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Isobaric vapor–liquid–liquid equilibria with a newly developed still
Fluid Phase Equilibria 192 (2001) 171–186
Isobaric vapor–liquid–liquid equilibria with a newly developed still Koichi Iwakabe, Hitoshi Kosuge∗ Department of Chemical Engineering, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8552, Japan Received 11 June 2001; accepted 11 September 2001
Abstract A new and simple apparatus for the measurement of isobaric vapor–liquid–liquid equilibrium (VLLE) is developed by modifying the still proposed by van Zandijcke et al. The still is used to measure the isobaric vapor–liquid equilibrium (VLE) data for the system ethanol–water, the isobaric VLE and VLLE data for the binary systems water–1-butanol and 2-butanol–water at atmospheric pressure. The obtained data for the binary systems are compared with the previous data in the literature. The thermodynamic consistencies of the obtained data for the binary systems are confirmed by the Herington’s area test. Furthermore, the isobaric VLLE data for the ternary systems ethanol–water–1-butanol and ethanol–2-butanol–water are obtained with the apparatus. The results show that the apparatus can be applied to the measurements of both isobaric VLE and VLLE successfully. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Experimental method; Vapor–liquid equilibria; Vapor–liquid–liquid equilibria
1. Introduction The isobaric vapor–liquid–liquid equilibrium (VLLE) data is one of the basic important physical properties for design and analysis of heterogeneous distillation columns. Since a huge number of vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE) data have been measured, VLLE data can be easily estimated by the parameter sets of liquid phase activity coefficient equations that are determined by the experimental VLE or LLE data. However, the VLLE data estimated with the parameters determined by the VLE ones are different from those by LLE, because the parameter sets of the activity coefficient equation are quite different with each other. To overcome the problem, the observed VLLE data are essential. However, VLLE data available in the previous literature are very few. This is due to the difficulties of VLLE measurements. In this study, a new and simple VLLE still is developed by modifying ∗
Corresponding author. Tel.: +81-3-5734-2151; fax: +81-3-5734-2151. E-mail address: [email protected] (H. Kosuge). 0378-3812/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 6 3 1 - 8
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the van Zandijcke and Verhoeye type VLLE still [1]. In order to evaluate the performance of the still, measurements of binary VLE data are carried out for the system ethanol (1)–water (2), and the observed data are rated by a thermodynamic consistency test. Then, the isobaric binary VLE and VLLE data for the systems water (1)–1-butanol (2) and 2-butanol (1)–water (2) are measured. The results obtained from the experiments are compared with previous literature. Finally, the isobaric VLLE data for the ternary systems ethanol (1)–water (2)–1-butanol (3) and ethanol (1)–2-butanol (2)–water (3) are obtained with the apparatus.
2. Structure of VLLE still The difficulty of VLLE measurements lies in the concentration analysis of two liquid phases that appear in a VLLE still. To measure the equilibrium compositions of two liquid phases, both liquids are drawn to a separate measuring cell immersed in a constant temperature bath that is controlled at the equilibrium temperature (van Zandijcke and Verhoeye [1] and Gomis et al. [2]). However, the equilibrium conditions in the measuring cell might differ from those in the VLLE still due to the evaporation in the cell. Also these entire equipments for VLLE measurement are much more complex and bigger than the conventional VLE equipments. Another difficulty of VLLE measurements lies in the mixing of two liquids in the boiling flask, as Gomis et al. mentioned [2]. For the case of the Othmer type still, the mixing of two liquids is usually done by a stirrer. However, it appears to be difficult to obtain well-mixed liquids in the boiling flask by this method. Therefore, it is difficult to generate a vapor, which is in equilibrium with two liquids in the Othmer type still. This type of still also has low thermodynamic reliability in its data, because of the rectifying effect present in the still (Malanowski [3]). For the case of the Gillespie type still, the mixing conditions of two liquids in the still, which is usually achieved by a stirrer, may affect the flow condition of the liquids and vapor in the Cottrell pump, and the compositions of the liquids and vapor in the equilibrium chamber. Recently, Gomis et al. [2] proposed the modified Gillespie type still with an ultrasonic homogenizer that stirs the suspended liquid in the flask. Alternatively, van Zandijcke and Verhoeye [1] developed the modified Gillespie type still with a liquid separator inside the boiling flask, which is completely partitioned into the upper and the lower chambers. The advantage of the still developed by van Zandijcke and Verhoeye [1] is that mechanical mixing of two liquids is unnecessary and the two liquids and vapor are able to rise up together in the Cottrell pump. In order to test the performance of the still by van Zandijcke and Verhoeye [1], we have measured the VLE and VLLE data using the still with a separator similar to the one by van Zandijcke and Verhoeye [1]. Nevertheless, the observed fluctuation of the temperature inside the equilibrium chamber was relatively large and the accuracy of the observed VLE and VLLE data were somewhat poor in terms of the thermodynamic consistency. The inaccuracy is caused by the incomplete separation of the light and heavy liquids at the upper and lower chambers inside the still, i.e. the amount of the light liquid in the lower chamber fluctuates with time. Based on the above discussion, a new and simple VLLE still was developed. The schematic diagram of the still is shown in Fig. 1. The still, which is made from Pyrex glass, is based on the van Zandijcke type still [1], i.e. consists of a boiling flask (A), a Cottrell pump (B), an equilibrium chamber (C) with a thermometer well (I), a vapor–liquid mixing chamber (F). A conical shaped cup (G) is placed above the electric heater (M) in the boiling flask to allow the heavier liquid and vapor to rise up together in the
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173
Fig. 1. Schematic diagram of the experimental apparatus.
Cottrell pump (B), and a conduit (H) is attached at the top of the boiling flask to send the lighter liquid and vapor to the Cottrell pump (B). To obtain LLE of two liquids flown down from the equilibrium chamber (C), a small cell (J) with the volume of 2 ml is placed in the liquid collector (D). The liquid samples in the small cell (J) are drawn through the sampling port (K) by a syringe.
3. Experimental 3.1. Experimental procedure Isobaric binary VLE for the systems ethanol (1)–water (2), water (1)–1-butanol (2), 2-butanol (1)–water (2) are measured at atmospheric pressure. Approximately 200 ml of the liquid mixture is loaded into the boiling flask and heated by the electric heater. After the liquid in the flask starts to boil, the accumulated liquid in the small cell (J) is sucked out by a syringe at least twice until the steady state. The steady state, where the fluctuation of the temperature in the equilibrium chamber becomes less than ±0.01 K, is usually attained within an hour from the beginning of the boiling. At the steady state, the temperature of the equilibrium chamber is recorded and the condensed vapor and liquid samples are taken from each tap to determine their compositions by gas chromatography (GC) analysis. If the condensed vapor and liquid samples are immiscible, 2-propanol is added to the sample to make them homogeneous.
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The isobaric VLLE data are measured for the binary systems water (1)–1-butanol (2) and 2-butanol (1)–water (2), and for the ternary systems ethanol (1)–water (2)–1-butanol (3) and ethanol (1)–2-butanol (2)–water (3) at atmospheric pressure. The procedure is similar to isobaric VLE measurements except for the sampling of the immiscible liquids. The liquids collected in the small cell (J) are sucked out at least twice by a syringe after boiling starts. Before taking the liquid samples, the liquids inside the cell (J) are allowed to settle for around 2 h so that the LLE condition can be attained. While the two liquids in the cell (J) are settling, the compositions of the upper and lower phases in the cell are checked by GC analysis. This procedure doesn’t affect the boiling point because a small enough volume of less than 3 l of the sample is taken by a syringe. After their compositions are confirmed to be constant, the upper and the lower liquid phases in the cell are again sampled with a syringe (3 l) and analyzed by GC. The analysis of the condensed vapor compositions is done in the same manner as VLE measurements. For ternary systems, total liquid compositions are also analyzed by GC to confirm the material balances of the liquid phases are kept. 3.2. Measurements of temperatures and compositions A Pt100 resistance thermometer inserted into the thermometer well in the equilibrium chamber is used to measure the boiling point. It was calibrated by the measurements of the boiling points of several pure chemicals. The accuracy of the temperature measurements is estimated to be ±0.03 K by the calibration. Compositions of the condensed vapor and liquid samples are analyzed with Shimadzu GC-8AIT and Shimadzu integrator C-R6A Chromatpac. The GC column used is SUNPAK A. Helium is used as a carrier gas for GC analysis at the flow condition of 50 ml/min. The GC was calibrated by the absolute calibration curve method. The consistencies of the GC calibration curves obtained for the components were examined by several mixtures with known compositions for each system. The accuracy of composition analysis with GC is estimated to be ±0.0005 mole fraction. 3.3. Materials All materials used in this study are supplied by Wako Pure Chemicals Industries Ltd., Japan. Nominal purities of ethanol, 2-propanol, 1-butanol and 2-butanol are 99.5, 99.5, 99.0 and 99.0%, respectively. Since 2-propanol is used as a solvent to make the immiscible liquid homogeneous as mentioned above, it is dried with Molecular Sieves 5A 1/16 to remove water. Water used in this study is distilled water. All materials except 2-propanol are used without further purification. The densities and the boiling points of the materials used are measured, and the results with those reported in the literature are listed in Table 1. The densities of the materials in the literature [4–8] are obtained by interpolations. The boiling points of the materials are compared with ones predicted by the Antoine equation mentioned in the next section. 3.4. Data reduction To obtain the boiling points at 101.3 kPa, the following equation is used [9]. 1 101.3 − P0 T = T0 + · N P0 Bi (ln 10) xi (T0 + C i )2 i=1
(1)
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Table 1 Physical properties of materials Material
Density
P0 (kPa)
T (K)
ρ 0 (g cm−3 )
ρ calc (g cm−3 )
Reference
Ethanol
301.81
0.7824
0.7820 0.7818 0.7820 0.7823
[4] [5] [6] [7]
1-Butanol
301.38
0.8021
0.8034 0.8033
2-Butanol
301.15
0.7988
Water
300.27
0.9965
Boiling point (K) T0
Tcalc
100.3
351.18
351.19
[4] [5]
100.0
390.49
390.51
0.7960 0.7999
[4] [5]
100.2
372.36
372.35
0.9965
[8]
100.9
373.04
373.04
where T0 is observed boiling point, P0 is atmospheric pressure, T is boiling point at 101.3 kPa, Bi and Ci are Antoine constants of the component i. Liquid phase activity coefficients are calculated by the following equation γi =
xi Pis ϕis
Pyi ϕi exp[viL (P − Pis )/RT]
(2)
where xi and yi are the observed liquid and vapor composition of the component i, and R is gas constant. The saturated vapor pressure of the component i, Pis , is calculated by the Antoine equation. logPis = Ai −
Bi T + Ci
(3)
The values of Antoine constants, Ai , Bi and Ci are taken from the literature [10]. The fugacity coefficient of the component i, ϕ i , and that of the pure component jis are calculated by using the second virial coefficients predicted by the Tsonopoulos method [11]. The molar volume of the component i, viL , are estimated by the Rackett equation modified by Spencer and Adler [12]. In order to examine the thermodynamical consistency of the experimental data, the Herington’s area test [13] is employed. The criterion of the area test is D − J < 10. Here, D and J are defined as follows: 1 | 0 ln(γ1 /γ2 ) dx1 | |A − B | D = 1 × 100 = × 100 (4) |A | + |B | |ln(γ1 /γ2 )| dx1 0
J =
Tmax − Tmin × 150 Tmin
(5)
where A and B are the positive and the negative area surrounded by the natural logarithmic values of the ratio of the liquid activity coefficients and the x1 axis in Figs. 3, 5 and 7. The natural logarithmic values of
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the ratio of the liquid phase activity coefficients in Eq. (4) are correlated by the extended Redlich–Kister expansion [13]: γ1 ln = a + b (x2 − x1 ) + c (6x1 x2 − 1) + d (x1 − x2 )(8x1 x2 − 1) (6) γ2 where the coefficients a , b , c and d are determined by fitting the experimental data.
4. Results and discussion 4.1. Ethanol–water system In order to validate the performance of the apparatus developed in this study, measurements of VLE data are carried out for the system ethanol (1)–water (2) because a number of VLE data and physical properties for the system are vastly available in the literature. The observed data, vapor and liquid compositions, boiling temperatures, calculated values of the activity coefficients, second virial coefficients and fugacity coefficients are shown in Table 2. The boiling and dew points of this study and those reported in the literature [14–16] are plotted against the compositions of ethanol in Fig. 2(a). As shown in Fig. 2(a), the observed boiling and dew points for this study are in good agreement with the values reported in the literature. The activity coefficients are plotted against the mole fraction of ethanol in the liquid phase in Fig. 2(b). The thermodynamic consistency of the experimental data for the system was examined by Herington’s area test [13], which is shown in Fig. 3. Coefficients of Eq. (6) are shown in Table 3. The obtained value of D − J for the observed data is −3.40. This satisfies the criteria of the area test, D − J < 10. Thus, the VLE data obtained by the present apparatus are thermodynamically consistent.
Fig. 2. Isobaric VLE for the system ethanol (1)–water (2) at 101.3 kPa: (a) boiling and dew points; (b) activity coefficients.
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Table 2 Isobaric VLE data for the system ethanol (1)–water (2) at 101.3 kPa x1
y1
T
γ1
γ2
Btotal
ϕ1
ϕ2
ϕ1s
ϕ2s
0.0402 0.0514 0.0580 0.0721 0.0729 0.0959 0.1072 0.1201 0.1237 0.1297 0.1399 0.1586 0.1935 0.1967 0.2363 0.2916 0.3507 0.3812 0.4157 0.4819 0.5189 0.5205 0.6382 0.7453 0.8396 0.8436 0.9370 0.9372
0.2981 0.3368 0.3564 0.3932 0.3868 0.4362 0.4546 0.4719 0.4725 0.4808 0.4909 0.5025 0.5176 0.5165 0.5385 0.5690 0.5913 0.6013 0.6164 0.6398 0.6578 0.6561 0.7245 0.7816 0.8491 0.8525 0.9341 0.9339
364.23 362.89 362.25 360.87 361.01 359.41 358.86 358.23 358.12 357.93 357.60 357.07 356.43 356.38 355.57 354.88 354.23 353.95 353.66 353.15 352.87 352.88 352.12 351.66 351.45 351.43 351.39 351.41
4.700 4.353 4.168 3.885 3.761 3.410 3.242 3.072 3.000 2.930 2.806 2.583 2.233 2.195 1.963 1.723 1.525 1.441 1.369 1.249 1.205 1.197 1.109 1.042 1.012 1.012 0.999 0.998
1.010 1.016 1.017 1.026 1.032 1.035 1.036 1.043 1.050 1.049 1.054 1.075 1.116 1.125 1.166 1.207 1.282 1.328 1.369 1.481 1.532 1.545 1.696 1.949 2.163 2.171 2.422 2.437
−0.0006586 −0.0006670 −0.0006715 −0.0006833 −0.0006822 −0.0006977 −0.0007040 −0.0007115 −0.0007128 −0.0007153 −0.0007196 −0.0007264 −0.0007352 −0.0007356 −0.0007477 −0.0007608 −0.0007731 −0.0007788 −0.0007860 −0.0007989 −0.0008080 −0.0008073 −0.0008432 −0.0008769 −0.0009192 −0.0009217 −0.0009801 −0.0009795
0.9817 0.9803 0.9795 0.9781 0.9783 0.9765 0.9758 0.9752 0.9751 0.9748 0.9745 0.9740 0.9733 0.9733 0.9725 0.9715 0.9707 0.9703 0.9699 0.9692 0.9687 0.9687 0.9672 0.9662 0.9654 0.9654 0.9649 0.9649
0.9767 0.9766 0.9766 0.9766 0.9765 0.9767 0.9768 0.9769 0.9769 0.9770 0.9771 0.9771 0.9772 0.9771 0.9773 0.9778 0.9782 0.9784 0.9787 0.9793 0.9798 0.9797 0.9819 0.9841 0.9870 0.9871 0.9911 0.9911
0.9537 0.9550 0.9556 0.9568 0.9567 0.9581 0.9586 0.9592 0.9593 0.9594 0.9597 0.9602 0.9607 0.9608 0.9614 0.9620 0.9626 0.9628 0.9630 0.9634 0.9637 0.9637 0.9643 0.9646 0.9648 0.9648 0.9648 0.9648
0.9820 0.9825 0.9827 0.9832 0.9831 0.9836 0.9838 0.9840 0.9840 0.9841 0.9842 0.9844 0.9846 0.9846 0.9848 0.9850 0.9852 0.9853 0.9854 0.9856 0.9856 0.9856 0.9859 0.9860 0.9861 0.9861 0.9861 0.9861
Fig. 3. Herington’s area test for the system ethanol (1)–water (2).
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Table 3 Coefficients of Eq. (6) and results of the Herington’s area test System
a
b
c
d
D−J
Ethanol–water Water–1-butanol 2-Butanol–water
−0.0117 −0.1389 0.0533
1.2018 2.2816 1.9974
−0.3894 1.1969 −0.9449
0.1956 0.4425 0.7338
−3.40 3.04 −9.65
4.2. Water–1-butanol and 2-butanol–water systems The isobaric VLE and VLLE data for the binary systems water (1)–1-butanol (2) and 2-butanol (1)–water (2) were measured at atmospheric pressure. The observed data and calculated values of the activity coefficients for VLE and VLLE are shown in Tables 4 and 5, respectively. The observed boiling and dew points and those reported in the literature [17–20] for the system water (1)–1-butanol (2), [23–25] for the system 2-butanol (1)–water (2)) are shown in Figs. 4(a) and 6(a), respectively. In Figs. 4(a) and 6(a), solubility data at various temperatures reported in the literature ([21,26], respectively) are also plotted. For the system water (1)–1-butanol (2), the observed liquid phase compositions of the organic and the aqueous phases for the isobaric binary VLLE are 0.6393 and 0.9781 mole fraction of, respectively. The values of compositions of both phases agreed well with the graphically interpolated values from the previous solubility data, which are 0.6492 and 0.9788 mole fractions, respectively. The observed azeotropic temperature and vapor composition are 365.92 K and 0.7590 mole fraction of water, respectively, while the average azeotropic temperature and vapor composition of the data in the literature [22] are 365.84 K
Fig. 4. Isobaric VLE and VLLE for the system water (1)–1-butanol (2) at 101.3 kPa: (a) boiling and dew points; (b) activity coefficients.
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Table 4 Isobaric VLE and VLLE data for the system water (1)–1-butanol (2) at 101.3 kPa x1
y1
T
γ1
γ2
Btotal
ϕ1
ϕ2
ϕ1s
ϕ2s
0.0168 0.0218 0.0297 0.0486 0.0575 0.0683 0.0811 0.0916 0.0955 0.0996 0.1045 0.1125 0.1284 0.1678 0.2125 0.2222 0.2354 0.2544 0.2640 0.2696 0.3196 0.3302 0.3988 0.4012 0.4203 0.4858 0.4927 0.5051 0.5191 0.5614 0.5945 0.6393a 0.9781a 0.9887 0.9929 0.9952 0.9964 0.9969 0.9992
0.1024 0.1318 0.1696 0.2513 0.2863 0.3279 0.3602 0.3972 0.4049 0.4128 0.4368 0.4468 0.5026 0.5670 0.6124 0.6272 0.6428 0.6550 0.6607 0.6648 0.6965 0.7009 0.7341 0.7297 0.7388 0.7542 0.7501 0.7518 0.7577 0.7561 0.7564 0.7590 0.7590 0.7950 0.8526 0.8867 0.9025 0.9121 0.9674
388.24 387.54 386.15 383.78 382.76 381.64 380.56 379.30 379.14 378.91 378.06 377.75 376.60 374.12 372.09 371.71 371.26 370.55 370.28 370.12 368.82 368.42 367.43 367.24 367.06 366.50 366.39 366.30 366.23 366.16 366.03 365.92 365.92 366.88 368.44 369.67 370.45 370.49 372.41
3.731 3.776 3.731 3.642 3.622 3.625 3.473 3.536 3.474 3.423 3.552 3.408 3.490 3.280 3.001 2.979 2.928 2.830 2.778 2.752 2.548 2.518 2.262 2.250 2.189 1.972 1.942 1.905 1.581 1.732 1.644 1.541 1.007 1.007 1.016 1.008 0.997 1.005 0.994
1.000 0.997 1.010 1.011 1.010 1.003 1.008 1.007 1.004 1.004 1.000 1.003 0.961 0.965 0.990 0.979 0.972 0.990 0.998 1.000 1.025 1.043 1.078 1.108 1.115 1.211 1.253 1.281 1.917 1.428 1.551 1.734 28.51 45.13 49.02 52.43 59.46 62.19 78.51
−0.0009344 −0.0009141 −0.0008937 −0.0008465 −0.0008280 −0.0008064 −0.0007927 −0.0007786 −0.0007747 −0.0007716 −0.0007638 −0.0007603 −0.0007375 −0.0007268 −0.0007254 −0.0007228 −0.0007211 −0.0007234 −0.0007240 −0.0007242 −0.0007268 −0.0007296 −0.0007307 −0.0007338 −0.0007335 −0.0007359 −0.0007381 −0.0007387 −0.0007755 −0.0007392 −0.0007406 −0.0007413 −0.0007412 −0.0007241 −0.0007007 −0.0006860 −0.0006777 −0.0006773 −0.0006601
0.9976 0.9967 0.9955 0.9929 0.9918 0.9906 0.9896 0.9884 0.9882 0.9879 0.9872 0.9869 0.9854 0.9834 0.9819 0.9815 0.9811 0.9806 0.9805 0.9803 0.9793 0.9791 0.9783 0.9782 0.9780 0.9776 0.9776 0.9775 0.9794 0.9774 0.9774 0.9773 0.9773 0.9773 0.9774 0.9777 0.9780 0.9779 0.9785
0.9681 0.9679 0.9675 0.9670 0.9669 0.9669 0.9668 0.9667 0.9668 0.9668 0.9668 0.9669 0.9674 0.9678 0.9681 0.9683 0.9686 0.9686 0.9687 0.9688 0.9692 0.9692 0.9700 0.9698 0.9700 0.9704 0.9702 0.9702 0.9660 0.9703 0.9703 0.9703 0.9703 0.9722 0.9751 0.9770 0.9779 0.9783 0.9812
0.9725 0.9728 0.9734 0.9745 0.9749 0.9754 0.9759 0.9764 0.9764 0.9765 0.9769 0.9770 0.9775 0.9784 0.9792 0.9793 0.9795 0.9798 0.9799 0.9799 0.9804 0.9806 0.9809 0.9810 0.9810 0.9812 0.9813 0.9813 0.9813 0.9814 0.9814 0.9814 0.9814 0.9811 0.9806 0.9801 0.9798 0.9798 0.9791
0.9710 0.9715 0.9725 0.9741 0.9747 0.9755 0.9761 0.9769 0.9770 0.9772 0.9777 0.9779 0.9785 0.9800 0.9811 0.9813 0.9815 0.9819 0.9820 0.9821 0.9828 0.9830 0.9835 0.9836 0.9837 0.9839 0.9840 0.9840 0.9841 0.9841 0.9842 0.9842 0.9842 0.9838 0.9830 0.9824 0.9819 0.9819 0.9809
a
VLLE data.
and 0.7468 mole fraction of water, respectively. From the comparison of these values, the heterogeneous azeotropic data obtained by the present apparatus appears to be reliable. The calculated activity coefficients for the system are shown in Fig. 4(b). With these activity coefficients, VLE and VLLE data of the system were examined by the area test [13], which is shown in Fig. 5 and Table 3. The value of D − J for
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Table 5 Isobaric VLE and VLLE data for the system 2-butanol (1)–water (2) at 101.3 kPa x1
y1
T
γ1
γ2
Btotal
ϕ1
ϕ2
ϕ1s
ϕ2s
0.0011 0.0040 0.0048 0.0048 0.0068 0.0078 0.0101 0.0117 0.0118 0.0136 0.0136 0.0164 0.0173 0.0182 0.0410a 0.2982a 0.3908 0.4134 0.4597 0.4598 0.5147 0.5289 0.5759 0.6344 0.6476 0.6605 0.6837 0.6986 0.7426 0.7760 0.7989 0.8918 0.9055
0.0810 0.1355 0.1658 0.1692 0.2065 0.2301 0.2573 0.2852 0.2819 0.3066 0.3031 0.3132 0.3175 0.3279 0.3799 0.3799 0.3866 0.3899 0.4035 0.4057 0.4187 0.4204 0.4393 0.4542 0.4683 0.4776 0.4921 0.5026 0.5378 0.5678 0.5907 0.7187 0.7446
371.84 368.96 368.16 368.25 367.04 366.11 365.02 364.22 364.28 363.35 363.56 362.79 362.49 362.26 360.47 360.47 360.50 360.45 360.56 360.56 360.63 360.73 360.90 361.30 361.39 361.61 361.84 362.05 362.78 363.40 363.90 366.80 367.36
78.51 39.61 41.78 42.22 38.07 37.84 34.26 33.70 32.88 32.31 31.50 27.97 27.09 26.83 14.78 2.032 1.575 1.505 1.394 1.401 1.287 1.253 1.194 1.102 1.109 1.099 1.084 1.074 1.050 1.035 1.026 1.000 0.999
0.963 1.008 1.002 0.995 0.995 1.000 1.006 1.000 1.002 1.004 1.001 1.019 1.025 1.019 1.031 1.409 1.604 1.660 1.755 1.749 1.899 1.943 2.076 2.310 2.328 2.355 2.437 2.486 2.634 2.769 2.868 3.306 3.371
−0.0006628 −0.0006932 −0.0007037 −0.0007031 −0.0007206 −0.0007347 −0.0007525 −0.0007686 −0.0007671 −0.0007851 −0.0007816 −0.0007938 −0.0007988 −0.0008051 −0.0008480 −0.0008480 −0.0008506 −0.0008528 −0.0008578 −0.0008589 −0.0008644 −0.0008640 −0.0008719 −0.0008749 −0.0008820 −0.0008847 −0.0008907 −0.0008946 −0.0009090 −0.0009226 −0.0009334 −0.0010054 −0.0010226
0.9793 0.9762 0.9746 0.9745 0.9726 0.9713 0.9697 0.9683 0.9684 0.9670 0.9673 0.9665 0.9662 0.9657 0.9628 0.9627 0.9625 0.9624 0.9620 0.9619 0.9615 0.9615 0.9610 0.9608 0.9604 0.9603 0.9600 0.9598 0.9594 0.9591 0.9589 0.9586 0.9586
0.9784 0.9775 0.9774 0.9775 0.9773 0.9772 0.9771 0.9771 0.9771 0.9771 0.9771 0.9770 0.9769 0.9770 0.9773 0.9773 0.9774 0.9775 0.9779 0.9779 0.9783 0.9783 0.9789 0.9794 0.9798 0.9802 0.9807 0.9810 0.9823 0.9834 0.9843 0.9895 0.9905
0.9612 0.9637 0.9644 0.9643 0.9653 0.9661 0.9670 0.9676 0.9675 0.9683 0.9681 0.9687 0.9689 0.9691 0.9705 0.9705 0.9704 0.9705 0.9704 0.9704 0.9704 0.9703 0.9702 0.9698 0.9698 0.9696 0.9694 0.9693 0.9687 0.9682 0.9678 0.9655 0.9650
0.9793 0.9804 0.9807 0.9806 0.9811 0.9814 0.9818 0.9820 0.9820 0.9823 0.9823 0.9825 0.9826 0.9827 0.9833 0.9833 0.9833 0.9833 0.9833 0.9833 0.9832 0.9832 0.9831 0.9830 0.9830 0.9829 0.9828 0.9828 0.9825 0.9823 0.9821 0.9811 0.9809
a
VLLE data.
the observed data is 3.04 and satisfies the criterion. With these considerations, isobaric VLE and VLLE data of the system are thermodynamically consistent. For the system 2-butanol (1)–water (2), the liquid phase compositions of isobaric VLLE in the organic and the aqueous phases at atmospheric pressure are 0.0410 and 0.2982 mole fraction of 2-butanol, while those interpolated from the solubility data are 0.0392 and 0.2905, respectively. Thus, it shows that the experimental LLE data obtained at boiling point from the present apparatus agrees well with those graphically interpolated ones of LLE. The azeotropic temperature and vapor composition of the system are determined by extrapolating the vapor compositions and temperatures with fourth order polynomial
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181
Fig. 5. Herington’s area test for the system water (1)–1-butanol (2).
equations. They are 360.42 K and 0.3820 mole fraction of water, respectively, while the average ones in the literature [22] are 360.63 K and 0.3859 mole fraction of water, respectively. The activity coefficients for the system are plotted against the liquid compositions in Fig. 6(b). Again the Herington’s area test [13] is performed to examine the thermodynamic consistency of these data. The value of D − J for this system, −9.65, passed the criterion as shown in Fig. 7 and Table 3. From all experimental results of the binary systems, the observed binary VLE and VLLE data obtained by the present still satisfy the thermodynamical consistency test.
Fig. 6. Isobaric VLE and VLLE for the system 2-butanol (1)–water (2) at 101.3 kPa: (a) boiling and dew points; (b) activity coefficients.
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Fig. 7. Herington’s area test for the system 2-butanol (1)–water (2).
4.3. Ethanol–water–1-butanol and ethanol–2-butanol–water systems Isobaric VLLE data for the ternary system ethanol (1)–water (2)–1-butanol (3) are measured at atmospheric pressure to investigate the applicability of the apparatus to the ternary systems. The observed compositions of two liquid phases and vapor phase are shown in Fig. 8 and Table 6. In Fig. 8, the data reported in the literature [2,27] are also plotted to compare the composition profiles. Vapor compositions of the system are on a dashed straight line. The experimental VLLE of this study are in good agreement with those data in the literature. From this result, the apparatus developed in this study can be applied to the isobaric VLLE measurements for the ternary system.
Fig. 8. Isobaric VLLE for the system ethanol (1)–water (2)–1-butanol (3) at 101.3 kPa.
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183
Table 6 Isobaric VLLE data for the system ethanol (1)–water (2)–1-butanol (3) at 101.3 kPa Data No.
xorg1
xorg2
xorg3
xaq1
xaq2
xaq3
y1
y2
y3
T
1 2 3 4
0.0094 0.0187 0.0296 0.0267
0.6406 0.6472 0.6977 0.6727
0.3501 0.3341 0.2726 0.3006
0.0025 0.0054 0.0109 0.0083
0.9746 0.9662 0.9590 0.9658
0.0229 0.0284 0.0300 0.0259
0.0171 0.0357 0.0613 0.0545
0.7621 0.7447 0.7328 0.7339
0.2209 0.2196 0.2058 0.2116
365.62 365.30 364.83 364.98
γ org1
γ org2
γ org3
γ aq1
γ aq2
γ aq3
Btotal
ϕ1
ϕ2
ϕ3
1.098 1.164 1.284 1.260
1.560 1.527 1.417 1.464
1.623 1.712 2.006 1.859
4.148 4.026 3.477 4.035
1.025 1.023 1.031 1.020
24.84 20.15 18.22 21.57
−0.0007377 −0.0007381 −0.0007365 −0.0007371
0.9825 0.9820 0.9816 0.9816
0.9768 0.9765 0.9759 0.9761
0.9503 0.9499 0.9495 0.9496
1 2 3 4
Isobaric VLLE for the ternary system ethanol (1)–2-butanol (2)–water (3) are measured at atmospheric pressure, of which data were not found in the literature. The observed compositions of two liquid phases and vapor phase are shown in Fig. 9 and Table 7. The results of the VLLE for the binary system 2-butanol–water are also plotted in the figure. The compositions of the two liquid phases and the vapor phase in equilibrium are connected by thin dashed straight lines. In Fig. 9, the vapor compositions of the system are on a dashed straight vapor line. However, unlike the system ethanol (1)–water (2)–1-butanol (3), the vapor compositions for the system ethanol (1)–2-butanol (2)–water (3) are completely outside the immiscible liquid region. Since there cannot be seen any large deviations in the compositions of both liquid phases for these two ternary systems, the isobaric ternary VLLE can be measured successfully with the present apparatus.
Fig. 9. Isobaric VLLE for the system ethanol (1)–2-butanol (2)–water (3) at 101.3 kPa.
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Table 7 Isobaric VLLE data for the system ethanol (1)–2-butanol (2)–water (3) at 101.3 kPa Data No.
xorg1
xorg2
xorg3
xaq1
xaq2
xaq3
y1
y2
y3
T
1 2 3 4 5 6 7 8 9 10 11 12
0.0206 0.0091 0.0118 0.0125 0.0219 0.0166 0.0148 0.0118 0.0086 0.0060 0.0153 0.0224
0.2048 0.2661 0.2536 0.2481 0.1973 0.2283 0.2387 0.2534 0.2687 0.2775 0.2385 0.1953
0.7746 0.7248 0.7347 0.7393 0.7808 0.7551 0.7465 0.7347 0.7227 0.7165 0.7463 0.7823
0.0111 0.0036 0.0048 0.0052 0.0122 0.0085 0.0065 0.0049 0.0034 0.0023 0.0069 0.0129
0.0593 0.0454 0.0478 0.0492 0.0610 0.0579 0.0531 0.0494 0.0463 0.0443 0.0540 0.0626
0.9296 0.9510 0.9474 0.9456 0.9268 0.9336 0.9404 0.9456 0.9503 0.9534 0.9392 0.9246
0.0435 0.0170 0.0231 0.0242 0.0468 0.0341 0.0274 0.0230 0.0159 0.0114 0.0294 0.0485
0.3465 0.3618 0.3565 0.3537 0.3424 0.3545 0.3585 0.3608 0.3609 0.3664 0.3502 0.3462
0.6100 0.6212 0.6205 0.6220 0.6108 0.6114 0.6142 0.6162 0.6232 0.6222 0.6204 0.6053
360.06 360.32 360.25 360.24 360.01 360.14 360.20 360.25 360.31 360.34 360.16 360.01
γ org1
γ org2
γ org3
γ aq1
γ aq2
γ aq3
Btotal
ϕ1
ϕ2
ϕ3
1.526 1.339 1.407 1.388 1.550 1.476 1.325 1.394 1.329 1.351 1.390 1.567
2.741 2.180 2.260 2.293 2.816 2.507 2.419 2.289 2.155 2.116 2.369 2.877
1.262 1.359 1.343 1.338 1.256 1.293 1.311 1.333 1.368 1.375 1.326 1.242
2.933 3.555 3.605 3.495 2.874 3.009 3.150 3.489 3.540 3.617 3.209 2.833
9.842 13.26 12.45 12.01 9.472 10.26 11.29 12.19 12.98 13.76 10.88 9.333
1.087 1.071 1.077 1.082 1.094 1.082 1.076 1.072 1.076 1.070 1.090 1.087
−0.0008388 −0.0008420 −0.0008406 −0.0008396 −0.0008376 −0.0008412 −0.0008421 −0.0008426 −0.0008418 −0.0008438 −0.0008390 −0.0008394
0.9634 0.9635 0.9635 0.9635 0.9634 0.9634 0.9635 0.9635 0.9635 0.9635 0.9635 0.9633
0.9623 0.9628 0.9627 0.9628 0.9623 0.9624 0.9625 0.9626 0.9628 0.9628 0.9627 0.9621
0.9669 0.9665 0.9666 0.9667 0.9670 0.9668 0.9667 0.9666 0.9665 0.9664 0.9667 0.9670
1 2 3 4 5 6 7 8 9 10 11 12
5. Conclusion Based on the considerations of the conventional VLLE stills, a new and simple VLLE still is proposed. It is used to measure the isobaric VLE data for the system ethanol–water, and the isobaric VLE and VLLE data for the binary systems water–1-butanol and 2-butanol–water, for the ternary systems ethanol–water–1-butanol and ethanol–2-butanol–water at atmospheric pressure. From the results of the thermodynamic consistency test for the binary VLE and VLLE measurements, the data taken from the apparatus developed in this study are reliable. Furthermore, the ternary VLLE data for the system ethanol–water–1-butanol are in good agreement with those reported in the literature. For the system ethanol–2-butanol–water, there is no large discordance in the composition profile. Hence this apparatus can be applied to VLLE measurements successfully. List of symbols A, B, C constants of the Antoine equation A positive area of the Herington’s area test a , b , c , d coefficients of extended Redlich–Kister equation, Eq. (6)
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Btotal B D J P R T v x y
185
second virial coefficient (m3 mol−1 ) negative area of the Herington’s area test value of the Herington’s area test, defined in Eq. (4) value of the Herington’s area test, defined in Eq. (5) pressure (kPa) gas constant (=8.314 J mol−1 K−1 ) temperature (K) molar liquid volume (m3 mol−1 ) mole fraction in the liquid phase mole fraction in the vapor phase
Greek letters γ activity coefficient ϕ fugacity coefficient ρ density (g cm−3 ) Superscript s saturated value of pure component Subscripts 0 aq calc i max min org
data obtained at atmospheric pressure aqueous phase calculated value component i maximum value, in Eq. (5) minimum value, in Eq. (5) organic phase
Acknowledgements The authors are thankful to Dr. Toshihiko Hiaki, an Associate Professor of Nihon University, for his comments and advices on the apparatus. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
F. van Zandijcke, L. Verhoeye, J. Appl. Chem. Biotechnol. 24 (1974) 709–729. V. Gomis, F. Ruiz, J.C. Asensi, Fluid Phase Equil. 172 (2000) 245–259. S. Malanowski, Fluid Phase Equil. 8 (1982) 197–219. I.B. Ravinovich, Izk. Akad. nauk SSSR Ser. Khim. 52 (1960) 62–68. J.L. Hales, J.H. Ellender, J. Chem. Thermodyn. 8 (1976) 1177–1184. E.B. Frever, J.C. Hubbard, D.H. Andrews, J. Am. Chem. Soc. 51 (1929) 759–770. M. Kikuchi, E. Oikawa, Nippon Kagaku Kaishi 88 (1967) 1259–1267. G.S. Kell, E. Whalley, J. Chem. Phys. 62 (1975) 3496–3503. T. Hiaki, A. Kawai, Fluid Phase Equil. 158–160 (1999) 979–989.
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[10] J. Gmehling, U. Onken, Vapor–Liquid Equilibrium Data Collection, DECHEMA Chemistry Data Series, Vol. I, Part 1, DECHEMA, Frankfurt, 1977. [11] C. Tsonopoulos, AIChE J. 20 (1974) 263–272. [12] C.F. Spencer, S.B. Adler, J. Chem. Eng. Data 23 (1978) 82–89. [13] E.F.G. Herington, J. Inst. Petrol. 37 (1951) 457–470. [14] C.A. Jones, E.M. Shoenborn, A.P. Colburn, Ind. Eng. Chem. 35 (1943) 666–672. [15] K. Kojima, K. Ochi, Y. Nakazawa, Int. Chem. Eng. 9 (1969) 342–347. [16] R.M. Rieder, A.R. Thompson, Ind. Eng. Chem. 41 (1949) 2905–2908. [17] T. Boublik, Collect. Czech. Chem. Commun. 25 (1960) 285. [18] S.R.M. Ellis, R.D. Garbett, Ind. Eng. Chem. 52 (1960) 385–388. [19] D. Hessel, G. Geiseler, Zh. Phys. Chem. Leipzig. 229 (1965) 199. [20] Z.-L. Zong, X.H. Yang, X.-Y. Zheng, J. Chem. Eng. Jpn. 16 (1983) 1–6. [21] N. Kagakukai (Ed.), Chem. Soc. Jpn., Kagaku Binran, Kisohen II, Maruzen, Tokyo, 1975. [22] J. Gmehling, J. Menke, J. Krafczyk, K. Fischer, Azeotropic Data, Part I, VCH, Weinheim, 1994. [23] A.I. Altsybeeva, V.P. Belousov, N.V. Ovtrakht, A.G. Morachevsky, Zh. Fiz. Khim. 38 (1964) 1242–1247. [24] J. Boeke, K.H. Hanewald, Rec. Trav. Chim. PAYS-BAS 61 (1942) 881–887. [25] Y. Yamamoto, T. Maruyama, Kagaku Kogaku 23 (1959) 635–640. [26] K. Ochi, T. Saito, K. Kojima, J. Chem. Eng. Data 41 (1996) 361–364. [27] D.M.T. Newsham, N. Vahdat, Chem. Eng. J. 13 (1977) 27–31.
Isobaric vapor–liquid–liquid equilibria with a newly developed still Koichi Iwakabe, Hitoshi Kosuge∗ Department of Chemical Engineering, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo 152-8552, Japan Received 11 June 2001; accepted 11 September 2001
Abstract A new and simple apparatus for the measurement of isobaric vapor–liquid–liquid equilibrium (VLLE) is developed by modifying the still proposed by van Zandijcke et al. The still is used to measure the isobaric vapor–liquid equilibrium (VLE) data for the system ethanol–water, the isobaric VLE and VLLE data for the binary systems water–1-butanol and 2-butanol–water at atmospheric pressure. The obtained data for the binary systems are compared with the previous data in the literature. The thermodynamic consistencies of the obtained data for the binary systems are confirmed by the Herington’s area test. Furthermore, the isobaric VLLE data for the ternary systems ethanol–water–1-butanol and ethanol–2-butanol–water are obtained with the apparatus. The results show that the apparatus can be applied to the measurements of both isobaric VLE and VLLE successfully. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Experimental method; Vapor–liquid equilibria; Vapor–liquid–liquid equilibria
1. Introduction The isobaric vapor–liquid–liquid equilibrium (VLLE) data is one of the basic important physical properties for design and analysis of heterogeneous distillation columns. Since a huge number of vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE) data have been measured, VLLE data can be easily estimated by the parameter sets of liquid phase activity coefficient equations that are determined by the experimental VLE or LLE data. However, the VLLE data estimated with the parameters determined by the VLE ones are different from those by LLE, because the parameter sets of the activity coefficient equation are quite different with each other. To overcome the problem, the observed VLLE data are essential. However, VLLE data available in the previous literature are very few. This is due to the difficulties of VLLE measurements. In this study, a new and simple VLLE still is developed by modifying ∗
Corresponding author. Tel.: +81-3-5734-2151; fax: +81-3-5734-2151. E-mail address: [email protected] (H. Kosuge). 0378-3812/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 6 3 1 - 8
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the van Zandijcke and Verhoeye type VLLE still [1]. In order to evaluate the performance of the still, measurements of binary VLE data are carried out for the system ethanol (1)–water (2), and the observed data are rated by a thermodynamic consistency test. Then, the isobaric binary VLE and VLLE data for the systems water (1)–1-butanol (2) and 2-butanol (1)–water (2) are measured. The results obtained from the experiments are compared with previous literature. Finally, the isobaric VLLE data for the ternary systems ethanol (1)–water (2)–1-butanol (3) and ethanol (1)–2-butanol (2)–water (3) are obtained with the apparatus.
2. Structure of VLLE still The difficulty of VLLE measurements lies in the concentration analysis of two liquid phases that appear in a VLLE still. To measure the equilibrium compositions of two liquid phases, both liquids are drawn to a separate measuring cell immersed in a constant temperature bath that is controlled at the equilibrium temperature (van Zandijcke and Verhoeye [1] and Gomis et al. [2]). However, the equilibrium conditions in the measuring cell might differ from those in the VLLE still due to the evaporation in the cell. Also these entire equipments for VLLE measurement are much more complex and bigger than the conventional VLE equipments. Another difficulty of VLLE measurements lies in the mixing of two liquids in the boiling flask, as Gomis et al. mentioned [2]. For the case of the Othmer type still, the mixing of two liquids is usually done by a stirrer. However, it appears to be difficult to obtain well-mixed liquids in the boiling flask by this method. Therefore, it is difficult to generate a vapor, which is in equilibrium with two liquids in the Othmer type still. This type of still also has low thermodynamic reliability in its data, because of the rectifying effect present in the still (Malanowski [3]). For the case of the Gillespie type still, the mixing conditions of two liquids in the still, which is usually achieved by a stirrer, may affect the flow condition of the liquids and vapor in the Cottrell pump, and the compositions of the liquids and vapor in the equilibrium chamber. Recently, Gomis et al. [2] proposed the modified Gillespie type still with an ultrasonic homogenizer that stirs the suspended liquid in the flask. Alternatively, van Zandijcke and Verhoeye [1] developed the modified Gillespie type still with a liquid separator inside the boiling flask, which is completely partitioned into the upper and the lower chambers. The advantage of the still developed by van Zandijcke and Verhoeye [1] is that mechanical mixing of two liquids is unnecessary and the two liquids and vapor are able to rise up together in the Cottrell pump. In order to test the performance of the still by van Zandijcke and Verhoeye [1], we have measured the VLE and VLLE data using the still with a separator similar to the one by van Zandijcke and Verhoeye [1]. Nevertheless, the observed fluctuation of the temperature inside the equilibrium chamber was relatively large and the accuracy of the observed VLE and VLLE data were somewhat poor in terms of the thermodynamic consistency. The inaccuracy is caused by the incomplete separation of the light and heavy liquids at the upper and lower chambers inside the still, i.e. the amount of the light liquid in the lower chamber fluctuates with time. Based on the above discussion, a new and simple VLLE still was developed. The schematic diagram of the still is shown in Fig. 1. The still, which is made from Pyrex glass, is based on the van Zandijcke type still [1], i.e. consists of a boiling flask (A), a Cottrell pump (B), an equilibrium chamber (C) with a thermometer well (I), a vapor–liquid mixing chamber (F). A conical shaped cup (G) is placed above the electric heater (M) in the boiling flask to allow the heavier liquid and vapor to rise up together in the
K. Iwakabe, H. Kosuge / Fluid Phase Equilibria 192 (2001) 171–186
173
Fig. 1. Schematic diagram of the experimental apparatus.
Cottrell pump (B), and a conduit (H) is attached at the top of the boiling flask to send the lighter liquid and vapor to the Cottrell pump (B). To obtain LLE of two liquids flown down from the equilibrium chamber (C), a small cell (J) with the volume of 2 ml is placed in the liquid collector (D). The liquid samples in the small cell (J) are drawn through the sampling port (K) by a syringe.
3. Experimental 3.1. Experimental procedure Isobaric binary VLE for the systems ethanol (1)–water (2), water (1)–1-butanol (2), 2-butanol (1)–water (2) are measured at atmospheric pressure. Approximately 200 ml of the liquid mixture is loaded into the boiling flask and heated by the electric heater. After the liquid in the flask starts to boil, the accumulated liquid in the small cell (J) is sucked out by a syringe at least twice until the steady state. The steady state, where the fluctuation of the temperature in the equilibrium chamber becomes less than ±0.01 K, is usually attained within an hour from the beginning of the boiling. At the steady state, the temperature of the equilibrium chamber is recorded and the condensed vapor and liquid samples are taken from each tap to determine their compositions by gas chromatography (GC) analysis. If the condensed vapor and liquid samples are immiscible, 2-propanol is added to the sample to make them homogeneous.
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The isobaric VLLE data are measured for the binary systems water (1)–1-butanol (2) and 2-butanol (1)–water (2), and for the ternary systems ethanol (1)–water (2)–1-butanol (3) and ethanol (1)–2-butanol (2)–water (3) at atmospheric pressure. The procedure is similar to isobaric VLE measurements except for the sampling of the immiscible liquids. The liquids collected in the small cell (J) are sucked out at least twice by a syringe after boiling starts. Before taking the liquid samples, the liquids inside the cell (J) are allowed to settle for around 2 h so that the LLE condition can be attained. While the two liquids in the cell (J) are settling, the compositions of the upper and lower phases in the cell are checked by GC analysis. This procedure doesn’t affect the boiling point because a small enough volume of less than 3 l of the sample is taken by a syringe. After their compositions are confirmed to be constant, the upper and the lower liquid phases in the cell are again sampled with a syringe (3 l) and analyzed by GC. The analysis of the condensed vapor compositions is done in the same manner as VLE measurements. For ternary systems, total liquid compositions are also analyzed by GC to confirm the material balances of the liquid phases are kept. 3.2. Measurements of temperatures and compositions A Pt100 resistance thermometer inserted into the thermometer well in the equilibrium chamber is used to measure the boiling point. It was calibrated by the measurements of the boiling points of several pure chemicals. The accuracy of the temperature measurements is estimated to be ±0.03 K by the calibration. Compositions of the condensed vapor and liquid samples are analyzed with Shimadzu GC-8AIT and Shimadzu integrator C-R6A Chromatpac. The GC column used is SUNPAK A. Helium is used as a carrier gas for GC analysis at the flow condition of 50 ml/min. The GC was calibrated by the absolute calibration curve method. The consistencies of the GC calibration curves obtained for the components were examined by several mixtures with known compositions for each system. The accuracy of composition analysis with GC is estimated to be ±0.0005 mole fraction. 3.3. Materials All materials used in this study are supplied by Wako Pure Chemicals Industries Ltd., Japan. Nominal purities of ethanol, 2-propanol, 1-butanol and 2-butanol are 99.5, 99.5, 99.0 and 99.0%, respectively. Since 2-propanol is used as a solvent to make the immiscible liquid homogeneous as mentioned above, it is dried with Molecular Sieves 5A 1/16 to remove water. Water used in this study is distilled water. All materials except 2-propanol are used without further purification. The densities and the boiling points of the materials used are measured, and the results with those reported in the literature are listed in Table 1. The densities of the materials in the literature [4–8] are obtained by interpolations. The boiling points of the materials are compared with ones predicted by the Antoine equation mentioned in the next section. 3.4. Data reduction To obtain the boiling points at 101.3 kPa, the following equation is used [9]. 1 101.3 − P0 T = T0 + · N P0 Bi (ln 10) xi (T0 + C i )2 i=1
(1)
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175
Table 1 Physical properties of materials Material
Density
P0 (kPa)
T (K)
ρ 0 (g cm−3 )
ρ calc (g cm−3 )
Reference
Ethanol
301.81
0.7824
0.7820 0.7818 0.7820 0.7823
[4] [5] [6] [7]
1-Butanol
301.38
0.8021
0.8034 0.8033
2-Butanol
301.15
0.7988
Water
300.27
0.9965
Boiling point (K) T0
Tcalc
100.3
351.18
351.19
[4] [5]
100.0
390.49
390.51
0.7960 0.7999
[4] [5]
100.2
372.36
372.35
0.9965
[8]
100.9
373.04
373.04
where T0 is observed boiling point, P0 is atmospheric pressure, T is boiling point at 101.3 kPa, Bi and Ci are Antoine constants of the component i. Liquid phase activity coefficients are calculated by the following equation γi =
xi Pis ϕis
Pyi ϕi exp[viL (P − Pis )/RT]
(2)
where xi and yi are the observed liquid and vapor composition of the component i, and R is gas constant. The saturated vapor pressure of the component i, Pis , is calculated by the Antoine equation. logPis = Ai −
Bi T + Ci
(3)
The values of Antoine constants, Ai , Bi and Ci are taken from the literature [10]. The fugacity coefficient of the component i, ϕ i , and that of the pure component jis are calculated by using the second virial coefficients predicted by the Tsonopoulos method [11]. The molar volume of the component i, viL , are estimated by the Rackett equation modified by Spencer and Adler [12]. In order to examine the thermodynamical consistency of the experimental data, the Herington’s area test [13] is employed. The criterion of the area test is D − J < 10. Here, D and J are defined as follows: 1 | 0 ln(γ1 /γ2 ) dx1 | |A − B | D = 1 × 100 = × 100 (4) |A | + |B | |ln(γ1 /γ2 )| dx1 0
J =
Tmax − Tmin × 150 Tmin
(5)
where A and B are the positive and the negative area surrounded by the natural logarithmic values of the ratio of the liquid activity coefficients and the x1 axis in Figs. 3, 5 and 7. The natural logarithmic values of
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the ratio of the liquid phase activity coefficients in Eq. (4) are correlated by the extended Redlich–Kister expansion [13]: γ1 ln = a + b (x2 − x1 ) + c (6x1 x2 − 1) + d (x1 − x2 )(8x1 x2 − 1) (6) γ2 where the coefficients a , b , c and d are determined by fitting the experimental data.
4. Results and discussion 4.1. Ethanol–water system In order to validate the performance of the apparatus developed in this study, measurements of VLE data are carried out for the system ethanol (1)–water (2) because a number of VLE data and physical properties for the system are vastly available in the literature. The observed data, vapor and liquid compositions, boiling temperatures, calculated values of the activity coefficients, second virial coefficients and fugacity coefficients are shown in Table 2. The boiling and dew points of this study and those reported in the literature [14–16] are plotted against the compositions of ethanol in Fig. 2(a). As shown in Fig. 2(a), the observed boiling and dew points for this study are in good agreement with the values reported in the literature. The activity coefficients are plotted against the mole fraction of ethanol in the liquid phase in Fig. 2(b). The thermodynamic consistency of the experimental data for the system was examined by Herington’s area test [13], which is shown in Fig. 3. Coefficients of Eq. (6) are shown in Table 3. The obtained value of D − J for the observed data is −3.40. This satisfies the criteria of the area test, D − J < 10. Thus, the VLE data obtained by the present apparatus are thermodynamically consistent.
Fig. 2. Isobaric VLE for the system ethanol (1)–water (2) at 101.3 kPa: (a) boiling and dew points; (b) activity coefficients.
K. Iwakabe, H. Kosuge / Fluid Phase Equilibria 192 (2001) 171–186
177
Table 2 Isobaric VLE data for the system ethanol (1)–water (2) at 101.3 kPa x1
y1
T
γ1
γ2
Btotal
ϕ1
ϕ2
ϕ1s
ϕ2s
0.0402 0.0514 0.0580 0.0721 0.0729 0.0959 0.1072 0.1201 0.1237 0.1297 0.1399 0.1586 0.1935 0.1967 0.2363 0.2916 0.3507 0.3812 0.4157 0.4819 0.5189 0.5205 0.6382 0.7453 0.8396 0.8436 0.9370 0.9372
0.2981 0.3368 0.3564 0.3932 0.3868 0.4362 0.4546 0.4719 0.4725 0.4808 0.4909 0.5025 0.5176 0.5165 0.5385 0.5690 0.5913 0.6013 0.6164 0.6398 0.6578 0.6561 0.7245 0.7816 0.8491 0.8525 0.9341 0.9339
364.23 362.89 362.25 360.87 361.01 359.41 358.86 358.23 358.12 357.93 357.60 357.07 356.43 356.38 355.57 354.88 354.23 353.95 353.66 353.15 352.87 352.88 352.12 351.66 351.45 351.43 351.39 351.41
4.700 4.353 4.168 3.885 3.761 3.410 3.242 3.072 3.000 2.930 2.806 2.583 2.233 2.195 1.963 1.723 1.525 1.441 1.369 1.249 1.205 1.197 1.109 1.042 1.012 1.012 0.999 0.998
1.010 1.016 1.017 1.026 1.032 1.035 1.036 1.043 1.050 1.049 1.054 1.075 1.116 1.125 1.166 1.207 1.282 1.328 1.369 1.481 1.532 1.545 1.696 1.949 2.163 2.171 2.422 2.437
−0.0006586 −0.0006670 −0.0006715 −0.0006833 −0.0006822 −0.0006977 −0.0007040 −0.0007115 −0.0007128 −0.0007153 −0.0007196 −0.0007264 −0.0007352 −0.0007356 −0.0007477 −0.0007608 −0.0007731 −0.0007788 −0.0007860 −0.0007989 −0.0008080 −0.0008073 −0.0008432 −0.0008769 −0.0009192 −0.0009217 −0.0009801 −0.0009795
0.9817 0.9803 0.9795 0.9781 0.9783 0.9765 0.9758 0.9752 0.9751 0.9748 0.9745 0.9740 0.9733 0.9733 0.9725 0.9715 0.9707 0.9703 0.9699 0.9692 0.9687 0.9687 0.9672 0.9662 0.9654 0.9654 0.9649 0.9649
0.9767 0.9766 0.9766 0.9766 0.9765 0.9767 0.9768 0.9769 0.9769 0.9770 0.9771 0.9771 0.9772 0.9771 0.9773 0.9778 0.9782 0.9784 0.9787 0.9793 0.9798 0.9797 0.9819 0.9841 0.9870 0.9871 0.9911 0.9911
0.9537 0.9550 0.9556 0.9568 0.9567 0.9581 0.9586 0.9592 0.9593 0.9594 0.9597 0.9602 0.9607 0.9608 0.9614 0.9620 0.9626 0.9628 0.9630 0.9634 0.9637 0.9637 0.9643 0.9646 0.9648 0.9648 0.9648 0.9648
0.9820 0.9825 0.9827 0.9832 0.9831 0.9836 0.9838 0.9840 0.9840 0.9841 0.9842 0.9844 0.9846 0.9846 0.9848 0.9850 0.9852 0.9853 0.9854 0.9856 0.9856 0.9856 0.9859 0.9860 0.9861 0.9861 0.9861 0.9861
Fig. 3. Herington’s area test for the system ethanol (1)–water (2).
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Table 3 Coefficients of Eq. (6) and results of the Herington’s area test System
a
b
c
d
D−J
Ethanol–water Water–1-butanol 2-Butanol–water
−0.0117 −0.1389 0.0533
1.2018 2.2816 1.9974
−0.3894 1.1969 −0.9449
0.1956 0.4425 0.7338
−3.40 3.04 −9.65
4.2. Water–1-butanol and 2-butanol–water systems The isobaric VLE and VLLE data for the binary systems water (1)–1-butanol (2) and 2-butanol (1)–water (2) were measured at atmospheric pressure. The observed data and calculated values of the activity coefficients for VLE and VLLE are shown in Tables 4 and 5, respectively. The observed boiling and dew points and those reported in the literature [17–20] for the system water (1)–1-butanol (2), [23–25] for the system 2-butanol (1)–water (2)) are shown in Figs. 4(a) and 6(a), respectively. In Figs. 4(a) and 6(a), solubility data at various temperatures reported in the literature ([21,26], respectively) are also plotted. For the system water (1)–1-butanol (2), the observed liquid phase compositions of the organic and the aqueous phases for the isobaric binary VLLE are 0.6393 and 0.9781 mole fraction of, respectively. The values of compositions of both phases agreed well with the graphically interpolated values from the previous solubility data, which are 0.6492 and 0.9788 mole fractions, respectively. The observed azeotropic temperature and vapor composition are 365.92 K and 0.7590 mole fraction of water, respectively, while the average azeotropic temperature and vapor composition of the data in the literature [22] are 365.84 K
Fig. 4. Isobaric VLE and VLLE for the system water (1)–1-butanol (2) at 101.3 kPa: (a) boiling and dew points; (b) activity coefficients.
K. Iwakabe, H. Kosuge / Fluid Phase Equilibria 192 (2001) 171–186
179
Table 4 Isobaric VLE and VLLE data for the system water (1)–1-butanol (2) at 101.3 kPa x1
y1
T
γ1
γ2
Btotal
ϕ1
ϕ2
ϕ1s
ϕ2s
0.0168 0.0218 0.0297 0.0486 0.0575 0.0683 0.0811 0.0916 0.0955 0.0996 0.1045 0.1125 0.1284 0.1678 0.2125 0.2222 0.2354 0.2544 0.2640 0.2696 0.3196 0.3302 0.3988 0.4012 0.4203 0.4858 0.4927 0.5051 0.5191 0.5614 0.5945 0.6393a 0.9781a 0.9887 0.9929 0.9952 0.9964 0.9969 0.9992
0.1024 0.1318 0.1696 0.2513 0.2863 0.3279 0.3602 0.3972 0.4049 0.4128 0.4368 0.4468 0.5026 0.5670 0.6124 0.6272 0.6428 0.6550 0.6607 0.6648 0.6965 0.7009 0.7341 0.7297 0.7388 0.7542 0.7501 0.7518 0.7577 0.7561 0.7564 0.7590 0.7590 0.7950 0.8526 0.8867 0.9025 0.9121 0.9674
388.24 387.54 386.15 383.78 382.76 381.64 380.56 379.30 379.14 378.91 378.06 377.75 376.60 374.12 372.09 371.71 371.26 370.55 370.28 370.12 368.82 368.42 367.43 367.24 367.06 366.50 366.39 366.30 366.23 366.16 366.03 365.92 365.92 366.88 368.44 369.67 370.45 370.49 372.41
3.731 3.776 3.731 3.642 3.622 3.625 3.473 3.536 3.474 3.423 3.552 3.408 3.490 3.280 3.001 2.979 2.928 2.830 2.778 2.752 2.548 2.518 2.262 2.250 2.189 1.972 1.942 1.905 1.581 1.732 1.644 1.541 1.007 1.007 1.016 1.008 0.997 1.005 0.994
1.000 0.997 1.010 1.011 1.010 1.003 1.008 1.007 1.004 1.004 1.000 1.003 0.961 0.965 0.990 0.979 0.972 0.990 0.998 1.000 1.025 1.043 1.078 1.108 1.115 1.211 1.253 1.281 1.917 1.428 1.551 1.734 28.51 45.13 49.02 52.43 59.46 62.19 78.51
−0.0009344 −0.0009141 −0.0008937 −0.0008465 −0.0008280 −0.0008064 −0.0007927 −0.0007786 −0.0007747 −0.0007716 −0.0007638 −0.0007603 −0.0007375 −0.0007268 −0.0007254 −0.0007228 −0.0007211 −0.0007234 −0.0007240 −0.0007242 −0.0007268 −0.0007296 −0.0007307 −0.0007338 −0.0007335 −0.0007359 −0.0007381 −0.0007387 −0.0007755 −0.0007392 −0.0007406 −0.0007413 −0.0007412 −0.0007241 −0.0007007 −0.0006860 −0.0006777 −0.0006773 −0.0006601
0.9976 0.9967 0.9955 0.9929 0.9918 0.9906 0.9896 0.9884 0.9882 0.9879 0.9872 0.9869 0.9854 0.9834 0.9819 0.9815 0.9811 0.9806 0.9805 0.9803 0.9793 0.9791 0.9783 0.9782 0.9780 0.9776 0.9776 0.9775 0.9794 0.9774 0.9774 0.9773 0.9773 0.9773 0.9774 0.9777 0.9780 0.9779 0.9785
0.9681 0.9679 0.9675 0.9670 0.9669 0.9669 0.9668 0.9667 0.9668 0.9668 0.9668 0.9669 0.9674 0.9678 0.9681 0.9683 0.9686 0.9686 0.9687 0.9688 0.9692 0.9692 0.9700 0.9698 0.9700 0.9704 0.9702 0.9702 0.9660 0.9703 0.9703 0.9703 0.9703 0.9722 0.9751 0.9770 0.9779 0.9783 0.9812
0.9725 0.9728 0.9734 0.9745 0.9749 0.9754 0.9759 0.9764 0.9764 0.9765 0.9769 0.9770 0.9775 0.9784 0.9792 0.9793 0.9795 0.9798 0.9799 0.9799 0.9804 0.9806 0.9809 0.9810 0.9810 0.9812 0.9813 0.9813 0.9813 0.9814 0.9814 0.9814 0.9814 0.9811 0.9806 0.9801 0.9798 0.9798 0.9791
0.9710 0.9715 0.9725 0.9741 0.9747 0.9755 0.9761 0.9769 0.9770 0.9772 0.9777 0.9779 0.9785 0.9800 0.9811 0.9813 0.9815 0.9819 0.9820 0.9821 0.9828 0.9830 0.9835 0.9836 0.9837 0.9839 0.9840 0.9840 0.9841 0.9841 0.9842 0.9842 0.9842 0.9838 0.9830 0.9824 0.9819 0.9819 0.9809
a
VLLE data.
and 0.7468 mole fraction of water, respectively. From the comparison of these values, the heterogeneous azeotropic data obtained by the present apparatus appears to be reliable. The calculated activity coefficients for the system are shown in Fig. 4(b). With these activity coefficients, VLE and VLLE data of the system were examined by the area test [13], which is shown in Fig. 5 and Table 3. The value of D − J for
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Table 5 Isobaric VLE and VLLE data for the system 2-butanol (1)–water (2) at 101.3 kPa x1
y1
T
γ1
γ2
Btotal
ϕ1
ϕ2
ϕ1s
ϕ2s
0.0011 0.0040 0.0048 0.0048 0.0068 0.0078 0.0101 0.0117 0.0118 0.0136 0.0136 0.0164 0.0173 0.0182 0.0410a 0.2982a 0.3908 0.4134 0.4597 0.4598 0.5147 0.5289 0.5759 0.6344 0.6476 0.6605 0.6837 0.6986 0.7426 0.7760 0.7989 0.8918 0.9055
0.0810 0.1355 0.1658 0.1692 0.2065 0.2301 0.2573 0.2852 0.2819 0.3066 0.3031 0.3132 0.3175 0.3279 0.3799 0.3799 0.3866 0.3899 0.4035 0.4057 0.4187 0.4204 0.4393 0.4542 0.4683 0.4776 0.4921 0.5026 0.5378 0.5678 0.5907 0.7187 0.7446
371.84 368.96 368.16 368.25 367.04 366.11 365.02 364.22 364.28 363.35 363.56 362.79 362.49 362.26 360.47 360.47 360.50 360.45 360.56 360.56 360.63 360.73 360.90 361.30 361.39 361.61 361.84 362.05 362.78 363.40 363.90 366.80 367.36
78.51 39.61 41.78 42.22 38.07 37.84 34.26 33.70 32.88 32.31 31.50 27.97 27.09 26.83 14.78 2.032 1.575 1.505 1.394 1.401 1.287 1.253 1.194 1.102 1.109 1.099 1.084 1.074 1.050 1.035 1.026 1.000 0.999
0.963 1.008 1.002 0.995 0.995 1.000 1.006 1.000 1.002 1.004 1.001 1.019 1.025 1.019 1.031 1.409 1.604 1.660 1.755 1.749 1.899 1.943 2.076 2.310 2.328 2.355 2.437 2.486 2.634 2.769 2.868 3.306 3.371
−0.0006628 −0.0006932 −0.0007037 −0.0007031 −0.0007206 −0.0007347 −0.0007525 −0.0007686 −0.0007671 −0.0007851 −0.0007816 −0.0007938 −0.0007988 −0.0008051 −0.0008480 −0.0008480 −0.0008506 −0.0008528 −0.0008578 −0.0008589 −0.0008644 −0.0008640 −0.0008719 −0.0008749 −0.0008820 −0.0008847 −0.0008907 −0.0008946 −0.0009090 −0.0009226 −0.0009334 −0.0010054 −0.0010226
0.9793 0.9762 0.9746 0.9745 0.9726 0.9713 0.9697 0.9683 0.9684 0.9670 0.9673 0.9665 0.9662 0.9657 0.9628 0.9627 0.9625 0.9624 0.9620 0.9619 0.9615 0.9615 0.9610 0.9608 0.9604 0.9603 0.9600 0.9598 0.9594 0.9591 0.9589 0.9586 0.9586
0.9784 0.9775 0.9774 0.9775 0.9773 0.9772 0.9771 0.9771 0.9771 0.9771 0.9771 0.9770 0.9769 0.9770 0.9773 0.9773 0.9774 0.9775 0.9779 0.9779 0.9783 0.9783 0.9789 0.9794 0.9798 0.9802 0.9807 0.9810 0.9823 0.9834 0.9843 0.9895 0.9905
0.9612 0.9637 0.9644 0.9643 0.9653 0.9661 0.9670 0.9676 0.9675 0.9683 0.9681 0.9687 0.9689 0.9691 0.9705 0.9705 0.9704 0.9705 0.9704 0.9704 0.9704 0.9703 0.9702 0.9698 0.9698 0.9696 0.9694 0.9693 0.9687 0.9682 0.9678 0.9655 0.9650
0.9793 0.9804 0.9807 0.9806 0.9811 0.9814 0.9818 0.9820 0.9820 0.9823 0.9823 0.9825 0.9826 0.9827 0.9833 0.9833 0.9833 0.9833 0.9833 0.9833 0.9832 0.9832 0.9831 0.9830 0.9830 0.9829 0.9828 0.9828 0.9825 0.9823 0.9821 0.9811 0.9809
a
VLLE data.
the observed data is 3.04 and satisfies the criterion. With these considerations, isobaric VLE and VLLE data of the system are thermodynamically consistent. For the system 2-butanol (1)–water (2), the liquid phase compositions of isobaric VLLE in the organic and the aqueous phases at atmospheric pressure are 0.0410 and 0.2982 mole fraction of 2-butanol, while those interpolated from the solubility data are 0.0392 and 0.2905, respectively. Thus, it shows that the experimental LLE data obtained at boiling point from the present apparatus agrees well with those graphically interpolated ones of LLE. The azeotropic temperature and vapor composition of the system are determined by extrapolating the vapor compositions and temperatures with fourth order polynomial
K. Iwakabe, H. Kosuge / Fluid Phase Equilibria 192 (2001) 171–186
181
Fig. 5. Herington’s area test for the system water (1)–1-butanol (2).
equations. They are 360.42 K and 0.3820 mole fraction of water, respectively, while the average ones in the literature [22] are 360.63 K and 0.3859 mole fraction of water, respectively. The activity coefficients for the system are plotted against the liquid compositions in Fig. 6(b). Again the Herington’s area test [13] is performed to examine the thermodynamic consistency of these data. The value of D − J for this system, −9.65, passed the criterion as shown in Fig. 7 and Table 3. From all experimental results of the binary systems, the observed binary VLE and VLLE data obtained by the present still satisfy the thermodynamical consistency test.
Fig. 6. Isobaric VLE and VLLE for the system 2-butanol (1)–water (2) at 101.3 kPa: (a) boiling and dew points; (b) activity coefficients.
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Fig. 7. Herington’s area test for the system 2-butanol (1)–water (2).
4.3. Ethanol–water–1-butanol and ethanol–2-butanol–water systems Isobaric VLLE data for the ternary system ethanol (1)–water (2)–1-butanol (3) are measured at atmospheric pressure to investigate the applicability of the apparatus to the ternary systems. The observed compositions of two liquid phases and vapor phase are shown in Fig. 8 and Table 6. In Fig. 8, the data reported in the literature [2,27] are also plotted to compare the composition profiles. Vapor compositions of the system are on a dashed straight line. The experimental VLLE of this study are in good agreement with those data in the literature. From this result, the apparatus developed in this study can be applied to the isobaric VLLE measurements for the ternary system.
Fig. 8. Isobaric VLLE for the system ethanol (1)–water (2)–1-butanol (3) at 101.3 kPa.
K. Iwakabe, H. Kosuge / Fluid Phase Equilibria 192 (2001) 171–186
183
Table 6 Isobaric VLLE data for the system ethanol (1)–water (2)–1-butanol (3) at 101.3 kPa Data No.
xorg1
xorg2
xorg3
xaq1
xaq2
xaq3
y1
y2
y3
T
1 2 3 4
0.0094 0.0187 0.0296 0.0267
0.6406 0.6472 0.6977 0.6727
0.3501 0.3341 0.2726 0.3006
0.0025 0.0054 0.0109 0.0083
0.9746 0.9662 0.9590 0.9658
0.0229 0.0284 0.0300 0.0259
0.0171 0.0357 0.0613 0.0545
0.7621 0.7447 0.7328 0.7339
0.2209 0.2196 0.2058 0.2116
365.62 365.30 364.83 364.98
γ org1
γ org2
γ org3
γ aq1
γ aq2
γ aq3
Btotal
ϕ1
ϕ2
ϕ3
1.098 1.164 1.284 1.260
1.560 1.527 1.417 1.464
1.623 1.712 2.006 1.859
4.148 4.026 3.477 4.035
1.025 1.023 1.031 1.020
24.84 20.15 18.22 21.57
−0.0007377 −0.0007381 −0.0007365 −0.0007371
0.9825 0.9820 0.9816 0.9816
0.9768 0.9765 0.9759 0.9761
0.9503 0.9499 0.9495 0.9496
1 2 3 4
Isobaric VLLE for the ternary system ethanol (1)–2-butanol (2)–water (3) are measured at atmospheric pressure, of which data were not found in the literature. The observed compositions of two liquid phases and vapor phase are shown in Fig. 9 and Table 7. The results of the VLLE for the binary system 2-butanol–water are also plotted in the figure. The compositions of the two liquid phases and the vapor phase in equilibrium are connected by thin dashed straight lines. In Fig. 9, the vapor compositions of the system are on a dashed straight vapor line. However, unlike the system ethanol (1)–water (2)–1-butanol (3), the vapor compositions for the system ethanol (1)–2-butanol (2)–water (3) are completely outside the immiscible liquid region. Since there cannot be seen any large deviations in the compositions of both liquid phases for these two ternary systems, the isobaric ternary VLLE can be measured successfully with the present apparatus.
Fig. 9. Isobaric VLLE for the system ethanol (1)–2-butanol (2)–water (3) at 101.3 kPa.
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Table 7 Isobaric VLLE data for the system ethanol (1)–2-butanol (2)–water (3) at 101.3 kPa Data No.
xorg1
xorg2
xorg3
xaq1
xaq2
xaq3
y1
y2
y3
T
1 2 3 4 5 6 7 8 9 10 11 12
0.0206 0.0091 0.0118 0.0125 0.0219 0.0166 0.0148 0.0118 0.0086 0.0060 0.0153 0.0224
0.2048 0.2661 0.2536 0.2481 0.1973 0.2283 0.2387 0.2534 0.2687 0.2775 0.2385 0.1953
0.7746 0.7248 0.7347 0.7393 0.7808 0.7551 0.7465 0.7347 0.7227 0.7165 0.7463 0.7823
0.0111 0.0036 0.0048 0.0052 0.0122 0.0085 0.0065 0.0049 0.0034 0.0023 0.0069 0.0129
0.0593 0.0454 0.0478 0.0492 0.0610 0.0579 0.0531 0.0494 0.0463 0.0443 0.0540 0.0626
0.9296 0.9510 0.9474 0.9456 0.9268 0.9336 0.9404 0.9456 0.9503 0.9534 0.9392 0.9246
0.0435 0.0170 0.0231 0.0242 0.0468 0.0341 0.0274 0.0230 0.0159 0.0114 0.0294 0.0485
0.3465 0.3618 0.3565 0.3537 0.3424 0.3545 0.3585 0.3608 0.3609 0.3664 0.3502 0.3462
0.6100 0.6212 0.6205 0.6220 0.6108 0.6114 0.6142 0.6162 0.6232 0.6222 0.6204 0.6053
360.06 360.32 360.25 360.24 360.01 360.14 360.20 360.25 360.31 360.34 360.16 360.01
γ org1
γ org2
γ org3
γ aq1
γ aq2
γ aq3
Btotal
ϕ1
ϕ2
ϕ3
1.526 1.339 1.407 1.388 1.550 1.476 1.325 1.394 1.329 1.351 1.390 1.567
2.741 2.180 2.260 2.293 2.816 2.507 2.419 2.289 2.155 2.116 2.369 2.877
1.262 1.359 1.343 1.338 1.256 1.293 1.311 1.333 1.368 1.375 1.326 1.242
2.933 3.555 3.605 3.495 2.874 3.009 3.150 3.489 3.540 3.617 3.209 2.833
9.842 13.26 12.45 12.01 9.472 10.26 11.29 12.19 12.98 13.76 10.88 9.333
1.087 1.071 1.077 1.082 1.094 1.082 1.076 1.072 1.076 1.070 1.090 1.087
−0.0008388 −0.0008420 −0.0008406 −0.0008396 −0.0008376 −0.0008412 −0.0008421 −0.0008426 −0.0008418 −0.0008438 −0.0008390 −0.0008394
0.9634 0.9635 0.9635 0.9635 0.9634 0.9634 0.9635 0.9635 0.9635 0.9635 0.9635 0.9633
0.9623 0.9628 0.9627 0.9628 0.9623 0.9624 0.9625 0.9626 0.9628 0.9628 0.9627 0.9621
0.9669 0.9665 0.9666 0.9667 0.9670 0.9668 0.9667 0.9666 0.9665 0.9664 0.9667 0.9670
1 2 3 4 5 6 7 8 9 10 11 12
5. Conclusion Based on the considerations of the conventional VLLE stills, a new and simple VLLE still is proposed. It is used to measure the isobaric VLE data for the system ethanol–water, and the isobaric VLE and VLLE data for the binary systems water–1-butanol and 2-butanol–water, for the ternary systems ethanol–water–1-butanol and ethanol–2-butanol–water at atmospheric pressure. From the results of the thermodynamic consistency test for the binary VLE and VLLE measurements, the data taken from the apparatus developed in this study are reliable. Furthermore, the ternary VLLE data for the system ethanol–water–1-butanol are in good agreement with those reported in the literature. For the system ethanol–2-butanol–water, there is no large discordance in the composition profile. Hence this apparatus can be applied to VLLE measurements successfully. List of symbols A, B, C constants of the Antoine equation A positive area of the Herington’s area test a , b , c , d coefficients of extended Redlich–Kister equation, Eq. (6)
K. Iwakabe, H. Kosuge / Fluid Phase Equilibria 192 (2001) 171–186
Btotal B D J P R T v x y
185
second virial coefficient (m3 mol−1 ) negative area of the Herington’s area test value of the Herington’s area test, defined in Eq. (4) value of the Herington’s area test, defined in Eq. (5) pressure (kPa) gas constant (=8.314 J mol−1 K−1 ) temperature (K) molar liquid volume (m3 mol−1 ) mole fraction in the liquid phase mole fraction in the vapor phase
Greek letters γ activity coefficient ϕ fugacity coefficient ρ density (g cm−3 ) Superscript s saturated value of pure component Subscripts 0 aq calc i max min org
data obtained at atmospheric pressure aqueous phase calculated value component i maximum value, in Eq. (5) minimum value, in Eq. (5) organic phase
Acknowledgements The authors are thankful to Dr. Toshihiko Hiaki, an Associate Professor of Nihon University, for his comments and advices on the apparatus. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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