Figure 7.

Efficient fronts for s(g<sup>E</sup> /RT) = f(s(h<sup>E</sup> )), obtained for acetone + ethanol. Arrows and labels indicate the chosen results on each of the fronts, using the models: (▴) M2; () M3; and (▾) M4.

N°

56

21

22

23

Limiting values: areas-test: d < 2;

notation: V

Table 2. Values obtained in the application

 of the

thermodynamic

consistency-test

 to VLE data of benzene + hexane at different conditions.

!

verified; FV

! fully verified. Test outcome: v

 39

 Iso-343 K

 7.4 Fredenslund-test:

 δy�100 < 1;

!

verified; nv

! not verified; nd/� ! not available.

 nv

 0.5

 v Wisniak-test:

 Dw < 3; Kojima-test:

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

 1.53

 v

 19

 v

 0.027

 v

 0.29

 v

 0.001

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

 v

 v

Distillation - Modelling, Simulation and Optimization

 41

 Iso-333 K

 1.2

 v

 0.4

 v

 1.22

 v

 88

 nv

 0.017

 v

 0.41

 v

 0.009

 v

 v

 42

 Iso-333 K

 1.7

 v

 0.1

 v

 1.31

 v

 12

 v

 0.002

 v

 0.5

 v

 0.017

 v

 v

 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

Acetone(1) + ethanol(2): the efficient fronts of results for the binary acetone + ethanol were obtained from sub-models M2, M3, and M4. Sub-model M1 did not produce an acceptable representation of the thermodynamic behavior, so it was ignored. The obtained fronts shown in Figure 7 reveal that the three submodels produced similar results when acceptable error in h<sup>E</sup> is greater than 140 J mol<sup>1</sup> . This implies that, from this limit on, the problem becomes monoobjective, regardless of the sub-model used. For smaller errors of the h<sup>E</sup> , s(h<sup>E</sup> ) < 140 J mol<sup>1</sup> , differences between sub-models M2, M3, and M4 to reproduce the VLE data are significant, reducing the maximum error by approximately δs (g E /RT) ≈ 0.15 between them. The efficient front achieved with model M4 shows an almost constant s(g E /RT). The other two sub-models reveal an exponential behavior as s(h<sup>E</sup> ) decreases. From the set of results obtained, three of them are chosen (see Figure 7) to carry out a more detailed analysis on their ability to describe simultaneously the VLE and h<sup>E</sup> . Some particular comments on those three results are:

activity coefficients (Figure 8(b)) is acceptable. Estimations of g

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

• Result 3 (M3) produces an unsatisfactory representation in the h<sup>E</sup>

presents an inversion of the thermal gradient of this property.

(benzene + hexane) on the results emitted by each of the models.

/RT), lower than 5.5 <sup>10</sup><sup>3</sup> J mol<sup>1</sup> for all <sup>s</sup>(h<sup>E</sup>

Benzene(1) + hexane(2): sub-model M4 was not used for the binary

extracted from Ref. [20].

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

validity region of the model (Figure 8(d)).

result 2 reproduces almost exactly the h<sup>E</sup>

g E

is involved.

s(g E

Figure 9.

59

Efficient fronts for s(g<sup>E</sup>

/RT) = f(s(h<sup>E</sup>

results on each of the fronts, using the models: (●) M1; (▴) M2; and () M3.

system are close to the set that displays the highest values. The estimate for the h<sup>E</sup> is acceptable, although the model does not reproduce the data series

• Result 2 (M3), which displays the highest error in the VLE estimate, wrongly estimates an azeotrope and a whole range immiscible region (Figure 8(a)). This poor description of the liquid phase is due to the high values of γ<sup>i</sup> and the

/RT (Figure 8(b and c)). At first, the h<sup>E</sup> is correctly represented by this parametrization, although the presence of the immiscibility truncates the

Final model selection should ensure that selected parametrization describes, at least qualitatively, the thermodynamic behavior closest to the real one. In this case,

This analysis will serve as a basis to inspect the results of the remaining binary

benzene + hexane because of the similarity with the efficient front produced by M3 model. Thus, sub-models M1, M2, and M3 were only applied, as shown in Figure 9. Sub-models M2 and M3 produce very similar results, with almost constant error,

fronts of sub-models M1 and M2 are evaluated. The efficient front of sub-model M1

behavior, hence limiting its subsequent applicability. The choice between results 1 and 3 will depend on the influence of the h<sup>E</sup> on the calculations in which the model

, although it produces an incorrect g

)), obtained for benzene + hexane. Arrows and labels indicate the chosen

). Consequently, those result

E

/RT for this

s, which also

E

• The result labeled as "1" (by M4) describes well the two properties under study, as seen in Figure 8, but at the expense of using more parameters. Specifically, this model links the state variables at equilibrium (Figure 8(a)), describing the observed folding at the lowest temperatures. The estimate of

Figure 8.

Plot of VLE at 101 kPa and hE estimates for binary acetone(1) + ethanol(2) at 101.32 kPa. Models drawn from Figure 7(a). Results (——) 1-(M4), 2-(M3), 3-(M3). (a) T vs x1,y1; (b)γ<sup>i</sup> vs x1; (c) g E /RT vs x1; (d) hE vs x1.

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

activity coefficients (Figure 8(b)) is acceptable. Estimations of g E /RT for this system are close to the set that displays the highest values. The estimate for the h<sup>E</sup> is acceptable, although the model does not reproduce the data series extracted from Ref. [20].


Final model selection should ensure that selected parametrization describes, at least qualitatively, the thermodynamic behavior closest to the real one. In this case, result 2 reproduces almost exactly the h<sup>E</sup> , although it produces an incorrect g E behavior, hence limiting its subsequent applicability. The choice between results 1 and 3 will depend on the influence of the h<sup>E</sup> on the calculations in which the model is involved.

This analysis will serve as a basis to inspect the results of the remaining binary (benzene + hexane) on the results emitted by each of the models.

Benzene(1) + hexane(2): sub-model M4 was not used for the binary benzene + hexane because of the similarity with the efficient front produced by M3 model. Thus, sub-models M1, M2, and M3 were only applied, as shown in Figure 9. Sub-models M2 and M3 produce very similar results, with almost constant error, s(g E /RT), lower than 5.5 <sup>10</sup><sup>3</sup> J mol<sup>1</sup> for all <sup>s</sup>(h<sup>E</sup> ). Consequently, those result fronts of sub-models M1 and M2 are evaluated. The efficient front of sub-model M1

## Figure 9.

Efficient fronts for s(g<sup>E</sup> /RT) = f(s(h<sup>E</sup> )), obtained for benzene + hexane. Arrows and labels indicate the chosen results on each of the fronts, using the models: (●) M1; (▴) M2; and () M3.

Acetone(1) + ethanol(2): the efficient fronts of results for the binary

objective, regardless of the sub-model used. For smaller errors of the h<sup>E</sup>

VLE data are significant, reducing the maximum error by approximately δs

140 J mol<sup>1</sup>

(g E

as s(h<sup>E</sup>

Figure 8.

/RT vs x1; (d) hE vs x1.

g E

58

< 140 J mol<sup>1</sup>

almost constant s(g

neously the VLE and h<sup>E</sup>

E

Distillation - Modelling, Simulation and Optimization

acetone + ethanol were obtained from sub-models M2, M3, and M4. Sub-model M1 did not produce an acceptable representation of the thermodynamic behavior, so it was ignored. The obtained fronts shown in Figure 7 reveal that the three submodels produced similar results when acceptable error in h<sup>E</sup> is greater than

. This implies that, from this limit on, the problem becomes mono-

/RT) ≈ 0.15 between them. The efficient front achieved with model M4 shows an

) decreases. From the set of results obtained, three of them are chosen (see Figure 7) to carry out a more detailed analysis on their ability to describe simulta-

• The result labeled as "1" (by M4) describes well the two properties under study, as seen in Figure 8, but at the expense of using more parameters. Specifically, this model links the state variables at equilibrium (Figure 8(a)), describing the observed folding at the lowest temperatures. The estimate of

Plot of VLE at 101 kPa and hE estimates for binary acetone(1) + ethanol(2) at 101.32 kPa. Models drawn from Figure 7(a). Results (——) 1-(M4), 2-(M3), 3-(M3). (a) T vs x1,y1; (b)γ<sup>i</sup> vs x1; (c)

, differences between sub-models M2, M3, and M4 to reproduce the

/RT). The other two sub-models reveal an exponential behavior

. Some particular comments on those three results are:

, s(h<sup>E</sup> ) produces a quasi-linear behavior with the variation of s(h<sup>E</sup> ). The difference between this front and that of sub-model M2 is δs(g E /RT) ≈ 0.14, when ε = 0. The fronts for models M1 and M2 do not intersect, unlike the earlier case, showing a maximum value of s(h<sup>E</sup> ) at 170 J mol<sup>1</sup> and 450 J mol<sup>1</sup> , respectively. The VLE diagrams produced by the four selected results are shown in Figure 10, along with one of the validated data series for this result. The best description of this system is achieved with result 4 (M1), which reproduces the behavior of T-x-y experimental data (Figure 10(a)) and the other quantities calculated (Figure 10(b and c)). Nevertheless, the description of h<sup>E</sup> with this model is not good. Result 1 (M2) produces an azeotrope at x<sup>1</sup> < 0.2, which does not occur experimentally. This poor estimation occurs even though the greater number of parameters, increasing the model's capacity to reproduce the h<sup>E</sup> , as proven in Figure 11. Results 2 and 3 overestimate γi, hence g E /RT (see Figure 10(b and c)).

representing the phase equilibria. This being said, result 3 represents the average

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

From previous observations, result 4 (M1) is recommended for those cases where the h<sup>E</sup> plays a secondary role in comparison to the reliable reproduction of the VLE diagram. Otherwise, result 1 (M2) is preferred, despite the qualitative misfit to experimental data. Table 3 presents an overview of the present section

with a summary of the models to be used in the simulation task.

4.2 Simulation results of a rectification process for each of the studied

The models obtained previously are used in the design of a simulation operation comparing their capacity in terms of some operation variables such as composition and temperature profiles, as well as energy consumption. General conditions for the simulations are summarized in Table 4. In all cases, columns are fed with a 1 kmol/h at equimolar composition of the corresponding solution, at 298.15 K and 101.32 kPa. Simulations are performed using the RadFrac block of AspenPlus© V8.8

Estimation of hE values at 101.32 kPa using the different results indicated in the fronts of Figure 9 for benzene (1) + hexane(2). (a) hE vs x1 (T = 298.15 K), (b) hE vs T (x1 = 0.5). Results (——) 1 (M2); 2

System M1 M2 M3 M4 Acetone + ethanol û ü üü üü Benzene + hexane üü üü ü û

Binary system Reflux ratio Distillate rate (kmol/h) n° stages Feed stage Acetone + ethanol 6 0.5 22 16 Benzene + hexane 10 0.6 30 20

üü ! used for modeling and simulation;ü ! used for modeling; û ! not used.

Operation data for the rectification columns to separate the binaries.

behavior of this property in the working range.

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

dissolutions

(AspenOne©, [59]).

Figure 11.

Table 3.

Table 4.

61

(M1); 3 (M1); 4 (M1).

List of sub-models applied to each system.

This discrepancy gives rise to the formation of minimum boiling point azeotropes, which are not in accordance with experimental data. Of all the results chosen, only result 1 (belonging to sub-model M2) shows a h<sup>E</sup> that varies significantly with temperature, since sub-model M1 is independent of this variable. The use of either result 2 or 3 is discouraged since their estimations of h<sup>E</sup> , especially at temperatures other than 298 K, are not correct, in addition to the described issues in

Figure 10. Plot of VLE at 101 kPa estimates for binary benzene(1) + hexane(2). Models drawn from Figure 9. Results (——) 1 (M2), 2 (M1), 3 (M1) and 4 (M1). (a) T vs x,y; (b)γ vs x; (c) gE /RT vs x.

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

representing the phase equilibria. This being said, result 3 represents the average behavior of this property in the working range.

From previous observations, result 4 (M1) is recommended for those cases where the h<sup>E</sup> plays a secondary role in comparison to the reliable reproduction of the VLE diagram. Otherwise, result 1 (M2) is preferred, despite the qualitative misfit to experimental data. Table 3 presents an overview of the present section with a summary of the models to be used in the simulation task.
