2. Azeotropy: description of the phenomenon and thermodynamic representation

Etymologically, the term "azeotrope," coined by the chemists J. Wade and R.W. Merriman [22], comes from the Greek combination of three words "a" (without), "zein" (boiling) and "trope" (change), in other words, to boil without change, referring to a solution for which the variables (p,T,x) remain unchanged, which is the main characteristic of this phenomenon. These authors described the phenomenon of azeotropy when studying the VLE of the mixture of water + ethanol at atmospheric pressure. They found that at a given composition of liquid solution the mixture cannot separate as the distilled vapor (with composition y) has the same composition as the remaining liquid (with composition x). Thermodynamic formalism establishes the equality x ¼ y, between the compositions vector of the liquid phase, x ¼ ½ � x1; x2; …; x<sup>n</sup> and the corresponding vapor phase, y ¼ y1; y2; …; y<sup>n</sup> � � of a system with ncomponents, to indicate the presence of an azeotrope. The previous identity implies that the solution behaves, in relation to the distillation process, as a pure product, giving rise to an unusual situation. The behavior is a result of changes in the structure of the final dissolution (in singular conditions), with a different reorganization compared to the original one of pure products. Changes occur in all non-ideal solutions, although not all of them are azeotropic. We may, therefore, ask, "what is the difference? In the case of azeotropes the average interactions that affect the molecules of different compounds in solution are equivalent, causing the volatilities are the same: All components have the same ability to change into the vapor phase, resulting in both phases (líquid and vapor) having the same composition.

VLE thermodynamics states that the partial pressure of each component, p<sup>i</sup> , of a mixture in VLE, is determined by a modified version of Raoult's law:

$$p\_i = y\_i p = \frac{\mathbf{x}\_i \mathbf{y}\_i p\_i^o}{\mathbf{\oplus}\_i} \tag{1}$$

γi

lnΦ<sup>i</sup> <sup>¼</sup> <sup>B</sup>ii <sup>p</sup> � <sup>p</sup><sup>o</sup>

<sup>¼</sup> ln <sup>p</sup><sup>o</sup> 2 po 1

ln <sup>γ</sup><sup>1</sup> γ2

Figure 1. Isobaric-VLE of a binary at different pressures.

binaries gives:

ð Þ¼ <sup>T</sup>; <sup>p</sup>; <sup>x</sup><sup>i</sup> <sup>p</sup>=p<sup>o</sup>

i � � <sup>þ</sup> ð Þ <sup>1</sup>=<sup>2</sup> <sup>p</sup>

<sup>þ</sup> <sup>B</sup><sup>11</sup> <sup>p</sup> � <sup>p</sup><sup>o</sup>

<sup>i</sup> and γ<sup>j</sup> T; p; x<sup>j</sup>

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

must have a real-valued solution. The γ's are a measurement of the non-ideal nature of the liquid phase owing to the interactional effects in the mixing process and depend upon each specific solution, they cannot be known a priori, but are modeled mathematically. The vapor pressures play an important role and depend only upon the equilibrium temperature which, in turn, depends upon the total pressure of the system studied, see Figure 1. For Eq. (4) to be rigorously applied, the parameter Φ<sup>i</sup> is required; this is calculated from expressions found in

> X j X k yj <sup>y</sup><sup>k</sup> <sup>2</sup>δji � <sup>δ</sup>jk � � h i=RT (6)

where δji = 2Bji-Bjj-Bii, and the δjk are easy to deduce; the virial coefficients of the pure compounds Bii and mixtures Bji can be calculated by a correlation process. Adaptation of Eq. (4) to

There is a clear dependence between the quotients of the activity coefficients and the vapor pressures. Bancroft [24] introduced a rule which, at least graphically is intuitive, that the appearance

any textbook on the Thermodynamics of Solutions [23]. Its more general expression is:

1 � � � <sup>B</sup><sup>22</sup> <sup>p</sup> � <sup>p</sup><sup>o</sup>

� � <sup>¼</sup> <sup>p</sup>=p<sup>o</sup>

2

� � <sup>þ</sup> <sup>p</sup>δ<sup>12</sup> <sup>y</sup><sup>1</sup> � <sup>y</sup><sup>2</sup>

<sup>j</sup> (5)

143

http://dx.doi.org/10.5772/intechopen.75786

� � (7)

where p is the total pressure of the system, x<sup>i</sup> and yi, the compositions of compound i in the liquid and vapor phase, respectively, γ<sup>i</sup> ¼ γ<sup>i</sup> x<sup>i</sup> ð Þ ; p; T is the activity coefficient of this compound in the liquid phase, p<sup>o</sup> <sup>i</sup> <sup>¼</sup> <sup>p</sup><sup>o</sup> <sup>i</sup> ð Þ T the vapor pressure of this component, and Φ<sup>i</sup> ¼ Φið Þ y; p; T , related to the fugacity coefficient of pure compound i in solution ϕb<sup>i</sup> , and as saturated vapor ϕ<sup>o</sup> <sup>i</sup> according to the equation,

$$
\ln \mathfrak{O}\_{\rm i} = \ln \left( \frac{\widehat{\phi}\_{\rm i}}{\phi\_{\rm i}^{\rm o}} \right) + \left[ \frac{-\upsilon\_{\rm i}^{\rm o} (p - p\_{\rm i}^{\rm o})}{RT} \right] \tag{2}
$$

The azeotropic condition established previously, x ¼ y, combined with Eq. (1), gives place to the following relationship for azeotropic pressure:

$$p = \gamma\_i p\_i^{\diamond} / \Phi\_i \tag{3}$$

which must be obeyed for all components of the system. Equation (4) implies the following identity between all components of the mixture:

$$\frac{\mathcal{V}\_1 p\_1^o}{\mathfrak{O}\_1} = \frac{\mathcal{V}\_2 p\_2^o}{\mathfrak{O}\_2} = \dots \frac{\mathcal{V}\_i p\_i^o}{\mathfrak{O}\_i} = \dots = \frac{\mathcal{V}\_n p\_n^o}{\mathfrak{O}\_n} \tag{4}$$

This equation is important because it can be used as a starting point for several considerations. For example, at low and moderate pressures Φi≈1 and often at high pressures its value would not vary significantly for different compounds and it is acceptable to assume that Φi=Φj≈1. Therefore, from Eq. (4) it can be deduced that the presence of an azeotrope is due to γ<sup>i</sup> and to po <sup>i</sup> , in other words, for there to be an azeotrope in the VLE equations.

Azeotropy: A Limiting Factor in Separation Operations in Chemical Engineering - Analysis, Experimental… http://dx.doi.org/10.5772/intechopen.75786 143

$$\gamma\_{\mathbf{i}}(T, p, \mathbf{x\_i}) = p/p\_{\mathbf{i}}^{\diamond} \text{ and } \quad \gamma\_{\mathbf{j}}(T, p, \mathbf{x\_j}) = p/p\_{\mathbf{j}}^{\diamond} \tag{5}$$

must have a real-valued solution. The γ's are a measurement of the non-ideal nature of the liquid phase owing to the interactional effects in the mixing process and depend upon each specific solution, they cannot be known a priori, but are modeled mathematically. The vapor pressures play an important role and depend only upon the equilibrium temperature which, in turn, depends upon the total pressure of the system studied, see Figure 1. For Eq. (4) to be rigorously applied, the parameter Φ<sup>i</sup> is required; this is calculated from expressions found in any textbook on the Thermodynamics of Solutions [23]. Its more general expression is:

$$\text{Tr}\Phi\_{\text{i}} = \left[ B\_{\text{ii}} (p - p\_{\text{i}}^{o}) + (1/2)p \sum\_{\text{j}} \sum\_{\text{k}} y\_{\text{j}} y\_{\text{k}} (2\delta\_{\text{ji}} - \delta\_{\text{jk}}) \right] / RT \tag{6}$$

where δji = 2Bji-Bjj-Bii, and the δjk are easy to deduce; the virial coefficients of the pure compounds Bii and mixtures Bji can be calculated by a correlation process. Adaptation of Eq. (4) to binaries gives:

$$\ln \frac{\mathcal{V}\_1}{\mathcal{V}\_2} = \ln \frac{p\_2^o}{p\_1^o} + B\_{11} \left( p - p\_1^o \right) - B\_{22} \left( p - p\_2^o \right) + p \delta\_{12} \left( y\_1 - y\_2 \right) \tag{7}$$

There is a clear dependence between the quotients of the activity coefficients and the vapor pressures. Bancroft [24] introduced a rule which, at least graphically is intuitive, that the appearance

Figure 1. Isobaric-VLE of a binary at different pressures.

mixture of water + ethanol at atmospheric pressure. They found that at a given composition of liquid solution the mixture cannot separate as the distilled vapor (with composition y) has the same composition as the remaining liquid (with composition x). Thermodynamic formalism establishes the equality x ¼ y, between the compositions vector of the liquid phase,

components, to indicate the presence of an azeotrope. The previous identity implies that the solution behaves, in relation to the distillation process, as a pure product, giving rise to an unusual situation. The behavior is a result of changes in the structure of the final dissolution (in singular conditions), with a different reorganization compared to the original one of pure products. Changes occur in all non-ideal solutions, although not all of them are azeotropic. We may, therefore, ask, "what is the difference? In the case of azeotropes the average interactions that affect the molecules of different compounds in solution are equivalent, causing the volatilities are the same: All components have the same ability to change into the vapor phase, resulting in both phases (líquid and vapor) having the same composition.

� � of a system with n-

, of a mixture in

(1)

(2)

(4)

<sup>i</sup> according

x ¼ ½ � x1; x2; …; x<sup>n</sup> and the corresponding vapor phase, y ¼ y1; y2; …; y<sup>n</sup>

142 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

VLE thermodynamics states that the partial pressure of each component, p<sup>i</sup>

lnΦ<sup>i</sup> <sup>¼</sup> ln <sup>ϕ</sup>b<sup>i</sup>

ϕo i

p ¼ γ<sup>i</sup> po

!

p<sup>i</sup> ¼ y<sup>i</sup>

<sup>p</sup> <sup>¼</sup> <sup>x</sup>iγ<sup>i</sup>

<sup>þ</sup> �v<sup>o</sup>

The azeotropic condition established previously, x ¼ y, combined with Eq. (1), gives place to

which must be obeyed for all components of the system. Equation (4) implies the following

<sup>¼</sup> … <sup>γ</sup><sup>i</sup> po i Φi

This equation is important because it can be used as a starting point for several considerations. For example, at low and moderate pressures Φi≈1 and often at high pressures its value would not vary significantly for different compounds and it is acceptable to assume that Φi=Φj≈1. Therefore, from Eq. (4) it can be deduced that the presence of an azeotrope is due to γ<sup>i</sup> and to

where p is the total pressure of the system, x<sup>i</sup> and yi, the compositions of compound i in the liquid and vapor phase, respectively, γ<sup>i</sup> ¼ γ<sup>i</sup> x<sup>i</sup> ð Þ ; p; T is the activity coefficient of this compound in the

po i Φi

<sup>i</sup> ð Þ T the vapor pressure of this component, and Φ<sup>i</sup> ¼ Φið Þ y; p; T , related to

<sup>i</sup> <sup>p</sup> � <sup>p</sup><sup>o</sup> i � � RT � �

<sup>¼</sup> … <sup>¼</sup> <sup>γ</sup>np<sup>o</sup>

n Φ<sup>n</sup>

, and as saturated vapor ϕ<sup>o</sup>

<sup>i</sup> =Φ<sup>i</sup> (3)

VLE, is determined by a modified version of Raoult's law:

the fugacity coefficient of pure compound i in solution ϕb<sup>i</sup>

the following relationship for azeotropic pressure:

identity between all components of the mixture:

γ1p<sup>o</sup> 1 Φ<sup>1</sup>

<sup>¼</sup> <sup>γ</sup>2p<sup>o</sup> 2 Φ<sup>2</sup>

<sup>i</sup> , in other words, for there to be an azeotrope in the VLE equations.

liquid phase, p<sup>o</sup>

to the equation,

po

<sup>i</sup> <sup>¼</sup> <sup>p</sup><sup>o</sup>

of an azeotrope in a homogeneous solution is dependent on the equality of the vapor pressures at a given temperature, ignoring the final summands of Eq. (7). The point of intersection of the vapor pressures is called the Bancroft point; although absence of this point does not imply that there is no azeotrope.We insist that one of the most important aspects is to determine the structural behavior of the solution, because the formation of these singular states that identify the azeotropic condition with a pure compound, as mentioned previously, is of significance in the applicability of specific fluids (as occurs in other phase equilibria). This is why it is interesting to define the formation of azeotropes knowing the existence of interactions between different molecules, which can be of attractive nature (favoring the mixing process), or repulsive (impeding it). In the first case, the solution presents a negative deviation of Raoult's law γ<sup>i</sup> < 1, and according to Eq.(4) the p<sup>o</sup> <sup>i</sup> will be higher than in an ideal solution as would also be the equilibrium temperatures,Figure 2(a). If the net interactional effect is repulsive, γ<sup>i</sup> > > 1, p<sup>o</sup> <sup>i</sup> would be lower to balance out the total pressure. Now, the equilibrium temperatures also diminish creating an azeotrope of minimum temperature, Figure 2 (b). Occasionally, the effects of the interactions of a solution are not entirely attractive or repulsive, but their sign varies depending on the state (T,p,x) of the system. In these cases, Eqs. (4) and (5) are satisfied in different regions of the equilibrium plots, and present more than one azeotrope (polyazeotropy), see Figure 2(c). When the solution is affected by strong repulsive effects, the liquid phase becomes unstable and separates into two immiscible liquid phases (liquid-liquid equilibrium, LLE) [25]. High values of the activity coefficients associated with this repulsion favor the formation of azeotropes at a minimum temperature. Sometimes, both phenomena (immiscibility and azeotropy) occur in the same conditions (p,T,x,y), Figure 2(d), giving rise to systems in LLE, VLLE. The types of azeotropes indicated in Figure 2 for binary solutions also occur in multicomponent systems, although the behavior of the solution is more complex. To illustrate this,Figure 3 shows the residues, see [3], of some examples of ternaries. The presence of an azeotrope in one of the binaries, Figure 3(a), divides the diagram into two distillation regions by a line that joins the stable node with the unstable node. None of the distillation processes occurring in either of the regions could pass from one to the other, because as they move closer to the region boundary, it will tend to fall to the azeotropic point (stable node). The presence of two azeotropic points would not necessarily change the behavior unless this corresponded to some kind of stable node. Hence, if the azeotrope corresponds to a maximum temperature, it can become an unstable node, Figure 3(b), altering the separation regions.

Ternary azeotropes (those produced in the presence of three solution components) do not necessarily correspond to the minimum points of the diagram; occasionally, Figure 3(c), they are presented as a saddle-point. However, when they do correspond to the minimum temperature, they also become the stable node for any distillation region. In these cases, the remaining

Figure 3. Examples of ternary VLE of azeotropic systems. ( ) stable node, ( ) unstable node, ( ) saddle-point, (———) separating line. (a) One binary azeotrope, (b) two binary azeotropes, (c) two binary azeotropes and one ternary, (d)

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

http://dx.doi.org/10.5772/intechopen.75786

145

In the experimental characterization of an azeotrope the following parameters or properties must also be specified: (a) composition, (b) boiling point at a given pressure, and (c) the differences between the boiling points of the azeotrope and the most volatile component (positive azeotrope) or that of the component of the lowest boiling point (negative azeotrope). It is usual to specify values for the variables of (a) and (b) to characterize the azeotrope,

3. Characterization of azeotropes. Results for ester + alkane solutions

3.1. Experimental techniques for the determination of azeotropes. Details and

although the result that establishes (c) should also be given in each case.

azeotropes also become saddle-points, Figure 3(d).

minimum temperature ternary azeotrope.

recommendation

Figure 2. Azeotrope types. (a) Maximum temperature, (b) minimum temperature, (c) polyazeotrope, and (d) nonhomogeneous azeotrope. V, vapor phase, L, homogeneous liquid phase, and L1 and L2 liquid phases of immiscible system.

Azeotropy: A Limiting Factor in Separation Operations in Chemical Engineering - Analysis, Experimental… http://dx.doi.org/10.5772/intechopen.75786 145

of an azeotrope in a homogeneous solution is dependent on the equality of the vapor pressures at a given temperature, ignoring the final summands of Eq. (7). The point of intersection of the vapor pressures is called the Bancroft point; although absence of this point does not imply that there is no azeotrope.We insist that one of the most important aspects is to determine the structural behavior of the solution, because the formation of these singular states that identify the azeotropic condition with a pure compound, as mentioned previously, is of significance in the applicability of specific fluids (as occurs in other phase equilibria). This is why it is interesting to define the formation of azeotropes knowing the existence of interactions between different molecules, which can be of attractive nature (favoring the mixing process), or repulsive (impeding it). In the first case, the solution presents a negative deviation of Raoult's law γ<sup>i</sup> < 1, and according to Eq.(4) the p<sup>o</sup>

higher than in an ideal solution as would also be the equilibrium temperatures,Figure 2(a). If the net

equilibrium temperatures also diminish creating an azeotrope of minimum temperature, Figure 2 (b). Occasionally, the effects of the interactions of a solution are not entirely attractive or repulsive, but their sign varies depending on the state (T,p,x) of the system. In these cases, Eqs. (4) and (5) are satisfied in different regions of the equilibrium plots, and present more than one azeotrope (polyazeotropy), see Figure 2(c). When the solution is affected by strong repulsive effects, the liquid phase becomes unstable and separates into two immiscible liquid phases (liquid-liquid equilibrium, LLE) [25]. High values of the activity coefficients associated with this repulsion favor the formation of azeotropes at a minimum temperature. Sometimes, both phenomena (immiscibility and azeotropy) occur in the same conditions (p,T,x,y), Figure 2(d), giving rise to systems in LLE, VLLE. The types of azeotropes indicated in Figure 2 for binary solutions also occur in multicomponent systems, although the behavior of the solution is more complex. To illustrate this,Figure 3 shows the residues, see [3], of some examples of ternaries. The presence of an azeotrope in one of the binaries, Figure 3(a), divides the diagram into two distillation regions by a line that joins the stable node with the unstable node. None of the distillation processes occurring in either of the regions could pass from one to the other, because as they move closer to the region boundary, it will tend to fall to the azeotropic point (stable node). The presence of two azeotropic points would not necessarily change the behavior unless this corresponded to some kind of stable node. Hence, if the azeotrope corresponds to a maximum temperature, it can become an unstable node, Figure 3(b), altering the

Ternary azeotropes (those produced in the presence of three solution components) do not necessarily correspond to the minimum points of the diagram; occasionally, Figure 3(c), they

Figure 2. Azeotrope types. (a) Maximum temperature, (b) minimum temperature, (c) polyazeotrope, and (d) nonhomogeneous azeotrope. V, vapor phase, L, homogeneous liquid phase, and L1 and L2 liquid phases of immiscible system.

<sup>i</sup> would be lower to balance out the total pressure. Now, the

interactional effect is repulsive, γ<sup>i</sup> > > 1, p<sup>o</sup>

144 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

separation regions.

<sup>i</sup> will be

Figure 3. Examples of ternary VLE of azeotropic systems. ( ) stable node, ( ) unstable node, ( ) saddle-point, (———) separating line. (a) One binary azeotrope, (b) two binary azeotropes, (c) two binary azeotropes and one ternary, (d) minimum temperature ternary azeotrope.

are presented as a saddle-point. However, when they do correspond to the minimum temperature, they also become the stable node for any distillation region. In these cases, the remaining azeotropes also become saddle-points, Figure 3(d).

## 3. Characterization of azeotropes. Results for ester + alkane solutions

#### 3.1. Experimental techniques for the determination of azeotropes. Details and recommendation

In the experimental characterization of an azeotrope the following parameters or properties must also be specified: (a) composition, (b) boiling point at a given pressure, and (c) the differences between the boiling points of the azeotrope and the most volatile component (positive azeotrope) or that of the component of the lowest boiling point (negative azeotrope). It is usual to specify values for the variables of (a) and (b) to characterize the azeotrope, although the result that establishes (c) should also be given in each case.

Azeotropic points are experimentally determined by several procedures that can be grouped into two categories: direct and indirect. Direct measurements are applied to determine the azeotropic composition inside the apparatus, with the greatest accuracy possible. Experimentalists frequently make mistakes when verifying the precision of the azeotropic coordinates, as the starting products do not always have the desired purity, which distorts the values of the state variables. The commonest example concerns the presence of moisture in the components of a binary system, resulting in the formation of binary or ternary azeotropes with the water; this can even give rise to the appearance of unexpected azeotropes in some systems. Hence, azeotropic experimentation must be rigorous and include a careful rectification procedure. The precise variables of azeotropes can be obtained in a differential ebulliometer [26], such as the one shown in Figure 4, with different regions for boiling and condensation, both working to rectify the study mixture, although the temperature on reaching equilibrium must be the same at a given pressure. A recent design for a differential ebulliometer has been proposed by Raal et al. [27].

Several studies are described in the literature [28–30] in which the authors use small or mediumscale installations with distillation columns with a high number of equilibrium phases, operating at total reflux and isobaric conditions. These columns can reach a very similar composition to that of the azeotrope in the reflux, after reaching a steady state. Figure 4 shows a diagram of an installation Figure 5. Packed-tower used for the direct determination of azeotropic points showing details of the installation and auxiliary apparatus. On right, data representations and flow control of these characteristics. To collect the purest fraction possible of an azeotrope a differential ebulliometer is placed adjacent to a distillation column. The pure azeotrope is, therefore, determined in the differential ebulliometer and the difference between the boiling points of the

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

http://dx.doi.org/10.5772/intechopen.75786

147

reference compound and that of the azeotrope, with the purpose of estimating the latter.

Figure 5 shows a diagram of the experimental apparatus used in our laboratory to directly measure azeotropic points using a distillation column. This experimental design is useful to characterize the azeotropic points relative to pressure, and to determine the separate regions in systems. The former is carried out by adjusting the pressure of the system to reach a stable temperature at the head of the column, to then take samples of the reflux for analysis. In the case of ternary systems, different starting compositions are used, with the purpose of conducting the experiment in the separate regions. The main drawback of this experimental technique is that the data obtained are not useful for the modeling process, as discrete points are obtained. In any

Figure 5. Packed-tower used for the direct determination of azeotropic points showing details of the installation and

auxiliary apparatus. On right, data representations and flow control.

Figure 4. Differential ebulliometer [26].

Several studies are described in the literature [28–30] in which the authors use small or mediumscale installations with distillation columns with a high number of equilibrium phases, operating at total reflux and isobaric conditions. These columns can reach a very similar composition to that of the azeotrope in the reflux, after reaching a steady state. Figure 4 shows a diagram of an installation Figure 5. Packed-tower used for the direct determination of azeotropic points showing details of the installation and auxiliary apparatus. On right, data representations and flow control of these characteristics. To collect the purest fraction possible of an azeotrope a differential ebulliometer is placed adjacent to a distillation column. The pure azeotrope is, therefore, determined in the differential ebulliometer and the difference between the boiling points of the reference compound and that of the azeotrope, with the purpose of estimating the latter.

Azeotropic points are experimentally determined by several procedures that can be grouped into two categories: direct and indirect. Direct measurements are applied to determine the azeotropic composition inside the apparatus, with the greatest accuracy possible. Experimentalists frequently make mistakes when verifying the precision of the azeotropic coordinates, as the starting products do not always have the desired purity, which distorts the values of the state variables. The commonest example concerns the presence of moisture in the components of a binary system, resulting in the formation of binary or ternary azeotropes with the water; this can even give rise to the appearance of unexpected azeotropes in some systems. Hence, azeotropic experimentation must be rigorous and include a careful rectification procedure. The precise variables of azeotropes can be obtained in a differential ebulliometer [26], such as the one shown in Figure 4, with different regions for boiling and condensation, both working to rectify the study mixture, although the temperature on reaching equilibrium must be the same at a given pressure. A recent design for a differential ebulliometer has been proposed by Raal et al. [27].

146 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

Figure 4. Differential ebulliometer [26].

Figure 5 shows a diagram of the experimental apparatus used in our laboratory to directly measure azeotropic points using a distillation column. This experimental design is useful to characterize the azeotropic points relative to pressure, and to determine the separate regions in systems. The former is carried out by adjusting the pressure of the system to reach a stable temperature at the head of the column, to then take samples of the reflux for analysis. In the case of ternary systems, different starting compositions are used, with the purpose of conducting the experiment in the separate regions. The main drawback of this experimental technique is that the data obtained are not useful for the modeling process, as discrete points are obtained. In any

Figure 5. Packed-tower used for the direct determination of azeotropic points showing details of the installation and auxiliary apparatus. On right, data representations and flow control.

case, the azeotropes measured must only be used to complement data available in the complete VLE diagrams.

3.2. Verification of experimental data

repercussions on subsequent operations.

is based on the following rules:

The high quality of the starting products and the improvement in the instrumentation and control systems combined with standardization of the experimental protocols, increase the probability of obtaining quality data. In any case, it is important to turn to mathematicalthermodynamic procedures that certify the quality of those dat, as these have important

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

http://dx.doi.org/10.5772/intechopen.75786

There is a widespread tendency in thermodynamics to establish relationships that verify the scientific coherence between the variables measured, in other words, that establish the thermodynamic consistency of the data. Although there are several ways to do this [31, 32], they are of limited scope. In other words, the verification of data must be applied to VLE data before determining the azeotropic coordinates (indirect method). A strategy to check the consistency

1. Experimental VLE data are analyzed in graphical form showing the variables measured (x, y, T, p) and those calculated with the thermodynamic formulation, γ<sup>i</sup> and g<sup>E</sup>

2. The experimental data must be modeled to solve most of the consistency tests. Recom-

3. A combination of several consistency tests must be used to confirm the quality of the data and their coherence. The tests as the Areas-test [33] and the Fredenslund-test [34] are recommended, together with a third procedure, although they cannot be used in some cases of azeotropy, such as those appearing in partially miscible systems, Figure 1(d), or polyazeotropes, Figure 1(c). Alternatively, a method proposed by the authors [19], with a

4. It is also worth mentioning here a method that should be avoided. The method of Herington [35] produces incorrect results by assuming false hypotheses [36] in certain cases. In general, no Area-test should be used as the sole test as they are insensitive to pressure errors [37]. The composition/resolution-test [38], or any other test aimed at exactly obeying thermodynamic relations should also be avoided as they are very limiting.

When applying the consistency test to azeotropic systems some peculiarities must be taken into account. As an example, a brief description is included below of the application of two

• Area-test (Redlich-Kister [33] or other): the method is based on solving the integral,

ð<sup>x</sup>1¼<sup>1</sup> x1¼0 ln <sup>γ</sup><sup>1</sup> γ2

dx<sup>1</sup> (8)

A ¼

mum temperature (or maximum or minimum pressures).

mendations for this are provided in Section 3 of this chapter.

more rigorous thermodynamic formulation, could be used.

tests commonly used to analyze VLE data.

coherence of these quantities must be illustrated in graphs, otherwise the location of the azeotropes can change. In azeotropic systems, the plot of (y-x) vs. x is important as the intersection of the distribution of points with the x-axis indicates the presence of an azeotrope. In binaries, the coordinates of this point coincide with the minimum or maxi-

. The

149

The indirect technique to determine the coordinates of the azeotropic points consists in interpolating from data determined for the VLE diagram. This is the most widespread procedure [13–15, 26], and the standard one recommended for azeotropes as it describes the entire VLE in given conditions of pressure and temperature. Likewise, an example of the experimental installation to determine VLE data is shown in Figure 6, with a small ebulliometer [13, 14] used in our laboratory equipped with a Cotrell pump and a small rectification zone, with temperature differences as specified previously. The samples for binary systems are studied by densimetry/refractometry for ternary systems by gas chromatography. Optimal functioning is achieved by automating the system with suitable software that can carefully control the different variables.

One advantage of the system is that it can obtain a large quantity of data to produce an precise characterization of the VLE. The combination of this technique with the direct method is optimum: the indirect method is used to determine the VLE diagrams of the system in discrete conditions and this information is complemented by azeotropic data at different pressures.

Figure 6. Experimental installation for the experimental determination of VLE, ebulliometer and details of auxiliary equipment.

#### 3.2. Verification of experimental data

case, the azeotropes measured must only be used to complement data available in the complete

The indirect technique to determine the coordinates of the azeotropic points consists in interpolating from data determined for the VLE diagram. This is the most widespread procedure [13–15, 26], and the standard one recommended for azeotropes as it describes the entire VLE in given conditions of pressure and temperature. Likewise, an example of the experimental installation to determine VLE data is shown in Figure 6, with a small ebulliometer [13, 14] used in our laboratory equipped with a Cotrell pump and a small rectification zone, with temperature differences as specified previously. The samples for binary systems are studied by densimetry/refractometry for ternary systems by gas chromatography. Optimal functioning is achieved by automating the system with suitable software

One advantage of the system is that it can obtain a large quantity of data to produce an precise characterization of the VLE. The combination of this technique with the direct method is optimum: the indirect method is used to determine the VLE diagrams of the system in discrete conditions and this information is complemented by azeotropic data at

Figure 6. Experimental installation for the experimental determination of VLE, ebulliometer and details of auxiliary

VLE diagrams.

different pressures.

equipment.

that can carefully control the different variables.

148 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

The high quality of the starting products and the improvement in the instrumentation and control systems combined with standardization of the experimental protocols, increase the probability of obtaining quality data. In any case, it is important to turn to mathematicalthermodynamic procedures that certify the quality of those dat, as these have important repercussions on subsequent operations.

There is a widespread tendency in thermodynamics to establish relationships that verify the scientific coherence between the variables measured, in other words, that establish the thermodynamic consistency of the data. Although there are several ways to do this [31, 32], they are of limited scope. In other words, the verification of data must be applied to VLE data before determining the azeotropic coordinates (indirect method). A strategy to check the consistency is based on the following rules:


When applying the consistency test to azeotropic systems some peculiarities must be taken into account. As an example, a brief description is included below of the application of two tests commonly used to analyze VLE data.

• Area-test (Redlich-Kister [33] or other): the method is based on solving the integral,

$$A = \int\_{\mathbf{x}\_1=0}^{\mathbf{x}\_1=1} \ln \frac{\mathcal{V}\_1}{\mathcal{V}\_2} d\mathbf{x}\_1 \tag{8}$$

which should produce a result close to zero. As mentioned above, the activity coefficients at the azeotropic points are identified with the quotient of the vapor pressures, which provides an additional verification of the data.

• Fredenslund-test [34]: in this case the inconsistency is quantified by the residue generated by this model when reproducing the vapor phase of the VLE system, determining the quality from the difference:

$$
\delta y = \left| y\_{\text{exp}} - y\_{\text{cal}} \right| \tag{9}
$$

According to this formation, the coordinates of the azeotropic point are only verified with data from the liquid phase:

$$\delta y\_1 = \left| \mathbf{x}\_{1,\text{exp}} - \frac{\mathbf{x}\_{1,\text{exp}} \boldsymbol{\gamma}\_1 \mathbf{p}\_1^o}{\mathbf{x}\_{2,\text{exp}} \boldsymbol{\gamma}\_2 \mathbf{p}\_2^o + \mathbf{x}\_{1,\text{exp}} \boldsymbol{\gamma}\_1 \mathbf{p}\_1^o} \right| = \mathbf{x}\_{1,\text{exp}} \mathbf{x}\_{2,\text{exp}} \left| \frac{\boldsymbol{\gamma}\_2 \mathbf{p}\_2^o - \boldsymbol{\gamma}\_1 \mathbf{p}\_1^o}{\boldsymbol{\gamma}\_2 \mathbf{p}\_2^o + \mathbf{x}\_{1,\text{exp}} \left(\boldsymbol{\gamma}\_1 \mathbf{p}\_1^o - \boldsymbol{\gamma}\_2 \mathbf{p}\_2^o\right)} \right| \tag{10}$$

which should have a value less than 0.01.

In the two cases presented here, the quality of the azeotropic data is linked to the determination of their coordinates by the indirect method. Hence, the azeotropes are verified in the same way as the rest of the data from the VLE series. In order to obtain a procedure that verify the data obtained by the direct method, it is convenient to recur to the test proposed by ours [19], which has the following general expression for a VLE binary (assuming an ideal vapor phase, see [19]):

$$\frac{y\_1 - x\_1}{y\_1(1 - y\_1)} = \left(\frac{1}{p} - \frac{v^\mathrm{E}}{RT}\right) dp + \left(\frac{h^\mathrm{E}}{RT^2} - \sum\_{i=1}^2 x\_i \frac{\partial \ln p\_i^o}{\partial T}\right) dT \tag{11}$$

and imposing the condition of azeotropy:

$$\frac{dT}{dp} = -\frac{\left(\frac{1}{p} - \frac{v^{\mathbb{E}}}{RT}\right)}{\left(\frac{h^{\mathbb{E}}}{RT^2} - \sum\_{i=1}^{2} \mathbf{x}\_i \frac{\partial \ln p\_i^o}{\partial T}\right)}\tag{12}$$

C

H5 12 Pentane

To

To

To

To

To

To

b ¼ 447.30 K

E

Z50

b ¼ 423.97 K

E

Z12

b ¼ 398.82 K

b ¼ 371.60 K

b ¼ 341.88 K

b ¼ 309.30 K

C

C

H3 O6 2

Ethyl methanoate

Methyl ethanoate

C

H4 O8 2

Ethyl ethanoate

Methyl propanoate Propyl methanoate

C

H5 10

O2.

Ethyl propanoate

Propyl

To

E

E

Z41

DZ7

Z41

> b ¼ 374.69 K

> > ethanoate

Methyl butanoate

Butyl methanoate

C

H6 12

O2

Ethyl butanoate

To

E

E

Z47,54

E

Z7,49

E(0.637,392.06)

D(0.646,391.65)

 7

 47

E

E

Z42

151

Z49

Z42

> b ¼ 394.60 K

To

E

E

Z43

Z39

> b ¼ 379.30 K

To

E

E

Z47

Z42

> b ¼ 375.90 K

To

E

E

Z47

DZ7

Z14

> b ¼ 372.20 K

To

¼354.00 K

E

Z39

> b

To

¼352.90 K

E

Z14

> b

To

¼350.26 K

E

Z40

> b

To

E(0.203,307.28)17

E(0.683,325.44)17

E(0.962,329.93)17

E

E

E

Z17

Z17

Z17

E(0.934,329.6)45

D(0.703,322.65)7

D(0.665,324.80)52

E(0.339,338.15)40

E(0.834,349.99)40

E

E

E

Z40

E

Z 7

Z40

E

Z7

Z40

E

Z7

D(0.947,350.05)

 7 E

Z56

E(0.343,338.00)46

E(0.343,338.30)53

E(0.279,339.38)47

E(0.844,351.86)14

E

E

E

Z42

Z14

Z47

E(0.929,352.75)

 7

E(0.216,339.95)7

E(0.283,339.10)43

E(0.763,352.20)12

E

E

E

Z50

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

Z12

E

Z55

Z12

E

Z55

E(0.736,351.35)7

E(0.786,352.20)55

E(0.481,366.61)14

E

E

E

Z42

Z14

Z47

E(0.465,366.15)7

E(0.423,366.99)41

E(0.973,374.31)41

E

E

Z41

Z41

E

Z48

D(0.421,366.75)29

DZ 7

E(0.423,366.90)48

E(0.404,367.65)49

E(0.974,375.59)47

E

E

Z42

http://dx.doi.org/10.5772/intechopen.75786

Z49

D(0.346,368.25)7

DZ7

E(0.398,368.22)45

E(0.297,368.80)12

E(0.872,379.10)12

 E

Z12

E

Z50

D(0.346,367.15)7

E(0.295,336.75)7

D(0.295,305.65)7

b ¼ 330.02 K

To

b ¼ 327.50 K

H2 O4 2

Methyl methanoate

To

E(0.558,293.90)39

E(0.832,302.62)43

E(0.992,304.69)45

E

Z12

E(0.849,302.65)57

E

Z12

D(0.575,294.15)7

D(0.574,294.85)7

E(0.218,306.50)39

E(0.703,323.32)43

E(0.988,327.30)7

E

E

E

Z50

E

Z51

Z12

E

Z51

Z12

E

Z51

D(0.973,329.75)7

E(0.709,323.21)51

D(0.669,324.90)7

E

Z51

D(0.215,307.15)7

DZ7

E

Z7

b ¼ 304.80 K

Hexane

Heptane

Octane

Nonane

Decane

C

H6 14

C

H7 16

C

H8 18

C

H9 20

C10

H22

Integration of Eq. (12), must be carried out numerically as it corresponds to a differential equation of non-separable variables that relates the azeotropic temperature with the pressure of the system. Estimation of the difference between the temperature obtained by Eq. (12) and the experimental temperature is sufficient to verify thermodynamic consistency.

#### 3.3. Azeotropy in ester-alkane solutions

#### 3.3.1. Preliminary analysis

The energetic and volumetric effects of the mixing process of esters and alkanes, due to inter/intra molecular interactions, present net positive values for g<sup>E</sup> function, with activity coefficients greater


Azeotropy: A Limiting Factor in Separation Operations in Chemical Engineering - Analysis, Experimental… http://dx.doi.org/10.5772/intechopen.75786

which should produce a result close to zero. As mentioned above, the activity coefficients at the azeotropic points are identified with the quotient of the vapor pressures, which provides

• Fredenslund-test [34]: in this case the inconsistency is quantified by the residue generated by this model when reproducing the vapor phase of the VLE system, determining the

> δy ¼ yexp � ycal � � �

According to this formation, the coordinates of the azeotropic point are only verified with data

In the two cases presented here, the quality of the azeotropic data is linked to the determination of their coordinates by the indirect method. Hence, the azeotropes are verified in the same way as the rest of the data from the VLE series. In order to obtain a procedure that verify the data obtained by the direct method, it is convenient to recur to the test proposed by ours [19], which has the following general expression for a VLE binary (assuming an ideal vapor phase, see [19]):

dp þ

1 <sup>p</sup> � <sup>v</sup><sup>E</sup> RT � �

hE RT<sup>2</sup> � <sup>P</sup> 2 i¼1 xi ∂lnp<sup>o</sup> i ∂T

Integration of Eq. (12), must be carried out numerically as it corresponds to a differential equation of non-separable variables that relates the azeotropic temperature with the pressure of the system. Estimation of the difference between the temperature obtained by Eq. (12) and

The energetic and volumetric effects of the mixing process of esters and alkanes, due to inter/intra molecular interactions, present net positive values for g<sup>E</sup> function, with activity coefficients greater

hE RT<sup>2</sup> �<sup>X</sup> 2

i¼1 xi ∂lnp<sup>o</sup> i ∂T

!

� <sup>¼</sup> <sup>x</sup>1, expx2, exp

1

� � �

1

<sup>2</sup> <sup>þ</sup> <sup>x</sup>1, expγ1p<sup>o</sup>

<sup>p</sup> � <sup>v</sup><sup>E</sup> RT � �

the experimental temperature is sufficient to verify thermodynamic consistency.

dT dp ¼ � � �

� (9)

<sup>2</sup> � <sup>γ</sup>1p<sup>o</sup> 1

> <sup>1</sup> � <sup>γ</sup>2p<sup>o</sup> 2

dT (11)

� � � � �

(10)

� �

γ2p<sup>o</sup>

� � (12)

<sup>2</sup> <sup>þ</sup> <sup>x</sup>1, exp <sup>γ</sup>1p<sup>o</sup>

γ2p<sup>o</sup>

� � � � �

an additional verification of the data.

quality from the difference:

<sup>δ</sup>y<sup>1</sup> <sup>¼</sup> <sup>x</sup>1, exp � <sup>x</sup>1, expγ1p<sup>o</sup>

which should have a value less than 0.01.

and imposing the condition of azeotropy:

3.3. Azeotropy in ester-alkane solutions

3.3.1. Preliminary analysis

x2, expγ2p<sup>o</sup>

150 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

y<sup>1</sup> � x<sup>1</sup> y<sup>1</sup> 1 � y<sup>1</sup>

� � <sup>¼</sup> <sup>1</sup>

from the liquid phase:

� � � � 151


Table 2. Experimental azeotropic coordinates of binary solutions of (an ester + an alkane) at p = 101.32 kPa, (xaze,Taze/K). Type of technique: E = ebulliometry, D = Distillation, Z = zeotropic system.

than one. This is demonstrated in previous studies [12, 14, 17], together with the presence of minimum boiling point azeotropic points for these solutions; we begin with systems at standard pressure. Table 2 gives the azeotropic coordinates at p = 101.32 kPa available in the literature for alkyl (methyl to butyl) alkanoate (methanoate to butanoate) + alkane (pentane to decane). The esters are arranged according to molecular weight, grouping together the different isomers with similar vapor pressures. Five systems (ethyl methanoate + pentane, methyl methanoate + hexane or heptane, and propyl ethanoate or methyl butanoate + octane) present different results depending of the consulted reference: most of the studies do not report azeotropy but others do.

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

In most cases, isomeric esters with the same molecular formula have azeotropes with the same alkanes, although this rule is not obeyed by the propyl ethanoate + octane system. An increase in the number of carbons in the ester produces an increase in the appearance of azeotropic points with a lower number of alkanes, resulting from a reduction in the activity coefficients and decreased net effects of the interactions. In esters of greater molecular weight, azeotropes are formed with hydrocarbons of similar vapor pressure as the esters, but with different boiling points for the last esters in the series. For example, propyl butanoate forms azeotropes

phenomenon is described if a hydrocarbon is taken as a reference and the ester is changed. This means that the temperature differences that produce the azeotropy tend to decrease as described in Figure 7. The azeotropes arise in solutions of compounds with similar boiling

<sup>b</sup><17 K, or with decane, δT<sup>o</sup>

<sup>b</sup><31 K. In a more

http://dx.doi.org/10.5772/intechopen.75786

153

<sup>b</sup>>37 K. The same

<sup>b</sup><8 K, but no with octane, δT<sup>o</sup>

extreme case, methyl methanoate forms an azeotrope with hexane, where δT<sup>o</sup>

Figure 7. Azeotropes-diagram for ester + alkane mixtures: ( ) zeotropic and ( ) azeotropic.

with nonane, δT<sup>o</sup>

than one. This is demonstrated in previous studies [12, 14, 17], together with the presence of minimum boiling point azeotropic points for these solutions; we begin with systems at standard pressure. Table 2 gives the azeotropic coordinates at p = 101.32 kPa available in the literature for alkyl (methyl to butyl) alkanoate (methanoate to butanoate) + alkane (pentane to decane). The esters are arranged according to molecular weight, grouping together the different isomers with similar vapor pressures. Five systems (ethyl methanoate + pentane, methyl methanoate + hexane or heptane, and propyl ethanoate or methyl butanoate + octane) present different results depending of the consulted reference: most of the studies do not report azeotropy but others do.

In most cases, isomeric esters with the same molecular formula have azeotropes with the same alkanes, although this rule is not obeyed by the propyl ethanoate + octane system. An increase in the number of carbons in the ester produces an increase in the appearance of azeotropic points with a lower number of alkanes, resulting from a reduction in the activity coefficients and decreased net effects of the interactions. In esters of greater molecular weight, azeotropes are formed with hydrocarbons of similar vapor pressure as the esters, but with different boiling points for the last esters in the series. For example, propyl butanoate forms azeotropes with nonane, δT<sup>o</sup> <sup>b</sup><8 K, but no with octane, δT<sup>o</sup> <sup>b</sup><17 K, or with decane, δT<sup>o</sup> <sup>b</sup><31 K. In a more extreme case, methyl methanoate forms an azeotrope with hexane, where δT<sup>o</sup> <sup>b</sup>>37 K. The same phenomenon is described if a hydrocarbon is taken as a reference and the ester is changed. This means that the temperature differences that produce the azeotropy tend to decrease as described in Figure 7. The azeotropes arise in solutions of compounds with similar boiling

Figure 7. Azeotropes-diagram for ester + alkane mixtures: ( ) zeotropic and ( ) azeotropic.

C

H5 12 Pentane

To

To

To

To

To

To

b ¼ 447.30 K

E

Z42

b ¼ 423.97 K

E

Z42,48

b ¼ 398.82 K

E(0.581,392.88)42

D(0.586,391.95)

 7

b ¼ 371.60 K

E

Z42

E

Z48

b ¼ 341.88 K

E

Z42

b ¼ 309.30 K

E

Z42

> Propyl propanoate

Butyl ethanoate

C

H7 14

O2

Propyl butanoate

Butyl propanoate

C

H8 16 Table 2. Z = zeotropic system.

Experimental

 azeotropic coordinates

 of binary solutions of (an ester + an alkane) at p = 101.32 kPa,

O2

Butyl butanoate

To

E

E

E

E

Z42

Z42

Z42

Z42

> b ¼ 419.65 K

To

E

E

E

E

E

Z42

E(0.790,438.29)42

Z42 (xaze,Taze/K).

 Type of technique: E =

ebulliometry,

 D = Distillation,

Z42

Z42

Z42

> b ¼ 438.61 K

To

E

E

E

Z48,42

E

Z42

E(0.713,415.16)42

E

Z42

E(0.726,414.40)48

152 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

E(0.628,417.12)42

 E

Z42

Z42

Z42

> b ¼ 416.20 K

To

E

E

Z20,44

E

Z20

E(0.553,394.00)20

E

E

Z20

Z20

D(0.486,393.65)

 7

Z20

> b ¼ 399.20 K

To

b ¼ 395.60 K

Hexane

Heptane

Octane

Nonane

Decane

C

H6 14

C

H7 16

C

H8 18

C

H9 20

C10

H22

points arranged near to the diagonal, from the bottom left corner (methyl methanoate +

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

http://dx.doi.org/10.5772/intechopen.75786

155

The distance from the azeotropic points to the diagonal becomes shorter as the boiling points of the products increase, and it is deduced that the probability that an ester forms an azeotrope with a given alkane varies with the molecular weight of that ester, although this is reflected in the VLE diagram of the system. Figure 8 shows the VLE curves of the solutions composed of the different esters and heptane. The difference between the liquid and vapor curves, which shows the volatility, is greater in systems with a smaller ester. This difference only significantly decreases with an increase in the molecular weight of the ester, but does not significantly change with the isomers. This is a result of a decrease in the non-ideality of the liquid phase (γ ≈ 1) in solutions of the larger esters. This change makes it possible to find azeotropes in esters with four carbons, but not in esters with six carbons, in spite of similar differences between the boiling point of the esters and heptane. In ester solutions with five carbons, important differences are observed between isomers, and the azeotrope is found in the equimolar composition in the ethyl propanoate + heptane solution, and in the other cases slightly displaced toward greater alkane compositions. In other words, when the vapor pressures of the compounds are very similar, slight differences in the activity of compounds (e.g., those derived from small steric effects caused by isomerism), have significant repercussions on the equilibrium diagrams. For example, the non-ideality of the solution produces a flat region in the diagram of the solution with methyl methanoate. This does not appear in the mixture with

Taking all this into consideration, it is important to study the behavior of the azeotropic phenomenon within the families of esters. Figures 9 and 10 show the matrix with diagrams of y vs. x for solutions of (an alkyl ethanoate + an alkane) and (an methyl alkanoate + an alkane), respectively. In both cases, the presence of azeotropic situations can be observed to shift from the mixtures of more volatile compounds to the less volatile ones, with the last azeotrope appearing in the solution of butyl ethanoate + octane in Figure 9, and in the solution of methyl butanoate + heptane in Figure 10. The increased chain length of the alkyl ester, Figure 9, systematically displaces the azeotrope to regions with a smaller ester

Figure 9. Plot of y vs. x ( ), for the VLE at 101.32 kPa of binaries (an alkyl ethanoate + an alkane).

pentane) to the top right (butyl butanoate + decane).

butyl butanoate, which has a practically ideal nature.

Figure 8. Representation of the VLE of alkyl alkanoate + heptane at 101.32 kPa. Labels indicate the differences of boiling points and the activity coefficients at infinity dilution. ( ) T vs. x, ( ) T vs. y, ( ) y-x vs. x. (a) methyl methanoate, (b) ethyl methanoate, (c) methyl ethanoate, (d) Propyl methanoate, (e) ethyl ethanoate, (f) methyl propanoate, (g) butyl methanoate, (h) propyl ethanoate, (i) ethyl propanoate, (j) methyl butanoate, (k) butyl ethanoate, (l) propyl propanoate, (m) ethyl butanoate, (n) butyl propanoate, (o) propyl butanoate and (p) butyl butanoate.

points arranged near to the diagonal, from the bottom left corner (methyl methanoate + pentane) to the top right (butyl butanoate + decane).

The distance from the azeotropic points to the diagonal becomes shorter as the boiling points of the products increase, and it is deduced that the probability that an ester forms an azeotrope with a given alkane varies with the molecular weight of that ester, although this is reflected in the VLE diagram of the system. Figure 8 shows the VLE curves of the solutions composed of the different esters and heptane. The difference between the liquid and vapor curves, which shows the volatility, is greater in systems with a smaller ester. This difference only significantly decreases with an increase in the molecular weight of the ester, but does not significantly change with the isomers. This is a result of a decrease in the non-ideality of the liquid phase (γ ≈ 1) in solutions of the larger esters. This change makes it possible to find azeotropes in esters with four carbons, but not in esters with six carbons, in spite of similar differences between the boiling point of the esters and heptane. In ester solutions with five carbons, important differences are observed between isomers, and the azeotrope is found in the equimolar composition in the ethyl propanoate + heptane solution, and in the other cases slightly displaced toward greater alkane compositions. In other words, when the vapor pressures of the compounds are very similar, slight differences in the activity of compounds (e.g., those derived from small steric effects caused by isomerism), have significant repercussions on the equilibrium diagrams. For example, the non-ideality of the solution produces a flat region in the diagram of the solution with methyl methanoate. This does not appear in the mixture with butyl butanoate, which has a practically ideal nature.

Taking all this into consideration, it is important to study the behavior of the azeotropic phenomenon within the families of esters. Figures 9 and 10 show the matrix with diagrams of y vs. x for solutions of (an alkyl ethanoate + an alkane) and (an methyl alkanoate + an alkane), respectively. In both cases, the presence of azeotropic situations can be observed to shift from the mixtures of more volatile compounds to the less volatile ones, with the last azeotrope appearing in the solution of butyl ethanoate + octane in Figure 9, and in the solution of methyl butanoate + heptane in Figure 10. The increased chain length of the alkyl ester, Figure 9, systematically displaces the azeotrope to regions with a smaller ester

Figure 9. Plot of y vs. x ( ), for the VLE at 101.32 kPa of binaries (an alkyl ethanoate + an alkane).

Figure 8. Representation of the VLE of alkyl alkanoate + heptane at 101.32 kPa. Labels indicate the differences of boiling points and the activity coefficients at infinity dilution. ( ) T vs. x, ( ) T vs. y, ( ) y-x vs. x. (a) methyl methanoate, (b) ethyl methanoate, (c) methyl ethanoate, (d) Propyl methanoate, (e) ethyl ethanoate, (f) methyl propanoate, (g) butyl methanoate, (h) propyl ethanoate, (i) ethyl propanoate, (j) methyl butanoate, (k) butyl ethanoate, (l) propyl propanoate,

(m) ethyl butanoate, (n) butyl propanoate, (o) propyl butanoate and (p) butyl butanoate.

154 Laboratory Unit Operations and Experimental Methods in Chemical Engineering

composition. This effect can also be observed with increased alkanoic chain length of the ester, Figure 10. By contrast, increases in the size of the alkane cause a shift toward a higher

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

http://dx.doi.org/10.5772/intechopen.75786

157

The pressure of the system is a determining factor in the azeotropes formation, so it is important to determine how this magnitude affects the presence of azeotropic points. Figure 11 shows the case of several azeotropic points determined by distillation for a set of ester + alkane systems, following indications described previously. In all cases, the composition of the azeotrope shifts toward greater alkane compositions as the pressure is reduced. The main reason for this is that the vapor pressure of the ester diminishes more slowly than that of the alkane, which increases the volatility of the hydrocarbon. The slope corresponding to the change in azeotropic composition is similar since the slope of the vapor pressure does not vary greatly between compounds from the same family. In spite of this, the methyl butanoate + heptane system, Figure 11(d), presents a gentler slope, since the differences in vapor pressure between

ester composition in both cases.

1. One for the vapor pressure, p<sup>o</sup>

3. A model for the activity coefficients: γ<sup>i</sup> ¼ γ<sup>i</sup>

2. One for phi Φ<sup>i</sup> ¼ Φið Þ y; p; T .

vapor phase.

as g<sup>E</sup> = gE

3.3.2. Changes in azeotropes with pressure

both compounds do not change significantly with temperature.

4. Modeling of azeotropic systems. Correlation and prediction

<sup>i</sup> <sup>¼</sup> <sup>p</sup><sup>o</sup> <sup>i</sup> ð Þ T .

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:

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

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

(x, p, T), and the dependence on γ<sup>i</sup> is related to its partial molar properties [23]:

ð Þ x; p; T .

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

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.

composition. This effect can also be observed with increased alkanoic chain length of the ester, Figure 10. By contrast, increases in the size of the alkane cause a shift toward a higher ester composition in both cases.

## 3.3.2. Changes in azeotropes with pressure

The pressure of the system is a determining factor in the azeotropes formation, so it is important to determine how this magnitude affects the presence of azeotropic points. Figure 11 shows the case of several azeotropic points determined by distillation for a set of ester + alkane systems, following indications described previously. In all cases, the composition of the azeotrope shifts toward greater alkane compositions as the pressure is reduced. The main reason for this is that the vapor pressure of the ester diminishes more slowly than that of the alkane, which increases the volatility of the hydrocarbon. The slope corresponding to the change in azeotropic composition is similar since the slope of the vapor pressure does not vary greatly between compounds from the same family. In spite of this, the methyl butanoate + heptane system, Figure 11(d), presents a gentler slope, since the differences in vapor pressure between both compounds do not change significantly with temperature.
