Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Experimental and Predicted Vapor−Liquid Equilibrium for Diisopropanolamine with m‑Cresol and 2,6-Dimethylphenol at 20.0 kPa Jun Wang,† Jie Ou,† Xueni Sun,† Xiangjun Tong,‡ Ben Gao,† Chunxiang Huang,† Hui Shao,*,† and Yixin Leng*,† †
School of Petrochemical Engineering, Changzhou University, Changzhou City, Jiangsu Province 213143, China China Petroleum Engineering Construction Company East China Design Branch, Qingdao City, Shandong Province 266071, China
‡
ABSTRACT: Measurements of isobaric vapor−liquid equilibrium (VLE) results for binary systems of m-cresol (MC) + diisopropanolamine (DIPA) and 2,6-dimethylphenol (DMP) + DIPA and the ternary system of MC + DMP + DIPA were conducted at the pressure of 20.0 kPa. The binary VLE experimental data showed that DIPA had stronger interaction with MC than DMP. The ternary system experimental VLE data showed that DIPA could improve the relative volatility of DMP to MC. The binary experimental data were checked by using Herington area and point test methods, and the checked results were thermodynamically consistent. Meanwhile, the VLE data were correlated by Wilson, nonrandom two-liquid, and universal quasichemical models, and the binary energy interaction parameters for these models were obtained. These activity coefficient models were used to predict the ternary system VLE data. The predictive results suggested that the Wilson model had the best prediction.
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INTRODUCTION m-Cresol (MC) and 2,6-dimethylphenol (DMP) are of great importance for the basic organic chemical industry. MC is mainly employed to synthesize spices, cosmetics, and pharmaceutical products et al.1 Furthermore, DMP can be employed to synthesize engineering plastic polyphenylene oxide (PPO), 2,6-diphenylamine, antiarrhythmic drugs, etc.2,3 MC and DMP are presenting in coal tar and products of chemical synthesis. MC and DMP should be separated and purified because of their wide applications. Unfortunately, conventional distillation causes significant difficulty in separating the two chemicals due to their extremely close boiling points (see detailed information in next section). Therefore, adductive crystallization is often used in industry to separate the two chemicals.4 However, this method may have the disadvantages of low yield and solvent recovery. Although obtaining a high product purity for the separation of systems containing close boiling components by using simple distillation is difficult, extractive distillation, which has a wide application in industry, can be used to address the problem.5 Solvent should be selected for this type of special distillation. Gaikar6 studied the vapor−liquid equilibrium (VLE) of alkanolamines with p-cresol (PC) and DMP and found that alkanolamines could improve the relative volatility of DMP to PC. Given that MC is an isomer of PC, the molecular structure difference of the two materials is extremely small. Thus, the solvent of alkanolamines should have similar effect on MC and DMP. Diisopropanolamine (DIPA) is an alkanolamine that is widely used in gas sweetening of refinery streams,7 and its normal boiling point is approximately 521.85 K.8 Thus, © XXXX American Chemical Society
extractive distillation with using DIPA as entrainer can be employed to separate the mixture of MC and DMP. VLE data is one of the most important factors that affects the design and optimization of the distillation process. To the best of our knowledge, VLE data among DIPA, MC, and DMP have yet to be reported. Therefore, supplementing the relevant VLE data can provide a reference for the development of distillation technology for MC and DMP purification. In our work, the binary VLE data for the system of ethanol + water at 19.71 and 101.3 kPa were measured to confirm the reliability of equilibrium apparatus. The VLE data for two binary systems of MC + DIPA and DMP + DIPA and the ternary system of MC + DMP + DIPA at 20.0 kPa were determined by a modified Othmer still. The thermodynamic consistency of binary VLE data determined in this work was examined by using Herington area9 and point test10 methods. Meanwhile, the binary VLE data were correlated using the Wilson,11 nonrandom two-liquid model (NRTL),12 and universal quasichemical (UNIQUAC)13 models, and the parameters involved in these models were established. In addition, the Wilson, NRTL, and UNIQUAC models were used to predict the ternary system VLE data.
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EXPERIMENTAL SECTION Materials. The ethanol, distilled water, MC, DMP, and DIPA were adopted in our experimental work. Ethanol (≥99.7 Received: September 16, 2017 Accepted: March 27, 2018
A
DOI: 10.1021/acs.jced.7b00827 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Mass Fraction Purity of the Chemical Reagent Used material
source
distilled water ethanol m-cresol diisopropanolamine 2,6-dimethylphenol
Sinopharm Chemical Regent Co., Ltd. Sinopharm Chemical Regent Co., Ltd. Sinopharm Chemical Regent Co., Ltd. Aladdin Reagent Co., Ltd.
CAS RN
mass fraction purity
purification method
analysis method
64-17-5 108-39-4 110-97-4 576-26-1
1.000 ≥0.997 ≥0.990 ≥0.990 ≥0.990
none none none none
GC GC GC GC GC
wt %), MC (≥99.0 wt %), and DMP (≥99.0 wt %) were purchased from Sinopharm Chemical Regent Co. Ltd., and DIPA (≥99.0 wt %) was supplied by Aladdin Regent Co. Ltd. Table 1 shows the initial mass fractions and some relevant detailed information on those chemicals. All reagents were used directly, and no further purification was conducted in this work. The measurement of the normal boiling point and the refractive index of MC, DMP, and DIPA were conducted. The measured results are listed in Table 2, and these values are Table 2. Normal Boiling Point and Refractive Index for Chemicals MC, DMP, and DIPAa normal boiling point, T/K
refractive index, nD chemical MC DMP DIPA
temperature/K 293.15 298.15 293.15 298.15 294.15
this work 1.5396 1.5374 1.5075 1.5053 1.4625
ref 19
1.5398 1.538020 1.507921 1.505622 1.463523
this work
ref
475.35
475.8514 475.2515 474.2216 474.5517 523.4618 521.858
474.35 522.30
Figure 1. Experimental device for VLE measurement. (1) Heating rod, (2) liquid phase sampling port, (3) equilibrium chamber, (4) mercury thermometer, (5) glycerol, (6) vapor phase sampling port, (7) condensing coil, (8) valve, (9) U-shaped differential manometer, (10) buffer bottle (Erlenmeyer flask), (11) vacuum pump.
a
Experimental pressure is 101.30 kPa, and standard uncertainties u are u(T) = 0.5 K, u(p) = 1 kPa, and u(nD) = 0.0002. Refractive index was determined at the sodium D line frequency. The radiation frequency is 589.3 nm.
rate of 2−3 drops per second was reached. When system temperature and pressure remained constant for a time period of 50 min or longer, the system assumed to achieve equilibrium state; then, liquid samples were withdrawn using syringes. The reliability of equilibrium apparatus was confirmed by measuring VLE data for the system of ethanol + water. The experimental values are reported in Tables 3 and 4. Comparisons of our experimental data with experimental results available in literature are shown in Figure 2. The figure
compared with the results in the literature. Table 2 shows that the measured refractive index and normal boiling point values are in accordance with reported values.8,14−23 VLE Measurements. A circulation VLE still (cf, Figure 1) was adopted to conduct the VLE measurement of systems, which consisted of MC, DMP, and DIPA. This still could contain approximately 50 cm3 of liquid in total, and usually 80% of the still volume was filled by the liquid solution in the experimental process. During the experiment, both liquid phase and condensed vapor phase were sufficiently mixed by successive recirculation, which ensured the immediate establishment of the equilibrium state. The system pressure in vacuum was measured by a U-shaped differential manometer, which was filled with mercury; the system atmospheric pressure was measured using a precision barometer (FYP-1, Beijing Instrument, China). The system temperature measurement was conducted by using a precision mercury thermometer. The type B uncertainties of temperature and pressure were 0.05 K, 0.07 kPa for the differential manometer and 0.1 kPa for the barometer, respectively. During the measurement, DMP or DIPA was melted into liquid in a constant temperature tank. Then, the liquid mixture was put into the boiling chamber. A vacuum pump (2XZ-4, Shanghai Instrument, China) was used to fix and hold the system pressure constant. On the basis of valve adjustment, the desired pressure could be achieved; the pressure was kept fixed, and the liquid started to be heated. The liquid was gradually heated until a suitable condensation reflux
Table 3. Experimental VLE Data for Binary System of Ethanol (1) + Water (2) at 101.3 kPaa no.
T/K
x1
x2
y1
y2
1 2 3 4 5 6 7 8 9 10 11 12
373.05 369.80 366.62 364.36 362.07 359.64 358.07 355.92 353.95 353.24 352.45 351.38
0.0000 0.0170 0.0287 0.0516 0.0655 0.1042 0.1355 0.2243 0.3695 0.4924 0.6529 1.0000
1.0000 0.9830 0.9713 0.9484 0.9345 0.8958 0.8645 0.7757 0.6305 0.5076 0.3471 0.0000
0.0000 0.1543 0.2627 0.3008 0.3770 0.4424 0.4846 0.5504 0.6052 0.6473 0.7212 1.0000
1.0000 0.8457 0.7373 0.6992 0.6230 0.5576 0.5154 0.4496 0.3948 0.3527 0.2788 0.0000
a Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.1 kPa, and u(x1) = u(y1) = 0.005.
B
DOI: 10.1021/acs.jced.7b00827 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 4. Experimental VLE Data for Binary System of Ethanol (1) + Water (2) at 19.71 kPaa no.
T/K
x1
x2
y1
y2
1 2 3 4 5 6 7 8 9
331.65 329.31 326.42 324.48 323.04 321.90 320.21 318.62 316.65
0.0106 0.0244 0.0454 0.0702 0.0958 0.1153 0.1482 0.2426 0.4449
0.9894 0.9696 0.9466 0.9260 0.9042 0.8847 0.8518 0.7574 0.5551
0.0661 0.1675 0.2752 0.3613 0.4153 0.4709 0.5167 0.5745 0.6568
0.9339 0.8325 0.7248 0.6387 0.5847 0.5291 0.4833 0.4255 0.3432
a Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.07 kPa, and u(x1) = u(y1) = 0.005.
Figure 3. Experimental and correlated VLE data for the binary system of MC (1) + DIPA (2) at 20.0 kPa.
Figure 2. T−x−y phase equilibrium for ethanol (1) + water (2) system at 101.3 and 19.71 kPa. Figure 4. Experimental and correlated VLE data for the binary system of DMP (1) + DIPA (2) at 20.0 kPa.
shows that the VLE experimental data agree well with those reported by Kurihara et al.24 at 101.30 kPa and Voutsas et al.25 at 19.71 kPa. Therefore, the verification shows the equilibrium still is reliable. Sample Analysis. For the systems of DIPA, MC, and DMP, the Agilent 7890B gas chromatograph was used to analyze the vapor and liquid samples, which was equipped with a flame ionization detector and an HP-ULTRA 2 (25 m × 0.320 mm × 0.52 μm) chromatographic column. The vaporization and detection temperatures were set as 533.15 and 543.15 K, respectively. The temperature of chromatographic column was adjusted to 413.15 K. For the system of ethanol + water, the gas chromatograph (Kexiao GC-1690) was used to analyze the samples, which was equipped with a thermal conductivity detector and a GDX-104 (30 m × 0.32 mm × 20 μm) chromatographic column. The vaporization temperature and detection temperature were set as 443.15 and 453.15 K, respectively. The temperature of the chromatographic column was adjusted to 423.15 K. In the measurement, we analyzed each sample three times, and the average value was used. The area of fraction data analyzed by gas chromatograph was converted to mole fraction.
⎡ V L(p − ps ) ⎤ i ⎥ s s ⎢ i φiyp = γ φ exp x p i i i i i ⎢⎣ ⎥⎦ RT
(1)
where yi and xi are the molar fractions of pure component i for the vapor phase and liquid phase, respectively; p is the system pressure; pis is the vapor pressure of pure component i; γi is its activity coefficient; φi is its fugacity coefficient in the mixture phase; φis is its fugacity coefficient in the pure vapor phase; ViL represents its molar volume in the liquid phase. Gaikar6 stated that for alkanolamines with high boiling points, the vapor phase shows an almost ideal behavior at reduced pressures, so much so that the φi and φis can be ruled out, i.e., φi = φis = 1. Furthermore, the term exp[ViL(p − pis)/RT] is approximately equal to 1 at reduced pressure. Ultimately, a simplified equation was obtained from eq 1,
yp = γixipis i Herein, the
pis
(2)
can be calculated by eq 3,
ln(pis /kPa) = A +
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B + E ln(T /K ) + F(T /K )G T /K + C (3)
RESULTS AND DISCUSSION Binary System. VLE data contained two binary systems, namely, MC and DIPA, and DMP and DIPA. Figures 3 and 4 show the measured VLE data of these systems, and the values are listed in Tables 5 and 6. The vapor−liquid equilibrium can be calculated by the following expression:
Table 7 shows the equation parameters,26,27 and Tables 5 and 6 show the calculated activity coefficients. Table 5 suggests that the activity coefficients in the MC and DIPA system are no more than 1.0, especially when the mole fractions of MC and DIPA are approximately less than 0.40 and C
DOI: 10.1021/acs.jced.7b00827 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 5. Experimental VLE Data for Binary System of MC (1) + DIPA (2) at 20.0 kPaa
a
no.
T/K
x1
x2
y1
y2
γ1
γ2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
422.28 423.66 424.57 426.04 426.73 427.67 429.36 430.78 432.07 433.64 435.36 436.28 440.37 442.27 445.56 447.15 449.56 453.46 456.27 458.82 460.09 461.87 465.01 466.45 468.25
1.0000 0.9594 0.9344 0.8969 0.8756 0.8523 0.7965 0.7690 0.7388 0.7075 0.6679 0.6403 0.5566 0.5315 0.4640 0.4489 0.3928 0.3324 0.2675 0.2351 0.2019 0.1593 0.1096 0.0538 0.0000
0.0000 0.0406 0.0656 0.1031 0.1244 0.1477 0.2035 0.2310 0.2612 0.2925 0.3321 0.3597 0.4434 0.4685 0.5360 0.5511 0.6072 0.6676 0.7325 0.7649 0.7981 0.8407 0.8904 0.9462 1.0000
1.0000 0.9968 0.9950 0.9908 0.9894 0.9851 0.9758 0.9698 0.9630 0.9539 0.9405 0.9296 0.8863 0.8661 0.8144 0.7845 0.7358 0.6479 0.5475 0.4821 0.4302 0.3354 0.2403 0.1169 0.0000
0.0000 0.0032 0.0050 0.0092 0.0106 0.0149 0.0242 0.0302 0.0370 0.0461 0.0595 0.0704 0.1137 0.1339 0.1856 0.2155 0.2642 0.3521 0.4525 0.5179 0.5698 0.6646 0.7597 0.8831 1.0000
1.0139 1.0026 0.9948 0.9798 0.9782 0.9683 0.9679 0.9490 0.9387 0.9209 0.9080 0.9081 0.8714 0.8390 0.8144 0.7717 0.7680 0.7103 0.6862 0.6382 0.6393 0.6003 0.5721 0.5447 -
0.4935 0.4566 0.4981 0.4603 0.5212 0.5678 0.5846 0.5972 0.6190 0.6519 0.6838 0.7511 0.7728 0.8174 0.8656 0.8750 0.9113 0.9596 0.9567 0.9630 0.9997 0.9650 1.0037 1.0106
γ2
Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.07 kPa, and u(x1) = u(y1) = 0.005.
Table 6. Experimental VLE Data for Binary System of DMP (1) + DIPA (2) at 20.0 kPaa
a
no.
T/ K
x1
x2
y1
y2
γ1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
418.21 419.85 422.43 422.45 424.45 424.53 427.16 429.28 430.12 431.25 432.66 434.64 436.77 439.73 441.85 446.54 448.52 452.65 454.08 456.43 457.52 460.24 461.53 462.35 468.25
1 0.9424 0.8549 0.8537 0.7857 0.7801 0.7134 0.6502 0.6009 0.5885 0.5342 0.4831 0.4297 0.3655 0.3265 0.2495 0.215 0.1488 0.1345 0.1138 0.0940 0.0738 0.0601 0.0471 0
0 0.0576 0.1451 0.1463 0.2143 0.2199 0.2866 0.3498 0.3991 0.4115 0.4658 0.5169 0.5703 0.6345 0.6735 0.7505 0.7850 0.8512 0.8655 0.8862 0.9060 0.9262 0.9399 0.9529 1
1 0.9912 0.9755 0.9754 0.9607 0.9602 0.9428 0.9224 0.9053 0.9011 0.8798 0.8545 0.8244 0.7826 0.7498 0.6713 0.6239 0.5103 0.4811 0.4338 0.3797 0.3172 0.2711 0.2215 0
0 0.0088 0.0245 0.0246 0.0393 0.0398 0.0572 0.0776 0.0947 0.0989 0.1202 0.1455 0.1756 0.2174 0.2502 0.3287 0.3761 0.4897 0.5189 0.5662 0.6203 0.6828 0.7289 0.7785 1
1.0100 1.0048 1.0000 1.0006 1.0024 1.0065 1.0049 0.9948 1.0286 1.0087 1.0379 1.0481 1.0648 1.0864 1.0937 1.1169 1.1379 1.1964 1.1991 1.1977 1.2319 1.2173 1.2347 1.2589
1.1552 1.1228 1.1170 1.1050 1.0863 1.0765 1.0631 1.0937 1.0518 1.0592 1.0573 1.0530 1.0312 1.0222 0.9936 1.0040 1.0255 1.0117 0.9865 1.0150 0.9889 0.9928 1.0155 1.0106
Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.07 kPa, and u(x1) = u(y1) = 0.005.
amine group in DIPA had a strong interaction (i.e., hydrogen bond formation) with the group of hydroxyls in MC.28,29 Similar behavior was found in the system of MC + quinoline.
0.50, respectively. This condition indicated that the system is a negative deviation solution compared with the ideal system. This phenomenon was easy to analyze because the secondary D
DOI: 10.1021/acs.jced.7b00827 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 7. Extended Antoine Constants for MCa, DMP,a and DIPAb
a
chemicals
A
B
C
E
F
G
MC DMP DIPA
88.4952 122.4222 12.5285
−10581.0000 −11290.0000 −2652.2056
0.0000 0.0000 −190.3367
−10.0040 −15.5460
4.3032 × 10−18 7.9759 × 10−6
6.0000 2.0000
Equation parameters cited from Aspen Plus 7.3 databank.26 bEquation parameters cited from reference.27
Quinoline is a polar compound capable of hydrogen bonding through the nitrogen atom. Therefore, strong intermolecular interactions would form between quinoline and MC, thereby resulting in negative deviations from ideality.30 Table 6 suggests that the activity coefficients of DMP and DIPA are marginally greater than 1.0. This condition indicates that the system is a nonideal solution with positive deviation. This result may be explained by the effects of steric hindrance and electron-donating induced by the methyl group in DMP. The effects would affect the hydrogen bond formation between hydroxyl and secondary amine groups, even though DMP and DIPA could form a hydrogen bond. Therefore, the hydrogen bond strength of DMP and DIPA should be less than that of MC and DIPA. In this case, the physical interaction between DMP and DIPA would be considered.31 Due to the comprehensive influence of two interactions (i.e., physical interaction and hydrogen bond formation), the binary system of DMP and DIPA presents nonideal characteristic with positive deviation from Raoult’s law. Thermodynamic Consistency Test. Herington analysis9 was used to check the thermodynamic consistency for the two binary systems, which could confirm the entire consistency on thermodynamics of experimental data. The equations can be expressed as 1
Figure 5. Values of ln(γ1/γ2) for the system of MC(1) + DIPA(2).
γ
∫0 ln γ1 dx 2
D = 100
1
γ1
∫0 ln γ dx
(4)
Tmax − Tmin Tmin
(5)
2
J = 150
Figure 6. Values of ln(γ1/γ2) for the system of DMP(1) + DIPA(2).
where Tmax and Tmin represent the highest and lowest experimental temperature in our studied system, respectively. Based on the analysis of Wisniak,32 the VLE data were considered to be thermodynamically consistent if the calculated result |D − J| < 10. The D and J were calculated using eqs 2−5, and the calculated results are given in Table 8. The table shows
sensitive to small deviations of MC concentrations (cf Figure 5). Therefore, the data in these regions could not be tested for consistency. For the DMP + DIPA system, the experimental points were discontinuously changed at the concentrations range of 0.6−0.8 (cf Figure 6). Interpolation was used for this system. To check the dependability of each point of the VLE data, the point to point test proposed by Van Ness10 was carried out in this work. In our work, the vapor composition yi was predicted by the Wilson model. The criterion of the point test method is described by eq 6.33
Table 8. Thermodynamic Consistency Test for Experimental Data of MC (1) + DIPA (2) and DMP (1) + DIPA (2) Mixtures system
p/kPa
ΔTmax/K
Tmin/K
D/%
J/%
|D − J|
MC + DIPA DMP + DIPA
20.0 20.0
45.97 50.04
422.28 418.21
13.03 12.42
16.33 17.95
3.30 5.53
Δy =
|D − J| values are 3.30 for MC + DIPA system and 5.53 for DMP + DIPA system. Although the calculated results showed that our experimental data entirely passed the thermodynamic consistency, the diagrams of ln(γ1/γ2) ∼ x1 for the two systems showed that several points are scattered or irregular (cf Figures 5 and 6). For the MC + DIPA system, the thermodynamic consistency test at high MC concentrations was extremely
1 N
N
∑ Δyi = i=1
1 N
N
∑ 100|yiexp − yical | i=1
(6)
where N represents the total experimental points. If Δy < 1, the isobaric VLE data were considered to be thermodynamic consistency. According to this test, Δy values are 0.22 for MC + DIPA system and 0.08 for DMP + DIPA system at 20.0 kPa. This result indicated that the VLE data of two binary systems passed the test. E
DOI: 10.1021/acs.jced.7b00827 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 9. Wilson, NRTL, and UNIQUAC Activity Coefficient Models Correlated Results for Binary Systems DMP (1) + DIPA (2), MC (1) + DIPA (2) at 20.0 kPaa quaternary interaction parametersb model
p/kPa
aij
Wilson NRTL UNIQUAC
20.0 20.0 20.0
2.1479 4.4605 0.4959
Wilson NRTL UNIQUAC
20.0 20.0 20.0
2.1334 2.7317 −0.6169
Wilson NRTL UNIQUAC
20.0 20.0 20.0
0 0 0
aji
bij
MC (1) + DIPA (2) −837.4372 −2230.6716 97.9689 DMP (1) + DIPA (2) −2.3501 −1129.6859 −2.6138 −1345.4643 0.8612 442.7349 DMP (1) + MC (2)a 0 72.1425 0 −117.4838 0 −48.9034 −3.4678 −3.1757 −1.2648
AAD bji
αij
δ(y1)c
δ(T)d
1752.8403 1323.1557 220.8477
0.3
0.0021 0.0021 0.0023
0.27 0.27 0.26
1112.2407 1412.6423 −603.5143
0.3
0.0007 0.0008 0.0008
0.22 0.22 0.22
−83.8355 133.1636 43.8361
0.3
Binary parameters were estimated by using UNIFAC. bEquations of energy interaction parameter for Wilson is ln Δij = aij + bij/T, for NRTL is N N Δgij/RT = aij + bij/T, for UNIQUAC model is Δuij/RT = aij + bij/T. cδ(y) = ∑1 |(yical − yiexp )| /N dδ(T)= ∑1 |(Tical − Tiexp)| /N a
Correlation for Binary VLE Data. The Wilson, NRTL, and UNIQUAC models were used to correlate the VLE data for the systems of MC+DIPA and DMP+DIPA. The fitted process was performed by the maximum-likelihood method. The following equation was used as objective function:34 ⎡⎛ 2 ⎛ p − p ⎞2 ⎛ x − x ⎞2 Ti , c − Ti , e ⎞ i,c i,e i,e ⎢ ⎟⎟ + ⎜ i , c OF = ∑ ⎜ ⎟ ⎟ + ⎜⎜ ⎢⎝ σT σ σ ⎠ ⎝ ⎠ ⎠ ⎝ p x i=1 ⎣ N
⎛ y − y ⎞2 ⎤ i,c i,e ⎥ ⎟⎟ + ⎜⎜ ⎝ σy ⎠ ⎥⎦
(6a)
where OF represents the objective function, which was minimized by regressing data; N represents the total experimental points; p and T are equilibrium temperature and pressure, respectively; y and x are the molar fractions for the vapor phase and liquid phase; σ represents the standard deviation of the indicated data; and the superscripts of c and e are experimental and calculated values. The minimization objective eq 6 was utilized in the ASPEN Plus 7.326 to obtain model parameters. The optimized interaction parameters are presented in Table 9. Using the above binary interaction energy parameters, the T and y at the bubble point can be calculated/predicted by the activity coefficient models used in this paper. Figures 3 and 4 show the T−x−y diagrams of binary systems MC + DIPA and DMP + DIPA at 20.0 kPa calculated by this work, respectively. Meanwhile, the average absolute deviations (AAD) of T and y between the experimental data and the calculated data were reported in Table 9. Figures 3 and 4 indicate that azeotrope behavior was not found in our experimental conditions. In addition, we found from the compared results of AAD that the activity coefficient models correlated results were in good agreement with the experimental data. The relative volatility values of the systems of MC + DIPA and DMP + DIPA were obtained by calculating the experimental VLE data. The relative volatility values predicted by the Wilson model were compared with the results calculated by experimental data. For the MC + DIPA system, Figure 7 clearly indicates that the relative standard uncertainty of the Wilson model for relative volatility is approximately 0.05 (23
Figure 7. Relative volatilities of the MC + DIPA system at 20.0 kPa. Comparison of results predicted by the Wilson model to the experimental data of this work.
out of 25 points or 92% are within the 5% corridor). At the same time, the relative volatility of experimental values may be very sensitive to small changes of liquid concentrations at high MC concentrations. For the DMP + DIPA system, Figure 8 indicates that the relative standard uncertainty of the Wilson model for relative volatility is less than 0.02 (all experimental points are within the 2% corridor). Ternary System. The measurement of VLE data of the ternary system DMP (1) + MC (2) + DIPA (3) were conducted at 20.0 kPa. The VLE data measured in this work were used to verify the effect of solvent DIPA on the volatility of DMP and MC; thus, VLE data were not measured in full concentration range. Table 10 shows the VLE data of the ternary system. From Tables 5 and 6, the boiling point difference of DMP and MC is approximately 4.1 K at 20.0 kPa, which indicates that the relative volatility α12 of DMP to MC should be close to 1.0. However, Table 10 shows that the values of relative volatility α12 are considerably larger than 1.0, which indicates that α12 is improved obviously with existing DIPA. Table 10 also shows that α12 increases with the mole fraction of DIPA. These results suggested that DIPA could be used as an entrainer for DMP and MC separation. Generally, the VLE data of multicomponent system could be estimated using binary energy interaction parameters. In this F
DOI: 10.1021/acs.jced.7b00827 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Figure 8. Relative volatilities of the DMP + DIPA system at 20.0 kPa. Comparison of results predicted by the Wilson model to the experimental data of this work.
Figure 9. Percentage errors of the relative volatilities (DMP to MC) predicted by Wilson, NRTL, and UNIQUAC models in comparison to the ternary VLE data of this work for the DMP + MC + DIPA ternary mixture at 20.0 kPa.
work, the VLE of the ternary system was predicted using the above optimized parameters involved in these models. The parameters for MC + DMP system were estimated by using UNIFAC. The results are shown in Table 9. We used Wilson, NRTL, and UNIQUAC models to predict T, y at bubble point, and relative volatility α12. At the same time, the error analyses for the prediction results of temperature, composition, and α12 were carried out. Table 10 and Figure 9 show the analytical results. It can be found from Table 10, the predicted equilibrium temperatures T by these models are slightly lower than the experimental data, and the Wilson model had the best prediction. Furthermore, Figure 9 shows that the α12 values predicted by the Wilson model agree well with the experimental data, and the relative standard uncertainty is less than 5%. The error points were evenly distributed around the zero line. However, the relative standard uncertainty was
