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Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Liquid−Liquid Equilibrium for Ternary Systems of Polyoxymethylene Dimethyl Ethers + o‑Xylene + Water at 293.15 K Xiangjun Li, Huaiyuan Tian, and Dianhua Liu*

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State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China ABSTRACT: Polyoxymethylene dimethyl ethers (PODEn) are excellent diesel blending components which can eliminate exhaust gas emissions compared to conventional diesel. During the production process of PODEn from methanol and formaldehyde solution, the most important key is to find an appropriate phenomenon for the separation of water and formaldehyde from PODE3−6 in advance. In this work, ternary liquid−liquid equilibrium (LLE) data were determined at T = 293.15 K under atmospheric pressure for the following systems: PODE1 + o-xylene (OX) + water, PODE2 + OX + water, PODE3 + OX + water, and PODE4 + OX + water. Hand and Othmer−Tobias equations were utilized to confirm consistency of the experimental LLE data. The NRTL and UNIQUAC activity coefficient models were applied to correlate the experimental LLE data, and the corresponding binary interaction parameters and LLE phase diagrams were obtained. The results indicate that both NRTL and UNIQUAC models agree well with the experimental LLE data, whereas the NRTL model gives a better agreement than the UNIQUAC model for ternary (PODE1−4 + o-xylene + water) systems.

1. INTRODUCTION With the increasing consumption of petroleum fuels, the environmental condition and energy demand are becoming much more serious. Compared to gasoline engines, diesel engines are widely used in industries and transportation because of higher thermal efficiency. Meanwhile, the exhaust gas emissions and soot formation have been aggravated as the consumption of diesel. While considering to reduce the emissions of diesel engines, oxygenated compounds such as methanol or dimethyl ether are known to improve diesel combustion performance when they are added to diesel fuels.1 However, these compounds cannot be blended directly with diesel fuels without the modification of engines. Polyoxymethylene dimethyl ethers (PODEn, CH3O(CH2O)CH3) are oligomers that are capped with methoxy and methyl and composed of CH2O units, which have received extensive attention for their excellent properties as clean diesel additives.2−4 PODE3−4 are considered to be optimum diesel additive components among PODEn compounds because they can be used in diesel engines without distinct change of engine structure.5 The production process of PODEn can be classified into two main categories: one is the anhydrous process of methylal with trioxane (or paraformaldehyde) and the other is the waterbearing process of methanol with formaldehyde.6 Because of high cost of raw materials, methylal and trioxane are mostly used in laboratory research and are not suitable for large-scale production. Therefore, the production of PODEn from methanol and formaldehyde solution has a better development prospect compared with that from methylal and trioxane.7 However, it is difficult to separate the product that is synthesized from methanol and formaldehyde solution in the © XXXX American Chemical Society

presence of water and high-content formaldehyde, which can result in hydrolysis of PODEn under high temperature and acid conditions and the formation of flocculated formaldehyde polymers. To avoid separation problems, water and most formaldehyde need to be separated with PODEn and methanol before distillation. Therefore, the solvent extraction process was well suited for the separation of PODEn, which was synthesized from methanol and formaldehyde solution. In a proper solvent extraction process, water and high-content formaldehyde could be recycled in aqueous phase, and the other compounds could be concentrated in organic phase. Experimental liquid−liquid equilibrium (LLE) data are valuable for the solvent extraction process. A reliable thermodynamic model is important for ternary systems investigation. Compared with the study of PODEn synthesis reaction, the study on separation of PODEn is relatively less. Kuhnert et al.8 researched ternary systems (formaldehyde + water + methylal) and (formaldehyde + methanol + methylal) and a quaternary system (formaldehyde + water + methanol + methylal) and found that the experimental results were consistent with the predicted results. Zhuang et al.9 measured the LLE data for ternary systems (PODE1−4 + p-xylene + water) and found that the UNIQUAC model showed a better correlation for ternary systems than the NRTL model. There are few available literature studies about LLE data on these ternary systems. In this work, we measured four groups of ternary systems water + PODE1−4 + o-xylene LLE data at 293.15 K under Received: October 4, 2018 Accepted: March 29, 2019

A

DOI: 10.1021/acs.jced.8b00891 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Supplier and Mass Fraction of the Chemical Reagents compound

supplier

purification method

mass fraction

purity analysis method

methanol methylal (PODE1) paraformaldehyde o-xylene sulfuric acid ethanol sodium sulfite thymolphthalein One-component Karl Fischer reagent titration 2,4,6-trioxaheptane (PODE2) 2,4,6,8-tetraoxanonane (PODE3) 2,4,6,8,10-pentaoxaundecane (PODE4)

Shanghai Titan Scientific Co., Ltd Shanghai Titan Scientific Co., Ltd Shanghai Titan Scientific Co., Ltd Shanghai Titan Scientific Co., Ltd Shanghai Titan Scientific Co., Ltd Shanghai LingFeng Reagent Co., Ltd Sinopharm Chemical Reagent Co., Ltd Sinopharm Chemical Reagent Co., Ltd Sinopharm Chemical Reagent Co., Ltd self-made self-made self-made

none none none none none none none none none distillation distillation distillation

0.995 0.995 0.950 0.995 0.980 0.995 0.980 0.990

GCa GCa TAc GCa KFb GCa

0.980 0.965 0.960

GCa GCa GCa

CAS 67-56-4 109-87-5 30525-89-4 95-47-6 7664-93-9 64-17-5 7757-83-7 125-20-2 52365-46-5 628-90-0 13353-03-2 13352-75-5

a

Gas chromatograph. bKarl Fischer (KF) reagent for volumetric one-component KF titration. cTitrimetric analysis.

After the temperature reached stability, the extractant and product were added into the flask in a certain ratio, and the magnetic stirring took a certain time. Preliminary sample analysis was conducted every 1 h until the analysis error of two adjacent results reached small, which can be considered to be balanced. In this work, there were almost no effects on sample composition with stirring time more than 1 h. Therefore, the stirring time was set to 2 h to ensure that the extraction procedure reaches complete equilibrium. When the equilibrium status of extraction was achieved, two phases appeared in the flask. The top phase named organic phase and the bottom phase named aqueous phase were sampled with two syringes and then analyzed three times by gas chromatography and KF titration (detailed information can be seen in Section 2.3). 2.3. Analytical Methods. The water content of samples was determined by volumetric one-component Karl Fischer titration method. The Karl Fischer standard curve of water should be made every day before sample analysis in order to reduce the analysis error. The standard uncertainty for the water content of an analyzed sample should be kept within 0.0005. Formaldehyde is analyzed using titration by the sodium sulfite method.10 All samples taken in the experiments were analyzed using gas chromatography by applying an internal standard, and ethanol was selected as the internal standard reagent. The accuracy of the mass fractions was determined about within 0.005. An elite-wax fused silica capillary column (30 m × 0.32 mm × 0.25 μm) with a flame ionization detector was used in a PerkinElmer Clarus 580 gas chromatograph. High-purity nitrogen was used as a carrier gas with a constant flow rate at 40 mL min−1. The injector and detector temperatures were both maintained at 523.15 K, and the column was heated according to the following program: an initial temperature of 318.15 K for 3 min, a temperature ramp of 20 K min−1, and a final temperature of 493.15 K for 3 min. In the process of internal standard preparation experiment, all reagents were weighed on a BEL electronic analytical balance (mark-720) with an accuracy of ±0.0001 g. In all the other experiments, weighing was operated by using BH-300 with ±0.005 g.

atmospheric pressure. The NRTL and UNIQUAC activity coefficient models were chosen to correlate the LLE data, and regression of thermodynamic model parameters were used to evaluate the accuracy of the experimental LLE data.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The reagents methanol, paraformaldehyde, methylal, o-xylene, and sulfuric acid were purchased from Shanghai Titan Scientific Co., Ltd and used without further purification. Anhydrous ethanol was supplied by Shanghai LingFeng Reagent Co., Ltd., and sodium sulfite, thymolphthalein, and one-component Karl Fischer Titration Reagent were supplied by Sinopharm Chemical Reagent Co., Ltd. Deionized water was self-prepared, and the product containing PODE1−4 was synthesized from methanol formaldehyde solution in laboratory, and these impurities could be quantified by an internal standard method. o-xylene and the product were used as the extraction agent and extraction raw material, respectively. The detailed information of used reagents in the experiment was listed in Table 1. 2.2. Apparatus and Procedure. The synthesis procedure of PODEn was carried out in a fixed bed reactor using a macroporous strong acid cation exchange resin as the catalyst and methanol and formaldehyde solution as the raw material. The reaction product consists of methanol, formaldehyde, water, methylal, and PODE2−6. The reaction product resulted from fixed bed reactor was sent to the first distillation tower to obtain the light components, which consist of methylal and methanol. The pure methanol and methylal can be obtained by simple distillation. The bottom mixture of the first distillation tower was sent to the extraction tank and intimately mixed with the extractant (o-xylene). Then, the organic phase consisted of PODE2−6 and o-xylene was transported to the following distillation tower. The higher purity of each PODEn (n ≥ 2) and extractant can be obtained by multiple rectification operations. It should be noted that the boiling points of PODEn (n > 2) are higher than 156 °C so that it is better to utilize vacuum distillation to separate PODE3−6. The mutual solubility of ternary liquid−liquid equilibria for water + PODE1−4 + o-xylene was measured by analyzing the composition of equilibrated two liquid phases in a thermostated flask. The LLE determination apparatus of this work was similar to that in our previous work.9 The temperature of the experiment was controlled steadily and accurately by a constant temperature circulating water device.

3. RESULTS AND DISCUSSION 3.1. Experimental LLE Data. The mutual solubility data for binary system (o-xylene + water) are presented in Table 2. B



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Table 2. Mutual Solubility Data (Mass Fraction) for Binary System {o-Xylene (1) + Water (2)} at T = 288.15, 293.15, 298.15, and 303.15 K and Pressure p = 101.3 kPaa T/K

W2/10−2 in the organic phase

W1/10−2 in the aqueous phase

288.15 293.15 298.15 303.15

0.0379 0.0407 0.0482 0.0578

0.0190 0.0208 0.0221 0.0240

a

Standard uncertainties u are u(T) = 0.1 K, u(W1) = 0.0003, u(W2) = 0.0005, and u(p) = 1 kPa. (W1 and W2 represent the mass fraction of o-xylene (1) and water (2) in two equilibrium phases, respectively).

The experimental LLE data for the four ternary systems (PODEn + o-xylene + water) were measured at T = 293.15 K under atmospheric pressure. The experimental LLE data are listed in Table 3. As can be seen in Table 3, when the ternary systems reached LLE, the water content in the organic phase was relatively low, whereas the o-xylene content in the aqueous phase was lower than 1% (mass fraction), which indicates that the extraction agent o-xylene can be recovered in subsequent operations. As the addition amount of o-xylene increased, the content of PODE1−4 increased in the organic phase and decreased in the aqueous phase, which confirmed that the increase of o-xylene had benefits on extraction and o-xylene can be used as an effective extractant for our reaction product system.

Figure 1. Distribution ratio of PODEn (DPODE) plotted against the mass fraction of PODEn in the organic phase at T = 293.15 K (■) PODE1, (red ●) PODE2, (blue ▲) PODE3, and (green ▼) PODE4.

The extraction property of distribution ratio D and the selective coefficient S of PODEn and water were calculated according to the LLE experimental data by the following equations and the results are listed in Table 3. The distribution ratio of PODEn as a function of the mass fraction PODEn in the organic phase is shown in Figure 1.

Table 3. Experimental LLE Data (Mass Fraction) and Distribution Coefficients for the Ternary Systems {Water (1) + PODEn (2) + o-Xylene (3)} at T = 293.15 K and Pressure p = 101.3 kPaa water (1) + PODEn (2) + o-xylene (3) organic phase mass fraction (O)

aqueous phase mass fraction (W)

PODEn

WO1

WO2

WO3

WW 1

WW 2

WW 3

DPODE

Dwater

S

PODE1

0.0207 0.0175 0.0153 0.0106 0.0054 0.0025 0.0150 0.0115 0.0102 0.0086 0.0076 0.0068 0.0329 0.0295 0.0226 0.0185 0.0147 0.0092 0.0130 0.0109 0.0094 0.0078 0.0051 0.0029

0.5018 0.4347 0.3733 0.3237 0.2982 0.2682 0.4109 0.3559 0.3277 0.2828 0.2584 0.2450 0.4094 0.3295 0.2691 0.2235 0.2012 0.1801 0.3976 0.3016 0.2666 0.2233 0.1930 0.1717

0.4775 0.5478 0.6114 0.6657 0.6964 0.7293 0.5741 0.6326 0.6621 0.7086 0.7340 0.7482 0.5577 0.6410 0.7083 0.7580 0.7841 0.8107 0.5894 0.6875 0.7240 0.7689 0.8019 0.8254

0.8657 0.8808 0.8902 0.8984 0.9013 0.9067 0.8664 0.8856 0.8955 0.9110 0.9178 0.9245 0.8709 0.8964 0.9082 0.9217 0.9256 0.9332 0.8948 0.9187 0.9236 0.9319 0.9404 0.9444

0.1250 0.1099 0.1002 0.0920 0.0890 0.0840 0.1236 0.1044 0.0948 0.0792 0.0726 0.0655 0.1194 0.0948 0.0820 0.0690 0.0649 0.0571 0.0960 0.0721 0.0668 0.0586 0.0500 0.0459

0.0093 0.0093 0.0096 0.0096 0.0097 0.0093 0.0100 0.0100 0.0097 0.0098 0.0096 0.0100 0.0097 0.0088 0.0098 0.0093 0.0095 0.0097 0.0092 0.0092 0.0096 0.0095 0.0096 0.0097

4.014 3.955 3.726 3.518 3.351 3.193 3.324 3.409 3.457 3.571 3.559 3.740 3.429 3.476 3.282 3.239 3.100 3.154 4.142 4.183 3.991 3.811 3.860 3.741

0.024 0.020 0.017 0.012 0.006 0.003 0.017 0.013 0.011 0.024 0.020 0.017 0.012 0.006 0.003 0.017 0.013 0.011 0.009 0.008 0.007 0.038 0.033 0.025

167.3 199.1 216.8 298.2 559.2 1158.0 192.0 262.5 303.5 378.2 429.8 508.5 90.8 105.6 131.9 161.4 195.2 319.9 285.1 352.6 392.1 455.3 711.8 1218.2

PODE2

PODE3

PODE4

a

Standard uncertainties u are u(T) = 0.1 K, u(W1) = 0.0005, u(W2) = 0.004, u(W3) = 0.005, and u(p) = 1 kPa. (WO1 , WO2 , and WO3 represent the W W equilibrium mass fraction of water (1), PODEn (2), and o-xylene (3) in organic phase, respectively; WW 1 , W2 , and W3 represent the equilibrium mass fraction water (1), PODEn (2), and o-xylene (3) in aqueous phase, respectively). C



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Table 5. Structural Parameters r and q for UNIQUAC Model component

r

q

water PODE1 PODE2 PODE3 PODE4 o-xylene

0.9200 2.9644 3.8827 4.8009 5.7192 4.6579

1.4000 2.7160 3.4960 4.2760 5.0560 3.5360

Figure 2. Hand fitting plot for ternary systems (PODEn + o-xylene + water) at 293.15 K under atmospheric pressure. (■) PODE1, (red ●) PODE2, (blue ▲) PODE3, and (green ▼) PODE4.

Figure 4. Phase diagram for LLE of (PODE1 + o-xylene + water) system at T = 293.15 K under atmospheric pressure: (■ and solid line) experimental data, (blue ● and dash line) calculated data from the NRTL model, and (red ▲ and dot line) calculated data from the UNIQUAC model.

indicating that o-xylene as an extractant is feasible to extract PODEn from aqueous solution. 3.2. Consistency of Experimental Tie-Line Data. The consistency of the investigated ternary experimental tie-line data was evaluated by the Hand11 and the Othmer−Tobias12 correlation equations.

Figure 3. Othmer−Tobias fitting plot for ternary systems (PODEn + o-xylene + water) at 293.15 K under atmospheric pressure. (■) PODE1, (red ●) PODE2, (blue ▲) PODE3, and (green ▼) PODE4.

DPODE = W 2O/W2W

(1)

Dwater = W1O/W1W

(2)

S = DPODE /Dwater

(3)

lg(W 2O/W 3O) = A1 + B1 lg(W2W /W1W )

(4)

ln[(1 − W1W )/W1W ] = A 2 + B2 ln[(1 − W 2O)/W 2O]

(5)

where A1, A2, B1, and B2 denote the constants. The Hand and Othmer−Tobias fitting plots are shown in Figures 2 and 3, respectively. It can be seen that all curves of experimental data show linear relationships. The correlation parameters and corresponding linear correlation coefficient R2 for Hand and Othmer−Tobias correlations are listed in Table 4. The values for R2 are close to 1, indicating that the experimental LLE data are highly consistent with the Hand and Othmer−Tobias

As can be seen in Figure 1, distribution coefficients are independent of concentration at high dilution. The selective coefficients of PODEn are larger than 1, and the distribution coefficient of PODE1−4 varies between 3.10 and 4.18,

Table 4. Hand and Othmer−Tobias Parameters for the Ternary (PODE1−4 + o-Xylene + Water) Systems hand correlation ternary systems water water water water water

+ + + + +

PODE1 PODE2 PODE3 PODE4 PODE4

+ + + + +

o-xylene o-xylene o-xylene o-xylene o-xylene

Othmer−Tobias correlation 2

A1

B1

R

A2

B2

R2

2.0511 0.8072 1.1826 1.2805 1.2805

2.3973 1.1351 1.5234 1.4967 1.4967

0.9949 0.9957 0.9961 0.9957 0.9957

−1.8809 −1.5671 −1.6954 −1.9034 −1.9034

−0.3965 −0.8167 −0.6129 −0.5899 −0.5899

0.9946 0.9975 0.9953 0.9954 0.9954

D



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ÅÄÅ ÑÉ 2 cal y2 Ñ ÅÅi exp ij W exp − W ijk zz ÑÑÑÑ ÅÅjj Tk − Tkcal yzz ijk j zz ÑÑ zz + jjj OF = ∑ ∑ ∑ ÅÅÅjjj zz ÑÑ z jj Å σ σ z ÑÑ Å T W i=1 j=1 k=1 Å ÅÇk { k { ÑÖ 3

2

n

(6)

where Wexp and Wcal are experimental mass fraction and calculated mass fraction, respectively. Subscripts i, j, k, and n refer to components, phases, and tie lines, respectively. Texp and Tcal are experimental temperature and calculated temperature, respectively. σT and σW represent the standard deviations of experimental temperature and mass fraction, respectively. The LLE data calculated by the NRTL and UNIQUAC models for the four ternary systems (PODEn + o-xylene + water) are plotted in ternary diagrams, as shown in Figures 4−7. The root-mean-square deviation (rmsd), used to check the agreement between the experimental LLE data and the calculated data, was calculated by the following equation15,16


É ÄÅ n ÅÅ ∑ ∑3 [(W O,exp − W O,cal)2 ] + [(W W,exp − W W,cal)2 ] ÑÑÑ0.5 ÑÑ Å i i i i ÑÑ rmsd = ÅÅÅÅ k = 1 i = 1 ÑÑ ÅÅ 6 n ÑÑÖ ÅÇ

(7)

WOi

WW i

where and represent the mass fraction of component i in the organic phase (O) and aqueous phase (W), respectively. The superscripts “exp” and “cal” refer to the experimental and calculated mass fraction, and k and n denote the number and total number of tie lines. The rmsd values in the correlation by NRTL and UNIQUAC models along with regressed binary interaction parameters for the ternary systems are shown in Table 6. As can be seen in Table 6, the rmsd values for the ternary systems correlated by NRTL and UNIQUAC models range from 0.0114 to 0.0225 and 0.0063 to 0.0316, respectively. Compared to the regression result of the UNIQUAC model, the deviations of the NRTL model are relatively smaller, which suggests that the NRTL model gives a better agreement for ternary systems (PODEn + o-xylene + water). As can be seen in Figures 4−7, the tie lines of experimental LLE data and all calculated data for the two models show a good coincidence, while the result obtained by the NRTL

equations and the satisfactory reliability of the experimental LLE data. 3.3. LLE Data Correlation. In this work, the experimental LLE data of ternary systems (PODEn + o-xylene + water) were correlated by using the thermodynamic NRTL 13 and UNIQUAC14 models. On the basis of rules of Renon and Prausnitz,13 the values of the nonrandomness α in the NRTL model for binary pairs (water + PODE1−4) and (PODE1−4 + oxylene) were set as 0.3, while those for the binary pairs (water + o-xylene) were set as 0.2. The pure component structural parameters of r (molecular-geometric volume) and q (molecular-geometric surface) in the UNIQUAC model were obtained by the Bondi method, as can be seen in Table 5. The binary interaction parameters of ternary systems in NRTL and UNIQUAC models were obtained by minimizing the objective function via Aspen plus simulation. The equation used in the calculated process was E



Article

Table 6. Interaction Parameters of the NRTL and UNIQUAC Models and rmsd for Ternary Systems (PODEn + o-Xylene + Water) at T = 293.15 K and Pressure p = 101.3 kPa NRTL ternary systems

i−j

bij/K

bij/K

rmsd

bij/K

bij/K

rmsd

water (1) + PODE1 (2) + o-xylene (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

779.69 1657.35 −241.87 715.54 1657.35 −512.12 −5545.70 1657.35 3240.86 1427.01 1657.35 2084.44

156.77 3328.48 919.76 −88.16 3328.48 2538.46 −582.19 3328.48 −7319.23 −479.08 3328.48 −571.80

0.0174

−50.43 −10.62 138.02 109.67 −10.62 329.08 −19.16 −10.62 262.04 −38.74 −10.62 −2849.77

−353.27 −4847.10 −371.00 −544.03 −4847.10 −807.74 −89.84 −4847.10 −446.83 −226.36 −4847.10 223.73

0.0316

water (1) + PODE2 (2) + o-xylene(3)



4. CONCLUSIONS The LLE data for the ternary systems (PODE1 + o-xylene + water), (PODE2 + o-xylene + water), (PODE3 + o-xylene + water), and (PODE4 + o-xylene + water) were measured at T = 293.15 K under atmospheric pressure. The selective coefficients and distribution coefficients of PODE1−4 indicated that o-xylene as an extractant is suitable to extract PODE1−4 from aqueous solution. The regression coefficients of Hand and the Othmer−Tobias correlation equations are close to 1, which demonstrated that a good linear correlation of the LLE experimental data. The NRTL and UNIQUAC models were used to correlate the LLE experimental data, and the corresponding binary interaction parameters for the ternary systems were obtained. The calculated results that are correlated by the NRTL and UNIQUAC models are in good agreement with the results when compared with the LLE experimental data. The NRTL model gives a better agreement than the UNIQUAC model for ternary systems (PODE1−4 + oxylene + water). AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Xiangjun Li: 0000-0003-1562-461X Dianhua Liu: 0000-0002-8528-4983 Funding

This work was financially supported by National Key Research and Development Program of China (no. 2018YFB0604804). Notes

The authors declare no competing financial interest.

■

0.0114

0.0121

0.0225

0.0063

0.0113

0.0153

on Exhaust Emissions. SAE Technical Paper Series, 2001, Vol. 101, Paper No. SAE-2001-01-3632. (2) Wang, Z.; Liu, H.; Zhang, J.; Wang, J.; Shuai, S. Performance, Combustion and Emission Characteristics of a Diesel Engine Fueled with Polyoxymethylene Dimethyl Ethers (PODE3-4)/ Diesel Blends. Energy Procedia 2015, 75, 2337−2344. (3) Liu, H.; Wang, Z.; Zhang, J.; Wang, J.; Shuai, S. Study on combustion and emission characteristics of Polyoxymethylene Dimethyl Ethers/diesel blends in light-duty and heavy-duty diesel engines. Appl. Energy 2017, 185, 1393−1402. (4) Iannuzzi, S. E.; Barro, C.; Boulouchos, K.; Burger, J. Combustion behavior and soot formation/oxidation of oxygenated fuels in a cylindrical constant volume chamber. Fuel 2016, 167, 49−59. (5) Burger, J.; Siegert, M.; Ströfer, E.; Hasse, H. Poly(oxymethylene) dimethyl ethers as components of tailored diesel fuel: Properties, synthesis and purification concepts. Fuel 2010, 89, 3315−3319. (6) Baranowski, C. J.; Bahmanpour, A. M.; Kröcher, O. Catalytic synthesis of polyoxymethylene dimethyl ethers (OME): A review. Appl. Catal., B 2017, 217, 407−420. (7) Schmitz, N.; Ströfer, E.; Burger, J.; Hasse, H. Conceptual Design of a Novel Process for the Production of Poly(oxymethylene) Dimethyl Ethers from Formaldehyde and Methanol. Ind. Eng. Chem. Res. 2017, 56, 11519−11530. (8) Kuhnert, C.; Albert, M.; Breyer, S.; Hahnenstein, I.; Hasse, H.; Maurer, G. Phase Equilibrium in Formaldehyde Containing Multicomponent Mixtures: Experimental Results for Fluid Phase Equilibria of (Formaldehyde + (Water or Methanol) + Methylal)) and (Formaldehyde + Water + Methanol + Methylal) and Comparison with Predictions. Ind. Eng. Chem. Res. 2006, 45, 5155−5164. (9) Zhuang, Z.; Zhang, J.; Liu, X.; Liu, D. Liquid−liquid equilibria for ternary systems polyoxymethylene dimethyl ethers+para-xylene +water. J. Chem. Thermodyn. 2016, 101, 190−198. (10) Walker, J. F., Formaldehyde, 3rd ed.; Reinhold: New York, 1964. (11) Hand, D. B. Dineric distribution. J. Phys. Chem. 1930, 34, 1961−2000. (12) Othmer, D. F.; Tobias, P. E. Liquid -Liquid Extraction Data -Toluene and Acetaldehyde Systems. Ind. Eng. Chem. 1942, 34, 693− 696. (13) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144. (14) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 1975, 21, 116−128. (15) Ghanadzadeh Gilani, H.; Ghanadzadeh Gilani, A.; Shekarsaraee, S.; Uslu, H. (Liquid+liquid) equilibrium data of (water+phosphoric acid+solvents) systems at T=(308.2 and 318.2)K. J. Chem. Thermodyn. 2012, 53, 52−59.

model provided a better description of tie lines for the ternary systems (PODEn + o-xylene + water) at T = 293.15 K under atmospheric pressure. The results show that the NRTL model is more appropriate for the studied ternary systems than the UNIQUAC model.

■

UNIQUAC

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