Experiments and COSMO-SAC Modeling of Methyl Isobutyl Ketone +

Article Cite This: J. Chem. Eng. Data 2019, 64, 3521−3534

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Experiments and COSMO-SAC Modeling of Methyl Isobutyl Ketone + Dimethylphenols + Water Mixtures Shuai Shen, Yun Chen,* and Meiling Jiang Department of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, 510640, P. R. China

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S Supporting Information *

ABSTRACT: Methyl isobutyl ketone (MIBK) had been successfully employed to extract phenols from coal gasification wastewater since 2009, and it has been proved to be an excellent extraction solvent. In this work, the liquid−liquid equilibrium (LLE) data were measured for the ternary systems MIBK + 2,3-/3,4-/3,5dimethylphenol + water from 298.15 to 343.15 K. High partition coefficient and separation factor indicated that MIBK could extract dimethylphenols from an aqueous solution well. The Hand equation and the Bachman equation were used for testing the consistency of the determined tie-line data. The NRTL and UNIQUAC thermodynamic models were utilized to correlate these measured LLE data, and their root-mean-square deviations did not exceed 0.5%. The conductor-like screening model for segment activity coefficient was employed to predict the LLE data. Results showed that the prediction values are close to the measured data.

1. INTRODUCTION Currently, the coal gasification industry is still an indispensable way for people to achieve energy.1 However, the coal gasification industries also produce a large amount of wastewater while coal has been converted into various products.2 These wastewaters contain a large amount of toxic phenolic substances. The low-concentration phenolic wastewater discharged without further treatment has serious impact on the health of human beings, animals, and plants.3,4 Many researchers studied to extract phenol, cresol, and dihydroxybenzene from coal gasification wastewater,5−8 but there have been few papers to focus on solvent extraction of dimethylphenol. Dimethylphenol is one of the various harmful phenols in coal gasification wastewater. Although it is not as much as phenol, cresol in wastewater, its use is very extensive.9 For example, dimethylphenol mixtures are common materials as disinfectants, textile auxiliaries, solvents, and flotation agent. Pure dimethylphenols are used for pharmaceuticals and synthesizing dyes or fragrances.10 Therefore, the removal of dimethylphenol from coal gasification wastewater can protect the environment and save water resource. There are many methods to reduce phenolic materials from wastewater including distillation, absorption, advanced oxidation, biodegradation, photocatalytic oxidation, and membrane filtration.11−14 However, these methods have different disadvantages in treatment on coal gasification wastewater.15 Solvent extraction is a common chemical technique for the removal and recovery of phenols, and this method achieves good results.16−19 At the same time, liquid−liquid extraction has many advantages such as ease of running automatically, large throughput, low operating cost, and high extraction efficiency.20−22 Although there are some alcohols or ester solvents used to extract phenols,23 they have some deficiencies, © 2019 American Chemical Society

such as high solubility in water, strong volatility, low extracting efficiency, and so on. Methyl isobutyl ketone (MIBK) is a very promising extractant that can effectively avoid these shortcomings.24−26 Thus, adopting MIBK as a solvent to extract dimethylphenols from aqueous solution would be a nice way. There are six isomeric forms of dimethylphenols. The concentration of 2,4-dimethylphenol, 2,5-dimethylphenol, and 2,6-dimethylphenol is very low in coal gasification wastewater.9,10 Therefore, this work will focus on extracting 2,3-dimethylphenol, 3,4-dimethylphenol, and 3,5-dimethylphenol from wastewater. Lin and Sandler27 proposed a new model of conductor-like screening model for segment activity coefficient (COSMOSAC) based on the Conductor-like Screening Model28 and the Conductor-like Screening Model for Real Solvents.29,30 Subsequently, a modified COSMO-SAC model31 was explored by Sandler where the interaction of hydrogen bond was better described. The COSMO-SAC model supposes that a molecule is made up of surface segments, and the accumulation of the activity coefficient of each segment forms that of a solute molecule. Subsequently, phase behavior, partition coefficient, solubility, and other thermodynamic properties can be obtained according to the activity factor of the solute molecule. The model was utilized to calculate liquid−liquid equilibrium (LLE) of 278 binary mixtures by Chieh-Ming Hsieh et al.32 The key step to COSMO-SAC prediction is to obtain a σprofile (p(σ)) of each pure substance.33 Meanwhile, Lin et al. divided the σ-profile (p(σ)) of the pure substance into the σprofile of a non-hydrogen bond atom pnhb(σ) and the σ-profile Received: April 6, 2019 Accepted: July 1, 2019 Published: July 11, 2019 3521

DOI: 10.1021/acs.jced.9b00300 J. Chem. Eng. Data 2019, 64, 3521−3534

Journal of Chemical & Engineering Data

Article

Table 1. Source and Purity of the Materials Studieda component

CAS reg. no.

source

mass fraction

purification

analysis method

methanol 2,3-dimethylphenol 3,4-dimethylphenol 3,5-dimethylphenol benzyl alcohol n-butyl acetate MIBK

67-56-1 526-75-0 95-65-8 108-68-9 100-51-6 123-86-4 108-10-1

Yonghua Chemical Technology Co., Ltd. Xiya Reagent Co., Ltd. Xiya Reagent Co., Ltd. Xiya Reagent Co., Ltd. Xiya Reagent Co., Ltd. Xiya Reagent Co., Ltd. Chinasun Specialty Products Co., Ltd.

≥0.999 ≥0.990 ≥0.980 ≥0.990 ≥0.995 ≥0.995 ≥0.990

none none none none none none none

GCa GCa GCa GCa GCa GCa GCa

a

Gas chromatography.

Table 2. Experimental LLE Data (Mass Fraction) for Ternary System MIBK (1) + 2,3-Dimethylphenol (2) + Water (3) at 298.15−343.15 K under 101.3 kPaa aqueous phase

organic phase

T/K

wA1

wA2

wA3

wO1

wO2

wO3

P

S

298.15

0.01546 0.01463 0.01360 0.01302 0.01228 0.01058 0.00947 0.00905 0.01257 0.01156 0.00982 0.00938 0.00884 0.00809 0.00710 0.00603 0.01129 0.01057 0.01005 0.00862 0.00788 0.00678 0.00630 0.00521 0.01053 0.00985 0.00830 0.00766 0.00713 0.00658 0.00590 0.00523 0.01030 0.00865 0.00816 0.00755 0.00699 0.00638 0.00571 0.00470

0.00033 0.00055 0.00082 0.00113 0.00148 0.00185 0.00217 0.00251 0.00047 0.00079 0.00121 0.00154 0.00195 0.00236 0.00265 0.00324 0.00046 0.00085 0.00128 0.00173 0.00214 0.00260 0.00293 0.00348 0.00051 0.00096 0.00143 0.00187 0.00224 0.00265 0.00312 0.00369 0.00101 0.00144 0.00195 0.00238 0.00285 0.00327 0.00373 0.00467

0.98422 0.98482 0.98558 0.98585 0.98624 0.98757 0.98837 0.98843 0.98697 0.98765 0.98897 0.98908 0.98921 0.98955 0.99025 0.99072 0.98825 0.98858 0.98867 0.98965 0.98998 0.99063 0.99076 0.99131 0.98896 0.98919 0.99027 0.99047 0.99064 0.99077 0.99098 0.99107 0.98869 0.98992 0.98989 0.99008 0.99016 0.99035 0.99055 0.99062

0.85636 0.80185 0.75822 0.71620 0.68065 0.64541 0.60446 0.56350 0.82718 0.77417 0.72051 0.68335 0.64494 0.60037 0.56849 0.50461 0.84128 0.76515 0.71138 0.66967 0.62336 0.58286 0.55812 0.50333 0.83289 0.76677 0.71766 0.67223 0.64285 0.60264 0.56056 0.50322 0.80258 0.73988 0.68173 0.63348 0.59059 0.54234 0.50112 0.44382

0.11060 0.16388 0.20687 0.24836 0.28284 0.31736 0.35722 0.39764 0.13802 0.19032 0.24316 0.27869 0.31639 0.35989 0.39031 0.45287 0.12351 0.19791 0.25103 0.29197 0.33677 0.37685 0.40024 0.45326 0.13030 0.19620 0.24410 0.28864 0.31657 0.35541 0.39681 0.45014 0.15984 0.22088 0.27824 0.32236 0.36380 0.41084 0.45026 0.50096

0.03304 0.03427 0.03491 0.03544 0.03651 0.03722 0.03833 0.03887 0.03480 0.03551 0.03633 0.03797 0.03867 0.03975 0.04120 0.04252 0.03521 0.03694 0.03760 0.03836 0.03987 0.04029 0.04164 0.04341 0.03681 0.03703 0.03824 0.03913 0.04059 0.04196 0.04263 0.04664 0.03758 0.03924 0.04002 0.04417 0.04561 0.04682 0.04862 0.05523

339.7 300.4 252.2 219.5 190.6 171.4 165.0 158.2 294.8 241.3 201.4 180.8 162.1 152.5 147.3 139.6 265.6 232.8 195.6 168.7 157.0 145.0 136.4 130.1 255.5 204.5 170.3 154.6 141.4 134.0 127.3 122.0 158.4 153.9 142.5 135.6 127.7 125.7 120.6 107.2

10 119 8633 7121 6105 5149 4548 4254 4023 8361 6713 5483 4711 4147 3798 3541 3252 7456 6230 5144 4351 3899 3566 3245 2971 6864 5462 4411 3913 3451 3165 2960 2591 4167 3883 3525 3039 2773 2658 2457 1923

313.15

323.15

333.15

343.15

a

Standard uncertainties (u) are u(T) = 0.1 K, u(p) = 1 kPa, u(wA1 ) = 0.0004, u(wA2 ) = 0.0020, u(wA3 ) = 0.0028, u(wO1 ) = 0.0153, u(wO2 ) = 0.0149, and u(wO3 ) = 0.0005.

pure substance, and others were non-hydrogen bond atoms.34 A detailed description of COSMO-SAC model was published in refs.27,31,32,35,36

of a hydrogen bond atom phb(σ). Hydrogen-bonding atoms were defined as nitrogen, oxygen, fluorine atoms, and hydrogen atoms combined with oxygen, nitrogen, fluorine atoms in a 3522



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organic phase

T/K

wA1

wA2

wA3

wO1

wO2

wO3

P

S

298.15

0.01509 0.01449 0.01373 0.01239 0.01205 0.01159 0.00983 0.00954 0.01225 0.01142 0.00945 0.00878 0.00842 0.00795 0.00728 0.00539 0.01048 0.01016 0.00963 0.00919 0.00824 0.00745 0.00680 0.00500 0.01186 0.01134 0.00877 0.00834 0.00793 0.00746 0.00679 0.00588 0.01022 0.00820 0.00779 0.00741 0.00671 0.00594 0.00533 0.00469

0.00031 0.00052 0.00064 0.00090 0.00111 0.00132 0.00161 0.00196 0.00035 0.00057 0.00077 0.00108 0.00136 0.00173 0.00219 0.00268 0.00037 0.00057 0.00078 0.00108 0.00154 0.00203 0.00242 0.00289 0.00040 0.00070 0.00103 0.00138 0.00169 0.00207 0.00248 0.00294 0.00048 0.00097 0.00134 0.00184 0.00232 0.00261 0.00305 0.00362

0.98460 0.98499 0.98563 0.98671 0.98685 0.98709 0.98857 0.98850 0.98741 0.98800 0.98978 0.99013 0.99022 0.99032 0.99054 0.99192 0.98915 0.98926 0.98958 0.98973 0.99023 0.99052 0.99078 0.99211 0.98775 0.98797 0.99020 0.99028 0.99038 0.99047 0.99073 0.99118 0.98930 0.99083 0.99087 0.99075 0.99097 0.99145 0.99162 0.99168

0.85426 0.80988 0.77224 0.73175 0.68991 0.64941 0.60843 0.56078 0.85560 0.80090 0.75618 0.71089 0.67088 0.62355 0.57565 0.51096 0.85225 0.80165 0.75787 0.70765 0.65720 0.60887 0.55778 0.48287 0.83803 0.77953 0.72338 0.67715 0.63423 0.59302 0.56281 0.50595 0.81688 0.74062 0.68765 0.63855 0.59683 0.55660 0.49264 0.42708

0.11235 0.15543 0.18975 0.22903 0.26948 0.30882 0.34865 0.39524 0.10811 0.16129 0.20514 0.24935 0.28919 0.33617 0.38189 0.44220 0.10826 0.15818 0.19886 0.24825 0.29810 0.34605 0.39576 0.46678 0.11026 0.17363 0.22913 0.27366 0.31464 0.35411 0.38847 0.43875 0.12564 0.20891 0.25918 0.30491 0.34451 0.38274 0.44323 0.50803

0.03339 0.03469 0.03801 0.03922 0.04061 0.04177 0.04293 0.04398 0.03629 0.03781 0.03868 0.03976 0.03994 0.04029 0.04245 0.04683 0.03949 0.04017 0.04327 0.04410 0.04471 0.04508 0.04646 0.05034 0.05171 0.04684 0.04749 0.04919 0.05113 0.05286 0.04873 0.05530 0.05748 0.05047 0.05317 0.05654 0.05866 0.06066 0.06413 0.06489

361.4 298.6 295.8 254.9 243.7 233.6 216.8 202.0 312.8 281.8 266.5 230.5 212.7 194.3 174.6 164.9 296.3 275.7 254.3 229.8 194.2 170.4 163.5 161.5 278.8 249.7 222.5 198.1 186.1 171.2 156.5 149.2 261.0 215.7 194.0 166.0 148.6 146.9 145.4 140.2

10 659 8480 7670 6413 5923 5521 4992 4540 8511 7363 6819 5740 5275 4776 4073 3493 7423 6789 5815 5158 4301 3744 3486 3182 5325 5267 4639 3989 3605 3207 3182 2675 4492 4235 3616 2909 2511 2401 2248 2143

313.15

323.15

333.15

343.15

a

Standard uncertainties (u) are u(T) = 0.1 K, u(p) = 1 kPa, u(wA1 ) = 0.0004, u(wA2 ) = 0.0001, u(wA3 ) = 0.0028, u(wO1 ) = 0.0161, u(wO2 ) = 0.0157, and u(wO3 ) = 0.0010.

2. EXPERIMENTAL SECTION 2.1. Materials. Table 1 shows the sources, basic specifications, and analytical method of the reagents in this study. All these chemicals were used as purchased. The purities of all the above materials were checked and confirmed by gas chromatography. Double-distilled water was directly used without any further purification in this study. 2.2. Experiments. The apparatuses used in the experiment were 100 mL glass balance kettle, constant temperature water bath, magnetic stirring apparatus, and electronic scales. A 100 mL volumetric glass balance vessel was used to perform LLE experiments.23 First of all, quantified MIBK, dimethylphenol, and double-distilled water were separately put into balance container and then the equilibrium vessel was mixed for 2 h thoroughly with a magnetic stirrer. During the process, the

In order to explore the effect of MIBK on the extraction of dimethylphenols at different temperatures, the extraction works were implemented at 298.15, 313.15, 323.15, 333.15, and 343.15 K under barometric pressure. The LLE data of ternary systems MIBK + 2,3-/3,4-/3,5-dimethylphenol + water were verified for their consistency by the Bachman and Hand equations. The LLE phase behavior was correlated with the NRTL37 and UNIQUAC38 activity coefficient models. In addition, the related interaction energy parameters were calculated and could be employed to simulate the dimethylphenols extraction process. Influence of extraction temperature on the separation factor and partition coefficient was investigated in this study. Meanwhile, all ternary systems were calculated by the COSMO-SAC equation to obtain the corresponding phase equilibria data.31,39 3523



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organic phase

T/K

wA1

wA2

wA3

wO1

wO2

wO3

P

S

298.15

0.01650 0.01555 0.01384 0.01387 0.01104 0.01055 0.01026 0.00936 0.01243 0.01122 0.01030 0.00942 0.00898 0.00832 0.00762 0.00680 0.01135 0.01033 0.00962 0.00917 0.00897 0.00831 0.00735 0.00651 0.00956 0.00895 0.00846 0.00804 0.00754 0.00715 0.00647 0.00587 0.00871 0.00837 0.00803 0.00767 0.00690 0.00659 0.00620 0.00547

0.00035 0.00047 0.00066 0.00083 0.00112 0.00146 0.00165 0.00194 0.00022 0.00042 0.00060 0.00078 0.00099 0.00121 0.00163 0.00208 0.00024 0.00047 0.00068 0.00095 0.00132 0.00165 0.00198 0.00239 0.00034 0.00061 0.00095 0.00124 0.00153 0.00193 0.00239 0.00289 0.00052 0.00082 0.00113 0.00140 0.00181 0.00214 0.00252 0.00308

0.98315 0.98398 0.98550 0.98530 0.98785 0.98799 0.98809 0.98869 0.98735 0.98836 0.98910 0.98979 0.99003 0.99048 0.99075 0.99112 0.98841 0.98920 0.98970 0.98987 0.98971 0.99004 0.99067 0.99110 0.99010 0.99044 0.99059 0.99072 0.99093 0.99092 0.99114 0.99125 0.99076 0.99081 0.99084 0.99092 0.99129 0.99128 0.99127 0.99144

0.84790 0.80876 0.76306 0.71908 0.66620 0.62566 0.59279 0.55176 0.88945 0.83557 0.78869 0.75141 0.70866 0.66851 0.62325 0.56972 0.88430 0.83092 0.78702 0.74017 0.69233 0.64698 0.60610 0.54252 0.86487 0.82164 0.76413 0.71989 0.67328 0.61775 0.54865 0.48833 0.83155 0.78481 0.73752 0.70242 0.65606 0.62168 0.58076 0.54582

0.11599 0.14838 0.19231 0.23617 0.28895 0.32906 0.36103 0.40156 0.06827 0.12032 0.16407 0.19895 0.24076 0.28021 0.32475 0.37634 0.06985 0.12261 0.16624 0.21290 0.26026 0.30465 0.34437 0.40631 0.08839 0.13228 0.18732 0.23074 0.27621 0.32925 0.39185 0.45053 0.11869 0.16355 0.20842 0.24211 0.28766 0.32051 0.35915 0.39232

0.03611 0.04286 0.04463 0.04475 0.04484 0.04528 0.04619 0.04668 0.04228 0.04411 0.04724 0.04964 0.05057 0.05128 0.05199 0.05394 0.04584 0.04648 0.04674 0.04693 0.04741 0.04837 0.04953 0.05117 0.04674 0.04608 0.04855 0.04937 0.05051 0.05300 0.05950 0.06113 0.04976 0.05164 0.05406 0.05547 0.05628 0.05781 0.06009 0.06186

334.1 316.7 293.4 283.7 258.3 225.0 219.2 206.7 311.1 284.4 272.9 254.4 242.7 232.4 199.7 180.8 289.7 260.2 244.7 222.9 196.7 184.7 174.0 170.3 259.3 216.6 197.7 186.6 180.8 170.7 164.3 156.1 227.8 199.2 185.0 172.4 159.0 150.0 142.3 127.2

9094 7270 6479 6246 5689 4910 4689 4377 7264 6373 5715 5072 4751 4488 3805 3322 6246 5538 5181 4703 4108 3781 3480 3299 5493 4656 4034 3745 3547 3192 2737 2532 4536 3822 3391 3079 2801 2572 2348 2039

313.15

323.15

333.15

343.15

a

Standard uncertainties (u) are u(T) = 0.1 K, u(p) = 1 kPa, u(wA1 ) = 0.0004, u(wA2 ) = 0.0001, u(wA3 ) = 0.0032. u(wO1 ) = 0.0171, u(wO2 ) = 0.0166, and u(wO3 ) = 0.0009.

detector and a 30 m × 0.32 mm × 0.25 μm DB-5MS capillary column. The internal standard method is adopted and n-butyl acetate and benzyl alcohol were selected as internal standard substances for MIBK and dimethylphenols, respectively. The weighed internal standard substance in the samples was also recorded carefully in order to calculate the content of each substance. The oven temperature of gas chromatography was controlled by temperature-program. The start column temperature was 313.15 K and kept for 2 min; accordingly, it was raised to 433.15 K at 15 K·min−1 and held for 2 min. The detecting temperature and injecting temperature were 543.15 and 523.15 K, separately.15,40 All samples were mixed with methanol to be diluted before performing gas chromatography. High-purity nitrogen was adopted as the carrier gas whose flow rate was fixed at 30 cm3·min−1. The water content in the

sampling port of organic phase and the sampling port of aqueous phase were linked with a rubber stopper to eliminate solvent evaporation from equilibria system. Subsequently, the container was placed into a thermostatic bath at a set temperature for 18 h. When phase equilibrium was formed, the samples in the two layers were drawn by injectors and measured by electronic balance (AUW220D, SHIMADZU) with a precision of 0.1 mg, respectively. In subsequent experiments, the weight of deionized water and MIBK would be fixed, then the mass of dimethylphenol increases continuously, and the two-phase region could be covered as much as possible.15,40 2.3. Analysis. The concentrations of MIBK and dimethylphenols were measured by gas chromatography (model 6820, Agilent Technology) assembled with a flame ionization 3524



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nonaqueous phase was titrated by a Karl Fischer titrator and that in the aqueous phase was used to deduct the mass fractions of MIBK and dimethylphenol from unity. To guarantee the repeatability and accuracy of these experiments in this work, every sample was measured three times to make the standard deviation lower than 0.002.

3. RESULTS AND DISCUSSION 3.1. Measured Data. The LLE data for ternary systems MIBK + dimethylphenols + water were obtained at different temperatures under barometric pressure. All experimental data are shown in Tables 2−4. Among them, wA1 , wA2 , and wA3 denote the mass concentration of MIBK, dimethylphenols, and water in the aqueous phase, respectively. wO1 , wO2 , and wO3 represent the mass concentration of MIBK, dimethylphenols, and water in organic phase, respectively. Uncertainties calculated by reference method are given as footnotes in the corresponding tables.41,42 Meanwhile, the ternary phase diagrams are plotted in Figures 1−3. As observed in Tables 2−4, the contents of MIBK and dimethylphenol in the aqueous phase are very low, which indicate that MIBK can effectively extract dimethylphenols from water. In addition, it could be found that the content of dimethylphenols in aqueous layer increases with increasing temperature. As the temperature increases, it becomes more difficult for MIBK to extract dimethylphenols from water. At the same time, as dimethylphenol is continuously added, the extractant in the solution is gradually reduced. According to the phase diagram, all data listed on the two flanks of the ternary phase diagram were the content of the compounds in the aqueous and organic phases, and a two-phase region with a wider range could be beneficial for extraction unit. Partition coefficient (P) and separation factor (S) are very important in determining whether it is feasible to extract dimethylphenols with MIBK. Their calculation equations are expressed as follows P=

w2O w2A

S=P

(1)

w3A w3O

(2)

where w2 and w3 are defined as mass concentrations of dimethylphenol and water, respectively. The superscripts A and O represent the aqueous layer and organic layer, respectively. Figures 4−6 illustrate the change rules of P and S for dimethylphenols in aqueous layer at varying temperatures. Obviously, P and S are much higher than 1. It is feasible to use MIBK as an extractant to separate dimethylphenols from coal gasification wastewater. When wA2 is the same, the values of P and S decrease significantly as the experimental temperature increases. It indicates that the temperature has an important influence on the extraction experiment results, and the lower the temperature, the better the extraction efficiency of MIBK on dimethylphenol is. One possible reason for extraction ability of MIBK on dimethylphenol reducing sharply with the elevating temperature is that the hydrogen network of water was broken. With the increase of wA2 , the D and S of MIBK on dimethylphenol decrease rapidly when wA2 is lower than 0.0015 and decrease slowly when wA2 is larger than 0.0015 at the measured temperature. When the dimethylphenol in water rises from a very low concentration to a high concentration, the extraction efficiency of MIBK is greatly

Figure 1. Ternary diagram for MIBK (1) + 2,3-dimethylphenol (2) + water (3) at (a) 298.15 K, (b) 313.15 K, (c) 323.15 K, (d) 333.15 K, and (e) 343.15 K; □, experimental data; △, calculated data from the NRTL model; ×, calculated data from the UNIQUAC model; ●, feed point; ☆, calculated data from the COSMO-SAC model.

reduced, but when the concentration of dimethylphenol further increases at higher concentration, the extraction efficiency of MIBK decreases slightly. Generally, partition coefficients and separation factors reduce with rising extraction temperature or concentration of dimethylphenols in the aqueous phase, but overall, their values are relatively high. Therefore, it is very promising to treat high concentration dimethylphenols-containing wastewater with MIBK. Moreover, 3525



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Figure 2. Ternary diagram for MIBK (1) + 3,4-dimethylphenol (2) + water (3) at (a) 298.15, (b) 313.15, (c) 323.15, (d) 333.15, and (e) 343.15 K; □, experimental data; △, calculated data from the NRTL model; ×, calculated data from the UNIQUAC model; ●, feed point; ☆, calculated data from the COSMO-SAC model.

Figure 3. Ternary diagram for MIBK (1) + 3,5-dimethylphenol (2) + water (3) at (a) 298.15, (b) 313.15, (c) 323.15, (d) 333.15, and (e) 343.15 K; □, experimental data; △, calculated data from the NRTL model; ×, calculated data from the UNIQUAC model; ●, feed point; ☆, calculated data from the COSMO-SAC model.

the solubility of MIBK and water is also measured, and there are lots of available references reporting the method of solubility measurements in aqueous solutions.43−46 The measured solubility data of MIBK and water in this work are close to the literature data,47,48 and the detailed comparison is showed in Table S1. The Hand49 and Bachman equations50 were employed to examine whether the LLE data of ternary systems met the

thermodynamic consistency, which was expressed as eqs 3 and 4

3526

ij w A yz ij w O yz lnjjj 2O zzz = a1 + b1 lnjjjj 2A zzzz jw z k 1 { k w3 {

(3) DOI: 10.1021/acs.jced.9b00300 J. Chem. Eng. Data 2019, 64, 3521−3534


Article

Figure 4. Partition coefficient (P) and separation factor (S) of 2,3dimethylphenol versus its mass fraction in aqueous phase at different temperatures.


(4)

function, the coefficients in both models can be obtained and the calculated method was as follows

ij w O yz w1O = a 2 + b2jjjj 1A zzzz k w3 {

3

where w1, w2, and w3 represent the mass concentrations of MIBK, dimethylphenol, and water in the mixture, respectively; a1, b1 and a2, b2 are the related parameters of the Hand and Bachman equations, respectively. Table 5 lists a1, b1 and a2, b2, and the R2 after the LLE data were regressed at different temperatures. Figures 7−9 show the relevant fitted curves with these two equations. The R2 of both equations are very close to 1, and all data show an evident linear relationship at different temperatures. Obviously, the experimental tie-line data are very coincident. 3.2. Data Correlation. All measured data of these ternary mixtures were associated with the NRTL and UNIQUAC equations. The data were correlated and plotted in Figures 1−3. From the figures, that little difference between the correlation data and the experimental data show that correlation results are consistent with the measured LLE data. Meanwhile, the interaction energy parameters are achieved for the designing and optimizing of treatment on coal gasification wastewater. The nonrandomness parameter αij in the NRTL model was generally 0.2 or 0.3. The structural parameters r and q of the materials in the UNIQUAC model are listed in Table 6 from the ref 51. To minimize the objective

OF =

2

n

∑ ∑ ∑ (wijkexp − wijkcal)2 (5)

i=1 j=1 k=1 exp

cal

in which n is the amount of tie-lines. w and w represent the determined mass concentration and fitted mass concentration, respectively. The subscripts i, j, and k are defined as the compounds, phase type, and determined data points, respectively. The detailed process of both equations has been described in many previous articles4,51 and is not repeated here. The interaction energy parameters correlated by both thermodynamic models are included in Table 7. The parameters for the NRTL model are calculated as bij = (gij − gjj)/R and bji = (gji − gii)/R. UNIQUAC binary interaction parameters is bij = (uij − ujj)/R and bji = (uji − uii)/R. They can be applied to predict the binary endpoint data of any two of MIBK, dimethylphenol, and water. 3.3. COSMO-SAC Model Prediction. Although both activity coefficient models can correlate the phase equilibrium data adequately, they require more parameters and original experimental data to correlate accurately. In addition, the liquid−liquid phase equilibrium experiment takes a lot of time and effort to complete, and improper operation is also prone to errors, which make the operator very cautious. However, the 3527



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Figure 7. Hand and Bachman plots for the experimental LLE data of ternary system MIBK (1) + 2,3-dimethylphenol (2) + water (3), (a) Hand equation and (b) Bachman equations.

Table 5. Fitting Parameters of the Hand and Bachman Equations for MIBK (1) + 2,3-Dimethylphenol/3,4-Dimethylphenol/ 3,5-Dimethylphenol (2) + Water (3) between 298.15 and 343.15 K Hand T/K

a1

298.15 313.15 323.15 333.15 343.15

4.33956 4.60621 4.74381 1.56518 6.20987

298.15 313.15 323.15 333.15 343.15

5.34702 5.21245 5.24535 5.17766 5.43278

298.15 313.15 323.15 333.15 343.15

5.66424 5.56194 5.38577 5.84517 5.02186

b1

Bachman R2

a2

MIBK (1) + 2,3-Dimethylphenol (2) + Water (3) 0.79579 0.99428 0.00766 0.84314 0.98666 0.00501 0.86961 0.99536 0.00427 0.85532 0.98752 0.00321 1.13771 0.99800 0.00178 MIBK (1) + 3,4-Dimethylphenol (2) + Water (3) 0.92160 0.99461 0.01258 0.91498 0.99748 0.00618 0.92450 0.99039 0.00582 0.92166 0.99850 0.02230 0.96690 0.97530 0.01110 MIBK (1) + 3,5-Dimethylphenol (2) + Water (3) 0.96180 0.99843 0.04420 0.96493 0.99851 −0.00092 0.95437 0.99686 0.00344 1.03285 0.98781 −0.08023 0.92602 0.99888 −0.02868 3528

b2

R2

0.97545 0.98143 0.98313 0.98536 0.98708

1.00000 0.99999 1.00000 0.99999 1.00000

0.96999 0.98106 0.98261 0.94976 0.96907

0.99963 0.99998 0.99984 0.99751 0.99874

0.91420 0.98629 0.98497 1.09967 1.05646

0.99759 0.99821 1.00000 0.99664 0.99007



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Table 6. The UNIQUAC Structural Parameters

COSMO-SAC model predicts LLE experiments requiring only initial feed point data, which saves the experiment time and difficulty. Previously, many papers reported prediction of LLE experiments using COSMO-SAC model and achieved good results.32,35,52 On the basis of COSMO-SAC theory, the activity factor of solute i in solvent S (γi/S) can be calculated by ln γi/S =

*res − ΔGi/i *res ΔGi/S RT

SG + ln γi/S

component

r

q

water MIBK 2,3-dimethylphenol 3,4-dimethylphenol 3,5-dimethylphenol

0.9200 4.5959 5.0217 5.0217 5.0217

1.4000 3.9520 3.8160 3.8160 3.8160

pi (σ ) =

A i (σ ) Ai

(7)

The σ-profile for mixture is calculated from

(6)

where ΔG*res denotes the restoring free energy from the chemical potential of segment in the COSMO-RS model, γSG i/S is calculated by the Staverman−Guggenheim combinatorial term. The most important procedure in the COSMO-SAC model prediction is to calculate the COSMO file for each pure substance, and the corresponding σ-profile would be obtained. In the COSMO solving process, the ideal screening charge density distribution of molecular surface is computed through dividing the total surface into several segments. Each segment has individual charge density and area, and the geometric charge density distribution in three dimensions is projected onto a two-dimensional histogram named the σ-profile p(σ). It indicates the possibility of having a surface segment with screening charge density σ

pS (σ ) =

∑i xiAi pi (σ ) ∑i xiAi

(8)

where Ai(σ) represents the superficial area of segments with charge density σ. Ai and xi are the overall superficial area and mole fraction of components i, respectively. Furthermore, σ-profile consists of hydrogen bonding σprofile (p hb (σ)) and non-hydrogen bonding σ-profile (pnhb(σ)). pi (σ ) = pihb (σ ) + pinhb (σ )

(9)

pihb (σ ) = pHB (σ ) × (Aihb(σ )/Ai ) 3529

(10)



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Table 7. Binary Interaction Parameters Calculated from the NRTL or UNIQUAC Models for All Ternary Systems components T/K

i−j

298.15

1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3

313.15

323.15

333.15

343.15

298.15

313.15

323.15

333.15

343.15

298.15

313.15

323.15

333.15

343.15

1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3 1−2 1−3 2−3

UNIQUAC bij/K

NRTL bji/K

MIBK (1) + 2,3-Dimethylphenol (2) + Water (3) −165.24 212.75 208.11 −360.05 −103.07 106.71 −110.45 −156.77 −71.54 −245.85 253.10 531.03 −357.52 −131.27 105.19 −113.33 −164.39 −126.41 158.68 0.43 −435.29 −351.52 −148.87 109.26 −88.97 −147.65 −61.12 −222.51 248.98 570.10 −348.19 −164.90 98.87 −111.66 −168.23 −147.72 400.27 −2182.32 −710.59 −359.94 −174.74 120.54 −163.67 −164.42 −201.94 MIBK (1) + 3,4-Dimethylphenol (2) + Water (3) −209.11 209.50 386.98 5744.80 1052.55 119.77 −7.72 −268.43 −219.54 121.01 7.28 −300.74 5796.10 1027.26 93.28 −61.96 −193.88 −84.63 −57.44 134.04 −1.47 5803.93 1024.51 70.94 −24.05 −255.35 −149.61 −41.24 127.63 1027.99 5861.94 1000.82 −10.55 −81.41 −212.66 −168.32 −210.80 226.93 556.19 5848.81 995.53 −25.89 3.75 −294.39 −244.19 MIBK (1) + 3,5-Dimethylphenol (2) + Water (3) 219.25 −121.79 −718.51 −342.11 −109.82 78.83 −38.82 −203.66 −121.36 329.34 −272.71 −1008.52 −285.51 −167.11 44.29 −26.40 −190.05 −162.35 −187.22 199.74 494.86 −260.18 −186.89 8.96 −72.96 −225.91 −136.61 −185.35 186.89 420.66 −277.61 −199.06 29.28 17.43 −313.25 −263.40 −26.96 115.89 892.35 −262.25 −218.15 5.03 45.03 −313.11 −334.72

pinhb (σ ) = [1 − pHB (σ )] × (Aihb(σ )/Ai ) + (Ainhb(σ )/Ai )

ij σ 2 yz pHB (σ ) = 1 − expjjj 2 zzz j 2σ z k 0 {

bij/K

bji/K

αij

−454.91 1589.70 1938.58 −597.61 1741.20 2079.32 −111.26 1829.06 1917.78 −628.47 1922.25 2181.05 743.40 1987.79 2236.97

0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2

−471.30 1593.77 2196.75 −126.56 1787.30 2013.40 −290.16 1877.41 2206.03 −724.99 2007.03 2270.72 −577.25 2098.98 2422.36

0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2

206.16 1617.94 1837.07 381.58 1837.45 1737.36 −503.80 1930.34 2237.74 −443.61 2012.24 2425.95 −701.48 2106.50 2448.52

0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2

The screening charge densities are averaged to get the apparent charge density ÄÅ ÉÑ Å Ñ r 2r 2 d 2 ∑n σn* 2n eff 2 expÅÅÅÅ−fdecay 2 mn 2 ÑÑÑÑ rn + reff r r + ÅÇ ÑÖ eff n σm = ÅÄÅ ÑÉÑ 2 rn 2reff 2 d ∑n 2 expÅÅÅÅ−fdecay 2 mn 2 ÑÑÑÑ rn + reff 2 rn + reff Ñ ÅÇ (13) Ö

(11)

(

(12)

)

(

(

where pHB(σ) is a Gaussian-type function which describes the possibility to form a hydrogen bond, and σ0 = 0.007 e/Å2. nhb Ahb i (σ) and Ai (σ) are the surface area of hydrogen bonding segments and non-hydrogen bonding segments.

)

)

where σ and σ* refer to the charge density after and before the average calculation, respectively. rn and reff are the radius and 3530



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effective radius of segment n, respectively. dmn denotes the distance between segment m and segment n, and the empirical parameter fdecay is 3.57.31 The restoring free energy is calculated by ΔGi*/ jres RT

nhb,hb

=n

∑ ∑ pis (σms )ln(Γ sj(σms )) s

σm

(14)

where n denotes the sum figure of all fragments in a molecule; subscript j is either a pure component or a mixture; superscript s and t mentioned below can be either a hydrogen bonding part or non-hydrogen bonding part, respectively. The activity coefficient (Γ) of segment m with a charge density of σm is obtained from ÄÅ ÅÅ nhb,hb Å t t ln Γ j(σm) = −lnÅÅÅÅ ∑ ∑ pjs (σns)Γtj(σns) ÅÅ s σ n ÅÇÅ ÉÑ ij −ΔW (σmt , σns) yzÑÑÑÑ zzÑÑ expjjj zzÑÑ j RT k {ÑÑÑÖ (15)

Figure 11. Hydrogen bonding σ-profiles (phb(σ)) of the chemicals used in this work.

where the segment-exchange energy is computed by the following equation 1.5 y ij 0.3aeff zz t z(σ + σns)2 − chb(σmt , σns) ΔW (σmt , σns) = fpol jjj j 2ε zz m 0 { k

(σmt − σns)2

(16)

where f pol = 0.6916 and ε0 is the dielectric constant of vacuum. t s l o o chb s = t = hb, σm × σn < 0 chb(σmt , σns) = m o o 0 otherwise n

(17)

The LLE data of ternary systems MIBK + dimethylphenols + water were calculated by the COSMO-SAC equations. The σ-profiles of MIBK, dimethylphenols, and water are plotted in Figure 10. The chemical formulas of these substances contain oxygen atoms with strong electronegativity, so there are strong peaks in the hydrogen bond acceptor region (σ > 0.0084 e/ Å2). The phb(σ) and pnhb(σ) of all materials are plotted in Figure 11 and 12. As seen from the figures, there are two strong peaks in the σ-profile of water between −0.02 and

Figure 12. Non-hydrogen bonding σ-profiles (pnhb(σ)) of the chemicals used in this work.

−0.0084 e/Å2. It shows that the water molecule has two hydrogen donors. Several other compounds have only one strong peak in the 0.0084−0.02 e/Å2, and they have only one hydrogen bond acceptor. Among them, MIBK has a stronger peak than water. As a result, MIBK is more likely to form a hydrogen bond with dimethylphenols, and this facilitates extracting dimethylphenols from the aqueous phase. In the vicinity of 0 e/Å2, the peaks formed by the alkyl chain of MIBK and the peaks by the benzene ring of dimethylphenols are very strong. They will interact through van der Waals forces, so MIBK has a stronger effect on dimethylphenols. The LLE data of COSMO-SAC model prediction and feed point data are drawn in Figures 1−3. As shown in the figures, the data predicted by the COSMO-SAC model are very matched with the investigated data, so it is feasible to use this model to predict the phase behavior. 3.4. rmsd Values of NRTL, UNIQUAC, and COSMOSAC Models. The root-mean-square deviation (rmsd) between the determined data and the simulated data was often used in liquid-phase extraction studies to assess the accuracy of the calculated data. The calculation method of rmsd is as follows

Figure 10. σ-Profiles (p(σ)) of the chemicals used in this work. 3531


É1/2 ÅÄÅ 3 exp cal 2 Ñ ÅÅ ∑i = 1 ∑2j = 1 ∑nk = 1 (wijk ) ÑÑÑÑ − wijk ÅÅ ÑÑ RMSD = ÅÅ ÑÑ ÅÅ 6n ÑÑ ÅÅÇ ÑÖ


Article

prove that the measured data was in good agreement. That R2 values were almost equal to 1 indicates that the experimental data were consistent. The tie-line data could be predicted by giving the feed point data into the COSMO-SAC model and the experimental determination could be omitted. All rmsd values did not exceed 3.43%. Therefore, MIBK was an excellent solvent to extract dimethylphenols from wastewater, and the COSMO-SAC model could be employed to predict MIBK + dimethylphenols + water mixture well. To a certain extent, the tie-line data predicted by COSMO-SAC model could be applied to simulate the extraction process of removing dimethylphenols from coal gasification wastewater.

(18)

in which cal and exp are the abbreviations of the calculated and experimental data, respectively; n, i, j, and k were expressed as described above. Table 8 lists the rmsd values between the Table 8. rmsd Values between Experimental Data and Calculated Data rmsd/% T/K

NRTL

UNIQUAC

■

COSMO-SAC

MIBK (1) + 2,3-Dimethylphenol (2) + Water (3) 298.15 0.238 0.240 1.882 313.15 0.200 0.220 2.370 323.15 0.248 0.247 2.914 333.15 0.268 0.288 3.412 343.15 0.204 0.222 3.429 MIBK (1) + 3,4-Dimethylphenol (2) + Water (3) 298.15 0.197 0.198 1.745 313.15 0.162 0.160 2.438 323.15 0.261 0.264 2.382 333.15 0.227 0.238 1.887 343.15 0.465 0.483 1.470 MIBK (1) + 3,5-Dimethylphenol (2) + Water (3) 298.15 0.264 0.256 0.977 313.15 0.127 0.156 0.954 323.15 0.138 0.147 1.454 s333.15 0.344 0.368 1.752 343.15 0.171 0.162 1.585

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00300. Comparisons of experimental solubilities in mass fraction between MIBK and water with those reported in literature at different temperatures under 101.3 kPa (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: + 86 13632384249. ORCID

Yun Chen: 0000-0001-5784-2602 Notes

The authors declare no competing financial interest.

■

determined data and the data calculated from the NRTL, UNIQUAC, and COSMO-SAC equations at different temperatures. All rmsd values of three models are less than 3.5%, so this means the calculated data are accurate. As seen from Table 8, the rmsd values of the first two models are very similar and small, which means that both models can correlate with the measured data well. Because the rmsd values of the NRTL and UNIQUAC models are less than 0.5%, both models can correlate the experimental data better than COSMO-SAC. However, the rmsd values of COSMO-SAC model are only up to 3.429%, so this model is also available. Although the accuracy of the data calculated by the COSMO-SAC model is still insufficient compared with the other activity coefficient models, it is also close to the researched LLE data. In addition, the rmsd values are between 0.95 and 3.43%. It showed that a good consistency between the investigated data and the calculated data was achieved for the research objects. Therefore, the COSMO-SAC model can be suitable to describe the LLE behavior.

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4. CONCLUSIONS MIBK was adopted as an extractant to reduce the content of dimethylphenols in the wastewater in this study. The partition coefficient and separation factor of dimethylphenols extracted by MIBK from wastewater were very high. It indicated that dimethylphenols can be efficiently separated from wastewater. All measured tie-line data were associated by the NRTL and UNIQUAC models to obtain the corresponding parameters and simulated data. Those rmsd values were lower than 0.5%. The results showed that both models could correlate with the LLE data well. The Hand and Bachman equations were used to 3532



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Experiments and COSMO-SAC Modeling of Methyl Isobutyl Ketone +

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