Multiphase Equilibria for Mixtures Containing Acetic Acid, Water

Ind. Eng. Chem. Res. , 2006, 45 (6), pp 2123–2130. DOI: 10.1021/ie051245t. Publication Date (Web): February 22, 2006. Copyright © 2006 American Che...
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Ind. Eng. Chem. Res. 2006, 45, 2123-2130

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Multiphase Equilibria for Mixtures Containing Acetic Acid, Water, Propylene Glycol Monomethyl Ether, and Propylene Glycol Methyl Ether Acetate Cheng-Ting Hsieh, 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

A static-type apparatus equipped with a visual cell was utilized in the present study to measure isothermal vapor-liquid equilibrium (VLE) and vapor-liquid-liquid equilibrium (VLLE) data over a temperature range of 323.24 to 393.15 K. The VLE data were determined experimentally for binary mixtures of propylene glycol monomethyl ether (PGME) + propylene glycol methyl ether acetate (PGMEA) and acetic acid + PGME. A minimum pressure azeotrope exhibits on each isotherm of acetic acid + PGME. The VLLE data were also measured for water + PGMEA and water + PGMEA + PGME. The VLLE data could be correlated well by the NRTL and the UNIQUAC models accompanied with the Hayden-O’Connell (HOC) correlation for water + PGMEA over a wide temperature range as linearly temperature-dependent parameters were adopted. The NRTL-HOC model, together with the parameters determined from the phase-equilibrium data of the constituent binaries, predicted reasonably well the binodal curves of water + PGMEA + PGME. By adjustment of six parameters simultaneously, the NRTL-HOC and the UNIQUAC-HOC models correlated satisfactorily the ternary VLLE properties of water + PGMEA + PGME. Introduction Propylene glycol methyl ether acetate (PGMEA) is widely used as a solvent in the preparation of photoresist agents for manufacturing color liquid crystal displays (LCD). It can be synthesized from acetic acid and propylene glycol methyl ether (PGME) via esterification, and water is a byproduct of this reaction. The phase-equilibrium properties, including vaporliquid equilibrium (VLE) and vapor-liquid-liquid equilibrium (VLLE), for the mixtures containing acetic acid, PGME, PGMEA, and water are fundamentally important in the development of chemical processes for producing PGMEA via either a conventional reaction-then-separation multistep method or an efficient reactive-distillation one-step method.1 The phaseequilibrium data are also useful in the process design for recovery of PGMEA from the spent aqueous solutions, which are often encountered in electronic plants. Chiavone-Filho et al.2 investigated the VLE behavior of water + PGME at 353.15 and 363.15 K. Maximum pressure azeotropes exist in this binary system. Although plenty of VLE data are available in DECHEMA3 for water + acetic acid, no published phase-equilibrium data are found for acetic acid + PGME, acetic acid + PEMEA, PGME + PGMEA, and water + PGMEA. In the present study, isotherm VLE data of acetic acid + PGME and PGME + PGMEA were measured over a temperature range of (333.15393.15) K. The VLLE measurements were also conducted for the binary system of water + PGMEA and the ternary system of water + PGMEA + PGME up to 358.11 K. These new binary VLE and VLLE data were correlated with a φ-γ method, in which the NRTL4 and the UNIQUAC5 models were used, respectively, to calculate the activity coefficient of each constituent component in the liquid phase(s) and the two-term virial equation was adopted to estimate the fugacity coefficient of each constituent component in the vapor phase. The second virial coefficients were calculated from the Hayden-O’Connell (HOC) model,6 in which the chemical effects of the associated * To whom correspondence should be addressed. Tel.: 886-2-27376626. Fax: 886-2-2737-6644. E-mail: [email protected].

components, acetic acid and water, in the vapor phase have been considered. The newly obtained ternary VLLE data were utilized to test the reliability of the NRTL-HOC and the UNIQUACHOC models for the multicomponent VLLE calculations. Experimental Section The VLE and VLLE measurements were made in a static VLLE apparatus. The schematic diagram and the detailed operation procedure have been given by our previous papers.7-9 The apparatus was equipped with a visual equilibrium cell, which was immersed in a visibility thermostatic bath (model TV 4000; stability ) ( 0.03 K, Neslab, U.S.A.). The phase behavior of the mixtures in the cell could be observed through the transparent windows. The bath temperature was measured by a precision thermometer (model 1506, Hart Scientific, U.S.A.) with a platinum resistance temperature detector (RTD) probe to an uncertainty of (0.02 K. A pressure transducer (model PDCR-912; 0-1000 kPa; Druck, U.K.) with a digital indicator (model DPI-261, Druck, U.K.) measured the equilibrium pressure. The uncertainty of the pressure measurement is about (0.1%. Both vapor and liquid circulation loops were installed to promote the attainment of equilibrium. The vapor circulation loop consisted of a six-port vapor-sampling valve (model 7010, Rheodyne, U.S.A.) with a 100 µL sample loop, a magnetic gear pump, and a preheater. The liquid circulation loop was made up of a four-port liquid-sampling valve (model 7410, Rheodyne, U.S.A.) with a 1 µL loop disk, a liquid pump, a switch valve, and a preheater. The switch valve, connected to the bottom of the cell, was used to select one of the coexistent liquid phases to be circulated. The composition of the liquid and the vapor samples was analyzed by a gas chromatography (model 8700, China Chromatography Co., Taiwan) with a thermal conductivity detector. High-purity helium (99.99%) was served as a carrier gas. A stainless steel column packed with Porapak Q 80/100 (1.83 m × 0.3175 cm) was capable of separating the constituent compounds of the samples. A proper amount of solution was loaded in the degassing unit at the beginning of a run. The degassing procedure is similar

10.1021/ie051245t CCC: $33.50 © 2006 American Chemical Society Published on Web 02/22/2006

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cally prepared samples within two composition ranges, in accordance with those in the organic-rich phase (including the vapor phase) and the water-rich phase. The uncertainty of the composition analysis for the minor components is tabulated in Table 1. Acetic acid (99.9+ mass %) was purchased from Merck, Germany. Propylene glycol monomethyl ether (PGME, 98+ mass %) and propylene glycol methyl ether acetate (PGMEA, 98+ mass %) were supplied by Aldrich, Germany. The purity of each chemical was checked with chromatographic analysis. The area fractions are 0.9903, 0.9998, and 0.9994 for acetic acid, PGME, and PGMEA, respectively, from the analysis. These chemicals were used without further purification. Deionized distilled water was prepared in our laboratory. The physical properties of the pure compounds are listed in Table 2.

Table 1. Average Deviations of the Gas Chromatography Calibration phase

average deviationa

organic aqueous organic aqueous organic vapor aqueous

0.0005 0.0005 0.0017 0.0017 0.0011 0.0004 0.0001

mixture PGME (1) + PGMEA (2) acetic acid (1) + PGME (2) PGMEA (1) + water (2)

a Average deviation ) (1/n ) ∑np calb - xact|) , where n is the p k p k)1 (|x number of calibration points and x is the mole fraction of the component 1. The superscript “calb” represents the calibrated values, and “act” refers to the actual values.

Experimental Results Binary VLE Systems. The isothermal VLE data of PGME + PGMEA and acetic acid + PGME are listed in Tables 3 and Table 3. VLE Data for PGME (1) + PGMEA (2) P (kPa)

x1

y1

P (kPa)

x1

y1

0.5591 0.6512 0.8190 1.0

0.7373 0.8051 0.8970 1.0

6.7 7.7 9.4 10.8 11.7

0.0 0.1128 0.2315 0.3485 0.4553

T ) 343.15 K 0.0 12.5 0.2300 13.2 0.4962 14.1 0.5811 15.8 0.6724

14.8 18.4 20.8 23.9 26.4

0.0 0.1075 0.2175 0.3387 0.4428

T ) 363.15 K 0.0 28.3 0.2741 30.2 0.4072 32.7 0.5719 35.8 0.6626

0.5489 0.6435 0.8082 1.0

0.7188 0.7818 0.8911 1.0

45.4 53.4 60.5 68.0 74.5

0.0 0.1001 0.2139 0.3311 0.4414

T ) 393.15 K 0.0 80.9 0.2283 85.4 0.3774 93.5 0.5284 102.1 0.6204

0.5587 0.6429 0.8032 1.0

0.7225 0.7801 0.8895 1.0

Table 4. VLE Data for Acetic Acid (1) + PGME (2) P (kPa) Figure 1. Pressure-composition diagram for PGME (1) + PGMEA (2).

to that of Lee and Hu.10 The degassed solution was then transferred into the equilibrium cell, in which the levels of the vapor-liquid-liquid interfaces should be adjusted properly in order that the upper liquid phase could be circulated. Both liquid and vapor mixtures were 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 the gas chromatography was converted into mole fraction via calibration equations. Calibrations were made with gravimetri-

x1

y1

P (kPa)

10.1 9.3 8.3 7.8 7.4 7.7

0.0 0.1102 0.2533 0.3311 0.4907 0.6259

T ) 333.15 K 0.0 8.2 0.0444 9.2 0.1748 10.1 0.2455 10.7 0.4674 12.1 0.6693

15.8 14.7 13.4 12.9 12.4 12.9

0.0 0.1206 0.2546 0.3395 0.4804 0.6360

T ) 343.15 K 0.0 14.1 0.0637 15.4 0.1780 16.3 0.2486 16.9 0.4599 18.5 0.6966

x1

y1

0.6914 0.7844 0.8587 0.9017 1.0

0.8142 0.9122 0.9577 0.9677 1.0

0.7348 0.8147 0.8713 0.9071 1.0

0.8549 0.9234 0.9615 0.9777 1.0

4, respectively. Each isotherm passes the thermodynamic consistency tests,11 including the point, the area, and the infinite dilution tests, as shown in Table 5. Figure 1 illustrates the phase-

Table 2. Physical Properties and Parameters for the Constituent Compoundsa compound

Tc (K)

Pc (kPa)

ω

µ (Debye)

ηb

rc

qc

C1d

C2d

C3d

C4d

C5d

C6d

C7d

C8d (K)

C9d (K)

water acetic acid PGME PGMEA

647.13 591.95 553.00 597.90

22055 5786 4340 3009

0.345 0.467 0.722 0.481

1.8 1.7 2.4 1.8

1.7 4.5 0 0

0.92 2.20 3.70 5.07

1.40 2.07 3.29 4.43

66.74 46.36 55.43 81.82

-7258.2 -6304.5 -6886.7 -8409.6

0 0 0 0

0 0 0 0

-7.30 -4.30 -5.59 -9.59

4.17E-06 8.89E-18 2.46E-17 4.52E-06

2 6 6 2

273.16 289.81 176.48 205

647.13 591.95 553 597.9

a Taken from Aspen property databank. b Association parameter of Hayden-O’Connell (HOC) model.6 c UNIQUAC constants. d Antoine equation: ln(PS) ) C1 + (C2/T + C3) + C4T + C5 ln T + C6TC7 for C8 < T < C9, where PS is in kPa and T is in K. The values of the coefficients were taken from Aspen property databank.

Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006 2125 Table 5. Results of the Thermodynamic Consistency Tests consistency test indexa,b T (K)

δ

A

I1

GE/RT coefficientc I2

C0

C1

343.15 363.15 393.15

4.63 (+) 3.96 (+) 4.53 (+)

0.56 (+) 2.55 (+) 0.85 (+)

7.56 (+) 3.89 (+) 25.05 (+)

24.00 (+) 22.58 (+) 20.12 (+)

PGME + PGMEA 0.263 0.054 0.344 -0.017 0.246 -0.019

333.15 343.15

4.98 (+) 4.98 (+)

1.44 (+) 1.35 (+)

11.36 (+) 7.33 (+)

10.11 (+) 16.16 (+)

acetic acid + PGME -1.570 -0.344 -1.280 -0.277

ln(γ1/γ2) coefficientd C2

D0

D1

-0.533 -0.011 -0.020

0.006 -0.025 -0.008

-0.131 -0.040

-0.014 0.014

D2

D3

0.181 0.303 0.171

0.070 -0.065 -0.086

-0.419 -0.005 0.079

-1.549 -1.325

-0.386 -0.453

-0.354 -0.114

a Criteria for passing the thermodynamic consistency tests: δ < 5, A < 3, I < 30, and I < 30. b (+): Passes the consistency test. c GE/RT ) x x [C 1 2 1 2 0 + C1(x1 - x2) + C2(x1 - x2)2]. d ln(γ1/γ2) ) D0 + D1(x2 - x1) + D2(6x1x2 - 1) + D3(x2 - x1)(1 - 8x1x2).

Figure 2. Pressure-composition diagram for acetic acid (1) + PGME (2).

equilibrium diagram for PGME + PGMEA over (343.15393.15) K. The deviation from Raoult’s law was positive. No azeotrope was formed in this binary system. Figure 2 is the isothermal pressure-composition diagram of acetic acid + PGME. A minimum pressure azeotrope exhibits on each isotherm. The azeotrope composition (xaz i ) can be determined by one of the following equations that were proposed by Hiaki et al.:12

yi - xi ) 0

(1)

nc

∆Py ∆Px

P)

∑ i)1

PSi yi

nc

P-

)1

(2)

PSi xi ∑ i)1

or

∂P )0 ∂xi

(3)

where PSi is the vapor pressure of component i. Figure 3 presents (x1 - y1), ∆Py/∆Px, and P varying with x1 around the azeotrope point. It shows that the relationships as given in eqs 1 and 2 are approximately linear and, thus, are much more convenient to accurately determine the azeotropic composition. Upon the value of xaz 1 being obtained, the corresponding azeotropic pressure could then be calculated from an empirical

Figure 3. Determination of azeotrope composition for acetic acid (1) + PGME (2) at 343.15 K. Table 6. Azeotropic Conditions for Acetic Acid (1) + PGME (2) T (K)

xaz 1

Paz (kPa)

333.15 343.15

0.5389 0.5175

7.4 12.4

Table 7. VLLE Data for Water (1) + PGMEA (2) T (K)

P (kPa)

organic phase, xI2

aqueous phase, xII2

vapor phase, y2

323.24 328.15 333.15 338.15 343.15 348.15 353.11 358.11

13.8 18.0 22.2 28.5 35.4 43.9 54.1 65.9

0.6569 0.6568 0.6473 0.6430 0.6262 0.6142 0.6011 0.5739

0.0196 0.0197 0.0199 0.0203 0.0215 0.0231 0.0240 0.0249

0.1389 0.1385 0.1380 0.1355 0.1323 0.1320 0.1318 0.1314

equation of equilibrium pressure in terms of x1 at the azeotropic point. The azeotrope conditions determined in this way are given in Table 6. Binary VLLE System. Table 7 lists the VLLE data of water + PGMEA at temperatures from 323.24 to 358.11 K. The superscripts I and II represent the organic-rich phase and the aqueous phase, respectively. Trace amounts of PGME and acetic acid were detected in the liquid phase at 353.11 and 358.11 K, indicating that hydrolysis of PGMEA took place slowly even without adding any acidic catalyst. The measurements for this

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Figure 6. VLLE phase diagram for water (1) + PGMEA (2) + PGME (3) at 343.15 K. Table 8. VLLE Data for Water (1) + PGMEA (2) + PGME (3)

Figure 4. Temperature-composition VLLE phase diagram for water (1) + PGMEA (2).

T (K)

P (kPa)

323.24

13.9 14.0 14.1 22.6 22.7 22.9 35.9 36.0 36.3 66.3 66.4 66.5

333.15 343.15 358.11

organic phase, xIi PGMEA PGME 0.5458 0.3818 0.3251 0.5193 0.3475 0.2976 0.4982 0.3201 0.2712 0.4743 0.3042 0.2289

0.0466 0.0800 0.0851 0.0509 0.0788 0.0856 0.0529 0.0807 0.0842 0.0549 0.0803 0.0804

aqueous phase, xIIi water PGME

vapor phase, yi water PGME

0.9439 0.9058 0.8895 0.9471 0.9110 0.8934 0.9494 0.9138 0.8985 0.9553 0.9240 0.8915

0.8465 0.8341 0.8324 0.8458 0.8294 0.8242 0.8429 0.8272 0.8254 0.8426 0.8263 0.8226

0.0195 0.0394 0.0461 0.0183 0.0372 0.0449 0.0176 0.0360 0.0430 0.0156 0.0320 0.0445

0.0214 0.0429 0.0450 0.0221 0.0414 0.0468 0.0259 0.0447 0.0482 0.0260 0.0443 0.0481

be primarily governed by the mutual solubilities of water and PGMEA (the edge of the water/PGMEA binary). Owing to the fact that the mutual solubility between water and PGMEA increases with increasing temperature, the area of the liquidliquid splitting region becomes smaller at higher temperatures. The phase compositions of the two ends of the tie-lines were correlated with the empirical equation of Othmer-Tobias,13

ln Figure 5. Saturated pressures for water (1) + PGMEA (2) at VLLE.

binary system were completed within about 3 h for each run. At the highest operating temperature, 358.11 K, the mole fractions of PGME and acetic acid are still negligible at the end of the run. Figure 4 presents the mole fractions of PGMEA, in the three coexistent phases, varying with temperature for the water + PGMEA system. Figure 5 is the P-T diagram of water + PGMEA at VLLE. The variation of equilibrium pressure with temperature appears to follow the Antoine relationship. Ternary VLLE System. Since only the water/PGMEA pair is partially miscible in the mixtures containing water, PGMEA, and PGME, this ternary system is thus classified as a type-1 LLE. Table 8 reports the VLLE data of water + PGMEA + PGME at temperatures from 323.24 to 358.11 K. Figure 6 is the phase diagram of this ternary system at 343.15 K. The solubilities of the organic compounds are rather small in the aqueous phase, while water dissolves appreciably in the organicrich phase. The area of the liquid-phase splitting region may

( ) 1 - w1II w1II

) n + m ln

( ) 1 - w2I w2I

(4)

where w1II is the weight fraction of water in the aqueous phase and w2I is the weight fraction of PGMEA in the organic phase. Figure 7 illustrates that the LLE data follow the linear relationship as given by eq 4. The experimental data appear to be well-consistent. VLE Calculation The binary VLE data of PGME + PGMEA and acetic acid + PGME were correlated with the φ-γ method. In the VLE data reduction, the components’ fugacity in the vapor phase was calculated by means of the virial equation of state truncated after the second term. The second virial coefficients were calculated from the Hayden-O’Connell model,6 in which the association of acetic acid in the vapor phase was accounted. The solution models of the NRTL and the UNIQUAC were utilized to represent the nonideality of the constituents in the liquid phase. Optimal values of the temperature-specific model

Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006 2127

as follows.

(KIi - 1)zi

nc

∑ i)1

β1 KIi + (1 - β1)[β2 + (1 - β2)KIi /KIIi ] (KIIi - 1)zi

nc

∑ i)1

)0

β1 KIIi + (1 - β1)[β2(KIIi /KIi ) + (1 - β2)]

)0

(6)

(7)

with

Figure 7. Othmer-Tobias correlation for water (1) + PGMEA (2) + PGME (3).

parameters were determined on the basis of the maximum likelihood principle by minimization of the following objective function, π1, np

π1 )

∑ k)1

{[

] [

(Pcalc - Pkexpt) k σp

[

2

+

σT

] [

calc expt (x1,k - x1,k )

σx1

]

(Tcalc - Texpt k k ) 2

+

KIi ) yi/xIi ) γIi φSi PSi exp[(P - PSi )VLi /RT]/φˆ iP

(8)

KIIi ) yi/xIIi ) γIIi φSi PSi exp[(P - PSi )VLi /RT]/φˆ iP

(9)

where β1 is the fraction of the total material in the vapor phase, β2 is the fraction of the first liquid phase (the organic-rich phase) in the total liquid, nc is the number of components, and Ki, PiS, and φi are the distribution ratio, the vapor pressure, and the fugacity coefficient for component i, respectively. Since the equilibrium pressures of the investigated VLLE systems are not greater than 67 KPa over the entire range of experimental conditions, the Poynting pressure correction factor was reasonably assumed to be unity in the present calculation. Equations 8 and 9 were thus simplified as

2

+

]}

calc expt (y1,k - y1,k )

σy1

2

KIi ) yi/xIi ) γIi φSi PSi /φˆ iP

(10)

KIIi ) yi/xIIi ) γIIi φSi PSi /φˆ iP

(11)

(5)

where σ2 is the variance of the measured variables. In the above VLE calculations, the standard deviation σ was set to 0.05 kPa for pressure, 0.02 K for temperature, 0.002 for liquid composition, and 0.005 for vapor composition. The optimization algorithm is based on the Britt-Luecke method.14 The smooth curves in Figures 1 and 2 are the calculated results. Table 9 reports the results of data reduction, indicating that the NRTLHOC and the UNIQUAC-HOC correlate equally well for PGME + PGMEA and acetic acid + PGME. VLLE Calculation The compositions of three coexistent phases (yi, xiI, and xiII) and the equilibrium pressures were calculated via VLLE flash calculations15 at a given temperature and feed composition (zi). According to the material balance equations and the equilibrium criteria for a VLLE system, two flash equations were obtained

While the activity coefficient γi was calculated from either the NRTL model or the UNIQUAC model, the nonideality of the vapor phase was represented by the two-term virial equation

ln φˆ i )

2

nc

∑yiBij - ln Z

(12)

V j)1

where the second virial coefficients Bij were estimated from the Hayden-O’Connell model6 to consider the association effects of water in the vapor phase. Upon specifying the values of solution model’s parameters, β1 and β2 can be solved simultaneously from eqs 6 and 7 at a given T and zi. The compositions of the coexistent liquid phases were then calculated from the following equations:

xIi )

zi β1 KIi

+ (1 - β1)[β2 + (1 - β2)KIi /KIIi ]

(13)

Table 9. Data Reduction from the NRTL-HOC and the UNIQUAC-HOC Models for VLE Binary Systems NRTL-HOC

UNIQUAC-HOC ∆x1 AADa

∆P/P AADb (%)

T (K)

a12 (K)

a21 (K)

R

∆T AADa (K)

343.15 363.15 393.15

-1704.82 -1704.82 -1704.82

1820.95 1820.95 1820.95

0.3 0.3 0.3

0.01 0.02 0.07

0.0077 0.0049 0.0089

333.15 343.15

107.96 -523.33

-257.02 781.44

0.3 0.3

0.004 0.007

0.0102 0.0107

b21 (K)

∆T AADa (K)

∆x1 AADa

∆P/P AADb (%)

∆y1 AADa

PGME (1) + PGMEA (2) 1.70 0.0085 621.07 0.41 0.0058 621.07 0.20 0.0064 621.07

-824.41 -824.41 -824.41

0.01 0.02 0.07

0.0076 0.0050 0.0089

1.72 0.41 0.20

0.0085 0.0058 0.0063

acetic acid (1) + PGME (2) 0.65 0.0084 81.56 0.40 0.0085 86.31

-30.65 -66.21

0.004 0.008

0.0102 0.0114

0.65 0.53

0.0085 0.0096

∆y1 AADa

b12 (K)

a ∆M AAD ) (1/n )∑np (|Mcalc - Mexpt|) , where n is the number of data points and M represents T, x , or y . b ∆P/P AAD (%) ) (100%/n ) ∑np (|Pcalc p k p 1 1 p k)1 k)1 - Pexpt|/Pexpt)k.

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Table 10. Correlated Results of VLLE for Water (1) + PGMEA (2) aqueous organic vapor phase phase phase I II a a ∆x2 AAD ∆x2 AAD ∆y2 AADa

∆T ∆P/P AADa AADb (K) (%)

model NRTL-HOC UNIQUAC-HOC

0.09 0.04

0.95 0.66

0.0121 0.0071

0.0005 0.0005

0.0095 0.0045

a ∆M AAD ) (1/n )∑np (|Mcalc - Mexpt|) , where n is the number of p k p k)1 data points and M represents T, xI2, xII2 , or y2. b ∆P/P AAD (%) ) (100%/ np np)∑k)1 (|Pcalc - Pexpt|/Pexpt)k.

xIIi )

zi β1 KIIi

+ (1 - β1)[β2(KIIi /KIi ) + (1 - β2)]

(14)

The vapor composition (yi) and the equilibrium pressure (P) can thus be obtained from the following equations: Π S S γΙi xΙi φSi PSi γΠ i xi φi Pi ) yi ) φiP φiP

(15)

and nc

γΙi xΙi φSi PSi

nc

yiP ) ∑ ∑ i)1 i)1

P)

φi

nc

)

∑ i)1

Π S S γΠ i xi φi Pi

(16) φi

Binary VLLE System. For the binary system of water (1) + PGMEA (2), the parameters of the NRTL (a12 and a21 with R ) 0.2) and UNIQUAC (b12 and b21) models were determined from the binary mutual solubility data by minimizing the objective function π2: np

π2 )

{[ [

∑

] [ ] [

(Pcalc - Pkexpt) k

k)1

σp

Ι,calc Ι,expt (x1,k - x1,k )

σx1I

2

+

2

+

]

(Tcalc - Tkexpt) k

2

σT

]

+

Π,calc Π,expt (x1,k - x1,k )

[

σx1Π

2

+

]}

calc expt (y1,k - y1,k )

σy 1

2

(17)

The standard deviation σ was set to 0.05 kPa for pressure, 0.02 K for temperature, 0.001 1 for organic-phase composition, 0.000 15 for aqueous-phase composition, and 0.000 4 for vapor composition. Good correlation was obtained while the model’s parameters were treated as linearly temperature-dependent functions:

a12 (K) ) -341.7057 + 5.3709T (K)

(18)

a21 (K) ) 998.0495 - 3.3721T (K)

(19)

b12 (K) ) 2.6262 + 0.1007T (K)

(20)

b21 (K) ) -573.2592 +0.3682T (K)

(21)

Table 10 lists the results of VLLE calculations for water + PGMEA. Figure 4 compares the calculated phase compositions with the experimental values. The results from the UNIQUACHOC appear to be marginally better than those from the NRTLHOC for this binary VLLE system. However, opposite trends were shown between the experimental values and the calculated values from both models for the temperature-dependent vapor compositions. Figure 5 illustrates that the calculated equilibrium pressures agree with the experimental values satisfactorily, regardless of the models being used. Ternary VLLE System. For the ternary system of water (1) + PGMEA (2) + PGME (3), the VLLE properties were predicted by using the parameters determined from their three constituent binaries; i.e., those of the PGMEA/water pair were taken from eqs 18-21 and those of the other two pairs were obtained by fitting the models to the corresponding binary VLE data. The predicted results from the NRTL-HOC and the UNIQUAC-HOC are listed in Tables 11 and 12, respectively. It appears that the NRTL-HOC is better than the UNIQUACHOC for this ternary system. The results from the NRTL-HOC are compared with the experimental data in Figure 6. The ternary mutual solubility data were also correlated respectively with the NRTL-HOC and the UNIQUAC-HOC models by adjusting six binary parameters simultaneously. Tables 13 and 14 list the correlated results. As expected, the correlated results are substantially better than the predictions from the models with the parameters obtained from the phaseequilibrium data of the constituent binaries. The tabulated parameters of the water/PGME pair are tested by the binary VLE data2 to verify whether these parameters could properly reproduce the existence of the azeotropes for water + PGME. Figure 8 shows that the azeotropic conditions of water + PGME can be represented satisfactorily from both the NRTL-HOC and the UNIQUAC-HOC models with those parameters taken from Tables 13 and 14, although the accuracy of the VLE calculations was slightly deteriorated. Conclusion Isothermal VLE and VLLE properties were measured for three binary systems and one ternary system containing water,

Table 11. Predicted Results from the NRTL-HOC Model for the VLLE Properties of Water (1) + PGMEA (2) + PGME (3) T (K)

i-j

Rij

aij (K)

aji (K)

source

∆T AADa (K)

∆P/P AADb (%)

∆xI AADc

∆xII AADc

∆y AADc

323.24

1-2d 1-3 2-3 1-2d 1-3 2-3 1-2d 1-3 2-3 1-2d 1-3 2-3

0.2 0.3 0.3 0.2 0.3 0.3 0.2 0.3 0.3 0.2 0.3 0.3

1394.38 -2926.36 1820.95 1447.61 -2926.36 1820.95 1501.32 -2926.36 1820.95 1581.68 -2926.36 1820.95

-91.95 -189.23 -1704.82 -125.37 -189.23 -1704.82 -159.09 -189.23 -1704.82 -209.53 -189.23 -1704.82

this work Chiavone-Filho et al.2 this work this work Chiavone-Filho et al.2 this work this work Chiavone-Filho et al.2 this work this work Chiavone-Filho et al.2 this work

0.13

7.65

0.0088

0.0208

0.0226

0.29

7.05

0.0063

0.0213

0.0219

0.63

6.55

0.0050

0.0208

0.0215

1.12

3.86

0.0087

0.0195

0.0207

333.15 343.15 358.11

a ∆T AAD (K) ) (1/n )∑np (|Tcalc - Texpt|) , where n is the number of data points. b ∆P/P AAD (%) ) (100%/n ) ∑np (|Pcalc - Pexpt|/Pexpt) , where n p k p p k p k)1 k)1 np nc is the number of data points. c ∆M AAD ) (1/(npnc)) ∑k)1 ∑j)1 (|Mjcalc - Mjexpt|)k, where nc is the number of components and M represents xI, xII, or y. d Parameters were calculated from eqs 18 and 19.

Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006 2129 Table 12. Predicted Results from the UNIQUAC-HOC Model for the VLLE Properties of Water (1) + PGMEA (2) + PGME (3) T (K)

i-j

bij (K)

bji (K)

source

∆T AADa (K)

∆P/P AADb (%)

∆xI AADc

∆xII AADc

∆y AADc

323.24

1-2d 1-3 2-3 1-2d 1-3 2-3 1-2d 1-3 2-3 1-2d 1-3 2-3

35.18 1190.16 -824.41 36.17 1190.16 -824.41 37.18 1190.16 -824.41 38.69 1190.16 -824.41

-454.24 -2250.32 621.07 -450.59 -2250.32 621.07 -446.91 -2250.32 621.07 -441.40 -2250.32 621.07

this work Chiavone-Filho et al.2 this work this work Chiavone-Filho et al.2 this work this work Chiavone-Filho et al.2 this work this work Chiavone-Filho et al.2 this work

0.22

12.43

0.0156

0.0431

0.0228

0.48

11.24

0.0130

0.0402

0.0225

1.00

9.91

0.0134

0.0380

0.0229

1.77

5.95

0.0149

0.0349

0.0228

333.15 343.15 358.11

a-c

As given in Table 11. d Parameters were calculated from eqs 20 and 21. Table 14. Correlated Results from the UNIQUAC Model for Water (1) + PGMEA (2) + PGME (3) T (K) i-j

bij (K)

bji (K)

323.24 1-2 1-3 2-3 333.15 1-2 1-3 2-3 343.15 1-2 1-3 2-3 358.11 1-2 1-3 2-3

49.60 635.04 -940.33 46.98 635.04 -940.33 44.34 635.04 -940.33 40.39 635.04 -940.33

-484.88 -1712.32 649.62 -473.04 -1712.32 649.62 -461.10 -1712.32 649.62 -443.23 -1712.32 649.62

a-c

∆xI ∆xII ∆y ∆T ∆P/P AADc (K) AAD (%)a AADb AADb AADb 0.02

1.13

0.0075 0.0044 0.0114

0.04

0.99

0.0030 0.0029 0.0097

0.09

0.95

0.0040 0.0053 0.0061

0.06

0.21

0.0065 0.0070 0.0077

As defined in Table 11.

better predictions than those from the UNIQUAC-HOC model for the ternary VLLE system. Moreover, the mutual solubility data of water + PGMEA + PGME could be correlated accurately with either the NRTL-HOC or the UNIQUACHOC model by adjusting six binary parameters simultaneously over the entire of experimental conditions. Figure 8. Comparison of the results of VLE calculations with literature values for water (1) + PGME (2) (parameters of the NRTL-HOC model were taken from Table 13, and those of the UNIQUAC-HOC model were taken from Table 14). Table 13. Correlated Results from the NRTL-HOC Model for Water (1) + PGMEA (2) + PGME (3)

T (K)

i-j Rij

323.24 1-2 1-3 2-3 333.15 1-2 1-3 2-3 343.15 1-2 1-3 2-3 358.11 1-2 1-3 2-3 a-c

0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

aij (K)

aji (K)

1277.87 -1803.56 3724.72 1371.90 -1803.56 3724.72 1466.79 -1803.56 3724.72 1608.74 -1803.56 3724.72

-70.94 -180.00 -2029.23 -114.50 -180.00 -2029.23 -158.45 -180.00 -2029.23 -224.20 -180.00 -2029.23

∆T ∆P/P ∆xII ∆y AADa AADb ∆xI (K) (%) AADc AADc AADc 0.01

0.91 0.0090 0.0039 0.0107

0.04

0.91 0.0084 0.0039 0.0103

0.10

1.10 0.0096 0.0072 0.0100

0.12

0.44 0.0149 0.0100 0.0180

As defined in Table 11.

acetic acid, PGME, and PGMEA at temperatures up to 393.15 K. The results of VLE measurements showed that minimum pressure azeotropes were formed in acetic acid + PGME. The NRTL-HOC and the UNIQUAC-HOC models with linearly temperature-dependent parameters could represent well the VLLE properties of water + PGMEA over a temperature range from 323.24 to 358.11 K. By using the parameters determined from the phase-equilibrium data of the constituent binaries, the NRTL-HOC model predicted the binodal curves of water + PGMEA + PGME to within reasonable accuracy and yielded

Acknowledgment Financial support from the Ministry of Economic Affairs, ROC, through Grant No. 93-EC-17-A-09-S1-019 is gratefully acknowledged. Nomenclature A ) index of area consistency test aij ) parameters of the NRTL model, (gij - gjj)/R (K) B ) second virial coefficient (cm3 mol-1) 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 m, n ) Othmer-Tobias constants nc ) number of components np ) number of data points P ) pressure (kPa) q ) surface area parameter of the UNIQUAC model r ) volume parameter of the UNIQUAC model R ) gas constant (J mol-1 K-1) T ) temperature (K) V ) molar volume (cm3 mol-1) w) weight fraction in liquid phase x ) mole fraction in liquid phase y ) mole fraction in vapor phase Z ) compressibility factor zi ) mole fraction of component i in feed R ) parameter of the NRTL model

2130

Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006

β1 ) fraction of the total material in the vapor phase β2 ) the fraction of the first liquid phase (the organic-rich phase) in the total liquid γ ) activity coefficient µ ) dipole moment (debye) π1, π2 ) objective functions δ ) index of point consistency test φi ) fugacity coefficient of pure compound i φˆ i ) fugacity coefficient of component i in vapor mixtures ω ) acentric factor σ ) standard deviation Subscripts i, j ) components i and j ) i-j pair interaction

ij

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 Literature Cited (1) Malon, M. F.; Doherty, M. F. Reactive Distillation. Ind. Eng. Chem. Res. 2000, 39, 3953. (2) Chiavone-Filho, O.; Proust, P.; Rasmussen, P. Vapor-Liquid Equilibria for Glycol Ether + Water Systems. J. Chem. Eng. Data 1993, 38, 128.

(3) Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collections Aqueous- Organic Systems, Chemistry Data Series; DECHEMA: Frankfurt, Germany, 1977; Vol. 1, pp 101-139. (4) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135. (5) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Free Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116. (6) Hayden, J. G.; O’Connell, J. P. A Generalized Method for Predicting Second Virial Coefficients. Ind. Eng. Chem. Process Des. DeV. 1975, 14, 209. (7) Lee, M. J.; Tsai, L. H.; Hong, G. B.; Lin, H. M. Multiphase Coexistence for Aqueous Systems with Amyl Alcohol and Amyl Acetate. Ind. Eng. Chem. Res. 2002, 41, 3247. (8) Hong, G. B.; Lee, M. J.; Lin, H. M. Vapor-Liquid and VaporLiquid-Liquid Equilibria for Mixtures Containing Water, Ethanol, and Ethyl Benzoate. Ind. Eng. Chem. Res. 2003, 42, 4234. (9) Lee, M. J.; Tsai, L. H.; Hong, G. B.; Lin, H. M. Multiphase Equilibria for Binary and Ternary Mixtures Containing Propionic Acid, n-Butanol, Butyl Propionate, and Water. Fluid Phase Equilib. 2004, 216, 219. (10) Lee, M. J.; Hu, C. H. Isothermal Vapor-Liquid Equilibria for Mixtures of Ethanol, Acetone, and Diisopropyl Ether. Fluid Phase Equilib. 1995, 109, 83. (11) Kojima, K.; Moon, H. M.; Ochi, K. Thermodynamic Consistency Test of Vapor-Liquid Equilibrium Data Methanol-Water, BenzeneCyclohexane and Ethyl Methyl Ketone-Water. Fluid Phase Equilib. 1990, 56, 269. (12) Hiaki, T.; Tochigi, K.; Kojima, K. Measurement of Vapor-Liquid Equilibrium and Determination of Azeotropic Point. Fluid Phase Equilib. 1986, 26, 83. (13) Othmer, D. F.; Tobias, P. E. Tie Line Correlation. Ind. Eng. Chem. 1942, 34, 693. (14) Britt, H. I.; Luecke, R. H. The Estimation of Parameters in Nonlinear, Implicit Models. Technometrics 1973, 15, 233. (15) Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth: Boston, MA, 1985.

ReceiVed for reView November 9, 2005 ReVised manuscript receiVed January 24, 2006 Accepted January 31, 2006 IE051245T