Liquid–liquid equilibria of lactam containing binary systems

Fluid Phase Equilibria 266 (2008) 90–100

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Liquid–liquid equilibria of lactam containing binary systems ´ ˜ Garc´ıa, Jose´ M. Leal Rafael Alcalde ∗ , Santiago Aparicio, Mar´ıa J. Davila, Begona Department of Chemistry, University of Burgos, 09001 Burgos, Spain

a r t i c l e

i n f o

Article history: Received 9 November 2007 Received in revised form 22 January 2008 Accepted 12 February 2008 Available online 16 February 2008 Keywords: Lactam Pyrrolidone Liquid–liquid equilibria Equations of state SAFT PC-SAFT

a b s t r a c t In this work, we report a study on the liquid–liquid phase equilibria for N-methyl-2-pyrrolidone (NMP) + hydrocarbon (n-hexane, n-octane, n-decane, cyclohexane, cyclooctane, 2-methylpentane, 3methylpentane, isooctane, 2,2-dimethylbutane and 2,3-dimethylbutane) and N-cyclohexyl-2-pyrrolidone (NCP) + water binary mixtures at ambient pressure. The studied systems, except NCP + water, present miscibility curves with upper critical solutions temperatures (UCSTs). The results for NMP + hydrocarbon mixtures are correlated using two different approaches: (i) NRTL and UNIQUAC semiempirical models and (ii) molecular-based equations of state (statistical associating fluid theory (SAFT) and perturbed-chain statistical associating fluid theory (PC-SAFT)). Accurate correlations are inferred for NRTL and UNIQUAC models whereas for SAFT and PC-SAFT EOS complex mixing rules are required to obtain accurate results. © 2008 Elsevier B.V. All rights reserved.

1. Introduction N-Methyl-2-pyrrolidone (NMP) is the lactam of the 4methylaminobutyric acid. It is a thermal and chemically stable polar compound with a very weak base character and with powerful solvent abilities [1]. Due to its unique physical and chemical properties, NMP is used for many industrial processes [2]. In the petrochemical industry, it is applied for the recovery of pure aromatics, what is of great economical importance because of the large use of these compounds in several areas, or for the production of butadiene. It is also used for the desulfuration of natural or synthetic gases. NMP is also a powerful selective solvent for the separation of polar and non-polar compounds [3]. For the plastics industry, it is used as a solvent for the production of thermoresistant polymers such as polyethersulfone or polyamides because NMP is a very good solvent for natural and synthetic plastics. NMP is also involved in processes within the electronic equipment manufacture, surface coatings, cleaning and agrochemistry. NMP is a volatile organic compound, VOC, but it has a low vapour pressure, 0.373 kPa at 330 K [4], and thus the atmospheric pollution rising from its use is clearly lower than with other VOCs; hence, it has replaced other solvents with less favourable toxicological profiles or with ozone-depleting ability. With regard to the toxicological properties of NMP, the main drawback of this molecule is its teratogenic ability but besides this, no remarkable effects have been described [5]. On the other side, NMP is non-toxic for aquatic life and can be readily biodegraded

∗ Corresponding author. Tel.: +34 947 258 820; fax: +34 947 258 831. E-mail address: [email protected] (R. Alcalde). 0378-3812/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2008.02.008

[6], thus it has a more favourable environmental profile than other VOCs. N-Cyclohexyl-2-pyrrolidone, NCP, is a high boiling, high flash point polar aprotic solvent for many industrial applications, and in particular for different extraction processes. The mixed solvent NCP/water has been applied successfully for the extraction of aromatics from hydrocarbon streams. It is also interesting because contains a substantial apolar region as well as a peptide bond-like moiety; therefore, this solvent provides a useful model for protein interiors [7]. Moreover, it has showed no teratogenic ability and a favourable toxicological profile [8]. Among the different technological applications of NMP and NCP, liquid solvent extraction is of remarkably great importance. The overall performance of an extractive solvent is directly related with its solvency and selectivity properties, thus the accurate knowledge of liquid–liquid equilibria for selected systems is a clear technological need. Hence, our previous studies on the thermodynamic properties of mixtures containing lactams [9,10] are extended to the liquid–liquid phase equilibria in this work. The objectives are (i) to obtain accurate phase equilibria data for selected systems and (ii) to study the performance of several models to correlate the obtained results. In order to perform a systematic research, the selected second compound for NMP containing binary mixtures is always a hydrocarbon, but properly selected to analyze several structural features on phase equilibria. Thus, NMP + lineal, +cyclic and +ramified hydrocarbons are studied. For NCP, we report here results for the NCP + water mixture because of its technological relevance. Experimental data are fitted to a simple empirical equation to calculate critical properties [11,12].

R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100

Data modelling is carried out according to two different approaches: (i) excess free energy models and (ii) molecular-based equations of state. Hence, non-random two liquid, NRTL, model [13], and the universal quasi-chemical, UNIQUAC, equation [14], are applied. Molecular-based equations of state, EOS, are considered because these EOS have deep molecular-level foundations, through statistical mechanics; thus, they are clearly superior to other available models. Within this approach, statistical associating fluid theory, SAFT [15,16], and perturbed-chain statistical associating fluid theory, PC-SAFT [17,18], are selected considering their wide use both in industry and academia, because of their reliability, accuracy and computational simplicity for complex systems like those studied in this work. 2. Experimental

91

order to obtain a single-phase sample, then, they were placed in the equilibrium cell, being the volume of the sample close to the volume of the cell to minimize preferential evaporation. Once the vessel was sealed and placed into the temperature control arrangement, samples were stirred using a Teflon paddle which speed was varied using a speed regulator. Turbidimetric method was used to determinate the phase-change temperature. Temperature sweeps at very low rates, 0.01 K min−1 , were carried out to detect visually the appearance of turbidity. Several sweeps up and down of the transition temperature assured its accurate determination. All measurements were carried out at ambient pressure. In order to check the reliability of the technique NMP + n-hexane was used as test system by comparison with literature available data.

3. Results and discussion

All reagents were obtained from Fluka and Aldrich Chemical Companies and used without further purification, Table 1. Millipore water (Milli-Q, resistivity 18.2 m cm) was used in all the experiments. The solvents were degassed with ultrasound and kept out of light over Fluka 0.3 nm molecular sieves before use. It is well known the effect of water impurities on phase equilibria, mainly in the vicinity of the critical region, thus, it was measured by Karl–Fischer titration. Purity was measured by gas chromatography, GC, and by comparison of selected thermophysical properties, measured with previously described equipments [10], with literature data [19–27], Table 1. Liquid–liquid equilibria measurements were carried out in a home made assembly. A double jacketed glass vessel with 36 cm3 of volume was used as equilibrium cell. The temperature control was done through two thermostatic baths, the cell was immersed in a liquid bath and at the same time fluid was circulated through the internal jacket with a Julabo F32 external circulator. With this arrangement, we obtained a high stability, ±0.01 K, for the cell temperature and temperature gradients along the cell were minimized. The temperature was measured within the cell using a Platinum resistance thermometer Guideline 9540 with an accuracy of ±0.01 K. Binary mixtures were prepared gravimetrically using a Mettler AT261 balance, with a stated accuracy of ±1 × 10−4 for the mole fraction. These samples were heated if necessary in

The purity and physical properties of pure compounds are reported in Table 1, good agreement with literature values may be inferred. Tables 2 and 3 list the liquid–liquid equilibria experimental results for the investigated mixtures. All the systems show an upper critical solution temperature, UCST, except the NCP + water mixture, Figs. 1–5. Liquid–liquid equilibria coexistence curves with UCST show a rather flat shape in the vicinity of the critical points and are highly symmetrical. The coordinates of the critical points, x1,C and TC (Table 4), were obtained by fitting the experimental data with Eq. (1) [11,12]. T = TC + k|y1 − y1,C |m

(1)

where y1 =

x1 1 + x1 ( + 1)

y1,C =

(2)

x1,C 1 + x1,C ( + 1)

(3)

In Eqs. (1)–(3), m, k, , TC , x1,C parameters are the fitting coefficients obtained from the experimental data using a least-squares procedure. The average absolute deviation measures the fits quality and

Table 1 Purity (GC), water content (Karl–Fischer), density (), speed of sound (u) and dynamic viscosity (), of the pure compounds at 298.15 K Compound

Purity (%)

Water content (ppm)

NMP n-Hexane n-Octane n-Decane Cyclohexane Cyclooctane Isooctane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane NCP Water

99.00 99.00 99.50 99.00 99.96 99.00 99.50 99.00 99.00 99.00 97.00 98.00 –

78.0 29.3 31.4 – 27.6 – 25.0 – – – – – –

a b c d e f g h i

Assarsson and Eirich [19]. Riddick et al. [20]. Martin and Symons [21]. ˜ et al. [22]. Pena Ohnishi et al. [23]. Dubey and Sharma [24]. ´ Gonzalez et al. [25]. Plantier and Daridon [26]. Lide [27].

 (g cm−3 )

u (m s−1 )

D

Experimental

Literature

Experimental

Literature

Experimental

Literature

1.027878 0.654961 0.698638 0.726176 0.773948 0.830967 0.687817 0.648614 0.659806 0.644430 0.658562 1.025559 0.997040

1.0286a 0.65484b 0.69862b 0.72635b 0.77389b 0.83199c 0.68767d 0.64852b 0.65976b 0.64451e 0.65689e – 0.9970474b

1545.0 1077.57 1170.38 1232.47 1254.90 1387.82 1082.58 1042.19 1072.06 999.69 1047.1 1555.69 1497.0

– 1078.50f 1170.88f 1235.44f 1254g – 1083.2h 1038.6h – 1000.6e 1047.9e – 1497.4i

1.46876 1.37237 1.39538 1.40990 1.42378 1.45624 1.38917 1.36893 1.37399 1.36608 1.37275 1.49750 1.33250

1.4675b 1.37226b 1.39505b 1.40967b 1.42354b – 1.3890d 1.36873b 1.37386b – – – 1.3325019b

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R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100

Table 2 Liquid–liquid equilibria data for the NMP (1) + hydrocarbon (2) system n-Hexane

n-Octane

n-Decane

Cyclohexane

Cyclooctane

x1

T (K)

x1

T (K)

x1

T (K)

x1

T (K)

x1

T (K)

0.0559 0.0727 0.1076 0.1592 0.2110 0.2757 0.3373 0.3991 0.4578 0.5165 0.5663 0.6255 0.7051 0.7304 0.7568 0.8028 0.8310 0.8542

284.92 291.08 300.87 310.61 316.61 320.93 322.55 322.98 323.53 322.94 322.34 320.36 315.36 312.54 308.89 300.41 293.67 286.23

0.1330 0.1723 0.2112 0.2502 0.2863 0.3578 0.4224 0.4835 0.5435 0.5992 0.6524 0.7014 0.7597 0.7928 0.8146 0.8345 0.8550 0.8753 0.8940 0.9127 0.9300

304.98 312.76 317.92 321.71 324.97 327.25 329.18 329.32 329.54 329.14 328.48 326.89 323.06 319.45 316.45 312.81 308.27 302.85 296.49 288.51 279.40

0.1068 0.1404 0.1888 0.2338 0.3167 0.4021 0.5023 0.5622 0.6185 0.6927 0.7594 0.8121 0.8404 0.8574 0.8769 0.8941 0.9109 0.9268 0.9424

309.35 314.62 321.13 326.31 333.13 336.54 338.62 338.65 338.59 337.07 334.89 331.73 328.10 324.94 320.70 316.12 310.20 303.27 293.88

0.1216 0.1339 0.1511 0.1672 0.1818 0.2110 0.2844 0.3270 0.3842 0.4399 0.4977 0.5536 0.5815 0.6097 0.6352 0.6625

280.79 283.93 286.33 287.30 288.52 289.12 289.26 289.36 289.32 289.10 288.59 287.73 286.38 284.81 283.21 281.51

0.1308 0.1826 0.2512 0.3173 0.3805 0.4404 0.4986 0.5548 0.6089 0.6619 0.7109 0.7587

279.89 285.17 288.66 289.90 290.24 290.35 290.01 289.65 288.72 287.03 284.07 279.68

2-Methylpentane

3-Methylpentane

Isooctane

2,2-Dimethylbutane

2,3-Dimethylbutane

x1

T (K)

x1

T (K)

x1

T (K)

x1

T (K)

x1

T (K)

0.0758 0.0968 0.1181 0.1441 0.1936 0.2464 0.2993 0.3503 0.4006 0.4469 0.4687 0.5080 0.5483 0.5965 0.6496 0.7059 0.7512 0.7991 0.8253 0.8495 0.8712

288.04 298.09 305.05 310.69 318.28 322.72 324.89 325.81 325.89 325.87 325.71 325.41 324.87 323.56 321.12 316.84 310.50 301.32 295.02 288.19 281.03

0.0987 0.1182 0.1466 0.1750 0.2081 0.2467 0.2964 0.3193 0.3469 0.3950 0.4458 0.4950 0.5428 0.5947 0.6481 0.7019 0.7529 0.7908 0.8219 0.8465

289.34 298.73 306.06 310.32 314.06 316.52 318.47 318.88 319.24 319.40 319.42 319.12 318.71 317.53 314.81 310.41 303.57 296.36 289.01 282.36

0.0675 0.0995 0.1365 0.1804 0.2148 0.2799 0.3199 0.3589 0.3962 0.4386 0.4595 0.4794 0.4999 0.5497 0.6040 0.6485 0.7038 0.7610 0.7950 0.8305 0.8616 0.8952

286.52 296.66 305.16 312.39 316.99 322.64 324.76 326.08 326.93 326.96 327.06 327.00 327.15 326.95 326.65 325.96 323.66 319.40 315.01 308.42 299.57 288.75

0.0690 0.0817 0.1031 0.1219 0.1485 0.2001 0.2501 0.2974 0.3497 0.3972 0.4495 0.4911 0.5549 0.6011 0.6509 0.7121 0.7616 0.8053 0.8293 0.8550

281.15 290.06 298.37 304.12 309.34 316.14 320.03 321.94 322.74 322.87 322.71 322.40 321.48 319.87 317.18 310.72 303.02 293.98 287.06 279.88

0.0736 0.0969 0.1189 0.1460 0.1944 0.2436 0.2951 0.3439 0.3897 0.4180 0.4432 0.4846 0.5432 0.5964 0.6493 0.6992 0.7509 0.7878 0.8205

283.20 290.65 296.08 301.74 308.39 312.44 314.64 315.45 315.78 315.97 315.97 316.03 315.70 314.27 311.45 307.22 300.37 293.83 286.23

it is defined as



 N  exp   Ti − Tical  1   AAD = 100  T exp  N i=1

(4)

i

where N is the number of data points. Due to the characteristics of the miscibility curve for the NCP + water system, Fig. 5, it could not be fitted to the aforementioned model and then a polynomial equation is considered: T=

A + Cx1 + Ex12 + Gx13 1 + Bx1 + Dx12 + Fx13

(5)

where A, B, C, D, E, F and G are correlation coefficients. The accuracy of the results reported in this work may be inferred by comparison with available experimental data. Thus, in Fig. 1 we compare our results for the test system NMP + n-hexane with those reported by Malanowski et al. [28]. Excellent agreement is obtained for both branches of the liquid–liquid equilibria curve and with AADs always below 1%. Results in the vicinity of the critical region are also very close to the literature values, a very flat

curve is also reported in [28] and the critical values 324.65 K and 0.443 for mole fraction show 0.54 and −0.67% deviations to our values, Table 4. These small deviations may be produced by the different water content of the used samples (70 ppm for NMP and 29.3 ppm for n-hexane in this work, 300 and 58 ppm, respectively in [28]). Similar deviations are obtained for NMP + n-decane [29] and NMP + cyclohexane, +cyclooctane [30,31]. Hence, the experimental procedure proposed in this work give rise to accurate data for the liquid–liquid equilibria in the studied systems. Results reported in Fig. 1 show that an increasing n-alkane chain length give rise to an increasing critical temperature and to a critical mole fraction remarkably richer in NMP. This may be justified considering the increasing differences, both in size and shape, of the mixed molecules as the n-alkane increases its length [30]. A similar effect is obtained for cycloalkanes (Fig. 2) [31]. The effect of n-alkane branching on phase equilibria is reported in Figs. 3 and 4. Results for systems containing alkanes with sis carbon atoms are very complex, the mixtures with 2-methylpentane and 3-methylpentane show critical temperatures 2.57 K higher and −3.88 K lower than the system with n-hexane. The mixture with 2-

R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100 Table 3 Liquid–liquid equilibria data for the NCP (1) + water (2) system x1

T (K)

0.0070 0.0072 0.0080 0.0099 0.0138 0.0198 0.0280 0.0333 0.0363 0.0452 0.0506 0.0550 0.0609 0.0647 0.0687 0.0720 0.0774 0.0857 0.0998 0.1113 0.1227 0.1382 0.1564

346.56 341.78 335.11 330.37 326.65 324.83 324.24 323.99 323.87 324.05 324.13 324.28 324.57 324.94 325.25 325.59 326.22 327.39 329.98 332.53 335.75 341.07 348.89

93

methylpentane shows a wider immiscibility region whereas with 3-methylpentane this is narrower than for n-hexane. The molecular asymmetry introduced by the presence of the methylene group in position 2 of the alkane chain seems to hinder the penetration of these molecules into NMP dominated liquid phases, thus increasing the immiscibility. When methylene group is placed in position 3, a more symmetrical quasi-globular structure is obtained with greater fitting ability in NMP dipolar dominated structures. This is in agreement with the results reported in panel (b) of Fig. 3 for mixtures containing alkanes with eight carbon atoms. Results reported in Fig. 4 and Table 4 show that an increasing globularity for the alkane, as for 2,2 or 2,3-dimethylbutane, hence a lower linearity, increases the miscibility of these alkanes with NMP. The results for NCP + water mixtures reported in Fig. 5 show a lower critical solution temperature, LCST, at very low mole fraction (xNCP = 0.04). This points to the existence of microheterogenities in water dominated phases with the presence of micelles, in agreement with literature results [32]. 4. Modelling Liquid–liquid equilibria data are commonly described in the literature according to Gibbs energy models. Liquid immiscibility rises from the highly non-ideal character of the involved systems. As it is well known, deviations from ideal mixing behaviour can be

Fig. 1. Isobaric liquid–liquid equilibrium diagram for (䊉) NMP (1) + n-hexane (2), () NMP (1) + n-octane (2) and () NMP (1) + n-decane (2) at ambient pressure. Dashed line in panel (a) values obtained from Malanowski et al. [28], () AADs from [28]. Continuous lines in panel (b) calculated from Eqs. (1)–(3).

Table 4 Fitting coefficients of Eqs. (1)–(3) for the NMP (1) + hydrocarbon (2) systems and of Eq. (5) for the NCP (1) + water (2) system System

TC (K)

x1,C

m



K

ADD (%)

n-Hexane n-Octane n-Decane Cyclohexane Cyclooctane 2-Methylpentane 3-Methylpentane Isooctane 2,2-Dimethylbutane 2,3-Dimethylbutane

322.92 328.99 338.03 289.39 290.17 325.49 319.04 326.93 322.32 315.88

0.4460 0.5289 0.5919 0.3185 0.4272 0.4219 0.4124 0.5081 0.4055 0.4320

3.5638 3.7526 3.6500 4.6524 3.5663 3.8428 4.0264 3.6555 3.8721 3.4557

1.0723 0.8009 0.5949 2.7140 1.1842 1.3038 1.4213 0.8673 1.4079 1.1537

−955.79 −1056.37 −840.55 −2827.79 −612.85 −1355.05 −1670.21 −1008.70 −1440.55 −891.65

0.07 0.12 0.13 0.05 0.02 0.10 0.11 0.07 0.16 0.05

NCP + water

A

B

C

D

E

F

G

 (K)

319.54

173.57

−56264.39

544.28

186872.01

−765.10

−415406.65

0.06

94

R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100

Fig. 2. Isobaric liquid–liquid equilibrium diagram for: () NMP (1) + cyclohexane (2) and () NMP (1) + cyclooctane (2) at ambient pressure. Continuous lines calculated from Eqs. (1)–(3).

Fig. 4. Isobaric liquid–liquid equilibrium diagram for (a) (⊕) NMP (1) + 2,2dimethylbutane (2) and () NMP (1) + 2,3-dimethylbutane (2) at ambient pressure. Continuous lines calculated from Eqs. (1)–(3).

accounted by a correction factor like the activity coefficient,  i G=

n  i=1

xi Gi + RT

n  i=1

xi ln(xi ) + RT

n 

xi ln(i )

(6)

i=1

where G is Gibbs energy of a non-ideal mixture, Gi is the Gibbs energy of pure components, xi is the molar fraction of components, n is the number of components and R is the Universal gas constant. The last term of the Eq. (6), which accounts for the nonideality, is called the excess Gibbs energy of the mixture, GE . The

second and third terms comprise the Gibbs energy of mixing, m G. Liquid–liquid phase equilibrium can be calculated by equality of the activities, ai =  i xi , of both coexisting phases through well-known thermodynamic relationships. In order to calculate the activity, a model is needed to describe the excess Gibbs energy. The models most frequently applied for liquid–liquid equilibria data correlations are NRTL [13] and UNIQUAC [14] equations. According to Eq. (6), the local Gibbs energy of mixing for a binary mixture can be

Fig. 3. Isobaric liquid–liquid equilibrium diagram for (a) (䊉) NMP (1) + n-hexane (2), (♦) NMP (1) + 2-methylpentane (2) and () NMP (1) + 3-methylpentane (2); (b) () NMP (1) + n-octane (2), () NMP (1) + isooctane (2) at ambient pressure. Continuous lines calculated from Eqs. (1)–(3).



System

ANRTL 12 (J mol−1 )

NRTL B12 (J mol−1 K−1 )

NRTL C12 (J mol−1 K−2 )

NRTL D12 (J mol−1 K−3 )

ANRTL 21 (J mol−1 )

NRTL B21 (J mol−1 K−1 )

NRTL C21 (J mol−1 K−2 )

NRTL D21 (J mol−1 K−3 )

TCEXP − TCNRTL (K)

NRTL EXP x1,C − x1,C

AAD (%)

n-Hexane n-Octane n-Decane Cyclohexane Cyclooctane 2-Methylpentane 3-Methylpentane Isooctane 2,2-Dimethylbutane 2,3-Dimethylbutane

2461.613 2545.660 3541.543 2719.193 2215.669 2316.574 2245.668 2375.124 2289.327 2328.040

−11.946 −21.322 −67.555 −152.911 −24.555 −3.093 −2.962 −7.751 −2.152 −7.508

0.329 0.506 1.163 13.908 2.069 0.182 0.271 0.170 0.188 0.288

−0.003 −0.004 −0.006 −0.413 −0.066 −0.002 −0.004 −0.001 −0.003 −0.004

1914.036 2115.737 2195.376 1690.165 1841.120 1978.475 1956.609 2100.979 1943.270 1899.353

9.824 5.959 5.993 34.373 23.372 5.978 7.414 3.546 6.297 9.533

−0.162 −0.038 0.027 −2.549 −1.782 −0.095 −0.174 0.024 −0.110 −0.190

0.002 0.000 −0.001 0.053 0.062 0.002 0.003 −0.000 0.002 0.003

−0.48 −0.24 −0.45 −0.25 −0.24 −0.76 −0.61 −0.21 −0.89 −0.70

0.0251 −0.0063 −0.0154 −0.0024 0.0153 0.0231 0.0113 −0.0041 −0.0074 0.0182

0.7767 1.9316 2.4889 2.7385 0.8483 1.1937 1.8809 0.2912 1.3301 0.7229

UNIQUAC B12 (J mol−1 K−1 )

UNIQUAC C12 (J mol−1 K−2 )

UNIQUAC D12 (J mol−1 K−3 )

AUNIQUAC 21 (J mol−1 )

UNIQUAC B21 (J mol−1 K−1 )

UNIQUAC C21 (J mol−1 K−2 )

UNIQUAC D21 (J mol−1 K−3 )

−56.531 −305.363 −1154.329 396.446 −234.042 −66.256 −25.888 −587.026 −310.193 −396.898

2.518 14.326 46.110 −94.076 −10.522 −8.052 −13.671 −0.217 −8.726 −2.479

−0.014 −0.348 −0.849 7.269 0.776 0.148 0.335 −0.025 0.149 0.044

−0.001 0.003 0.006 −0.250 −0.029 −0.002 −0.005 −0.000 −0.002 −0.001

2839.650 3393.102 7034.879 2686.557 2556.261 2494.830 2293.716 3405.777 2661.647 2862.372

−44.060 −79.636 −250.780 −187.084 −69.935 −10.216 −3.667 −41.479 −5.494 −27.411

0.995 1.859 4.725 17.430 5.444 0.323 0.299 0.952 0.274 0.782

−0.010 −0.016 −0.032 −0.477 −0.174 −0.004 −0.004 −0.009 −0.004 −0.010

TCEXP −

EXP − x1,C

TCUNIQUAC (K)

UNIQUAC x1,C

−0.88 −0.79 −0.70 −0.40 −0.59 −1.21 −0.99 −0.21 −1.20 −0.82

0.0027 0.0029 0.0029 −0.0062 0.0061 0.0008 −0.0001 0.0007 −0.0001 0.0019

AAD (%)

1.4073 1.9693 2.1417 2.6810 1.1267 1.6041 2.2313 1.3202 1.6146 1.1263

95

n-Hexane n-Octane n-Decane Cyclohexane Cyclooctane 2-Methylpentane 3-Methylpentane Isooctane 2,2-Dimethylbutane 2,3-Dimethylbutane

AUNIQUAC 12 (J mol−1 )

R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100

(7)

(8)

(9)

(10)

Fig. 5. Isobaric liquid–liquid equilibrium diagram for (a) () NCP (1) + water (2) at ambient pressure. Continuous lines calculated from Eq. (5).

written as

21 G21 12 G12 + x1 + x2 G21 x2 + x2 G12

GE m G = x1 ln(x1 ) + x2 ln(x2 ) + RT RT

The excess Gibbs energy is described by the NRTL model according to Eqs. (8)–(10):



gij − gjj

GE = x1 x2 RT

ij = RT

Gij = exp(−˛ ij )

(11)

where gij is the interaction energy between an i–j pair of molecules, and ˛ is the non-randomness parameter. The temperature dependence of the interaction energies (g12 − g22 ) and (g21 − g11 ) are calculated by means of the following polynomial equations:

g12 − g22 = A12 − B12 (T − Tref ) + C12 (T − Tref )2 + D12 (T − Tref )3

g21 − g11 = A21 − B21 (T − Tref ) + C21 (T − Tref )2 + D21 (T − Tref )3 (12)

where A12 , B12 , C12 , D12 , A21 , B21 , C21 and D21 are the fitting coefficients, and Tref is the reference temperature, 273.15 K. The parameter ˛ was fixed to 0.2. The temperature and critical composition should fulfil the (x − xC )˛ ≈ (T − TC )ˇ condition, thus, a critical exponent, ˇ, close to 1/3 is required by the scaling theory of Bittrich et al. [33]. The model parameters and the average absolute deviation are given in Table 5, low deviations are obtained for all the studied mixtures. In Fig. 6a the dependence of the parameters gij − gjj with temperature is reported. Although we tried to correlate the experimental data using a single, temperature independent, parameter, this was not possible. From Fig. 6, a clearly

Table 5 Parameters of the NRTL and UNIQUAC equations, Eqs. (8)–(10) and Eqs. (14)–(19), for NMP (1) + hydrocarbon (2) systems calculated from liquid–liquid equilibrium data

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R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100

Fig. 6. Temperature dependence of (a) parameters in NRTL equation and (b) UNIQUAC equation for the NMP (1) + n-hexane (2) system calculated from isobaric (ambient pressure) liquid–liquid equilibrium data. (—) g12 − g22 or u12 and (- - -) g21 − g11 or u21 .

non-linear trend, justifying the use of Eqs. (11) and (12), may be inferred. In order to analyze the quality of the obtained parameters and their ability to predict phase equilibria no included in the model fitting, the vapour liquid equilibrium has been predicted, Fig. 7. The predictions are satisfactory in spite of the complexity of the equilibrium curves for the studied system. Another useful model to describe the excess Gibbs energy is UNIQUAC. Introduced by the mid 1970s by Abrahams and Prausnitz [14], it is one of the most frequently employed tools in correlating phase equilibria experimental data. In the UNIQUAC model, the excess

Gibbs free energy is made up of two parts, a combinatorial part due to molecular size and shape (GCE ), and a residual contribution, rising primarily from intermolecular forces (GRE ). Thus, for a binary mixture: GE = GCE + GRE GCE RT GRE RT

= x1 ln

(13)

 z

1

2 + x2 ln + x1 x2 2

q1 x1 ln

 2

1 + q2 x2 ln

1

2

(14)

= −q1 x1 ln[1 + 2 21 ] − q2 x2 ln[2 + 1 12 ]

(15)

1 =

x1 r1 x1 r1 + x2 r2

(16)

1 =

x1 q1 x1 q1 + x2 q2

(17)

where is the segment fraction;  is the area fraction; r and q are pure component relative volume and surface area parameters, respectively; and ij (= ji ) is the interaction parameter. With these equations, and assuming a certain value for the coordination number (z = 10) it is possible to calculate activity coefficients for liquid–liquid equilibria. The adjustable parameters 12 and 21 are expressed as a function of the characteristic energies as

 U  12

12 = exp −

(18)

RT

 U  21

21 = exp −

(19)

RT

These characteristic energies, U12 and U21 , are calculated considered as temperature dependent according to the following eqautions: U12 = A12 − B12 (T − Tref ) + C12 (T − Tref )2 + D12 (T − Tref )3 2

U21 = A21 − B21 (T − Tref ) + C21 (T − Tref ) + D21 (T − Tref )

Fig. 7. Isothermal vapour–liquid equilibrium diagram for NMP (1) + n-hexane (2). Experimental data from Gierycz et al. [34] (䊉) at 333.25 K and at () 343.15 K. Predicted values at (—) 333.25 K and (- - -) 343.15 K from NRTL parameters, Table 5, obtained from isobaric liquid–liquid equilibrium data.

3

(20) (21)

where A12 , B12 , C12 , D12 , A21 , B21 , C21 and D21 are the fitting coefficients. Tref is the reference temperature, 273.15 K. The structural parameters for the pure components, qi and ri were obtained from Reid et al. [35]. UNIQUAC fitting parameters are reported in Table 5 with a correlation quality similar to that for NRTL. The highly nonlinear temperature dependence of the energy parameters uij is reported in Fig. 6b.

R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100

Although excess Gibbs free energy models are very useful for data correlation, which is of great importance for engineering purposes, they are semiempirical in nature and thus their molecular foundations are very scarce. Hence, the relationships, if present, among model parameters and molecular-level behaviour of the studied fluids are hardly obtained. Another more rigorous approach, because of its deeper molecular basis, is developed using molecular-based EOS. EOS are commonly applied for the calculation of phase equilibria in multicomponent systems with compounds having very different chemical nature. In spite of the relative success obtained with different EOS for the correlation and/or prediction of vapour–liquid equilibria, the application of these models to study the partial miscibility of liquid mixtures produce less reliable results. The modelling of thermodynamic behaviour of systems in which molecules of very different chemical nature are involved, such as the ones considered in this work, cannot be carried out with simple cubic EOS and thus more complex models in which molecular-level structural effects are included have to be considered. Hence, in this work the modelling of liquid–liquid equilibria for NMP + hydrocarbon mixtures is done within the molecular-based EOS framework. Among the available alternatives within this approach, SAFT family EOS have attracted

97

great attention among the academic and industrial community, even they are included in several process modelling packages. The original SAFT engineering EOS developed by Chapman et al. [15,16] together with the recent modification by Gross and Sadowski [18], so-called PC-SAFT, are studied in this work for the NMP + hydrocarbon binary systems. The characteristics of both EOS are widely known and details about their application can be found in the original works, thus they are not described here in detail. The application of both EOS requires the introduction of adequate mixing rules, in this work two different mixing rules are applied for SAFT (one monoparametric and another one biparametric) and a single monoparametric one for PC-SAFT. For SAFT EOS, both mixing rules were previously described (mixing rule I and mixing rule III in Ref. [36]). For the monoparametric rule, a binary interaction parameter, BIP, k12 , is introduced to correct the segment energy, u/kT, Eq. (22), whereas in the biparametric mixing rule an additional term, l12 , is considered for the average segment number of mixtures, m, Eq. (23). u12 = (u11 u22 )1/2 (1 − k12 ) m12 =

(22)

m1 + m2 (1 − l12 ) 2

(23)

Table 6 Pure compound parameters used for SAFT and PC-SAFT calculations SAFT v00 (mL mol−1 )

NMP n-Hexane n-Octane n-Decane Cyclohexane Cyclooctane 2-Methylpentane 3-Methylpentane Isooctane 2,2-Dimethylbutane 2,3-Dimethylbutane

9.044 12.475 12.234 11.723 13.502 15.081 12.941 12.514 13.970 13.700 12.775

PC-SAFT m

6.4105 4.7240 6.0450 7.5270 3.9700 4.5734 4.5438 4.6296 5.4998 4.3378 4.5651

u0 /k (K)

246.21 202.72 206.03 205.46 236.41 260.01 201.99 202.10 199.96 200.01 200.10

AAD (%) Psat

sat liq

7.10 2.30 1.60 2.20 0.68 0.06 0.10 0.06 0.17 0.11 0.10

15.77 3.50 3.40 3.50 1.00 0.16 0.25 0.15 0.36 0.23 0.19

T range (K)

278–358 243–493 303–543 313–573 283–513 288–466 289.463 283–483 282–484 274–451 275–472

Literature source

m

(1) (2) (2) (2) (2) (4) (4) (4) (4) (4) (4)

3.7424 3.0576 3.8176 4.6627 2.5303 2.9292 2.9317 2.8852 4.1194 2.6008 2.6853

˚  (A)

3.6285 3.7983 3.8373 3.8384 3.8499 3.9809 3.8535 3.8605 3.0805 4.0042 3.9545

ε/k (K)

302.90 236.77 242.78 243.87 278.11 304.53 235.58 240.48 252.40 243.51 246.07

AAD (%) Psat

sat liq

7.23 0.31 0.77 0.24 0.53 0.24 0.61 0.33 1.37 0.32 0.38

12.73 0.76 1.59 1.18 3.12 0.07 0.59 0.65 0.33 0.21 0.46

T range (K)

Literature source

278–358 177–503 216–569 243–617 279–553 288–466 119–498 110–504 282–484 174–488 145–500

(1) (3) (3) (3) (3) (4) (3) (3) (4) (3) (3)

(1) Parameters obtained in this work from saturation pressure experimental data, Ref. [1], and compressed liquid density data, Ref. [37], extrapolated to saturation conditions, Ref. [1], forced to reproduce experimental critical point, Ref. [1]; (2) Huang et al. [38]; (3) Gross et al. [18]; and (4) parameters obtained in this work from Smith and Srivastava experimental saturation data, Ref. [39].

Fig. 8. (a) Isobaric (ambient pressure) liquid–liquid and (b) isothermal vapour–liquid equilibria diagrams for NMP (1) + n-hexane (2). Vapour–liquid experimental data from Gierycz et al. [34] (䊉) at 333.25 K and at () 343.15 K. Predicted values from (—) SAFT, and (- - -) PC-SAFT EOS with k12 = 0.0493 (SAFT) and k12 = 0.0426 (PC-SAFT). k12 are considered temperature independent and used both for liquid–liquid and vapour–liquid calculations.

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R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100

For PC-SAFT a single monoparametric mixing rule is studied in which a BIP, k12 , is considered to correct the segment–segment interaction of unlike chains, Eq. (24). ε12 =

√

ε1 ε2 (1 − k12 )

Table 7 Temperature linear dependence (k12 = A0 + A1 T) of binary interaction parameters, k12 , for the monoparametric mixing rule used in the calculation of isobaric (ambient pressure) liquid–liquid equilibria for the NMP (1) + hydrocarbon (2) systems SAFT

(24)

The application of both models requires the knowledge of pure fluids parameters which are reported in Table 6. Most of them are obtained from the original SAFT and PC-SAFT works and when not available they are obtained from simultaneous fittings to experimental vapour pressure and saturated liquid density data. From the results reported in Table 6 we may conclude that both models correlate successfully the saturation data of the studied compounds in the wide pressure and temperature ranges considered. The case of NMP parameters requires a more detailed attention, for this fluid, experimental saturation pressure data are available but saturated liquid density data are absent, thus, in a previous work we calculated the saturated liquid density data by extrapolation of compressed liquid data to the experimental pressure–temperature saturation conditions [37], then a simultaneous fitting of both experimental saturation pressure and extrapolated saturated liquid density data was done in order to obtain EOS parameters. With the NMP parameters obtained in this way, we calculate the liquid–liquid equilibria for the studied mixtures but too high deviations are obtained mainly in the NMP rich phase compositions. In order to decrease these deviations, we refit the NMP parameters forcing EOS to reproduce the critical properties of the fluid; thus, the parameters reported in Table 6 were obtained with this procedure and used for the remaining phase equilibria calculations. In a first attempt, we try to correlate the miscibility data with a single temperature independent BIP for both EOS, results obtained with this approach are reported in Fig. 8a for the NMP + n-hexane system although similar results are obtained for the remaining mixtures. Although the NMP rich branch together with the region close to the upper critical solution temperature (UCST) are properly reproduced, the hydrocarbon rich branch is poorly correlated by both EOS and higher NMP molar fractions for the hydrocarbon rich phases are obtained for all the studied systems. With the single BIPs obtained from the liquid–liquid equilibria correlation we have predicted the available literature experimental vapourequilibria data for NMP + n-hexane mixture, the results reported

n-Hexane n-Octane n-Decane Cyclohexane Cyclooctane 2-Methylpentane 3-Methylpentane Isooctane 2,2-Dimethylbutane 2,3-Dimethylbutane

PC-SAFT

A0

A1

A0

A1

0.186292 0.201806 0.294832 0.245054 0.350414 0.163706 0.146762 0.206086 0.155299 0.186889

−0.000420 −0.000464 −0.000738 −0.000620 −0.000932 −0.000341 −0.000300 −0.000488 −0.000324 −0.000444

0.190826 0.181483 0.264882 0.199578 0.248623 0.145916 0.131128 0.166688 0.133052 0.164113

−0.000457 −0.000426 −0.000669 −0.000518 −0.000692 −0.000318 −0.000276 −0.000395 −0.000290 −0.000394

in Fig. 8b show that both EOS give rise to remarkable deviations for the two studied temperatures. Thus, the use of a monoparametric mixing rule, with temperature independent BIPs, produce similar results for both EOS with correlations and/or predictions not accurate enough. In order to improve the correlative ability of both EOS we consider temperature BIPs, in Fig. 9 we show the results within this approach. The BIPs reported in Fig. 9b show an almost linear trend and thus a linear function, Table 7, is used in order to calculate the liquid–liquid equilibria. The results obtained with this method give rise to a remarkable improvement in the hydrocarbon rich phase correlations whereas in the NMP rich phase the results are worse. The region in the vicinity of UCST is properly described although the molar fraction of the UCST is over predicted. Similar results are obtained for all the studied NMP + hydrocarbon binary systems, Fig. 10. Finally, we have studied the quality of SAFT EOS correlation considering the biparametric mixing rule, with temperature dependent BIPs. Results reported in Fig. 11 show a linear temperature dependence of the two BIPs, accurate correlations are obtained with this approach for both phases in equilibrium and also in the critical region. Thus, we may conclude that the correlation of liquid–liquid equilibria for NMP + hydrocarbon mixtures requires the use of

Fig. 9. (a) Isobaric (ambient pressure) liquid–liquid equilibrium diagram for NMP (1) + n-hexane (2), (䊉) experimental values and calculated with (—) SAFT, and (- - -) PC-SAFT EOS with k12 temperature dependent parameters, Table 7. (b) k12 as a function of temperature together with linear fittings, Table 7, for (—) SAFT, and (- - -) PC-SAFT EOS.

R. Alcalde et al. / Fluid Phase Equilibria 266 (2008) 90–100

99

Fig. 10. Isobaric (ambient pressure) liquid–liquid equilibrium diagram for NMP (1) + hydrocarbon (2) calculated with (—) SAFT, and (- - -) PC-SAFT EOS with k12 temperature dependent parameters according to the linear dependence reported in Table 7.

Fig. 11. (a) Isobaric (ambient pressure) liquid–liquid equilibrium diagram for NMP (1) + n-hexane (2) calculated with (—) SAFT EOS with k12 and l12 temperature dependent parameters. (b) k12 and l12 as a function of temperature together with linear fittings for (—) SAFT EOS.

complex mixing rules. Both EOS give arise to similar results and unsuccessful results are obtained if only a single BIP is considered, constant or temperature dependent, whereas the use of biparametric mixing rule with temperature dependent parameters produce very accurate correlations. 5. Concluding remarks Liquid–liquid equilibria for the NMP + hydrocarbons and NCP + water binary mixtures are measured at ambient pressure. Our results are in good agreement with experimental values when available and small deviations may be justified considering the different water content of the samples. For the NMP + hydrocarbon mixtures remarkable effect rising from the size and shape of the

involved hydrocarbon may be inferred. The mixture NCP + water shows a complex behaviour wit a LCST at low NCP mole fractions pointing to the formation of microheterogenities. NRTL and UNIQUAC, with temperature dependent parameters, show good correlative ability for the studied systems and their predictive ability for vapour–liquid equilibria is accurate enough. Data correlation using SAFT and PC-SAFT EOS is strongly dependent on the chosen mixing rule, a complex one with temperature dependent parameters is required to obtain accurate results. List of symbols A fitting parameter, Eq. (5) A12 , A21 fitting parameter, Eqs. (11), (12), (20) and (21) AAD average absolute deviation, Eq. (4)

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B fitting parameter, Eq. (5) B12 , B21 fitting parameter, Eqs. (11), (12), (20) and (21) BIP binary interaction parameter C fitting parameter, Eq. (5) C12 , C21 fitting parameter, Eqs. (11), (12), (20) and (21) D fitting parameter, Eq. (5) D12 , D21 fitting parameter, Eqs. (11), (12), (20) and (21) E fitting parameter, Eq. (5) EOS equation of state F fitting parameter, Eq. (5) k fitting parameter, Eqs. (1)–(3) k12 binary interaction parameter, Eqs. (22) and (23) l12 binary interaction parameter, Eqs. (22) and (23) LCST lower critical solution temperature m fitting parameter, Eqs. (1)–(3) NCP N-cyclohexyl-2-pyrrolidone NMP N-methyl-2-pyrrolidone NRTL non-random two liquid model PC-SAFT perturbed-chain statistical associating fluid SAFT statistical associating fluid theory T temperature UCST upper critical solution temperature UNIQUAC Universal quasi-chemical model xi mole fraction for i-th compound Greek letter  fitting parameter, Eqs. (1)–(3) Subscripts and supercripts c critical property E excess property i i-th compound m mixing property Acknowledgements ´ The financial support by Junta de Castilla y Leon, Pro´ y Ciencia, Project ject BU020A07, and Ministerio de Educacion CTQ2005-06611/PPQ, (Spain), is gratefully acknowledged. References [1] G. Hradetzky, I. Hammerl, H.J. Bittrich, K. Wehner, W. Kisan, Selective Solvents. Physical Sciences Data 31, Elsevier, 1989. [2] A. Henni, J.J. Hromek, P. Tontiwachwuthikul, A. Chakma, J. Chem. Eng. Data 49 (2004) 231–234.

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