- Email: [email protected]
Phase stability of the system limonene + linalool + 2-aminoethanol
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 2004 Available 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 last equation was used to determine binodal and spinodal curves. The second derivatives of the Gibbs free energy of mixing for binary systems were calculated with the aim to predict the slopes of the ternary tie-lines. Experimental data were also compared with the predictions of the UNIFAC group contribution method. © 2004 Elsevier B.V. All rights reserved. Keywords: LLE; Limonene; Linalool; 2-Aminoethanol
1. Introduction Essential oils represent the “essences” or odor constituents of the plants and they are conventionally processed by distillation or solvent extraction. This last method reduces energy consumption and avoids thermal degradation of valuable components. As part of our research on the citrus essential oil terpeneless by liquid–liquid extraction, we have undertaken a systematic study [1,2] of the phase equilibrium established between limonene, linalool (two main components of citrus essential oil) and different solvents. These solvents have the presence of polar groups as common factor. In this work, liquid–liquid equilibria for the system limonene + linalool + 2-aminoethanol at 298.15, 308.15 and 318.15 K have been determined. The experimental data were correlated using the UNIQUAC and NRTL equations and the energetic parameters of these models at each temperature are obtained.
∗
Corresponding author. E-mail address: [email protected] (A. Arce). 1 Facultad de Ciencias Naturales, Universidad Nacional de la Patagonia, Argentina. Tel.: +34 981 563100x16790; fax: +34 981 595012. 0378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2004.09.030
These models enable us to calculate a continuous set of equilibrium compositions which forms the binodal curve. Mixtures with an overall composition within the area enclosed by the binodal curve are thermodynamically unstable and usually, but not always, split. There is an area inside the binodal curve where a mixture must get over an energy barrier before it can separate into two phases. Thus, in the absence of external disturbances such a solution would remain homogeneous, and it is named metastable. The compositions bound between the metastable and unstable areas form the spinodal curve. Using an appropriate model to represent the activity coefficients, the molar Gibbs free energy of mixing is given as a function of the composition of the mixture by: N
GM = xi ln γi xi RT
(1)
i=1
thus being possible to calculate the second derivatives G11 = ∂2 [GM /RT ]/∂x12 , G22 = ∂2 [GM /RT ]/∂x22 and G12 = ∂2 [GM /RT )]/∂x1 ∂x2 . For a ternary system, mixtures belonging to the spinodal curve must accomplish that: D = G11 × G22 − (G12)2 = 0
(2)
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A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127
with G11 > 0 and G22 > 0. In the critical point, together with Eq. (2), it must be accomplished that: D∗ =
D# =
∂D ∂x1
G22 −
∂D∗ ∂x1
∂D ∂x2
G22 −
∂D∗ ∂x2
G12 = 0
(3)
G12 ≥ 0
(4)
again being G11 > 0 and G22 > 0. In this work, G11, G22 and G12 were calculated at each temperature using the NRTL equation and as stated by Novak et al. [3]. Both the spinodal curves and the critical points were calculated using the equations above. Moreover, Novak et al. [3] also provide a series of qualitative rules in terms of positions and values of the minima of the G11(x1) curves of the binary subsystems. According to these rules, tie-lines on a ternary diagram slope down towards the binary subsystem with a lower minimum of G11. We have used the NRTL parameters obtained from the ternary data correlation to calculate the G11(x1) curves of the binary subsystems. Then the slopes of the experimental tie-lines can be compared with those predicted by the above rules. In the last part of our work, LLE data have also been predicted using the UNIFAC group contribution method and they were compared with our experimental data.
2. Experimental section 2.1. Chemicals The chemicals used were supplied by Fluka and were of chromatographic quality. The purities are >99 mass% for 2-aminoethanol, 98 mass% for limonene and 97 mass% for linalool. These purities were verified by gas chromatography and the chemicals were used without further purification. The densities and refractive indices of pure substances were measured and compared with literature values [4,5] at 298.15 K and atmospheric pressure (Table 1). Densities were measured with an Anton Paar DMA 60/602 densimeter precise to within ±10−2 kg m−3 . Refractive indexes were measured with an Atago RX-5000 refractometer with an accuracy of ±4 × 10−5 .
Table 1 Densities (ρ) and refractive indices (nD ) of the pure components at 298.15 K and atmospheric pressure Component
Limonene Linalool 2AE
ρ (g cm−3 )
nD
Experimental
Literature
Experimental
Literature
0.83717 0.85774 1.01216
0.8383 [4] 0.85760 [5] 1.0127 [4]
1.47027 1.45970 1.45256
1.4701 [4] Not found 1.4525 [4]
2.2. Procedure First, the solubility curves at 298.15, 308.15 and 318.15 K were determined by the cloud point method [6]. Fig. 1 shows the solubility curve obtained for limonene + linalool + 2aminoethanol ternary system at 298.15 K. Curves obtained in this way are qualitative and they are only useful to calibrate the gas chromatograph in the composition range of interest. An internal standard calibration method was used, limonene being the standard for the limonene-rich phase and 2-aminoethanol for the 2-aminoethanol-rich phase. Chromatograph used was a Hewlett-Packard 5890 Series II equipped with a TCD. A capillary column Hewlett-Packard HP5 (30 m × 0.32 mm × 0.25 m) was used. Helium was used as mobile phase and the injection volume was 0.5 l with a split ratio of 1:100. Separation was made at 398.15 K under isothermal conditions. The greatest errors in the determination of the mole fraction compositions were ±0.003 in the limonene-rich phase and ±0.004 in the 2-aminoethanolrich phase. Liquid–liquid equilibrium data were obtained by direct analysis of the two layers of a heterogeneous mixture, as follows: a mixture with partial miscibility was placed inside a jacketed cell, where it was agitated for 1 h in order to allow an intimate contact between the phases, and then thermodynamic equilibrium was achieved by letting the mixture settle for 4 h. The whole procedure was carried out at constant temperature circulating water from a thermostat (Selecta Ultraterm 6000383) through the jacketed cell. Water temperature was measured with a thermometer Heraeus Quat 100 precise to within ±0.01 K. When the thermodynamic equilibrium was achieved, samples of both liquid phases were collected and analysed by gas chromatography.
3. Results and discussion 3.1. Experimental data The experimental liquid–liquid equilibrium data for limonene + linalool + 2-aminoethanol at the three temperatures studied are listed in Table 2. 3.2. Correlation of LLE data The correlation of the experimental data was done with the NRTL [7] and the UNIQUAC [8] equations, as they are two of the most used in the literature. The value of the nonrandomness parameter in NRTL equation was previously assigned to 0.1, 0.2 and 0.3. The structural parameters for UNIQUAC, r and q, were taken from literature [9] or calculated from group contribution data [10]. The binary interaction parameters for both NRTL and UNIQUAC equations were obtained using a computer program described by Srensen and Arlt [11], which uses two objective functions. First, Fa , does not require any previous
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 2 Experimental tie-lines of the system limonene (1) + linalool (2) + 2aminoethanol (3) (compositions in molar fraction) 2AE-rich phase
Limonene-rich phase
x1
x2
x3
x1
x2
x3
T = 298.15 K 0.0045 0.0050 0.0065 0.0127 0.0156 0.0209 0.0217 0.0300
0.0000 0.0231 0.0358 0.0540 0.0664 0.0751 0.0776 0.0942
0.9955 0.9719 0.9577 0.9333 0.9181 0.9039 0.9008 0.8758
0.9935 0.9100 0.7774 0.6509 0.5142 0.4224 0.3721 0.3212
0.0000 0.0642 0.1371 0.1819 0.2234 0.2337 0.2374 0.2248
0.0065 0.0258 0.0855 0.1672 0.2624 0.3439 0.3905 0.4540
T = 308.15 K 0.0043 0.0068 0.0076 0.0054 0.0063 0.0103 0.0125 0.0355
0.0000 0.0176 0.0304 0.0345 0.0410 0.0534 0.0615 0.0977
0.9957 0.9756 0.9620 0.9601 0.9528 0.9363 0.9260 0.8667
0.9763 0.9373 0.8689 0.7828 0.6522 0.5406 0.4355 0.3307
0.0000 0.0446 0.0887 0.1370 0.1853 0.2303 0.2462 0.2286
0.0237 0.0181 0.0425 0.0802 0.1625 0.2291 0.3184 0.4406
T = 318.15 K 0.0041 0.0071 0.0091 0.0094 0.0158 0.0224 0.0258 0.0267 0.0331
0.0000 0.0245 0.0324 0.0463 0.0606 0.0761 0.0810 0.0845 0.0909
0.9959 0.9683 0.9585 0.9443 0.9236 0.9014 0.8932 0.8888 0.8760
0.9918 0.8973 0.8417 0.7703 0.6686 0.5630 0.5010 0.4499 0.4136
0.0000 0.0679 0.1003 0.1464 0.1766 0.2072 0.2187 0.2265 0.2217
0.0082 0.0348 0.0579 0.0833 0.1548 0.2298 0.2803 0.3236 0.3647
guess for parameters, and after convergence these parameters are used in the second function, Fb , to fit the experimental concentrations: I 2 II aijk − aijk Fa = (5) +Q Pn2 I II a + a ijk ijk n i j k Fb =
min
k
+ ln
i
I γˆ S∞
II γˆ S∞
(xijk − xˆ ijk )2 + Q
j
Pn2
2 β∞
(6)
where a is the activity, Pn the parameter value, Q = 10−6 for Eq. (5) and Q = 10−10 for Eq. (6) [11]; x the composition in mole fraction, γˆ the calculated activity coefficient and β the solute distribution ratio between the organic and the aqueous phases. min refers to the minimum obtained by the Marquardt method. The subscripts and superscripts are: i for the components (1–3), j for the phases (I, II), k for the tie-lines (1, 2, . . ., M) and n for the parameters (1, . . . ,6). The symbol ˆ refers to calculated magnitudes, s to the solute and ∞ to infinite dilution. The second terms of both Eqs. (5) and (6) are penalty terms designed to reduce risks of multiple solutions associated with high parameter values. In Fb objective function (Eq. (6)) the third term ensures that the binary interaction parameters give a solute distribution ratio at infinite dilution, β∞ , which approximates to a value previously defined by the user.
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Table 3 LLE data correlation Model
r.m.s.d.
Temperature 298.15 K
UNIQUAC
NRTL (α = 0.2)
308.15 K
318.15 K
β∞ β (%) F (%)
4.96 0.2976
1.39 4.65 0.2965
24.07 0.6428
0.81 9.18 0.5137
4.33 0.2478
2.08 2.60 0.2539
β∞ β (%) F (%)
11.01 0.3379
1.79 4.81 0.3445
33.42 0.6817
1.29 19.82 0.5904
5.55 0.2592
2.46 2.77 0.2836
Structural parameters for the UNIQUAC equation
r q
Limonene [9]
Linalool [9]
2AE [8]
6.2783 5.2080
7.0365 6.0600
2.5735 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 dilution β∞ . Table 4 LLE data correlation of the system limonene (1) + linalool (2) + 2-aminoethanol (3) Temperature (K)
Pair i–j
NRTL
UNIQUAC
gij (J mol−1 )
gji (J mol−1 )
uij (J mol−1 )
uji (J mol−1 )
298.15
1–2 1–3 2–3
14011 7731.1 −5850.5
−8271.9 10663 8521.9
−4501.3 4287.3 −1561.9
1643.1 1546.5 −774.46
308.15
1–2 1–3 2–3
16016 7688.1 −5280.2
−8471.2 10160 8052.8
−5563.6 3679.7 −2338.9
8681.5 3689.2 850.94
318.15
1–2 1–3 2–3
12819 8083.1 −2814.2
−8693.1 10725 1748.3
−2708.2 4914.9 −1557.5
1322.1 1287.8 1017.9
Binary interaction parameters for NRTL (α = 0.2) and UNIQUAC equations for each temperature, specifying the optimal value of the solute distribution ratio at infinite dilution β∞ .
The quality of the correlation is measured by the residual function F and by the mean error of the solute distribution ratio, β:
F = 100 ×
min
(xijk − xˆ ijk )2 i
k
j
6M
0.5
(7)
β = 100 ×
((βk − βˆ k )/βk )2 k
0.5 (8)
M
Three different kinds of correlations were made. First, the experimental data were fitted at each temperature with both NRTL and UNIQUAC equations, at each temperature and without defining a value for the solute distribution ratio at
Table 5 Simultaneous correlation of the data at the three temperatures Model
Pair i–j
Parameters uij
UNIQUAC
NRTL (α = 0.2)
1–2 1–3 2–3
1–2 1–3 2–3
(J mol−1 )
r.m.s.d. (%) uji
(J mol−1 )
−5558.1 3980.1 −1478.3
4698.1 1855.2 −1039.3
gij (J mol−1 )
gji (J mol−1 )
−7614.5 7557.3 −6683.3
−630.56 9444.7 6012.1
Binary interaction parameters and root mean square deviations (r.m.s.d.) of the models.
Temperature 298.15 K
308.15 K
318.15 K
β F
6.4 0.3655
12.7 0.7824
6.1 0.5148
β F
8.6 0.3465
18.2 0.8516
12.1 0.5431
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 for this parameter. In the latter case, the optimal β∞ was found by trial and error with β as optimality criterion. Table 3 lists the root mean square deviations found with both models, NRTL (α optimized at 0.2) and UNIQUAC, obtained for each temperature defining the solute distribution ratio at infinite dilution, β∞ , or not. When the solute distribution ratio at infinite dilution, β∞ is defined, the residual β decreases extensively, and the residual F slightly increases. As the residual β shows the fitness of the LLE data at solute low concentrations, and due to the importance of this region, the correlation defining β∞ is usually preferred [11], thus we have decided to fix β∞ for correlation. Table 4 lists the NRTL (α = 0.2) and UNIQUAC parameters obtained at each temperature when the optimal value of the solute distribution ratio at infinite dilution, β∞ , is defined. Fig. 1 shows a comparison of the experimental tie-lines and those calculated with UNIQUAC defining β∞ for ternary system at 298.15 K. Graphs for the other temperatures are similar. Since the correlations are correct only at each temperature and to obtain a set of parameters valid in the range of the three temperatures we have also carried out the simultaneous correlation of the all data sets. Table 5 lists the results (binary parameters and residuals) obtained with this correlation for both models NRTL (α = 0.2) and UNIQUAC for ternary system.
rameters are listed in Table 4. G11, G22 and G12 were calculated following Novak et al. [3]. Spinodal curves were determined by using Eq. (2) and critical points by means of Eqs. (2)–(4). Fig. 2 shows the results in triangular diagram at 298.15 K. 3.4. Prediction of tie-lines slopes Fig. 3 shows the G11(x1) curves for the binary subsystems of limonene + linalool + 2-aminoethanol ternary system at 298.15 K. These curves were calculated using the NRTL equation (α = 0.2) with the aim to compare the slopes of the experimental tie-lines with those predicted by means of the Novak et al. [3] rules. The values of G11 minima imply positive tie-line slopes for the ternary system at the three temperatures.
3.3. Determination of binodal and spinodal curves The bimodal and spinodal curves and the critical points were calculated using NRTL (α = 0.2) equation whose pa-
Fig. 3. Variation of G11 of the binary systems calculated from NRTL equations with α = 0.2 at 298.15 K.
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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 predicted by the UNIFAC method [12]. The interaction and structural parameters were taken from literature [13] and are specific for LLE, but those for the –CNH2 – group (present in 2-aminoethanol) which cannot be found. Thus, parameters for this group were taken from VLE data [14]. The quality of the prediction is evaluated with the residual F (Eq. (7)). Its value was 10.58% at 298.15 K, 10.34% at 308.15 K and 8.35% at 318.15 K. Fig. 4 shows the comparison of 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 different temperatures. Temperature has practically no effect on the liquid–liquid equilibrium for the working temperatures. The experimental LLE data were correlated using the NRTL and UNIQUAC activity models, without defining a value to the solute distribution ratio at infinite dilution and also using the optimal value to this parameter. The correlation using the optimal β∞ provided the best results. In some cases both residuals are lowered and in some others the residual F give a slightly larger value than the correlation without defining β∞ , but the value of the residual β is much smaller. Thus, this method of correlation was selected in the work. New UNIQUAC and NRTL interaction parameters between solvent, terpene and oxygenated compounds
were found. The correlation with the UNIQUAC equation gives the best results, but also the NRTL equation with a value of the nonrandomness parameter optimized in α = 0.2 fits the experimental data satisfactorily. The simultaneous correlation of the data at the three temperatures gives common parameters in the considered temperature range increasing in this way their application, nonetheless residuals are slightly higher. As there is not practically influence of temperature on LLE, considering temperature dependence of parameters does not improve the correlation. Binodal curve for ternary system determine the miscibility limits, but also in this work spinodal curve has been determined with the aim to know the stability limits or incipient instability points. The slopes of tie-lines of limonene + linalool + 2aminoethanol ternary system were correctly predicted by means of the Novak et al. rules, calculating the G11(x1) minima for the binary subsystems from the NRTL parameters obtained from correlation of ternary data. The LLE data predicted with the UNIFAC method gives high values of the residual F. Thus, the results could not be considered quantitative and should only be used in preliminary studies. The improvement of UNIFAC parameters for LLE would reflect well on results. List of symbols a activity F rms deviation of phase composition Fa activity objective function Fb concentration objective function
A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127
g M Pn Q u x xˆ
optimizable binary NRTL parameters number of tie-lines parameter value constant optimizable binary UNIQUAC parameters experimental mole fraction calculated mole fraction
Greek letters α NRTL nonrandomness parameter β experimental solute distribution ratio βˆ calculated solute distribution ratio β rms relative deviation of solute distribution ratio γ activity coefficient γˆ calculated activity coefficient Subscripts i component identifier j phase identifier k tie-line identifier n parameter identifier in the term Q n Pn2 ∞ infinite dilution
Acknowledgements The authors are grateful to the Ministerio de Ciencia y Tecnolog´ıa of Spain for financial support (Project PPQ2003-
127
01326). AM is grateful to the European Union for financial support (Project ALFA-PROQUIFAR).
References [1] A. Arce, A. Machiaro, O. Rodr´ıguez, 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. Physical 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. Srensen, 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. Process Des. 20 (1981) 331–339. [14] J. Gmehling, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem. Process Des. 21 (1982) 118–127.
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 2004 Available 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 last equation was used to determine binodal and spinodal curves. The second derivatives of the Gibbs free energy of mixing for binary systems were calculated with the aim to predict the slopes of the ternary tie-lines. Experimental data were also compared with the predictions of the UNIFAC group contribution method. © 2004 Elsevier B.V. All rights reserved. Keywords: LLE; Limonene; Linalool; 2-Aminoethanol
1. Introduction Essential oils represent the “essences” or odor constituents of the plants and they are conventionally processed by distillation or solvent extraction. This last method reduces energy consumption and avoids thermal degradation of valuable components. As part of our research on the citrus essential oil terpeneless by liquid–liquid extraction, we have undertaken a systematic study [1,2] of the phase equilibrium established between limonene, linalool (two main components of citrus essential oil) and different solvents. These solvents have the presence of polar groups as common factor. In this work, liquid–liquid equilibria for the system limonene + linalool + 2-aminoethanol at 298.15, 308.15 and 318.15 K have been determined. The experimental data were correlated using the UNIQUAC and NRTL equations and the energetic parameters of these models at each temperature are obtained.
∗
Corresponding author. E-mail address: [email protected] (A. Arce). 1 Facultad de Ciencias Naturales, Universidad Nacional de la Patagonia, Argentina. Tel.: +34 981 563100x16790; fax: +34 981 595012. 0378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2004.09.030
These models enable us to calculate a continuous set of equilibrium compositions which forms the binodal curve. Mixtures with an overall composition within the area enclosed by the binodal curve are thermodynamically unstable and usually, but not always, split. There is an area inside the binodal curve where a mixture must get over an energy barrier before it can separate into two phases. Thus, in the absence of external disturbances such a solution would remain homogeneous, and it is named metastable. The compositions bound between the metastable and unstable areas form the spinodal curve. Using an appropriate model to represent the activity coefficients, the molar Gibbs free energy of mixing is given as a function of the composition of the mixture by: N
GM = xi ln γi xi RT
(1)
i=1
thus being possible to calculate the second derivatives G11 = ∂2 [GM /RT ]/∂x12 , G22 = ∂2 [GM /RT ]/∂x22 and G12 = ∂2 [GM /RT )]/∂x1 ∂x2 . For a ternary system, mixtures belonging to the spinodal curve must accomplish that: D = G11 × G22 − (G12)2 = 0
(2)
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A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127
with G11 > 0 and G22 > 0. In the critical point, together with Eq. (2), it must be accomplished that: D∗ =
D# =
∂D ∂x1
G22 −
∂D∗ ∂x1
∂D ∂x2
G22 −
∂D∗ ∂x2
G12 = 0
(3)
G12 ≥ 0
(4)
again being G11 > 0 and G22 > 0. In this work, G11, G22 and G12 were calculated at each temperature using the NRTL equation and as stated by Novak et al. [3]. Both the spinodal curves and the critical points were calculated using the equations above. Moreover, Novak et al. [3] also provide a series of qualitative rules in terms of positions and values of the minima of the G11(x1) curves of the binary subsystems. According to these rules, tie-lines on a ternary diagram slope down towards the binary subsystem with a lower minimum of G11. We have used the NRTL parameters obtained from the ternary data correlation to calculate the G11(x1) curves of the binary subsystems. Then the slopes of the experimental tie-lines can be compared with those predicted by the above rules. In the last part of our work, LLE data have also been predicted using the UNIFAC group contribution method and they were compared with our experimental data.
2. Experimental section 2.1. Chemicals The chemicals used were supplied by Fluka and were of chromatographic quality. The purities are >99 mass% for 2-aminoethanol, 98 mass% for limonene and 97 mass% for linalool. These purities were verified by gas chromatography and the chemicals were used without further purification. The densities and refractive indices of pure substances were measured and compared with literature values [4,5] at 298.15 K and atmospheric pressure (Table 1). Densities were measured with an Anton Paar DMA 60/602 densimeter precise to within ±10−2 kg m−3 . Refractive indexes were measured with an Atago RX-5000 refractometer with an accuracy of ±4 × 10−5 .
Table 1 Densities (ρ) and refractive indices (nD ) of the pure components at 298.15 K and atmospheric pressure Component
Limonene Linalool 2AE
ρ (g cm−3 )
nD
Experimental
Literature
Experimental
Literature
0.83717 0.85774 1.01216
0.8383 [4] 0.85760 [5] 1.0127 [4]
1.47027 1.45970 1.45256
1.4701 [4] Not found 1.4525 [4]
2.2. Procedure First, the solubility curves at 298.15, 308.15 and 318.15 K were determined by the cloud point method [6]. Fig. 1 shows the solubility curve obtained for limonene + linalool + 2aminoethanol ternary system at 298.15 K. Curves obtained in this way are qualitative and they are only useful to calibrate the gas chromatograph in the composition range of interest. An internal standard calibration method was used, limonene being the standard for the limonene-rich phase and 2-aminoethanol for the 2-aminoethanol-rich phase. Chromatograph used was a Hewlett-Packard 5890 Series II equipped with a TCD. A capillary column Hewlett-Packard HP5 (30 m × 0.32 mm × 0.25 m) was used. Helium was used as mobile phase and the injection volume was 0.5 l with a split ratio of 1:100. Separation was made at 398.15 K under isothermal conditions. The greatest errors in the determination of the mole fraction compositions were ±0.003 in the limonene-rich phase and ±0.004 in the 2-aminoethanolrich phase. Liquid–liquid equilibrium data were obtained by direct analysis of the two layers of a heterogeneous mixture, as follows: a mixture with partial miscibility was placed inside a jacketed cell, where it was agitated for 1 h in order to allow an intimate contact between the phases, and then thermodynamic equilibrium was achieved by letting the mixture settle for 4 h. The whole procedure was carried out at constant temperature circulating water from a thermostat (Selecta Ultraterm 6000383) through the jacketed cell. Water temperature was measured with a thermometer Heraeus Quat 100 precise to within ±0.01 K. When the thermodynamic equilibrium was achieved, samples of both liquid phases were collected and analysed by gas chromatography.
3. Results and discussion 3.1. Experimental data The experimental liquid–liquid equilibrium data for limonene + linalool + 2-aminoethanol at the three temperatures studied are listed in Table 2. 3.2. Correlation of LLE data The correlation of the experimental data was done with the NRTL [7] and the UNIQUAC [8] equations, as they are two of the most used in the literature. The value of the nonrandomness parameter in NRTL equation was previously assigned to 0.1, 0.2 and 0.3. The structural parameters for UNIQUAC, r and q, were taken from literature [9] or calculated from group contribution data [10]. The binary interaction parameters for both NRTL and UNIQUAC equations were obtained using a computer program described by Srensen and Arlt [11], which uses two objective functions. First, Fa , does not require any previous
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 2 Experimental tie-lines of the system limonene (1) + linalool (2) + 2aminoethanol (3) (compositions in molar fraction) 2AE-rich phase
Limonene-rich phase
x1
x2
x3
x1
x2
x3
T = 298.15 K 0.0045 0.0050 0.0065 0.0127 0.0156 0.0209 0.0217 0.0300
0.0000 0.0231 0.0358 0.0540 0.0664 0.0751 0.0776 0.0942
0.9955 0.9719 0.9577 0.9333 0.9181 0.9039 0.9008 0.8758
0.9935 0.9100 0.7774 0.6509 0.5142 0.4224 0.3721 0.3212
0.0000 0.0642 0.1371 0.1819 0.2234 0.2337 0.2374 0.2248
0.0065 0.0258 0.0855 0.1672 0.2624 0.3439 0.3905 0.4540
T = 308.15 K 0.0043 0.0068 0.0076 0.0054 0.0063 0.0103 0.0125 0.0355
0.0000 0.0176 0.0304 0.0345 0.0410 0.0534 0.0615 0.0977
0.9957 0.9756 0.9620 0.9601 0.9528 0.9363 0.9260 0.8667
0.9763 0.9373 0.8689 0.7828 0.6522 0.5406 0.4355 0.3307
0.0000 0.0446 0.0887 0.1370 0.1853 0.2303 0.2462 0.2286
0.0237 0.0181 0.0425 0.0802 0.1625 0.2291 0.3184 0.4406
T = 318.15 K 0.0041 0.0071 0.0091 0.0094 0.0158 0.0224 0.0258 0.0267 0.0331
0.0000 0.0245 0.0324 0.0463 0.0606 0.0761 0.0810 0.0845 0.0909
0.9959 0.9683 0.9585 0.9443 0.9236 0.9014 0.8932 0.8888 0.8760
0.9918 0.8973 0.8417 0.7703 0.6686 0.5630 0.5010 0.4499 0.4136
0.0000 0.0679 0.1003 0.1464 0.1766 0.2072 0.2187 0.2265 0.2217
0.0082 0.0348 0.0579 0.0833 0.1548 0.2298 0.2803 0.3236 0.3647
guess for parameters, and after convergence these parameters are used in the second function, Fb , to fit the experimental concentrations: I 2 II aijk − aijk Fa = (5) +Q Pn2 I II a + a ijk ijk n i j k Fb =
min
k
+ ln
i
I γˆ S∞
II γˆ S∞
(xijk − xˆ ijk )2 + Q
j
Pn2
2 β∞
(6)
where a is the activity, Pn the parameter value, Q = 10−6 for Eq. (5) and Q = 10−10 for Eq. (6) [11]; x the composition in mole fraction, γˆ the calculated activity coefficient and β the solute distribution ratio between the organic and the aqueous phases. min refers to the minimum obtained by the Marquardt method. The subscripts and superscripts are: i for the components (1–3), j for the phases (I, II), k for the tie-lines (1, 2, . . ., M) and n for the parameters (1, . . . ,6). The symbol ˆ refers to calculated magnitudes, s to the solute and ∞ to infinite dilution. The second terms of both Eqs. (5) and (6) are penalty terms designed to reduce risks of multiple solutions associated with high parameter values. In Fb objective function (Eq. (6)) the third term ensures that the binary interaction parameters give a solute distribution ratio at infinite dilution, β∞ , which approximates to a value previously defined by the user.
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Table 3 LLE data correlation Model
r.m.s.d.
Temperature 298.15 K
UNIQUAC
NRTL (α = 0.2)
308.15 K
318.15 K
β∞ β (%) F (%)
4.96 0.2976
1.39 4.65 0.2965
24.07 0.6428
0.81 9.18 0.5137
4.33 0.2478
2.08 2.60 0.2539
β∞ β (%) F (%)
11.01 0.3379
1.79 4.81 0.3445
33.42 0.6817
1.29 19.82 0.5904
5.55 0.2592
2.46 2.77 0.2836
Structural parameters for the UNIQUAC equation
r q
Limonene [9]
Linalool [9]
2AE [8]
6.2783 5.2080
7.0365 6.0600
2.5735 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 dilution β∞ . Table 4 LLE data correlation of the system limonene (1) + linalool (2) + 2-aminoethanol (3) Temperature (K)
Pair i–j
NRTL
UNIQUAC
gij (J mol−1 )
gji (J mol−1 )
uij (J mol−1 )
uji (J mol−1 )
298.15
1–2 1–3 2–3
14011 7731.1 −5850.5
−8271.9 10663 8521.9
−4501.3 4287.3 −1561.9
1643.1 1546.5 −774.46
308.15
1–2 1–3 2–3
16016 7688.1 −5280.2
−8471.2 10160 8052.8
−5563.6 3679.7 −2338.9
8681.5 3689.2 850.94
318.15
1–2 1–3 2–3
12819 8083.1 −2814.2
−8693.1 10725 1748.3
−2708.2 4914.9 −1557.5
1322.1 1287.8 1017.9
Binary interaction parameters for NRTL (α = 0.2) and UNIQUAC equations for each temperature, specifying the optimal value of the solute distribution ratio at infinite dilution β∞ .
The quality of the correlation is measured by the residual function F and by the mean error of the solute distribution ratio, β:
F = 100 ×
min
(xijk − xˆ ijk )2 i
k
j
6M
0.5
(7)
β = 100 ×
((βk − βˆ k )/βk )2 k
0.5 (8)
M
Three different kinds of correlations were made. First, the experimental data were fitted at each temperature with both NRTL and UNIQUAC equations, at each temperature and without defining a value for the solute distribution ratio at
Table 5 Simultaneous correlation of the data at the three temperatures Model
Pair i–j
Parameters uij
UNIQUAC
NRTL (α = 0.2)
1–2 1–3 2–3
1–2 1–3 2–3
(J mol−1 )
r.m.s.d. (%) uji
(J mol−1 )
−5558.1 3980.1 −1478.3
4698.1 1855.2 −1039.3
gij (J mol−1 )
gji (J mol−1 )
−7614.5 7557.3 −6683.3
−630.56 9444.7 6012.1
Binary interaction parameters and root mean square deviations (r.m.s.d.) of the models.
Temperature 298.15 K
308.15 K
318.15 K
β F
6.4 0.3655
12.7 0.7824
6.1 0.5148
β F
8.6 0.3465
18.2 0.8516
12.1 0.5431
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 for this parameter. In the latter case, the optimal β∞ was found by trial and error with β as optimality criterion. Table 3 lists the root mean square deviations found with both models, NRTL (α optimized at 0.2) and UNIQUAC, obtained for each temperature defining the solute distribution ratio at infinite dilution, β∞ , or not. When the solute distribution ratio at infinite dilution, β∞ is defined, the residual β decreases extensively, and the residual F slightly increases. As the residual β shows the fitness of the LLE data at solute low concentrations, and due to the importance of this region, the correlation defining β∞ is usually preferred [11], thus we have decided to fix β∞ for correlation. Table 4 lists the NRTL (α = 0.2) and UNIQUAC parameters obtained at each temperature when the optimal value of the solute distribution ratio at infinite dilution, β∞ , is defined. Fig. 1 shows a comparison of the experimental tie-lines and those calculated with UNIQUAC defining β∞ for ternary system at 298.15 K. Graphs for the other temperatures are similar. Since the correlations are correct only at each temperature and to obtain a set of parameters valid in the range of the three temperatures we have also carried out the simultaneous correlation of the all data sets. Table 5 lists the results (binary parameters and residuals) obtained with this correlation for both models NRTL (α = 0.2) and UNIQUAC for ternary system.
rameters are listed in Table 4. G11, G22 and G12 were calculated following Novak et al. [3]. Spinodal curves were determined by using Eq. (2) and critical points by means of Eqs. (2)–(4). Fig. 2 shows the results in triangular diagram at 298.15 K. 3.4. Prediction of tie-lines slopes Fig. 3 shows the G11(x1) curves for the binary subsystems of limonene + linalool + 2-aminoethanol ternary system at 298.15 K. These curves were calculated using the NRTL equation (α = 0.2) with the aim to compare the slopes of the experimental tie-lines with those predicted by means of the Novak et al. [3] rules. The values of G11 minima imply positive tie-line slopes for the ternary system at the three temperatures.
3.3. Determination of binodal and spinodal curves The bimodal and spinodal curves and the critical points were calculated using NRTL (α = 0.2) equation whose pa-
Fig. 3. Variation of G11 of the binary systems calculated from NRTL equations with α = 0.2 at 298.15 K.
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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 predicted by the UNIFAC method [12]. The interaction and structural parameters were taken from literature [13] and are specific for LLE, but those for the –CNH2 – group (present in 2-aminoethanol) which cannot be found. Thus, parameters for this group were taken from VLE data [14]. The quality of the prediction is evaluated with the residual F (Eq. (7)). Its value was 10.58% at 298.15 K, 10.34% at 308.15 K and 8.35% at 318.15 K. Fig. 4 shows the comparison of 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 different temperatures. Temperature has practically no effect on the liquid–liquid equilibrium for the working temperatures. The experimental LLE data were correlated using the NRTL and UNIQUAC activity models, without defining a value to the solute distribution ratio at infinite dilution and also using the optimal value to this parameter. The correlation using the optimal β∞ provided the best results. In some cases both residuals are lowered and in some others the residual F give a slightly larger value than the correlation without defining β∞ , but the value of the residual β is much smaller. Thus, this method of correlation was selected in the work. New UNIQUAC and NRTL interaction parameters between solvent, terpene and oxygenated compounds
were found. The correlation with the UNIQUAC equation gives the best results, but also the NRTL equation with a value of the nonrandomness parameter optimized in α = 0.2 fits the experimental data satisfactorily. The simultaneous correlation of the data at the three temperatures gives common parameters in the considered temperature range increasing in this way their application, nonetheless residuals are slightly higher. As there is not practically influence of temperature on LLE, considering temperature dependence of parameters does not improve the correlation. Binodal curve for ternary system determine the miscibility limits, but also in this work spinodal curve has been determined with the aim to know the stability limits or incipient instability points. The slopes of tie-lines of limonene + linalool + 2aminoethanol ternary system were correctly predicted by means of the Novak et al. rules, calculating the G11(x1) minima for the binary subsystems from the NRTL parameters obtained from correlation of ternary data. The LLE data predicted with the UNIFAC method gives high values of the residual F. Thus, the results could not be considered quantitative and should only be used in preliminary studies. The improvement of UNIFAC parameters for LLE would reflect well on results. List of symbols a activity F rms deviation of phase composition Fa activity objective function Fb concentration objective function
A. Arce et al. / Fluid Phase Equilibria 226 (2004) 121–127
g M Pn Q u x xˆ
optimizable binary NRTL parameters number of tie-lines parameter value constant optimizable binary UNIQUAC parameters experimental mole fraction calculated mole fraction
Greek letters α NRTL nonrandomness parameter β experimental solute distribution ratio βˆ calculated solute distribution ratio β rms relative deviation of solute distribution ratio γ activity coefficient γˆ calculated activity coefficient Subscripts i component identifier j phase identifier k tie-line identifier n parameter identifier in the term Q n Pn2 ∞ infinite dilution
Acknowledgements The authors are grateful to the Ministerio de Ciencia y Tecnolog´ıa of Spain for financial support (Project PPQ2003-
127
01326). AM is grateful to the European Union for financial support (Project ALFA-PROQUIFAR).
References [1] A. Arce, A. Machiaro, O. Rodr´ıguez, 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. Physical 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. Srensen, 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. Process Des. 20 (1981) 331–339. [14] J. Gmehling, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem. Process Des. 21 (1982) 118–127.