Fluid Phase Equilibria 226 (2004) 121–127

Phase stability of the system limonene + linalool + 2-aminoethanol

Alberto Arce∗, Alicia Marchiaro1, Ana Soto

Department of Chemical Engineering, University of Santiago de Compostela, E-15782 Santiago, Spain

Received 3 June 2004; received in revised form 28 September 2004; accepted 29 September 2004Available online 5 November 2004

Abstract

Liquid–liquid equilibrium data for the ternary system limonene + linalool + 2-aminoethanol at 298.15, 308.15 and 318.15 K are reported.The experimental data have been correlated using UNIQUAC and NRTL equations obtaining the binary interaction parameters. This lastequation was used to determine binodal and spinodal curves. The second derivatives of the Gibbs free energy of mixing for binary systemswere calculated with the aim to predict the slopes of the ternary tie-lines. Experimental data were also compared with the predictions of theUNIFAC group contribution method.©

K

1

otec

psbep

l3ceo

A

set ofve.en-tablee therrier

nce ofoge-oundinodal

oef-as a

riva-

0d

2004 Elsevier B.V. All rights reserved.

eywords:LLE; Limonene; Linalool; 2-Aminoethanol

. Introduction

Essential oils represent the “essences” or odor constituentsf the plants and they are conventionally processed by dis-

illation or solvent extraction. This last method reduces en-rgy consumption and avoids thermal degradation of valuableomponents.

As part of our research on the citrus essential oil ter-eneless by liquid–liquid extraction, we have undertaken aystematic study[1,2] of the phase equilibrium establishedetween limonene, linalool (two main components of citrusssential oil) and different solvents. These solvents have theresence of polar groups as common factor.

In this work, liquid–liquid equilibria for the systemimonene + linalool + 2-aminoethanol at 298.15, 308.15 and18.15 K have been determined. The experimental data wereorrelated using the UNIQUAC and NRTL equations and thenergetic parameters of these models at each temperature arebtained.

These models enable us to calculate a continuousequilibrium compositions which forms the binodal curMixtures with an overall composition within the areaclosed by the binodal curve are thermodynamically unsand usually, but not always, split. There is an area insidbinodal curve where a mixture must get over an energy babefore it can separate into two phases. Thus, in the abseexternal disturbances such a solution would remain homneous, and it is named metastable. The compositions bbetween the metastable and unstable areas form the spcurve.

Using an appropriate model to represent the activity cficients, the molar Gibbs free energy of mixing is givenfunction of the composition of the mixture by:

GM

RT=

N∑i=1

xi ln γixi (1)

thus being possible to calculate the second detivesG11 = ∂2[GM/RT ]/∂x2

1,G22 = ∂2[GM/RT ]/∂x22 and

G12 = ∂2[GM/RT )]/∂x1∂x2.

∗ Corresponding author.E-mail address:eqaaarce@usc.es (A. Arce).

1 Facultad de Ciencias Naturales, Universidad Nacional de la Patagonia,rgentina. Tel.: +34 981 563100x16790; fax: +34 981 595012.

For a ternary system, mixtures belonging to the spinodalcurve must accomplish that:

D = G11× G22− (G12)2 = 0 (2)

d.

378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserveoi:10.1016/j.fluid.2004.09.030

122 A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127

withG11 > 0 andG22 > 0. In the critical point, together withEq.(2), it must be accomplished that:

D∗ =(

∂D

∂x1

)G22−

(∂D

∂x2

)G12 = 0 (3)

D# =(

∂D∗

∂x1

)G22−

(∂D∗

∂x2

)G12 ≥ 0 (4)

again beingG11 > 0 andG22 > 0.In this work,G11,G22 andG12 were calculated at each

temperature using the NRTL equation and as stated by Novaket al.[3]. Both the spinodal curves and the critical points werecalculated using the equations above.

Moreover, Novak et al.[3] also provide a series of qualita-tive rules in terms of positions and values of the minima of theG11(x1) curves of the binary subsystems. According to theserules, tie-lines on a ternary diagram slope down towards thebinary subsystem with a lower minimum ofG11. We haveused the NRTL parameters obtained from the ternary datacorrelation to calculate theG11(x1) curves of the binary sub-systems. Then the slopes of the experimental tie-lines can becompared with those predicted by the above rules.

In the last part of our work, LLE data have also beenp andt

2

2

wereo for2 forl phya .

ncesw2 em pre-c a-s racyo

TD Ka

C

re

LL2

2.2. Procedure

First, the solubility curves at 298.15, 308.15 and 318.15 Kwere determined by the cloud point method[6]. Fig. 1showsthe solubility curve obtained for limonene + linalool + 2-aminoethanol ternary system at 298.15 K. Curves obtainedin this way are qualitative and they are only useful tocalibrate the gas chromatograph in the composition rangeof interest. An internal standard calibration method wasused, limonene being the standard for the limonene-richphase and 2-aminoethanol for the 2-aminoethanol-rich phase.Chromatograph used was a Hewlett-Packard 5890 Series IIequipped with a TCD. A capillary column Hewlett-PackardHP5 (30 m× 0.32 mm× 0.25�m) was used. Helium wasused as mobile phase and the injection volume was 0.5�lwith a split ratio of 1:100. Separation was made at 398.15 Kunder isothermal conditions. The greatest errors in the deter-mination of the mole fraction compositions were±0.003 inthe limonene-rich phase and±0.004 in the 2-aminoethanol-rich phase.

Liquid–liquid equilibrium data were obtained by directanalysis of the two layers of a heterogeneous mixture, as fol-lows: a mixture with partial miscibility was placed inside ajacketed cell, where it was agitated for 1 h in order to allowan intimate contact between the phases, and then thermody-n ttlef tem-p ltra-t aturew reciset mw ecteda

3

3

orl era-t

3

h theN oft om-n ed to0 C,a pc

andU pro-g oo us

redicted using the UNIFAC group contribution methodhey were compared with our experimental data.

. Experimental section

.1. Chemicals

The chemicals used were supplied by Fluka andf chromatographic quality. The purities are >99 mass%-aminoethanol, 98 mass% for limonene and 97 mass%

inalool. These purities were verified by gas chromatogrand the chemicals were used without further purification

The densities and refractive indices of pure substaere measured and compared with literature values[4,5] at98.15 K and atmospheric pressure (Table 1). Densities wereasured with an Anton Paar DMA 60/602 densimeter

ise to within±10−2 kg m−3. Refractive indexes were meured with an Atago RX-5000 refractometer with an accuf ±4× 10−5.

able 1ensities (ρ) and refractive indices (nD) of the pure components at 298.15nd atmospheric pressure

omponent ρ (g cm−3) nD

Experimental Literature Experimental Literatu

imonene 0.83717 0.8383[4] 1.47027 1.4701[4]inalool 0.85774 0.85760[5] 1.45970 Not foundAE 1.01216 1.0127[4] 1.45256 1.4525[4]

amic equilibrium was achieved by letting the mixture seor 4 h. The whole procedure was carried out at constanterature circulating water from a thermostat (Selecta U

erm 6000383) through the jacketed cell. Water temperas measured with a thermometer Heraeus Quat 100 p

o within ±0.01 K. When the thermodynamic equilibriuas achieved, samples of both liquid phases were collnd analysed by gas chromatography.

. Results and discussion

.1. Experimental data

The experimental liquid–liquid equilibrium data fimonene + linalool + 2-aminoethanol at the three tempures studied are listed inTable 2.

.2. Correlation of LLE data

The correlation of the experimental data was done witRTL [7] and the UNIQUAC[8] equations, as they are two

he most used in the literature. The value of the nonrandess parameter in NRTL equation was previously assign.1, 0.2 and 0.3. The structural parameters for UNIQUArndq, were taken from literature[9] or calculated from grouontribution data[10].

The binary interaction parameters for both NRTLNIQUAC equations were obtained using a computerram described by S�rensen and Arlt[11], which uses twbjective functions. First,Fa, does not require any previo

A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127 123

Fig. 1. Experimental tie-lines (©) and the corresponding UNIQUAC correlation using the optimal value of the solute distribution ratio at infinite dilution (�)at 298.15 K.

Table 2Experimental tie-lines of the system limonene (1) + linalool (2) + 2-aminoethanol (3) (compositions in molar fraction)

2AE-rich phase Limonene-rich phase

x1 x2 x3 x1 x2 x3

T = 298.15 K0.0045 0.0000 0.9955 0.9935 0.0000 0.00650.0050 0.0231 0.9719 0.9100 0.0642 0.02580.0065 0.0358 0.9577 0.7774 0.1371 0.08550.0127 0.0540 0.9333 0.6509 0.1819 0.16720.0156 0.0664 0.9181 0.5142 0.2234 0.26240.0209 0.0751 0.9039 0.4224 0.2337 0.34390.0217 0.0776 0.9008 0.3721 0.2374 0.39050.0300 0.0942 0.8758 0.3212 0.2248 0.4540

T = 308.15 K0.0043 0.0000 0.9957 0.9763 0.0000 0.02370.0068 0.0176 0.9756 0.9373 0.0446 0.01810.0076 0.0304 0.9620 0.8689 0.0887 0.04250.0054 0.0345 0.9601 0.7828 0.1370 0.08020.0063 0.0410 0.9528 0.6522 0.1853 0.16250.0103 0.0534 0.9363 0.5406 0.2303 0.22910.0125 0.0615 0.9260 0.4355 0.2462 0.31840.0355 0.0977 0.8667 0.3307 0.2286 0.4406

T = 318.15 K0.0041 0.0000 0.9959 0.9918 0.0000 0.00820.0071 0.0245 0.9683 0.8973 0.0679 0.03480.0091 0.0324 0.9585 0.8417 0.1003 0.05790.0094 0.0463 0.9443 0.7703 0.1464 0.08330.0158 0.0606 0.9236 0.6686 0.1766 0.15480.0224 0.0761 0.9014 0.5630 0.2072 0.22980.0258 0.0810 0.8932 0.5010 0.2187 0.28030.0267 0.0845 0.8888 0.4499 0.2265 0.32360.0331 0.0909 0.8760 0.4136 0.2217 0.3647

guess for parameters, and after convergence these parametersare used in the second function,Fb, to fit the experimentalconcentrations:

Fa =∑

k

∑i

∑j

[aIijk − aII

ijk

aIijk + aII

ijk

]2

+ Q∑n

P2n (5)

Fb =∑

k

min∑

i

∑j

(xijk − xijk)2 + Q∑

P2n

+[

ln

(γ IS∞

γ IIS∞

β∞

)]2

(6)

wherea is the activity,Pn the parameter value,Q= 10−6 forEq. (5) andQ= 10−10 for Eq. (6) [11]; x the composition inmole fraction,γ the calculated activity coefficient andβ thesolute distribution ratio between the organic and the aque-ous phases. min refers to the minimum obtained by the Mar-quardt method. The subscripts and superscripts are:i for thecomponents (1–3),j for the phases (I, II),k for the tie-lines(1, 2,. . .,M) andn for the parameters (1,. . . ,6). The sym-bol ˆ refers to calculated magnitudes,s to the solute and∞to infinite dilution.

The second terms of both Eqs.(5) and (6)are penalty termsd withht giveap

esigned to reduce risks of multiple solutions associatedigh parameter values. InFb objective function (Eq.(6)) the

hird term ensures that the binary interaction parameterssolute distribution ratio at infinite dilution,β∞, which ap-roximates to a value previously defined by the user.

124 A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127

Table 3LLE data correlation

Model r.m.s.d. Temperature

298.15 K 308.15 K 318.15 K

UNIQUAC β∞ 1.39 0.81 2.08�β (%) 4.96 4.65 24.07 9.18 4.33 2.60F (%) 0.2976 0.2965 0.6428 0.5137 0.2478 0.2539

NRTL (α = 0.2) β∞ 1.79 1.29 2.46�β (%) 11.01 4.81 33.42 19.82 5.55 2.77F (%) 0.3379 0.3445 0.6817 0.5904 0.2592 0.2836

Structural parameters for the UNIQUAC equation

Limonene[9] Linalool [9] 2AE [8]

r 6.2783 7.0365 2.5735q 5.2080 6.0600 2.3600

Root mean square deviations (r.m.s.d., %) for each model and each temperature, defining or not the solute distribution ratio at infinite dilutionβ∞.

Table 4LLE data correlation of the system limonene (1) + linalool (2) + 2-aminoethanol (3)

Temperature (K) Pairi–j NRTL UNIQUAC

�gij (J mol−1) �gji (J mol−1) �uij (J mol−1) �uji (J mol−1)

298.15 1–2 14011 −8271.9 −4501.3 1643.11–3 7731.1 10663 4287.3 1546.52–3 −5850.5 8521.9 −1561.9 −774.46

308.15 1–2 16016 −8471.2 −5563.6 8681.51–3 7688.1 10160 3679.7 3689.22–3 −5280.2 8052.8 −2338.9 850.94

318.15 1–2 12819 −8693.1 −2708.2 1322.11–3 8083.1 10725 4914.9 1287.82–3 −2814.2 1748.3 −1557.5 1017.9

Binary interaction parameters for NRTL (α = 0.2) and UNIQUAC equations for each temperature, specifying the optimal value of the solute distribution ratioat infinite dilutionβ∞.

The quality of the correlation is measured by the residualfunctionF and by the mean error of the solute distributionratio,�β:

F = 100×∑

k

min∑

i

∑j

(xijk − xijk)2

6M

0.5

(7)

Table 5Simultaneous correlation of the data at the three temperatures

Model Pairi–j Parameters r.m.s.d. (%) Temperature

�uij (J mol−1) �uji (J mol−1) 298.15 K 308.15K 318.15K

UNIQUAC 1–2 −5558.1 4698.11–3 3980.1 1855.2 �β 6.4 12.7 6.12–3 −1478.3 −1039.3 F 0.3655 0.7824 0.5148

�gij (J mol−1) �gji (J mol−1)

NRTL (α = 0.2) 1–2 −7614.5 −630.561–3 7557.3 9444.7 �β 8.6 18.2 12.12–3 −6683.3 6012.1 F 0.3465 0.8516 0.5431

Binary interaction parameters and root mean square deviations (r.m.s.d.) of the models.

�β = 100×[∑

k

((βk − βk)/βk)2

M

]0.5

(8)

Three different kinds of correlations were made. First, theexperimental data were fitted at each temperature with bothNRTL and UNIQUAC equations, at each temperature andwithout defining a value for the solute distribution ratio at

A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127 125

Fig. 2. Binodal (—) and spinodal (- - -) curves at 298.15 K.

infinite dilution, β∞, and also using the optimal value forthis parameter. In the latter case, the optimalβ∞ was foundby trial and error with�β as optimality criterion.Table 3lists the root mean square deviations found with both mod-els, NRTL (α optimized at 0.2) and UNIQUAC, obtained foreach temperature defining the solute distribution ratio at infi-nite dilution,β∞, or not. When the solute distribution ratio atinfinite dilution,β∞ is defined, the residual�β decreases ex-tensively, and the residualF slightly increases. As the residual�β shows the fitness of the LLE data at solute low concentra-tions, and due to the importance of this region, the correlationdefiningβ∞ is usually preferred[11], thus we have decided tofix β∞ for correlation.Table 4lists the NRTL (α = 0.2) andUNIQUAC parameters obtained at each temperature whenthe optimal value of the solute distribution ratio at infinitedilution, β∞, is defined.Fig. 1 shows a comparison of theexperimental tie-lines and those calculated with UNIQUACdefiningβ∞ for ternary system at 298.15 K. Graphs for theother temperatures are similar.

Since the correlations are correct only at each tempera-ture and to obtain a set of parameters valid in the range of thethree temperatures we have also carried out the simultaneouscorrelation of the all data sets.Table 5lists the results (bi-nary parameters and residuals) obtained with this correlationfor both models NRTL (α = 0.2) and UNIQUAC for ternarys

3

intsw a-

rameters are listed inTable 4. G11,G22 andG12 were cal-culated following Novak et al.[3]. Spinodal curves were de-termined by using Eq.(2) and critical points by means ofEqs.(2)–(4). Fig. 2shows the results in triangular diagram at298.15 K.

3.4. Prediction of tie-lines slopes

Fig. 3 shows theG11(x1) curves for the binary subsys-tems of limonene + linalool + 2-aminoethanol ternary systemat 298.15 K. These curves were calculated using the NRTLequation (α = 0.2) with the aim to compare the slopes of theexperimental tie-lines with those predicted by means of theNovak et al.[3] rules. The values ofG11 minima imply pos-itive tie-line slopes for the ternary system at the three tem-peratures.

F ua-t

ystem.

.3. Determination of binodal and spinodal curves

The bimodal and spinodal curves and the critical poere calculated using NRTL (α = 0.2) equation whose p

ig. 3. Variation ofG11 of the binary systems calculated from NRTL eqions withα = 0.2 at 298.15 K.

126 A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127

Fig. 4. Experimental (©) and predicted using the UNIFAC method (�) tie-lines at 298.15 K.

3.5. Prediction of LLE data

The experimental data were compared with those pre-dicted by the UNIFAC method[12]. The interaction andstructural parameters were taken from literature[13] and arespecific for LLE, but those for the –CNH2– group (presentin 2-aminoethanol) which cannot be found. Thus, parametersfor this group were taken from VLE data[14].

The quality of the prediction is evaluated with the residualF (Eq. (7)). Its value was 10.58% at 298.15 K, 10.34% at308.15 K and 8.35% at 318.15 K.Fig. 4shows the comparisonof the predicted and experimental tie-lines at 298.15 K.

4. Conclusions

Liquid–liquid equilibrium data of the limonene + linalool+ 2-aminoethanol system have been obtained at three differ-ent temperatures. Temperature has practically no effect onthe liquid–liquid equilibrium for the working temperatures.

The experimental LLE data were correlated using theNRTL and UNIQUAC activity models, without defining avalue to the solute distribution ratio at infinite dilution andalso using the optimal value to this parameter. The corre-lation using the optimalβ∞ provided the best results. Ins otherst la-tm ctedi m-e ounds

were found. The correlation with the UNIQUAC equationgives the best results, but also the NRTL equation with avalue of the nonrandomness parameter optimized inα = 0.2fits the experimental data satisfactorily.

The simultaneous correlation of the data at the threetemperatures gives common parameters in the consideredtemperature range increasing in this way their application,nonetheless residuals are slightly higher. As there is notpractically influence of temperature on LLE, consideringtemperature dependence of parameters does not improve thecorrelation.

Binodal curve for ternary system determine the miscibilitylimits, but also in this work spinodal curve has been deter-mined with the aim to know the stability limits or incipientinstability points.

The slopes of tie-lines of limonene + linalool + 2-aminoethanol ternary system were correctly predicted bymeans of the Novak et al. rules, calculating theG11(x1) min-ima for the binary subsystems from the NRTL parametersobtained from correlation of ternary data.

The LLE data predicted with the UNIFAC method giveshigh values of the residualF. Thus, the results could not beconsidered quantitative and should only be used in prelim-inary studies. The improvement of UNIFAC parameters forLLE would reflect well on results.

LaFFF

ome cases both residuals are lowered and in somehe residualF give a slightly larger value than the correion without definingβ∞, but the value of the residual�β isuch smaller. Thus, this method of correlation was sele

n the work. New UNIQUAC and NRTL interaction paraters between solvent, terpene and oxygenated comp

ist of symbolsactivityrms deviation of phase composition

a activity objective functionb concentration objective function

A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127 127

�g optimizable binary NRTL parametersM number of tie-linesPn parameter valueQ constant�u optimizable binary UNIQUAC parametersx experimental mole fractionx calculated mole fraction

Greek lettersα NRTL nonrandomness parameterβ experimental solute distribution ratioβ calculated solute distribution ratio�β rms relative deviation of solute distribution ratioγ activity coefficientγ calculated activity coefficient

Subscriptsi component identifierj phase identifierk tie-line identifiern parameter identifier in the termQ

∑nP

2n

∞ infinite dilution

Acknowledgements

ia yT 03-

01326). AM is grateful to the European Union for financialsupport (Project ALFA-PROQUIFAR).

References

[1] A. Arce, A. Machiaro, O. Rodrıguez, A. Soto, Chem. Eng. J. (2002)89.

[2] A. Arce, A. Machiaro, A. Soto, Fluid Phase Equil. (2003) 211.[3] J.P. Novak, J. Matous, J. Pick, Liquid–liquid equilibria, Elsevier,

Amsterdam, 1987.[4] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents. Phys-

ical Properties and Methods of Purification, 4th ed., Wiley,1986.

[5] F. Comelli, S. Ottani, R. Francesconi, C. Castellari, J. Chem. Eng.Data 47 (2002) 93–97.

[6] D.F. Othmer, R.E. White, E. Trueger, Ind. Eng. Chem. 33 (1940)1240–1248.

[7] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144.[8] D.S. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) 116–128.[9] T.E. Daubert, R.P. Danner, Physical and Thermodynamic Properties

of Pure Chemical Data Compilation, 1989.[10] A. Bondi, Physical properties of molecular crystals, in: Liquids and

Glasses, Wiley, New York, 1968.[11] J.M. S�rensen, W. Arlt, Liquid–Liquid Equilibrium Data Collection,

DECHEMA Chemistry Data Series, Frankfurt, 1980.[12] A. Fredenslund, R.L. Jones, J.M. Prausnitz, AIChE J. 21 (1975)

1086–1099.[13] T. Magnussen, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem. Pro-

[ rocess

The authors are grateful to the Ministerio de Ciencecnologıa of Spain for financial support (Project PPQ20

cess Des. 20 (1981) 331–339.14] J. Gmehling, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem. P

Des. 21 (1982) 118–127.