Fluid Phase Equilibria 370 (2014) 34–42
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Vapor–liquid equilibrium for the binary mixtures of dipropylene glycol with aromatic hydrocarbons: Experimental and regression Marilena Nicolae ∗ , Florin Oprea Petroleum Processing and Environmental Engineering Department, Universitatea Petrol-Gaze, 39 Bucures¸ti, Blvd., Ploies¸ti, Romania
a r t i c l e
i n f o
Article history: Received 22 September 2013 Received in revised form 27 February 2014 Accepted 1 March 2014 Available online 12 March 2014 Keywords: VLE Dipropylene glycol Aromatic hydrocarbons Regression
a b s t r a c t Vapor–liquid equilibrium data was determined by using a static method for the binary mixtures of dipropylene glycol (4-oxa-2,6-heptanediol) with benzene, toluene, ethylbenzene, o-xylene, m-xylene, and p-xylene at temperatures within 293.15 K–481.15 K. The p–T–x experimental data obtained was regressed with NRTL and UNIQUAC thermodynamic models in order to obtain the binary interaction parameters of the models, specific to each mixture. Furthermore, the T–x–y diagrams were determined based on these parameters and then compared with the diagrams calculated using the UNIFAC predictive model. We observed differences between the T–x curves calculated with the two models mentioned above and the UNIFAC predictive model. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Aromatic hydrocarbon extraction from mixtures is a process with significant importance for industry and for researchers. Throughout the years a large number of solvents for the liquid–liquid extraction were researched and used, such as ethylene glycols, sulfolane, n-methyl-2-pyrrolidone, formylmorpholine or dimethyl-sulfoxide. Ethylene glycols, have widespread applicability in petrochemical installations. Although the extraction processes are widespread in the industry, there is limited documented data set related to the liquid–liquid and vapor–liquid equilibrium between aliphatic and aromatic hydrocarbons and the solvents mentioned above. During our research process we identified a number of articles on this subject, such as:
- Vapor–liquid equilibrium and the density measurement for mixtures formed by sulfolane and aromatics hydrocarbons were reported by Wei-Kuan et al. [1], by Rappel et al. [2] and for mixtures of aromatics and NMF vapor–liquid equilibrium and density data was reported by Wei-Kuan [3]. - Equilibrium data between n-methyl-2-pyrrolidone and aromatics was reported by Al-Zayied et al. [4] and by Gupta et al. [5].
∗ Corresponding author. Tel.: +40 723945332. E-mail addresses: nicolae
[email protected],
[email protected] (M. Nicolae). http://dx.doi.org/10.1016/j.fluid.2014.03.003 0378-3812/© 2014 Elsevier B.V. All rights reserved.
- Dimethyl sulphoxide and aromatic hydrocarbon systems vapor–liquid equilibrium data was reported by Al-Sahhaf, Kapetanovic [6]. - For ethylene glycols, limited data about the liquid–liquid and vapor–liquid equilibrium for the mixtures ethylene glycols–hydrocarbons is available, although the ethylene glycols are still used for the extraction of aromatics from gasoline. Vapor–liquid equilibria for mixtures of triethylene glycol and aromatics hydrocarbons are presented by Gupta et al. [5] and by Ng et al. [7]. - The mixtures of tetraethylene glycols and aromatics data concerning phase equilibria are mentioned by Al-Sahhaf and Kapetanovic [8], and by Yu et al. [9]. The propylene glycols have an increased potential to be used as solvents for the extractions of aromatics from mixtures, due to their similarities in terms of chemical structure and properties with the ethylene glycols. Taking into account this assertion and the results from previous works [10,11] related to the utilization of propylene glycols as solvents, dipropylene glycol (which is similar to diethylene glycol) could be used successfully and with good results as solvent for aromatics extraction. As we mentioned in a previous paper [12], equilibrium data for the systems formed by dipropylene glycol and inferior aromatics (BTX) or aliphatic hydrocarbons (with six, seven and eight atoms of carbon) was not previously documented. In order to design a new process for the extraction of aromatics hydrocarbons from mixtures, using as solvent dipropylene glycol, it is required to have consistent equilibrium data of mixtures. These data will be used further for the liquid–liquid
M. Nicolae, F. Oprea / Fluid Phase Equilibria 370 (2014) 34–42
a,b,c G
l P p q R r T u x z
binary interaction parameters of the NRTL model adjustable parameter which depends on the interaction energy between molecules of component i and component j parameter of the molecule of the UNIQUAC model pressure vapor pressure surface area parameter of the UNIQUAC model universal gas constant (J mol−1 K−1 ) volume parameter of the UNIQUAC model temperature (K) uncertainty concentration of the component in liquid phase of the mixture expressed as molar fraction coordination number of the tridimensional network of the liquid
Greek symbols difference ϕ average fraction of the segment in UNIQUAC model activity coefficient i average fraction of the area in UNIQUAC model adjustable parameter ˛,˛ ,ˇ nonrandomness parameters of the NRTL model Subscripts i,j components i and j i–j pair interaction ij ji j–i pair interaction k component k calculated value calc expt experimental value Superscripts (c) combinatorial component of the variable (r) residual component of the variable
extraction or/and extractive distillation processes design using computer simulated chemical processes. In this study, vapor–liquid equilibrium experimental data was measured for binary mixtures formed by dipropylene glycol and inferior aromatics: benzene, toluene, ethylbenzene, o-xylene, mxylene and p-xylene. Vapor–liquid equilibrium for the binaries mentioned above was determined by measuring the vapor pressure of the mixtures with a static apparatus described in detail in [13]. The p–T–x experimental data acquired was regressed with the NRTL [14] and UNIQUAC [15] models to obtain the binary interaction parameters of the thermodynamic model, specific to each binary. Parameters obtained on this way could be used further in the liquid–liquid extraction process or extractive distillation process design, using computer simulated chemical processes. Using the binary parameters of the NRTL and UNIQUAC models obtained for each binary and PRO II simulation software [16] were calculated the T–x–y diagrams and then were plotted and compared with the T–x–y diagrams for the same binaries calculated with the UNIFAC predictive model. 2. Experimental 2.1. Materials The suppliers and the purity levels of the chemical substances utilized in this work are reported in Table 1. Purity was verified
35
through gas chromatography analysis per the ASTM D 6370 method using a Clarus 500 instrument from Perkin Elmer equipped with a split/splitless injector, a flame ionization detector, and using a capillary column coated with methyl silicon in liquid phase. No impurities were detected. 2.2. Apparatus and procedures We used a static apparatus in our laboratory, purpose-built to determine p–T–x equilibrium data, by measuring vapor pressure. The apparatus is made up of an equilibrium cell connected with a U-shaped tube which contains a manometric liquid (mercury). The U-shaped tube is connected to a DPI 705 pressure sensor (measuring range between 0 and 100 kPa, which indicates the experimental values of sample’ vapor pressure) and to a couple of valves: one for communication with the vacuum pump, another for communication with atmosphere. The two branches of the U-shaped tube are connected through another way valve which is held open during the degassing operation and it is closed during the rest of the experiment. For ease of reading of the manometric liquid level in the tube’s branches, we used a graduated scale attached to it. During the experimental determination of the vapor pressure, the equilibrium cell containing the analyzed mixture sample and the tube are sunk in a thermostatic oil bath equipped with a NIST Traceable Digital Thermometer (±0.05% accuracy and 0.001 K resolution) provided by VWR International, LLC. Using the apparatus, we determined the vapor pressures of mixtures and pure components at temperatures between 293.15 K and 481.15 K. The experimental procedure is described below: (1) a mixture sample of approximately 30 ml with a known concentration (prepared by weighing in laboratory conditions (101.3 kPa, 293.15 K) using a Mettler Toledo AB204-S electronic balance accurate to 0.0001 g) was introduced in the equilibrium cell, was cooled near the liquid nitrogen temperature and then was degassed with a vacuum pump; (2) the tube was introduced in the thermostatic bath which is heated at the desired temperature after degassing the cell; (3) the bath was maintained at this temperature, until the level of the manometric liquid in the two branches of the tube does not vary for at least 30 min (while it is considered that the equilibrium state was attained); (4) after this period, the level of the manometric liquid in the tube was equalized introducing air in the tube; (5) in the last step the temperature and pressure are recorded. This procedure was repeated at least 3 times for each concentration of each binary mixture. The vapor pressure was determined for the following concentrations of the mixtures: 0.1, 0.3, 0.5, 0.7 and 0.9 molar fraction of hydrocarbon. Same measuring process was applied to the pure components (aromatic hydrocarbons and dipropylene glycol). The results of the experimental measurements of the vapor pressures are displayed in Tables 5–10. 3. Experimental results The experimental method was validated by measuring the vapor pressure of the mixture 1,2-propanediol (1) + dipropylene glycol (2), mixture for which accurate data can be calculated using simulation software [16]. The experimental results (T, x1 , and p) are listed in Table 4. Fig. 1 charts the experimental results against the data calculated with simulation software [16] using PRO II 9.2 database. As expected, the two data sets are similar. After the experimental method was validated, we determined vapor pressure for six binary systems formed by dipropylene glycol and benzene, toluene, ethylbenzene, o-xylene, m-xylene, and p-xylene. Tables 5–10 report the experimental measurements results for each binary: molar fraction
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M. Nicolae, F. Oprea / Fluid Phase Equilibria 370 (2014) 34–42 Table 1 Materials description. Chemical name
Source
Mass fraction purity
Benzene Toluene Ethylbenzene o-Xylene m-Xylene p-Xylene Dipropylene glycol
Lach-NER sro, Czech Republic Chemical Company, Romania Merck KGaA, Germany Merck KGaA, Germany Merck KGaA, Germany Merck KGaA, Germany Dow Chemical, Germany
0.9994 0.993 >0.99 0.98 >0.99 >0.99 0.9989
4. Binary interaction parameters of NRTL model and VLE calculation The experimental p–T–x data was regressed using the PRO II regress module and the NRTL and UNIQUAC thermodynamic models. Eqs. (1)–(5) describe the NRTL binary interaction parameters specific for each binary. Fig. 1. Experimental vapor pressure of mixture 1,2-propanediol (1) + dipropylene glycol (2): () pure 1,2-propanediol; () 0.8876 molar fraction of 1,2-propanediol; () 0.6846 molar fraction of 1,2-propanediol; () 0.4831 molar fraction of 1,2propanediol; () 0.2538 molar fraction of 1,2-propanediol; (䊉) 0.09941 molar fraction of 1,2-propanediol; () pure dipropylene glycol against vapor pressure of the same mixture calculated with simulation software [16]: (–) vapor pressure calculated with PRO II 9.2 simulation software.
of aromatic hydrocarbon x1 , temperature T, vapor pressure p, and uncertainty of the vapor pressure u(p). As we did not measure the compositions of vapor phases, thermodynamic consistency was not determined at this stage.
xj Gij G x j ji ji ji ln i = + k
ij = aij + ij = aij +
bij T bij RT
Gki xk + +
cij T2
˛ji =
+ ˇji T
Gkj xk
ij −
(unit is K)
cij 2 R T2
Gij = exp (−˛ji ij ) ˛ji
j
(unit is kcal or kj)
x G k k kj kj Gkj xk
(1)
(2) (3) (4) (5)
Fig. 2. Relative differences p/p = (pexpt − pcalc )/pcalc of the experimental vapor pressures pexpt from those calculated with NRTL and UNIQUAC models, pcalc for six binary mixtures: (a) benzene (1) + dipropylene glycol (2). () NRTL model; () UNIQUAC model; (b) toluene (1) + dipropylene glycol (2). () NRTL model; (♦) UNIQUAC model; (c) ethylbenzene (1) + dipropylene glycol (2). (䊉) NRTL model; () UNIQUAC model; (d) o-xylene (1) + dipropylene glycol (2). () NRTL model; () UNIQUAC model; (e) m-xylene (1) + dipropylene glycol (2). () NRTL model; ( ) UNIQUAC model; (f) p-xylene (1) + dipropylene glycol (2). () NRTL model; ( ) UNIQUAC model.
M. Nicolae, F. Oprea / Fluid Phase Equilibria 370 (2014) 34–42
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Table 2 The maximum and the average percent deviation of molar composition for each binary involved. Thermodynamic model
NRTL
UNIQUAC
Maximum percent deviation Benzene + DPG Toluene + DPG Ethylbenzene + DPG o-Xylene + DPG m-Xylene + DPG p-Xylene + DPG
2.470 −3.010 2.36 3.83 3.616 3.581
Average percent deviation
Maximum percent deviation −7.57 −8.514 4.18 −7.516 −9.583 −8.809
0.459 0.713 0.348 0.459 0.784 0.46
Average percent deviation 0.957 1.286 0.483 0.788 0.990 1.229
Table 3 Binary interaction parameters of NRTL and UNIQUAC thermodynamic models. Mixture
Binary interaction parameters of NRTL model
Benzene + dipropylene glycol Toluene + dipropylene glycol Ethylbenzene + dipropylene glycol o-Xylene + dipropylene glycol m-Xylene + dipropylene glycol p-Xylene + dipropylene glycol
aij
bij
aji
bji
˛ij
2.05763 2.87115 −0.19214 −0.03556 −3.37899 2.99324
370.5516 423.679 986.4034 1572.6 2586.195 721.2453
−2.19241 −2.71711 −2.68897 −2.12113 −1.22426 −3.68925
587.4975 506.8978 998.8956 208.8128 142.8919 599.2381
0.36711 0.18054 0.31843 0.11933 0.18212 0.09886
Binary interaction parameters of UNIQUAC model aij
bij
−494.847 −239.297 −126.966 236.555 618.4039 −57.7952
Benzene + dipropylene glycol Toluene + dipropylene glycol Ethylbenzene + dipropylene glycol o-Xylene + dipropylene glycol m-Xylene + dipropylene glycol p-Xylene + dipropylene glycol
2.61948 1.78298 1.17368 0.23797 −0.64769 1.07953
aji
bji
397.2162 305.1539 360.7408 133.0389 16.65462 286.7363
−1.60568 −1.29826 −1.2561 −0.68224 −0.41895 −1.11505
Table 4 Experimental VLE data for temperature T, pressure p and mole fraction x1 for the system 1,2-propanediol (1) + dipropylene glycol (2)a . T/K
p/kPa
u(p)
1.1462 1.4611 1.8491 2.3274 2.9115 3.6211 4.4798 5.513 6.751 8.228 9.981 12.054 14.497 20.713 20.713
0.0052 0.0033 0.0030 0.0042 0.0051 0.0083 0.0116 0.013 0.023 0.022 0.015 0.025 0.023 0.023 0.033
x1 = 0 385.15 390.15 395.15 400.15 405.15 410.15 415.15 420.15 425.15 430.15 435.15 440.15 445.15 455.15 455.15
T/K
a
u(p)
T/K
2.1033 2.6585 3.3258 4.1416 5.106 6.312 7.717 9.535 11.455 13.870 16.606 19.849 23.691 28.176 33.249
0.0095 0.0127 0.0116 0.0232 0.020 0.025 0.032 0.033 0.035 0.040 0.036 0.046 0.056 0.059 0.057
x1 = 0.09941 390.15 395.15 400.15 405.15 410.15 415.15 420.15 425.15 430.15 435.15 440.15 445.15 450.15 455.15 460.15
x1 = 0.6846 370.15 375.15 380.15 385.15 390.15 395.15 400.15 405.15 410.15 415.15 417.15 420.15 425.15 427.15 430.15
p/kPa
p/kPa
u(p)
1.9115 2.4738 3.1048 3.9637 4.9155 6.053 7.502 9.247 11.290 13.774 16.664 19.775 23.339 27.808 33.182
0.0133 0.0109 0.0177 0.0183 0.0156 0.015 0.021 0.018 0.020 0.023 0.021 0.044 0.034 0.049 0.047
x1 = 0.2538 380.15 385.15 390.15 395.15 400.15 405.15 410.15 415.15 420.15 425.15 430.15 435.15 440.15 445.15 450.15
0.0152 0.0182 0.0113 0.0201 0.023 0.019 0.031 0.022 0.019 0.027 0.023 0.027 0.032 0.038 0.037
360.15 365.15 370.15 375.15 380.15 385.15 390.15 395.15 400.15 405.15 410.15 415.15 420.15 425.15 430.15
Standard uncertainties u are u(T) = 0.01 K and u(x) = 0.0002.
p/kPa
u(p)
2.1088 2.7006 3.4431 4.4075 5.556 6.844 8.458 10.466 12.869 15.724 19.183 20.657 23.049 27.657 32.938
0.0182 0.0230 0.0212 0.0245 0.031 0.012 0.033 0.040 0.037 0.043 0.035 0.029 0.038 0.045 0.042
x1 = 0.4831
x1 = 0.8876 2.1315 2.7354 3.4557 4.3496 5.440 6.821 8.608 10.512 13.170 16.270 17.721 20.042 24.151 25.974 29.084
T/K
375.15 380.15 385.15 390.15 395.15 400.15 405.15 410.15 415.15 420.15 425.15 427.15 430.15 435.15 440.15
x1 = 1.0000 1.3635 1.7857 2.3107 3.0514 3.9504 5.023 6.330 7.946 9.920 12.301 15.260 18.713 22.943 27.704 33.106
0.0092 0.0114 0.0112 0.0141 0.0162 0.017 0.012 0.013 0.021 0.023 0.026 0.020 0.027 0.030 0.037
350.15 355.15 360.15 365.15 370.15 375.15 380.15 385.15 390.15 395.15 400.15 405.15 410.15 415.15 420.15
0.8421 1.1313 1.5067 1.9877 2.5968 3.3612 4.3166 5.496 6.946 8.715 10.858 13.440 16.533 20.218 24.584
0.0118 0.0153 0.0181 0.0223 0.0245 0.0141 0.0185 0.022 0.024 0.028 0.031 0.034 0.026 0.028 0.340
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M. Nicolae, F. Oprea / Fluid Phase Equilibria 370 (2014) 34–42
Table 5 Experimental VLE data for temperature T, pressure p with standard uncertainty u(p), and mole fraction x1 for the System benzene (1) + dipropylene glycol (2)a . T/K
p/kPa
u(p)
x1 = 0 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 473.15 483.15
T/K
0.3627 0.6227 1.0387 1.6844 2.6627 4.2031 7.104 10.524 15.117 21.914 30.564 42.295 53.10
0.0125 0.0079 0.0043 0.0093 0.0046 0.0079 0.013 0.008 0.016 0.024 0.031 0.015 0.04
333.15 338.15 343.15 348.15 353.15 358.15 368.15 378.15 388.15 398.15 408.15 418.15 428.15
x1 = 0.7031
u(p)
T/K
p/kPa
9.800 12.234 15.468 19.075 23.000 27.757 33.920 40.667 48.343 57.16 67.16 78.75 90.52
0.008 0.008 0.016 0.015 0.016 0.023 0.025 0.018 0.020 0.01 0.02 0.03 0.01
u(p)
x1 = 0.3009 9.030 10.553 12.333 14.017 16.390 18.677 24.613 31.087 38.479 48.159 59.45 70.70 85.45
0.016 0.064 0.042 0.118 0.046 0.038 0.031 0.029 0.016 0.019 0.02 0.01 0.04
303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 368.15
T/K
p/kPa
u(p)
8.441 10.578 12.958 16.181 19.908 24.008 28.821 34.379 40.870 48.104 56.36 65.80 76.43
0.012 0.016 0.008 0.016 0.024 0.008 0.016 0.012 0.016 0.016 0.02 0.03 0.02
x1 = 0.5000 8.945 11.148 13.703 16.393 19.723 23.253 27.088 31.616 36.846 42.897 49.584 56.94 74.61
x1 = 0.8992
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 a
p/kPa
x1 = 0.0999
0.016 0.008 0.027 0.043 0.034 0.025 0.012 0.020 0.019 0.012 0.020 0.03 0.02
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15
x1 = 1.000
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15
9.627 12.180 12.250 18.937 23.237 28.910 35.000 41.540 50.63 59.91 70.64 82.54 96.97
0.013 0.023 0.018 0.019 0.018 0.018 0.014 0.027 0.02 0.02 0.01 0.02 0.01
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15
9.983 12.639 15.852 19.709 24.300 29.725 36.092 43.514 52.11 62.01 73.35 86.27 100.91
0.006 0.012 0.005 0.016 0.012 0.016 0.008 0.016 0.03 0.02 0.01 0.02 0.02
Standard uncertainties u are u(T) = 0.01 K and u(x) = 0.0003.
Table 6 Experimental VLE data for temperature T, pressure p with standard uncertainty u(p), and mole fraction x1 for the system Toluene (1) + dipropylene glycol (2).a T/K
p/kPa
u(p)
0.3627 0.6227 1.0387 1.6844 2.6627 4.2031 7.104 10.524 15.117 21.914 30.564 42.295 53.10
0.0125 0.0079 0.0043 0.0093 0.0046 0.0079 0.013 0.008 0.016 0.024 0.031 0.015 0.04
x1 = 0 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 473.15 483.15
T/K
a
u(p)
T/K
5.690 7.913 10.396 13.704 15.840 18.069 23.455 26.519 34.099 38.545 47.273 60.73 92.11
0.011 0.018 0.008 0.016 0.012 0.012 0.008 0.008 0.021 0.012 0.011 0.01 0.01
x1 = 0.0999 343.15 353.15 363.15 373.15 378.15 383.15 393.15 398.15 408.15 413.15 423.15 433.15 453.15
x1 = 0.7005 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 358.15 368.15 378.15
p/kPa
p/kPa
u(p)
5.160 7.808 9.352 11.337 13.669 16.351 19.172 22.655 30.840 40.994 53.70 69.32 87.61
0.013 0.010 0.008 0.008 0.008 0.008 0.008 0.008 0.013 0.021 0.01 0.02 0.02
x1 = 0.3030 313.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 363.15 373.15 383.15 393.15 403.15
0.0138 0.013 0.013 0.013 0.012 0.010 0.018 0.010 0.017 0.015 0.009 0.02 0.02
303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 358.15 368.15 378.15
Standard uncertainties u are u(T) = 0.01 K and u(x) = 0.0002.
p/kPa
u(p)
4.5693 5.765 6.960 8.585 10.443 12.718 15.527 18.649 22.236 26.206 36.479 49.607 65.87
0.0123 0.008 0.013 0.008 0.013 0.009 0.013 0.008 0.008 0.008 0.008 0.008 0.02
x1 = 0.5010
x1 = 0.9008 4.8467 6.140 7.650 9.521 11.708 14.520 17.657 21.310 25.560 30.460 42.480 58.04 78.51
T/K
303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 358.15 368.15 378.15
x1 = 1.000 4.7200 6.013 7.587 9.500 11.790 14.523 17.753 21.553 25.883 31.147 43.908 60.38 81.34
0.0141 0.018 0.014 0.017 0.011 0.007 0.012 0.007 0.011 0.014 0.025 0.01 0.02
303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 358.15 368.15 378.15
4.9048 6.257 7.963 9.959 12.309 15.142 18.856 22.61 27.311 32.719 46.175 63.84 86.25
0.0082 0.008 0.008 0.012 0.008 0.012 0.021 0.013 0.012 0.016 0.01 0.01 0.01
M. Nicolae, F. Oprea / Fluid Phase Equilibria 370 (2014) 34–42
39
Table 7 Experimental VLE data for temperature T, pressure p with standard uncertainty u(p), and mole fraction x1 for the system ethylbenzene (1) + dipropylene glycol (2)a . T/K
p/kPa
u(p)
x1 = 0 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 473.15 483.15
T/K
0.3627 0.6227 1.0387 1.6844 2.6627 4.2031 7.104 10.524 15.117 21.914 30.564 42.295 53.10
0.0125 0.0079 0.0043 0.0093 0.0046 0.0079 0.013 0.008 0.016 0.024 0.031 0.015 0.04
343.15 348.15 353.15 358.15 363.15 373.15 383.15 393.15 403.15 423.15 433.15 443.15 463.15
x1 = 0.6942 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 378.15 393.15 408.15 a
p/kPa
u(p)
T/K
x1 = 0.1017
p/kPa
4.0300 4.7800 5.587 6.513 7.627 10.187 13.517 17.485 22.087 34.603 44.477 54.66 83.35
0.0155 0.0178 0.017 0.016 0.014 0.014 0.011 0.012 0.016 0.012 0.009 0.01 0.01
333.15 338.15 343.15 348.15 353.15 363.15 373.15 383.15 388.15 393.15 403.15 413.15 423.15
0.0095 0.008 0.015 0.020 0.012 0.016 0.019 0.020 0.027 0.008 0.019 0.02 0.02
T/K
p/kPa
u(p)
7.104 8.617 10.469 12.486 15.019 17.814 24.973 33.535 38.742 45.638 52.25 76.25 97.24
0.008 0.008 0.012 0.024 0.016 0.012 0.016 0.016 0.008 0.027 0.01 0.02 0.01
x1 = 0.5000 6.210 7.530 9.077 10.788 12.804 17.485 23.560 31.518 36.276 41.626 54.29 68.92 85.89
x1 = 0.8992 4.5933 5.722 7.235 8.978 10.941 13.199 15.972 19.041 22.605 26.804 36.911 57.83 87.15
u(p)
x1 = 0.3191 0.008 0.010 0.008 0.008 0.025 0.020 0.011 0.016 0.008 0.024 0.01 0.02 0.02
333.15 338.15 343.15 348.15 353.15 358.15 368.15 378.15 383.15 388.15 393.15 408.15 418.15
x1 = 1.000
323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 378.15 393.15 408.15
4.5378 5.756 7.097 8.797 10.817 13.210 16.020 19.524 23.351 27.648 38.216 60.71 91.94
0.0077 0.008 0.008 0.010 0.007 0.015 0.013 0.016 0.020 0.019 0.028 0.02 0.02
308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 358.15 368.15 383.15 403.15
2.2227 2.0989 3.7459 4.7117 5.967 7.448 9.251 11.407 13.789 20.421 29.113 47.752 85.64
0.0077 0.0310 0.0195 0.0122 0.012 0.012 0.008 0.008 0.012 0.020 0.02 0.01 0.02
Standard uncertainties u are u(T) = 0.01 K and u(x) = 0.0002.
Table 8 Experimental VLE data for temperature T, pressure p with standard uncertainty u(p), and mole fraction x1 for the system o-xylene (1) + dipropylene glycol (2)a . T/K
p/kPa
u(p)
0.3627 0.6227 1.0387 1.6844 2.6627 4.2031 7.104 10.524 15.117 21.914 30.564 42.295 53.10
0.0125 0.0079 0.0043 0.0093 0.0046 0.0079 0.013 0.008 0.016 0.024 0.031 0.015 0.04
x1 = 0 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 473.15 483.15
T/K
a
u(p)
T/K
2.8533 4.0100 5.703 7.827 10.700 14.113 18.672 24.360 31.905 41.373 52.59 64.68 81.85
0.0072 0.0085 0.007 0.007 0.011 0.005 0.012 0.016 0.013 0.008 0.01 0.40 0.01
x1 = 0.1117 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15
x1 = 0.7004 323.15 333.15 343.15 353.15 363.15 373.15 383.15 388.15 393.15 398.15 403.15 408.15 418.15
p/kPa
p/kPa
u(p)
1.7167 2.7833 4.1967 6.194 8.829 12.485 17.454 23.270 30.640 40.205 52.20 66.72 84.19
0.0076 0.0072 0.0083 0.012 0.016 0.016 0.012 0.012 0.017 0.025 0.03 0.02 0.02
x1 = 0.3001 313.15 323.15 333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15
0.0094 0.007 0.013 0.012 0.025 0.021 0.013 0.017 0.025 0.02 0.01 0.03 0.04
318.15 323.15 333.15 343.15 353.15 363.15 373.15 383.15 388.15 393.15 403.15 413.15 418.15
Standard uncertainties u are u(T) = 0.01 K and u(x) = 0.0003.
p/kPa
u(p)
2.1133 3.3853 5.203 7.757 11.273 16.057 22.380 30.437 40.194 53.26 69.78 89.93 99.51
0.0072 0.0124 0.010 0.011 0.010 0.015 0.011 0.006 0.012 0.01 0.01 0.02 0.02
x1 = 0.4966
x1 = 0.8994 3.3700 5.307 8.179 11.916 17.431 24.314 33.437 39.021 45.370 52.67 60.74 69.24 89.98
T/K
313.15 323.15 333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 427.15
x1 = 1.000 2.5733 3.2867 5.250 8.113 12.170 17.777 25.330 35.724 41.748 48.390 65.39 86.35 98.56
0.0083 0.0106 0.012 0.007 0.008 0.007 0.011 0.021 0.017 0.006 0.03 0.02 0.03
313.15 323.15 333.15 343.15 353.15 363.15 373.15 378.15 383.15 388.15 393.15 403.15 413.15
2.0521 3.4562 5.613 8.542 12.727 18.651 26.731 31.656 37.354 43.632 51.01 68.42 90.18
0.0163 0.0082 0.0216 0.022 0.008 0.012 0.013 0.017 0.012 0.017 0.02 0.02 0.03
40
M. Nicolae, F. Oprea / Fluid Phase Equilibria 370 (2014) 34–42
Table 9 Experimental VLE data for temperature T, pressure p with standard uncertainty u(p), and mole fraction x1 for the system m-xylene (1) + dipropylene glycol (2)a . T/K
p/kPa
u(p)
x1 = 0 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 473.15 483.15
T/K
0.3627 0.6227 1.0387 1.6844 2.6627 4.2031 7.104 10.524 15.117 21.914 30.564 42.295 53.10
0.0125 0.0079 0.0043 0.0093 0.0046 0.0079 0.013 0.008 0.016 0.024 0.031 0.015 0.04
343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 418.15 423.15 433.15 443.15 453.15
x1 = 0.7006 318.15 323.15 328.15 333.15 338.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 a
p/kPa
u(p)
T/K
x1 = 0.1032
p/kPa
3.1500 4.5233 6.542 8.957 11.873 15.712 20.160 25.953 29.310 33.449 43.211 54.48 67.40
0.0108 0.0095 0.012 0.021 0.011 0.012 0.008 0.011 0.010 0.025 0.021 0.01 0.01
0.0082 0.0072 0.010 0.011 0.016 0.010 0.011 0.008 0.010 0.010 0.00 0.03 0.05
T/K
p/kPa
u(p)
3.1812 5.173 7.973 11.957 16.810 23.213 27.130 31.500 42.077 55.07 70.64 80.17 90.73
0.0108 0.017 0.017 0.014 0.009 0.011 0.009 0.013 0.013 0.01 0.02 0.02 0.02
x1 = 0.5012
323.15 328.15 333.15 343.15 348.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15
3.4833 4.3167 5.423 7.910 9.480 11.244 15.353 20.912 28.110 37.082 48.086 61.88 78.3
x1 = 0.9003 3.2500 4.1233 5.532 6.460 8.190 9.943 14.680 21.170 29.820 40.423 53.81 69.70 90.91
u(p)
x1 = 0.2999 0.0072 0.0095 0.009 0.009 0.013 0.012 0.017 0.025 0.026 0.025 0.025 0.03 0.01
318.15 328.15 338.15 348.15 358.15 368.15 373.15 378.15 388.15 398.15 408.15 413.15 418.15
x1 = 1.000
313.15 318.15 323.15 328.15 333.15 338.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15
2.5333 3.5707 4.5033 5.613 6.883 8.481 10.227 14.897 21.203 29.933 41.760 56.87 75.56
0.0089 0.0062 0.0072 0.011 0.009 0.010 0.006 0.008 0.008 0.007 0.025 0.02 0.03
308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 353.15 363.15 373.15 383.15 403.15
2.6307 3.5244 4.3720 5.370 6.496 7.750 9.305 11.116 15.968 22.758 32.056 44.232 80.20
0.0216 0.0125 0.0163 0.021 0.016 0.016 0.013 0.012 0.016 0.016 0.022 0.03 0.02
Standard uncertainties u are u(T) = 0.02 K and u(x) = 0.0003.
Table 10 Experimental VLE data for temperature T, pressure p with standard uncertainty u(p), and mole fraction x1 for the system p-xylene (1) + dipropylene glycol (2)a T/K
p/kPa
u(p)
0.3627 0.6227 1.0387 1.6844 2.6627 4.2031 7.104 10.524 15.117 21.914 30.564 42.295 53.10
0.0125 0.0079 0.0043 0.0093 0.0046 0.0079 0.013 0.008 0.016 0.024 0.031 0.015 0.04
x1 = 0 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 473.15 483.15
T/K
a
u(p)
T/K
3.2467 4.5467 6.327 8.320 11.140 14.723 19.183 24.817 31.897 41.353 51.91 65.39 82.05
0.0083 0.0095 0.011 0.008 0.007 0.010 0.013 0.011 0.012 0.016 0.01 0.01 0.01
x1 = 0.1003 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15
x1 = 0.7008 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 383.15 393.15 403.15 413.15
p/kPa
p/kPa
u(p)
6.543 7.910 9.497 11.283 13.303 15.747 21.403 28.510 37.423 48.773 62.61 70.63 80.01
0.017 0.011 0.007 0.010 0.010 0.010 0.008 0.009 0.009 0.009 0.01 0.01 0.01
x1 = 0.3033 338.15 343.15 348.15 353.15 358.15 363.15 373.15 383.15 393.15 403.15 413.15 418.15 423.15
0.010 0.009 0.013 0.017 0.016 0.016 0.016 0.021 0.021 0.011 0.01 0.01 0.01
328.15 338.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 393.15 403.15 408.15
Standard uncertainties u are u(T) = 0.01 K and u(x) = 0.0003.
p/kPa
u(p)
6.508 7.947 9.618 11.557 13.960 16.722 19.683 26.937 36.420 48.528 63.88 82.78 93.01
0.017 0.017 0.013 0.017 0.017 0.017 0.017 0.008 0.029 0.025 0.02 0.02 0.01
x1 = 0.5009
x1 = 0.8994 6.743 8.207 10.199 12.358 15.028 18.023 21.331 25.045 29.317 40.840 54.82 72.35 94.06
T/K
333.15 338.15 343.15 348.15 353.15 358.15 363.15 373.15 383.15 393.15 403.15 413.15 418.15
x1 = 1.000 5.237 8.153 12.330 14.970 18.060 21.643 25.813 31.012 36.606 42.677 57.62 76.78 88.12
0.007 0.010 0.011 0.008 0.011 0.010 0.010 0.022 0.029 0.025 0.02 0.03 0.02
303.15 313.15 323.15 333.15 343.15 353.15 358.15 363.15 373.15 383.15 393.15 403.15 408.15
1.5615 2.4901 4.422 6.997 10.635 15.721 19.037 22.803 32.043 44.565 60.79 80.87 92.43
0.0125 0.0163 0.016 0.016 0.016 0.029 0.022 0.017 0.025 0.029 0.03 0.03 0.02
M. Nicolae, F. Oprea / Fluid Phase Equilibria 370 (2014) 34–42
41
Fig. 3. Plot of calculated boiling point temperature against mole fraction: (—) predicted liquid and vapor compositions with UNIFAC model, at 6.664 kPa; () calculated liquid and vapor compositions with NRTL model completed with the binary interaction parameters obtained from regression, at 6.664 kPa; () calculated liquid and vapor compositions with UNIQUAC model completed with the binary interaction parameters obtained from regression, at 6.664 kPa; (– – –) predicted liquid and vapor compositions with UNIFAC model, at 26.658 kPa; () calculated liquid and vapor compositions with NRTL model completed with the binary interaction parameters obtained from regression, at 26.658 kPa; ( ) calculated liquid and vapor compositions with UNIQUAC model completed with the binary interaction parameters obtained from regression, at 26.658 kPa; (· · ·) predicted liquid and vapor compositions with UNIFAC model, at 101.33 kPa; () calculated liquid and vapor compositions with NRTL model completed with the binary interaction parameters obtained from regression, at 101.33 kPa; (♦), calculated liquid and vapor compositions with UNIQUAC model completed with the binary interaction parameters obtained from regression, at 101.33 kPa for three binary mixtures: (a) benzene (1) + dipropylene glycol (2); (b) toluene (1) + dipropylene glycol (2); (c) ethylbenzene (1) + dipropylene glycol (2); (d) o-xylene (1) + dipropylene glycol (2); (e) m-xylene (1) + dipropylene glycol (2); (f) p-xylene (1) + dipropylene glycol (2).
Eqs. (6)–(13) describe the UNIQUAC parameters: ln i = ln (r)
ln i
(c) i
+ ln
⎛
(r) i
= −qi ln ⎝
⎞
j ji ⎠ + qi − qi
(6)
j ij
j (c)
ln i
= ln
j
ϕi z ϕ + qi ln i + li − i xj lj xi 2 ϕi xi
k k kj
(7)
(8)
j
z (r − qj ) − (rj − 1) 2 j rx qx i = i i , ϕi i i q x rx j i i j j j lj =
ij = exp
−
ij = exp
−
Uij T Uij RT
Uij = aij + bij T
(9) (10)
, when unit is K
(11)
, when unit is kcal or kJ
(12)
(13)
To obtain parameters for the NRTL model (with five and eight interaction parameters) and for the UNIQUAC model (with two and four parameters) we used regression analysis of the experimental data. We obtained good results for the NRTL model with five
interaction parameters. For this regression version, we obtained the smallest relative deviations of calculated values for vapor pressure and compositions from the experimental values of the same variables. We calculated the percentage of relative deviations of calculated vapor pressure from the values of the experimental vapor pressure using Eq. (14). Our objective was to find relative deviations approximately ±1.5% for vapor pressure and relative deviations approximately ±3% for molar compositions of hydrocarbon and dipropylene glycol. Deviations of the vapor pressure are shown in Fig. 2 and the parameters resulted from the regression are listed in Table 3. pcalc − pexpt p · 100 = · 100 p pexpt
(14)
Furthermore, regressions have been achieved for the UNIQUAC model. Although our best results were obtained using a four parameters model, the deviations of compositions were unsatisfactory. In Table 2 we listed the maximum and the average deviations of molar composition for each binary studied, for both NRTL and UNIQUAC models. We calculated and plotted the T–x–y diagrams for all binaries studied using the two models specific for each binary mixture, at three different pressures (6.664 kPa, 26.584 kPa and 101.33 kPa). We compared the results to those predicted using the UNIFAC Dortmund model (diagrams are shown in Fig. 3).
42
M. Nicolae, F. Oprea / Fluid Phase Equilibria 370 (2014) 34–42
As per Fig. 3, the T–x–y diagrams calculated with NRTL and UNIQUAC models, completed with the binary interaction parameters obtained from regression, are overlapping. Furthermore, there are large differences between the boiling point curves calculated with NRTL and UNIQUAC models and those predicted with UNIFAC Dortmund [16,17] model. The reason is that UNIFAC (a combination of the UNIQUAC model with the concept of functional groupcontribution) is a predictive thermodynamic model utilized to calculate the activity coefficients in a solution of non-electrolytes, which is a mixture of functional groups, not a mixture of molecular species. As UNIFAC is an approximate method, its accuracy improves as the distinction between groups increases. The UNIFAC Dortmund model better describes the adjustable parameters’ temperature dependence implied in the calculation of activity coefficients [18]. 5. Conclusion We obtained experimental vapor liquid equilibrium data using a static apparatus for the following binary mixtures: benzene + dipropylene glycol, toluene + dipropylene glycol, ethylbenzene + dipropylene glycol, o-xylene + dipropylene glycol, mxylene + dipropylene glycol, and p-xylene + dipropylene glycol. We applied regression analysis for this data using the NRTL and UNIQUAC thermodynamic models to obtain the binary interaction parameters, specific for each binary. Furthermore, we used the resulting parameters to calculate the T–x–y diagrams. Although the resulted diagrams, (calculated with these two models) are in agreement, there are considerable differences between the boiling point curves (calculated with the models and those predicted with the UNIFAC Dortmund model). Acknowledgements The authors would like to thank Mr. Alexandru Pan˘a, Head of Quality Control Department, S. C. Oltchim S. A. Râmnicu Vâlcea, România, for assistance and fruitful discussions, S. C. Oltchim S. A. Râmnicu Vâlcea, România, for assistance and Dow Chemical, Germany, for materials. References [1] C. Wei-Kuan, L. Kun-Jung, J.C. Chieh-Ming, K. Jing-Wei, L. Liang-Sung, Vapor–liquid equilibria and density measurement for binary mixtures of toluene, benzene, o-xylene, m-xylene, sulfolane and nonane at 333.15 K and 353.15 K, Fluid Phase Equilib. 287 (2010) 126–133.
[2] R. Rappel, L.M. Nelson de Góis, S. Mattedi, Liquid–liquid data for systems containing aromatic + nonaromatic + sulfolane at 308.15 and 323.15 K, Fluid Phase Equilib. 202 (2) (2002) 263–276. [3] C. Wei-Kuan, L. Kun-Jung, J.C. Chieh-Ming, K. Jing-Wei, L. Liang-Sung, Vapor–liquid equilibria and density measurement for binary mixtures of o-xylene +NMF, m-xylene + NMF and p-xylene + NMF at 333.15 K, 343.15 K and 353.15 K from 0 kPa to 101.3 kPa, Fluid Phase Equilib. 291 (2010) 40–47. [4] T.A. Al-Zayied, T.A. Al-Sahhaf, M.A. Fahim, Measuremment of phase equilibrium in multicomponent systems of aromatics with n-methylpyrrolidone and predictions with unifac, Fluid Phase Equilib. 61 (1–2) (1990) 131–144. [5] S.K. Gupta, B.S. Rawat, A.N. Goswami, S.M. Nanoti, R. Krishna, Isobaric vapour–liquid equilibria of the systems: benzene-trietylene glycol, toluenetriethylene glycol and benzene-N-methylpyrrolidone, Fluid Phase Equilib. 46 (1) (1989) 95–102. [6] T.A. Al-Sahhaf, E. Kapetanovic, Liquid–liquid equilibria for the system reformate-dimethyl sulphoxide, Fluid Phase Equilib. 119 (1–2) (1996) 153–163. [7] H.-J. Ng, C.-J. Chen, M. Razzaghi, Vapor–liquid equilibria of selected aromatic hydrocarbons in triethylene glycol, Fluid Phase Equilib. 82 (1993) 207–214. [8] T.A. Al-Sahhaf, E. Kapetanovic, Measurement and prediction of phase equilibria in the extraction of aromatics from naphta reformate by tetraethylene glycol, Fluid Phase Equilib. 118 (2) (1996) 271–285. [9] Y.-X. Yu, J.-G. Liu, G.-H. Gao, Isobaric vapor–liquid equilibria of three aromatic hydrocarbon-tetraethylene glycol binary systems, Fluid Phase Equilib. 157 (2) (1999) 299–307. [10] F. Oprea, O.A. Gut¸u, Experimental data and regressions concerning the evaluation of 1,2 propylene glycol as a new solvent for aromatic hydrocarbons liquid–liquid extraction from catalytic reformer products, in: B.A. Moyer (Ed.), Solvent Extraction – Fundamentals to Industrial Applications, Proceedings of International Solvent Extraction Conference, Tucson, AZ, USA, 15–19 September, 2008, Canadian Institute of Mining, Metallurgy and Petroleum, Montreal, 2008, pp. 1075–1080. [11] F. Oprea, Evaluation of 1,2-propylene glycol as a New Solvent for Aromatic Hydrocarbons Liquid–Liquid Extraction from Catalytic Reformer Products, Buletinul Universit˘at¸ii Petrol-Gaze, Seria tehnic˘a, LX, 4B, 2008, pp. 18–24. [12] M. Nicolae, F. Oprea, Liquid–liquid equilibria for dipropylene glycol–hydrocarbons binary systems: experimental data and regression, J. Chem. Eng. Data 57 (12) (2012) 3690–3695. [13] E.M. Fendu, F. Oprea, Vapor pressure, density, viscosity, and surface tension of tetrapropylene glycol, J. Chem. Eng. Data 58 (11) (2013) 2898–2903. [14] H. Renon, J.M. Prausnitz, Local compositions in thermodynamic excess functions for liquid mixtures, AIChE J. 14 (1968) 135–144. [15] D.S. Abrams, J.M. Prausnitz, Statistical Thermodynamic of liquid mixtures: a new expression for the excess Gibbs Energy of partly or completely miscible systems, AIChE J. 21 (1975) 116–128. [16] Simulation Software PRO/II of SimSci-Esscor, version 9.2, Invensys Systems, Inc., 26561 Rancho Parkway, South Lake Forest, CA 92630, U.S.A., 2013. [17] A. Jakob, H. Grensemann, J. Lohmann, J. Gmehling, Further development of modified UNIFAC (Dortmund): revision and extension 5, Ind. Eng. Chem. Res. 45 (23) (2006) 7924–7933. [18] DDBST GmbH, UNIFAC Documentation, Dortmund Data Bank Software & Separation Technology GmbH, 2013 http://www.ddbst.com/tl files/ img/products/2013/Doc/UNIFAC.pdf
