vapor-liquid equilibrium of the methanol[1,1-dimethylethyl methyl ether (mtbe) or 1,1-dimethylpropyl...

RglBPBAE [OIIIUBRIA

ELSEVIER Fluid Phase Equilibria 133 (1997) 89-103

Vapor-liquid equilibrium of the methanol-[ 1,1-dimethylethyl methyl ether (MTBE) or 1,1-dimethylpropyl methyl ether (TAME)] systems

Baudi l io Coto, Frank MiSssner, Concepc i6n Pando, Ram6n G. Rubio, Juan A.R. Renuncio *

Departamento de Qu(mica F(sica I, Universidad Complutense, E-28040 Madrid, Spain

A b s t r a c t

Isothermal vapor-liquid equilibria (VLE) for methanol-l,l-dimethylethyl methyl ether (tert-butyl methyl ether or MTBE) and for methanol-l,l-dimethylpropyl methyl ether (tert-amyl methyl ether or TAME) measured at temperatures ranging from 288.15 to 338.15 K have been correlated by means of the UNIQUAC model and by means of the Peng-Robinson equation of state and the Wong-Sandler mixing rule. The systems show positive deviations from Raoult's law with an azeotrope, whose coordinates have been interpolated and compared with experimental values. Predictions of VLE data and azeotrope coordinates have been made by means of several versions of the group contribution UNIFAC model and by means of the modified Huron-Vidal second order (MHV2) model used in conjunction with the same UNIFAC model versions.

In order to study the effect of the hydrogen-bond interaction in these mixtures, the lattice-fluid associated solution (LFAS) model and the extended real associated solution (ERAS) model have been used to simultaneously describe excess enthalpy and VLE data. Results from these calculations have been compared with those obtained by means of the purely physical lattice-fluid model (LF) of Sanchez-Lacombe. © 1997 Elsevier Science B.V.

Keywords: Vapor- l iquid equilibrium; Alcohol; Ether; Group contribution; Association

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

Branched ethers such as tert-butyl methyl ether (MTBE) and tert-amyl methyl ether (TAME) have been the subject of numerous investigations in the recent years because of their anti-knock properties and relatively low cost that make them good candidates to be used as additives in lead free gasoline. These ethers are obtained by means of the reaction between an unsaturated hydrocarbon and an alcohol. The final steps in this synthesis process are the separations of the ether from both the unreacted hydrocarbons and the alcohol which are carried out through two azeotropic distillations. In the last step of the synthesis of MTBE and TAME, a binary mixture of such ethers and methanol must

* Corresponding author. Fax: + 34 13944135 e-mail: [email protected].

0378-3812/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S 0 3 7 8 - 3 8 1 2 ( 9 7 ) 0 0 0 0 9 - 5

90 B. Coto et al. / Fluid Phase Equilibria 133 (1997) 89-103

be separated. The study of the thermodynamic properties of such binary mixtures is of great interest for a correct design of the distillation processes.

The purpose of this paper is to discuss a wide set of experimental vapor-liquid equilibrium (VLE) data for the methanol-MTBE and methanol-TAME systems measured at our laboratory at temperatures ranging from 288.15 to 338.15 K and covering the whole composition range, as well as other related properties. Due to the industrial relevance of the azeotropic distillation to obtain the pure ether, special attention will be given to the interpolated azeotrope coordinates for both systems as well as to the comparison of these coordinates with those previously reported in the literature. The UNIQUAC model and the Peng-Robinson (PR) equation of state (EOS) will be used to correlate VLE data. The ability of several group contribution models to predict VLE data will be also examined.

In addition to their industrial interest, this kind of oxygenated compound mixtures is also very interesting from the theoretical point of view because the alcohols present amphoteric behavior and ethers are Lewis bases and therefore the interaction due to the hydrogen bond has to be taken into account. In order to include such interactions, the lattice-fluid associated solution (LFAS) model and the extended real associated solution (ERAS) model will be used in this paper to simultaneously describe excess enthalpy ( H E) and VLE data. Results from these calculations will be compared with those obtained by means of the purely physical lattice-fluid model (LF) of Sanchez-Lacombe.

2. Correlation and prediction of VLE data

VLE measurements were carried out using a Gibbs-Van Ness type static apparatus (Gibbs and Van Ness [1]) at 298.15, 303.15, 308.15, 318.15, 328.15, and 338.15 K for the methanol-MTBE system (Coto et al. [2]) and at 288.15, 298.15,308.15,318.15, and 328.15 K for the methanol-TAME system (MSssner et al. [3], Coto et al. [4]). A detailed description of the apparatus, the experimental method, and the data reduction procedure has been given by Coto et al. [5].

Deviations from Raoult's law are positive and an azeotrope is exhibited at all the temperatures studied in both systems. The azeotrope appears in the ether-rich region for the methanol-MTBE system and in the alcohol-rich region for the methanol-TAME system and becomes more pronounced as the temperature increases. Uncertainties in the azeotrope coordinate values are of approximately _+0.003 in the liquid mole fraction, and of lower than 0.25% in the pressure. The interpolated azeotrope coordinates are listed in Table 1. Figs. 1 and 2 represent temperature vs. methanol mole fraction for the azeotropes of the methanol-MTBE and methanol-TAME systems, respectively. Most of the values reported in the literature for both systems are obtained from isobaric VLE measurements at atmospheric pressure and are also included in Table 1 and in the plots of Figs. 1 and 2. The azeotrope coordinates here reported seem to be in good agreement with those previously reported. The dashed lines shown in Figs. 1 and 2 represent linear fits of the azeotrope coordinates and have been obtained taking into account all the plotted experimental data. Significant differences can be observed in the behavior of the azeotrope for the two systems. It was already pointed out that the azeotrope for the methanol-MTBE system appears in the ether-rich region while that for the methanol-TAME system appears in the methanol-rich region. On the other hand, values for the slope of the T vs. x l fitted line are (246 _+ 6) and (523 _+ 19) K for the methanol-MTBE and methanol-TAME systems, respectively.

B. Coto et al. / Fluid Phase Equilibria 133 (1997) 89-103

Table 1 Azeotrope coordinates for methanol(1)-MTBE(2) and methanol(1)-TAME(2)

91

x t T (K) p (kPa) Ref.

Methanol-MTBE 0.2081 298.15 36.24 Coto et al. [2] 0.2302 303.15 44.55 Coto et al. [2] 0.2480 308.15 54.43 Coto et al. [2] 0.2897 318.15 80.44 Coto et al. [2] 0.3242 328.15 115.88 Coto et al. [2] 0.3694 338.15 162.65 Coto et al. [2] 0.3268 324.75 101.33 Evans and Edlund [6] 0.2091 298.15 35.30 Velasco et al. [7] 0.3150 324.42 101.33 Aim and Ciprian [8] 0.2840 315 71.36 Farkova et al. [9] 0.3140 325 103.15 Farkova et al. [9] 0.2006 296.5 32.84 Gmehling et al. [10] 0.2135 300.5 39.36 Gmehling et al. [10] 0.2659 313.5 66.57 Gmehling et al. [ 10] 0.3056 324.3 100.50 Gmehling et al. [10] Methanol-TAME 0.6823 288.15 11.59 M~Sssner et al. [3] 0.6996 298.15 19.52 Coto et al. [4] 0.7166 308.15 31.73 M~Sssner et al. [3] 0.7336 318.15 49.48 Coto et al. [4] 0.7630 328.15 75.66 MiSssner et al. [3] 0.7674 335.37 101.33 Palczewska-Tulinska and Wyrzykowska-Stankiewicz [ 11 ] 0.7613 335.45 101.33 Evans and Edlund [6] 0.7656 335.29 101.33 Pavlova et al. [12] 0.7710 335.41 101.33 Cervenkova and Boublik [13] 0.6943 297.65 19.47 Gmehling et al. [ 10] 0.7075 303.85 26.21 Gmehling et al. [10] 0.7403 319.35 53.02 Gmehling et al. [10] 0.7735 335.55 101.68 Gmehling et al. [10]

The U N I Q U A C mode l ( A b r a m s and Prausni tz [14]) was used to correlate the i sothermal V L E data.

The interact ion parameters o f this model , At/, were cons idered to be dependen t on tempera ture accord ing to the relat ion

Aj i = Aj i , l .-t- A j i , 2 ( T - To) (1)

where Aji A and Aji,2 are interact ion parameters and T O is a reference temperature , taken as 298.15 K. Corre la t ions us ing the P e n g - R o b i n s o n equa t ion o f state (Peng and R o b i n s o n [15]) were also carr ied

out. The P R E O S is g iven by

R T a p (2)

v - b v ( v + b ) + b ( v - b )

Mixing rules have to be in t roduced in order to calculate the parameters a and b for mixtures. The W o n g - S a n d l e r ( W S ) mix ing rule ( W o n g and Sandler [16]) has been used in this work. In this rule,


3 5 0 I I

3 4 0

3 3 0

3 2 0

3 1 0

3 0 0

2 9 0

/

/

/ /

D / /

/ +

/ /

D /

/ ra/

/ /

/El ' /

/ t

/

2 8 0 I , I i 0 . 2 0 .3

X 1

Fig. 1. Plot of the temperature against methanol mole fraction for the azeotrope of methanol(l)-MTBE(2): t3, Coto et al. [2]; O, Evans and Edlund [6]; zx, Gmehling et al. [10]; ,7, Velasco et al. [7]; O, Aim and Ciprian [8]; +, Ffirkovfi et al. [9]; ---, linear regression.

the compos i t ion dependence is based on the use o f the excess He lmhol tz free energy, A E, to combine the EOS and an activity coeff ic ient model , and the second virial concentration dependence boundary condit ion is satisfied. The W o n g - S a n d l e r rule defines the mixture parameters a and b as those which s imultaneously satisfy the relations

and

a ( a ) b RT = y'~ Z x i x j b R-T ij (3)

i J

A E a a i - - - - E X i - - ( 4 )

CRT bRT i b i RT

where C is a numerical constant characteristic o f the cubic EOS used and A E is described by any o f the liquid activity coef f ic ient mode l s proposed for the excess Gibbs energy, since the He lmhol t z and Gibbs excess free energy terms are indistinguishable at low pressures. In this work, the above ment ioned U N I Q U A C mode l was used to evaluate A E. For the cross-virial coeff ic ient term one may u s e

b i R T ] + t b j - a J t ] ( 1 - k i j ) (5)

B. Coto et al. / Fluid Phase Equilibria 133 (1997) 89-103

3 5 0 , t

93

3 4 0 /

/ /

3 3 0 / / / O

z /

/ /

z

3 2 0 i ~ , / S

/

[ , , i 3 1 0 , / j~

z

/

3 0 0

/ /

/ 2 9 0

/in /

2 8 0 I , ! ,

0 . 7 0 0 . 7 5

l 1

Fig. 2. Plot of the temperature against methanol mole fraction for the azeotrope of methanol(1)-TAME(2): D, MGssner et al. [3], Coto et al. [4]; O, Evans and Edlund [6]; r,, Gmehling et al. [10]; v, Palzewska-Tulinska and Wyrzykowska-Stan- kiewicz [11]; O, Pavlova et al. [12]; +, Cervenkova and Boublik [13]; ---, linear regression.

where k u is a binary interaction parameter. The Wong-Sandler mixing rule given by Eqs. (3)-(5) requires the parameter kij = kji and the parameters of the excess Gibbs energy model.

The above models were used to correlate the isothermal VLE data. Values for the pure-component parameters used in these calculations and values obtained for the interaction parameters are available on request. Values for the standard deviations between experimental and calculated vapor compositions, ~v, and vapor pressures, o-p, for the UNIQUAC model and for the PR EOS are given in Table 2. Experimental and calculated VLE data at 298.15 K using the PR EOS are plotted in Fig. 3 for the two systems. Similar plots are obtained at the other temperatures studied. A comparison of the deviations and plots obtained using the PR EOS and the UNIQUAC model indicates that the PR EOS leads only to a small improvement in the correlation.

Predictions of VLE data from pure components data and the model parameters available in the literature are of great industrial interest. Vetere et al. [17] have shown that UNIFAC model provides good VLE predictions for the methanol-MTBE system. Therefore, calculations for the methanol- MTBE and methanol-TAME systems were carried out using the UNIFAC (Fredenslund et al. [18], Hansen et al. [19]), modified UNIFAC (Larsen et al. [20]), and new UNIFAC (Hansen et al. [21]) models. Predictions using the modified Huron-Vidal second order (MHV2) model (Dahl et al. [22]) were also carried out. MHV2 is a combination of the Soave-Redlich-Kwong (SRK) equation of state (Soave [23]) and a G E model. The SRK EOS is given by

R T a p -- - - (6)

v - b v (v+b)


Table 2 Standard deviations between experimental and calculated alcohol vapor composition and vapor pressure values for methanol(1)-MTBE(2) and methanol(1)-TAME(2) using the UNIQUAC model and the Peng-Robinson EOS and the Wong-Sandler mixing rule

T (K) UNIQUAC PR + WS

o'~, ~rp (kPa) o~, ~rp (kPa)

Methanol-MTBE 298.15 0.006 303.15 0.006 308.15 0.004 318.15 0.006 328.15 0.004 338.15 0.005 Methanol-TAME 288.15 0.007 298.15 0.007 308.15 0.005 318.15 0.009 328.15 0.010

0.19 0.004 0.10 0.17 0.004 0.10 0.12 0.002 0.13 0.27 0.004 0.17 0.35 0.002 0.25 0.21 0.003 0.44

0.07 0.009 0.05 0.12 0.005 0.08 0.11 0.002 0.09 0.32 0.004 0.21 0.43 0.004 0.38

40

35

30

25

X 20

Methanol-MTBE

o ~ ° ¢ , o , , ~ . o o

• ~

~ t • t

- ~

,o,o .- '°:xr , ' " "-:.. '~

7 ~ e~ anoI-TAME

I0,

0.0 I I i I , I I I i

0 . 2 0 . 4 0 . 6 0 . 8 1 .0

xI,Yl

Fig. 3. Correlation of VLE data for methanol(t)-MTBE(2) and methanol(l)-TAME(2) at 298.15 K: C), experimental values; ---, PR EOS.

B. Coto et al. / Fluid Phase Equilibria 133 (1997) 89-103 95

Table 3 Standard deviations between experimental and calculated alcohol vapor composition and vapor pressure values for methanol(1)-MTBE(2) and methanol(1)-TAME(2) using the UNIFAC, modified UNIFAC and new UNIFAC models

T (K) UNIFAC Mod. UNIFAC New UNIFAC

o-3. trp (kPa) o~v trp (kPa) o~. trp (kPa)

Methanol-MTBE 298.15 0.006 0.60 0.012 0.98 0.015 0.74 303.15 0.005 0.77 0.014 1.0 0.015 0.84 308.15 0.007 0.90 0.013 1.4 0.013 0.93 318.15 0.005 1.4 0.011 1.6 0.009 0.99 328.15 0.005 1.9 0.010 1.9 0.007 1.1 338.15 0.004 2.2 0.010 2.5 0.006 0.93 Methanol-TAME 288.15 0.014 0.33 0.013 0.34 0.025 0.27 298.15 0.010 0.48 0.015 0.61 0.017 0.33 308.15 0.012 0.88 0.011 0.74 0.017 0.55 318.15 0.014 1.3 0.011 1.1 0.017 0.88 328.15 0.011 1.8 0.011 1.6 0.012 0.82

The MHV2 mixing rule for the parameter a is expressed as

( ) ( b ql O~mix-- ~i Zi°tii +q2 a 2 i x - ~i Zi 012 = --~-]- ~i ziln-~ i (7)

where a is given by

e~ = a / b R T (8)

and zi is the phase composit ion ( x i and Yi for the liquid and vapor phases, respectively). Values for ql and q2 were taken from Dahl et al. [22] (ql = - 0 . 4 7 8 and q2 = - 0 . 0 0 4 7 ) . Values for G E in Eq. (7) may be obtained by means of any well defined G E model. In this work, the UNIFAC model versions already mentioned were used to estimate G E values.

Values for the standard deviations between experimental and calculated vapor compositions, o~v, and vapor pressures, O'p, for the three UNIFAC models mentioned above and for the MH V 2 model used in conjunction with the same UNIFAC models are given in Tables 3 and 4, respectively. Experimental vapor pressures and VLE data calculated by means of these models are plotted in Figs. 4 and 5 for the two systems at 298.15 K. Similar plots are obtained at the other temperatures studied.

Vapor composit ions and vapor pressures are accurately predicted by means of the three UNIFAC model versions above described and by means of the MHV2 EOS used in conjunction with these UNIFAC model versions. The UNIFAC and MHV2 + UNIFAC models provide better predictions of the vapor phase composit ion than the other UNIFAC and MHV2 + UNIFAC model versions, o-~ values obtained by means of the UNIFAC and MHV2 + UNIFAC models for the m e t h a n o l - M T B E system are similar to those obtained when the experimental data are correlated using the UNIQUAC model or the PR EOS. Vapor pressures are predicted more accurately by means of the new UNIFAC model. The highest o-p value (7.0 kPa) is obtained for the m e t h a n o l - M T B E system at 338.15 K when the MHV2 + Mod. UNIFAC model is used. This value of o-p is about 4% of the maximum pressure


Table 4 Standard deviations between experimental and calculated alcohol vapor composition and vapor pressure values for me thano l ( l ) -MTBE(2) and methanol ( l ) -TAME(2) using the MHV2 model with the UNIFAC, modified UNIFAC and new UNIFAC models

MHV2 + UNIFAC MHV2 + Mod. UNIFAC MHV2 + New UNIFAC

T (K) ~r~, crp (kPa) o~,, % (kPa) o~,, gp (kPa)

Methano l -MTBE 298.15 0.008 0.29 0.019 1.8 0.014 0.62 303.15 0.008 0.37 0.022 2.1 0.018 0.81 308.15 0.007 0.46 0.022 2.7 0.016 1.2 318.15 0.009 0.65 0.021 3.8 0.014 1.7 328.15 0.007 1.0 0.018 5.1 0.013 2.8 338.15 0.009 2.0 0.020 7.0 0.015 4.8 Me thano l -TAME 288.15 0.016 0.32 0.015 0.41 0.015 0.23 298.15 0.013 0.38 0.018 0.83 0.015 0.23 308.15 0.012 0.64 0.014 1.2 0.014 0.33 318.15 0.013 0.78 0.013 1.9 0.015 0.59 328.15 0.010 1.0 0.014 2.8 0.011 0.53

40

35

30

Methanol-MTBE

%

25

-&

20

10

Methanol-TAME

0.0 0.2 0.4 0.6 0 8 1.0

Xl,Y 1

Fig. 4. Prediction of VLE data for methanol(1)-MTBE(2) and methanol(1)-TAME(2) at 298.15 K: O , experimental values; - - , UNIFAC model; - - - , Modified UNIFAC model; • • . , New UNIFAC model.


40

35

30

~ - . Methanol-MTBE

%

25

20

I0

Methanol-TAME

0.0 0.2 0.4 0.6 0.8 110

xI~Yl

Fig. 5. Prediction of VLE data for methanol(1)-MTBE(2) and methanol(1)-TAME(2) at 298.15 K: O, experimental values; --, MHV2 + UNIFAC model; ---, MHV2 + modified UNIFAC model; • - . , MHV2 + new UNIFAC model.

values (the azeotrope pressure). The change from the UNIFAC to the MHV2 + UNIFAC model leads in most cases to a more accurate prediction for the vapor pressure, and the same occurs for the change from the new UNIFAC to the MHV2 + new UNIFAC for the me thano l -TAME system. The change from the mod. UNIFAC to the MHV2 + mod. UNIFAC model leads to a less accurate prediction for the vapor pressure, and the same occurs for the change from new UNIFAC to MHV2 + new UNIFAC for the me thano l -MTBE system. It may be concluded that there is not any relation between the accuracy of predictions obtained by means of a particular UNIFAC model version and that of predictions obtained when the same UNIFAC model version is used in conjunction with the MHV2 model.

All the above indicated models were used to interpolate the azeotrope coordinates for both systems. For the sake of simplicity, a table with such calculated coordinates has not been included in this paper. The comparison between the experimental and calculated values has been made by means of the standard deviations, O-x,az and O'p,az, defined as follows

~ ~ ( Xaz -- Xaz,calc) 2 xaz =

trp.az(% ) = 1 0 0 ~ ~ [ ( P , z - Paz,ca,c)/Paz] 2 n - - 1

(9)


Table 5 Standard deviations between experimental and calculated azeotrope coordinates values for methanol(1)-MTBE(2) and methanol(1)-TAME(2) using several models

Model Me thano l -MTBE Methano l -TAME

o-~,~ o-f .... (kPa) ~ . . . . (Tp,az (kPa)

UNIQUAC 0.007 0.4 0.010 0.3 PR + WS 0.005 0.4 0.005 0.3 UNIFAC 0.011 2 0.02 3 Mod. UNIFAC 0.02 2 0.010 3 New UNIFAC 0.017 2 0.03 0.5 MHV2 + UNIFAC 0.02 1.0 0.004 2 MHV2 + Mod. UNIFAC 0.010 5 0.03 4 MHV2 + New UNIFAC 0.08 1.8 0.014 0.4

where Xaz and Paz are the azeotrope experimental composition and pressure, respectively, Xaz,cal c and Paz,calc are the azeotrope calculated composition and pressure, respectively, and n is the number of experimental data that in this case is the number of temperatures studied. The values for O'x,az and Crp,az are listed in Table 5. Trends in these values are similar to those observed for O-y and trp in the VLE calculation. The best description of the azeotrope coordinates here reported is provided by the PR EOS and the UNIQUAC model. These two models lead to values for O'x,az similar tO values for t r listed in Table 2 and to values for o-p.~z lower than 0.5%. In general, accurate predictions are obtained for the azeotrope coordinates when the UNIFAC or MHV2 + UNIFAC models are used. With the exception of the MHV2 + new UNIFAC, values for o~,~z range from 0.01 to 0.05. On the other hand, values for O'p,az are always lower than 5%.

3. Simultaneous correlation of H E and VLE data

Since the alcohol behaves as a Lewis amphoteric compound and the ether as a basic one, the possibility of interaction due to the hydrogen bond must be taken into account. Two association models have been considered: the lattice-fluid associated solution (LFAS) model association (Panayiotou [24], Panayiotou [25]) and the extended real association solution (ERAS) model (Heintz [26], Reimann and Heintz [27]). These models have several points in common: both consider the possibility of self- and cross-association, the intermolecular interactions are separated into chemical and physical parts, and the chemical interactions lead to the consecutive formation of association complexes according to chemical reactions characterized by an equilibrium constant, K. In the LFAS model, these constants are related to the thermodynamic magnitudes involved in the chemical process by

A u + p A y -- T A s INK-- - R T (10)

where A u, Av, and A s are the energy, volume, and entropy change, respectively, upon hydrogen-bond


T a b l e 6

S t a n d a r d d e v i a t i o n s b e t w e e n e x p e r i m e n t a l a n d c a l c u l a t e d e x c e s s e n t h a i p y , o'/4, a n d v a p o r p r e s su re , o'p, v a l u e s fo r

m e t h a n o l ( l ) - M T B E ( 2 ) a nd m e t h a n o l ( 1 ) - T A M E ( 2 ) u s in g the LF , L F A S an d E R A S m o d e l s

L F L F A S E R A S

T ( K ) o- n (J m o l - ' ) o-p ( k P a ) O-H (J m o l - 1 ) ~p ( k P a ) o-n (J m o l - ' ) o-p ( k P a )

M e t h a n o l - M T B E

2 9 8 . 1 5 80 0.51 73 0 .29 100 0 .33

3 0 3 . 1 5 - 0 .48 - 0 .37 - 0 .36

3 0 8 . 1 5 - 0 .40 - 0 .59 - 0 .35

3 1 3 . 1 5 70 - 68 - 90 -

3 1 8 . 1 5 - 0 . 6 4 - 0 .78 - 0 .58

3 2 3 . 1 5 80 - 62 - 80 -

3 2 8 . 1 5 - 0 . 9 6 - 0 .78 - 0 .79

3 3 8 . 1 5 - 1.4 - 1.1 - 1.1

M e t h a n o l - T A M E

2 8 8 . 1 5 - 0 .19 - 0 .18 - 0 .14

2 9 8 . 1 5 55 0 . 4 0 52 0 .28 55 0 .27

75 - 79 - 73 -

3 0 8 . 1 5 - 0.41 - 0 .44 - 0 .37

3 1 3 . 1 5 83 - 66 - 89 -

3 1 8 . 1 5 - 0 .52 - 0 .46 - 0 .38

3 2 8 . 1 5 - 1.0 - 0 .78 - 0 .65

500

4 0 0

3 0 0

'7, -~ 200

1 0 0

Ot

- 1 0 0

o . . . . . . ° .- .° °- °.

,° ,° °.

." s :° s I

o' •

- 7 , 0 0 1 , I , I ,

0 . 0 0 .2 0 . 4

X 1

,° °°

"o

i •

I L °.o

\°~

I , I f 0 .6 0 . 8 1.0

Fig. 6. S i m u l t a n e o u s d e s c r i p t i o n o f V L E a nd H E data . H E d a t a f o r m e t h a n o l ( 1 ) - M T B E ( 2 ) at 2 9 8 . 1 5 K: n , T u s e l - L a n g e r et

al. [33]; - - , L F m o d e l ; - - - , L F A S m o d e l ; - - . , E R A S m o d e l .


formation. In the ERAS model these constants are directly obtained by correlating the experimental data and assuming that their temperature dependence is given by

InK o R T T o (11)

where A h is the enthalpy change upon hydrogen-bond formation, and T o is a reference temperature. Associated complexes and unassociated molecules interact through a physical model. The Sanchez- Lacombe lattice-fluid theory (LF) (Lacombe and Sanchez [28], Sanchez and Lacombe [29]) and the free volume theory of Flory (Flory [30]) describe the physical interactions in the LFAS and ERAS models, respectively.

In the LF and LFAS models, each fluid is characterized by the number of segments of the molecule, r, and two scaling constants: the closed-packed volume, v *, and the characteristic temperature, T *. The mixing rules include two binary parameters, the volume interaction parameter, CAB' and the energy interaction parameter, ~'AB" Both parameters are expected to have values close to unity. In the Flory and ERAS models, each fluid is characterized by three characteristic magnitudes, p *, v *, and T * which are evaluated from volumetric properties (molar volumes, cubic expansion coefficients and isothermal compressibilities). The mixing rules introduced include the binary parameter of energy interaction, XAB. An entropic correction parameter, qaB, is introduced in the expression for the chemical potential in the LF, LFAS and ERAS models.

m

400

300

200

~ " 1 0 0

-100

i

0 . 0

. . . ~ ...... .

.' s : t :F .#

g :s

:e I

g

1,

o . .

I i I i I i I i

0.2 0.4 0.6 0.8 1.0

X 1

Fig. 7. Simultaneous description of VLE and H E data. H E data for methanol( l ) -TAME(2) at 298.15 K: ~ , Letcher and Govender [34]; - - , LF model; - - - , LFAS model; • • . , ERAS model.


The pure-component parameters of methanol for the LF and LFAS models were taken from Lacombe and Sanchez [28] and Panayiotou and Sanchez [31], respectively. Values for the MTBE and TAME parameters were calculated from the vapor pressures and molar volumes. The values obtained were r = 8.69, v* = 11.44 cm 3 mol - t , and T* = 454 K for MTBE and r = 9.12, v* = 12.50 cm 3 mol - ~, and T * = 484 K for TAME.

The usual procedure used to calculate values for the energy interaction parameters, ~'AU (LF and LFAS models), XA8 (ERAS model), A UA8 (LFAS model), and A hAB (ERAS model), and for those involved in the description of the association process, A SAB (LFAS model), and KAB (ERAS model), was the correlation of excess enthalpy data. The value for the qAB parameter (LF, LFAS and ERAS models) must be obtained from VLE data. The qAB parameter is assumed to be temperature independent, hence its value is obtained from the correlation of only one set of isothermal VLE data and the others sets of data are predicted. Such procedure can be inappropriate when the association models are applied to simultaneously describe H E and VLE data for mixtures exhibiting self- and cross-association. The parameter values that best describe H E data by means of the LFAS or ERAS models are sometimes not compatible with an accurate correlation of VLE data and, in general, a compromise between both properties has to be adopted. Such conclusion has been already reported for alcohol-ether mixtures described by means of the LFAS (Coto et al. [2]) or ERAS (Keller et al. [32]) models. To improve the VLE description obtained by means of the LFAS model, the value adopted by ASAB must be less negative than that obtained exclusively from H E data. This corresponds to a higher cross-association. The situation is identical for the ERAS model and the improvement in the

40

Methanol-MTBE

35

30

~ z5

20

10~

l I , I i I , I

0.0 0.2 04 0.6 0.$ 1.0

Xl,Yl

Fig. 8. Simultaneous description of VLE and H E data. VLE data for me thano l (1 ) -MTBE(2) and me thano l (1 ) -TAME(2) at

298.15 K: O , experimental values; - - , LF model; - - - , LFAS model; • • . , ERAS model.


VLE description is obtained using a value for the association constant higher than that obtained from H E data.

H E data for the methanol-MTBE system were measured at 298.15, 313.15 and 323.15 K by Tusel-Langer et al. [33]. H E data for the methanol-TAME system were measured at 298.15 K by Letcher and Govender [34] and at 298.15 and 313.15 K by Kammerer and Lichtenthaler [35]. The values for the standard deviation between experimental and calculated excess enthalpies, o- H, for the LF, LFAS and ERAS models are listed in Table 6. Values for the experimental H E data and those calculated by means of the LF, LFAS and ERAS models are plotted in Fig. 6 for the methanol-MTBE system at 298.15 K and in Fig. 7 for the methanol-TAME system at 298.15 K. Similar plots are obtained at the others temperatures studied. Even though o- H values for the three models are similar, it should be noted that the models which include the hydrogen-bond interaction provide a better H E description. H E values obtained by means of the LF model are always endothermic and the calculated H E vs. x~ curve is very symmetric. When association is included, the balance between the two contributions of opposite sign (self- and cross-association) can explain the asymmetry of the experimental H E vs. x~ curve and the change from endothermic to exothermic H E values which is exhibited in the data of Tusel-Langer et al. [33] for the methanol-MTBE system and in those of Letcher and Govender [34] for the methanol-TAME system. Both, the LFAS and ERAS models describe the exothermic values in the methanol-rich region and the highly asymmetric H E vs. x~ curves.

The values for the standard deviation between experimental and calculated vapor pressures, O-p, for the LF, LFAS and ERAS models are listed in Table 6. Values for O-p are lower for the association models. The improvement provided by the association models in the VLE description may be observed in Fig. 8. In this figure, experimental vapor pressures and VLE data calculated by means of the LF, LFAS and ERAS models are plotted for the two systems at 298.15 K. Similar plots are obtained at the others temperatures studied. It may be concluded that the simultaneous description of VLE and H E data for the methanol-MTBE and methanol-TAME systems is improved to some extent by the introduction of the associated complexes in the LFAS and ERAS models.

4. Conclusions

VLE data for the methanol-MTBE and methanol-TAME systems are accurately correlated by means of the UNIQUAC model and the Peng-Robinson EOS. The Peng-Robinson EOS used in conjunction with the Wong-Sandler mixing rule, requires five binary interaction parameters and provides correlations which are a little more accurate than those provided by the UNIQUAC model with four interaction parameters.

Vapor compositions and vapor pressures are accurately predicted by means of the three UNIFAC model versions used in this paper and by means of the MHV2 EOS used in conjunction with these UNIFAC model versions. Deviations between experimental and calculated vapor compositions and vapor pressures are not substantially higher than those obtained when the experimental data are correlated using the UNIQUAC model and the Peng-Robinson EOS. The accuracy of predictions obtained by means of a particular UNIFAC model version is not related to that of predictions obtained when the same UNIFAC model version is used in conjunction with the MHV2 model.

When VLE and H E data for the methanol-MTBE and methanol-TAME systems are simultane-


ous ly corre la ted by means o f the L F A S and E R A S associa t ion models , the pa ramete r values that best descr ibe H E data are not compat ib le with an accurate corre la t ion o f V L E data and a c o m p r o m i s e be tween both proper t ies has to be adopted. The associa t ion mode l s require four interact ion parameters and lead to l ower devia t ions be tween exper imenta l and ca lcula ted excess enthalpies and vapor pressures than those ob ta ined when the L F mode l is used.

Acknowledgements

This w o r k was funded by the Spanish Minis t ry o f Educat ion , D G I C Y T Projects P B - 9 4 - 0 3 2 0 and

PB-93-0448 . F.M. a c knowl e dge s the European Union for its support th rough a H C M grant (contrac t E R B C H B G C T 930261) .

References

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vapor-liquid equilibrium of the methanol[1,1-dimethylethyl methyl ether (mtbe) or 1,1-dimethylpropyl...

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