Ind. Eng. Chem. Res. 2003, 42, 937-944
937
Multiphase Coexistence for Mixtures Containing Water, 2-Propanol, and Isopropyl Acetate Gui-Bing Hong, Ming-Jer Lee,* and Ho-mu Lin Department of Chemical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106-07, Taiwan
Isothermal vapor-liquid equilibrium (VLE) data were measured for isopropyl acetate + 2-propanol at temperatures from 333.15 to 373.15 K, and isothermal vapor-liquid-liquid equilibrium (VLLE) data were determined experimentally for isopropyl acetate + water and water + 2-propanol + isopropyl acetate at temperatures from 308.15 to 358.15 K. The UNIQUAC model with linearly temperature-dependent parameters and ideal gas-phase assumption represents satisfactorily the VLLE properties for the binary system of isopropyl acetate + water. With the parameters determined from the VLE or the mutual solubility data of the constituent binaries, the UNIQUAC model predicts well the VLLE properties of the ternary system of water + 2-propanol + isopropyl acetate, except for the compositions in the organic-rich phase. The representation for the binodal loci was improved, while the six parameters of the UNIQUAC model were determined, simultaneously, from the isothermal VLLE ternary data. Introduction 2-Propanol (or isopropyl alcohol, IPA) is an important cleaning agent that has been used in the manufacture of many electronic devices. Separation of 2-propanol from the spent aqueous solutions is needed in order to recover and reuse the chemical. However, the traditional distillation method is economically infeasible to separate such a mixture because of the existence of a minimum boiling azeotrope at T az ) 353.27 K and xIPAaz ) 0.68.1 Heterogeneous extractive distillation is considered as a potential method to overcome this azeotropic problem. Alternatively, reactive distillation is another route of possible solution that converts the spent 2-propanol into isopropyl acetate via esterification of 2-propanol with acetic acid over acidic catalyst. Phase equilibrium data of the related mixtures are fundamentally important for the simulation and design of the separation processes.2 In the present study, the phase equilibria [vapor-liquid equilibrium (VLE) and vapor-liquid-liquid equilibrium (VLLE)] data are measured for the mixtures composed of water, 2-propanol, and isopropyl acetate, a potent entrainer or the product of the esterification. Although plenty of VLE data is available in DECHEMA3 for water + 2-propanol, the published phase equilibrium data are rather limited for the other two pairs. The mutual solubility data of water + isopropyl acetate were reported by Stephenson and Stuart.4 Recently, Hong et al.5 measured the liquid-liquid equilibrium (LLE) data for water + 2-propanol + isopropyl acetate in a temperature range of 283.15-323.15 K at atmospheric pressure. The same research group6 later reported the isothermal VLLE data for water + 2-propanol + ethyl acetate at temperatures from 308.15 to 348.15 K. In this study, isothermal VLE data of isopropyl acetate + 2-propanol were measured over a temperature range of 333.15-373.15 K. The VLLE data were also determined experimentally for a binary system of isopropyl acetate + water and a ternary system of water + 2-propanol + * Corresponding author. E-mail:
[email protected]. Fax: 886-2-2737-6644. Tel: 886-2-2737-6626.
isopropyl acetate up to 358.15 K. There are no multiphase equilibrium data in the literature for water + 2-propanol + isopropyl acetate at these comparable conditions. The new VLLE data are utilized to test the reliability of the VLLE calculation by using the UNIQUAC7 model. Experimental Section A static VLLE apparatus was used in the present study to measure the VLE and the VLLE data. The equipment is similar to that of Lee et al.8 The heart of the apparatus is a visual equilibrium cell that is immersed in a visibility thermostatic bath (model TV 4000, Neslab, stability ) (0.03 K). The phase behavior in the equilibrium cell can be observed through the transparent windows. The bath temperature is measured by a precision thermometer (model 1506, Hart Scientific) with a platinum resistive temperature detector (RTD) time distribution probe to an accuracy of (0.02 K. A pressure transducer (model PDCR-912, Druck, U.K., 0-1000 kPa) with a digital indicator (model DPI-261, Druck, U.K.) measures the equilibrium pressure. The accuracy of the pressure measurement is about (0.1%. This apparatus is equipped with both liquid and vapor circulation loops to promote the attainment of equilibrium. A four-port liquid-sampling valve (model 7410, Rheodyne) with a 1 µL loop disk is installed in the liquid circulation loop to trap the liquid sample, while a preheater is used to reheat the returned liquid to the cell if not sampling. A switch valve is utilized to select one of the coexistent liquid phases to be circulated. The gas circulation loop consists of a six-port vapor-sampling valve (model 7010, Rheodyne) with a 100 µL sample loop, a magnetic gear pump, and a preheater. The composition of the sample is analyzed by a gas chromatograph (GC; model 8700, China Chromatography Co., Taiwan) with a thermal conductivity detector. High-purity helium (99.99%) is used as a carrier gas. A stainless steel column packed with 10% Porapak Q 80/ 100 (2 m × 1/8 in.) is able to clearly separate the constituent compounds of the samples.
10.1021/ie020583g CCC: $25.00 © 2003 American Chemical Society Published on Web 01/22/2003
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Table 1. Average Deviations of GC Calibration phase
average deviationa
organic aqueous organic aqueous
0.0021 0.00013 0.0006 0.0006
mixture isopropyl acetate + water 2-propanol + isopropyl acetate
Table 2. VLE Data for Isopropyl Acetate (1) + 2-Propanol (2) T (K)
P (kPa)
x1
y1
333.15
38.8 41.8 43.8 45.3 46.0 46.3 46.1 45.4 44.0 41.7 37.6 93.0 97.2 99.5 100.4 100.2 99.2 97.0 93.8 89.4 83.9 76.6 197.9 201.4 202.3 201.0 198.2 193.9 187.4 178.9 168.5 156.7 143.4
0.0 0.0934 0.1880 0.2938 0.3926 0.4951 0.5969 0.7026 0.8057 0.9038 1.0 0.0 0.0930 0.1891 0.2924 0.3941 0.4945 0.6033 0.7068 0.8088 0.9046 1.0 0.0 0.0926 0.1922 0.2968 0.3949 0.4950 0.6039 0.7123 0.8157 0.9111 1.0
0.0 0.1461 0.2581 0.3456 0.4266 0.4892 0.5666 0.6432 0.7213 0.8260 1.0 0.0 0.1229 0.2096 0.2992 0.3841 0.4549 0.5425 0.6263 0.7178 0.8468 1.0 0.0 0.1016 0.1971 0.2892 0.3501 0.4302 0.5203 0.6206 0.7288 0.8393 1.0
a Average deviation ) (1/n )∑np (|xcalb - xact|) , where n is the p j p j)1 number of calibration points and x is the mole fraction of the minor constituent compound. The superscript “calb” represents the calibrated values and “act” the actual values.
A proper amount of solution is loaded in the degassing unit at the beginning of an experiment. The degassing procedure is similar to that of Lee and Hu.9 The degassed solution is then transferred into the equilibrium cell, in which the levels of the vapor-liquid-liquid interfaces should be adjusted properly such that the upper liquid phase can be circulated. Both liquid and vapor mixtures are circulated alternatively by the circulation pumps to promote equilibration. While the system reaches equilibrium, the pressure reading of the cell approaches a constant. Five samples were taken for each phase at a fixed experimental condition. Generally, the repeatability of the area fractions is about (0.2%. The averaged area fraction from GC was converted into a mole fraction via the calibration equations. Calibrations were made with gravimetrically prepared samples within two composition ranges, in accordance with those in the organic-rich (including the vapor phase) and water-rich phases for the ternary system. The accuracy of the composition analysis for the minor components is tabulated in Table 1. 2-Propanol (99.5 mass%) was purchased from Aldrich Co. Isopropyl acetate (99+ mass%) was supplied by Acros. Deionized distilled water was prepared in our laboratory. No impurity peaks were detected by the chromatographic analysis for any one of the chemicals. These chemicals were used without further purification.
353.15
373.15
yiP
PSi ,
exp[(P -
PSi )VLi /RT]
(1)
VLi
where xi, yi, and are the liquid mole fraction, vapor mole fraction, saturated vapor pressure, and liquid molar volume for component i, respectively. The liquid molar volume was estimated from the modified Rackett model.10 The excess Gibbs free energy (GE) was calculated from its definition: nc
E
GE/(RTx1x2)
0.5547 0.4689 0.3464 0.2818 0.1930 0.1490 0.0984 0.0465 0.0162
0.0105 0.0241 0.0698 0.1026 0.1778 0.2344 0.3295 0.4786 0.6596
0.7245 0.7056 0.7280 0.7253 0.7414 0.7623 0.7998 0.8332 0.8987
0.4968 0.3426 0.2712 0.2210 0.1543 0.1113 0.0661 0.0237 0.0185
0.0062 0.0350 0.0589 0.0830 0.1329 0.1798 0.2493 0.3524 0.3786
0.6146 0.6078 0.5949 0.5754 0.5741 0.5786 0.5783 0.5594 0.6125
0.3901 0.3269 0.2707 0.1644 0.1259 0.0878 0.0587 0.0313 0.0025
0.0046 0.0121 0.0234 0.0723 0.1030 0.1449 0.1905 0.2485 0.3912
0.4795 0.4675 0.4638 0.4547 0.4574 0.4617 0.4715 0.4746 0.4009
yi - xi ) 0
Binary VLE of Isopropyl Acetate + 2-Propanol. The new isothermal VLE data are listed in Table 2 for the binary system of isopropyl acetate + 2-propanol at temperatures from 333.15 to 373.15 K. The tabulated activity coefficients (γi) were calculated from the criteria of phase equilibria with the assumption of an ideal vapor phase, i.e.,
xiPSi
ln γ2
Figure 1 is the pressure-composition diagram for isopropyl acetate + 2-propanol. Each isotherm shows the existence of a maximum pressure azeotrope. The azeotropic composition (xiaz) can be determined by one of the following equations:
Experimental Results
γi )
ln γ1
xi ln γi ∑ i)1
G ) RT
(2)
Table 3 shows the results of the thermodynamic consistency test of the experimental data. All of the isothermal VLE data passed the point, the area, and the infinite-dilution tests.11
(3)
nc
∆Py ∆Px
P)
PSi yi ∑ i)1 nc
P-
)1
(4)
PSi xi ∑ i)1
or
∂P )0 ∂xi
(5)
Figure 2 presents x1 - y1, ∆Py/∆Px, and P varying with x1 around the azeotropic point. It shows that the relationships as given in eqs 3 and 4 are approximately linear and thus are more convenient to apply for the determination of the azeotropic composition. Upon the value of x1az being obtained, the corresponding azeotropic pressure can then be calculated from an empirical equation of equilibrium pressure in terms of x1 at the azeotropic point. The azeotropic conditions determined by this way are given in Table 4. Binary VLLE of Isopropyl Acetate + Water. Table 5 lists the equilibrium pressures and the phase compositions for the binary system of isopropyl acetate
Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003 939 Table 3. Results of the Thermodynamic Consistency Test for 2-Propanol (1) + Isopropyl Acetate (2) consistency test indexa,b
GE/RT coefficientc
ln(γ1/γ2) coefficientd
T (K)
δ
A
I1
I2
C0
C1
C2
D0
D1
D2
D3
333.15 353.15 373.15
1.64 (+) 3.01 (+) 3.33 (+)
0.40 (+) 2.62 (+) 2.94 (+)
3.87 (+) 5.82 (+) 10.05 (+)
6.87 (+) 24.00 (+) 15.79 (+)
0.741 0.572 0.466
0.104 -0.013 -0.021
0.101 0.055 -0.023
-0.004 0.026 0.029
0.711 0.514 0.454
0.083 -0.029 0.022
0.087 0.036 0.054
a Criteria for passing the thermodynamic consistency tests: δ < 5, A < 3, I < 30, and I < 30. The definitions of these indices have 1 2 been given in Kojima et al.11 and Lee and Hu.9 b (+): passes the consistency test. c GE/RT ) x1x2[C0 + C1(x1 - x2) + C2(x1 - x2)2]. d ln(γ /γ ) ) D + D (x - x ) + D (6x x - 1) + D (x - x )(1 - 8x x ). 1 2 0 1 2 1 2 1 2 3 2 1 1 2
Figure 1. Pressure-composition diagram for isopropyl acetate (1) + 2-propanol (2). Table 4. Azeotropic Points for Isopropyl Acetate (1) + 2-Propanol (2) Taz (K)
Paz (kPa)
x1az
333.15 353.15 373.15
46.3 100.4 202.2
0.492 0.321 0.203
+ water at VLLE in a temperature range of 308.15358.15 K. Trace amounts of acetic acid were detected in the liquid phase, indicating that hydration of isopropyl acetate took place slowly. However, the measurements were completed within about 3 h for each run, within which the mole fractions of acetic acid are still negligible at the end of the run even at the highest operating temperature, 358.15 K. Figure 3 illustrates the composition of isopropyl acetate in each coexistent phase varying with temperature in which the literature values of mutual solubilities4 are also shown for comparison. The agreement is reasonably well, except for the organic-rich phase at higher temperatures. Figure 4 is the P-T diagram at VLLE for isopropyl acetate + water. The variation of saturated pressures with temperature appears to follow the Antoine relationship. Ternary VLLE of Water + 2-Propanol + Isopropyl Acetate. The ternary VLLE measurements were
Figure 2. Determination of the azeotropic conditions for isopropyl acetate (1) + 2-propanol (2) at 333.15 K. Table 5. VLLE Data for Isopropyl Acetate (1) + Water (2) T (K)
P (kPa)
organic phase, xI1
aqueous phase, xII 1
vapor phase, y1
308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15
17.8 22.5 27.5 33.8 42.4 52.4 64.6 78.6 95.3 114.5 136.7
0.9013 0.8863 0.8848 0.8790 0.8731 0.8706 0.8619 0.8507 0.8424 0.8277 0.8165
0.0044 0.0041 0.0038 0.0036 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029
0.7032 0.6888 0.6762 0.6616 0.6487 0.6352 0.6249 0.6141 0.6024 0.5864 0.5659
made at temperatures from 318.15 to 358.15 K. The results are reported in Table 6, where the superscript I represents the organic-rich phase and II the aqueous
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Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003
Figure 3. Temperature-composition VLLE phase diagram for isopropyl acetate (1) + water (2).
amounts of the organic compounds dissolved in the aqueous phase are so minute (say, xII i < 0.02 in some conditions) that they may reduce the efforts for further wastewater treatment. Because the mutual solubility between water and isopropyl acetate increases with increasing temperature, the area of the liquid-liquid splitting region becomes smaller at higher temperatures. As is also seen from Figures 5 and 6, the points of the vapor phase stretch from the two-liquid-phase region to the one-liquid-phase region. This phase behavior governs the operation of the condenser in the extractive or reactive distillation column. Phase splitting occurs in the condenser if the compositions of the vapor phase are located in the two-phase region. Otherwise, it is a homogeneous liquid phase. VLE Calculation
Figure 4. Saturated pressures at VLLE for isopropyl acetate + water.
phase. Figures 5 and 6 are the phase diagrams for the ternary system at 318.15 and 358.15 K, respectively. Among these three constituent compounds, isopropyl acetate and water are partially miscible. Both water and isopropyl acetate, however, are completely miscible with 2-propanol, resulting in the fact that the LLE of this ternary system exhibits type 1 behavior as shown in the figures. The experimental results showed that the
The binary VLE data of isopropyl acetate + 2-propanol are correlated with the φ-γ method. Because the equilibrium pressures are sufficiently low (no higher than 210 kPa), the vapor phase is reasonably assumed to be ideal. In fact, this assumption was further examined by comparing the results with those from the twoterm virial equation. The effect was found to be insignificant by the addition of the second virial. The solution model of the UNIQUAC was utilized to represent the nonideality of the constituents in the liquid phase. The optimal values of temperature-specific model parameters were determined on the basis of the maximum likelihood principle by minimization of the following objective function π:
Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003 941 Table 6. VLLE Data for Water + 2-Propanol + Isopropyl Acetate organic phase, xIi T (K)
P (kPa)
318.15
27.5 28.6 28.4 28.3 27.2 27.1 27.0 26.1 26.0 64.6 65.7 66.9 66.2 65.4 64.8 63.9 63.1 62.5 136.7 139.6 141.3 141.2 140.3 139.1 137.8 136.7 135.5
338.15
358.15
2-propanol
aqueous phase, xII i
isopropyl acetate
2-propanol
0.8848 0.7916 0.6702 0.5399 0.4182 0.3253 0.2392 0.1646 0.1422 0.8619 0.7376 0.6166 0.4932 0.3643 0.2778 0.2080 0.1563 0.1057 0.8165 0.6897 0.5647 0.4568 0.3396 0.2567 0.1849 0.1303 0.0854
0.0561 0.1258 0.1857 0.2366 0.2576 0.2701 0.2600 0.2399 0.0647 0.1368 0.1859 0.2401 0.2547 0.2614 0.2436 0.2117 0.0678 0.1382 0.1866 0.2256 0.2454 0.2444 0.2213 0.1841
0.0089 0.0192 0.0230 0.0401 0.0416 0.0462 0.0544 0.0641 0.0073 0.0170 0.0211 0.0275 0.0359 0.0439 0.0542 0.0733 0.0043 0.0149 0.0169 0.0296 0.0345 0.0472 0.0588 0.0794
isopropyl acetate 0.0038 0.0040 0.0043 0.0048 0.0052 0.0059 0.0064 0.0083 0.0107 0.0033 0.0036 0.0044 0.0047 0.0064 0.0072 0.0104 0.0142 0.0169 0.0029 0.0031 0.0033 0.0037 0.0042 0.0079 0.0119 0.0148 0.0226
vapor phase, yi 2-propanol 0.0710 0.1211 0.1787 0.2077 0.2238 0.2460 0.2682 0.2899 0.0683 0.1279 0.1684 0.1966 0.2171 0.2479 0.2655 0.2785 0.0792 0.1295 0.1756 0.2175 0.2358 0.2638 0.2771 0.2902
isopropyl acetate 0.6762 0.6031 0.5521 0.4922 0.4616 0.4443 0.4210 0.3937 0.3671 0.6249 0.5714 0.5118 0.4680 0.4344 0.4064 0.3739 0.3507 0.3326 0.5659 0.5026 0.4623 0.4188 0.3797 0.3635 0.3234 0.3018 0.2872
Figure 5. VLLE phase diagram for water (1) + 2-propanol (2) + isopropyl acetate (3) at 318.15 K. np
π)
∑
k)1
[(
) (
pcalc - pexpt k k σp
(
2
+
)
Tcalc - Texpt k k σT
) (
calc expt x1,k - x1,k
σx1
2
+
that of Prausnitz et al.12 Table 7 reports the results of data reduction. It appears that the solution model correlates well for isopropyl acetate + 2-propanol. The smooth curves in Figure 1 are the calculated results.
2
+
)]
calc expt y1,k - y1,k
σy 1
2
(6)
The standard deviations σ used in the calculation are 0.05 kPa for pressure, 0.05 K for temperature, 0.002 for liquid composition, and 0.005 for vapor composition, respectively. The optimization algorithm is similar to
VLLE Calculation At VLLE, the compositions of three coexistent phases (yi, xIi , and xII i ) and the fraction of each phase were calculated via flash calculation13 at given temperature and feed composition (zi). In the calculation, the flash
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Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003
Figure 6. VLLE phase diagram for water (1) + 2-propanol (2) + isopropyl acetate (3) at 358.15 K. Table 7. Data Reduction of Isopropyl Acetate (1) + 2-Propanol (2) with the UNIQUAC Models
Table 8. Calculated Results from the UNIQUAC Model for Isopropyl Acetate (1) + Water (2)
RMSDa T (K)
b12 (K)
b21 (K)
∆P (kPa)
∆y1
333.15 353.15 373.15
236.94 102.69 77.60
-98.20 -14.25 -2.80
0.32 0.20 0.13
0.008 0.014 0.018
a RMSD: root-mean-square deviation, defined as RMSD np 2 1/2 (Pcalc - Pexpt ∆P ) {[∑k)1 and RMSD ∆y ) k k ) ]/nP} np expt 2 1/2. {[∑k)1 (ycalc y ) ]/n } p k k
equations with the criteria of VLLE were solved simultaneously: nc
∑ i)1 nc
∑ i)1
(KIi - 1)zi RKIi + (1 - R)[β + (1 - β)KIi /KII i ]
)0
(KII i - 1)zi
I II RKII i + (1 - R)[β(Ki /Ki ) + (1 - β)]
)0
organic phase ∆xI1 AADb
aqueous phase b ∆xII 1 AAD
vapor phase ∆y1 AADb
1.38
0.0038
0.0001
0.0122
np ∆P/P AAD ) (100/np)∑k)1 (|Pcalc np calc expt (1/np)∑k)1(|M - M |)k, where np is and ∆M represents ∆xI1, ∆xII 1 , or ∆y1.
a
(8)
KIi ) yi/xIi ) γIi φSi PSi exp[(P - PSi )VLi /RT]/φˆ iP (9) II II S S S L KII ˆ iP (10) i ) yi/xi ) γi φi Pi exp[(P - Pi )Vi /RT]/φ
where R is the fraction of the total material in the vapor phase and β is the fraction of the first liquid phase (organic-rich phase) in the total liquid, nc is the number of components, and Ki is the distribution ratio for component i. Under the experimental conditions of the present study, the values of φSi , φˆ i, and the Ponyting pressure correction factor were assumed to be unity and eqs 9 and 10 become
(11)
Pexpt|/Pexpt)k. b
∆M AAD ) the number of data points
II II S KII i ) yi/xi ) γi Pi /P
(12)
where the equilibrium pressure (P) at VLLE were calculated from nc
(7)
with
KIi ) yi/xIi ) γIi PSi /P
∆P/P AADa (%)
P)
nc
yiP ) ∑ ∑ i)1 i)1
nc
γIi xIi PSi
)
II S γII ∑ i xi Pi i)1
(13)
The UNIQUAC model was used in this study to calculate activity coefficient γi for each constituent component. Binary System. For the system of isopropyl acetate (1) + water (2), the temperature-specific parameters of the UNIQUAC (b12 and b21) were correlated with the mutual solubility data. These two parameters are found to be a linear function of temperature over a temperature range of 293.15-358.15 K. The linear relationships are given by
b12 (K) ) 1360.6 - 2.9153T (K)
(14)
b21 (K) ) -535.31 + 2.1142T (K)
(15)
With these temperature-dependent parameters and an ideal vapor-phase assumption, the results of VLLE calculations for isopropyl acetate + water are reported in Table 8. Figures 3 and 4 compare the calculated results with the experimental values. The agreement is generally satisfactory.
Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003 943 Table 9. Predicted Results of Water (1) + 2-Propanol (2) + Isopropyl Acetate (3) from the UNIQUAC Model with Parameters Determined from Phase Equilibrium Data of the Constituent Binaries T (K)
i-j
aij (K)
aji (K)
data sourcea
318.15
1-2 1-3 2-3 1-2 1-3 2-3 1-2 1-3 2-3
109.19 216.08d -98.2 109.19 214.94d -98.2 109.19 208.74d -98.2
91.71 360.87d 236.94 91.71 340.02d 236.94 91.71 309.85d 236.94
3 this work this work 3 this work this work 3 this work this work
338.15 358.15
pressure ∆P/P AADb (%)
organic phase ∆xI AADc
aqueous phase ∆xII AADc
vapor phase ∆y AADc
3.86
0.0963
0.0038
0.0068
4.12
0.1045
0.0066
0.0122
2.39
0.0935
0.0090
0.0148
a Reference 3: binary VLE data. b ∆P/P AAD (%) as defined in Table 8. c ∆M AAD ) (1/n )∑np ∑3 (|M calc - M expt|) , where n is the p i i k p k)1 i)1 number of data points and ∆M represents ∆xI, ∆xII, or ∆y. d Parameters were calculated from eqs 14 and 15.
Table 10. Correlated Results of Water (1) + 2-Propanol (2) + Isopropyl Acetate (3) from the UNIQUAC Model T (K)
i-j
bij (K)
bji (K)
318.15
1-2 1-3 2-3 1-2 1-3 2-3 1-2 1-3 2-3
-12.73 146.27 -249.52 -20.64 142.47 -295.89 -8.77 127.80 -270.92
183.00 395.54 643.33 169.09 363.09 654.69 199.52 370.34 630.70
338.15 358.15
a
pressure ∆P/P AADa (%)
organic phase ∆xI AADa
aqueous phase ∆xII AADa
vapor phase ∆y AADa
1.61
0.0312
0.0085
0.0348
8.84
0.0317
0.0089
0.0356
4.21
0.0251
0.0141
0.0189
AADs as defined in Table 9.
Ternary System. The ternary VLLE calculations for water (1) + 2-propanol (2) + isopropyl acetate (3) were implemented with the method as mentioned above. For a type 2 LLE system, the VLLE behavior of ternary systems can be estimated directly by using the model parameters determined from phase equilibrium data of the constituent binaries.8 The prediction was also made for this type 1 LLE system by using the binary parameters as given in Table 9. As seen from Figures 5 and 6, the agreement between the predicted results and experimental values is fairly well, except for the organicrich phase. To improve the representation for the VLLE behavior of this ternary system, the isothermal ternary VLLE data were correlated with the UNIQUAC model by adjusting six binary parameters, simultaneously. The objective function of the parameter determination is defined as
listed in Table 10 was tested with VLE calculations for the binary systems of water + 2-propanol and 2-propanol + isopropyl acetate. The calculated results indicate that the UNIQUAC model with those binary parameters is capable of describing quantitatively the existence of azeotropes in both water + 2-proanol and 2-propanol + isopropyl acetate. Additionally, the results of VLLE flash calculation also indicate that the vapor fractions R vary from 1.1 × 10-5 to 1.3 × 10-1 over the entire range of experimental conditions. In the cases of such small R, the calculated results are very close to those from the bubble-point calculation at VLLE (i.e., assuming that R is infinitely small), which computes the compositions of two coexistent liquid phases by solving the criteria of LLE together with the material balance equation, simultaneously, at a given temperature and feed composition: nc
nTL 3
∆)(
1-
3
∑ ∑∑
|(xˆ ijk - xijk)|)/9nTL
(16)
zi
)0 ∑ i)1β + K (1 - β)
(17)
i
k)1j)1 i)1
with where xijk and xˆ ijk are the observed and calculated mole fractions of component i in phase j on tie line k, respectively, and nTL is the number of tie lines. Table 10 presents the correlated results from the UNIQUAC. Figures 5 and 6 compare the calculated binodal locus, the vapor compositions, and the tie lines with the experimental results. As expected, the figures show that the correlated results for the organic-rich phase are much better than the predictions with the parameters obtained from the constituent binaries. Although the binodal locus of a ternary system can be well represented by the model with the parameters determined from ternary data, these parameters should still be able to represent the phase behavior of the constituent binaries, especially for the existence of azeotropes. The validity of the binary parameters as
I I II Ki ) xII i /xi ) γi /γi
(18)
Equilibrium pressure and vapor composition are then calculated from eqs 13 and 11 or eq 12. The later method is much simple for the VLLE calculation and, at least, can provide a set if good initial values for the rigorous VLLE flash calculation. Conclusion Isothermal VLE and VLLE properties were measured for two binary and one ternary systems containing water, 2-propanol, and isopropyl acetate at temperatures up to 373.15 K. The results of VLE measurement show that maximum pressure azeotropes were formed
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in isopropyl acetate + 2-propanol. The UNIQUAC model with linearly temperature-dependent parameters represents well the mutual solubilities of isopropyl acetate + water at temperatures up to 358.15 K. It was found that the UNIQUAC model, with the parameters obtained from the constituent binaries, predicted fairly well the VLLE behavior of the ternary water + 2-propanol + isopropyl acetate (a type 1 LLE system), except for the organic-rich phase. The isothermal VLLE data of this ternary system were correlated accurately over the experimental conditions by using the UNIQUAC model with six adjustable parameters. The UNIQUAC model with these parameters determined from ternary data was capable of representing the azeotropic behavior for water + 2-propanol and 2-propanol + isopropyl acetate. Acknowledgment Financial support from the National Science Council, ROC, through Grant No. NSC89-2214-E011-037 is gratefully acknowledged. Nomenclature A ) index of area consistency test bij ) parameters of the UNIQUAC model, (uij - ujj)/R (K) G ) Gibbs free energy (J mol-1) I1, I2 ) indices of infinite dilution consistency test Ki ) distribution ratio for component i nc ) number of components np ) number of data points nTL ) number of tie lines P ) pressure (kPa) R ) gas constant (J mol-1 K-1 or kPa cm3 mol-1 K-1) T ) temperature (K) V ) molar volume (cm3 mol-1) x ) mole fraction in the liquid phase xijk ) observed mole fractions of component i in phase j on tie line k xˆ ijk ) calculated mole fractions of component i in phase j on tie line k y ) mole fraction in the vapor phase zi ) mole fraction of component i in the feed R ) fraction of the total material in the vapor phase β ) fraction of the total material in the organic-rich phase γ ) activity coefficient δ ) index of point consistency test ∆, π ) objective functions σ ) standard deviation φi ) fugacity coefficient for component i Subscripts b ) boiling i, j ) components i and j ij ) i-j pair interaction
Superscripts act ) actual value az ) azeotropic calc ) calculated calb ) calibration expt ) experimental E ) excess property L ) liquid phase S ) saturation I ) organic phase II ) aqueous phase
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Received for review August 1, 2002 Revised manuscript received December 17, 2002 Accepted December 20, 2002 IE020583G
