Isothermal vapor-liquid equilibria for mixtures of methyl tert-butyl ether, methyl acetate, and ethyl acetate

mllnP/ EQUILIBRIA ELSEVIER

FluidPhaseEquilibria 137 (] 997) 193-207

Isothermal vapor-liquid equilibria for mixtures of methyl tert-butyl ether, methyl acetate, and ethyl acetate Ming-Jer Lee *, Chien-Chih Hsiao, Ho-mu Lin Department of Chemical Engineering, National Taiwan Institute of Technology, Taipei 106, Taiwan Received 7 November 1996; accepted 19 March 1997

Abstract

A static apparatus was applied to measure isothermal vapor-liquid equilibrium (VLE) data for binary and ternary mixtures composed of methyl tert-butyl ether (MTBE), methyl acetate, and ethyl acetate at temperatures from 353 K to 373 K. Maximum pressure azeotropes were exhibited in the MTBE + methyl acetate system. All the binary data passed thermodynamic consistency tests. Data reduction was made by both 05-y and 05-05 methods. The model parameters determined from the binary VLE data were used for predicting the phase equilibrium behavior of the ternary system. © 1997 Elsevier Science B.V.

Keywords: Experiments; Data; VLE low pressure; Polar; Azeotropes; MTBE; Acetates

1. I n t r o d u c t i o n

Vapor-liquid equilibrium (VLE) data are fundamentally important for model development and separation process design. A static-type apparatus was employed in the present study to measure isothermal VLE data for mixtures containing methyl tert-butyl ether (MTBE), methyl acetate, or ethyl acetate at 353 K, 363 K and 373 K over the entire composition range. No literature data are available for MTBE + methyl acetate, MTBE + ethyl acetate and methyl acetate + ethyl acetate + MTBE systems. Even though there are several sets of isobaric and isothermal data for methyl acetate + ethyl acetate in the DECHEMA VLE Data Collection [1], only the data ( P - T - x i) reported by Schmidt [2] are at comparable conditions. All the binary data determined in this work were examined by point, area, and infinite dilution thermodynamic consistency tests. The new binary data were also correlated by both &-'g and &-q5 methods. The activity coefficient models used in the VLE calculations include the Wilson [3], the * Corresponding author. 0378-3812/97/$17.00 © 1997 ElsevierScienceB.V. All rightsreserved. PH S0378-3812(97)00078-2

194

M.-J. Lee et a l . / Fluid Phase Equilibria 137 (1997) 193-207

N R T L [4], and the UNIQUAC [5], while the equations of state (EOS) used include the Soave (SRK) [6], the P e n g - R o b i n s o n (PR) [7], the Patel-Teja (PT) [8], the I w a i - M a r g e r u m - L u (IML) [9], and the J a n - T s a i (JT) [10]. Each model accompanying the determined binary parameters was applied to predict the phase behavior of methyl acetate + ethyl acetate + M T B E ternary mixtures.

2. Experimental section The static-type VLE apparatus used in the present study has been detailed in Ref. [11]. Temperature of the equilibrium system was measured by a Microtherm (Model: 1506, Hart Scientific, USA) with a platinum RTD probe accurate to 4-0.02 K. A pressure transducer (Model: PDCR-330, up to 500 kPa, Druck, UK) with a digital indicator (Model: DPI 262, Druck, UK) measured the equilibrium pressure. The accuracy of the pressure measurement is better than ___1%. Vapor and liquid samples were analyzed by a thermal conductivity detector (TCD) gas chromatography (Model: 8700, China Chromatography, Taiwan) with a stainless steel column (10% Carbowax on Chromosorb W-HP 8 0 / 1 0 0 , 20 m × 1 / 8 " ) and using helium (99.99% purity) as a carrier gas. Calibrations were made with gravimetrically prepared samples over the entire composition range for each binary system. The uncertainty of calibrations is to within _+0.0005 in tool fraction for methyl acetate + MTBE, _+0.0015 for ethyl acetate + MTBE, and + 0.0005 for methyl acetate + ethyl acetate. Degassed solution was charged into the equilibrium cell and the liquid-phase mixture was circulated by a liquid-pump to promote equilibration. While system attained equilibrium state, liquid and vapor samples were taken and the equilibrium phase compositions were analyzed by on-line gas chromatography. Four to five samples were replicated. The averaged area fraction was converted into mol fraction via the calibrated correlations. The accuracy of composition analysis is estimated to be _+ 2% for the minor components. M T B E (99.8%), methyl acetate (99 + %), and ethyl acetate (99.8%) were supplied by Aldrich, USA. No impurity peak was detected by the chromatographic analysis. The chemicals were used without further purification. Table 1 lists the properties of these substances.

Table 1 Properties of pure substances~ Compound Tb (K) TC(K) Pc (kPa) V,. (cm3 mol i) Z~ 6o ZRA MTBE 328.3 496.4 3 3 7 0 322.58 0.263 0.269 0.2669c Methyl acetate 330.4 506.8 4 6 9 0 228.0 0.254 0.326 0.2552 Ethyl acetate 350.3 523.2 3 8 3 0 286.0 0.252 0.362 0.2539

/z (Debye) r q ~'~ F 1.2 4.07 d 3.63~ 0.331f 0.875769f 1.7 2.80e 2.58e 0.311f 0.863487f 1.9 3.48e 3.12e 0.296 g 0.842965g

"Taken from Reid et al. [12], unless noted. bEstimated from the Joback method [12]. CEstimated from ZnA = 0.29056-0.08775 w [12]. ~Estimated from the group-contribution method [13]. eTaken from Prausnitz et al. [14]. fDetermined by fitting the Patel-Teja equation to the smoothed vapor pressure data [12]. gTaken from Georgeton et al. [15].

M.-J. Lee et al. / Fluid Phase Equilibria 137 (1997) 193-207

195

3. Experimental results Vapor pressures of the pure compounds from different sources are compared in Table 2. The literature values were either taken from DECHEMA [1] or calculated from the correlations that were provided by Reid et al. [12], Daubert and Danner [16], and the TRC Thermodynamic Tables [17]. The agreement is generally within _+ 1%. Only the value of ethyl acetate reported by Schmidt [2] is obviously higher than the others. The new isothermal VLE data are listed in Tables 3 - 5 for methyl acetate + ethyl acetate, MTBE + methyl acetate, and MTBE + ethyl acetate, respectively, at temperatures from 353 K to 373 K. The entries of activity coefficients (%'s) are calculated from the following equation: Yi Pq~i ~i=

Xi --iPSd)Sri e x p [ ( P - P i s ) v i L / ( R T ) ]

(1)

In the calculations, experimental T, P, xi, y~ and vapor pressure Pi~ were used. Meanwhile, the modified Rackett model [18] was applied to estimate the liquid molar volume (V~L) and the two-term virial equation to calculate the fugacity coefficients (~bi' and ~b~), i.e.,

In ~bi = ~-~ 2

ysBsj -

(2)

B m

i=1

with nc

nc

(3)

B., = Y'. E yiy B,j i=1 j = l

where the second virial coefficients (Bij' s) were computed from the correlations of Tsonopoulos [19]

Table 2 Comparison of vapor pressures from this work with those from the literature Compound

T (K)

This work

Literature

P~ (kPa) MTBE

Methyl acetate

353.15 363.15 373.17 353.15

215.8 282.7 363.8 213.6

Ethyl acetate

363.15 373.17 353.15

285.5 373.3 110.9

363.15 373.17

151.9 203.7

P~ (kPa) 214.5 a 280.5 ~ 360.9 a 211.4 a 215.98 a 282.6 a 369.9 a 111.0 a 122.39 a 151.9 a 203.6 ~

214.4 b 280,5 b 360,8 b 212.3 b 211.72 e 282.7 b 369.7 b 111.5 b 111.38 e 152.3 b 203.9 b

212.6 ~ 283.2 c 370.6 c 111.5 ~ 152.2c 203.6 ~

aCalculated from the correlations provided by Reid et al. [12]. bCalculated from the correlations provided by Daubert and Danner [16]; Reliability: M T B E ( 1 - 3 % ) , methyl acetate ( < 1%), ethyl acetate ( < 1%). CCalculated from the correlations reported in the TRC Thermodynamic Tables [17]. aSchmidt [2], as also appeared in D E C H E M A [ 1]. e D E C H E M A [1].

196

M.-J. Lee et al. / Fluid Phase Equilibria 137 (1997) 193-207

Table 3 VLE data for methyl acetate ( 1 ) + ethyl acetate (2) T (K)

P (kPa)

xI

y~

In 71

In Y2

GE/(RTxl x2)

353.15

121.5 131.5 141.6 151.5 161.7 172.2 182.1 193.2 203.2 165.9 179.0 192.0 204.6 217.9 230.9 244. l 258.7 272.1 220.2 237.2 253.6 269.8 287.2 304.3 320.8 339.5 356.1

0.0851 0.180 0.283 0.381 0.481 0.582 0.681 0.790 0.893 0.0848 0.182 0.284 0.380 0.483 0.582 0.681 0.794 0.896 0.0878 0.186 0.284 0.379 0.482 0.583 0.681 0.792 0.894

0.160 0.302 0.431 0.537 0.634 0.721 0.795 0.870 0.935 0.156 0.297 0.424 0.529 0.628 0.714 0.791 0.870 0.937 0.151 0.293 0.415 0.521 0.622 0.710 0.788 0.867 0.934

0.102 0.061 0.033 0.022 0.014 0.011 0.005 0.002 - 0.001 0.105 0.057 11.031 0.023 0.012 0.007 0.005 0.001 0.000 0.060 (I.038 0.027 0.020 0.015 0.011 0.007 0.004 0.001

0.002 0.002 0.003 0.007 0.013 0.019 0.034 0.052 0.081 0.002 0.004 0.005 0.007 0.013 0.018 0.027 0.044 0.059 0.001 0.002 0.002 0.004 0.007 0.013 0.019 0.032 0.050

0.130 0.084 0.057 0.054 0.054 0.060 0.066 0.077 0.086 0.143 0.090 0.061 0.054 0.050 0.049 0.054 0.058 0.065 0.074 0.057 0.046 0.044 0.044 0.047 0.050 0.059 0.063

363.15

373.17

assuming a zero binary interaction parameter in the combining rule of the pseudo-critical temperature. The excess Gibbs free energy (G E) was calculated according to the definition nc

G E= RT E

xiln3/i

(4)

i=1

Table 6 presents the results of the thermodynamic consistency tests. All the new binary VLE data passed the point, area, and infinite dilution tests. The method of the consistency tests has been detailed in Ref. [11]. While the phase behavior of methyl acetate + ethyl acetate is nearly ideal as presented in Fig. 1, positive deviations from Raoult's law are shown in Fig. 2 for MTBE + ethyl acetate. Fig. 3 exhibits a maximum pressure azeotrope in MTBE + methyl acetate at 373.17 K. The azeotropic composition (x~ x) can be determined by one of the following equations: x i - y~ = 0

(5)

M.-J. Lee et al. / Fluid Phase Equilibria 137 (1997) 193-207

197

=1

(6)

nc

APy

p-

y~ PiSyi i= 1

P-

E

Be

A Px

PiSxi

i=1

and OP

(7)

---~-0 OX i

Fig. 4 shows (xl -y~) and (APy/AP x) varying with x 1 linearly around the azeotropic point, Table 4 VLE data for MTBE ( 1 ) + methyl acetate (2) T (K)

P (kPa)

xI

YI

In Yl

In 3/2

GE/(RTxlx 2 )

353.15

223.4 229.9 234.1 236.8 237.7 237.8 237.5 236.8 234.3 230.0 223.1 296.3 305.0 309.5 312.5 313.3 313.5 313.0 311.6 307.5 301.9 292.3 387.3 396.2 402.9 405.0 404.8 404.5 403.2 401.8 396.0 387.9 377.3

0.0958 0.190 0.293 0.393 0.457 0.477 0.538 0.586 0.681 0.783 0.897 0.0961 0.194 0.294 0.397 0.461 0.480 0.540 0.585 0.686 0.786 0.896 0.0956 0.191 0.295 0.405 0.462 0.485 0.540 0.581 0.683 0.787 0.896

0.126 0.227 0.328 0.413 0.465 0.482 0.529 0.567 0.653 0.748 0.873 0.125 0.228 0.321 0.411 0.465 0.481 0.530 0.564 0.651 0.751 0.870 0.122 0.222 0.317 0.412 0.459 0.479 0.526 0.560 0.650 0.751 0.870

0.315 0.242 0.192 0.137 0.109 0.102 0.073 0.054 0.034 0.014 0.004 0.311 0.236 0.175 0.130 0.103 0.098 0.075 0.055 0.026 0.014 0.002 0.306 0.232 0.169 0.116 0.092 0.085 0.067 0.054 0.026 0.011 0.003

0.008 0.022 0.035 0.065 0.087 0.093 0.121 0.144 0.176 0.223 0.257 0.002 0.018 0.036 0.060 0.081 0.087 0.110 0.132 0.177 0.211 0.244 0.004 0.016 0.038 0.064 0.080 0.087 0.104 0.119 0.159 0.197 0.243

0.428 0.416 0.393 0.391 0.391 0.390 0.383 0.377 0.365 0.348 0.322 0.366 0.387 0.371 0.368 0.368 0.367 0.367 0.357 0.340 0.333 0.293 0.382 0.369 0.368 0.353 0.346 0.344 0.338 0.333 0.316 0.303 0.301

363.15

373.17

198

M.-J. Lee et al. / Fluid Phase Equilibria 137 (1997) 193-207

Table 5 VLE data for MTBE ( 1 ) + ethyl acetate (2) T (K)

P (kPa)

xI

Yt

In Yl

In Y2

G E / ( R T x I x2)

353.15

126.6 137.8 149.4 161.4 172.2 182.2 ! 91.7 201.4 208.4 171.9 185.3 ! 99.8 215.4 228.7 241.5 253.1 264.9 273.6 227.4 244.5 262.3 281.2 298.0 313.7 327.7 342.3 352.4

0.102 0.186 0.284 0.393 0.500 0.599 0.703 0.816 0.902 0.104 0.185 0.285 0.393 0.495 0.599 0.703 0.814 0.900 0.103 0.184 0.285 0.394 0.495 0.599 0.703 0.814 0.900

0.208 0.332 0.451 0.558 0.650 0.728 0.803 0.879 0.935 0.201 0.317 0.436 0.546 0.638 0.720 0.797 0.874 0.931 0.189 0.305 0.423 0.535 0.628 0.713 0.791 0.869 0.930

0.212 0.160 0.12 ! 0.079 0.052 0.038 0.023 0.010 0.003 0.198 0.148 0.106 0.078 0.059 0.040 0.024 0.012 0.004 0.178 0.143 0.098 0.073 0.057 0.040 0.023 0.011 0.003

0.003 0.013 0.022 0.047 0.069 0.092 0.122 0.161 0.206 0.005 0.015 0.027 0.047 0.062 0.087 0.113 0. 147 0.195 0.005 0.014 0.028 0.044 0.060 0.079 0.105 0.147 0.179

0.264 0.267 0.247 0.250 0.243 0.249 0.250 0.252 0.260 0.265 0.262 0.243 0.248 0.242 0.245 0.242 0.244 0.257 0.243 0.253 0.235 0.232 0.234 0.233 0.229 0.237 0.232

363.15

373.17

Table 6 Results of the thermodynamic consistency tests Mixture

T (K) Consistency test index ~' 6

A

Il

12

G E / R T coefficient b

In ( Y l / ' ~ 2 ) coefficientC

Co

DO

C1

C2

Methyl acetate + ethylacetate

353.15 2 . 6 ( + ) d 0 . 1 ( + ) 1 . 7 ( + ) 6 . 7 ( + ) 0.051 --0.010 0.084 0.001 363.152.3(+) 0.6(+)7.6(+)1.7(+) 0.046--0.031 0.083 0.006 373.17 1 . 0 ( + ) 0 . 4 ( + ) 1 . 2 ( + ) 1 . 8 ( + ) 0.043 --0.001 0.039 0.004 MTBE + methyl acetate 353.15 1 . 5 ( + ) 0 . 4 ( + ) 7 . 9 ( + ) 10.7(+)0.385 -0.059 -0.016 0.004 363.15 1 . 2 ( + ) 0 . 8 ( + ) 3 . 0 ( + ) 2 . 2 ( + ) 0.367 - 0 . 0 4 5 - 0 . 0 5 1 0.008 373.17 1 . 0 ( + ) 0 . 8 ( + ) 0 . 4 ( + ) 2 . 6 ( + ) 0.342 - 0 . 0 5 4 - 0 . 0 0 5 0.008 MTBE+ethylacetate 353.150.6(+) 0.3(+)6.0(+) 1 . 8 ( + ) 0.246 - 0 . 0 0 5 0.027 - 0.003 0.029 - 0 . 0 0 3 363.150.9(+) 0.3(+)2.1(+)1.0(+) 0.242 - 0 . 0 0 8 373.17 1 . 2 ( + ) 0 . 4 ( + ) 1 . 0 ( + ) 3 . 2 ( + ) 0.231 - 0 . 0 0 8 0.013 - 0.004 ~Criteria for passing the thermodynamic consistency tests: 6 < 5, A < 3, l I < 30, 12 < 30. b G E / R T = XlX2[C 0 + C l ( X I - x 2 ) + C 2 ( x I - x2)2]. Cln ( 7 j / 7 2 ) = Do + Dr(x2 - x j ) + D z ( 6 x l x 2 1 ) + D3(x 2 - x l ) ( 1 - 8 x l x 2 ) .

a ( + ): passes the consistency test.

Dl

D2

D3

0.099 0.087 0.060 0.357 0.347 0.336 0.248 0.227 0.211

- 0.006 -0.019 -0.003 - 0.038 - 0.040 -0.042 - 0.019 -0.012 - 0.007

0.041 0.037 0.022 - 0.036 - 0.024 0.003 0.031 0.048 0.037

M.-J. Lee et a l . / Fluid Phase Equilibria 137 (1997) 193-207 4OO o o o o o expt. {liquid phase) o e o o e expt. (,vapor phase)

.:

ealc. (Wilson)

300

e--

I~_

.- .oto'"

-*"

.""

m-"

K

"~'2;°-" "" 373.17

200.

~ - - . w.o:,~'" _~-'

.

100 0.0

~-'"

. -t--

4D

353.15

K

................................................

0.2

0.4

0.6

0.8

1.0

xl ,Yl

Fig. 1. Pressure-composition phase diagram for methyl acetate (1)+ ethyl acetate (2).

400 o o o o o expt. {liquid p h a s e ) * e o o o expt. {,vapor phase) .._

calc. (Wilson)

.~v. ~°

~z

300

..~,--"

D £I_

o • ~'"-~'-

B_

/;s-

.

.o

°,"

.••-

373.17

K

200

_.o---2.--" _e J _c,-"-..°-"" je-'" re""

~f 353.15

1 0 0 . . . . . . . . . , ....................................... 0.0 0,2 0,4 0.6

K

0.8

1.0

xl,Yl

Fig. 2. Pressure-composition phase diagram for MTBE (1) + ethyl acetate (2).

410 ,s,

"ta

400

a

/i:/

390

13__ 3 8 0

,,;,'

370~

360

"22', ",,,

o o o o o expt. ( l i q u i d p h a s e ) ,,*,, expt. ~vapor phase) .. caFc. LWilson) ...

0.0

0.2

0.4

0.6

0.8

(),

"

.0

Xl,Yl

Fig. 3. Pressure-composition phase diagram for MTBE (1) + methyl acetate (2) at 373.17 K.

199

200

M.-J. Lee et a l . / F l u i d Phase Equilibria 137 (1997) 193-207 0.04

:7.

T L

o.oo

I

--~Q ____

o~--

-0.04 × 1.005 rl

<3 ~,o00 Q.. 0. 995

o-.

.

l

1.... I :i .....oo

. . . . . . . .

",","", ?

. . . . .

315~

-.~

310 1 305 -7-~0.2

~'±--~

~,.

~ 0.4

0.6

_

"'~

_

0.8

X1 Fig. 4. Determination of the azeotropic composition for MTBE (1) + methyl acetate (2) at 363.15 K.

whereas, high nonlinearity is exhibited between equilibrium pressures ( P ) and x~. The determination of azeotropic composition from either Eq. (5) or Eq. (6) is more reliable than from Eq. (7). For this reason, x az was calculated from Eq. (5) in the present study. The corresponding azeotropic pressure (paz) was computed from a cubic polynomial equation, P =f(xi), whose coefficients were obtained by fitting to the experimental results around the azeotropic point. The correlation for equilibrium pressures is insensitive to the composition in the vicinity of azeotropic point. Table 7 lists the azeotropic points of MTBE + methyl acetate, indicating that the azeotropic tool fraction of MTBE (x~ z) decreases with increasing temperature. The equilibrium phase compositions were also measured for the ternary system of methyl acetate + ethyl acetate + MTBE at 363.15 K. Table 8 presents the experimental results. Similarly, Eq. (1) was applied to calculate the activity coefficient for each constituent component. Fig. 5 shows the experimental tie-lines from which it appears that no ternary azeotrope exists in this ternary system.

4. VLE calculation

4.1. ~b- y method While the ~b-y method was in use, the two-term virial equation calculated the fugacity coefficients (~b) in vapor-phase and one of the solution models, including the Wilson, the NRTL, and the

Table 7 Azeotropic points for MTBE (1)+ methyl acetate (2) T (K)

x az 1

p az ( k P a )

353.15 363.15 373.17

0.493 0.481 0.445

237.8 313.4 404.9

201

M.-J. Lee et al. / Fluid Phase Equilibria 137 (1997) 193-207

Table 8 VLE data for methyl acetate ( 1 ) + ethyl acetate ( 2 ) + M T B E (3) at 363.15 K P (kPa)

xI

x2

Yl

Y2

In 71

In 72

In 3'3

196,3 208.6 222.3 234.7 244.8 254.5 262.9 270.4 277.0 233.7 244.4 255.0 261.5 270.9 275.3 279.5 282.6 283.2 273.0 281.9 287.6 293.3 295.8 296.8 296.5 294.0 289.5

0.183 0.155 0.133 0.111 0.0940 0.0716 0.0540 0.0351 0.0243 0.437 0.392 0.347 0.298 0.240 0.199 0,154 0.110 0.0534 0.717 0.628 0.555 0.481 0.399 0.319 0.241 0.162 0.0846

0.722 0.655 0.572 0.484 0.409 0.324 0.243 0.161 0.0796 0.457 0.414 0.361 0.311 0.254 0.203 0.156 0.101 0.0478 0.181 0.161 0.151 0.121 0.104 0.0845 0.0664 0.0421 0.0226

0.270 0.221 0,179 0.140 0.116 0.0887 0.0715 0.0414 0.0300 0.539 0.472 0.413 0.349 0.281 0.232 0.182 0.134 0.0656 0.760 0.657 0.585 0.508 0.425 0.353 0.274 0.194 0.105

0.573 0.501 0.419 0,335 0,280 0,222 0.159 0.106 0.0468 0.312 0.270 0.226 0.190 0.152 0.122 0.0941 0.0629 0.0302 0.102 0.0861 0.0791 0.0623 0.0619 0.0504 0.0400 0.0257 0.0140

0.033 0.055 0.065 0.056 0.060 0.110 0.208 0.119 0.188 0.023 0.040 0.069 0.080 0.112 0.122 0.149 0.188 0.203 0.017 0.033 0.060 0.081 0.096 0.138 0.167 0.214 0.235

0.012 0.032 0.045 0.036 0.064 0.102 0.080 0.114 0.020 0.020 0.013 0.009 0.006 0.022 0.036 0.052 0.094 0.111 -0.038 - 0.060 - 0.061 - 0.058 0.088 0.096 0.105 0.110 0.111

0.162 0.102 0.089 0.090 0.064 0.036 0.025 0.019 0.012 0.166 0.157 0.121 0.095 0.074 0.054 0.039 0.018 0.008 0.275 0.201 0.151 0.110 0.075 0.045 0.033 0.015 0.008

1.0

~

0.8

O.6 X

0.4

~-

.....

liquid-phase

vapor-phase

~, ,~, b

\\, q ",\

0.2 ~ '~I" °'.'~'".. ,. 0.0

0.2

0.4

. '~-0.6

0.8

1.0

xl,y~ Fig. 5. Tie-lines for the ternary system of MTBE (1) + methyl acetate (2) + ethyl acetate (3) at 363.15 K.

m= ,

d

RMSD Ay, = 100

RMSD AP =

?1

defined as:

260.33 357.52 69.03 38.54 25.15 69.60 - 4.89 ~ 41.43 -48.nl 123.16 x7 31 90.80 127.29 131.21

116.3

I

200. I Y

- 257.3 -4847

0.4 0.4 0.4 0.4 0.6 0.4 0.3 0.4 0.4 0.4

A P (kPa)

A J,

0.4 0.2 0.3 0.3 03 0.2 0.2 0.3 0.3

0.3

Rzz)/

- 146.88 -212.21 35.31 ~ 62.65 -66.X 136.65 26.32 77.23 82.19

(KF R (K)

RMSD’

NRTL (AZ, - Azz)/ K(k)

models

(A,? - A,,)/ R (K)

the NRTL, and the UNIQUAC

Wilson

“RMSD: root mean square deviation,

Grand average

MTBE + ethyl acetate

acetate

353.15 363.15 373.17 353.15 363.15 373.17 353.15 363.15 373.17

Methyl acetate/ ethyl acetate

MTBE/methyl

T (K)

with the Wilson,

Mixture (l)/(2)

Table 9 VLE datza reduction

298.16 - 14.68 2 19.66 217 59 302.34 58.81 7.99 0.58

200.55

(g21 _K,,)/ R(K) 0.34 0.34 0.30 0.31 0.29 0.28 0.34 0.31 0.30

a

0.4 0.5 0.4 0.4 0.6 0.4 0.3 0.4 0.4 0.4

AP (kPa)

RMSD”

0.3 0.3 0.2 0.3 0.3 0.3 0.2 0.2 0.3 0.3

A?,

UNIQUAC

~ 104.50 - 142.32 - 35.37 58.29 66.07 2x 02 54.49 85.09 88.19

(u,,u&/ R (K)

135.66 191.34 47.15 - 4.54 ~ 12.76 22.17 - 25.98 - S2.49 - 95.40

(u*, -u,,)/ R (K)

0.4 0.5 0.4 0.4 0.6 0.4 0.3 0.3 0.4 0.4

AP (kPa)

RMSD’

0.3 0.3 0.2 0.3 0.3 0.3 0.2 0.2 0.3 0.3

Ay,

203

M.-J, L e e et a l . / F l u i d P h a s e Equilibria 137 ( 1 9 9 7 ) 1 9 3 - 2 0 7

UNIQUAC, calculated the activity coefficients ( y ) in liquid-phase. The optimal values of temperature-specific binary parameters of the solution models were obtained on the basis of the maximum likelihood principle by minimization of the following objective function ~-~:

7TI~ k= 1

OrP

O" T

O'~. I

O'vl

(8) where o-2 is the variance of the measured variables. In the above VLE calculations, the standard deviation cr was set to 0.13 kPa for pressure, 0.05 K for temperature, 0.001 for liquid composition, and 0.003 for vapor composition. The liquid molar volumes required in the calculations were estimated from the modified Rackett model [1 8]. Basically, the optimization algorithm is similar to that of Prausnitz et al. [14]. Only a minor revision has been made for estimating the second virial coefficients from the correlations of Tsonopoulos [19]. All the activity coefficient models gave satisfactory representations for the investigated binary systems, as shown in Table 9 and also illustrated in Figs. 1-3. The smooth curves in the figures represent the calculated values from the Wilson model. Furthermore, each solution model with the determined binary parameters was utilized to predict the bubble points of methyl acetate + ethyl acetate + MTBE ternary system. The results are given in Table 10, indicating that the Wilson model yields the best prediction.

4.2. 05-05 method While the 05-05 method was in use, the 05 of the constituent components in both vapor and liquid phases were calculated from EOS, e.g., the SRK, PR, PT, IML, and the JT equations. Two versions of the Patel-Teja EOS were applied. The first one (denoted as PT-1) estimated fluid's parameters, F and ~'c, from the generalized correlations that were reported by Patel and Teja [8]. The other version (denoted as PT-2) used fluid-specific F and ~',., which were determined by fitting the PT equation to the vapor pressure data. The optimized values are tabulated in Table 1.

T a b l e 10 V L E prediction for m e t h y l acetate ( 1 ) + ethyl acetate ( 2 ) + M T B E (3) at 363.15 K with the d e t e r m i n e d binary p a r a m e t e r s of Table 9 RMSD a

Wilson NRTL UNIQUAC

RMSD AM =

~

d i P (kPa)

Ay I

Ay 2

0.8 1.0 1.0

0.3 0.3 0.3

0.3 0.4 0.4

E (aM,,,) 2

m= ]

n ~expt) ' w h e r e M = P , Yl, or Y2, and P = pcalc _ p e x p t , dxy 1 = i. L. .P.~. . .~, i J. . . . . ..rl pt~/, AV~ 2 = 100(y~],: _ -~2

M.-J. Lee et al. / Fluid PhaseEquilibria 137 (1997) 193-207

204

To calculate mixture properties, the mixture constants, nc

am

and

bm,

in each EOS were defined as:

nc

am= E

(9)

E Z i Z j ( 1 - - k a i j ) ( a i a j ) 0"5

i=1 j=l

and Be

bm = E

(10)

zibi

i=1

where kai j in Eq. (9) is a binary interaction parameter. The constant c m in the PT equation was calculated by: nc

(11)

Cm = E ZiCi i=1

Eq. (11) was also applied to compute c m for the IML equation with (12)

Ci = - b i g i The constants u m and w m in the JT equation were calculated, respectively, from nc bi l'tm = E Z i H i - i= I bm

(13)

and bi

nc

(14)

w m = Y'~ z i w i -

i= 1

bm

The optimal kai j for each binary system was determined from bubble-point calculations by minimizing the objective function 7re: ~ "/T2 : k= 1

( pcalc__pexpt I ~k

~k

p e"~pt --k

I

~expt [

+ [ y C a2,k 'c-:z,k[

]1 (15)

Table 11 compiles the correlated results. Since the methyl acetate + ethyl acetate system behaves as a nearly ideal mixture, the values of k , i i are close to zero for any of the equations. With these optimized k a i f s obtained from the bubble-point calculations, each EOS was found capable of calculating the vaporization equilibrium ratios (K-values) for all three binary systems to about within their experimental accuracies, as shown in Table 11. Among the EOS tested, the PT-2 gives the best results for the MTBE-containing systems and the SRK for methyl acetate + ethyl acetate. Table 12 presents the predicted results for the ternary system from the EOS with the optimized kai j values from binary mixtures. According to the results of Tables 9-12, the root mean square deviations (RMSD's) of the bubble-point calculations from the ~b-q5 method are slightly greater than those from the ~b-y method for both binary and ternary systems. However, it should notice that the EOS (~b-~ method) used a single temperature-independent adjustable parameter, kai j, for each binary system, whereas the ~b-y method (activity coefficient models) used at least two temperature-dependent adjustable parameters. The average absolute deviations (AAD's) in K-value predictions with any of the EOS are generally lower than 5.0% for both binary and ternary systems. The PT-2 model predicts

205

M.-J. Lee et al. / Fluid Phase Equilibria 137 (1997) 193-207

Table 11 VLE data reduction with the equations of state (EOS) EOS

Methyl acetate + ethyl acetate RMSD ~

kai j

SRK PR FF-1 PT-2 IML JT

0.0057 0.0062 0.0096 0.0040 0.0034 0.0056

MTBE + methyl acetate

M T B E + ethyl acetate

A A D (%)b k , i j

RMSD

A p (kPa)

Ay I

Kl

K2

A p (kPa)

Ay 1 K 1

K2

1.1 1.5 2.1 1.2 1.1 1.5

0.2 0.3 0.4 0,3 0,4 0.3

0.5 0.6 0.8 0.6 0.9 0.6

0.7 1.2 1.8 0.9 1.0 1.2

0.8 1.4 1.5 0.7 1.1 1.4

0.6 0.8 0.9 0.5 0.6 0.6

1.5 2.0 2.1 1.2 1.4 1.5

0.0300 0.0313 0.0334 0.0302 0.0256 0.0269

A A D (%)

1.5 2.0 2.3 1.4 1.4 1.6

k,i j

0.0189 0.0201 0.0226 0.0168 0.0160 0.0180

RMSD

AAD (%)

AP(kPa)

Ay I

K~

K2

1.8 2.7 2.7 1.4 2.0 2.2

0.4 0.6 0.7 0.4 0.5 0.5

0.5 0.8 1.4 0.6 0.7 0.7

1.8 2.6 3.0 1.6 2.0 2.2

aRMSD A M as defined in Table 10. 100 ~ ]h"~zalc- K expt --t,m --i.m AAD% K i = 25 Kexpt n

rn = I

--t,m

Table 12 VLE predictions for methyl acetate (1) + ethyl acetate (2) + MTBE (3) at 363.15 K with k,,ij determined from binary mixtures EOS

SRK PR PT-I PT-2 IML JT

RMSD a

AAD

(%)b

A p (kPa)

A Yl

A Y2

KI

K2

K3

1.5 2.1 2.3 1.3 1.5 1.9

0.6 0.7 0.8 0.6 0.6 0.6

0.5 0.6 0.7 0.5 0.5 0.5

3.5 4.2 4.8 3.4 3.4 3.4

4.3 4.9 5.5 4.3 4.4 4.8

2.3 2.8 3.1 2.2 2.2 2.4

aRMSD A M as defined in Table 10. bAAD% K i as defined in Table 11.

the K-values, for example, to an AAD of 3.4% for K 1, 4.3% for K 2, and 2.2% for K 3. The results from the PT-1 are the worst of all the EOS, implying that individual parameters ( ~'~ and F) should be used in the PT equation for each of strongly polar compounds. 5. Conclusion Isothermal VLE data were determined experimentally with a static-type apparatus for the mixtures composed of MTBE, methyl acetate, and ethyl acetate in a temperature range from 353 K to 373 K. All the binary data passed the point, area, and infinite dilution thermodynamic consistency tests. Maximum pressure azeotropes exhibited in MTBE + methyl acetate. Both the solution models (Wilson, NRTL, and UNIQUAC) and the EOS (SRK, PR, PT-2, IML, and JT) were capable of correlating the binary VLE data quantitatively. The Wilson model and the Patel-Teja equation with fluid-specific parameters yielded good predictions for the ternary system.

206

M.-J. Lee et a l . / F l u i d Phase Equilibria 137 (1997) 193 207

6. List of Symbols a, b, c, u, w A B

Ck Dk F GE

gij

-

gjj

11, 12

Ki kaij n

nc

P q r

R T

rb U ij - - Ll.jj

V x

y Z

Z ZRA

Constants in the EOS Index of area consistency test Second virial coefficient (cm 3 mol- 1) Coefficients, k = 0, 2. Coefficients, k = 0, 3. parameter in the Patel-Teja EOS Excess Gibbs free energy (J mol ~) Parameters of the NRTL model (kPa cm 3 mol- 1) Indices of infinite dilution consistency test Vaporization equilibrium ratio for component i Binary interaction parameter Number of data points Number of component Pressure (kPa) Surface area parameter of the UNIQUAC model Volume parameter of the UNIQUAC model Gas constant (kPa cm 3 tool ~ K-~) Temperature (K) Normal boiling temperature (K) Parameters of the UNIQUAC model (kPa cm 3 mol- 1) Molar volume (cm 3 tool 1) Mol fraction in liquid phase Mol fraction in vapor phase Mol fraction Compressibility factor Parameter in the modified Rackett equation

Greek letters ol

Y 6 Aij - Aii /x 77"1, 7r 2

o-~ 4, OA

Parameter of the NRTL model Activity coefficient Index of point consistency test Parameters of the Wilson model (kPa cm 3 mol- 1) Dipole moment (Debye) Objective functions Variance of the measured variable M Fugacity coefficient Acentric factor Hypothetical critical compressibility factor in the Patel-Teja EOS

Subscripts c

i,j

Critical Components i and j

M.-J. Lee et al. / Fluid Phase Equilibria 137 (1997) 193-207

U

i-j Pair interaction

m

Mixture

207

Superscripts

az calc expt L s

V

Azeotrope Calculated Experimental Liquid phase Saturation Vapor phase

Acknowledgements

Financial support from the National Science Council, R.O.C., through Grant No. NSC84-2214E011-012 is gratefully acknowledged.

References [1] J. Gmehling, U. Onken, P. Grenzheuser, Vapor-Liquid Equilibrium Data Collection-Carboxylic Acids, Anhydrides, Esters, Chemistry Data Series, Vol. 1, Part 5, DECHEMA, Frankfurt, Germany, 1982. [2] G.C. Schmidt, Z. Phys. Chem., 121 (1926) 221-253. Also appeared in Ref. [1], pp. 363-370. [3] G.M. Wilson, J. Am. Chem. Soc. 86 (1964) 127-130. [4] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135-144. [5] D.S. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) 116-128. [6] G. Soave, Chem. Eng. Sci. 27 (1972) 1197-1203. [7] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59-64. [8] N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37 (1982) 463-473. [9] Y. lwai, M.R. Margerum, B.C.-Y. Lu, Fluid Phase Equilibria 42 (1988) 21-41. [10] D.S. Jan, F.N. Tsai, Can. J. Chem. Eng. 70 (1992) 320-329. [1 l] M.J. Lee, C.H. Hu, Fluid Phase Equilibria 109 (1995) 83-98. [12] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, 4th edn., McGraw-Hill, New York, 1987. [13] J. Gmehling, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem. Process Des. Dev. 21 (1982) 118-127. [14] J.M. Prausnitz, T.F. Anderson, E.A. Grens, C.A., Eckert, R. Shieh, J.P. O'Connell, Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria, Prentice-Hall, New York, NY, 1980. [15] G.K. Georgeton, R.L. Smith, Jr., A.S. Teja, in: K.C. Chao, R.L. Robinson, Jr. (Eds.), Equations of State Theories and Applications, ACS Symp. Ser. 300, American Chemical Society, Washington, DC, 1986, pp. 434-451. [16] T.E. Daubert, R.P. Danner, Data Compilation Tables of Properties of Pure Compounds, Design Institute for Physical Property Data, AIChE, New York, 1984. [17] TRC Thermodynamic Tables, Nonhydrocarbons, Thermodynamics Research Center, The Texas A and M University System, College Station, TX, 1994. [18] C.F. Spencer, R.P. Danner, J. Chem. Eng. Data 17 (1972) 236-241. [19] C. Tsonopoulos, AIChE J. 20 (1974) 263-272.