Figure 2.

hE values for the binary acetone(1) + ethanol(2). (a) p = 101.32 kPa; (b) p = 400 kPa. (○) Ref. [20]; (�) Ref. [21]; (□) Ref. [22]; (+) Ref. [23]; (△) Ref. [24]; (◊) Ref. [25].

## Figure 3.

Plot of iso-p VLE data of the binary benzene + hexane at 101 kPa. (a) T,x,y; (b) γ,x; g<sup>E</sup> /RT,x. (○) Ref. [34] Ref. [35] (+) Ref. [26] (◊) Ref. [37]; (�) Ref. [29]; (∇) Ref. [32]; (▷) Ref. [31]; (◁) Ref. [37].

Figure 4 depicts the iso-p data set at pressures other than the atmospheric. Figure 5(b) indicates that three of the published series [28] (the ones that correspond to p = 610.8 kPa, 810.8 kPa, and 1013.5 kPa) show systematic errors, giving rise to g E /RT < 0; thus γ<sup>i</sup> < 1 as x<sup>1</sup> ! 1. However, the representation of T vs x,y does not reflect this anomalous behavior, so that probably they will be caused by a systematic deficiency in the monitored temperature.

Available iso-T data series are represented in Figure 5. Data are found for the whole composition interval only at 333 and 345 K. Several series were measured at 333 K [40–42], allowing their comparison. From the representation of p,x,y (Figure 5(a)) and related mixing quantities (Figure 5(b)), an acceptable coincidence is observed. Two of the data sets (Ref. [41]) show negative values of g E /RT in the extreme points, at infinite dilution, which is a clear sign of inconsistency.

Conclusions drawn from the visual inspection are confirmed by the consistency analysis presented in Table 2. Data series n° 11 is discarded since consistency cannot be evaluated due to the lack of data in the zone corresponding to x<sup>1</sup> > 0.2. All consistency tests, except the direct van Ness, did not accept the series measured at

N°

52

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Limiting values: areas-test: d < 2;

notation: V

Table 1. Values obtained in the application

 of the

thermodynamic

consistency-test

 to VLE data of acetone + ethanol at different conditions.

!

verified; FV

! fully verified. Test outcome: v

 19

 Iso-363 K

 0.2 Fredenslund-test:

 δy�100 < 1;

!

verified; nv

! not verified; nd/� ! not available.

 v

 0.2

 v Wisniak-test:

 Dw < 3; Kojima-test:

 M(I )i < 30; Direct Van Ness-test: δ(ln γ1/ln γ2) < 0.16; proposed-test:

 2.5

 v

 19

 v

 0.01

 v

 0.83

 v

 0.029

 f-int > 0, f-dif > 0. Header

 v

 v

 19

 Iso-358 K

 3.3

 nv

 0.3

 v

 3

 v

 9

 v

 0.01

 v

 0.64

 v

 0.014

 v

 v

 19

 Iso-344 K

 2.8

 nv

 0.3

 v

 2.1

 v

 14

 v

 0.01

 v

 0.42

 v

 0.016

 v

 v

 18

 Iso-423 K

 12

 nv

 0.6

 v

 4.4

 nv

 159

 nv

 0.01

 v

�24.5

 nv

�0.01

 nv

 nv

 18

 Iso-398 K

 0.4

 v

 0.6

 v

 3

 v

 69

 nv

 0.02

 v

�2

 nv

 0.001

 v

 nv

 18

 Iso-372 K

 3.3

 nv

 0.4

 v

 3.3

 nv

 14

 v

 0.02

 v

 0.11

 v

 0.009

 v

 v

 17

 Iso-298 K

 41

 nv

 2.7

 nv

 1.5

 v

 82

 nv

 0.18

 nv

�0.09

 nv

�0.370

 nv

 nv

 14

 Iso-328 K

 1.7

 v

 0.9

 v

 2.1

 v

 74

 nv

 0.01

 v

 0.36

 v

�0.050

 nv

 nv

 16

 Iso-101 kPa

 1.4

 v

 0.6

 v

 2.8

 v

 40

 nv

 0

v

 0.02

 v

 0.006

 v

 v

 15

 Iso-101 kPa

 7.1

 nv

 0.5

 v

 2.1

 v

 16

 v

 0.02

 v

 0.16

 v

 0.005

 v

 v

 14

 Iso-101 kPa

 5

 nv

 1.2

 nv

 0.5

 v

 27

 v

 0.04

 v

 0

 v

 0.003

 v

 v

Distillation - Modelling, Simulation and Optimization

 13

 Iso-101 kPa

 23

 nv

 2.2

 nv

 2

 v

 15

 v

 0.09

 v

 0.11

 v

�0.08

 nv

 nv

 12

 Iso-101 kPa

 15

 nv

 1.8

 nv

 1.7

 v

 10

 v

 0.09

 v

 0.14

 v

�0.05

 nv

 nv

 11

 Iso-101 kPa

 13

 nv

 1.8

 nv

 2.6

 v

 18

 v

 0.09

 v

 0

 v

 0.004

 v

 v

 10

 Iso-101 kPa

 15

 nv

 1.9

 nv

 2.5

 v

 24

 v

 0.09

 v

 0.06

 v

�0.06

 nv

 nv

 Ref.

 Type

 Area

d%

V

�100

 V

D

V

 M(I )

i

 V

δln(γ1/γ2)

 V

f-int.

V

f-dif.

V

 VF

> w

Fredenslund

 Wisniak

 Kojima

Direct-Van

 Ness

 Proposed test

Figure 4.

Plot of iso-p VLE of the binary benzene(1) + hexane(2). (a) T,x,y; (b) gE /RT,x. Ref. [33]: (○) p = 26 kPa; (□) p = 40 kPa; (+) p = 53 kPa; (◊) Ref. [26]; Ref. [28]: () p = 405.4 kPa; (△) p = 610.8 kPa; (▽) p = 810.8 kPa; (▷) p = 1013.5 kPa.

## Figure 5.

Plot of iso-T VLE data of the binary benzene(1) + hexane(2). (a) p,x,y; (b) gE /RT,x. (○) Ref. [40]; (□) Ref. [42] Ref. [41]: (+) T = 314 K; (◊) T = 323 K; () T = 333 K; (△) T = 303 K; (▽) Ref. [39].

the highest pressures (n° 13–16). This is due to the wrong relationship between the pure component saturation temperature (Appendix Table A1) and equilibrium temperature. However, it is interesting to recognize that when using other vapor pressure parameters this defect can be solved. The data series (n° 3, 4, 6–9, 19, 21–23) accepted by the proposed test [7] offer the highest consensus among all the battery of test about the quality of data, so these series could be used for subsequent tasks.

A total of 17 references were found in literature [36, 43–58] of h<sup>E</sup> measured in the range of [293–323] K and atmospheric pressure, except those data of Yi et al. [58], at 80 kPa. Figure 6(a) presents the data series considered in this study. It refers to a solution with endothermic effects (h<sup>E</sup> ≈ 900 J mol<sup>1</sup> at x = 0.5 and T = 298 K), decreasing as temperature increases; however, the high observed dispersion of experimental values is not sufficient evidence to ensure this effect. Inspection of the h<sup>E</sup> does not recommend excluding any of these data series; thus they will be considered in the data treatment.

N°

55

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

 40

 Iso-333 K

 31.1

 nv

 1.8

 nv

 2.42

 v

 41

 nv

 0.082

 v

0.33

 nv

0.048

 nv

 nv

 41

 Iso-323 K

 7.9

 nv

 0.6

 v

 0.97

 v

 270

 nv

 0.048

 v

 0.13

 v

 0.006

 v

 v

 41

 Iso-314 K

 17.5

 nv

 2.7

 nv

 0.68

 v

 1149

 nv

 0.312

 nv

 0

 nv

0.122

 nv

 nv

 41

 Iso-303 K

 16.8

 nv

 1.6

 nv

 0.61

 v

 670

 nv

 0.167

 nv

 0.03

 v

0.096

 nv

 nv

 28

 Iso-1010 kPa

 95.4

 nv

 3

 nv

 14.97

 nv

 6776

 nv

 0.364

 nv

0.07

 nv

0.192

 nv

 nv

 28

 Iso-810 kPa

 96.3

 nv

 2

 nv

 11.5

 nv

 291

 nv

 0.124

 v

0.16

 nv

0.08

 nv

 nv

 28

 Iso-610 kPa

 58.9

 nv

 1.1

 nv

 7.51

 nv

 343

 nv

 0.043

 v

0.14

 nv

0.079

 nv

 nv

 28

 Iso-405 kPa

 59

 nv

 1.2

 nv

 5.9

 nv

 1319

 nv

 0.2

 nv

0.21

 nv

0.145

 nv

 nv

 37

 Iso-101 kPa

 9

 nv

 0.7

 v

 2.77

 v

 52

 nv

 0.043

 v

 0.02

 v

0.018

 nv

 nv

 32

 Iso-101 kPa

 nd

—

nd

—

nd

—

nd

—

nd

—

nd

—

nd

—

nv

 29

 iso-101 kPa

 12.3

 nv

 0.6

 v

 1.66

 v

 22

 v

 0.048

 v

0.01

 nv

0.013

 nv

 nv

A Practical Fitting Method Involving a Trade-Off Decision in the Parametrization Procedure…

 37

 iso-101 kPa

 9

 nv

 0.4

 v

 1.75

 v

 44

 nv

 0.159

 v

 0.05

 v

 0.004

 v

 v

 35

 Iso-101 kPa

 1.5

 v

 0.1

 v

 1.7

 v

 27

 v

 0.003

 v

 0.01

 v

 0.014

 v

 v

 34

 Iso-101 kPa

 2.5

 nv

 0.3

 v

 1.63

 v

 24

 v

 0.004

 v

 0.04

 v

 0.007

 v

 v

 26

 Iso-101 kPa

 3.6

 nv

 0.4

 v

 1.6

 v

 24

 v

 0.020

 v

 0.11

 v

 0.006

 v

 v

 31

 Iso-101 kPa

 36.5

 nv

 0.6

 v

 1.65

 v

 10

 v

 0.012

 v

 0.02

 v

0.047

 nv

 nv

 26

 Iso-97 kPa

 19.2

 nv

 0.6

 v

 1.7

 v

 54

 nv

 0.02

 v

 0.05

 v

 0.005

 v

 v

DOI: http://dx.doi.org/10.5772/intechopen.85743

 33

 Iso-53 kPa

 17.5

 nv

 0.8

 v

 1.93

 v

 31

 nv

 0.063

 v

 0.04

 v

 0.001

 v

 v

 33

 Iso-40 kPa

 16.3

 nv

 1.2

 nv

 1.02

 v

 19

 v

 0.068

 v

0.02

 nv

0.013

 nv

 nv

 33

 Iso-26 kPa

 23.2

 nv

 1.2

 nv

 1.45

 v

 74

 nv

 0.123

 v

0.06

 nv

0.073

 nv

 nv

 Ref.

 Type

 Area

d%

 V

100

 V

D

V

 M(I )

i

 V

δln(γ1/γ2)

 V

f-int.

V

f-dif.

V

 FV

> w

Fredenslund

 Wisniak

 Kojima

Direct-Van

 Ness

 Proposed test


A Practical Fitting Method Involving a Trade-Off Decision in the Parametrization Procedure… DOI: http://dx.doi.org/10.5772/intechopen.85743

the highest pressures (n° 13–16). This is due to the wrong relationship between the pure component saturation temperature (Appendix Table A1) and equilibrium temperature. However, it is interesting to recognize that when using other vapor pressure parameters this defect can be solved. The data series (n° 3, 4, 6–9, 19, 21–23) accepted by the proposed test [7] offer the highest consensus among all the battery of test about the quality of data, so these series could be used for subsequent

(□) p = 40 kPa; (+) p = 53 kPa; (◊) Ref. [26]; Ref. [28]: () p = 405.4 kPa; (△) p = 610.8 kPa; (▽)

Ref. [42] Ref. [41]: (+) T = 314 K; (◊) T = 323 K; () T = 333 K; (△) T = 303 K; (▽) Ref. [39].

/RT,x. (○) Ref. [40]; (□)

/RT,x. Ref. [33]: (○) p = 26 kPa;

Plot of iso-T VLE data of the binary benzene(1) + hexane(2). (a) p,x,y; (b) gE

Plot of iso-p VLE of the binary benzene(1) + hexane(2). (a) T,x,y; (b) gE

Distillation - Modelling, Simulation and Optimization

A total of 17 references were found in literature [36, 43–58] of h<sup>E</sup> measured in the range of [293–323] K and atmospheric pressure, except those data of Yi et al. [58], at 80 kPa. Figure 6(a) presents the data series considered in this study. It refers to a solution with endothermic effects (h<sup>E</sup> ≈ 900 J mol<sup>1</sup> at x = 0.5 and T = 298 K), decreasing as temperature increases; however, the high observed dispersion of experimental values is not sufficient evidence to ensure this effect. Inspection of the h<sup>E</sup> does not recommend excluding any of these data series; thus

they will be considered in the data treatment.

tasks.

54

Figure 5.

Figure 4.

p = 810.8 kPa; (▷) p = 1013.5 kPa.

