Vapor–liquid equilibrium of octane-enhancing additives in gasolines: 5. Total pressure data and GE for binary and ternary mixtures containing 1,1-dimethylpropyl methyl ether (TAME),

Fluid Phase Equilibria 212 (2003) 81–95

Vapor–liquid equilibrium of octane-enhancingadditives in gasolines

5. Total pressure data andGE for binary and ternary mixturescontaining 1,1-dimethylpropyl methyl ether (TAME),

1-propanol andn-hexane at 313.15 K�

Cristina Alonsoa, Eduardo A. Monteroa, César R. Chamorrob, José J. Segoviab,Marıa C. Martınb, Miguel A. Villamañánb,∗

a Departamento de Ingenier´ıa Electromecánica, Escuela Politécnica Superior, Universidad de Burgos, E-09006 Burgos, Spainb Laboratorio de Termodinámica y Calibración (TERMOCAL), Departamento Ingenier´ıa Energética y Fluidomecánica,

E.T.S. de Ingenieros Industriales, Universidad de Valladolid, E-47071 Valladolid, Spain

Abstract

Experimental isothermalP–x data atT = 313.15 K for the binary systems 1,1-dimethylpropyl methyl ether(TAME)+1-propanol, 1-propanol+n-hexane and the ternary system TAME+1-propanol+n-hexane are reported.Data reduction by Barker’s method provides correlations forGE using the Margules equation for the binary systemsand the Wohl expansion for the ternary system. Wilson, NRTL and UNIQUAC models have been applied successfullyto both the binary and the ternary systems. Moreover, we compare the experimental results for these binary mixturesto the prediction of the UNIFAC (Dortmund) model. Experimental results have been compared to predictions forthe ternary system obtained from the Wilson, NRTL, UNIQUAC and UNIFAC models. The presence of azeotropesin the binary systems has been studied.© 2003 Elsevier B.V. All rights reserved.

Keywords:Data; VLE low pressure; Hydrocarbons; 1,1-Dimethylpropyl methyl ether (TAME); Excess Gibbs energy;Correlations

1. Introduction

1,1-Dimethylpropyl methyl ether, also known astert-amyl methyl ether or TAME, could be used asa blending agent in the formulation of the new gasolines for enhancing the octane number in substitu-

� This paper is part of the Doctoral Thesis of C. Alonso.∗ Corresponding author. Tel.:+34-983-423-364; fax:+34-983-423-363.

E-mail address:[email protected] (M.A. Villamañan).

0378-3812/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0378-3812(03)00268-1

82 C. Alonso et al. / Fluid Phase Equilibria 212 (2003) 81–95

tion of the traditional leaded products. To better understand and model the new formulated gasolines westarted a research program on the thermodynamic characterization of ternary mixtures, as the simplestmulticomponent system, containing oxygenated additives (ethers and alcohols) and different type of hy-drocarbons (alkanes, cycloalkanes, aromatics, alkenes); 1,1-dimethylethyl methyl ether (MTBE), TAMEand diisopropyl ether (DIPE) were chosen as additives. Initially, we choose four-type hydrocarbons forthe purpose of modeling of an actual gasoline: alkanes are represented byn-heptane, cycloalkanes bycyclohexane, alkenes by 1-hexene and aromatics by benzene.

In previous papers[1–5], we published the study of vapor–liquid equilibrium (VLE) for binary andternary systems containing MTBE and these substitution hydrocarbons at 313.15 K. Also some resultswith DIPE [6–12]and with TAME[13–15]have already been published.

This paper will contribute with an experimental investigation of the thermodynamic parameters of VLEat T = 313.15 K of the ternary system TAME+ 1-propanol+ n-hexane and the corresponding binarysystems TAME+1-propanol and 1-propanol+n-hexane, the third binary system involved was publishedpreviously[15].

2. Materials

All the chemicals used were purchased from Fluka Chemie AG and were of the highest purity available,chromatography quality reagents (of the series puriss p.a.) with a stated purity >97.0% (GC) for TAME,>99.5% (GC) for 1-propanol andn-hexane. Only TAME was distilled, at atmospheric pressure, in apacked column. The first and last portions of the distillate were discarded and the intermediate fractiondistilling at constant temperature was collected; the purity was improved >99.7% (GC).

All reagents were thoroughly degassed using a modified distillation method based on the one suggestedby Van Ness and Abbott[16]. The purity of the products after degassing was checked in our laboratoryby gas chromatography, and the values obtained were >99.5% (GC) for all the compounds. InTable 1,the vapor pressures of the pure constituents measured in this work are compared with those reported inthe literature as a check for complete degassing.

2.1. Experimental method

A static VLE apparatus, consisting of an isothermal total pressure cell, has been employed for measuringthe VLE of binary and ternary mixtures. The apparatus and measuring technique were based on those ofVan Ness and coworkers[17,18].

The sample injectors were three 100 cm3 positive displacement pumps (Ruska model 2200-801) witha resolution of 0.01 cm3 and an estimated total uncertainty of±0.03 cm3. These allowed the injection ofknown volumes of the pure components, previously degassed, into the cell which was immersed in a highprecision water bath (Hart Scientific model 6020), assuring a stability of±0.5 mK when thermostated atT = 313.15 K.

The cell was a cylindrical stainless steel piece with a capacity of about 180 cm3 fitted with a magnetic stir-rer coupled to an external drive. An initial volume of about 50 cm3 of one component was injected into theevacuated cell, and the vapor pressure was measured. Successive injections of a second or a third compo-nent were made over a desired composition range until the cell was nearly full. The total mass injected wasdetermined accurately from the volumetric displacement of the pistons, the temperature of the injectors andthe known densities for the pure components. This resulted in uncertainties in mole fraction of±0.0001.

C. Alonso et al. / Fluid Phase Equilibria 212 (2003) 81–95 83

Table 1Average values of experimental vapor pressures(Psat

i ) for the pure compounds measured in this work and literature values(Psati )

(lit), molar volumes of pure liquids(V Li ), second virial coefficients (Bii, Bij) and van deer Waals molecular volumes (ri) and

surfaces (qi) at 313.15 K used for the reduction of the systems

TAME (i = 1) 1-Propanol (i = 2) n-Hexane (i = 3)

Psati (kPa) 19.559 7.000 37.276

Psati (lit) (kPa) 19.556a 6.988a 37.239a

19.567b 7.008c 37.283c

19.587d 6.987e 37.267f

37.278e

V Li (cm3/mol)g 136 76 134

Bi1 (cm3/mol)h −1988 −1481 −1759Bi2 (cm3/mol)h −1481 −1988 −999Bi3 (cm3/mol)h −1759 −999 −1595ri i 4.3059 3.1277 3.795qi

i 5.4927 3.3697 4.954

a Calculated from Antoine equation using constants reported in TRC[35].b Reported by Chamorro[36].c Calculated from Antoine equation using constants reported by Reid et al.[37].d Reported by Toghiani et al.[38].e Reported by Zielkiewicz[34].f Reported by Lozano et al.[39].g Reported in[40].h Calculated by Hayden and O’Connell[24] from Dymond and Smith[25].i Reported by Gmehling et al.[32].

Experimental values of total vapor pressure for the binary mixtures were obtained in two overlappingsruns starting from opposite ends of the composition range. For the ternary mixtures, data were obtainedby addition of a pure species to a mixture of the other two at a fixed temperature. Six runs (dilution lines)were made starting from the corresponding binary system at mole fractions close to 0.3 or 0.7 and addingthe third pure component up to a mole fraction of 0.5.

Temperature was measured by means of a calibrated platinum resistance thermometer (SDL model5385/100) and an ac resistance bridge (ASL model F250) with a resolution of 1 mK and an estimatedoverall uncertainty of±10 mK. The measurement of pressure was done indirectly through a differentialpressure cell and indicator (Ruska models 2413-705 and 2416-711, respectively). Air was used on thereference side of the differential pressure cell and the pressure required to obtain a null indication wasmeasured with a fused quartz Bourdon pressure gauge (Texas Instruments model 801). The overalluncertainties of the pressure was estimated to be±5 Pa.

2.2. Experimental results and correlations

The use of the static measurement technique described above allows a condition of true thermodynamicequilibrium to be established. As a consequence of Duhem’s theorem, sampling of the phases is notnecessary. Instead, given a set of isothermal pressure and total composition data, thermodynamics allowscalculation of the compositions of the coexisting liquid and vapor phases. Thus, the equilibrium vapor


need not be sampled for analysis and the data are thermodynamically consistent “per se”[19,20]. Datareduction for the binary and ternary mixtures was done by Barker’s method[21] according to wellestablished procedures[22,23].

The non-ideality of the vapor phase was taken into account with the virial equation of state, truncatedafter the second term. The pure-component and interaction second virial coefficients (Bij) are given inTable 1. They were calculated by the Hayden and O’Connell method[24] using the parameters given byDymond and Smith[25].

The ternary system TAME+1-propanol+n-hexane has been measured together with the binary systemsTAME + 1-propanol and 1-propanol+ n-hexane at 313.15 K.

Data for these ternary systems are adequately correlated by the three-parameter Wohl equation[26]:

g123 = GE

RT= g12 + g13 + g23 + (C0 + C1x1 + C2x2)x1x2x3 (1)

Here,GE is the excess molar Gibbs free energy and the parametersC0, C1 andC2 were found by regressionof the ternary data. The parametersgij of the constituent binary systems were represented by the Margulesequation up to six parameters[27]:

gij = GE

RT= [Ajixi + Aijxj − (λjixi + λijxj)xixj + (ηjixi + ηijxj)x

2i x

2j ]xixj (2)

The ternary systems have also been correlated using Wilson[28], NRTL [29] and UNIQUAC[30] models,in terms of which the excess Gibbs energy is given respectively by

GE

RT= −

∑i

xi ln

∑

j

xjAij

(3)

GE

RT=∑i

xi

∑jAjiGjixj∑kGkixk

(4)

GE

RT=∑i

xi lnϕi

xi+ z

2

∑i

qixi lnϑi

qi−∑i

qixi ln

∑

j

ϑjAji

(5)

where

Gji = exp(−αjiAji ), ϑi = qixi∑jqjxj

, ϕi = rixi∑jrjxj

andz = 10.

VLE data may be calculated through the activity coefficients with the aid of a group-contribution modelsuch as modified UNIFAC (Dortmund) model (Gmehling et al.[31,32]). Modified UNIFAC differs fromthe original UNIFAC (Fredenslund et al.[33]) by the combinatorial term and the temperature dependenceof the group interaction parameters. The expression for the excess Gibbs energy is

GE

RT=

N∑i=1

xi ln γi =N∑i=1

xi(ln γci + ln γγR

i ) (6)


where the combinatorial term is

ln γci = 1 = V ′

1 + lnV ′1 − 5qi

(1 − Vi

Fi

+ ln

(Vi

Fi

))(7)

with

V ′i = r

3/4i∑M

j=1xjr3/4j

, Vi = ri∑Mj=1xjrj

andFi = qi∑Mj=1xjqj

.

ri andqi represent the van der Waals’ relative molecular volume and surface area respectively and aregiven by

ri =M∑k=1

νikRk, qi =M∑k=1

νikQk

The residual term is given by

ln γRi =

N∑k=1

νik(lnΓk − lnΓ ik) (8)

where

lnΓk = Qk

(1 − ln

(N∑

m=1

ϑmτmk

)−

N∑m=1

ϑmτKm∑Nn=1ϑnτnm

),

ϑm = QmXm∑Nn=1QnXn

andXm =∑M

j=1νjmxj∑M

j=1

∑Nn=1ν

jnxj

.

The term

τnm = exp

(−anm + bnmT + cnmT

2

T

)

represents the temperature dependence of the functional groups.Only a small number of structural groups are necessary to predict the phase equilibrium behavior of

binaries and ternary studied. The values of the UNIFAC (Dortmund) parameters are summarized inTable 2.Tables 3 and 4give experimental values of total pressure and the corresponding compositions of

the liquid and vapor phases for the binary systems TAME+ 1-propanol and 1-propanol+ n-hexane,respectively, the vapor phase composition was calculated using Margules equation.Table 5gives similarinformation for the ternary system TAME+ 1-propanol+ n-hexane where the Wohl expansion has beenused in the data reduction.

Results of data correlation for both binary systems are summarized inTable 6, it also includes thebinary system TAME+ n-hexane that has been published previously[15]. For the ternary system, theresults of the correlation are given inTable 7. These tables contain values of the adjustable parameters ofthe different models which lead to the correlated results using Barker’s method. The root mean square ofthe difference between experimental and calculated pressures (rms(P) and the maximum value of thesepressure residuals (max |(P|) are indicators of the quality of the agreement with data.


Table 2UNIFAC (Dortmund) parameters used for the prediction of the binary and ternary systems, taken from Gmeling et al.[32]

Sub-group CH3 CH2 C CH3–O OH(p) OH(t) Rk Qk

CH3

anm 0 0 0 233.1 2777 2777 0.6325 1.0608bnm 0 0 0 233.1 2777 2777cnm 0 0 0 0 1.551E−3 1.551E−3

CH2

anm 0 0 0 233.1 2777 2777 0.6325 0.7081bnm 0 0 0 233.1 2777 2777cnm 0 0 0 0 1.551E−3 1.551E−3

Canm 0 0 0 233.1 2777 2777 0.6325 0.0000bnm 0 0 0 233.1 2777 2777cnm 0 0 0 0 1.551E−3 1.551E−3

CH3–Oanm −9.654 −9.654 −9.654 0 650.9 650.9 1.1434 1.6022bnm −3.242E−2 −3.242E−2 −3.242E−2 0 −0.7132 −0.7132cnm 0 0 0 0 8.2E−4 8.2E−4

OH(p)anm 1606 1606 1606 816.7 0 0 1.2302 0.8927bnm −4.746 −4.746 −4.746 −5.092 0 0cnm 9.18E−4 9.18E−4 9.18E−4 6.07E−3 0 0

We have made also the prediction of the fluid phase equilibrium behavior for the ternary systemTAME +1-propanol+n-hexane. The equations forGE in multicomponent systems in Wilson, NRTL andUNIQUAC models only depend on the binary interaction parameters which can be adjusted directly fromthe multicomponent data. The results of the prediction for the measured ternary system are included inTable 7, together with a comparison between predictions by NRTL, UNIQUAC, and Wilson, showing the

Table 3Total pressure VLE data for TAME(1) + 1-propanol (2) at 313.15 K

x1 y1,calc P (kPa) x1 y1,calc P (kPa)

0.0000 0.0000 7.000 0.5012 0.7473 17.2410.0607 0.2837 9.217 0.5476 0.7651 17.6430.1042 0.4010 10.570 0.5496 0.7659 17.6580.1540 0.4930 11.922 0.5992 0.7840 18.0390.2019 0.5562 13.033 0.5997 0.7842 18.0380.2551 0.6089 14.078 0.6526 0.8032 18.3980.3008 0.6443 14.850 0.7008 0.8208 18.6970.3480 0.6746 15.547 0.7494 0.8395 18.9560.4006 0.7029 16.216 0.7966 0.8594 19.1740.4026 0.7039 16.226 0.8509 0.8856 19.3920.4470 0.7246 16.731 0.8965 0.9120 19.5350.4525 0.7270 16.774 0.9426 0.9449 19.6060.4988 0.7463 17.223 1.0000 1.0000 19.551


Table 4Total pressure VLE data for 1-propanol(1) + n-hexane (2) at 313.15 K

x1 y1,calc P (kPa) x1 y1,calc P (kPa)

0.0000 0.0000 37.283 0.5516 0.1449 37.5790.0548 0.0947 39.935 0.5528 0.1450 37.5520.1023 0.1081 40.074 0.6019 0.1501 36.8830.1539 0.1130 39.999 0.6036 0.1503 36.8680.1995 0.1166 39.858 0.6508 0.1567 36.0190.2522 0.1211 39.646 0.6993 0.1654 34.8530.3056 0.1258 39.400 0.7510 0.1783 33.1560.3549 0.1299 39.140 0.8039 0.1978 30.7100.4001 0.1334 38.873 0.8512 0.2257 27.6500.4014 0.1335 38.873 0.9044 0.2846 22.6950.4509 0.1370 38.522 0.9424 0.3747 17.7900.4516 0.1371 38.531 0.9647 0.4804 14.1680.4979 0.1405 38.133 1.0000 1.0000 7.0010.5029 0.1408 38.097

Table 5Total pressure VLE data for TAME(1) + 1-propanol(2) + n-hexane (3) at 313.15 K

x1 x2 y1,calc y2,calc P (kPa)

1.00000 0.00000 1.00000 0.00000 19.56700.29303 0.70697 0.63890 0.36110 14.72620.28394 0.68498 0.50305 0.30115 17.58190.27744 0.66926 0.43409 0.27081 19.38340.26428 0.63739 0.33678 0.22842 22.53530.24893 0.60025 0.26450 0.19776 25.47560.23455 0.56549 0.21845 0.17898 27.71050.22090 0.53252 0.18594 0.16629 29.45730.20602 0.49657 0.15827 0.15597 31.04960.19115 0.46067 0.13600 0.14802 32.39190.17593 0.42394 0.11706 0.14149 33.55240.16136 0.38880 0.10158 0.13624 34.50350.14672 0.35349 0.08800 0.13160 35.33520.00000 1.00000 0.00000 1.00000 6.99570.70225 0.29775 0.82143 0.17857 18.71670.67811 0.28749 0.73028 0.16576 20.11530.66360 0.28134 0.68303 0.15928 20.90070.63173 0.26780 0.59473 0.14753 22.51720.59699 0.25305 0.51698 0.13760 24.13590.56034 0.23748 0.44997 0.12937 25.69330.52690 0.22329 0.39865 0.12326 26.98920.49152 0.20828 0.35194 0.11779 28.26130.45716 0.19370 0.31227 0.11318 29.41010.42220 0.17888 0.27643 0.10900 30.49030.38499 0.16310 0.24224 0.10495 31.56670.35158 0.14894 0.21436 0.10156 32.47141.00000 0.00000 1.00000 0.00000 19.55520.30047 0.00000 0.19633 0.00000 32.87210.29178 0.02901 0.17875 0.04289 33.8220


Table 5 (Continued)

x1 x2 y1,calc y2,calc P (kPa)

0.28326 0.05743 0.16718 0.06753 34.25690.26985 0.10212 0.15493 0.08985 34.52650.25480 0.15226 0.14565 0.10411 34.57680.24014 0.20106 0.13883 0.11335 34.53520.22429 0.25385 0.13261 0.12109 34.41710.21016 0.30088 0.12754 0.12704 34.26120.19620 0.34735 0.12271 0.13251 34.06870.18351 0.38956 0.11838 0.13735 33.84810.16532 0.45008 0.11218 0.14441 33.45920.15008 0.50077 0.10696 0.15075 33.04050.00000 0.00000 0.00000 0.00000 37.27090.69513 0.00000 0.53115 0.00000 26.15100.67156 0.03394 0.50213 0.03520 26.45700.65945 0.05140 0.48983 0.04942 26.56640.62237 0.10477 0.45962 0.08205 26.72310.58911 0.15264 0.43890 0.10235 26.72680.55506 0.20163 0.42151 0.11803 26.63600.51895 0.25359 0.40574 0.13134 26.48310.48401 0.30386 0.39214 0.14239 26.28660.45015 0.35257 0.37990 0.15229 26.04530.41818 0.39855 0.36881 0.16144 25.77040.38336 0.44863 0.35691 0.17169 25.41970.34834 0.49899 0.34485 0.18275 24.98930.00000 1.00000 0.00000 1.00000 6.99810.00000 0.30059 0.00000 0.12539 39.40410.02931 0.29178 0.01516 0.12427 38.75660.06061 0.28237 0.03207 0.12322 38.08490.10024 0.27044 0.05442 0.12201 37.22550.15167 0.25495 0.08489 0.12050 36.12390.20171 0.23989 0.11610 0.11895 35.05820.25102 0.22504 0.14843 0.11718 34.02580.29704 0.21120 0.18016 0.11521 33.07400.34976 0.19533 0.21856 0.11246 31.98670.40128 0.17984 0.25845 0.10915 30.94650.45257 0.16441 0.30075 0.10517 29.91850.49972 0.15023 0.34213 0.10083 28.98120.00000 0.00000 0.00000 0.00000 37.26780.00000 0.68775 0.00000 0.16316 35.11650.03027 0.66689 0.02295 0.16459 34.16620.04902 0.65399 0.03782 0.16529 33.59340.09989 0.61889 0.08006 0.16656 32.18310.14954 0.58465 0.12318 0.16713 30.91910.19909 0.55050 0.16737 0.16719 29.76930.25049 0.51509 0.21401 0.16677 28.68030.30259 0.47921 0.26186 0.16588 27.66760.34768 0.44818 0.30366 0.16467 26.86740.39838 0.41330 0.35107 0.16274 26.03910.45047 0.37747 0.40025 0.15999 25.25180.50130 0.34252 0.44876 0.15638 24.5502


Table 6Summary of the data reduction results and UNIFAC prediction for binary systems TAME(1) + 1-propanol (2), TAME(1) +n-hexane (3) and 1-propanol(2) + n-hexane (3) at 313.15 K

Binary system Correlation Prediction

Margules Wilson NRTL NRTL(3p) UNIQUAC UNIFACa

TAME (1) + 1-propanol (2)A12 0.8807 0.7396 1.0102 0.8696 0.4693A21 1.1639 0.4037 0.1290 0.3483 1.4531λ12 0.0629λ21 0.2231α12 0.3 0.52rms(P (kPa) 0.005 0.009 0.016 0.007 0.022 0.240max |(P| (kPa) 0.010 0.020 0.028 0.013 0.036 0.370x2(azeotrope) 0.9559 0.9556 0.9610 0.9580 0.9633 0.9423P(azeotrope) 19.621 19.606 19.610 19.613 19.606 19.665

TAME (1) + n-hexane (3)b

A13 0.1867 0.9673 0.0316 0.9176A31 0.1837 0.8224 0.1493 1.0509λ13 0.0333λ31 0.0333α13 0.3rms(P (kPa) 0.005 0.010 0.010 0.010 0.072max |(P| (kPa) 0.030 0.019 0.019 0.019 0.109

1-Propanol (2)+ n-hexane (3)A23 3.1274 0.0858 0.9115 1.1759 1.5212A32 1.8551 0.3778 1.9507 2.2003 0.3170λ23 5.1523�32 1.0589η23 6.6359η32 1.3453α23 0.4 0.49rms(P (kPa) 0.038 0.126 0.494 0.204 0.750 0.617max |(P| (kPa) 0.080 0.323 1.001 0.472 1.298 0.909x2(azeotrope) 0.1089 0.1096 0.1150 0.1150 0.1141 0.1122P(azeotrope) 40.027 39.816 39.220 39.220 38.909 40.285

Parameters for UNIFAC prediction are given inTable 2.a Parameters for UNIFAC prediction are given inTable 2.b Experimental data published in[15].

maximum deviation of the pressure residuals given for the referred models. In all cases, the correlationparameters of the binary systems given inTable 6have been used.

The binary and ternary vapor–liquid equilibria data are also predicting using the modified UNIFAC(Dortmund) group contribution model these results are inTables 6 and 7, respectively.

As an example of the fits of models to the data (Fig. 1) shows a plot of the pressure residuals,P −Pexp

defined as differences between calculated pressuresP and experimental pressuresPexp versus liquidcomposition for the binary TAME+ 1-propanol using Margules equation with four parameters. It can be


Table 7Summary of the data reduction results obtained for the ternary system TAME(1) + 1-propanol(2) + n-hexane (3) at 313.5 K

Wohl Wilson NRTL UNIQUAC

C0 2.8760C1 0.8236C2 −0.5035A12 0.7287 0.8980 0.4782A21 0.3974 0.3492 1.4171A13 0.7572 −0.1353 1.1087A31 1.0767 0.3500 0.8592A23 0.0812 1.1945 1.5150A32 0.3936 2.1812 0.3000α12 0.52α13 0.30α23 0.49rms(P (kPa) 0.054 0.046 0.060 0.144max |(P| (kPa) 0.166 0.122 0.172 0.429

Prediction UNIFAC (Dortmund)a

rms(P (kPa) 0.087 0.089 0.378 1.557max |(P| (kPa) 0.196 0.240 0.875 4.420%max (|(P|/Pexp) 0.65 0.70 2.49 12.6

a Parameters for UNIFAC prediction are given inTable 2.

x1 (1-Propanol)

P-P

EX

P / k

Pa

-0.20

-0.10

0.00

0.10

0.20

0.00 0.20 0.40 0.60 0.80 1.00

±0.1%PEXP

Fig. 1. Comparison for the binary system TAME(1) + 1-propanol (2) at 313.15 K of the pressure residuals,P − Pexp definedas differences between calculated pressuresP and experimental pressuresPexp: ( ) this work; (�) Zielkiewicz [34]. A ±0.1%band of the experimental pressure in each point is indicated on the diagram.


seen that both branches, necessary to cover the entire composition range, exhibit good agreement closeto equimolar concentrations. The most of the deviations are less than 0.1% of total pressure.

3. Discussion

Both binary systems studied TAME+ 1-propanol and 1-propanol+n-hexane present a strong positivedeviation from the ideality. These systems exhibit an azeotrope in the alcohol poor region atx1 =0.9559 andP = 19.621 kPa for TAME+ 1-propanol and atx1 = 0.1089 andP = 40.027 kPa for1-propanol+ n-hexane, calculated using Margules equation. This model leads to the best fit with a rootmean square pressure residuals of 5 and 38 Pa and a maximum deviation of 10 and 80 Pa, respectively.

We have only found literature data available for the binary system TAME+ 1-propanol at 313.15 Kfor comparison[34], in Fig. 1, we have represented the pressure residuals for both set of data.

Concerning the ternary system, the results of the correlation give a root mean square pressure residualsbetween 46 Pa for Wilson equation and 144 Pa for UNIQUAC model with a maximum deviation of 122 Pain the best fit.

In Figs. 2–5, there are graphical results for the ternary system.Figs. 2 and 3show respectively isobarand the iso-GE lines as a function of the ternary liquid composition.Figs. 4 and 5show a three-dimensionaloblique view of pressure and molar excess Gibbs energy as a function of the ternary liquid composition.

x1 x2

x3

30

33

28

25

36

Fig. 2. Isobar lines in kPa as a function of the ternary liquid composition,xi, for the VLE at 313.15 K of the ternary systemTAME (1) + 1-propanol(2) + n-hexane (3).


x1 x2

x3

1000

800

900

700

600500

400300

200

Fig. 3. Iso-GE lines in J/mol as a function of the ternary liquid composition,xi, for the VLE at 313.15 K of the ternary systemTAME (1) + 1-propanol(2) + n-hexane (3).

5

10

15

20

25

30

35

40

P /k

Pa

x2

x1

x3

Fig. 4. Oblique view of the pressure surface,P(kPa), reduced by the Wilson equation for the ternary system TAME(1)+1-propanol(2) + n-hexane (3) at 313.15 K.


200

400

600

800

1000

1200

1400

GE /J

mol

-1

x3

x2

x1

Fig. 5. Oblique view of the excess Gibbs energy surface,GE (J/mol), reduced by the Wilson equation for the ternary systemTAME (1) + 1-propanol(2) + n-hexane (3) at 313.15 K.

The ternary system shows a positive deviation from ideality; the behavior of the molar excess Gibbsenergy is also increasing up to a maximum value, which corresponds to the less ideal binary system1-propanol+ n-hexane with a maximum value ofGE of 1287 J/mol.

Finally, UNIFAC (Dortmund) prediction gives a root mean square pressure residuals of 240 Pa and amaximum absolute deviation of 370 Pa for the binary TAME+1-propanol and a root mean square pressureresiduals of 617 Pa and a maximum absolute deviation of 909 Pa for the binary 1-propanol+ n-hexane;the model also predicts the presence of an azeotrope in the binary systems. The prediction of the ternarygives a root mean square pressure residuals of 1557 Pa and a maximum absolute deviation of 4420 Pa(about 12.6% of the experimental pressure data). Better results are obtained for the prediction of theternary system using Wilson, NRTL or UNIQUAC models with a root mean square pressure residuals of87 Pa and a maximum absolute deviation of 196 Pa using Wilson equation.

List of symbolsanm UNIFAC group interaction parameter between groupsn andmAij, Aji adjustable parameters of the correlation modelsbnm UNIFAC group interaction parameter between groupsn andmBii, Bij, Bjj second virial coefficientscnm UNIFAC group interaction parameter between groupsn andmC0, C1, C2 parameters inEq. (1)Fi auxiliary property for componenti (surface fraction/mole fraction)


g value ofGE/RT for a binary or a ternary mixtureGE molar excess Gibbs energyGk

i UNIFAC group activity coefficient of groupk in the pure substancei, j constituent identification: 1, 2 or 3lit literature valuemax maximum value of the indicated quantityP total pressurePsati vapor pressure of pure constituenti

qi relative van der Waals surface area of componentiQk relative van der Waals surface area of subgroupk.ri relative van der Waals volume of componentirms root mean squareR universal gas constantRk relative van der Waals volume of subgroupk.T absolute temperatureVi auxiliary property for componenti (volume fraction/mole fraction)V ′i empirically modifiedVi-value

V Li molar volume of pure liquidi = 1,2,3

x mole fraction, liquid phaseXm group mole fraction of groupm in the liquid phase.y mole fraction, vapor phase

Greek lettersα parameter inEq. (4)γi activity coefficient of componentiΓ k UNIFAC group activity coefficient of groupk in the mixture∆ signifies differenceη parameter inEq. (2)λ parameter inEq. (2)νki number of structural groups of typek in moleculeiϑm surface fraction of groupm in the liquid phaseτnm UNIFAC group interaction parameter between groupsn andm

Acknowledgements

Support for this work came from the Dirección General de Enseñanza Superior e Investigación Cientıficaof the Spanish Ministery of Education, Project PB-98-0366 and from Junta de Castilla y León (Consejerıade Educación y Cultura) project VA 71/00B.

References

[1] J.J. Segovia, M.C. Martın, C.R. Chamorro, M.A. Villamañán, Fluid Phase Equilib. 133 (1997) 163–172.[2] J.J. Segovia, M.C. Martın, C.R. Chamorro, E.A. Montero, M.A. Villamañán, Fluid Phase Equilib. 152 (1998) 265–276.


[3] J.J. Segovia, M.C. Martın, C.R. Chamorro, M.A. Villamañán, J. Chem. Eng. Data 43 (1998) 1014–1020.[4] J.J. Segovia, M.C. Martın, C.R. Chamorro, M.A. Villamañán, J. Chem. Eng. Data 43 (1998) 1021–1026.[5] J.J. Segovia, M.C. Martın, C.R. Chamorro, M.A. Villamañán, J. Chem. Thermodyn. 31 (1999) 1231–1246.[6] C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, Entropie 224–225 (2000) 86–92.[7] C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, Fluid Phase Equilib. 182 (1–2) (2001) 229–239.[8] C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, Fluid Phase Equilib. 191 (2001) 71–82.[9] C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, J. Chem. Eng. Data 46 (2001) 1574–1579.

[10] C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, J. Chem. Eng. Data 47 (2002) 316–321.[11] C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, Fluid Phase Equilib. 193 (1–2) (2002) 289–301.[12] C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, J. Chem. Thermodyn. 34 (2002) 13–28.[13] C.R. Chamorro, J.J. Segovia, M.C. Martın, E.A. Montero, M.A. Villamañán, Fluid Phase Equilib. 156 (1999) 73–87.[14] C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, Fluid Phase Equilib. 165 (1999) 197–208.[15] C. Alonso, E. Montero, C.R. Chamorro, J.J. Segovia, M.C. Martın, M.A. Villamañán, Fluid Phase Equilib. 182 (1–2) (2001)

241–255.[16] H.C. Van Ness, M.M. Abbott, Ind. Eng. Chem. Fundam. 17 (1978) 66–67.[17] R.E. Gibbs, H.C. Van Ness, Ind. Eng. Chem. Fundam. 11 (1972) 410–413.[18] D.P. DiElsi, R.B. Patel, M.M. Abbott, H.C. Van Ness, J. Chem. Eng. Data 23 (1978) 242–245.[19] H.C. Van Ness, M.M. Abbott, Classical Thermodynamics of Non-electrolyte Solutions with Applications to Phase Equilibria,

McGraw-Hill, New York, 1982.[20] H.C. Van Ness, J. Chem. Thermodyn. 27 (1995) 113–134.[21] J.A. Barker, Aust. J. Chem. 6 (1953) 207–210.[22] M.M. Abbott, H.C. Van Ness, AIChE J. 21 (1975) 62–71.[23] M.M. Abbott, J.K. Floess, G.E. Walsh Jr., H.C. Van Ness, AIChE J. 21 (1975) 72–76.[24] J.G. Hayden, J.P. O’Connell, Ind. Eng. Chem. Process Des. Dev. 14 (1975) 209–216.[25] J.H. Dymond, E.B. Smith, The Virial Coefficients of Pure Gases and Mixtures— A Critical Compilation, Clarendon Press,

Oxford, 1980.[26] K. Wohl, Chem. Eng. Prog. 49 (1953) 218.[27] M. Margules, Akad. Wiss. Wien, Mtah. Naturw. K1.II (1895) 104, 1243.[28] G.M. Wilson, J. Am. Chem. Soc. 86 (1964) 127–130.[29] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144.[30] D.S. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) 116–128.[31] J. Gmehling, J. Li, M. Schiller, Ind. Eng. Chem. Res. 32 (1993) 178–193.[32] J. Gmehling, J. Lohmann, A. Jakob, J. Li, R. Joh, Ind. Eng. Chem. Res. 37 (1998) 4876–4882.[33] A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor Liquid Equilibria using UNIFAC, Elsevier, Amsterdam, 1977.[34] J. Zielkiewicz, J. Chem. Thermodyn. 23 (1991) 605–612.[35] TRC-thermodynamic tables of hydrocarbons, in: Vapor Pressures, Thermodynamics Research Center, The Texas A&M

University System, College Station, 1976.[36] C.R. Chamorro, Ph.D. Thesis, University of Valladolid, Spain, 1998.[37] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, McGraw-Hill, New York, 1987.[38] R.K. Toghiani, H. Toghiani, G. Venkateswarlu, Fluid Phase Equilib. 122 (1996) 157–168.[39] L.M. Lozano, E.A. Montero, M.C. Martın, M.A. Villamañán, Fluid Phase Equilib. 110 (1995) 219–230.[40] TRC-thermodynamic tables of hydrocarbons and non-hydrocarbons, in: Densities, Thermodynamics Research Center, The

Texas A&M University System, College Station, 1973.

Documents

Vapor–liquid equilibrium of octane-enhancing additives in gasolines: 5. Total pressure data and GE for binary and ternary mixtures containing 1,1-dimethylpropyl methyl ether (TAME),