Experimental determination and modeling of liquid-liquid equilibrium for water + diethoxymethane + methyl tert-butyl ether (or methyl isobutyl ketone) at 298.15, 308.15, and 318.15 K

Fluid Phase Equilibria 505 (2020) 112353

Contents lists available at ScienceDirect

Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Experimental determination and modeling of liquid-liquid equilibrium for water þ diethoxymethane þ methyl tert-butyl ether (or methyl isobutyl ketone) at 298.15, 308.15, and 318.15 K Qingsong Li*, Wenyang Fan, Houchun Yan, Xin Huang, Lili Zhang, Zhanhua Ma** The State Key Lab of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum e East China, Qingdao, 266580, Shandong, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 March 2019 Received in revised form 17 September 2019 Accepted 6 October 2019 Available online 9 October 2019

The liquid-liquid equilibrium (LLE) data of ternary systems water þ diethoxymethane (DEM) þ Methyl tert-butyl ether (MTBE) and water þ DEM þ Methyl isobutyl ketone (MIBK) were determined experimentally at 298.15, 308.15, and 318.15 K under the atmospheric pressure condition. The solvents' extraction capacity was assessed by the solute distribution coefficient and selectivity. Othmer-Tobias and Hand equations were utilized to validate the accuracy and reliability of the measured data, which the linear correlation (R2)  0.99. Experimental LLE data was correlated utilizing the NRTL and UNIQUAC thermodynamic models with all of the RMSD values below 0.002 meaning that each ternary system satisfactory agreement at temperatures studied. Also, the reliability of binary interaction parameters was validated by the topological analysis based on the Gibbs tangent plane test using a graphical user interface. © 2019 Elsevier B.V. All rights reserved.

Keywords: Liquid-liquid equilibria Diethoxymethane Methyl tert-butyl ether Methyl isobutyl ketone Thermodynamic modeling

1. Introduction Diethoxymethane (DEM) is a very useful compound, which is widely used in pharmaceutical extraction, organic intermediates synthesis and chemical industry. DEM is typically used as a solvent with the low boiling, azeotropes with water, low affinity for water and stability. For example, it is a useful solvent for the following process: phase-transfer reactions, copper-catalyzed conjugate additions, organolithium chemistry and sodium hydride reactions [1]. Meanwhile, DEM could be used as reaction reagent. For example, it was used as methylation reagent to improve the yield of 6methylene-substituted steroid derivatives [2]. Moreover, DEM is a functional diesel additive to increase octane number and reduce carbon monoxide emissions. Synthesis of DEM by formaldehyde and ethanol is the most economical and reasonable method [3]. Water is generated as a byproduct in this synthetic route [4]. However, DEM can form azeotropic mixtures with water as well as ethanol [5], which makes it difficult to obtain high-purity DEM by simple distillation operation.

* Corresponding author. ** Corresponding author. E-mail address: [email protected] (Q. Li). https://doi.org/10.1016/j.fluid.2019.112353 0378-3812/© 2019 Elsevier B.V. All rights reserved.

Azeotropic distillation represents an effective method in separation of DEM ethanol and water, while its energy consumption is slightly higher than that of the extraction method. Reliable LLE data is the foundation for the design and optimization of the liquid-liquid extraction process. Jia et al. [6] measured the LLE data of ethanol þ DEM þ different extractants (formamide, ethylene glycol 1,4-butanediol, 1,3-propanediol, and water). Most kinds of literature report the separation of DEM þ ethanol systems, while account little research on DEM þ water systems. In this work, in order to explore the possibility of more extractants, such as MTBE and MIBK, of extracting DEM from water, under 101.3 Kpa the figures concerning ternary phase equilibrium system water þ DEM þ MTBE and water þ DEM þ MIBK were investigated at 298.15, 308.15, and 318.15 K. Distribution coefficients (D) and separation factors (S) were used for calculating the extraction effect of the extractant [7,8]. Othmer-Tobias [9] and Bachman [10] equations can confirm the trustworthiness of these results. Additionally, all reasonable values of the tie-line were fitted utilizing NRTL [11] and UNIQUAC [12] models, meanwhile, it is fruitful to achieve the binary interaction parameters.

2

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

2. Experimental 2.1. Materials The source and purity of the substances which were used in this tentative are shown in Table 1. Water, DEM, MTBE, and MIBK were available from Aladdin reagent company. Gas chromatography (GC) is used to determine their purity because of the adverse effects of impurities on experimental measurements. There were no noteworthy impurity peaks in the spectrum, so all substances were used straightforwardly, which were not used further purification. 2.2. Experimental procedures The experiments were completed in the experimental apparatus and the detailed of that were shown as follows [13,14]. Firstly, water and solvent were added to a 100 mL LLE cell at a mass ratio of 1:1 and DEM was added to the cell by mass with a gradient of 5%. Stir energetically for 4 h after fixing the equilibrium cell and circulating

water, then the mixture system was stood for at least 4 h for achieving the stability of the system, keep the temperature of the system constant by a constant temperature water bath, with an accuracy of 0.1 K, the temperature of the mixed solution amounted in a mercury thermometer. Ethanol was used as an internal standard substance to obtain a calibration factor and an internal standard method was used to define the composition of the sample. All samples in the experiments were quantitatively examined by gas chromatography (GC). A Porapak N column (3 m  3 mm) with a thermal conductivity detector (TCD) was used in the Agilent 6820 GC. Meanwhile, the injection amount of each sample was 0.6 mL. The normalization method was utilized to calculate the concentration of each component. The chromatographic output peak area can be converted to a mass ratio. All samples were injected into the gas chromatograph with a detector and injector temperature of 523.2 K, a high purity carrier gas flow rate of hydrogen with 60.0 mL min1. The column temperature was programmed at 393.2 K for 1.0 min firstly, then increased to the final temperature of

Table 1 Detaila of the chemical reagents used in this work. Component

Supplier

Mass purity (mass%)

GCa Purity (mass%)

CAS

Purification method

Diethoxymethane Methyl tert-butyl ether Methyl isobutyl ketone Water

Aladdin Aladdin Aladdin Self-made

99.50 99.50 99.50 e

99.55 99.50 99.80 99.98

462-95-3 1634-04-4 108-10-1 7732-18-5

None None None None

a

Gas chromatography.

Table 2 Experimental LLE results in mole fraction for water (1) þ DEM (2) þ MTBE (3) system at 298.15, 308.15, and 318.15 K under atmospheric pressure.a T/K

298.15

308.15

318.15

Water phase(I)

MTBE phase(II)

xI1

xI2

xI3

xII1

xII2

xII3

0.9934 0.9928 0.9925 0.9923 0.9921 0.9919 0.9917 0.9916 0.9914 0.9912 0.9911 0.9940 0.9944 0.9942 0.9940 0.9937 0.9935 0.9933 0.9930 0.9927 0.9926 0.9923 0.9943 0.9945 0.9943 0.9942 0.9940 0.9939 0.9938 0.9936 0.9934 0.9933 0.9931

e 0.0008 0.0012 0.0016 0.0020 0.0024 0.0029 0.0032 0.0036 0.0041 0.0045 e 0.0004 0.0006 0.0010 0.0014 0.0018 0.0022 0.0028 0.0033 0.0038 0.0043 e 0.0005 0.0008 0.0011 0.0015 0.0019 0.0023 0.0029 0.0034 0.0039 0.0043

0.0066 0.0064 0.0063 0.0061 0.0059 0.0057 0.0054 0.0052 0.0050 0.0047 0.0044 0.0060 0.0052 0.0052 0.0050 0.0049 0.0047 0.0045 0.0042 0.0040 0.0036 0.0034 0.0057 0.0050 0.0049 0.0047 0.0045 0.0042 0.0039 0.0035 0.0032 0.0028 0.0026

0.0508 0.0543 0.0555 0.0577 0.0604 0.0636 0.0666 0.0693 0.0733 0.0805 0.0843 0.0584 0.0678 0.0694 0.0711 0.0728 0.0745 0.0762 0.0782 0.0801 0.0816 0.0830 0.0611 0.0695 0.0715 0.0741 0.0758 0.0775 0.0792 0.0813 0.0827 0.0841 0.0860

e 0.0871 0.1180 0.1524 0.1857 0.2271 0.2523 0.2819 0.3106 0.3325 0.3689 e 0.0476 0.0649 0.0938 0.1268 0.1498 0.1836 0.2277 0.2713 0.3072 0.3435 e 0.0396 0.0559 0.0879 0.1167 0.1456 0.1730 0.2221 0.2603 0.2961 0.3320

0.9492 0.8586 0.8265 0.7899 0.7539 0.7093 0.6811 0.6488 0.6161 0.5870 0.5468 0.9416 0.8846 0.8657 0.8351 0.8004 0.7757 0.7402 0.6941 0.6486 0.6112 0.5735 0.9389 0.8909 0.8726 0.8380 0.8075 0.7769 0.7478 0.6966 0.6570 0.6198 0.5820

D

S

e 108.8750 98.3333 95.2500 92.8500 94.6250 87.0000 88.0938 86.2778 81.0976 81.9778 e 119.0000 108.1667 93.8000 90.5714 83.2222 83.4545 81.3214 82.2121 80.8421 79.8837 e 79.2000 79.8571 79.9091 77.8000 76.6316 75.2174 76.5862 76.5588 75.9231 75.4545

e 1990.6280 1758.4835 1638.0689 1525.1074 1475.7632 1295.4640 1260.5161 1166.9275 998.5578 963.7980 e 1745.3333 1549.5576 1311.3530 1236.2751 1109.8158 1087.8661 1032.6366 1018.8761 983.3808 955.0436 e 1133.3007 1110.6286 1072.1406 1020.2269 982.7629 943.8263 935.9908 919.6316 896.7229 871.2368

a Standard uncertainties: u are u(T) ¼ 0.1 K, u(P) ¼ 1.5 kPa, u(xI1) ¼ 0.0006, u(xI2) ¼ 0.0005, u(xI3) ¼ 0.0007, u(xII1) ¼ 0.0005, u(xII2) ¼ 0.0006, u(xII3) ¼ 0.0007. Notation: x1, mole fraction of water; x2: mole fraction of DEM; x3: mole fraction of MIBE.

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

3

Table 3 Experimental LLE results in mole fraction for water (1) þ DEM (2) þ MIBK (3) system at 298.15, 308.15, and 318.15 K under atmospheric pressure.a T/K

298.15

308.15

318.15

Water phase(I)

MIBK phase(II)

xI1

xI2

xI3

xII1

xII2

xII3

0.9968 0.9965 0.9963 0.9959 0.9956 0.9952 0.9948 0.9944 0.9940 0.9936 0.9931 0.9970 0.9968 0.9966 0.9963 0.9961 0.9955 0.9951 0.9946 0.9943 0.9939 0.9935 0.9973 0.9969 0.9967 0.9964 0.9963 0.9957 0.9953 0.9948 0.9945 0.9942 0.9939

e 0.0004 0.0007 0.0012 0.0016 0.0021 0.0026 0.0032 0.0038 0.0043 0.0049 e 0.0003 0.0006 0.0010 0.0013 0.0021 0.0025 0.0032 0.0035 0.0040 0.0045 e 0.0003 0.0006 0.0010 0.0013 0.0020 0.0024 0.0030 0.0034 0.0038 0.0042

0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 0.0024 0.0022 0.0021 0.0020 0.0030 0.0029 0.0028 0.0027 0.0026 0.0024 0.0024 0.0022 0.0022 0.0021 0.0020 0.0027 0.0028 0.0027 0.0026 0.0024 0.0023 0.0023 0.0022 0.0021 0.0020 0.0019

0.0973 0.0984 0.1004 0.1020 0.1072 0.1125 0.1145 0.1157 0.1177 0.1197 0.1213 0.1135 0.1160 0.1171 0.1181 0.1191 0.1208 0.1219 0.1244 0.1268 0.1293 0.1317 0.1217 0.1214 0.1225 0.1236 0.1246 0.1262 0.1273 0.1298 0.1327 0.1351 0.1375

e 0.0488 0.0755 0.1113 0.1422 0.1809 0.2213 0.2643 0.2998 0.3418 0.3810 e 0.0401 0.0707 0.1029 0.1240 0.1886 0.2222 0.2807 0.3073 0.3425 0.3764 e 0.0386 0.0690 0.1003 0.1209 0.1839 0.2176 0.2692 0.2995 0.3338 0.3659

0.9027 0.8528 0.8241 0.7867 0.7506 0.7066 0.6642 0.6200 0.5825 0.5385 0.4977 0.8865 0.8439 0.8122 0.7790 0.7569 0.6906 0.6559 0.5949 0.5659 0.5282 0.4919 0.8783 0.8400 0.8085 0.7761 0.7545 0.6899 0.6551 0.6010 0.5678 0.5311 0.4966

D

S

e 122.0000 107.8571 92.7500 88.8750 86.1429 85.1154 82.5938 78.8947 79.4884 77.7551 e 133.6667 117.8333 102.9000 95.3846 89.8095 88.8800 87.7188 87.8000 85.6250 83.6444 e 128.6667 115.0000 100.3000 93.0000 91.9500 90.6667 89.7333 88.0882 87.8421 87.1190

e 1235.4980 1070.2995 905.5855 825.4100 762.0389 739.5003 709.8637 666.2818 659.8133 636.5919 e 1148.6115 1002.8412 868.0717 797.7550 740.1108 725.5495 701.3269 688.4822 658.1801 630.9852 e 1056.5717 935.6776 808.5673 743.6268 725.4724 708.8809 687.7251 660.1639 646.4295 629.7282

a Standard uncertainties: u are u(T) ¼ 0.1 K, u(P) ¼ 1.5 kPa, u(xI1) ¼ 0.0005, u(xI2) ¼ 0.0007, u(xI3) ¼ 0.0006, u(xII1) ¼ 0.0005, u(xII2 ) ¼ 0.0005, u(xII3) ¼ 0.0006. Notation: x1, mole fraction of water; x2: mole fraction of DEM x3: mole fraction of MIBK.

503.2 K at the rate of 15 K min1 and maintained 2 min. The sample was obtained from the upper and lower phases by a chromatographic needle and analyzed at least three times to ensure that the error of the calculation result was less than 0.1%. A series of liquid-liquid equilibrium data was gotten by changing the composition and temperature of the mixture.

sample are usually small. The urðcalÞ , urðtrueÞ , urðrepÞ , urðLODÞ have been calculated by the corresponding equations given in their report.

2.3. Uncertainty calculation

The experimental data of the mixtures {water þ DEM þ MTBE and water þ DEM þ MIBK} which were presented in Tables 2e3 were determined in different temperatures (298.15, 308.15, and 318.15 K). Ternary phase diagrams were displayed in Figs. 1e6. In addition, the slope of the connecting line indicates the positive

According to the GUM standard [15e17], the combined uncertainty for experimental data was estimated using the following formula:

3. Results and discussion 3.1. Experimental LLE data

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 12 u !2 !2 0 2 u 2  u u ¼ t urðsampleÞ þ urðcalÞ þ urðtrueÞ þ urðrepÞ þ @urðLODÞ A

where u is the combined uncertainty, urðsampleÞ is the uncertainty of sample volume, urðcalÞ is the relative uncertainty of the calibration step, urðtrueÞ is the uncertainty of recovery of extraction, urðrepÞ is the uncertainty of reliability and urðLODÞ is the uncertainty of the limit of detection. The urðsampleÞ is not taken into account of the uncertainty budget since the inherent uncertainty in the measurement of a

(1)

effect of extracting DEM from aqueous solution using MTBE and MIBK as extraction solvents. As the DME increase, the phase points of the MTBE or MIBK phase always move along the MTBE and MIBK combination lines to the pure component points of the DEM. It can be seen from the ternary phase diagram that a large range of twophase regions can be used for the extraction operation, and the feed composition is all located on the connection line, which proves that

4

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

Fig. 1. Ternary phase diagram for water (1) þ DEM (2) þ MTBE (3) system at 298.15 K, (*) feed composition; (,) experimental data; (B) NRTL model; (△) UNIQUAC model. (a) Complete phase diagram; (b) points in water phase.

Fig. 2. Ternary phase diagram for water (1) þ DEM (2) þ MTBE (3) system at 308.15 K, (*) feed composition; (,) experimental data; (B) NRTL model; (△) UNIQUAC model. (a) Complete phase diagram; (b) points in water phase.

the experimental process conforms to the law of conservation of mass and the accuracy of experimental data. The binary solubilities between water and MTBE, water and MIBK at different temperatures and that of literature data were shown in Tables 4, 5 and compared graphically in Fig. 7 [18e23]. The data showed that the binary solubility achieved in the experiment within each allowable error caused by different measurement methods is consonant with the data in the literature. Temperature shows an important affecting for the liquid-liquid equilibrium. In this work, the effect of three temperature points (298.15, 308.15, and 318.15 K) on LLE data was studied. From the triangular phase diagrams, there is no significant change in the immiscible area with the temperature rising, which indicates that temperature shows a limited effect on liquid-liquid equilibrium for water þ DEM þ MTBE and water þ DEM þ MIBK. To evaluate the suitability of MTBE and MIBK, D (the distribution coefficient) and S (the separation factor) were respectively calculated by equations (1) and (2) [24].

Tables 2e3 To investigate the effect of temperature on the selectivity of DEM solvents (MTBE and MIBK), experimental separation factors at different temperatures were plotted in Fig. 8. For the system under study, the distribution coefficient is much larger than 1, indicating that MTBE and MIBK have excellent effects on the extraction of DEM. Therefore, the result also showed DEM had a stronger interaction with MTBE and MIBK. Meanwhile, the separation factors are considerably higher than 1, which indicate MTBE and MIBK have a good extraction capacity and high selectivity. With the increase of DEM content in MTBE and MIBK phase, the distribution coefficient decrease slightly, indicating that the extraction ability of MTBE and MIBK decrease with high DEM content. It can be seen from Fig. 8 that with the increase of DEM content in the MIBK phase, the separation factor of the MIBK system decreases slightly and the change of the separation factor is not obvious with the increase of temperature. However, separation factors for MTBE system show a significant reduction with the increase of DEM in MTBE phase, while separation factors at 298.15 K are much larger than that of 308.15 and 318.15 K. Compared the separation factors for these two systems, the MTBE system is much larger than that of MIBK system, which indicates that MTBE shows a better extraction capacity.

. D ¼ xII2 xI2

(2)

 . . .  xII1 xI1 S ¼ xII2 xI2

(3) 3.2. Correlation of experimental tie-line data

where xII1 and xI1 are the concentrations of water in solvents phase and water phase, respectively. xII2 , xI2 indicate the mole fractions of DEM in the two phases, respectively. The D and S are given in

In this paper, the Othmer-Tobias equation and the Bachman equation were used to correlate the measured data to test the

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

Fig. 3. Ternary phase diagram for water (1) þ DEM (2) þ MTBE (3) system at 318.15 K, (*) feed composition; (,) experimental data; (B) NRTL model; (△) UNIQUAC model. (a) Complete phase diagram; (b) points in water phase.

correlation of the experimental data. The expressions are as follows [25]:

. i h . i h xII3 ¼ a þ bln 1  xI1 xI1 ln 1  xII3

(4)

 .   .  ln xII2 xII3 ¼ c þ dln xI2 xI1

(5)

where a, b, c, and d are the constants of the above equations. xII2 and xII3 are the mole fractions of DEM and solvents in the solvents phase, respectively. While xI1 and xI2 are mole fractions of water and DEM in the water phase. The equation constants and the linear correlation (R2) for solvents systems are given in Table 6. Simultaneously, the OthmerTobias and Bachman plots are demonstrated in Fig. 9 and Fig. 10, respectively. The results of both empirical equations displayed a linearity behaviour with R2  0.99 indicating excellent consistency of the data correlations [26].

5

Fig. 4. Ternary phase diagram for water (1) þ DEM (2) þ MIBK (3) system at 298.15 K, (*) feed composition; (,) experimental data; (B) NRTL model; (△) UNIQUAC model. (a) Complete phase diagram; (b) points in water phase.

gIi xIi ¼ gIIi xIIi where gIi and gIIi are the activity coefficients of component i in the water phase and solvent phase, respectively. xIi and xIIi are the mole fractions of component i in the water phase and solvent phase, respectively. The NRTL model is presented as follows

P j lngi ¼ P

tji Gji xj

k Gki xk

þ

X j

xG P j ij k Gkj xk

P

xk tkj Gkj k xk Gkj

!

k tij  P

(6)

With:

  gij  gjj  bij Gij ¼ exp  aij tij ; aij ¼ aji ; tij ¼ aij þ ¼ RT T 

The UNIQUAC model is given by 3.3. Thermodynamic modeling Aspen Plus offers a variety of models and physical methods to choose from, laying the foundation for accurate regression of physical data. This paper uses Aspen Plus V10, software and selects NRTL and UNIQUAC model to regression the data. In this model, the LLE of the ternary system water (1) þ DEM (2) þ solvents (3) are described by

lnti ¼ ln "

∅i z q ∅ X þ q ln i þ l  i xl xi 2 i ∅i i xi j j j

þ qi 1  ln

 X qt X P j ij ∅j tji  j

With:

j

k qk tkj

# (7)

6

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

Fig. 5. Ternary phase diagram for water (1) þ DEM (2) þ MIBK (3) system at 308.15 K, (*) feed composition; (,) experimental data; (B) NRTL model; (△) UNIQUAC model. (a) Complete phase diagram; (b) points in water phase.

Fig. 6. Ternary phase diagram for water (1) þ DEM (2) þ MIBK (3) system at 318.15 K, (*) feed composition; (,) experimental data; (B) NRTL model; (△) UNIQUAC model. (a) Complete phase diagram; (b) points in water phase.

  X b z li ¼ ðri  qi Þ  ðri  1Þ; t ti ¼ qi tij ; tij ¼ exp  aij þ ij 2 T 

 uij  ujj ;  ¼ exp  RT

Table 4 Solubility data in mole fraction for MTBE-water systems measured at 298.15 K under 101.3 KPa and comparison with literature data.a T/K

where i, j, k represents the components; gi represent the activity coefficient of component i; xi is the mole fraction of component; aij represent the nonrandomness of the NRTL model, which was fixed at 0.3; Parameters gij represent the intermolecular attractive energy (J$mol1), individually, and gij ¼ gji; qi and ri are van der Waals surface and surface area parameters of a component for the UNIQUAC model, and listed in Table 7; z is the coordination number fixed to 10; Øi and qi are the segment fraction and area fraction; uij is the interaction energy of the molecular pair ij, uijsuji, and its value is determined by the measured data. The objective function (OF) is calculated to get the regression interaction parameters of the above thermodynamic model, as disclosed below [27,28].

OF ¼

M X 2 X 3  X

exp

xijk  xcal ijk

2

(8)

k¼1 j¼1 i¼1

where wcal and wexp refer to the calculated and experimental composition of components; subscripts k, j and i denote the tie-

MTBE in the water

water in MTBT

xI3

xlit

xII1

xlit

298.15

0.0066

0.0508

308.15

0.0060

318.15

0.0057

0.0079 0.0058 0.0096 0.0064 0.0062 0.0055

0.0511 0.0586 0.0544 0.0511 0.0596 0.0532

[15] [16] [17] [15] [16] [15]

0.0584 0.0611

[15] [16] [17] [15] [16] [15]

a

Standard uncertainties u are u(T) ¼ 0.1 K, u(p) ¼ 1.5 kPa, 298.15 K: u(xI3) ¼ 0.0007, u(xII1) ¼ 0.0006; 308.15 K: u(xI3) ¼ 0.0005, u(xII1) ¼ 0.0006; 318.15 K: I u(x3) ¼ 0.0006, u(xII1 ) ¼ 0.0006.

line, phase and components respectively; M refers to the quantity of tie lines. The obtained binary interaction parameters of both models are summarized in Table 8. The correlated results using NRTL and UNIQUAC models for these two ternary systems are also plotted in Figs. 1e6. The root means square deviation (RMSD) and absolute average relative deviation (AARD) are obtained by calculating the difference between the experimental value and the simulated value and is used to evaluate the correlation effect of the liquid-liquid equilibrium data. The formula is as follows [29]:

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

7

Table 5 Solubility data in mole fraction for MIBK-water systems measured at 298.15, 308.15, and 318.15 K under 101.3 KPa and comparison with literature data.a T/K

MIBK in the water

water in MIBK

xI3

xlit

xII1

xlit

298.15

0.0032

0.0973

308.15

0.0030

318.15

0.0027

0.0033 0.0031 0.0031 0.0029 0.0031 0.0027 0.0028

0.1010 0.0992 0.0992 0.1112 0.1195 0.1176 0.1373

[18] [19] [20] [18] [19] [18] [19]

0.1135 0.1217

[18] [19] [20] [18] [19] [18] [19]

a Standard uncertainties u are u(T) ¼ 0.1 K, u(p) ¼ 1.5 kPa, 298.15 K: u(xI3) ¼ 0.0005, u(xII1) ¼ 0.0006; 308.15 K: u(xI3) ¼ 0.0005, u(xII1) ¼ 0.0006; 318.15 K: I u(x3) ¼ 0.0006, u(xII1) ¼ 0.0006.

Fig. 8. Experimental separation factor versus mole fraction of DEM in the solvents phase at 298.15, 308.15 and 318.15 K under atmospheric pressure, MTBE: (-) 298.15 K, (C) 308.15 K, (:) 318.15 K; MIBK: (,) 298.15 K, (B) 308.15 K, (△) 318.15 K.

Table 6 Parameters of Othmer-Tobias and Bachman Equations for water þ DEM þ solvents systems at 298.15, 308.15 and 318.15 K in atmospheric pressure.a Solvent

MTBE

MIBK a

Fig. 7. Comparison of our experimental datas with literature datas: (a) the water-MTBE two-phase system; (b) the water-MIBK two-phase system.

T/K

298.15 308.15 318.15 298.15 308.15 318.15

Othmer-Tobias

Bachman equation 2

a1

b1

R

7.5590 5.4617 7.5900 2.5577 2.3474 2.3443

35.4120 26.2510 37.3940 12.7460 11.8500 11.9340

0.9964 0.9981 0.9912 0.9986 0.9980 0.9966

a2

b2

R2

0.0053 0.0066 0.0045 0.0095 0.0094 0.0090

0.9881 0.9885 0.9904 0.9884 0.9889 0.9894

0.9918 0.9913 0.9908 0.9986 0.9982 0.9980

R2 is correlation coefficient.

Fig. 9. Othmer-Tobias plots for ternary systems water þ DEM þ solvents (MTBE and MIBK) at 298.15, 308.15 and 318.15 K under atmospheric pressure, MTBE: (-) 298.15 K, (C) 308.15 K, (:) 318.15 K; MIBK: (,) 298.15 K, (B) 308.15 K, (△) 318.15 K.

8

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

Fig. 10. Bachman plots for ternary systems water þ DEM þ solvents (MTBE and MIBK) at 298.15, 308.15 and 318.15 K under atmospheric pressure, MTBE: (-) 298.15 K, (C) 308.15 K, (:) 318.15 K; MIBK: (,) 298.15 K, (B) 308.15 K, (△) 318.15 K.

RMSD ¼

8  2 91=2 > exp > > M X 2 X 3 = > : k¼1

j¼1 i¼1

(9)

> ;

6M

Table 7 UNIQUAC structural parameters (r and q)a. Component

r

q

water DEM MTBE MIBK

0.9200 4.3131 4.0678 4.5967

1.3997 3.7960 3.6320 3.9560

a

Taken from Aspen Plus physical properties databanks.

Fig. 11. NRTL binary parameter miscibility boundary for the tenary system of water (1) þ DEM (2) þ MTBE (3) at 298.15 K.

 !  exp  M X 2 X 3 xijk  xcal 1 X ijk  AARD ¼ 6M xexp ijk k¼1 j¼1 i¼1

(10)

As showed in Table 8, The value of RMSD was less than or equal to 0.002, which indicated that there was a good agreement between NRTL and UNIQUAC models and the measured LLE values. Simultaneously, it can be seen that between the calculated and experimental data showed a nice coincidence in Figs. 1e6. However, Aspen as a regression parameter tool makes it impossible to visually express the correlation of phase equilibrium. Therefore, the stability of all solutions found in the correlation of phase equilibrium is checked [30]. In this work, using a graphical user interface (GUI) written in MatLab software code systematically tests for consistent results in NRTL or UNIQUAC correlations of LLE data for ternary systems [31]. For example, Figs. 11 and 12 show the

Table 8 Binary interaction parameters of NRTL and UNIQUAC models for water (1) þ DEM (2) þ solvent (3) system at different temperatures. T/K

i-j

NRTL parameters gij-gjj

a

water (1) þ DEM (2) þ MTBE (3) 298.15 1e2 10212.24 1e3 9807.39 2e3 1994.87 308.15 1e2 7993.23 1e3 10772.44 2e3 4799.22 318.15 1e2 6375.79 1e3 11320.84 2e3 5249.38 water (1) þ DEM (2) þ MIBK (3) 298.15 1e2 8183.08 1e3 11788.82 2e3 4784.92 308.15 1e2 8501.66 1e3 12198.70 2e3 4211.68 318.15 1e2 9057.65 1e3 12817.85 2e3 3837.90 a

The unit of parameters is J/mol.

RMSD

AARD

gji-giia

a

3485.54 5563.67 185.33 4461.13 5100.96 6092.14 4561.17 5309.31 3781.97

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

0.0002

0.0019

0.0011

0.0024

0.0008

0.0023

2867.60 4720.39 7521.39 3951.85 4080.59 4056.59 3849.19 4151.38 3761.25

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

0.0006

0.0039

0.0007

0.0037

0.0007

0.0027

UNIQUAC parameters uij-ujj

a

uij-ujj

RMSD

AARD

a

665.59 470.18 30785.20 84.13 740.93 1018.45 1474.15 781.88 2005.92

5112.23 5327.15 1947.74 4843.82 4756.89 951.70 6228.98 4886.22 674.35

0.0013

0.0034

0.0005

0.0024

0.0004

0.0018

16.89 665.38 1445.65 463.53 850.74 233.58 475.63 932.91 532.76

4345.85 4015.14 1868.13 4001.60 3602.62 103.69 4097.30 3635.58 964.36

0.0004

0.0018

0.0006

0.0028

0.0006

0.0039

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

consistency of the parameters of the LLE data for the ternary system {water (1) þ DEM(2) þ MTBE(3)} obtained at 298.15 K by the description presented in this section. It is observed that, as shown in Fig. 11, only 1e3 are partially miscible, and the calculated connection line is consistent with the GM/RT surface obtained by the calculation parameters as shown in Fig. 12. Fig. 12bee shows

9

cross-section connections #5 and #9 along the two specific experiments and calculations (the number increases with the mole fraction of the (2)-component) as shown in the sample. All connections were calculated and tested and a common tangent between the conjugated liquids was obtained. These numbers again show the consistency between the experimental line and the NRTL

Fig. 12. Calculated GM/RT surface and experimental LLE tie lines for the water (1) þ DEM (2) þ MTBE (3) system at 298.15 K: (a) 3D representation (b) sectional plane in the direction defined by the calculated ternary tie-line #5; (c) sectional plane in the direction defined by the experimental ternary tie-line #5; (d) sectional plane in the direction defined by the calculated ternary tie-line #9; (e) sectional plane in the direction defined by the experimental ternary tie-line #9.

10

Q. Li et al. / Fluid Phase Equilibria 505 (2020) 112353

regression parameters of the ternary system. 4. Conclusions LLE values of water þ DEM þ MTBE and water þ DEM þ MIBK systems were studied in 298.15, 308.15, and 318.15 K under 101.3 Kpa. The results indicated that MTBE and MIBK showed extraction capacity for DEM extraction from water solution. The distribution coefficients and selectivity values were reported. Consistency tests were carried out on the measured experimental data using Othmer-Tobias and Bachman equations. The results show that the experimental data has good thermodynamic consistency. With the Aspen Plus software, the experimental data were correlated by NRTL and UNIQUAC thermodynamic model and were used to regress the binary interaction parameters. Using the model parameters obtained by regression, the phase equilibrium data of the ternary system was fitted and regression, and the RMSD of the regression data and the experimental values were both less than 0.002. According to the Gibbs cut plane test, the reliability of checking binary interaction parameters using a graphical user interface is derived from the GM/RT surface containing all experimental connection lines and NRTL binary parameter boundaries. Experimental LLE data and associated binary interaction parameters can provide basic data for the simulation and design of the separation process. References [1] B. Lehrheuer, F. Hoppe, K.A. Heufer, S. Jacobs, H. Minwegen, J. Klankermaer, B. Heuser, S. Pischinger, Diethoxymethane as tailor-made fuel for gasoline controlled autoignition, Proc. Combution Inst. 37 (2019) 4691e4698. € € [2] L.C. KrOger, M. DOtgen, D. Firaha, W.A. Kopp, K. Leonhard, Ab initio kinetics

[3]

[4] [5]

[6]

[7]

[8]

[9] [10] [11]

predictions for H-atom abstraction from diethoxymethane by hydrogen, methyl, and ethyl radicals and the subsequent unimolecular reactions, Proc. Combust. Inst. 37 (2019) 275e282. M.X. Zhu, W.L. Fan, Y. Xu, Q.Y. Zhou, 1,1-Diethoxymethane and methanethiol as age markers in Chinese roasted-sesame-like aroma and flavour type liquor, Eur. Food Res. Technol. 242 (2016) 1985e1992. C.H. Zhang, J.N. He, Y.L. Li, P. Li, Ignition delay times and chemical kinetics of diethoxymethane/O2/Ar mixtures, Fuel 154 (2015) 346e351. B. Jia, K. Xin, L.P. Wang, Y.M. Yu, Q.S. Li, Experiments and thermodynamic models for ternary liquid-liquid equilibrium systems of diethoxymethane þ ethanol þ water system at different temperatures, J. Mol. Liq. 242 (2017) 907e912. B. Jia, K. Xin, T.F. Yang, J.S. Yu, Y.M. Yu, Q.S. Li, Measurement and thermodynamic modeling of ternary (liquid þ liquid) equilibrium for extraction of ethanol from diethoxymethane solution with different solvents, J. Chem. Thermodyn. 111 (2017) 1e6. L.L. zhang, Z.H. Liao, C.F. Zhu, Y.M. Yu, Q.S. Li, Determination and correlation of liquidliquid equilibria data for ternary system isopropyl acetate þ isopropanol þ water at different temperatures, J. Chem. Eng. Data 64 (2019) 972e978. X.L. Meng, X.W. Liu, J. Gao, Liquid-liquid equilibrium for lsobutyl acetate þ lsobutyl alcohol þ lmidazolium-based lonic liquids at 298.15 and 308.15 K, J. Chem. Eng. Data 64 (2019) 778e783. D.F. Othmer, P.E. Tobias, The line correlation, Ind. Eng. Chem. 34 (1942) 693e700. I. Bachman, Tie lines in ternary liquid systems, Ind. Eng. Chem., Anal. Ed. 12 (1940) 38e39. H. Renon, J.M. Prausnitz, Local compositions in thermodynamic excess

functions for liquid mixtures, AIChE J. 14 (1968) 135e144. [12] D.S. Abrams, J.M. Prausnitz, Statistical thermodynamics of liquid mixtures: a new expression for the excess gibbs energy of partly or completely miscible systems, AIChE J. 21 (1975) 116e128. [13] L.P. Wang, S.S. Zhou, P. Li, Measurement and thermodynamic models for ternary liquid-liquid equilibrium systems water þ polyoxymethylene dimethyl ethers þ 4-methyl-2-pentanol at different temperatures, J. Chem. Eng. Data 63 (2018) 3074e3082. [14] C. Yang, H. Liu, C.F. Zhu, M.D. Shi, G.Y. He, Q.S. Li, Measurement and correlation of ternary (liquid þ liquid) equilibria for separation of cyclohexanone from water via isophorone or mesityl oxide, J. Chem. Eng. Data 63 (2018) 178e186. [15] JCGM, 100:2008 GUM 1995 with Minor Corrections, Evaluation of Measurement Data-Guide to the Expression of Uncertainty in Measurement, JCGM, 2008, pp. 1e120. [16] P. Konieczka, J. Namiesnik, Estimating uncertainty in analytical procedures based on chromatographic techniques, J. Chromatogr. A 1217 (2010) 882e891.  ska, G. Siedlewicz, K. Kornowska, J. Kumirska, [17] M. Borecka, A. Białk-Bielin P. Stepnowski, K. Pazdro, A new approach for the estimation of expanded uncertainty of results of an analyticalmethod developed for determining antibiotics in seawater using solid-phase extraction disks and liquid chromatography coupled with tandem mass spectrometry technique, J. Chromatogr. A 1304 (2013) 138e146. [18] J.A. Alkandary, A.S. Aljimaz, M.S. Fandary, M.A. Fahim, Liquideliquid equilibria of water þ MTBE þ reformate, Fluid Phase Equilib. 181e188 (2001) 131e138. [19] A. Arce, A. Blanco, M. Blanco, A. Soto, I. Vidal, Liquideliquid equilibria of water þ methanol þ (MTBE or TAME) mixtures, Can. Chem. Eng. 72 (1994) 935e938. [20] H.X. Zhang, T.G. Wang, Measurement and correlation of liquid-liquid Equilibrium data for water þ acetic acid þ methyl tert-butyl ether þ NaCl, J. Chem. Eng. Data 54 (2009) 945e949. [21] C.F. Yang, Y. Qian, J.W. Guo, J.R. Chen, J.P. Peng, Liquidliquid equilibria for the ternary system methyl isobutyl ketone þ m-benzenediol þ water, J. Chem. Eng. Data 59 (2014) 3324e3328. [22] C.F. Yang, Y.B. Jiang, L.J. Zhang, Y. Qian, Liquid-liquid equilibria for the ternary system methyl isobutyl ketone þ water þ hydroquinone, J. Chem. Eng. Data 51 (2006) 2107e2109. [23] C.F. Yang, Y. Qian, Y.B. Jiang, L.J. Zhang, Liquideliquid equilibria for the quaternary system methyl isobutyl ketoneewaterephenolehydroquinone, Fluid Phase Equilib. 258 (2007) 73e77. [24] Y.S. Zhang, B.K. Chen, S.Y. Yang, Liquideliquid equilibrium for the ternary systems (methyl isobutyl ketone þ quinoline or isoquinoline þ water) at 298.15, 318.15, and 338.15 K, J. Chem. Eng. Data 63 (2018) 2758e2765. [25] H. Liu, X.M. Yu, P. Cui, B. Jia, Y.M. Yu, Q.S. Li, Liquidliquid equilibria for the ternary systems water þ cyclohexanol þ methyl isobutyl carbinol and water þ cyclohexanol þ methyl isobutyl ketone at different temperatures, J. Chem. Eng. Data 63 (2018) 95e101. [26] Z.J. Wang, K. Liu, P. Wang, D.M. Xu, J. Gao, L.Z. Zhang, M. Li, Y.L. Wang, Liquideliquid equilibrium measurements and correlation for ternary systems (buty acetate þ1-butanol þ ethylene glycoi/1,3-popanediol/ethanolamine) at 298.15 K, J. Chem. Eng. Data 64 (2019) 3244e3249. [27] C.F. Zhu, Y.M. Yu, Determination and correlation of liquideliquid equilibria data for water þ cyclohexanol þ (mesityl oxide, toluene, and p-xylene) ternary systems at different Temperatures, J. Chem. Eng. Data 63 (2018) 1190e1197. [28] Q.S. Li, B. Jia, L.P. Wang, Liquid-liquid equilibrium for ternary systems of water þ 2,2,3,3-tetrafluoro-1-propanol þ isopropyl ether/tert-butyl methyl ether at 298.2, 308.2 K, J. Chem. Thermodyn. 124 (2018) 32e37. [29] Y.S. Zhang, B.K. Chen, S.Y. Yang, Liquideliquid equilibrium for the ternary systems (methyl isobutyl ketone þ quinoline or isoquinoline þ water) at 298.15, 318.15, and 338.15 K, J. Chem. Eng. Data 63 (2018) 2758e2765. [30] A. Marcilla, J.A. Reyes-Labarta, M.M. Olaya, Should we trust all the published LLE correlation parameters in phase equilibria? Necessity of their assessment prior to publication, Fluid Phase Equilib. 433 (2017) 243e252. [31] J. A. Reyes-Labarta, Graphical User Interface (GUI) for the Representation of GM Surfaces (Using the NRTL Model) and Curves, Including Tie-Lines and Hessian Matrix, Institutional Repository of the University of Alicante (RUA) http://hdl.handle.net/10045/51725