Determination and correlation of ternary isobaric vapour-liquid equilibrium data of (dimethyl succinate + dimethyl glutarate + dimethyl adipate) at 2, 5 and 8 kPa

J. Chem. Thermodynamics 143 (2020) 106047

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Determination and correlation of ternary isobaric vapour-liquid equilibrium data of (dimethyl succinate + dimethyl glutarate + dimethyl adipate) at 2, 5 and 8 kPa Chunli Zhi a, Yang Tang b, Jinru Wan b, Xingming Liu a, Honglin Chen a, Xunqiu Wang a,⇑ a b

School of Chemical Engineering, Zhengzhou University, Zhengzhou, Henan 450001, China Zhejiang Jusheng Fluoro-Chemistry Limited Corporation, Quzhou, Zhejiang 324004, China

a r t i c l e

i n f o

Article history: Received 24 October 2019 Received in revised form 30 December 2019 Accepted 31 December 2019 Available online 03 January 2020 Keywords: Dimethyl succinate Dimethyl glutarate Dimethyl adipate NRTL Wilson Uniquac

a b s t r a c t Isobaric vapour-liquid equilibrium data of {dimethyl succinate (DMS) + dimethyl glutarate (DMG) + dimethyl adipate (DMA)} ternary system was measured at 2 kPa, 5 kPa and 8 kPa with a dynamic recirculating apparatus and the temperature ranged from 364.46 to 403.55 K. The experimental data was correlated with NRTL, Wilson and Uniquac models. The results showed that the maximum value of the root mean square deviation of the vapour phase mole fraction of the ternary system correlated by the three models is 0.0083, 0.0076 and 0.0084, respectively. The vapour-liquid equilibrium data of the ternary system was predicted by the interaction parameters of NRTL, Wilson and the Uniquac models in the literature. The results showed that the maximum value of the root mean square deviation of the vapour phase mole fraction of the ternary system predicted by the three models is 0.0547, 0.0471, and 0.0498, respectively. The deviation between the experimental value and the regression value or the predicted value was small, and both met the needs of design calculation of the engineering separation. The results obtained from the regression of experimental values are significantly better. Ó 2020 Elsevier Ltd.

1. Introduction Dimethyl succinate (DMS) is an important synthetic fragrance and food additive that can be used as an edible preservative. In addition, DMS is an important chemical intermediate, which can be applied to the preparation of chemicals such as 1,4butanediol, c-butyrolactone, tetrahydrofuran and itaconic acid [1–3]. Dimethyl glutarate (DMG) is an environmentally friendly high boiling point solvent, which has good dissolving power, low volatility, low viscosity, high safety, non-toxicity, photochemical stability, etc. DMG is widely used as a diluent, paint remover, remover and plasticizer in coatings and other industries. At the same time, it is also used as an important intermediate for fine chemicals, which can be applied to the preparation of chemicals such as ketorolac, 1,5-pentanediol, co-polyesters, etc. [4–6]. Dimethyl adipate (DMA) is mainly used as a solvent for highgrade coatings, inks, and detergent. It also can be used as a fixative solution or a calibration solution for spectrum analysis. DMA is also an important chemical intermediate, which was widely used in the production of 1,6-hexanediol and d-decalactone. Moreover, it also ⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (X. Wang). https://doi.org/10.1016/j.jct.2019.106047 0021-9614/Ó 2020 Elsevier Ltd.

can be used in papermaking, cellulose resin, etc. [7–9]. The three dibasic acid dimethyl esters are produced by esterification of the corresponding dibasic acid (succinic acid, glutaric acid, adipic acid) with methanol under the catalysis of sulfuric acid or an organic acid. [10–11]. However, the prices of succinic acid, glutaric acid and adipic acid are relatively expensive, and the corresponding dibasic acid dimethyl ester produced by this method has high cost and low profit. Mixed dibasic acid (DBA) is the by-product of adipic acid production, which composition is roughly 25% of succinic acid, 60% of glutaric acid and 15% of adipic acid. The by-product (DBA) produced by the production of adipic acid is at least 50,000 tons every year in China. By the esterification reaction of DBA, the mixed dibasic acid dimethyl ester (DBE) can be directly obtained at a low cost, and then DMS, DMG and DMA can be obtained by distillation [12–15]. Compared with the traditional method of obtaining the dibasic acid dimethyl ester by esterification using a corresponding dibasic acid, this method improves the utilization value of the by-product DBA, not only reduces environmental pollution, but also reduces resource waste. Vapour-liquid equilibrium data are the basis of calculation of distillation design. However, there are fewer vapour-liquid equilibrium values related to the separation and purification of mixed dibasic acid dimethyl ester. In addition to the vapour-liquid

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C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047

equilibrium data of (DMG + DMA) at around 10 kPa measured by Vlasov, O. N et al. [16], just only the isobaric vapour-liquid equilibrium data of three binary systems containing {dimethyl succinate (DMS) + dimethyl glutarate (DMG)}, {dimethyl succinate (DMS) + dimethyl adipate (DMA)} and {dimethyl glutarate (DMG) + Dimethyl adipate (DMA)} at (2, 5.2 and 8.3) kPa measured by Honglin Chen et al. [17] can be found in the literature. If the vapour-liquid equilibrium data of binary system is directly applied to the ternary system, it may cause large deviation. Therefore, the isobaric vapour-liquid equilibrium data of the ternary system of {DMS (1) + DMG (2) + DMA (3)} were measured directly at 2 kPa, 5 kPa and 8 kPa using the VLE110 vapour-liquid equilibrium device manufactured by PILODIST, Germany. Moreover, the reliability of the ternary system vapour-liquid equilibrium data predicted by the binary system vapour-liquid equilibrium data can be verified.

Table 2 The boiling temperatures of pure DMS, DMG, and DMA at the (2.0, 5.0, 8.0) kPa.

DMS

DMG

DMA

P/kPa

T/K

(Pexp
Pcala)/Pcal100

2.0 5.0 8.0 2.0 5.0 8.0 2.0 5.0 8.0

363.3 381.7 393.1 376.1 395.4 406.7 390.9 410.5 422.1


4.05
0.14
2.20 3.18 4.21 3.32
3.19
0.85
1.41

Standard uncertainty u of T and P are: u(T) = 0.5 K, u(P) = 0.1 kPa. a Pcal is calculated by the extended Antoine equation (the Eq. (2)), and the parameters of extended Antoine equation are list in Table 4.

2. Experimental

70

2.1. Materials

60

The chemical reagents used in this study were dimethyl succinate (DMS), dimethyl glutarate (DMG) and dimethyl adipate (DMA). All three chemical reagents were detected by gas chromatography (GC7980, Techcomp LTD, China) and hydrogen flame ionization detector (FID). The purity met the experimental needs. The specifications of the chemical reagents used in this study are shown in Table 1.

P/kPa

50 40 30 20

2.2. Apparatus and procedure The experiment was carried out using VLE110 vapour-liquid balance device made of glass produced by PILODIST, Germany. The detail of the device had been described in literature [17]. The whole device is composed of a heating kettle, a vapour-liquid balance chamber, two water-cooled condensers. The vapour and liquid phase could be continuously circulated at the same time thereby the vapour-liquid equilibrium state could be quickly reached. In addition, the unit is equipped with a Cottrell pump for exchange and separation between vapour and liquid phases; two temperature sensors, Pt-100 class A with standard uncertainty of 0.5 K, are used to measure the temperature of the vapour phase and liquid phase during the experiment. The device is equipped with a vacuum pump, the pressure required for the experiment is set by the pressure controller with a standard uncertainty of 0.1 kPa, and its measurement pressure ranges from 0.25 kPa to 300 kPa. The boiling points of the three pure components at (2.0, 5.0, and 8.0) kPa measured in this work, which are shown in Table 2, have also been compared to the earlier measurements in the other publications [17–29], which are graphically displayed in Figs. 1–3. At the same time, we also calculated the percent deviations of pressure between the experimental value, which is the measured value of this work or in the literatures, and the calculated value, which is calculated by the extended Antoine equation, and illustrated in Figs. 4–6. From the Fig.4, we can see that all the percent deviations of pressure for pure DMS are located in the range of
10% to 4%.

10 0 290

310

330

350

370

390

410

430

450

T/K Fig. 1. Vapour pressures of pure DMS (, experimental data; s, data from the literature [17,18,20,21]).

And as seen from the Fig. 5, most of the percent deviations of pressure for pure DMG are within ±15%, except for some individual points from Lee et al. [19] that deviates from other data by about 60%. At the same time, the Fig. 6 demonstrates that the percent deviations of pressure for pure DMA are between ±10%, except for some individual points. The percent deviations of pressure for three pure components measured in this work are between ±5%, which indicates that our measurements are reasonable and reliable. The instrument was calibrated with the system of cyclohexane + n-heptane and the details were described in our previous work [17]. The results showed that the device was reliable. First, a total of about 60 mL DMS was added through the feed port. The cooling system was turned on and all cocks closed that were connected to the atmosphere. The vacuum pump was turned on and the system pressure adjusted to the pressure required in

Table 1 Specification of chemical reagents.

a

Chemical name

Sources

CAS RN

Mass fraction purity

Analysis

Dimethyl succinate (DMS) Dimethyl glutarate (DMG) Dimethyl adipate (DMA)

Shanghai Aladdin Bio-Chem Technology Co, Ltd Shanghai Aladdin Bio-Chem Technology Co, Ltd Shanghai Aladdin Bio-Chem Technology Co, Ltd

106-65-0 1119-40-0 627-93-0

0.999 0.999 0.999

GCa GC GC

Gas chromatography.

3

70

60

60

50

50

40

(Pexp/lit-Pcal)/Pcal×100

P/kPa

C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047

40 30 20 10 0 320

340

360

380

400

420

440

16 14 12 10 8 6 4 2 330

350

370

390

340

360

380

400

420

440

460

T/K

18

P/kPa

10

-10 320

460

Fig. 2. Vapour pressures of pure DMG (, experimental data; s, data from the literature [17–19,22,23]).

410

430

450

T/K Fig. 3. Vapour pressures of pure DMA (, experimental data; s, data from the literature [17–19,24–29]).

Fig. 5. Percent deviation of pressure from extended Antoine equation for DMG (, experimental data; s, data from the literature [17–19,22,23]).

the experiment using the pressure controller. The heating and stirring device was activated after the pressure was stabilized. In order to ensure a suitable gasification speed, the heating power of the immersion heater was set at an appropriate level, so that the vapour phase condensate reflux rate was about 30 drops per min. When the vapour phase temperature was stable for 30 min to 45 min, the boiling point of DMS was reached. After the pressure release, a small amount of DMS was discharged from the discharge port, and then an equal amount of the DMG and DMA mixture was added from the feed port. After heating and sufficient stabilization, the sample could be withdrawn through a sampling valve and the vapour phase and liquid phase samples were analysed by gas chromatography. The above operation was repeated until the content of the second substance in the mixture reached about 15%. The pure sample for DMG, DMA was loaded and the process repeated. The same measurement method was used to determine the vapourliquid equilibrium values for {DMG (1) + DMA (2)} at 10 kPa. The values were compared to those in the literature to verify the reliability of the measurement method. The experimental values of the

20

4

15

(Pexp/lit-Pcal)/Pcal×100

2

(Pexp/lit-Pcal)/Pcal×100

20

0

T/K

0 310

30

0 -2 -4

10 5 0

-6

-5

-8 -10 290

310

330

350

370

390

410

430

450

470

T/K Fig. 4. Percent deviation of pressure from extended Antoine equation for DMS (, experimental data; s, data from the literature [17,18,20,21]).

-10 310

330

350

370

390

410

430

450

T/K Fig. 6. Percent deviation of pressure from extended Antoine equation for DMA (, experimental data; s, data from the literature [17–19,24–29]).

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C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047

All samples obtained from the experiment were analysed three times. When the deviations between the analytical values were less than 0.3%, the average value was taken as the result. And then the mass fraction and mole fraction were determined according to the standard curve. The standard uncertainty of liquid and vapour composition was 0.009.

liquid and vapour phase composition agreed well with literature values. This results shows that our measurements are reliable. The detailed process has been described by Honglin and Chen [17]. 2.3. Analysis All samples were analysed by gas chromatography (GC7980) with a hydrogen flame ionization detector (FID). The column for gas chromatography was capillary column OV-17 (50 m  0.32 m m  0.5um), and the carrier gas was nitrogen. The analysis conditions were as follows: the flow rate of nitrogen and hydrogen were (50 and 10) mL∙min
1, respectively. The temperature of the oven, vaporisation chamber and detector were 453.15 K, 518.15 K and 523.15 K, respectively, and the injection volume was 0.1 uL.

3. Results and discussion 3.1. Experimental results The vapour-liquid equilibrium data of the (DMS + DMG + DMA) ternary system were measured at 2 kPa, 5 kPa and 8 kPa, respectively. The results are shown in Table 3.

Table 3 Vapour-liquid equilibrium data of DMS(1)-DMG(2)-DMA(3) at (2.0, 5.0, 8.0) kPa.a P/kPa

T/K

x1

x2

x3

y1

y2

y3

c1

c2

c3

2.0

364.5 365.2 366.6 367.4 368.5 369.1 369.7 370.9 371.3 372.2 372.6 374.4 375.2 375.3 375.6 375.6 375.8 375.9 384.9 385.7 386.0 386.2 386.7 387.1 387.2 387.9 388.0 388.5 388.9 389.2 389.4 390.0 390.8 391.4 391.7 392.0 392.9 393.5 393.9 394.5 395.0 395.5 395.8 396.3 396.4 396.6 397.8 398.3 398.8 399.7 400.0 401.3 402.2 403.6

0.790 0.730 0.659 0.577 0.532 0.476 0.407 0.358 0.285 0.239 0.203 0.163 0.135 0.110 0.092 0.079 0.067 0.056 0.746 0.703 0.675 0.646 0.644 0.606 0.577 0.496 0.477 0.447 0.405 0.377 0.345 0.284 0.255 0.220 0.195 0.161 0.852 0.826 0.795 0.754 0.717 0.686 0.660 0.636 0.596 0.568 0.524 0.478 0.433 0.386 0.345 0.293 0.224 0.164

0.200 0.262 0.331 0.416 0.396 0.439 0.525 0.580 0.662 0.716 0.763 0.656 0.698 0.752 0.795 0.823 0.854 0.872 0.031 0.074 0.117 0.161 0.203 0.249 0.288 0.351 0.402 0.444 0.493 0.522 0.554 0.622 0.664 0.707 0.746 0.786 0.140 0.163 0.192 0.231 0.266 0.294 0.318 0.341 0.378 0.406 0.445 0.488 0.527 0.569 0.608 0.659 0.720 0.785

0.010 0.008 0.010 0.007 0.072 0.085 0.068 0.061 0.053 0.045 0.034 0.181 0.167 0.138 0.114 0.098 0.079 0.072 0.223 0.223 0.208 0.192 0.153 0.145 0.135 0.154 0.120 0.109 0.102 0.100 0.100 0.095 0.081 0.073 0.059 0.053 0.009 0.011 0.013 0.015 0.018 0.020 0.021 0.023 0.026 0.026 0.031 0.034 0.040 0.045 0.047 0.048 0.056 0.051

0.890 0.864 0.788 0.740 0.718 0.669 0.599 0.530 0.462 0.398 0.345 0.325 0.267 0.221 0.189 0.167 0.135 0.116 0.939 0.911 0.884 0.854 0.835 0.807 0.787 0.685 0.711 0.669 0.629 0.594 0.567 0.504 0.453 0.407 0.356 0.324 0.935 0.928 0.886 0.878 0.840 0.815 0.798 0.778 0.759 0.740 0.678 0.655 0.623 0.575 0.552 0.465 0.390 0.311

0.109 0.134 0.211 0.258 0.261 0.310 0.383 0.453 0.522 0.588 0.643 0.602 0.664 0.721 0.762 0.796 0.834 0.858 0.017 0.041 0.069 0.101 0.125 0.155 0.179 0.268 0.258 0.300 0.343 0.379 0.406 0.471 0.523 0.571 0.625 0.660 0.063 0.070 0.110 0.118 0.155 0.180 0.197 0.216 0.235 0.254 0.312 0.335 0.367 0.413 0.437 0.520 0.594 0.671

0.002 0.002 0.002 0.002 0.021 0.021 0.018 0.017 0.016 0.014 0.012 0.073 0.069 0.058 0.049 0.037 0.031 0.026 0.044 0.047 0.046 0.045 0.040 0.038 0.034 0.047 0.031 0.031 0.028 0.027 0.027 0.025 0.023 0.022 0.019 0.017 0.002 0.002 0.004 0.004 0.006 0.005 0.006 0.006 0.006 0.007 0.010 0.010 0.010 0.012 0.011 0.015 0.016 0.019

1.020 1.031 0.970 1.005 0.999 1.010 1.030 0.975 1.046 1.032 1.036 1.110 1.062 1.072 1.090 1.107 1.056 1.076 1.093 1.087 1.084 1.082 1.039 1.050 1.070 1.050 1.130 1.113 1.134 1.138 1.176 1.236 1.199 1.217 1.186 1.289 1.086 1.081 1.057 1.075 1.059 1.054 1.059 1.050 1.091 1.106 1.045 1.087 1.114 1.117 1.186 1.117 1.185 1.223

1.026 0.931 1.071 1.004 1.003 1.041 1.044 1.050 1.038 1.035 1.040 1.032 1.028 1.030 1.018 1.025 1.023 1.028 0.925 0.900 0.944 0.993 0.952 0.946 0.939 1.116 0.935 0.964 0.973 1.003 1.003 1.007 1.012 1.009 1.033 1.019 0.845 0.781 1.017 0.888 0.986 1.017 1.015 1.017 0.993 0.991 1.054 1.012 1.002 1.006 0.984 1.024 1.025 1.004

0.697 0.887 0.668 0.931 0.912 0.747 0.771 0.749 0.809 0.772 0.856 0.908 0.884 0.901 0.902 0.803 0.814 0.751 0.642 0.659 0.681 0.713 0.776 0.763 0.729 0.853 0.719 0.775 0.732 0.711 0.703 0.665 0.692 0.713 0.751 0.736 0.744 0.640 0.991 0.868 1.017 0.837 0.821 0.815 0.727 0.756 0.855 0.796 0.681 0.678 0.599 0.736 0.664 0.792

5.0

8.0

Standard uncertainty u of T, P, x and y are: u(T) = 0.5 K, u(P) = 0.1 kPa, u(x1) = 0.009, u(x2) = 0.009, u(y1) = 0.009, u(y2) = 0.009. a P is the system pressure, T is system temperature, xi and yi are the liquid phase mole fraction and the vapour phase mole fraction composition and ci is the activity coefficient.

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C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047

At low pressure, the vapour phase could be regarded as an ideal gas [30–33], and the vapour-liquid equilibrium relationship could be simplified as the following:

pyi ¼ ci xi pi s

ð1Þ

The saturated vapour pressure P si of the pure component could be obtained by the following extended Antoine equation [17,34]:


   ln Psi =kPa ¼ C 1;i þ C 2;i = ðT=K Þ þ C 3;i þ C 4;i ðT=K Þ þ C 5;i lnðT=K Þ þ C 6;i ðT=K ÞC 7;i

ð2Þ

The value of constants C1,i-C7,i of the pure components are listed in Table 4, and the experimental activity coefficients calculated by Eqs. (1) and (2) are listed in Table 3.

Dy ¼

N N   1X 1X Dy i ¼ 100yiexp
yical  N i¼1 N i¼1

ð8Þ

DP ¼

  N N Piexp
Pical  1X 1 X  DP i ¼ 100 N i¼1 N i¼1 Piexp 

ð9Þ

where N is the number of experimental points, the subscript ‘‘exp” represent the experimental data, and the subscript ‘‘cal” represent the calculated value. When DP and Dy are less than 1, the experimental data were considered to be thermodynamically consistent. The results of the thermodynamic consistency test are reported in Table 5. 3.3. Correlation of vapour-liquid equilibrium data of ternary system

3.2. Thermodynamic consistency test The thermodynamic consistency test of the ternary system vapour-liquid equilibrium data was carried out by the method of point test, which was proposed by Van ness [35,36]. The NRTL model was used to calculate the bubble point pressure for a given temperature and liquid composition. The NRTL equation in Aspen are expressed as follows:

P

0 1 P xj sji Gji xm smj Gmj X xG j C m P j ij B lnci ¼ P þ @sij
P A xk Gki xk Gkj xk Gkj j k

k

ð3Þ

k


 Gij ¼ exp
aij sij

sij ¼ aij þ

ð4Þ

bij þ eij lnðT=K Þ þ f ij ðT=K Þ ðT=K Þ

ð5Þ

3.4. Prediction of vapour-liquid equilibrium data of ternary system

aij ¼ cij þ dij ½ðT=K Þ
273:15K 

ð6Þ

sii ¼ 0Gii ¼ 1

ð7Þ

For the complete T-P-x-y ternary data, after determining the required parameters and completing the fitting process, the following criteria were applied to calculate the pressure and composition [37,38].

Table 4 The parameters of extended Antoine equationa.

a

Component

DMS

DMG

DMA

C1 C2 C3 C4 C5 C6 C7 Tmin/K Tmax/K

96.9822
10753.0000 0 0
11.3100 1.0653  10 ( 6 291.35 657.00

85.3278
10614.4198 0 0
9.5211 4.9889  10(
1 6 309.15 667.59

90.0494
11297.4614 0 0
10.1264 4.6881  10(
1 6 320.15 679.58


1 7)

In order to obtain the binary interaction parameters of the ternary system of (DMS + DMG + DMA) the NRTL, Wilson and Uniquac models in Aspen Plus V7.3 were used for the regression of the ternary vapour-liquid equilibrium experimental values [39–44]. The binary interaction parameters of NRTL, Wilson, and Uniquac models obtained from regression are listed in Table 9, and the temperature, pressure and vapour phase mole fractions obtained from regression are listed in Tables 6–8. According to Tables 6–8, it can be seen that the three models of NRTL, Wilson and Uniquac represent satisfactorily the vapourliquid equilibrium data of (DMS + DMG + DMA) at 2 kPa, 5 kPa and 8 kPa. According to the calculation, the average root mean square deviations of the three models were 0.0047, 0.0043, and 0.0039, respectively. Therefore, the regression results of the Uniquac model were slightly better than the NRTL and Wilson models.

8)

Taken from Aspen Plus V7.3 physical properties databanks [17,34].

8)

According to the literature [17], the binary interaction parameters of NRTL, Wilson and Uniquac models could be obtained. The activity coefficients of DMS, DMG and DMA can be calculated by the NRTL, Wilson and Uniquac equations. The composition yipre (predicted value) of vapour phase at the corresponding temperature and liquid phase composition can be calculated. The results are shown in Tables 6–8. According to Tables 6–8, it can be concluded that the three models of NRTL, Wilson, and Uniquac models could predict the vapour-liquid equilibrium data of (DMS + DMG + DMA) at 2 kPa, 5 kPa and 8 kPa, which meet the needs of design calculation of engineering separation. According to the calculation, the average root mean square deviations of the three models were 0.0247, 0.0216 and 0.0227, respectively. Furthermore, it also indirectly proved that the binary vapour-liquid equilibrium values in the literature [17] are reliable. 3.5. Ternary system vapour-liquid equilibrium phase diagram The vapour-liquid equilibrium phase diagram of ternary system of {DMS(1) + DMG(2) + DMA(3)} at 2 kPa, 5 kPa and 8 kPa is shown in Fig. 7. According to Fig. 7, it can be seen that the regression

Table 5 Thermodynamic consistency test results of DMS + DMG + DMA. P/kPa

Dy 1

Dy2

Dy 3

DP

Result

2.0 5.0 8.0

0.2414 0.4585 0.5548

0.3044 0.3069 0.3455

0.1135 0.2083 0.3632

0.9971 0.2962 0.1361

Pass Pass Pass

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C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047

Table 6 Prediction and correlation of vapour-liquid equilibrium data for DMS(1) + DMG(2) + DMA(3) ternary system at 2.0 kPa.a NRTL Eq NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d


0.004
0.007
0.076
0.060
0.071
0.069
0.063
0.104
0.057
0.062
0.054
0.044
0.055
0.043
0.033
0.025
0.028
0.021 0.055


0.001 0.009
0.007 0.006 0.001
0.001 0.002
0.004 0.002 0.001
0.002 0.003
0.001
0.001
0.001
0.001
0.003
0.002 0.003

0.001
0.010 0.014 0.005
0.001 0.012 0.020 0.026 0.025 0.025 0.029 0.021 0.022 0.024 0.016 0.022 0.021 0.025 0.020

0.001
0.009 0.007
0.006
0.001 0.002
0.001 0.006
0.001 0.001 0.001
0.002 0.001
0.001
0.001 0.003 0.004 0.006 0.004


0.002
0.002
0.003
0.001
0.013
0.020
0.017
0.016
0.013
0.012
0.008
0.033
0.032
0.026
0.021
0.022
0.018
0.018 0.018


0.001 0.001
0.001
0.001 0.001
0.002
0.001
0.002
0.001
0.001 0.001
0.001
0.001 0.001 0.001
0.003
0.002
0.004 0.001


0.1
0.1
0.1
0.1
0.1
0.1
0.1 0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1 0.1

0.1 0.1
0.1 0.1 0.1 0.1 0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d


0.027
0.030
0.092
0.068
0.075
0.068
0.053
0.083
0.037
0.039
0.032
0.013
0.024
0.017
0.011
0.006
0.012
0.008 0.047


0.004
0.002
0.004
0.007
0.002
0.001 0.001
0.003 0.004 0.004 0.002 0.001
0.002
0.001 0.001 0.001
0.001 0.001 0.003


0.008
0.018 0.009
0.001
0.001 0.012 0.017 0.023 0.021 0.021 0.026 0.021 0.020 0.022 0.015 0.020 0.020 0.024 0.018

0.002 0.001 0.005 0.008
0.005
0.001
0.001 0.008 0.001 0.003 0.006
0.001 0.001
0.001
0.002 0.002 0.001 0.002 0.004


0.001
0.001
0.002
0.001
0.007
0.013
0.010
0.010
0.007
0.007
0.004
0.019
0.019
0.015
0.012
0.015
0.012
0.013 0.011

0.002 0.002
0.001
0.001 0.007 0.002
0.001
0.005
0.005
0.007
0.008 0.001 0.001 0.002 0.002
0.003
0.001
0.002 0.004


0.1 0.1 0.1 0.1
0.2
0.1
0.1 0.2
0.1
0.1
0.1 0.1 0.1 0.1
0.1
0.1
0.1
0.1 0.1

0.1
0.1 0.1 0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.1
0.1
0.1 0.1 0.1 0.1 0.1 0.1

NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d


0.020
0.025
0.089
0.068
0.069
0.062
0.050
0.081
0.036
0.037
0.031
0.012
0.024
0.017
0.010
0.006
0.011
0.007 0.045


0.002 0.009
0.007 0.006
0.001
0.001 0.003
0.004 0.002 0.001
0.002 0.002
0.001
0.001
0.001
0.001
0.002
0.002 0.003


0.010
0.019 0.009 0.001
0.003 0.010 0.017 0.024 0.022 0.023 0.028 0.020 0.020 0.023 0.016 0.021 0.020 0.025 0.019

0.002
0.009 0.007
0.006
0.001 0.002
0.002 0.006
0.001 0.001 0.002
0.001 0.001
0.001
0.001 0.003 0.004 0.005 0.004


0.002
0.001
0.003
0.001
0.013
0.021
0.017
0.016
0.013
0.012
0.008
0.034
0.033
0.026
0.022
0.023
0.018
0.018 0.018

0.001 0.001
0.001
0.001 0.001
0.002
0.001
0.002
0.001
0.001 0.001
0.001
0.001 0.001 0.002
0.002
0.001
0.003 0.001


0.1
0.1
0.1
0.1
0.1
0.1
0.1 0.1
0.1
0.1
0.1
0.2
0.1
0.1
0.1
0.1
0.1
0.1 0.1

0.1 0.1
0.1 0.1 0.1 0.1 0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

Wilson Eq

Uniquac Eq

a

Dyipre ¼ yiexp
yipre Dyical ¼ yiexp
yical DT cal ¼ T exp
T cal DP cal ¼ P exp
P cal dyical ¼ !1=2 !1=2 N
N
2 2 P P T iexp
T ical dP cal ¼ 1=N  P iexp
P ical . 1=N  i¼1

i¼1

1=N 

N  P i¼1

yiexp
yical

2

!1=2 dyipre ¼

1=N 

2 N  P yiexp
yipre i¼1

!1=2 dT cal ¼

7

C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047 Table 7 Prediction and correlation of vapour-liquid equilibrium data for DMS(1) + DMG(2) + DMA(3) ternary system at 5.0kPaa. NRTL Eq NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d

0.076 0.065 0.061 0.056 0.014 0.017 0.028 0.007 0.049 0.029 0.030 0.027 0.040 0.050 0.022 0.018 0.001 0.023 0.040

0.001 0.003 0.001
0.001
0.004
0.002 0.003
0.025 0.013 0.005 0.007 0.002 0.004 0.004
0.001
0.001
0.005
0.001 0.007


0.004
0.011
0.014
0.013
0.020
0.024
0.027 0.010
0.034
0.026
0.023
0.012
0.011
0.007
0.003
0.002 0.015 0.008 0.017

0.002
0.003
0.002 0.001 0.002 0.001
0.001 0.018
0.010
0.004
0.004 0.002
0.001
0.001 0.001
0.001 0.005 0.001 0.005


0.013
0.015
0.014
0.012
0.007
0.009
0.010
0.008
0.012
0.010
0.012
0.013
0.015
0.017
0.015
0.014
0.011
0.011 0.012


0.003
0.001
0.001 0.001 0.003 0.001
0.002 0.007
0.003
0.001
0.003
0.003
0.003
0.003
0.001 0.001 0.001 0.001 0.003


0.1
0.1
0.1
0.1 0.3 0.3 0.2
0.2 0.1 0.1 0.1
0.1
0.1
0.2 0.1 0.1 0.1
0.1 0.1

0.1 0.1 0.1 0.1
0.1
0.1
0.1
0.1 0.1 0.1
0.1 0.1 0.1 0.1
0.1
0.1 0.1 0.1 0.1

NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d

0.069 0.064 0.062 0.058 0.016 0.020 0.030 0.010 0.051 0.030 0.031 0.026 0.039 0.049 0.020 0.015
0.001 0.020 0.039

0.006 0.006 0.003
0.001
0.004
0.002 0.002
0.026 0.012 0.004 0.005 0.001 0.003 0.005 0.001 0.001
0.006 0.001 0.008


0.003
0.010
0.013
0.013
0.020
0.025
0.028 0.009
0.035
0.027
0.025
0.013
0.012
0.007
0.003
0.003 0.014 0.008 0.018

0.002 0.001 0.001 0.003 0.001
0.001
0.003 0.020
0.012
0.005
0.005 0.001
0.002
0.001 0.001 0.001 0.006 0.002 0.006


0.015
0.018
0.017
0.015
0.009
0.011
0.012
0.010
0.014
0.011
0.013
0.015
0.016
0.018
0.016
0.014
0.011
0.011 0.014


0.008
0.007
0.005
0.002 0.003 0.003 0.001 0.006
0.001 0.001
0.001
0.002
0.002
0.005
0.003
0.002
0.001
0.001 0.004


0.3
0.2
0.2
0.2 0.3 0.3 0.2
0.1 0.1 0.1 0.1 0.1
0.1
0.3
0.1
0.1
0.1
0.2 0.2

0.1 0.1 0.1 0.1
0.1
0.1
0.1 0.1
0.1
0.1
0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d

0.073 0.066 0.066 0.065 0.023 0.030 0.043 0.031 0.069 0.048 0.049 0.044 0.058 0.066 0.035 0.029 0.010 0.030 0.050

0.007 0.006 0.002
0.002
0.004
0.002 0.001
0.031 0.011 0.003 0.005
0.001 0.003 0.004 0.001 0.002
0.004 0.002 0.008

0.004 0.003 0.001
0.001
0.011
0.019
0.025 0.009
0.038
0.031
0.029
0.018
0.018
0.012
0.008
0.006 0.011 0.006 0.018

0.001
0.001 0.001 0.003 0.001
0.001
0.003 0.021
0.011
0.006
0.006
0.001
0.003
0.002 0.001 0.001 0.005 0.002 0.006


0.011
0.012
0.010
0.007
0.001
0.001
0.002 0.001
0.004
0.002
0.005
0.006
0.008
0.011
0.010
0.010
0.007
0.008 0.008


0.008
0.006
0.004
0.001 0.004 0.003 0.002 0.009 0.001 0.003 0.001 0.001 0.001
0.003
0.002
0.002
0.001
0.002 0.004


0.2
0.1
0.1
0.1 0.4 0.4 0.3
0.1 0.1 0.2 0.1 0.1
0.1
0.2
0.1 0.1
0.1
0.2 0.2

0.1 0.1 0.1 0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1 0.1 0.1 0.1
0.1 0.1 0.1 0.1

Wilson Eq

Uniquac Eq

a

Dyipre ¼ yiexp
yipre Dyical ¼ yiexp
yical DT cal ¼ T exp
T cal DP cal ¼ P exp
P cal dyical ¼ !1=2 !1=2 N
N
2 2 P P T iexp
T ical dP cal ¼ 1=N  P iexp
P ical . 1=N  i¼1

i¼1

1=N 

N  P i¼1

yiexp
yical

2

!1=2 dyipre ¼

1=N 

N  P i¼1

yiexp
yipre

2

!1=2 dT cal ¼

8

C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047

Table 8 Prediction and correlation of vapour-liquid equilibrium data for DMS(1) + DMG(2) + DMA(3) ternary system at 8.0kPaa. NRTL Eq NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d

0.070 0.062 0.038 0.047 0.028 0.019 0.019 0.007 0.031 0.037
0.016 0.004 0.012 0.004 0.031
0.012 0.005 0.005 0.032

0.016 0.020 0.001 0.014 0.003
0.001
0.001
0.003 0.004 0.006
0.016
0.004 0.001
0.001 0.006
0.003
0.001 0.001 0.008


0.016
0.025
0.004
0.023
0.011
0.006
0.006
0.006
0.011
0.011 0.006
0.005
0.008
0.006
0.015 0.005 0.009
0.001 0.011


0.001
0.007 0.003
0.008
0.001 0.003 0.003 0.004
0.001
0.003 0.013 0.004 0.000 0.002
0.002 0.003 0.002
0.002 0.005

0.001
0.001 0.001 0.001 0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.002
0.005
0.006
0.008
0.007
0.011
0.008 0.004


0.015
0.013
0.004
0.006
0.002
0.002
0.002
0.001
0.003
0.003 0.002
0.001
0.002
0.002
0.004
0.001
0.002 0.001 0.005


0.3
0.1
0.1 0.1 0.1 0.1 0.1 0.1
0.1
0.2 0.2 0.1 0.1 0.1
0.1
0.1
0.3
0.1 0.1

0.1 0.1 0.1
0.1
0.1
0.1
0.1
0.1 0.1 0.1
0.1
0.1
0.1
0.1 0.1 0.1 0.1 0.1 0.1

NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d

0.067 0.059 0.035 0.045 0.027 0.018 0.018 0.007 0.032 0.037
0.014 0.006 0.015 0.007 0.033
0.011 0.004 0.002 0.031

0.004 0.009
0.007 0.003
0.005
0.006
0.005
0.005
0.001 0.001
0.011
0.002 0.004 0.002 0.008
0.002 0.001 0.001 0.005


0.016
0.025
0.004
0.022
0.010
0.006
0.006
0.006
0.011
0.012 0.005
0.007
0.010
0.008
0.016 0.003 0.008
0.002 0.012


0.005
0.010 0.005
0.005 0.003 0.005 0.004 0.004
0.001
0.002 0.011 0.001
0.004
0.002
0.006 0.002 0.001
0.003 0.005


0.001
0.001 0.001 0.000 0.001
0.001
0.001
0.001
0.002
0.002
0.001
0.003
0.005
0.007
0.009
0.007
0.011
0.008 0.005

0.001 0.001 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.000 0.001 0.000 0.000
0.002 0.000
0.001 0.002 0.001


0.2 0.1
0.1 0.1 0.1 0.1 0.1 0.1
0.1
0.2 0.1 0.1 0.1 0.1
0.1 0.1
0.1 0.1 0.1

0.1
0.1 0.1
0.1
0.1
0.1
0.1
0.1 0.1 0.1
0.1
0.1
0.1
0.1
0.1
0.1 0.1
0.1 0.1

NO

4y1pre

4y1cal

4y2pre

4y2cal

4y3pre

4y3cal

4Tcal/K

4Pcal/kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 d

0.067 0.060 0.036 0.046 0.028 0.019 0.020 0.009 0.035 0.041
0.010 0.012 0.022 0.015 0.043
0.001 0.016 0.013 0.033

0.010 0.011 0.001 0.004
0.001
0.001
0.001
0.001
0.001
0.001
0.002
0.001 0.000 0.001 0.001 0.001
0.001 0.001 0.004


0.014
0.024
0.003
0.022
0.010
0.006
0.007
0.007
0.012
0.013 0.003
0.009
0.013
0.011
0.020
0.001 0.004
0.005 0.012

0.001
0.003 0.002
0.002
0.001 0.001 0.000 0.000
0.001
0.001 0.001
0.001
0.001 0.000
0.001 0.001 0.000
0.002 0.001

0.001 0.000 0.002 0.002 0.003 0.002 0.002 0.002 0.001 0.001 0.002 0.001
0.001
0.002
0.005
0.003
0.008
0.006 0.003


0.011
0.008
0.003
0.002 0.000 0.000 0.000 0.000 0.001 0.002 0.001 0.001
0.001
0.001
0.001
0.002 0.000 0.001 0.003


0.2 0.1
0.1 0.1 0.1 0.1 0.1 0.1
0.1
0.1
0.1
0.1 0.1 0.1 0.1 0.1
0.1 0.1 0.1

0.1
0.1 0.1
0.1
0.1
0.1
0.1
0.1 0.1 0.1 0.1 0.1
0.1
0.1
0.1 0.1 0.1
0.1 0.1

Wilson Eq

Uniquac Eq

a

Dyipre ¼ yiexp
yipre Dyical ¼ yiexp
yical DT cal ¼ T exp
T cal DP cal ¼ P exp
P cal dyical ¼ !1=2 !1=2 N
N
2 2 P P T iexp
T ical dP cal ¼ 1=N  P iexp
P ical . dT cal ¼ 1=N  i¼1

i¼1

1=N 

N  P i¼1

yiexp
yical

2

!1=2 dyipre ¼

1=N 

2 N  P yiexp
yipre i¼1

!1=2 -

P/kPa

NRTL 2 5 8

Interaction parameters a12

a21

a13

a31

a23

a32

b12

b21

b13

b31

b23

b32

cdij


2.0415 12.1195 14.2954

9.0528 10.0442 3.0365

11.9053 131.5575 40.6306

6.6751
22.6371 7.4037


0.3910 214.3598
3.6409


3.9579
49.1806
6.5802

373.4195
4852.2490
5066.0734


2746.9052
3754.8952
1565.8421


4272.2056
44611.3900
12560.4980


2532.9359 8471.5950
3392.0242


38.8387
82193.9400 1580.7145

1652.6745 18385.6842 2470.2978

0.3 0.3 0.3


4.2188
17.4695
14.8804


34.8782
9.4424 3.8754


82.1244
10.9421
2.9393


89.6987
11.6246
89.6987

1.5296
13.9578 4.4831

709.7184 2.5748 34.6424

1973.7602 7147.5783 6295.0514


34293.2670
434.4372
3117.5698

30827.3692 4706.6186 1818.9456


10000.4330 23.0685
10000.4330


124.0664 5123.0182
1474.5709


267701.2000
711.5779
14439.0280

0 0 0


0.9652
0.7487 29.1004


3.2058
1.9784
193.1602


3.3191
1.0286 33.0880

1.6118
4.0154
114.4661

1.5090
2.7420 27.9863

203.2451 267.8296
2100.6588

77.3505 353.8621
12762.4070

1177.3252 210.6236
3150.8777

1211.9483 719.7831
13343.0330


500.6435 1260.2784 45834.6490


680.3886 1310.8056
10970.8990

0 0 0

a

Wilsonb 2 5 8

Uniquacc 2
0.0155 5
0.9258 8 6.2847 a b c

C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047

Fig. 7. Vapour-liquid equilibrium phase diagram of DMS(1) + DMG(2) + DMA(3) ternary system at 2 kPa(a), 5 kPa(b), 8 kPa(c).

values of the three models are closer to the experimental values than the predicted values, and the deviation is smaller. Therefore, it is certain that the result obtained by direct regression of experimental values is better than the predicted value.

Table 9 Binary interaction parameters of the NRTL, Wilson and Uniquac.

NRTL, sij = aij + bij/T d the value of cij was fixed at 0.3 for ternary system. Wilson, lnAij = aij + bij/T. Uniquac, sij = exp(aij + bij/T).

9

10

C. Zhi et al. / J. Chem. Thermodynamics 143 (2020) 106047

4. Conclusion The isostatic vapour-liquid equilibrium data of ternary system of {DMS(1) + DMG(2) + DMA(3)} at 2 kPa, 5 kPa and 8 kPa in the temperature range of (364.46–403.55) K were determined. The values for the ternary system of vapour-liquid met the thermodynamic consistency test. The NRTL, Wilson and Uniquac models were used to correlate the experimental results. The maximum root mean square deviations of the vapour phase mole fractions of the ternary systems of the three models were 0.0083, 0.0076 and 0.0084, respectively. The vapour-liquid equilibrium data of the ternary system were predicted by the interaction parameters of NRTL, Wilson and Uniquac models in the literature [17]. The maximum root mean square deviations of the vapour phase mole fractions of the ternary systems of the three models were 0.0547, 0.0471 and 0.0498, respectively. The errors between the experimental values and the regression values or the predicted values were small, and both met the needs of the engineering separation design calculation. Whereas the results obtained by regression of experimental values were significantly better than the predicted results. CRediT authorship contribution statement Chunli Zhi: Formal analysis, Writing - original draft, Writing review & editing. Yang Tang: Resources, Investigation. Jinru Wan: Investigation. Xingming Liu: Investigation, Data curation. Honglin Chen: Validation. Xunqiu Wang: Conceptualization, Methodology, Supervision. 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. References [1] P. Kasinathan, D. Hwang, U.H. Lee, Y.K. Hwang, J.-S. Chang, Effect of Cu particle size on hydrogenation of dimethyl succinate over Cu–SiO2 nanocomposite, Catal. Commun. 41 (2013) 17–20, https://doi.org/10.1016/ j.catcom.2013.06.034. [2] H. Negoro, A. Kotaka, K. Matsumura, H. Tsutsumi, Y. Hata, Enhancement of malate-production and increase in sensitivity to dimethyl succinate by mutation of the VID24 gene in Saccharomyces cerevisiae, J. Biosci. Bioeng. 121 (2016) 665–671, https://doi.org/10.1016/j.jbiosc.2015.11.012. [3] D. Zhao, M. Liu, Z. Xu, J. Zhang, D. Zhang, J. Fu, P. Ren, synthesis of dimethyl succinate catalyzed by ionic liquids, CIESC J. 63 (4) (2012) 1089–1094, https:// doi.org/10.3969/j.issn.0438-1157.2012.04.015. [4] N. Ilayaraja, S. Radhakrishnan, N.G. Renganathan, Electrochemical fluorination of dimethyl glutarate and its characterization, Ionics 16 (2) (2010) 137–144, https://doi.org/10.1007/s11581-009-0366-9. [5] M. Wojtczak, S. Dutkiewicz, L. Pietrzak, A. Galeski, E. Piorkowska, Nucleation and crystallization of random aliphatic-butylene terephtalate copolyester, Eur. Polym. J. 71 (2015) 289–303, https://doi.org/10.1016/j.eurpolymj.2015.08.004. [6] M. Huang, B. Sun, H. Tian, et al., Study on catalytic synthesis of dimethyl glutarate by p-toluene sulfonic acid, China Chem. 20 (1) (2006) 4–6, https:// doi.org/10.3969/j.issn.1002-1124.2006.01.002. [7] L. Fan, L. Han, Synthesis of dimethyl adipate, J. Hebei United Univ. (Nat. Sci. Ed.) 28 (2) (2006) 100–102, https://doi.org/10.3969/j.issn.1674-0262.2006.02.025. [8] Y. Zhao, Z. Guo, H. Zhang, Y. Xu, Y. Wang, J. Zhang, Y. Xu, S. Wang, X. Ma, Ordered Mesoporous CuZn/HPS Catalysts for the Chemoselective Hydrogenation of Dimethyl Adipate to 1,6-Hexanediol, Chem. Lett. 46 (2017) 1079–1082, https://doi.org/10.1246/cl.170358. [9] Z. Mao, X. Sun, K. Ren, G. Liu, Study on kinetics of synthesis of dimethyl adipate, Chem. Ind. Times 20 (10) (2006) 24–26, https://doi.org/10.3969/j. issn.1002-154X.2006.10.009. [10] Y. Tsai, H. Lin, M. Lee, Kinetics of heterogeneous esterification of glutaric acid with methanol over Amberlyst 35, J. Taiwan Inst. Chem. Eng. 42 (2) (2011) 271–277, https://doi.org/10.1016/j.jtice.2010.07.010. [11] N. Yu, L. Li, M. Chen, J. Wang, D. Liu, L. Sun, Novel reactive distillation process with two side streams for dimethyl adipate production, Chem. Eng. Process. 118 (2017) 9–18, https://doi.org/10.1016/j.cep.2017.04.010.

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