Multiphase equilibria for mixtures containing water, acetic acid, propionic acid, methyl acetate and methyl propionate

Fluid Phase Equilibria 271 (2008) 69–75

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Multiphase equilibria for mixtures containing water, acetic acid, propionic acid, methyl acetate and methyl propionate Cheng-Ting Hsieh, Wan-Yun Ji, Ho-mu Lin, Ming-Jer Lee ∗ Department of Chemical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106-07, Taiwan

a r t i c l e

i n f o

Article history: Received 27 May 2008 Received in revised form 3 July 2008 Accepted 3 July 2008 Available online 12 July 2008 Keywords: Vapor–liquid equilibrium Vapor–liquid–liquid equilibria Water Acetic acid Propionic acid Methyl acetate Methyl propionate

a b s t r a c t Isobaric vapor–liquid equilibrium (VLE) data were measured for the binary mixtures of acetic acid + methyl propionate, propionic acid + methyl acetate, propionic acid + methyl propionate, and methyl propionate + methyl acetate in a temperature range of 330.05–413.15 K at 101.3 kPa. Isothermal vapor–liquid–liquid equilibrium (VLLE) data were also measured for water + methyl acetate + methyl propionate over a pressure range of 43.7–157.0 kPa at 323.24 and 343.15 K. The NRTL-HOC and the UNIQUAC-HOC models with the model parameters determined from the phase equilibrium data of the constituent binaries were applied to predict the VLLE properties for water + methyl acetate + methyl propionate. The validity of the prediction from the UNIFAC-HOC and the UNIFAC-Lyngby-HOC was also tested with the ternary VLLE data. Additionally, the best-fitted values of the six binary parameters of the UNIQUAC-HOC were determined, simultaneously, from the isothermal VLLE ternary data as well. © 2008 Elsevier B.V. All rights reserved.

1. Introduction This is a continuous study on the phase equilibrium measurement for developing a reactive distillation process to recover mixture of acetic acid and propionic acid from caprolactam plants via esterification of the carboxylic acids with methanol. The phase equilibrium properties, including vapor–liquid equilibrium (VLE) and vapor–liquid–liquid equilibrium (VLLE), of the mixtures containing methanol, acetic acid, propionic acid, methyl acetate, methyl propionate, and water are needed in the process development. In our previous paper [1], the available data sources have been surveyed and the VLLE data were measured for water + methyl acetate, water + methyl propionate, water + methyl acetate + methanol, and water + methyl propionate + methanol at temperatures ranging from 313.24 to 348.15 K. The phase equilibrium data of the other missing systems in literature were determined experimentally in the present study which include the isobaric VLE data of binary mixtures of acetic acid + methyl propionate, propionic acid + methyl acetate, propionic acid + methyl propionate, and methyl propionate + methyl acetate at 101.3 kPa and the isothermal VLLE data of the ternary system of water + methyl acetate + methyl propionate at 323.24

∗ Corresponding author. Tel.: +886 2 2737 6626; fax: +886 2 2737 6644. E-mail address: [email protected] (M.-J. Lee). 0378-3812/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2008.07.004

and 343.15 K. These new binary VLE and ternary VLLE data were correlated with the - method, in which the NRTL [2] and the UNIQUAC [3] 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 vaporphase. The second virial coefficients were calculated from the Hayden–O’Connell (HOC) model [4], in which self-association and cross-association effects in the vapor-phase have been taken into account. The ternary VLLE data were also utilized to test the reliability of the NRTL-HOC, the UNIQUAC-HOC, the UNIFAC-HOC [5] and the UNIFAC-Lyngby-HOC [6] models for the phase equilibrium calculations. 2. Experimental 2.1. Apparatus A recirculation-type phase equilibrium apparatus (NGW Co., Germany) was used in this study to measure the isobaric VLE data. The schematic diagram and the detailed operation procedure have been given by Shiah et al. [7]. The major parts of the equilibrium still were made up of a liquid-phase chamber, a condenser, a vaporphase cell, and two coil heaters. A silicon oil jacket surrounded the outer spaces of the liquid-phase chamber and the vapor-phase cell. To maintain isothermal condition inside the jacket, the coil heaters

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Table 1 Composition analysis and gas chromatography calibration Mixture

Column

Phase

Average deviationa

Acetic acid (1) + methyl propionate (2)

CP-WAXb

Organic Aqueous

0.0018 0.0018

Propionic acid (1) + methyl acetate (2)

Porapak QSc

Organic Aqueous

0.0013 0.0013

Propionic acid (1) + methyl propionate (2)

Porapak QSc

Organic Aqueous

0.0026 0.0026

Methyl propionate (1) + methyl acetate (2)

Porapak QSc

Organic Aqueous

0.0010 0.0010

Water (1) + methyl acetate (2)

Porapak QSc

Organic Aqueous

0.0010 0.0001

Water (1) + methyl propionate (2)

Porapak QSc

Organic Aqueous

0.0017 0.0001

a b c

np

Average deviation = (1/np )

k=1

(|xcalb − xact |)k , where np is the number of calibration points and x is the mole fraction of the component 1.

CP-WAX (model CP7668, Varian, USA). Porapak QS (80–100 mesh, 1.83 m × 3.175 mm, SUPELCO, USA).

were controlled by a PID controller. The top of the equilibrium still was connected to a burette and an adjustable water reservoir to manipulate the total pressure of the system at 101.3 ± 0.2 kPa. The boiling temperature was measured by a series of precision thermometers (models N6000-N6020, stability = ±0.1 K, Amarell Electronic Co., Germany). The atmospheric pressure was measured by a Fortin mercury barometer (model 453, stability = ±0.1 kPa, Princo Instruments, USA). The VLLE data were measured with a static-type phase equilibrium apparatus. The schematic diagram and the detailed operation procedure have been presented elsewhere [8–11]. The main part of the apparatus is a visual equilibrium cell that was immersed in a visibility thermostatic bath (model TV 4000, stability = ±0.03 K, Tamson, Netherlands). The phase behavior in the equilibrium cell can be observed through the transparent window. The equilibrium pressure was measured by a pressure transducer (model PDCR-912, 0–1000 kPa, Druck, UK) with a digital indicator (model DPI-261, Druck, UK). A precision thermometer (model 1560, Hart Scientific, USA) with a platinum RTD probe measured the bath temperature. The uncertainties of pressure and temperature measurements are ±0.1% and ±0.02 K, respectively. This apparatus was equipped with both liquid and vapor circulation loops to promote the attainment of equilibrium. The liquid circulation loop was made up of a four-port liquid-sampling valve (model 7410, Rheodyne, USA) with a 1 ␮l cavity 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 vapor circulation loop consisted of a six-port vapor-sampling valve (model 7010, Rheodyne, USA) with a 100 ␮l sample loop, a magnetic gear pump, and a preheater.

2.2. Composition analysis The phase compositions were analyzed by gas chromatography (GC) with a thermal conductivity detector. GC models 8700 and 8900 (China Chromatography, Taiwan) were employed to the isobaric VLE and the isothermal VLLE measurements, respectively. High-purity helium (99.99%) was used as a carrier gas. The information of the GC columns for composition analysis is given in Table 1. Four to five samples were replicated for individual phase measurements at each experimental condition. The average area fraction was converted into mole fraction via an equation determined by calibration on mixtures of known mole fraction prepared gravimetrically. The uncertainties of the composition analysis are tabulated in Table 1. 2.3. Materials Acetic acid (99+ %), propionic acid (99.5+ %), methyl acetate (99%) and methyl propionate (99+ %) were supplied by Acros, USA. The purity of each chemical was checked with chromatographic 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. 3. Experimental results 3.1. Binary VLE systems Table 3 reports the isobaric VLE data of acetic acid + methyl propionate, propionic acid + methyl acetate, propionic acid + methyl propionate, and methyl propionate + methyl acetate in a temperature range of 330.05–413.15 K at 101.3 kPa. Fig. 1 illustrates the VLE

Table 2 Physical properties and parameters for the constituent compoundsa Compound

Tc (K)

Pc (kPa)

ω

 (debye)

rb

qb

c

C1 d

C2 d

C3 d

C4 d

C5 d

C6 d

C7 d

C8 d (K)

C9 d (K)

Water Acetic acid Propionic acid Methyl acetate Methyl propionate

647.13 591.95 600.81 506.55 530.60

22064 5786 4617 4750 4004

0.345 0.467 0.575 0.331 0.347

1.8 1.7 1.8 1.7 1.7

0.92 2.20 2.86 2.80 3.48

1.40 2.07 2.61 2.58 3.12

1.70 4.50 4.50 0.85 0.00

66.74 46.36 47.64 54.36 63.81

−7258.2 −6304.5 −7149.4 −5618.6 −6439.7

0 0 0 0 0

0 0 0 0 0

−7.30 −4.30 −4.28 −5.65 −6.98

4.17E−06 8.89E−18 1.18E−18 2.11E−17 2.01E−17

2 6 6 6 6

273.16 289.81 252.45 175.15 185.65

647.13 591.95 600.81 506.55 530.60

a b c d

Taken from Aspen property databank. Surface area and volume parameters of the UNIQUAC model. Self-association parameter in the HOC model. Extended Antoine equation: ln(P S ) = C1 + (C2 /(T + C3 )) + C4 T + C5 ln T + C6 T C7 for C8 < T < C9 , where PS is in kPa and T in K.

C.-T. Hsieh et al. / Fluid Phase Equilibria 271 (2008) 69–75

71

Table 3 Binary VLE data at 101.3 kPa T (K)

x1

y1

T (K)

x1

y1

Acetic acid (1) + methyl propionate (2) 352.65 0.0 356.75 0.2077 358.25 0.2705 360.85 0.3708 362.15 0.4251 365.05 0.5328 368.15 0.6060 371.05 0.6798 373.65 0.7374 375.45 0.7661

0.0 0.0665 0.0979 0.1572 0.1806 0.2622 0.3356 0.4243 0.4849 0.5355

375.65 378.65 379.75 380.95 381.45 381.95 382.05 385.65 388.35 390.65

0.7700 0.8165 0.8472 0.8665 0.8707 0.8836 0.8872 0.9377 0.9721 1.0

0.5365 0.6293 0.6609 0.7071 0.7197 0.7326 0.7367 0.8502 0.9313 1.0

Propionic acid (1) + methyl acetate (2) 330.05 0.0 335.65 0.1066 338.95 0.2285 341.65 0.2921 342.95 0.3364 346.65 0.4499 349.65 0.5199 353.45 0.5909 354.75 0.6203 358.35 0.6557 362.15 0.6929 364.35 0.7136

0.0 –a 0.0113 0.0184 0.0220 0.0403 0.0558 0.0801 0.0892 0.1156 0.1406 0.1550

366.35 369.35 371.65 376.05 383.05 387.85 395.55 400.65 403.55 405.55 410.65 413.58

0.7256 0.7407 0.7603 0.7864 0.8389 0.8762 0.9219 0.9457 0.9550 0.9639 0.9871 1.0

0.1740 0.2017 0.2280 0.2785 0.3727 0.4707 0.6210 0.7114 0.7743 0.8062 0.9164 1.0

Propionic acid (1) + methyl propionate (2) 352.65 0.0 357.25 0.1828 359.35 0.2725 361.45 0.3184 362.65 0.3537 368.05 0.4896 370.75 0.5404 376.95 0.6405 380.65 0.6859

0.0 0.0187 0.0324 0.0501 0.0638 0.1073 0.1401 0.2140 0.2687

382.45 392.35 396.55 403.75 405.55 406.75 410.45 410.85 413.58

0.7090 0.8239 0.8669 0.9372 0.9507 0.9567 0.9826 0.9848 1.0

0.2884 0.4751 0.5624 0.7467 0.7935 0.8372 0.9288 0.9347 1.0

Methyl propionate (1) + methyl acetate (2) 330.05 0.0 332.75 0.1799 334.15 0.2494 335.25 0.3190 337.45 0.4362 338.95 0.5076 340.05 0.5558 340.55 0.5783 342.35 0.6485

0.0 0.0865 0.1387 0.1826 0.2681 0.3300 0.3865 0.4090 0.4919

342.95 344.25 345.45 346.55 348.15 349.65 351.05 351.25 352.65

0.6738 0.7355 0.7764 0.8131 0.8636 0.9034 0.9555 0.9651 1.0

0.5135 0.5712 0.6303 0.6833 0.7721 0.8509 0.9249 0.9356 1.0

a

The vapor composition of propionic acid was too dilute to be measured accurately.

phase equilibrium diagram of the binary VLE systems. No azeotrope was formed in these binary VLE systems. Each binary system passes the thermodynamic consistency test of Herington [12]. The results of area test are given in Table 4. 3.2. Ternary VLLE system Table 5 lists the VLLE phase equilibrium data for the ternary system of water + methyl acetate + methyl propionate at 323.24 and 343.15 K over a pressure range of 43.7–157.0 kPa. Figs. 2 and 3 illustrate the phase diagrams for this ternary system at 323.24 and 343.15 K, respectively. Among these three constituent compounds, Table 4 Results of the thermodynamic consistency test Mixture

Area testa

Acetic acid + methyl propionate Propionic acid + methyl acetate Propionic acid + methyl propionate Methyl propionate + methyl acetate

−6.6% (+) 7.3% (+) −7.9% (+) 6.9% (+)

a

Tolerance for the area test is 10%; (+): pass the consistency test.

methyl acetate and methyl propionate are completely miscible but both methyl acetate and methyl propionate are partially miscible with water. This ternary system is thus classified as a type-2 LLE. While the solubility of the methyl propionate is relatively minute in the aqueous phase, water dissolves appreciably in the organic-rich phase. The phase diagrams also show that the saturated vapor curve crosses the organic-rich phase curve. Since the mutual solubilities of water/methyl acetate and water/methyl propionate increase with increasing temperature, the area of liquid–liquid splitting region becomes smaller at higher temperatures. 4. VLE calculation The isobaric binary data were correlated with the - method. In the VLE data reduction, the component’s fugacity in the vaporphase was calculated from the two-term virial equation of state. The second virial coefficients were estimated from the HOC model [4], in which the self-association of acetic acid and propionic acid molecules as well as the cross-association between propionic acid and methyl acetate in the vapor-phase were taken into account. The self-association and the cross-association parameters of the

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Table 5 VLLE data for water (1) + methyl acetate (2) + methyl propionate (3) T (K)

P (kPa)

Organic-phase, xI

Aqueous-phase, xII

i

Vapor-phase, yi

i

Methyl acetate

Methyl propionate

Methyl acetate

Methyl propionate

Methyl acetate

Methyl propionate

323.24

78.2 66.1 57.4 49.5 47.1 43.7

0.6594 0.4992 0.2847 0.1098 0.0693 0.0

0.0 0.2671 0.5496 0.7604 0.8067 0.8838

0.0700 0.0292 0.0138 0.0056 0.0033 0.0

0.0 0.0052 0.0087 0.0080 0.0100 0.0109

0.8613 0.6502 0.4259 0.1959 0.0773 0.0

0.0 0.1884 0.3910 0.6167 0.7205 0.7532

343.15

157.0 144.7 136.5 121.5 108.1 102.5 95.3

0.5571 0.5258 0.4672 0.2821 0.1186 0.0687 0.0

0.0 0.1494 0.2516 0.5099 0.7187 0.7823 0.8230

0.0770 0.0440 0.0289 0.0138 0.0054 0.0030 0.0

0.0 0.0048 0.0054 0.0074 0.0095 0.0099 0.0101

0.8249 0.6902 0.5585 0.3801 0.1309 0.0806 0.0

0.0 0.1028 0.2270 0.3753 0.6145 0.6513 0.7267

Fig. 3. VLLE phase diagram for water (1) + methyl acetate (2) + methyl propionate (3) at 343.15 K; open circle, liquid-phase; open triangle, vapor-phase; dashed-dot curves, the UNIQUAC-HOC prediction; dot curves, the UNIFAC-HOC prediction; dashed curves, the UNIFAC-Lyngby-HOC prediction; solid curves, the UNIQUAC-HOC correlation.

Fig. 1. Temperature-composition diagram for the binary systems at 101.3 kPa; open square, acetic acid (1) + methyl propionate (2); open triangle, propionic acid (1) + methyl acetate (2); open circle, propionic acid (1) + methyl propionate (2); open diamond, methyl propionate (1) + methyl acetate (2); solid curves, calculated from the UNIQUAC-HOC model.

HOC model are given in Tables 2 and 6, respectively. The NRTL and the UNIQUAC models were adopted, respectively, to represent the non-ideality of the constituent compounds in the liquid-phase. The binary interaction parameters of the solution models (˛ij value of the NRTL was fixed to be 0.3 through the VLE data reduction) were determined on the basis of the maximum likelihood principle by minimization of the following objective function, 1 :

1 =

 np expt 2  (Pkcalc − Pk ) p

k=1



+

Fig. 2. VLLE phase diagram for water (1) + methyl acetate (2) + methyl propionate (3) at 323.24 K; open circle, liquid-phase; open triangle, vapor-phase; dashed-dot curves, the UNIQUAC-HOC prediction; dot curves, the UNIFAC-HOC prediction; dashed curves, the UNIFAC-Lyngby-HOC prediction; solid curves, the UNIQUAC-HOC correlation.

expt

calc − x (x1,k ) 1,k

x1

2

 +

 +

expt

(Tkcalc − Tk

)

2

T

expt

calc − y (y1,k ) 1,k

y1

2 ⎫ ⎬ ⎭

(1)

The standard deviations  of the measured variables are 0.1 kPa for pressure, 0.1 K for temperature, 0.002 for liquid composition, and 0.005 for vapor composition. The optimization algorithm is based on the Britt–Luecke method [13]. Table 7 lists the results of the data reduction, indicating that the NRTL-HOC and the UNIQUACHOC correlate equally well for each binary VLE system. The smooth curves in Fig. 1 are the calculated results of the UNIQUAC-HOC. The agreement between the correlated values and the experimental data is satisfactory for each binary system.

C.-T. Hsieh et al. / Fluid Phase Equilibria 271 (2008) 69–75 Table 6 Cross-association parameter of the HOC model

virial equation:

Mixture

ij a

Acetic acid + methyl propionate Propionic acid + methyl acetate Propionic acid + methyl propionate Methyl propionate + methyl acetate Water + methyl acetate Water + methyl propionate

0.0 2.0 0.0 0.0 1.3 0.0

a

 ˆi = 2 yi Bij − ln Z ln  V nc

where the second virial coefficients Bij were also estimated from the HOC model, which considered the self-association of water and methyl acetate plus the cross-association between water and methyl acetate in the vapor-phase. Upon specifying the values of solution model’s parameters, ˇ1 and ˇ2 can be solved simultaneously from Eqs. (2) and (3) at given T and zi . The compositions of the coexisting liquid-phases were then calculated from the following equations:

5. VLLE calculation For water + methyl acetate + methyl propionate ternary VLLE system, the compositions of three coexisting phases (yi , xiI , and xiII ) and the equilibrium pressures (P) were calculated via the VLLE flash calculation [14] at given temperature (T) and feed composition (zi ). The flash equations together with the criteria of VLLE were solved, simultaneously, in the calculation:



(KiI

ˇ1 KiI i=1

− 1) zi

+ (1 − ˇ1 )[ˇ2 + (1 − ˇ2 )KiI /KiII ]

nc 

=0

(KiII − 1) zi

ˇ1 KiII i=1

+ (1 − ˇ1 )[ˇ2 (KiII /KiI ) + (1 − ˇ2 )]

KiII

=

yi xiI yi xiII

yi =

KiII =

yi xiI yi xiII

iI xiI iS PiS i P

=

exp[(P

P=

=

iII iS PiS exp[(P − PiS )ViL /RT ]

=

iI iS PiS

=

(6)

ˆ iP  iII 2S PiS

(7)

ˆ iP 

(11)

i P

nc 

yi P =

nc   I xI S P S i i

i=1

i

i

i

=

nc   II xII S P S i

i=1

i

i

i

i

(12)

The experimental ternary VLLE data of water + methyl acetate + methyl propionate form a basis for testing the validity of using the binary model parameters, which were determined from the phase equilibrium data of the constituent binaries, for the phase equilibrium calculation of the multi-component system. Those pre-determined binary parameters of the NRTL-HOC and the UNIQUAC-HOC models are given in Table 8 and the predicted results are listed in Table 9. It appears that the UNIQUAC-HOC is slightly better than the NRTL-HOC for this ternary system. Additionally, two versions of the UNIFAC group-contribution model were also applied to predict the ternary VLLE properties. The original version of the UNIFAC model [5] is denoted as the UNIFAC. The modified version of the UNIFAC model [6] is referred to the UNIFAC-Lyngby, in which more temperature-dependent terms of the group interaction parameters were included in the model. The predicted results from these two versions of the UNIFAC model are also reported in Table 9. The predicted values are compared graphically with the experimental data in Figs. 2 and 3. As shown in the graphs and Table 9, the predicted values of

(5)

ˆ iP 

iII xiII iS PiS

5.1. VLLE prediction

(4)

ˆ iP 

=

and

(3)

− PiS )ViL /RT ]

(10)

and subsequently the vapor composition (yi ) and the equilibrium pressure (P) can be computed from the following equations:

Since the equilibrium pressures are sufficiently low (no greater than 157 kPa) over the entire experimental conditions, the Poynting pressure correction factor was thus reasonably assumed to be unity. Eqs. (4) and (5) were then simplified as KiI =

zi ˇ1 KiII + (1 − ˇ1 )[ˇ2 (KiII /KiI ) + (1 − ˇ2 )]

i=1

iI iS PiS

(9)

ˇ1 KiI + (1 − ˇ1 )[ˇ2 + (1 − ˇ2 )KiI /KiII ]

xiII =

where KiI =

zi

xiI =

(2)

=0

(8)

j=1

Taken from Aspen property databank.

nc

73

In the VLLE calculation, the NRTL, the UNIQUAC, and the UNIFAC models were applied, respectively, to calculate the activity coefficient of component i,  i . Meanwhile, the non-ideality of each component in the vapor-phase was represented by the two-term Table 7 Data reduction for binary VLE systems at 101.3 kPa Mixturea

M1 M2 M3 M4

NRTL-HOCb

UNIQUAC-HOCb AADc

b12 (K)

b21 (K)

˛

T

−148.70 −15.03 −276.04 −18.72

428.76 108.18 582.47 53.09

0.3 0.3 0.3 0.3

0.17 0.37 0.24 0.09

(K)

x1

AADc

0.0030 0.0091 0.0050 0.0019

P/P

AADd

0.001 0.002 0.001 0.001

(%)

y1

AADc

0.0150 0.0162 0.0179 0.0107

b12 (K)

b21 (K)

T AADc (K)

x1 AADc

P/P AADd (%)

y1 AADc

165.72 10.62 211.21 −19.98

−347.67 −46.22 −382.89 5.74

0.18 0.37 0.22 0.09

0.0031 0.0093 0.0047 0.0019

0.001 0.002 0.001 0.001

0.0156 0.0162 0.0181 0.0108

a M1: acetic acid (1) + methyl propionate (2); M2: propionic acid (1) + methyl acetate (2); M3: propionic acid (1) + methyl propionate (2); M4: methyl propionate (1) + methyl acetate (2). b NRTL model: = b /T; UNIQUAC model: = exp(b /T). ij ij ij ij c d

np

M AAD = (1/np )

k=1

(|M calc − M expt |)k , where np is the number of data points and M represents T, x1 , or y1 .

np

P/P AAD (%) = (100%/np )

k=1

(|P calc − P expt |/P expt )k .

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Table 8 The model parametersa determined from the phase equilibrium data of the constituent binaries for water (1) + methyl acetate (2) + methyl propionate (3) i–j

aji

bij (K)

NRTL-HOCa 1–2 5.9416 1–3 9.0944 2–3 0.0

−3.9098 −5.9567 0.0

−949.90 −1644.66 53.09

1296.36 2151.45 −18.72

UNIQUAC-HOCa 1–2 −1.3552 1–3 −1.9435 2–3 0.0

2.5064 4.2758 0.0

353.01 507.79 5.74

−1089.65 −1818.00 −19.98

a

aij

bji (K)

˛

Source

0.2 0.2 0.3

Hsieh et al. [1] Hsieh et al. [1] This work

– – –

Hsieh et al. [1] Hsieh et al. [1] This work

Table 9 Predicted results for the VLLE properties of water (1) + methyl acetate (2) + methyl propionate (3) T AADa (K)

P/P AADb (%)

xI AADc

xII AADc

y AADc

NRTL-HOC 323.24 0.38 343.15 1.26

1.69 1.48

0.0062 0.0162

0.0020 0.0027

0.0347 0.0351

UNIQUAC-HOC 323.24 0.30 343.15 1.08

1.36 1.30

0.0058 0.0149

0.0017 0.0025

0.0338 0.0342

UNIFAC-HOC 323.24 0.21 343.15 0.38

0.90 0.86

0.0189 0.0644

0.0021 0.0026

0.0335 0.0287

UNIFAC-Lyngby-HOC 323.24 0.19 343.15 0.38

1.03 0.54

0.0162 0.0399

0.0024 0.0028

0.0333 0.0289

a

np

T AAD (K) = (1/np )

k=1

(|T calc − T expt |)k , where np is the number of data

points. np calc expt expt b P/P AAD (%) = 100%/n (|P −P |P )k , where np is the number p

of data points. np c M AAD = (1/n × n ) p c

k=1

nc

of components and M represents

expt |) , where nc j k

(|M calc − M

k=1

j=1 xI , xII , or

j

is the number

y.

equilibrium temperature, pressure and vapor compositions from the UNIFAC-Lyngby-HOC model are more accurate than those from the NRTL-HOC, the UNIQUAC-HOC, and the UNIFAC-HOC models. For the compositions of both organic and aqueous-phases, the UNIQUAC-HOC model yielded the better results. 5.2. Ternary VLLE data correlation In order to improve the representation for the ternary VLLE system, the ternary VLLE data were correlated with the NRTL-HOC and the UNIQUAC-HOC models, respectively. The optimal values of the six binary parameters (˛ij value of the NRTL was fixed to be 0.2 through the data reduction) were determined simultaneously based on the maximum likelihood principle with the following objective function, 2 : 2 =

⎧ nP ⎨ expt 2  (P calc − P ) k=1

+

⎩

nc 

k

⎛ ⎝

P

+

 +

I,expt

I,calc (xj,k − xj,k

)

xI

j=1



k

j

expt

calc − y (yj,k ) j,k

yj

2 ⎞⎫ ⎬ ⎠ ⎭

expt

(Tkcalc − Tk

)

2

T

2

 +

II,expt

II,calc (xj,k − xj,k

)

P/P AADb (%)

xI AADc

xII AADc

y AADc

NRTL-HOC 323.24 0.25 343.15 0.63

0.72 0.61

0.0044 0.0124

0.0024 0.0028

0.0346 0.0328

UNIQUAC-HOC 323.24 0.22 343.15 0.55

0.68 0.55

0.0041 0.0111

0.0021 0.0024

0.0335 0.0318

T (K)

a–c As

T AADa (K)

defined in Table 9.

Table 11 The optimized parameters for correlation of water (1) + methyl acetate (2) + methyl propionate (3)

NRTL model: ij = aij + (bij /T); UNIQUAC model: ij = exp(aij + (bij /T)).

T (K)

Table 10 Correlated results for water (1) + methyl acetate (2) + methyl propionate (3)

2

xII j

(13)

i–j

aji

bij (K)

NRTL-HOCa 1–2 5.4668 1–3 8.6941 2–3 0.0

−3.5321 −3.9272 0.0

−779.06 −1480.57 64.01

1166.79 1498.82 32.97

UNIQUAC-HOCa 1–2 −1.2341 1–3 −1.9884 2–3 0.0

2.2032 2.9588 0.0

309.09 509.17 48.67

−985.52 −1388.52 −88.44

a

aij

bji (K)

˛ 0.2 0.2 0.2 – – –

NRTL model: ij = aij + (bij /T); UNIQUAC model: ij = exp(aij + (bij /T)).

where the standard deviations  used in the calculation were 0.05 kPa for pressure, 0.02 K for temperature, 0.0005 for the organic-phase composition, 0.0001 for the aqueous-phase composition, and 0.0009 for the vapor composition. Table 10 lists the correlated results and Table 11 reports the optimal parameters for the ternary system. In general, the UNIQUAC-HOC with the optimal parameters gives the best representation for the ternary system. It was found that the deviations of the VLLE calculations were markedly reduced, especially for the saturated pressure and the compositions of the organic-phase. 6. Conclusion The isobaric VLE data were measured for the binary mixtures of acetic acid + methyl propionate, propionic acid + methyl acetate, propionic acid + methyl propionate, and methyl propionate + methyl acetate at 101.3 kPa. No azeotrope was formed in these four binary systems. Isothermal VLLE properties were also determined experimentally for the ternary system of water + methyl acetate + methyl propionate at 323.24 and 343.15 K. This ternary system was categorized as a type-2 LLE. The UNIQUACHOC and the NRTL-HOC models with the parameters determined from the phase equilibrium data of the constituent binaries predicted the ternary VLLE properties to within reasonable accuracy. It was also found that the UNIFAC-Lyngby-HOC model yielded good prediction for the VLLE properties of the ternary system. The ternary VLLE data of water + methyl acetate + methyl propionate can be correlated satisfactorily with either the NRTL-HOC or the UNIQUAC-HOC model over the entire of experimental conditions and, of the models or versions tested, the UNIQUAC-HOC with the optimal parameters of Table 11 yielded the best VLLE representation for the ternary system. List of symbols aij , bij parameters of the activity coefficient models Ki distribution ratio for component i number of components nc np number of data points P pressure (kPa)

C.-T. Hsieh et al. / Fluid Phase Equilibria 271 (2008) 69–75

q r R T V x y zi

surface area parameter of the UNIQUAC model volume parameter of the UNIQUAC model gas constant (J mol−1 K−1 ) temperature (K) molar volume (cm3 mol−1 ) mole fraction in liquid-phase mole fraction in vapor-phase mole fraction of component i in feed

Greek letters ˛ non-randomness parameter of the NRTL model ˇ1 the fraction of the total material in the vapor-phase ˇ2 the fraction of the first liquid-phase (organic-rich phase) in the total liquid  activity coefficient  association parameter of the HOC model  dipole moment (debye) 1 , 2 objective functions  standard deviation fugacity coefficient of compound i i ˆi  fugacity coefficient of component i in vapor mixture ω acentric factor Subscripts i, j components i and j ij i–j pair interaction Superscripts act actual value calc calculated

calb expt L S I II

75

calibration experimental liquid-phase saturation organic-phase aqueous-phase

Acknowledgement Financial support from the Ministry of Economic Affairs, Taiwan, through Grant No. 95-EC-17-A-09-S1-019 is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

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