China (No. 21978155). References [1] S.F. Zakko, J.C. Scirica, M.C. Guttermuth, J. Dodge, J.J. Hajjar, Ethyl propionate is more effective and less cytotoxic than methyl tert-butyl ether for topical gallstone dissolution, Gastroenterology. 113 (1997) 232–237.

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