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J. Chem. Thermodynamics 38 (2006) 484–489

Quaternary (liquid + liquid) equilibria for (water + 2-propanol +1,1-dimethylethyl methyl ether + diisopropyl ether)

at the temperature 298.15 K

Yao Chen *, Yanhui Dong

Department of Chemistry, Jinan University, Guangzhou 510632, China

Received 4 May 2005; received in revised form 26 June 2005; accepted 27 June 2005Available online 6 September 2005

Abstract

(Liquid + liquid) equilibrium tie-lines were measured for one ternary system {x1H2O + x2(CH3)2CHOH + (1 � x1 � x2)CH3

C(CH3)2OCH3} and one quaternary system {x1H2O + x2(CH3)2CHOH + x3CH3C(CH3)2OCH3 + (1 � x1 � x2 � x3)(CH3)2

CHOCH(CH3)2} at T = 298.15 K and P� = 101.3 kPa. The experimental (liquid + liquid) equilibrium results were satisfactorilycorrelated by modified and extended UNIQUAC models both with ternary and quaternary parameters in addition to binary ones.� 2005 Elsevier Ltd. All rights reserved.

Keywords: (Liquid + liquid) equilibria; Oxygenate additives; Ternary mixtures; Quaternary mixtures

1. Introduction

Reformulated gasoline includes certain oxygenateethers. These are commonly 1,1-dimethylethyl methylether (MTBE), 1,1-dimethylpropyl methyl ether(TAME), and diisopropyl ether (DIPE). These oxygen-ated compounds are added into the gasoline to improvethe octane rating and reduce the air-pollution. The mul-ticomponent (liquid + liquid) equilibria of the oxygenateether and alcohol mixtures with water are useful andconsiderably focused not only on process design forreformulated gasoline production but also on the prob-lem of contamination of groundwater. Here we report(liquid + liquid) equilibrium measurements on one qua-ternary mixture (water + 2-propanol + MTBE + DIPE)and one relevant ternary mixture (water + 2-propanol +MTBE) at T = 298.15 K. The experimental LLE datawere correlated by means of the modified UNIQUAC

0021-9614/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jct.2005.06.016

* Corresponding author. Tel.: +86 20 85220223; fax: +86 2085221697.

E-mail address: tlirq@jnu.edu.cn (Y. Chen).

and extended UNIQUAC models [1,2] including bothternary and quaternary parameters coming from multi-component intermolecular interactions, in addition tobinary parameters. The binary parameters of misciblebinary mixtures constituting the ternary and quaternarymixtures measured in this work were obtained from(vapor + liquid) equilibrium data [3–6] and those ofimmiscible mixtures were obtained from mutual solubi-lity data [7,8]. The constituent ternary mixtures (water +MTBE + DIPE) [9], (water + 2-propanol + DIPE) [10],and (water + 2-propanol + MTBE), were used to obtainternary parameters for accurate representation of theexperimental quaternary (liquid + liquid) equilibriumdata studied in this work.

2. Experimental

The MTBE was supplied by Tedia Company, Inc.with nominal minimum mass fraction purity of 0.998.The DIPE and 2-propanol were obtained from theTianjin Chemical Reagent Institute with mass fraction

TABLE 1Experimental phase compositions in mole fraction (x) for the ternaryof {x1H2O + x2(CH3)2CHOH + (1 � x1 � x2)CH3C(CH3)2OCH3}mixtures at T = 298.15 K

x1 x2 1 � x1 � x2

Phase I

0.0574 0.0000 0.94260.0867 0.0545 0.85880.1115 0.0834 0.80510.1619 0.1255 0.71260.2151 0.1608 0.62410.2889 0.1936 0.51750.3174 0.2212 0.46140.3499 0.2353 0.41480.4210 0.2438 0.33520.4963 0.2460 0.25770.5808 0.2266 0.1926

Phase II

0.9933 0.0000 0.00670.9794 0.0134 0.00720.9707 0.0216 0.00770.9623 0.0299 0.00780.9561 0.0356 0.00830.9524 0.0388 0.00880.9473 0.0431 0.00960.9429 0.0474 0.00970.9369 0.0532 0.00990.9262 0.0609 0.01290.9080 0.0737 0.0183

Y. Chen, Y. Dong / J. Chem. Thermodynamics 38 (2006) 484–489 485

purities of 0.990 and 0.997, respectively. Water was pro-vided from Jinan University with mass fraction purity of0.999. The g.c. analysis did not detect appreciable peaks,and determined the mass fraction purities of 0.995 forDIPE, and >0.998 for MTBE and 2-propanol. Ternaryand quaternary (liquid + liquid) equilibrium measure-ments were carried out at the temperature (298.15 ±0.01) K. The quaternary mixtures were prepared bymixing stepwise the binary mixtures (MTBE + DIPE)whose compositions are M1, M2, and M3 with water,and then 2-propanol to cover the two-phase regions.The values of M1, M2, and M3 are 0.25, 0.50, and0.75, respectively, indicating the mole fraction of MTBEin the binary (MTBE + DIPE) mixtures. About 60 cm3

of each mixture was loaded into the equilibrium glasscell placed in a thermostated water bath. The mixturewas then stirred vigorously by magnetic stirrer for 3 hand allowed to settle 3 h, which was sufficient for sepa-ration into two phases. Dry nitrogen gas was used toprevent contamination with moisture in the headspaceof the equilibrium cell. Samples, withdrawn from upperand lower phases in the cell by a microsyringe, were ana-lyzed by a gas chromatograph (Shanghai AnalysesApparatus Factory, GC-122) equipped with a thermalconductivity detector. Each component of the ternaryand quaternary mixtures was separated clearly using astainless steel column (2 m long, 3 mm i.d.) packed withPorapak SQ. The temperatures of the injection anddetector were set at T = 483.15 K. The initial tempera-ture and final temperature of the oven were kept atT = 453.15 K. The hydrogen flow rates for both the sep-aration and reference columns were set at 1.0 cm3 Æ s�1.The peak areas of the components, detected with a chro-matopac (Zhejiang university, MR98S), were calibratedwith weighed mixtures. The mass of each component ofthe mixture was determined from the calibration andconverted to mole fraction. Three analyses were done

FIGURE 1. Phase equilibria of (water + 2-propanol + MTBE +DIPE). M1, M2 and M3 denote quaternary section planes.

for each sample to obtain a mean value with a reproduc-ibility of better than 0.001. The mole fraction uncer-tainty was estimated to be 0.001.

Figure 1 shows a tetrahedron to depict three planes ofthe quaternary (liquid + liquid) equilibrium for thequaternary mixtures (water + 2-propanol + MTBE +DIPE). Tables 1 and 2 list the experimental ternaryand quaternary tie line results for {x1H2O + x2(CH3)2-CHOH + (1� x1� x2)CH3C(CH3)2OCH3} and {x1H2O +x2(CH3)2CHOH + x3CH3C(CH3)2OCH3 + (1 � x1 �x2 � x3)(CH3)2CHOCH(CH3)2} at T = 298.15 K.

3. Results and analyses

The experimental results were correlated with themodified UNIQUAC [1] and extended UNIQUAC [2]models. Our modified model assumes that the combina-torial term can be expressed by a modification of thetreatment of Gmehling et al. [11] The residual term isintroduced by a third parameter C. The adjustable bin-ary parameter sji obtained from binary experimentalphase equilibrium data, is defined by the binary energyparameter aji

sji ¼ expð�aji=CT Þ; ð1Þwhere the third parameter C is set equal to 0.65 in themodified UNIQUAC model and T is the Kelvin temper-ature. The additional ternary parameters, s231, s132, and

TABLE 2Experimental (liquid + liquid) equilibrium results for the quaternarymixtures at T = 298.15 K

x1 x2 x3

{x1H2O + x2(CH3)2CHOH + x3CH3C(CH3)2OCH3 +(1 � x1 � x2 � x3)(CH3)2CHOCH(CH3)2}

M1 = 0.25Phase I

0.0548 0.0394 0.19530.0961 0.0828 0.18190.1217 0.1739 0.15830.1931 0.2530 0.12220.2768 0.2928 0.09810.3398 0.3275 0.06890.4183 0.3341 0.05220.4637 0.3331 0.046

Phase II

0.9838 0.0151 0.00110.9679 0.0302 0.00150.9582 0.0398 0.00130.9461 0.0510 0.00190.9352 0.0607 0.00210.9240 0.0712 0.00250.9158 0.0785 0.00290.9044 0.0889 0.0032

M2 = 0.50Phase I

0.0515 0.0354 0.42250.0867 0.0849 0.38440.1183 0.1366 0.34540.1501 0.1801 0.31240.2103 0.2474 0.25130.2869 0.2871 0.20240.3510 0.3001 0.16430.4429 0.3064 0.12030.5147 0.2978 0.0902

Phase II

0.9849 0.0123 0.00280.9715 0.0254 0.00310.9589 0.0370 0.00340.9551 0.0403 0.00360.9435 0.0513 0.00370.9376 0.0566 0.00430.9316 0.0613 0.00500.9223 0.0699 0.00570.9053 0.0860 0.0063

M3 = 0.75Phase I

0.0679 0.0435 0.65170.1021 0.0968 0.58990.1410 0.1425 0.52500.1835 0.1777 0.47150.2667 0.2288 0.37140.3496 0.2671 0.28500.4413 0.2772 0.20660.4950 0.2704 0.17890.5851 0.2548 0.1209

Phase II

0.9809 0.0139 0.00520.9679 0.0266 0.00550.9631 0.0316 0.0053

TABLE 2 (continued)

x1 x2 x3

0.9565 0.0378 0.00570.9469 0.0470 0.00610.9676 0.0564 0.00600.9250 0.0674 0.00720.9192 0.0714 0.00840.8980 0.0896 0.0108

486 Y. Chen, Y. Dong / J. Chem. Thermodynamics 38 (2006) 484–489

s123 are obtained from the ternary (liquid + liquid) equi-librium results and the quaternary parameters, s2341,s1342, s1243 and s1234, are obtained from the correlationof the quaternary (liquid + liquid) equilibrium result.

The extended UNIQUAC model has been describedin detail elsewhere.[2] The binary parameter in the ex-tended model is expressed by

sji ¼ expð�aji=T Þ. ð2ÞTable 3 shows the molecular–structural volume and

area parameters, r and q, for MTBE and DIPE takenfrom Arce et al. [7,8], while the others are taken fromPrausnitz et al. [12], together with the interaction correc-tion factor q 0, for which the value for self-associatingcomponents was taken from the literature [1,2], whilethat for nonassociating components was set toq 0 = q0.75 in the modified UNIQUAC model andq 0 = q0.20 in the extended UNIQUAC model. Theexpressions for lnc1 of the modified and extended UNI-QUAC models are described in [13].

The parameters for completely miscible binary mix-tures were obtained from experimental (vapor + liquid)equilibrium data. The binary data reduction was per-formed by using a computer program described byPrausnitz et al. [12] according to the following thermo-dynamic equations

Pyi/i ¼ xiciPSi /

Si exp V L

i P � P Si

� ��RT

� �; ð3Þ

ln /i ¼ 2X

j

yjBij �X

i

Xj

yiyjBij

!P=RT ; ð4Þ

where P, x, y, and c are the total pressure, liquid-phasemole fraction, vapor-phase mole fraction, and activitycoefficient, respectively. The pure component vapor pres-sure PS was calculated by using the Antoine equationwith coefficients taken from the literature values [14].The liquid molar volume VL was obtained by a modified

TABLE 3Structural parameters for pure components

Component r q q 0a q 0b

H2O 0.92 1.40 1.28 0.96CH3C(CH3)2OCH3 4.07 3.63 q0.75 q0.20

(CH3)2CHOCH(CH3)2 4.74 4.09 q0.75 q0.20

(CH3)2CHOH 2.78 2.51 1.32 0.89a Modified UNIQUAC model.b Extended UNIQUAC model.

Y. Chen, Y. Dong / J. Chem. Thermodynamics 38 (2006) 484–489 487

Rackett equation [15]. The fugacity coefficient / calcu-lated by the virial equation of state with the second virialcoefficient B was expressed by equation (4). The super-script S stands for a value at saturation vapor pressure.The pure and cross-second virial coefficients were esti-mated by the method of Hayden and O�Connell [16].

An optimum set of binary parameters was obtainedby minimizing the following objective function

F ¼X

i

½ðP cali � P exp

i Þ2=r2

P þ ðT cali � T exp

i Þ2=r2

Tþ

ðxcali � xexp

i Þ2=r2

x þ ðycali � yexp

i Þ2=r2

y �; ð5Þ

where the superscripts cal and exp indicate, respectively,the most probable calculated value corresponding toeach measured point and the experimental value. Theroot-mean-square deviations in the experimental valuesused in equation (5) were taken as: rP = 0.133 kPa forpressure, rT = 0.05 K for temperature, rx = 0.001 for li-quid-phase mole fraction, and ry = 0.003 for vapor-phase mole fraction. Table 4 lists the binary parametersof the modified UNIQUAC model and the extendedUNIQUAC models for the constituent binary mixtures,along with the root-mean-square deviations betweenexperimental and calculated values: rP for pressure, rT

for temperature, rx for liquid-phase mole fraction, andry for vapor-phase mole fraction. Good agreement be-tween experimental results and those calculated by bothmodels was obtained. The binary parameters for themutual solubility were obtained by solving the isoactiv-ity of each component in two liquid phases (I and II)and the mass balance.

ðxiciÞI ¼ ðxiciÞ

II; ð6ÞX

i

xIi ¼ 1 and

Xi

xIIi ¼ 1; ð7Þ

where i is the number of component, x the liquid-phasemole fraction, c the activity coefficient given by the

TABLE 4The results of fitting both models to (vapour + liquid) and (liquid + liquid) emixtures

Mixture T/K

{x(CH3)2CHOH + (1 � x)(CH3)2CHOCH(CH3)2} 313.15

{xCH3C(CH3)2OCH3 + (1 � x)(CH3)2CHOCH(CH3)2} 338.05�325.95

{xCH3C(CH3)2OCH3 + (1 � x)(CH3)2CHOH} 308.24�335.40

{x(CH3)2CHOH + (1 � x)H2O} 303.15

{xCH3C(CH3)2OCH3 + (1 � x)H2O} 298.15

{x(CH3)2CHOCH(CH3)2 + (1 � x)H2O} 298.15

a I, modified UNIQUAC model; II, extended UNIQUAC model.

modified UNIQUAC or extended UNIQUAC modelspreviously described in detail [1,2]. For the ternarymixtures having a plait point, two-parameter originalUNIQUAC model predicts generally larger solubilityenvelope than the experimental one. Good quantitativedescription of the ternary (liquid + liquid) equilibriummixtures usually needs ternary parameters in additionto the binary parameters. Ternary parameters s231,s312, and s123 were obtained by fitting the two modelsto the ternary (liquid + liquid) equilibria data and thenthe quaternary parameters s2341, s1342, s1243 and s1234,were determined from the quaternary experimental(liquid + liquid) equilibria data using a simplex method[17] by minimizing the objective function:

F ¼ 102 �X

k

minX

i

Xj

ðxexpijk � xcal

ijk Þ2M

" #0.5

; ð8Þ

where min denotes minimum values, i = 1 to 3 forternary mixtures or i = 1 to 4 for quaternary mixtures,j = 1, 2 (phases), k = 1,2, . . .,M (number of tie lines),M = 2ni, and x is the liquid-phase mole fraction. Table5 presents the ternary parameters, together with theroot-mean-square deviation between the experimentaland calculated tie-lines for the ternary (liquid + liquid)equilibria. Figure 2 compares the experimental andcorrelated (liquid + liquid) equilibria of the ternarymixtures making up the quaternary mixtures{x1H2O + x2(CH3)2CHOH + x3CH3C(CH3)2OCH3 +(1 � x1 � x2 � x3)(CH3)2CHOCH(CH3)2} at T =298.15 K. Good agreement between the experimentalvalues and those correlated using the additional ternaryparameters show in the figure. The quaternary mixtureexhibits type 2 quaternary (liquid + ! liquid) behavior[18], which are composed of two ternary (liquid +liquid) equilibrium for the mixtures {x1H2O + x2

(CH3)2CHOH + (1 � x1 � x2)CH3C(CH3)2OCH3} and{x1H2O + x2(CH3)2CHOH + (1 � x1 � x2)(CH3)2CHO

quilibria and root-mean-square deviations dP, dT, dx and dy for binary

Modela a12/K a21/K dP/kPa dT/K 103 dx 103 dy

I 6.39 537.51 0.0 0.0 0.1 0.3II 0.51 522.15 0.0 0.0 0.0 0.2

I �178.45 255.08 0.3 0.1 0.9 5.3II �219.26 319.95 0.3 0.1 0.9 5.2

I 429.52 �28.82 0.1 0.1 0.7 4.9II 421.07 �44.85 0.1 0.1 0.7 4.9

I 330.21 �44.88 0.2 0.0 1.3 8.0II 308.89 �80.30 0.2 0.0 1.3 8.0

I 1196.10 173.24II 1023.70 399.09

I 1590.60 166.69II 1209.00 157.70

FIGURE 2. Experimental and calculated (liquid + liquid) equilibria of three ternary mixtures making up (water + 2-propanol + MTBE + DIPE) atT = 298.15 K. � -� -�, Experimental tie line; –––, correlated by the modified UNIQUAC model with binary and ternary parameters taken from tables4 and 5.

TABLE 5The results of fitting both models with ternary (liquid + liquid) equilibria at T = 298.15 K

Mixture No. of tie lines Ternary parameters Deviationsc

Ia IIb Ia IIb

{x1H2O + x2(CH3)2CHOH +(1 � x1 � x2)CH3C(CH3)2OCH3}

11 s231 = �0.23212 s231 = �0.28283 3.42d 4.51

s132 = 0.05420 s132 = 0.25142 0.53e 0.75s123 = 1.49930 s123 = 4.33250

{x1H2O + x2CH3C(CH3)2OCH3 +(1 � x1 � x2)(CH3)2CHOCH(CH3)2}

10 s231 = 0.11104 s231 = 0.07873 1.57 1.25

s132 = �0.07585 s132 = �0.25175 0.72 1.01s123 = 0.40548 s123 = 0.59069

{x1H2O + x2(CH3)2CHOH +(1 � x1 � x2)(CH3)2CHOCH(CH3)2}

14 s231 = 0.47817 s231 = 0.00034 1.91 9.26

s132 = 0.51775 s132 = 2.26310 0.70 6.28s123 = 0.41049 s123 = �0.00810

a I, modified UNIQUAC model.b II, extended UNIQUAC model.c Root-mean-square deviation (mol%).d Predicted results using only binary parameters.e Correlated results using binary and ternary parameters.

TABLE 6The results of fitting both models to the quaternary (liquid + liquid) equilibria at T = 298.15 K

Mixture No. of tie lines Quaternary parameters Deviationsc

Ia IIb Ia IIb

{x1H2O + x2(CH3)2CHOH + x3CH3C(CH3)2OCH3 +(1 � x1 � x2 � x3)(CH3)2CHOCH(CH3)2}

26 s2341 = � 0.1320 s2341 = �0.3218 2.20d 2.73

s1342 = �0.4500 s1342 = 0.6573 1.08e 1.74s1243 = �8.1800 s1243 = 15.9820s1234 = 0.2600 s1234 = 0.2185

a I, modified UNIQUAC model.b II, extended UNIQUAC model.c Root-mean-square deviations (mol%).d Predicted results using binary and ternary parameters.e Correlated results using binary, ternary and quaternary parameters.

488 Y. Chen, Y. Dong / J. Chem. Thermodynamics 38 (2006) 484–489

Y. Chen, Y. Dong / J. Chem. Thermodynamics 38 (2006) 484–489 489

CH(CH3)2} classified as type 1, and one ternary (liquid +liquid) equilibrium for the mixtures {x1H2O + x2CH3-C(CH3)2OCH3 + (1 � x1 � x2)(CH3)2-CHOCH(CH3)2}as type 2, illustrated in figure 2.

Table 6 summarizes the correlated results for the qua-ternary mixtures obtained in fitting the modified UNI-QUAC model and the extended UNIQUAC modelwith binary, ternary, and quaternary parameters to theexperimental quaternary (liquid + liquid) equilibriumdata, together with the predicted results by these modelswith the binary and ternary parameters listed in tables 4and 5. The correlated results obtained from the bothmodels are better than the predicted ones in representingthe quaternary (liquid + liquid) equilibrium measured inthis work and are in good agreement with the experi-mental ternary and quaternary (liquid + liquid) equilib-rium results.

4. Conclusions

(Liquid + liquid) equilibrium tie-line data were mea-sured for one ternary system {x1H2O + x2(CH3)2

CHOH + (1 � x1 � x2)CH3C(CH3)2OCH3} and onequaternary system {x1H2O + x2(CH3)2CHOH + x3

CH3C(CH3)2OCH3 + (1 � x1 � x2 � x3)(CH3)2CHOCH(CH3)2} at T = 298.15 K and P� = 101.3 kPa. Theexperimental ternary and quaternary (liquid + liquid)equilibrium data were successfully correlated by usingboth models including binary, ternary and quaternaryparameters. The quaternary (liquid + liquid) equilib-rium results calculated by the modified UNIQUACmodel are in better agreement with experimental results.

Acknowledgements

Supported by the Foundation of Ministry of Edu-cation of China (2002-247), Foundation of Scientific

Research from Guangdong Province of China (2003-C33101), and Foundation of Jinan University ofChina (640071).

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JCT 05-112