Phase behavior of the binary system ethane+linalool

Journal of Supercritical Fluids 24 (2002) 111– 121 www.elsevier.com/locate/supflu

Phase behavior of the binary system ethane+linalool S. Raeissi a, J.C. Asensi b, C.J. Peters a,* a

Delft Uni6ersity of Technology, Faculty of Applied Sciences, Laboratory of Applied Thermodynamics and Phase Equilibria, Julianalaan 136, 2628 BL Delft, Netherlands b Departamento de Ingenierı´a Quı´mica, Uni6ersidad de Alicante, Apdo 99, Alicante, Spain Received 9 August 2001; received in revised form 5 February 2002; accepted 9 February 2002

Abstract As part of a study to assess the capacity of supercritical fluids in deterpenating citrus essential oils, high-pressure vapor–liquid equilibria of the binary system ethane + linalool were determined experimentally. Bubble and dew points were measured at ethane mole fractions ranging from 0.2 to 0.9998 and within temperature and pressure ranges of 278–368 K and 2.6–11.4 MPa, respectively. This binary system also exhibited a region of liquid– liquid two-phase split, resulting in the presence of a three-phase liquid– liquid– vapor equilibrium. Experimental values of the upper and lower critical endpoints, in addition to normal critical points are presented. From the experimental results it could be concluded that the system ethane +linalool shows type-V fluid phase behavior in the classification of Van Konynenburg and Scott. The experimental results also show the interesting phenomenon of double retrograde vaporization, in which the dew point curve has a double-domed shape. In this limited region, increasing the pressure at fixed concentration results in triple- or quadruple-valued dew points. The experimental results were correlated by the Stryjek–Vera modified version of the Peng–Robinson equation of state using the Mathias– Klotz– Prausnitz mixing rule. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Ethane; Linalool; Citrus peel oil; Vapor–liquid equilibrium; Critical point; Peng– Robinson– Stryjek– Vera (PRSV) equation of state; Double retrograde vaporization

Nomenclature A a B b g

more volatile component equation of state constant less volatile component equation of state constant gaseous phase

* Corresponding author. Tel.: + 31-15-278-2660; fax: + 31-15-278-8047. E-mail address: [email protected] (C.J. Peters). 0896-8446/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 8 9 6 - 8 4 4 6 ( 0 2 ) 0 0 0 3 5 - 9

S. Raeissi et al. / J. of Supercritical Fluids 24 (2002) 111–121

112

kij lij l N P R s T LCEP UCEP x y

binary interaction parameter binary interaction parameter liquid phase number of components pressure universal gas constant solid phase temperature lower critical endpoint upper critical endpoint mole fraction in liquid phase mole fraction in vapor phase

Greek letters h temperature-dependent equation of state parameter s Peng–Robinson equation parameter s0 PRSV equation parameter s1 PRSV equation parameter w molar volume … Pitzer acentric factor Subscripts c critical i species i j species j r reduced Superscripts cal calculated exp experimental

1. Introduction Supercritical deterpenation of citrus oils has been the subject of much research in the past two decades. However, in all this research, it is carbon dioxide that is used as the supercritical fluid [1–12]. As part of a study to investigate the possibility of using ethane as an alternative supercritical fluid [13– 15], this work focuses on the phase behavior of linalool, one of the aroma compounds of citrus oils, in ethane. Experimental phase behavior data are presented for the

binary system of ethane+ linalool within a temperature and pressure range of 278–368 K and 2.6–11.4 MPa, respectively. The data are modeled using the Stryjek– Vera modified version of the Peng–Robinson (PRSV) equation of state using the Mathias–Klotz–Prausnitz mixing rule.

2. Phase behavior As will be discussed in more detail later, the system ethane+ linalool shows both a lower

S. Raeissi et al. / J. of Supercritical Fluids 24 (2002) 111–121

critical endpoint (LCEP) of the nature l1 =l2 + g, and an upper critical endpoint (UCEP) of the nature l1 = g+l2. Therefore, the fluid phase behavior of the system most likely belongs to type-V in the classification of Van Konynenburg and Scott [16]. Fig. 1 shows a schematical p,T,x-projection of type-V fluid phase behavior. Although no measurements have been carried out with the solid linalool phase (sB) in this work, to show the general phase behavior of such systems, Fig. 1 also schematically shows the triple point (filled triangle) of the pure component B (linalool), together with the three twophase lines solid–gas (sBg), solid– liquid (sBl) and liquid–vapor (lg(B)) of pure component B. The saturated vapor pressure curve of the more volatile component A (ethane) is indicated by lg(A). Characteristic of this type of fluid phase behavior is the presence of a three-phase equilibrium l1l2g in the vicinity of the critical point of component A (ethane). The p,T-part of this phase diagram (upper part of Fig. 1) also in-

Fig. 1. Schematical P,T,x projection of the phase behavior of the binary system ethane (A) + linalool (B).

113

cludes the higher temperature part of the binary three-phase locus solid B-liquid–vapor (sBlg), which ends in the triple point of component B. The T,x-part of the figure (lower part of Fig. 1) provides information on the composition of the coexisting phases as a function of temperature of the various three-phase equilibria as far as shown in this diagram.

3. Experimental The Cailletet apparatus used for performing phase behavior experiments, operates according to the synthetic method. At any desired temperature, the pressure is varied for a sample of constant overall composition until a phase change is observed visually. A sample of fixed known composition is confined over mercury in the sealed end of a thick walled Pyrex glass tube. The open end of the tube is placed in an autoclave and immersed in mercury. Thus, mercury is used for both sealing and transmitting pressure to the sample. The sample is stirred by a stainless steel ball, of which the movement is activated by reciprocating magnets. The autoclave is connected to a hydraulic oil system, generating the pressure by means of a screw type hand pump. A dead weight pressure gauge is used to measure the pressure inside the autoclave with an accuracy of 0.03% of the reading. The temperature of the sample is kept constant by circulating thermostat liquid through a glass thermostat jacket surrounding the glass tube. The thermostat bath is capable of maintaining the thermostat liquid at the desired temperature with a constancy better than 90.01 K. A platinum resistance thermometer, located close to the sample-containing part of the Cailletet tube, records the temperature of the thermostat liquid with a maximum error of 0.02 K. Further details of the apparatus and experimental procedure may be found elsewhere [12,17]. Linalool (purity ] 97%) and ethane (purity 99.95 vol%) were purchased from Fluka and Messer Griesheim, respectively, and were used without further purification.

S. Raeissi et al. / J. of Supercritical Fluids 24 (2002) 111–121

114

4. Correlation The Peng –Robinson equation of state [18] is used to calculate the vapor– liquid equilibria: RT a P= − (1) 6− b 6(6 +b)+ b(6 −b) The constants a and b can be obtained from the pure fluid critical properties using a= 0.457235

R 2T 2c h Pc

(2)

b= 0.077796

RTc Pc

(3)

h = [1+ s(1− T/Tc)]2

(4)

where Tc and Pc are the critical temperature and pressure, respectively. The parameter s is calculated according to the equations of Stryjek and Vera [19] to provide more accurate vapor pressure correlations: s= s0 +s1(1+ T 0.5 r )(0.7 − Tr)

(5)

s0 = 0.378893+1.4897153… − 0.17131848… +0.0196554… 3

2

(6)

Tr is the reduced temperature and … is the Pitzer acentric factor. The mixing rule of Mathias– Klotz –Prausnitz [20] is used as follows: N

N

a= % % xi xj ai aj (1 − kij ) i = 1j = 1 N



N

+ % xi % xj ( ai ajlji )1/3 i=1



3

(7)

j=1

b= %xi bi

(8)

i

kij and lji are the binary interaction parameters where kij = kji and lji = − lij.

5. Results and discussion Table 1 summarizes all the different types of experimentally measured phase transition temperatures and pressures for the binary system ethane +linalool at 14 different overall composi-

tions. Within a certain concentration range, a liquid–liquid two-phase split was observed resulting in the presence of a three-phase liquid– liquid–vapor (l1l2g) equilibrium. The data presented in Table 1 indicate that the system ethane+ linalool has a LCEP of the nature l1 = l2 + g at (314.5 K and 5.57 MPa), and also an UCEP of the nature l1 = g+l2 at (316.0 K and 5.75 MPa). Therefore, most likely the fluid phase behavior of the system belongs to type-V in the classification of Van Konynenburg and Scott, although type-IV should not be excluded as a possibility. Fig. 2 shows, as an example, the P,T diagram of the 96.03 mole% ethane isopleth. For a binary system, the Gibb’s phase rule prescribes that the three-phase equilibrium l1l2g should appear as a line in a P,T diagram. However, an enlargement of the three-phase region (see also Fig. 2) indicates that there is a very narrow three-phase area, instead of a line. In addition, the phase rule also dictates that there are no degrees of freedom for the LCEP and UCEP of the three-phase equilibrium l1l2g. Nevertheless, Table 1 indicates a maximum difference in the P,T co-ordinates of the UCEP of 0.021 MPa and of 0.14 K, respectively. Both of these discrepancies may be the result of impurities in the chemicals; especially linalool is suspected for that. An interesting phenomenon has been observed in the samples highest in ethane concentration. When the pressure is decreased at constant composition and temperature, the following sequence of phase transitions occur: vapor“ vapor+liquid“ vapor “vapor + liquid, and if it were experimentally possible to go to even lower pressures, there would even be another transition from vapor+ liquid to vapor. This phenomenon is called double retrograde vaporization and is shown schematically in Fig. 3a. Parts of the experimental dew point curves of ethane+linalool exhibiting double retrograde vaporization are shown graphically in Fig. 3b. This type of phase behavior occurs at very high concentrations of the more volatile component at temperatures very close to the critical temper-

l1 = l2+g l1 = g+l2

98.00 l+g“ l l+g“g

l1l2g upper boundary

l1 = l2+g l1 = g+l2 l1l2g lower boundary

l+g“g

l= g l+g“g 96.03 l+g“ l

91.49 l+g“l

80.95 l+g“l

59.90 l+g“l

39.92 l+g“ l

19.95 l+g“l

% Ethane

4.337 6.044 8.719 5.570 5.738

2.808 5.458 5.533 5.804 7.379 5.574 5.759 5.533 5.574 5.659 5.533 5.728 5.759

280.41 313.19 313.90 315.73 327.63 314.48 316.09 313.99 314.45 315.25 313.89 315.76 316.09

300.98 318.10 343.18 314.58 315.95

2.628 5.404 7.240 8.675 8.830 8.956 9.126

3.224 8.535

2.786 5.616

2.087 3.187

1.054 1.545

P (MPa)

278.08 313.02 327.04 338.94 340.31 341.49 343.06

288.23 342.69

289.08 333.18

293.34 322.86

293.18 323.15

T (K)

308.65 320.45 315.10

314.16 314.46 316.10 314.05 316.01 316.15

313.99 316.10 332.92

283.25

347.83

282.96 317.61 329.61 339.03 340.85

293.13 352.90

292.82 342.48

297.67 332.64

297.92 333.35

T (K)

5.028 6.353 5.662

5.544 5.574 5.756 5.553 5.754 5.764

5.548 5.853 7.999

2.988

9.616

2.928 5.960 7.565 8.685 8.885

3.569 9.570

2.996 6.251

2.237 3.567

1.129 1.715

P (MPa)

312.96 322.83 315.38

314.15 316.07

314.26 314.47

314.41 316.20 337.69

293.15

350.85

287.80 322.87 331.04 339.09 341.08

302.95 362.98

297.46 302.86

302.97 343.07

303.26 343.35

T (K)

5.443 6.633 5.697

5.558 5.756

5.554 5.574

5.603 5.863 8.514

3.688

9.916

3.253 6.694 7.745 8.695 8.916

4.344 10.495

3.261 3.586

2.432 3.977

1.214 1.885

P (MPa)

315.02 327.80 315.95

314.27 316.07

314.31 314.50

314.58 316.48 342.67

303.03

352.94

293.27 324.39 333.14 339.23

312.91 369.65

302.95

307.74

307.96

T (K)

5.644 7.203 5.773

5.568 5.759

5.559 5.576

5.634 5.903 9.019

4.493

10.116

3.648 6.895 8.000 8.705

5.260 11.050

3.586

2.612

1.290

P (MPa)

314.93 333.02 314.52

314.39 316.08

314.41 314.73

314.75 317.99 348.25

307.97

359.72

297.79 324.50 334.98 339.54

322.84

313.08

313.03

313.35

T (K)

Table 1 Experimental bubble points, critical points and dew points for the system ethane+linalool at fixed molar compositions

5.637 7.773 5.607

5.588 5.759

5.569 5.599

5.664 6.118 9.554

4.943

10.726

4.004 6.905 8.220 8.740

6.315

4.231

2.807

1.380

P (MPa)

337.61

315.25 316.08

314.44 314.90

315.02 322.89

312.79

367.62

303.13 325.22 337.11 339.75

332.93

323.00

317.46

317.86

T (K)

8.223

5.673 5.759

5.574 5.619

5.704 6.773

5.418

11.371

4.449 7.000 8.465 8.765

7.465

4.891

2.977

1.455

P (MPa)

S. Raeissi et al. / J. of Supercritical Fluids 24 (2002) 111–121 115

99.92 l+g“ l l= g l+g“ g

l= g l+g“ g

99.88 l+g“ l

l=g l+g“g

99.79 l+g“ l

l =g l+g“g

99.59 l+g“l

l =g l+g“g

99.31 l+g“ l

293.06 306.00 306.00

293.16 306.64 306.65 306.66 308.21 314.17 320.29 325.67 330.26 336.77

281.84 307.34 307.41 307.43 322.80 346.87

293.51 309.35 309.45 309.58 313.00 322.89 337.37

294.03 313.38 314.06 314.06 314.50 343.06

314.27 314.65 315.10 314.11 314.93

l1l2g lower boundary

l1l2g upper boundary

T (K)

% Ethane

Table 1 (continued)

3.785 4.937 4.937

3.787 4.980 4.980 4.980 5.008 5.289 5.500 5.547 5.508 5.420

2.971 5.049 5.052 5.054 5.958 6.114

3.814 5.202 5.212 5.222 5.508 6.383 7.260

3.806 5.503 5.563 5.563 5.598 8.155

5.539 5.580 5.624 5.538 5.628

P (MPa)

4.181 4.942

306.04

4.986 5.018 5.335 5.516 5.537 5.498 5.376

4.173

5.075 6.129 5.865

3.391 5.049

5.242 5.573 6.544 7.360

4.165 5.207

5.563 5.919 8.656

4.121 5.528

5.547 5.585 5.654 5.548 5.682

P (MPa)

297.80

306.78 308.67 315.23 321.35 326.75 331.48 337.86

297.82

307.76 327.48 352.27

287.87 307.39

309.86 313.61 324.81 340.25

297.73 309.43

314.08 317.50 352.95

297.90 313.66

314.35 314.69 315.39 314.17 315.38

T (K)

306.09

302.94

307.16 309.60 316.18 322.39 327.86 332.42

303.20

308.13 332.74

293.07 307.40

310.07 314.76 327.67 342.84

303.09

314.09 323.28 362.35

303.00 313.95

314.39 314.87 315.95 314.26 315.95

T (K)

4.947

4.651

5.011 5.059 5.370 5.521 5.532 5.489

4.663

5.100 6.220

3.796 5.054

5.257 5.683 6.729 7.460

4.645

5.566 6.529 8.932

4.561 5.553

5.549 5.600 5.719 5.567 5.737

P (MPa)

306.17

303.69

307.50 310.66 317.18 323.46 328.15 333.53

304.74

308.20 337.50

303.05 307.41

310.68 316.64 330.09 345.13

307.95

314.13 327.60

307.89

314.40 315.98

314.58 314.93

T (K)

4.942

4.721

5.017 5.124 5.410 5.536 5.523 5.484

4.809

5.100 6.261

4.662 5.052

5.302 5.858 6.884 7.461

5.091

5.568 6.954

5.007

5.587 5.743

5.570 5.609

P (MPa)

306.20

305.91

307.59 311.66 318.07 324.41 329.09 334.74

306.38

313.02 342.09

307.27

311.06 318.76 332.82 346.74

309.08

314.20 333.13

313.01

314.52 316.03

314.58 315.09

T (K)

4.948

4.937

5.017 5.169 5.425 5.547 5.513 5.459

4.960

5.402 6.212

5.044

5.332 6.038 7.059 7.461

5.182

5.578 7.429

5.473

5.597 5.748

5.572 5.625

P (MPa)

306.22

305.97

307.88 313.28 319.24 325.62 329.37 335.78

306.63

317.48 342.71

307.32

311.78 320.34 334.92 353.21

309.28

314.29 337.35

313.21

314.58 316.17

314.58 315.10

T (K)

4.948

4.937

5.013 5.244 5.470 5.552 5.503 5.439

4.980

5.692 6.162

5.044

5.387 6.178 7.159 7.462

5.197

5.583 7.779

5.488

5.605 5.759

5.570 5.648

P (MPa)

116 S. Raeissi et al. / J. of Supercritical Fluids 24 (2002) 111–121

278.58 303.11 305.58 305.60 305.63 298.10 301.70 304.79

2.741 4.668 4.907 4.908 4.910 3.999 4.446 4.802

3.762 4.862 4.929 4.931 4.935 4.939 4.698 4.807 4.906 4.634 4.621 4.641 4.676 4.727 4.714 4.572 4.421

4.943 4.750 4.854 4.720 4.701 4.755 4.871 5.007

306.23 305.19 305.77 305.19 305.97 307.51 310.81 319.93

292.77 305.11 305.85 305.93 305.93 306.09 304.68 305.33 305.95 304.68 305.15 305.80 307.03 309.28 314.36 320.34 323.19

P (MPa)

T (K)

305.60 298.14 302.82 305.01

283.14 304.17

305.94 306.10 304.69 305.56 305.99 304.69 305.25 306.02 307.30 309.96 315.33 321.44

294.96 305.63 305.88

306.23 305.26 305.96 305.26 306.08 307.95 311.65 323.08

T (K)

4.910 4.000 4.575 4.832

3.046 4.773

4.931 4.940 4.699 4.842 4.911 4.655 4.626 4.646 4.682 4.742 4.714 4.538

3.942 4.910 4.929

4.948 4.770 4.889 4.681 4.706 4.770 4.896 4.958

P (MPa)

305.62 299.21 303.38 305.18

288.30 305.43

305.97 306.10 304.71 305.66 306.06 304.71 305.30 306.24 307.54 310.46 316.38 321.86

298.00 305.66

305.34 306.15 305.32 306.40 308.41 313.02 324.18

T (K)

4.910 4.129 4.644 4.852

3.411 4.904

4.934 4.938 4.703 4.857 4.926 4.639 4.626 4.651 4.687 4.752 4.695 4.503

4.202 4.918

4.790 4.923 4.681 4.715 4.785 4.921 4.908

P (MPa)

300.10 303.72 305.34

293.17 305.01

304.76 305.83 306.08 304.80 305.47 306.41 307.76 311.41 317.39 321.99

306.00

300.57 305.68

305.41 306.17 305.41 306.57 309.03 314.73 327.01

T (K)

4.268 4.679 4.866

3.792 4.858

4.714 4.886 4.930 4.645 4.631 4.661 4.692 4.758 4.680 4.444

4.939

4.427 4.915

4.799 4.928 4.680 4.720 4.810 4.981 4.883

P (MPa)

300.88 304.17 305.46

297.64 305.54

304.81 305.87 306.09 304.81 305.53 306.65 308.10 312.41 318.38 322.44

306.01

303.04 305.79

305.65 306.18 305.46 306.79 309.59 314.81 329.51

T (K)

4.362 4.733 4.881

4.167 4.904

4.724 4.891 4.932 4.635 4.636 4.671 4.707 4.743 4.641 4.394

4.939

4.663 4.925

4.829 4.933 4.676 4.730 4.831 4.981 4.859

P (MPa)

301.20 304.45 305.63

300.59 305.57

305.11 306.00 306.10 305.04 305.64 306.86 308.66 313.42 319.39 322.45

306.06

304.77 305.80

305.73 306.22 305.71 307.07 310.14 317.43

T (K)

4.396 4.763 4.907

4.437 4.910

4.768 4.939 4.933 4.620 4.636 4.671 4.717 4.724 4.606 4.369

4.939

4.828 4.929

4.844 4.943 4.696 4.735 4.851 5.006

P (MPa)

l and g symbolize liquid and vapor phases, respectively. Subscripts 1 and 2 symbolize the lighter and heavier liquid phase, respectively. The type of transition is given upon increasing pressure. For example ‘‘l+g“ l’’ indicates a transition from liquid+vapor to liquid by increasing pressure. The ‘‘equal sign’’ indicates a critical point.

l =g l+g“ g g“l+g

99.98 l+g“l

l+g“g

g“ l+g

l= g l+g“ g

99.95 l+g“ l

l+g“ g

g“ l+g

% Ethane

Table 1 (continued)

S. Raeissi et al. / J. of Supercritical Fluids 24 (2002) 111–121 117

S. Raeissi et al. / J. of Supercritical Fluids 24 (2002) 111–121

118

Table 2 Bubble point and dew pressures of the system ethane+linalool at specified temperatures (the points indicated by * are dew points, all other points are bubble points) Mole% ethane

Pressure (MPa) Temperature (K)

99.98 99.95 99.92 99.88 99.79 99.59 99.31 98.00 96.03 91.49 80.95 59.90 39.92 19.95

293.15

303.15

313.15

323.15

333.15

343.15

3.791 3.792 3.792 3.784 3.808 3.785 3.730 3.688 3.683 3.615 3.554 3.011 2.077 1.053

4.675 4.670 4.669 4.655 4.679 4.651 4.578 4.527 4.507 4.448 4.351 3.609 2.441 1.211

– 4.738* 4.942* 5.251* 5.438* 5.535* 5.482* 5.460* 5.451* 5.505 5.306 4.238 2.815 1.375

– 4.376* 4.948* 5.526* 5.961* 6.400* 6.517* 6.673* 6.812* 6.730 6.364 4.899 3.197 1.542

– – – 5.479* 6.226* 7.068* 7.445* 7.778* 8.023* 7.996 7.469 5.591 3.587 1.711

– – – – 6.191* 7.452* 8.171* 8.721* 9.065* 9.164* 8.568 6.312 3.983 1.880

ature of the more volatile component. Fig. 3b also illustrates the gradual transition in the shape of the dew point curve from the usual single-dome to the double-dome of double retrograde vaporization as the concentration appro-aches closer and closer to pure ethane. The authors are aware that within the region that double retrograde vaporization occurs, the impurities of the chemicals may cause slight errors, shifting the measured data compared to that of 100% pure chemicals. But the impurities do not affect the occurrence of double retrograde vaporization, or the trend of changes in the shape of the dew point curves as it progresses from single-dome to double-dome. Detailed explanation of double retrograde vaporization in this system is given elsewhere [15]. The measurements presented in Table 1 are in the form of P,T data at constant composition, but for modeling purposes it would be more convenient to have P,x,y data at constant temperature. For this reason, Table 2 presents

correlated P,x,y data at six different temperatures. These data are graphically shown in Fig. 4. Double retrograde vaporization is not observed in this graph because the temperatures of the isotherms are too far away from the critical temperature of pure ethane. The data are simulated using the program PE [21], applying the equations of Section 4, and the pure component properties as summarized in Table 3. The optimized values of the binary

Table 3 Pure component properties used in the simulation Substance

Tc (K)

Pc (MPa)

…

s1

Ethane Linalool

305.32a 630.5c

4.87a 2.42c

0.106a 0.748c

1.0×10−6b −0.3727d

a

Ref. [22]. Data bank of Ref. [21]. c Ref. [8]. d Estimated using Ref. [21] by fitting to vapor pressure data of [23] from 313 to 471 K. b

S. Raeissi et al. / J. of Supercritical Fluids 24 (2002) 111–121

Fig. 2. Pressure – temperature diagram at a constant composition of 96.03% ethane for the binary system ethane + linalool. The three phase region is enlarged in the lower graph.

Table 4 Calculated binary interaction parameters and deviations between experimental and calculated values for the PRSV EOS using the Mathias–Klotz–Prausnitz mixing rule T (K)

k12

l12

AAD%

313.15 323.15 333.15 343.15

0.0643 0.0732 0.0769 0.0765

0.0166 0.0407 0.0557 0.0589

0.32 0.79 1.31 1.11

1 denotes ethane and 2 denotes linalool. AAD%=

100 N exp % x i −x cal i N i

where N is the number of data points.

119

Fig. 3. (a) Schematic diagram of double retrograde vaporization behavior. The dashed and solid curves represent bubble point and dew point curves, respectively, and the filled circle symbolizes the critical point. (b) Experimental pressure – temperature isopleths for five different concentrations of the binary system ethane +linalool. Concentrations are given in mole% ethane.

interaction parameters kij and lij are given in Table 4, along with the estimated deviations from the experimental bubble point data. The correlation results are compared to the experimental values in Fig. 5 for four selected temperatures. It is shown that the PRSV equation of state using the Mathias–Klotz –Prausnitz mixing rule gives satisfactory results for the binary system ethane+ linalool.

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Fig. 4. Experimental bubble point and dew point pressures for the system ethane +linalool at six selected temperatures.

Fig. 5. Correlated and experimental vapor –liquid equilibria for the system ethane + linalool at 313.15, 323.15, 333.15, 343.15 K. The points represent experimental data and the curves are correlated using the PRSV EOS.

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