4. Modeling of azeotropic systems. Correlation and prediction

## 4.1. Correlation of vapor-liquid equilibria according to the gamma-phi approximation

The modeling of systems presenting azeotropes is not different from that used for any other system in vapor-liquid equilibrium. In order to do this, the following models must be defined:


Figure 10. Plot of y vs. x ( ), for the VLE at 101.32 kPa of binaries (methyl alkanoates + alkanes).

156 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

Figure 11. Sensitivity of the azeotropic coordinates to pressure in ester + alkane solutions. (a) Ethyl ethanoate + heptane, (b) ethyl ethanoate + hexane, (c) propyl ethanoate + heptane, (d) methyl butanoate + heptane, (e) methyl propanoate +

heptane, (f) methyl propanoate + hexane.

3. A model for the activity coefficients: γ<sup>i</sup> ¼ γ<sup>i</sup> ð Þ x; p; T .

The relationship between vapor pressures and temperature is established by Clapeyron's equation [23], although it is standard practice to use other empirical equations such as those of Wagner or Antoine [25]. The parameter Φi, defined in Eq. (2), depends on the fugacity coefficient of compound i as saturated vapor phase and in solution. For the calculation, state equations can be used that may be different depending on if they are applied to the liquid or vapor phase.

The activity coefficients are inherent to the formation of the solution and are related to the interactions occurring therein. The phenomenological description of the fluid material is still not precise, although there are some models for which the formulation takes into account the molecular interactions that generate the macroscopic properties. In practice, depending on the theory of the model chosen, some experimental data are required for their accurate representation. For the gamma-phi method, models are written for the function of Gibbs excess energy as g<sup>E</sup> = gE (x, p, T), and the dependence on γ<sup>i</sup> is related to its partial molar properties [23]:

$$\mathcal{O}\_{\rm i} = \exp\left\{ \left[ \mathbf{g}^{\rm E} + \left( \frac{\partial \mathbf{g}^{\rm E}}{\partial \mathbf{x}\_{\rm i}} \right)\_{\mathbf{p}, \mathbf{T}, \mathbf{x}\_{\rm j \neq i}} - \sum \mathbf{x}\_{\rm k} \left( \frac{\partial \mathbf{g}^{\rm E}}{\partial \mathbf{x}\_{\rm k}} \right)\_{\mathbf{p}, \mathbf{T}, \mathbf{x}\_{\rm j \neq k}} \right] \right\} \,\mathrm{RT} \right\} \tag{13}$$

The model most used to date is NRTL [57]:

$$\mathbf{g}^{\rm E} = RT \sum\_{\mathbf{i}} \mathbf{x}\_{\mathbf{i}} \frac{\sum\_{\mathbf{j}} \tau\_{\mathbf{j}\overline{\mathbf{i}}} G\_{\overline{\mathbf{j}}} \mathbf{x}\_{\mathbf{j}}}{\sum\_{\mathbf{k}} \mathbf{G}\_{\mathbf{k}i} \mathbf{x}\_{\mathbf{k}}} \text{ where } \mathbf{G}\_{\overline{\mathbf{i}}} = \exp\{-a\_{\overline{\mathbf{i}}} \tau\_{\overline{\mathbf{i}}}\} \text{ and } \tau\_{\overline{\mathbf{i}}} = f(\mathbf{x}, T) \tag{14}$$

Our research group has used a polynomial model [14–17], with the general expression:

$$\mathbf{g}\_{n,N}^{\to} = \sum\_{i\_1 i\_2 \dots i\_{n-1} \in \mathcal{C}(n, n-1)} \mathbf{g}\_{n-1,N}^{\to (i\_1 - i\_2 - i\_3 \dots - i\_{n-1})} + Z\_n \cdot \mathbf{P}\_N \tag{15}$$

Where n is the number of components present, N the maximum interaction order, g Eð Þ i1�i2�i3…�in�<sup>1</sup> n�1,N the excess Gibbs function of all the subsystems of inferior order that are present in the system and the product Z<sup>n</sup> � P<sup>N</sup> is a polynomial made up of multiple products of (z1z2…zn) and a polynomial in zi:

$$Z\_n = z\_1 z\_2 \dots z\_n = T\_n = \frac{\prod\_{i=2}^n k^{\mathrm{j}} \prod\_{i=1}^n \mathbf{x\_i}}{\left[\mathbf{x\_1} + \sum\_{j=2}^n k^{\mathrm{j}} \mathbf{x\_j}\right]^n}, \quad P\_N = \sum\_{j=0}^N P\_{\mathbf{j}} \mathbf{z\_n^{\mathrm{j}}} \tag{16}$$

For a binary or ternary solution, the model (Eq. (15)) can be written, respectively, as:

$$\mathbf{g^{E(i\tau)}} = \mathbf{z}\_{i}\mathbf{z}\_{\mathbf{j}} \sum\_{\mathbf{k}=\mathbf{0}}^{\text{N-2}} \mathbf{g^{(i\tau)}\_{\mathbf{k}}} \mathbf{z}\_{\mathbf{i}}^{\text{k}} \tag{17}$$

recommended here (see [58, 59]). For example the solution butyl ethanoate + octane [20], and reproduced in Figure 12(b), for which NRTL estimates Taz = 393.4 K, while model (17) gives

Figure 12. Modeling examples of azeotropic systems using correlative models for: (a) methyl methanoate(1) + pentane(2), (b) butyl ethanoate(1) + octane (2), (c) propyl ethanoate(1) + heptane(2). (——) Eq. (17), ( ) NRTL, Eq. (14).

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In some cases, a considerable amount of data is modeled together. When these extend over a broad range of pressures and temperatures the ability of both models to accurately reproduce the azeotropic coordinates, or any other property, diminishes. In other words, the resolution capacity in the calculation of coordinates, at a given p, becomes smaller as the range of estimation increases. This case was studied [60] for the solution propyl ethanoate + heptane, where VLE data were available for temperatures between 273 and 373 K. Estimations for the two models, for iso-101.32 kPa VLE, are shown in Figure 12(c), which shows that the azeotropic temperature calculated for the two models (367.17 K with our model and 367.19 K with NRTL) is slightly higher than the experimental value (367.0 K). These results are considered here to be positive. In conclusion, from observations made from the modeling described in numerous articles [10–17, 39–41], the model (17) appears to be recommendable to correlate VLE data and hence, to estimate azeotropic conditions. Either model can be used for the individual correlation of VLE data, although the modeling obtained should not be used to extrapolate azeotropic coordinates to conditions different from the experimental conditions.

Taz = 394.1 K, close to the experimental value of Taz,exp = 394.0 K.

$$\mathbf{g}\_{3,4}^{\mathrm{E}} = \mathbf{g}\_{2,4}^{\mathrm{E(1-2)}} + \mathbf{g}\_{2,4}^{\mathrm{E(1-3)}} + \mathbf{g}\_{2,4}^{\mathrm{E(2-3)}} + z\_1 z\_2 z\_3 (\mathbf{C}\_0 + \mathbf{C}\_1 z\_1 + \mathbf{C}\_2 z\_2) \tag{18}$$

with the possibility of extending this rule to any number of components. This model has been used to represent the behavior of many binary and ternary systems and has provided excellent results when used in combined correlation procedures of all the properties. This combined modeling method, adapted to suit to each case, was applied to binaries composed of esters and alkanes [10–17, 39–56]. The two following models: NRTL [57] and the Eq. (17) were used. Several of the systems modeled present azeotropy, so the results obtained are described briefly below. In many cases, the two models reproduce the VLE diagram with similar errors. An example is that shown in Figure 12(a) for the solution methyl methanoate + pentane, with iso-101.32 VLE data [39]. Slight differences can be observed in the azeotropic coordinates (Taz/K; xaz) calculated by each model [the proposed model (17) estimates the coordinates to be (293.8; 0.54), while the NRTL model gives (293.7; 0.57)]. However, Eq. (17) is better at predicting the remaining properties and, therefore, guarantees a better global capacity of representation (see details in [39, 41]). Occasionally, the NRTL model does not adequately represent the VLE behavior of azeotropic systems, especially when the parameters are obtained in a combined correlation process as

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<sup>γ</sup><sup>i</sup> <sup>¼</sup> exp <sup>g</sup><sup>E</sup> <sup>þ</sup>

The model most used to date is NRTL [57]:

i xi P <sup>j</sup> τjiGjix<sup>j</sup>

gE

P <sup>k</sup> Gkix<sup>k</sup>

158 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

Zn ¼ z1z2::…zn ¼ Tn ¼

E 1ð Þ -2 <sup>2</sup>, <sup>4</sup> þ g

gE <sup>3</sup>,<sup>4</sup> ¼ g

n,N <sup>¼</sup> <sup>X</sup>

i1i2…in�<sup>1</sup> ∈C nð Þ ;n�1

Where n is the number of components present, N the maximum interaction order, g

<sup>g</sup><sup>E</sup> <sup>¼</sup> RT<sup>X</sup>

in zi:

∂g<sup>E</sup> ∂x<sup>i</sup> � �

p,T,xj6¼<sup>i</sup>

Our research group has used a polynomial model [14–17], with the general expression:

g

the excess Gibbs function of all the subsystems of inferior order that are present in the system and the product Z<sup>n</sup> � P<sup>N</sup> is a polynomial made up of multiple products of (z1z2…zn) and a polynomial

> Qn i¼2

<sup>x</sup><sup>1</sup> <sup>þ</sup> <sup>P</sup><sup>n</sup>

For a binary or ternary solution, the model (Eq. (15)) can be written, respectively, as:

<sup>g</sup>E ið Þ -j <sup>¼</sup> <sup>z</sup>iz<sup>j</sup>

E 1ð Þ -3 <sup>2</sup>, <sup>4</sup> þ g <sup>k</sup>ij <sup>Q</sup><sup>n</sup> i¼1 xi

X N-2

k¼0 g ð Þ i-j <sup>k</sup> <sup>z</sup><sup>k</sup>

E 2ð Þ -3

with the possibility of extending this rule to any number of components. This model has been used to represent the behavior of many binary and ternary systems and has provided excellent results when used in combined correlation procedures of all the properties. This combined modeling method, adapted to suit to each case, was applied to binaries composed of esters and alkanes [10–17, 39–56]. The two following models: NRTL [57] and the Eq. (17) were used. Several of the systems modeled present azeotropy, so the results obtained are described briefly below. In many cases, the two models reproduce the VLE diagram with similar errors. An example is that shown in Figure 12(a) for the solution methyl methanoate + pentane, with iso-101.32 VLE data [39]. Slight differences can be observed in the azeotropic coordinates (Taz/K; xaz) calculated by each model [the proposed model (17) estimates the coordinates to be (293.8; 0.54), while the NRTL model gives (293.7; 0.57)]. However, Eq. (17) is better at predicting the remaining properties and, therefore, guarantees a better global capacity of representation (see details in [39, 41]). Occasionally, the NRTL model does not adequately represent the VLE behavior of azeotropic systems, especially when the parameters are obtained in a combined correlation process as

<sup>j</sup>¼<sup>2</sup> <sup>k</sup>ij xj h i<sup>n</sup> , PN <sup>¼</sup> <sup>X</sup><sup>N</sup>

�Xx<sup>k</sup>

where Gji ¼ exp �αjiτji

Eð Þ i1�i2�i3…�in�<sup>1</sup>

( )

" #

∂g<sup>E</sup> ∂x<sup>k</sup> � �

p,T, xj6¼<sup>k</sup>

=RT

� � and <sup>τ</sup>ji <sup>¼</sup> <sup>f</sup>ð Þ <sup>x</sup>; <sup>T</sup> (14)

<sup>n</sup>�1,N <sup>þ</sup> Zn � PN (15)

<sup>j</sup>¼<sup>0</sup> <sup>P</sup>jz<sup>j</sup>

<sup>i</sup> (17)

<sup>2</sup>,<sup>4</sup> þ z1z2z3ð Þ C<sup>0</sup> þ C1z<sup>1</sup> þ C2z<sup>2</sup> (18)

(13)

Eð Þ i1�i2�i3…�in�<sup>1</sup> n�1,N

<sup>n</sup> (16)

Figure 12. Modeling examples of azeotropic systems using correlative models for: (a) methyl methanoate(1) + pentane(2), (b) butyl ethanoate(1) + octane (2), (c) propyl ethanoate(1) + heptane(2). (——) Eq. (17), ( ) NRTL, Eq. (14).

recommended here (see [58, 59]). For example the solution butyl ethanoate + octane [20], and reproduced in Figure 12(b), for which NRTL estimates Taz = 393.4 K, while model (17) gives Taz = 394.1 K, close to the experimental value of Taz,exp = 394.0 K.

In some cases, a considerable amount of data is modeled together. When these extend over a broad range of pressures and temperatures the ability of both models to accurately reproduce the azeotropic coordinates, or any other property, diminishes. In other words, the resolution capacity in the calculation of coordinates, at a given p, becomes smaller as the range of estimation increases. This case was studied [60] for the solution propyl ethanoate + heptane, where VLE data were available for temperatures between 273 and 373 K. Estimations for the two models, for iso-101.32 kPa VLE, are shown in Figure 12(c), which shows that the azeotropic temperature calculated for the two models (367.17 K with our model and 367.19 K with NRTL) is slightly higher than the experimental value (367.0 K). These results are considered here to be positive. In conclusion, from observations made from the modeling described in numerous articles [10–17, 39–41], the model (17) appears to be recommendable to correlate VLE data and hence, to estimate azeotropic conditions. Either model can be used for the individual correlation of VLE data, although the modeling obtained should not be used to extrapolate azeotropic coordinates to conditions different from the experimental conditions.

#### 4.2. The prediction of azeotropes by activity coefficients. Application to ester + alkane solutions

When experimental VLE data are not available, azeotropic points are estimated using predictive procedures. In the field of chemical engineering, the UNIFAC model by Gmehling et al. [61] (referenced as UNIFAC-DM), mainly designed for phase equilibria and some derived properties, is well known. Nonetheless, advances in the molecular sciences have helped to understand the intrinsic behavior of fluids in greater depth, with more solid phenomenological bases. This is the case of the quantum chemistry-based COSMO-RS model [62], which is able to estimate a significant number of properties of solutions. This chapter compares the results obtained after applying the two models to ester-alkane binaries, enabling us to establish certain criteria for their use.

Figure 13 represents the relative errors obtained with each of models in the estimation of azeotropic points of ester-alkane systems. The plot is constructed with color gradient according to the magnitude of the error (white cells indicate non-azeotrope). The error measurement is evaluated as:

> ARDf ¼ f exp � f est

azeotropes obtained with the models UNIFAC-DM and COSMO-RS.

COSMO-RS model is also smaller.

 

colored according to the scale shown in Figure 13. In general, an acceptable description is observed for both models for the azeotropic systems studied, although both are less effective at estimating the composition, max(ARDx) = 33%, than the equilibrium temperature of the azeotrope, max(ARDT) = 0.6%. However, there are some differences in the qualitative description produced by both models. Hence, UNIFAC-DM does not estimate an azeotrope in the systems methyl ethanoate + heptane, propyl ethanoate + octane and methyl butanoate + octane, but considers the system ethyl methanoate + heptane to be azeotropic, which is regarded as zeotropic in the literature. With regards to the COSMO-RS model [61], all the systems described in the literature as azeotropic qualified to be so by the model, with the exception of methyl methanoate + heptane and ethyl methanoate + heptane, which are qualifies as azeotropic (see Figure 13) when experimentally they are not obtained at the pressure studied. In summary, estimation of the azeotropic coordinates is slightly more accurate when using the COSMO-RS model than the UNIFAC-DM model, as can be observed in the box-and-whiskers diagrams of Figure 14. Although both models give a similar mean error, the errors presented by estimations obtained with COSMO-RS have a significantly smaller interquartile range than those obtained with UNIFAC-DM; in other words, they have less dispersion. The same pattern can be observed in the estimation of compositions but with the additional factor that the mean error with the

Figure 14. Plot of boxs and whiskers of ARD distribution on the estimation of temperature (a) and composition (b) of the

Azeotropy: A Limiting Factor in Separation Operations in Chemical Engineering - Analysis, Experimental…

In the preliminary design of separation equipment or screening procedures involving ester + alkane systems it is recommended to use COSMO-RS rather than UNIFAC-DM to predict the azeotrope. This is not because of the quantitative difference between the estimations, but because of the qualitative improvement obtained with the former model in several of the cases

� <sup>100</sup>=<sup>f</sup> exp where <sup>f</sup> � <sup>x</sup>az or <sup>T</sup>az=<sup>K</sup> (19)

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Figure 13. Matrices of estimated ARD for azeotropic coordinates of ester + alkane: Cu-1H2<sup>u</sup> + 1 COOCvH2<sup>v</sup> + 1 + CnH2<sup>n</sup> + 2. Errors in composition with UNIFAC-DM (a) and COSMO-RS (b); and in temperature using UNIFAC-DM (c) and COSMO-RS (d). Model fails to estimate the azeotrope; Model wrongly considers the system as azeotropic.

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4.2. The prediction of azeotropes by activity coefficients. Application to ester + alkane

160 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

When experimental VLE data are not available, azeotropic points are estimated using predictive procedures. In the field of chemical engineering, the UNIFAC model by Gmehling et al. [61] (referenced as UNIFAC-DM), mainly designed for phase equilibria and some derived properties, is well known. Nonetheless, advances in the molecular sciences have helped to understand the intrinsic behavior of fluids in greater depth, with more solid phenomenological bases. This is the case of the quantum chemistry-based COSMO-RS model [62], which is able to estimate a significant number of properties of solutions. This chapter compares the results obtained after applying the two models to ester-alkane binaries, enabling us to establish certain criteria for their

Figure 13 represents the relative errors obtained with each of models in the estimation of azeotropic points of ester-alkane systems. The plot is constructed with color gradient according to the magnitude of the error (white cells indicate non-azeotrope). The error measurement

Figure 13. Matrices of estimated ARD for azeotropic coordinates of ester + alkane: Cu-1H2<sup>u</sup> + 1 COOCvH2<sup>v</sup> + 1 + CnH2<sup>n</sup> + 2. Errors in composition with UNIFAC-DM (a) and COSMO-RS (b); and in temperature using UNIFAC-DM (c) and COSMO-RS (d). Model fails to estimate the azeotrope; Model wrongly considers the system as azeotropic.

solutions

use.

is evaluated as:

Figure 14. Plot of boxs and whiskers of ARD distribution on the estimation of temperature (a) and composition (b) of the azeotropes obtained with the models UNIFAC-DM and COSMO-RS.

$$ARD\_f = \left| f\_{\text{exp}} - f\_{\text{est}} \right| \cdot 100 / f\_{\text{exp}} \quad \text{where } f \equiv \text{x}\_{\text{ax}} \text{ or } T\_{\text{ax}} / \text{K} \tag{19}$$

colored according to the scale shown in Figure 13. In general, an acceptable description is observed for both models for the azeotropic systems studied, although both are less effective at estimating the composition, max(ARDx) = 33%, than the equilibrium temperature of the azeotrope, max(ARDT) = 0.6%. However, there are some differences in the qualitative description produced by both models. Hence, UNIFAC-DM does not estimate an azeotrope in the systems methyl ethanoate + heptane, propyl ethanoate + octane and methyl butanoate + octane, but considers the system ethyl methanoate + heptane to be azeotropic, which is regarded as zeotropic in the literature. With regards to the COSMO-RS model [61], all the systems described in the literature as azeotropic qualified to be so by the model, with the exception of methyl methanoate + heptane and ethyl methanoate + heptane, which are qualifies as azeotropic (see Figure 13) when experimentally they are not obtained at the pressure studied. In summary, estimation of the azeotropic coordinates is slightly more accurate when using the COSMO-RS model than the UNIFAC-DM model, as can be observed in the box-and-whiskers diagrams of Figure 14. Although both models give a similar mean error, the errors presented by estimations obtained with COSMO-RS have a significantly smaller interquartile range than those obtained with UNIFAC-DM; in other words, they have less dispersion. The same pattern can be observed in the estimation of compositions but with the additional factor that the mean error with the COSMO-RS model is also smaller.

In the preliminary design of separation equipment or screening procedures involving ester + alkane systems it is recommended to use COSMO-RS rather than UNIFAC-DM to predict the azeotrope. This is not because of the quantitative difference between the estimations, but because of the qualitative improvement obtained with the former model in several of the cases

studied here. Without ignoring these observations, if experimental data are available the model that best represents the real behavior of each system must be chosen in each case.

The pressure in the second column is extremely low, which is difficult to get in practice, but is established here to emphasize the characteristics of pressure-swing-distillation operation. As can be observed in Figure 16, the difference in pressure between the columns significantly displaces the coordinates of the azeotropic point, as estimated by Eq. (17). So, in the first column there is a partial separation of the solution, with the alkane, of high purity, collected in the bottom. The composition obtained in the head of the atmospheric column that feeds the second tower, Figure 15, was established between the azeotropic composition at each pressure, in

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The influence of the model used on the design was studied [21], and the most significant discrepancy that arises when changing the model occurs in the composition and temperature profiles in the inside of the column as shown in Figure 17, where important differences can be found. Use of the proposed model can therefore, guarantee reproduction of the real behavior of the apparatus.

In the previous case, it was proposed to reduce the pressure in order to separate the azeotropic solution. Alternatively, an extractant (entrainer) can be used to displace or destroy the azeotrope. This can be illustrated by separating the azeotropic solution ethyl butanoate(1) + octane(2) (x1,az = 0.63, Taz = 392 K a p = 101 kPa). For the preliminary design of this type of process a suitable entrainer must be chosen. In the absence of experimental data, theoretical models are chosen to establish the feasibility of the process. As possible entrainers for the binary selected, two compounds were chosen from the same families (ester and alkane) but with some structural differences, with greater molecular weights and, therefore, higher boiling points: (1) decane (2) butyl

Figure 16. Representation of T vs. x,y of propyl ethanoate(1) + heptane(2). ( ) Experimental values, (–––), Eqs. (8–10).

5.2. Separation of the binary ethyl butanoate + octane by extractive distillation

order to optimize the number of stages.

#### 5. The use of advanced separation techniques in ester + alkane solutions

Advanced distillation techniques for the separation of azeotropic systems are described in detail in Table 1. This section shows some simulated cases of the use of these techniques for the treatment of azeotropic solutions of esters and alkanes. This was carried out using the commercial software Aspen Plus v.8.8 [63], using RadFrac blocks for distillation columns.

#### 5.1. Separation of the binary propyl ethanoate + heptane by pressure-swing-distillation

A complete modeling using a multiobjective correlation procedure [60] to represent Gibbs excess function, g<sup>E</sup> /RT, with the proposed model (17), was carried out for the binary propyl ethanoate + heptane in a previous work using extensive experimental data, with iso-T [64] and iso-p [4] VLE data as well as other properties (h<sup>E</sup> , v<sup>E</sup> , c<sup>E</sup> <sup>p</sup> [65]). The resulting model is dependent on the different intensive variables and can estimate VLE in different conditions of pressure and temperature to those used in the combined correlation process with a high degree of reliability. This work compares the degree of representation with those obtained by NRTL and UNIFAC-DM, although the authors' observations are not included here (they are not relevant to this chapter as both models are implemented in ASPEN). Hence, simulation of the separation of the binary is proposed by means of a distillation train with two towers, see diagram in Figure 15, operating at different pressure conditions; the first at atmospheric pressure (p = 101.32 kPa) and the second at high vacuum (p = 7 Pa).

Figure 15. Simulation-scheme to separate the binary propyl ethanoate + heptane by a pressure-swing distillation process.

The pressure in the second column is extremely low, which is difficult to get in practice, but is established here to emphasize the characteristics of pressure-swing-distillation operation. As can be observed in Figure 16, the difference in pressure between the columns significantly displaces the coordinates of the azeotropic point, as estimated by Eq. (17). So, in the first column there is a partial separation of the solution, with the alkane, of high purity, collected in the bottom. The composition obtained in the head of the atmospheric column that feeds the second tower, Figure 15, was established between the azeotropic composition at each pressure, in order to optimize the number of stages.

The influence of the model used on the design was studied [21], and the most significant discrepancy that arises when changing the model occurs in the composition and temperature profiles in the inside of the column as shown in Figure 17, where important differences can be found. Use of the proposed model can therefore, guarantee reproduction of the real behavior of the apparatus.

#### 5.2. Separation of the binary ethyl butanoate + octane by extractive distillation

studied here. Without ignoring these observations, if experimental data are available the model that best represents the real behavior of each system must be chosen in each case.

5. The use of advanced separation techniques in ester + alkane solutions

Advanced distillation techniques for the separation of azeotropic systems are described in detail in Table 1. This section shows some simulated cases of the use of these techniques for the treatment of azeotropic solutions of esters and alkanes. This was carried out using the commercial software Aspen Plus v.8.8 [63], using RadFrac blocks for distillation columns.

5.1. Separation of the binary propyl ethanoate + heptane by pressure-swing-distillation

excess function, g<sup>E</sup>

iso-p [4] VLE data as well as other properties (h<sup>E</sup>

162 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

pressure (p = 101.32 kPa) and the second at high vacuum (p = 7 Pa).

A complete modeling using a multiobjective correlation procedure [60] to represent Gibbs

ethanoate + heptane in a previous work using extensive experimental data, with iso-T [64] and

on the different intensive variables and can estimate VLE in different conditions of pressure and temperature to those used in the combined correlation process with a high degree of reliability. This work compares the degree of representation with those obtained by NRTL and UNIFAC-DM, although the authors' observations are not included here (they are not relevant to this chapter as both models are implemented in ASPEN). Hence, simulation of the separation of the binary is proposed by means of a distillation train with two towers, see diagram in Figure 15, operating at different pressure conditions; the first at atmospheric

Figure 15. Simulation-scheme to separate the binary propyl ethanoate + heptane by a pressure-swing distillation process.

, v<sup>E</sup> , c<sup>E</sup>

/RT, with the proposed model (17), was carried out for the binary propyl

<sup>p</sup> [65]). The resulting model is dependent

In the previous case, it was proposed to reduce the pressure in order to separate the azeotropic solution. Alternatively, an extractant (entrainer) can be used to displace or destroy the azeotrope. This can be illustrated by separating the azeotropic solution ethyl butanoate(1) + octane(2) (x1,az = 0.63, Taz = 392 K a p = 101 kPa). For the preliminary design of this type of process a suitable entrainer must be chosen. In the absence of experimental data, theoretical models are chosen to establish the feasibility of the process. As possible entrainers for the binary selected, two compounds were chosen from the same families (ester and alkane) but with some structural differences, with greater molecular weights and, therefore, higher boiling points: (1) decane (2) butyl

Figure 16. Representation of T vs. x,y of propyl ethanoate(1) + heptane(2). ( ) Experimental values, (–––), Eqs. (8–10).

need to use two columns (separation and recovery) increases the number of design criteria. Therefore, six variables have been taken to configure the first column: number of steps, reflux ratio, solvent/feed ratio, feed stage, solvent stage, and temperature of the solvent. To obtain the best conditions for the planned operation a sensitivity analysis was carried out in relation to different variables, the results of which are summarized in Figure 19. The solvent-feed ratio is the design variable with the most impact on the compositions of ethyl butanoate in the head and octane in the bottom, together with the energy consumption of the process. The reflux

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Maximization of the ethyl butanoate composition in the head and minimization of the composition of solvent (decane) in the head, together with maximization of octane in the bottoms and the energy consumption are the main goals that must be found in the design of the extractive distillation column. The final configuration generated by the simulator is shown in Figure 20.

Figure 19. Sensitivity analysis curves for the following conditions: N = 30, F-S = 20 and S-Stage = 7. (o) S/F = 5; (%) S/F = 6; (1) S/F = 7. ( ) R = 1; ( ) R = 1.33; ( ) R = 1.66; ( ) R = 2. (a) Top composition of ethyl butanoate; (b) bottom

Figure 20. Simulation-scheme to separate the binary ethyl butanoate + octane by extractive distillation.

ratio largely determines the decane contents in the head.

composition of octane; and (c) top composition of decane.

Figure 17. Profiles of temperature (a) and composition (b) for the first and second tower, obtained with Eqs. (17) (–––), NRTL ( ), and UNIFAC ( ). ( )T/K, ( ) liquid phase composition, x; ( ) vapor phase composition, y.

butanoate. Taking into consideration the comments made in Section 3.2 of this chapter, the results obtained by UNIFAC-DM and COSMO-RS are compared being the representation of this azeotropic system more accurate with the former model. On the other hand, the ester + alkane binaries resulting from combining compounds of the mixture with potential solvents give rise to zeotropic systems of high relative volatility, with both models producing good estimations.

The final selection of one solvent or the other is based on the dynamics of the ternary system formed in the column, from analysis of the residual curves, Figure 18. The results obtained show that decane is the best option, since the residual curves rapidly veer toward the line x<sup>1</sup> = 0, facilitating the subsequent separation. Introduction of the solvent in the process and the

Figure 18. Residue curve map for best solvent selection for extractive distillation operation using different entrainers. (a) Decane, (b) butyl butanoate. Curves obtained with UNIFAC-DM.

need to use two columns (separation and recovery) increases the number of design criteria. Therefore, six variables have been taken to configure the first column: number of steps, reflux ratio, solvent/feed ratio, feed stage, solvent stage, and temperature of the solvent. To obtain the best conditions for the planned operation a sensitivity analysis was carried out in relation to different variables, the results of which are summarized in Figure 19. The solvent-feed ratio is the design variable with the most impact on the compositions of ethyl butanoate in the head and octane in the bottom, together with the energy consumption of the process. The reflux ratio largely determines the decane contents in the head.

Maximization of the ethyl butanoate composition in the head and minimization of the composition of solvent (decane) in the head, together with maximization of octane in the bottoms and the energy consumption are the main goals that must be found in the design of the extractive distillation column. The final configuration generated by the simulator is shown in Figure 20.

butanoate. Taking into consideration the comments made in Section 3.2 of this chapter, the results obtained by UNIFAC-DM and COSMO-RS are compared being the representation of this azeotropic system more accurate with the former model. On the other hand, the ester + alkane binaries resulting from combining compounds of the mixture with potential solvents give rise to zeotropic systems of high relative volatility, with both models producing good estimations.

Figure 17. Profiles of temperature (a) and composition (b) for the first and second tower, obtained with Eqs. (17) (–––), NRTL ( ), and UNIFAC ( ). ( )T/K, ( ) liquid phase composition, x; ( ) vapor phase composition, y.

164 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

The final selection of one solvent or the other is based on the dynamics of the ternary system formed in the column, from analysis of the residual curves, Figure 18. The results obtained show that decane is the best option, since the residual curves rapidly veer toward the line x<sup>1</sup> = 0, facilitating the subsequent separation. Introduction of the solvent in the process and the

Figure 18. Residue curve map for best solvent selection for extractive distillation operation using different entrainers. (a)

Decane, (b) butyl butanoate. Curves obtained with UNIFAC-DM.

Figure 19. Sensitivity analysis curves for the following conditions: N = 30, F-S = 20 and S-Stage = 7. (o) S/F = 5; (%) S/F = 6; (1) S/F = 7. ( ) R = 1; ( ) R = 1.33; ( ) R = 1.66; ( ) R = 2. (a) Top composition of ethyl butanoate; (b) bottom composition of octane; and (c) top composition of decane.

Figure 20. Simulation-scheme to separate the binary ethyl butanoate + octane by extractive distillation.
