doi:10.1006/jcht.2000.0712Available online at http://www.idealibrary.com on

J. Chem. Thermodynamics2001, 33, 139–146

(Liquid + liquid) equilibria of ( tert-amyl ethylether+ ethanol+ water) at several temperatures

Alberto Arce,a Jose Mart ınez-Ageitos, Oscar Rodrıguez, andAna SotoDepartment of Chemical Engineering, University of Santiago deCompostela, E-15706 Santiago, Spain

(Liquid + liquid) equilibrium data of (tert amyl ethyl ether+ ethanol+ water) weredetermined experimentally atT = (298.15, 308.15, and 318.15) K. The experimentalresults were correlated with the NRTL and UNIQUAC equations. The correlations weremade at each temperature and for the three temperatures simultaneously. The best resultswere achieved with the NRTL equation, usingα = 0.2 for the individual correlations ateach temperature andα = 0.1 for the overall correlation. The experimental data were alsocompared with predicted values by the UNIFAC method.c© 2001 Academic Press

KEYWORDS: liquid; TAEE; ethanol; water; correlation; prediction

1. Introduction

The use oftert-amyl ethyl ether (TAEE) as an anti-knock additive for reformulatedgasoline has been suggested in the recent literature. There are a few papers published onmixtures involving TAEE,(1–3) but none about (liquid+ liquid) equilibria (l.l.e.) whichare important for the calculation of the number of stages in the design of extractionequipment. We report here the experimental tie-lines of (TAEE+ ethanol+ water) atT = (298.15, 308.15, and 318.15) K. The experimental data is correlated using theUNIQUAC and NRTL equations. We also report the energetic parameters of these modelsfor each temperature and also the parameters for the case of a simultaneous fit to all thethree considered temperatures. A comparison of experimental and calculated tie linesusing the UNIFAQ method is also presented.

2. ExperimentalMATERIALS

TAEE was supplied by the Yarsintez Research Institute (Yaroslav, Russia) and ethanol(Gradient grade) was supplied by Merck, both with nominal mass fraction purities of 0.998

aTo whom correspondence should be addressed.

0021–9614/01/020139 + 08 $35.00/0 c© 2001 Academic Press

140 A. Arceet al.

TABLE 1. Densitiesρ and refractive indicesnD of the purecomponents atT = 298.15 K and atmospheric pressure

Component ρ/(g · cm−3) nD

Expt. Lit.(4) Expt. Lit.(4)

Water 0.99704 0.99704 1.33250 1.33250

Ethanol 0.78522 0.78493 1.35920 1.35941

TAEE 0.76050 not found 1.38857 not found

and mass fraction water content of 4· 10−4 and 5· 10−4, respectively. These purities werechecked chromatographically and the compounds were used without further purification.Water was obtained from a Milli-Q Plus system. Table1 lists the experimental densitiesand refractive indices together of the substances used with their published values.(4)

APPARATUS

All weighing was carried out on a Mettler Toledo AT 261 balance with a precision of1 · 10−4 g. Water content was measured with a Metrohm 737 KF coulometer. Phaseanalysis was carried out by gas chromatography using a Hewlett-Packard 6890 Serieschromatograph equipped with a thermal conductivity detector and a HP-FFAP capillarycolumn (25 m length, 0.2 mm i.d., 0.3µm film thickness). The injection volume was 1µlwith a split ratio of 250: 1. The injector and detector temperatures were held at 433.15 K,and the column temperature at 348.15 K. The carrier gas was helium, with a flow rate of1.2 cm3

· s−1 in the column.

PROCEDURE

First, using the cloud-point method,(5) we obtained the solubility curves, which were usedlater to carry out the calibration of the gas chromatograph. Conjugate phases were obtainedwith mixtures having compositions in the immiscible region that were vigorously stirredfor at least 1 h in jacketed cells with septum outlets, and then left to stand for at least 4 h(the time necessary to attain equilibrium was established in preliminary experiments). Thetemperature was controlled using water from a thermostat (Selecta Ultraterm 6000383)and the water temperature was measured with a Heraeus Quat 100 thermometer with anaccuracy of±0.01 K. Finally a sample of each phase was withdrawn and injected intothe gas chromatograph.(6) The compositions of the tie-lines ends are listed in table2. Thebiggest error in mole fraction composition during calibration was±3 ·10−3 in the aqueousphase and±5 · 10−3 in the organic phase.

3. Correlation

The NRTL(7) and UNIQUAC(8) equations have proven their usefulness in the literature, sothey were used to fit the experimental data. The non-randomness parameterα for the NRTL

l.l.e. of (TAEE+ ethanol+ water) 141

TABLE 2. Experimental tie-lines for (TAEE+ ethanol+ water), wherex1, x2 and x3 are the mole fractions of

TAEE, ethanol, and water, respectively

Organic phase Aqueous phase

x1 x2 x3 x1 x2 x3

T = 298.15 K

0.9576 0.0000 0.0424 0.0000 0.0000 1.0000

0.8399 0.1019 0.0582 0.0024 0.0978 0.8998

0.7770 0.1532 0.0698 0.0023 0.1362 0.8615

0.6974 0.2058 0.0968 0.0037 0.1626 0.8337

0.6134 0.2628 0.1238 0.0043 0.1890 0.8067

0.4743 0.3355 0.1902 0.0088 0.2299 0.7613

0.3610 0.3755 0.2635 0.0181 0.2678 0.7141

0.2018 0.3897 0.4085 0.0480 0.3195 0.6325

T = 308.15 K

0.9560 0.0000 0.0440 0.0000 0.0000 1.0000

0.8499 0.0919 0.0582 0.0022 0.0824 0.9154

0.6931 0.2130 0.0939 0.0031 0.1595 0.8374

0.6162 0.2633 0.1205 0.0039 0.1863 0.8098

0.4698 0.3358 0.1944 0.0096 0.2316 0.7588

0.3766 0.3693 0.2541 0.0170 0.2618 0.7212

0.2217 0.3902 0.3881 0.0411 0.3105 0.6484

T = 318.15 K

0.9546 0.0000 0.0454 0.0000 0.0000 1.0000

0.8723 0.0834 0.0443 0.0023 0.0688 0.9289

0.8453 0.1027 0.0520 0.0022 0.0864 0.9114

0.8033 0.1413 0.0554 0.0026 0.1146 0.8828

0.6754 0.2267 0.0979 0.0027 0.1582 0.8391

0.5603 0.2949 0.1448 0.0047 0.2025 0.7928

0.4291 0.3556 0.2153 0.0131 0.2438 0.7431

0.3423 0.3781 0.2796 0.0200 0.2706 0.7094

equation was previously assigned to the values 0.1, 0.2, and 0.3. The structural parametersfor UNIQUAC, r andq, were taken from the literature.(9,10)

Using a computer program,(11) the interaction parameters for both the NRTL andUNIQUAC equations were determined by minimizing two objective functions: the first,Fa,does not require initial guesses of the parameters, and after convergence uses the secondfunction to fit the experimental mole fraction compositions

Fa =∑

k

∑i

∑j

{(aIi jk − aI I

i jk )/(aIi jk + aI I

i jk )}2+ Q

∑n

P2n , (1)

142 A. Arceet al.

TABLE 3. L.l.e. data correlation. Root mean square deviations (r.m.s.d.) foreach model and each temperatureT with and without specifying, the solute

distribution ratio at infinite dilution,β∞

Model r.m.s.d. T/K

298.15 308.15 318.15

UNIQUAC β∞ 0.89 1.06 1.20

102·1β 3.71 2.55 3.16 2.24 2.56 3.67

102· F 0.4273 0.4523 0.4175 0.4317 0.4200 0.4307

NRTL β∞ 0.87 0.98 1.06

(α = 0.2) 102 ·1β 2.86 2.53 2.82 1.92 2.79 2.74

102· F 0.4388 0.4372 0.4287 0.4306 0.4753 0.4748

Structural parameters for the UNIQUAC equation

TAEE(9) Ethanol(10) Water(10)

r 5.4166 2.11 0.92

q 4.712 1.97 1.40

Fb =∑

k

min∑

i

∑j

(xi jk − xi jk )2+ Q

∑n

P2n +

{ln

(γ I

S∞

γ I IS∞

β∞

)}2

, (2)

wherea is the activity,Pn an adjustable parameter,Q a constant,x the mole fractioncomposition,γ the calculated activity coefficient,β the solute distribution ratio betweenthe organic and the aqueous phases(xTAEE

2 /xwater2 ), and min refers to the minimum

obtained by the Nelder–Mead method. The subscriptsi refer to the components(1,2,3),j to the phases (I, II),k to the tie-lines(1,2, . . . ,M) andn to the parameters(1,2, . . .).The symbol∧ refers to calculated values,s to the solute (component 2) and∞ to infinitedilution.

The second terms in both equations (1) and (2) are penalty terms introduced to reduce therisk of multiple solutions associated with high parameter values. In the objective functionFb (2) the third term ensures that the binary interaction parameters give a solute distributionratio at infinite dilution,β∞, which tends to a value previously defined by the user.

The quality of the correlation is measured by the residual functionF and by the meanerror of the solute distribution ratio,1β:

F = 100·

{∑k

min∑

i

∑j

(xi jk − xi jk )2

6M

}0.5

, (3)

1β = 100·

{∑k

((βk − βk)/βk)2

M

}0.5

. (4)

l.l.e. of (TAEE+ ethanol+ water) 143

Ethanol0

0.2

0.4

0.6

0.8

10 0.2 0.4 0.6 0.8 1

TAEEWater

1

0.8

0.6

0.4

0.2

0

Ethanol0

0.2

0.4

0.6

0.8

10 0.2 0.4 0.6 0.8 1

TAEEWater

1

0.8

0.6

0.4

0.2

0

Ethanol0

0.2

0.4

0.6

0.8

10 0.2 0.4 0.6 0.8 1

TAEEWater

1

0.8

0.6

0.4

0.2

0

a

b c

FIGURE 1. Experimental tie-lines (◦) and the corresponding values calculated using the NRTL(α = 0.2) correlation with an optimal value of the solute distribution ratio at infinite dilution (�) atT = {298.15 (a), 308.15 (b), and 318.15 (c)} K.

At first, the correlation of the experimental data was made with and without specifyingan optimal value forβ∞. Subsequently, the optimalβ∞ was found by trial and error with1β as optimality criterion. Table3 lists the root mean square deviations found for bothNRTL (α = 0.2) and UNIQUAC models obtained for each temperature with and withoutspecifying the solute distribution ratio at infinite dilution,β∞. The correlation obtained byspecifyingβ∞ fit the experimental data best. Table4 lists the NRTL (α set at the optimumvalue of 0.2) and UNIQUAC parameters using the optimal value of the solute distributionratio at infinite dilution,β∞ obtained for each temperature. Figure1 shows a comparisonof experimental tie-lines and those calculated with NRTL (α = 0.2) for each temperature.

144 A. Arceet al.

TABLE 4. L.l.e. data correlation. Binary interaction parameters for NRTL(α = 0.2) and UNIQUAC for each temperature using the optimal solute

distribution ratio at infinite dilution,β∞

T/K Components NRTL UNIQUAC

i − j1gi j

J ·mol−1

1g j i

J ·mol−1

1ui j

J ·mol−1

1u j i

J ·mol−1

298.15 1−2 4416.1 −1031.3 3892.9 −1810.4

1−3 4945.3 21029 5281.0 1924.1

2−3 1285.2 1383.9 −122.57 −601.65

308.15 1−2 4059.1 −881.20 3859.2 −1701.4

1−3 5133.1 22190 5563.9 1447.2

2−3 498.84 2132.4 2378.5 −1870.8

318.15 1−2 4168.1 −1120.5 3754.3 −1930.1

1−3 5461.0 21365 5794.0 1968.4

2−3 −204.03 2879.0 1721.7 −1989.3

TABLE 5. Simultaneous correlation of all the data at the three temperatures considered. Binaryinteraction parameters and root mean square deviations r.m.s.d. of the models

Model Pair Parameters r.m.s.d. T/K

i − j 1ui j /(J ·mol−1) 1u j i /(J ·mol−1) 298.15 308.15 318.15

UNIQUAC 1−2 3957.4 −1771.5

1−3 5770.7 1501.2 102 ·1β 4.25 1.60 2.59

2−3 4516.0 −2529.7 102 · F 0.4630 0.4642 0.4837

1gi j /(J ·mol−1) 1g j i /(J ·mol−1)

NRTL 1−2 11362 −6297.4

(α = 0.1) 1−3 −77.713 22646 102 ·1β 5.21 3.14 2.96

2−3 −8119.6 14369 102 · F 0.4586 0.4698 0.4754

An overall correlation including all the data at the three investigated temperatures wasalso made. Table5 lists the results (binary parameters and residuals) obtained with thiscorrelation for both models NRTL (α = 0.2) and UNIQUAC.

4. Prediction

The experimental data were compared with predicted valueby the UNIFAC method.(12)

The interaction and structural parameters were taken from Magnussenet al.(13) Thequality of the predictions is evaluated using residual F as defined by equation (3). Theresulting values were 8.6171 atT = 298.15 K, 8.0504 atT = 308.15 K and 4.8839 at

l.l.e. of (TAEE+ ethanol+ water) 145

Ethanol

0

0.2

0.4

0.6

0.8

10 0.2 0.4 0.6 0.8 1

TAEEWater

1

0.8

0.6

0.4

0.2

0

a

Ethanol

0

0.2

0.4

0.6

0.8

10 0.2 0.4 0.6 0.8 1

TAEEWater

1

0.8

0.6

0.4

0.2

0

b Ethanol

0

0.2

0.4

0.6

0.8

10 0.2 0.4 0.6 0.8 1

TAEEWater

1

0.8

0.6

0.4

0.2

0

c

FIGURE 2. Experimental tie-lines (◦) and corresponding values calculated using the UNIFACmethod (1) at T = {298.15 (a), 308.15 (b), and 318.15 (c)} K.

T = 318.15 K. Figure2 shows a comparison of the predicted and experimental tie-linesfor each temperature.

5. Conclusions

(Liquid + liquid) equilibrium data of (TAEE+ ethanol+ water) were determinedexperimentally atT = (298.15, 308.15, and 318.15) K. The temperature has practically noeffect on the size of the immiscibility region at the temperatures considered.

The l.l.e. data were correlated using the NRTL and UNIQUAC activity models withand without specifying a value of the solute distribution ratio at infinite dilution. As canbe seen from table3, the correlation using an optimalβ∞ has a slightly larger value of

146 A. Arceet al.

the residualF than the correlation without the specification ofβ∞, but the value of theresidual1β is much smaller. Thus, this method of correlation was selected in this work.The same behaviour is frequently found in the open literature. The correlation with theNRTL equation with an optimal value of the nonrandomness parameterα = 0.2 gives thebest results, but the UNIQUAC equation also fits the experimental data satisfactorily.

The simultaneous correlation of the data at the three temperatures gives commonparameters in the range of the temperature considered, increasing in this way theirapplication. As was expected, the residuals were higher than when individual correlationsat each temperature were used.

The l.l.e. data calculated with the UNIFAC method have a high value of the residualFand, as can be seen from figure2, and a nonphysical change in the slope of the tie-lines(solutropy) of the system. This method is particularly unsuitable for the l.l.e. prediction of(TAEE+ ethanol+ water).

We acknowledge the help of Professor S. Pavlov (Yaroslav, Russia) in supplying TAEE.

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(Received 13 December 1999; in final form 27 April 2000)

WA 99/064