Problem Formulation and Predicted Phase Equilibria of VLLE

Isobaric VLE and VLLE data of the water-ethanol-hydrocarbon system is important to design the distillation column for the dehydrogenation of ethanol. Ethanol-gasoline blends are particularly important because alcohol increases the octane level and promotes complete fuel burning (Gomis, Font, & Saquete, 2006). Small amount of water causes harmful effect in end application; therefore, different entrainers are used to dehydrate it prior to blending with gasoline. Traditionally, benzene is used as an entrianer in the heterogeneous azeotropic distillation of a water-ethanol system. Due to the carcinogenic effect of benzene, other entrainers are also investigated. Here, we consider experimental data involving hexane, heptane, cyclohexane, toluene and isooctane as entrainers to water-ethanol systems. Diisopropyl ethers

FIGURE 4.3

Flow chart of Henley-Rosen algorithm with Sampath and Leipziger approximation.

and di-n-propyl ethers are other important additives used to enhance octane number for gasoline. Thus, VLLE data of two ether-alcohol-water containing systems (Lladosa, Monton, Burguet, & de la Torre, 2008) were taken into consideration here. We took an equilibrium data of ternary water-alcohol systems (Asensi, Molto, del Mar Olaya, Ruiz, & Gomis, 2002) as a flagship of hydrogen- bond-containing systems. The aim to consider this system is whether predictive models like COSMO-SAC can efficiently handle hydrogen-bond- containing systems. Gomis and coworkers (Asensi et al., 2002; Gomis, Font, Pedraza, & Saquete, 2005, 2007; Gomis, Font, & Saquete, 2008; Gomis et al., 2000, 2006; Lladosa et al., 2008; Pequenin, Asensi, & Gomis, 2010) did a series

TABLE 4.1

List of VLLE Systems Studied

of VLLE experiments of ternary and quaternary systems. The experimental data are usually compared with NRTL, UNIQuAc and UNIFAC models. All the experiments are performed at a pressure of 1 atmosphere and a short temperature difference (~5 K). Lladosa et al. (2008) did the VLLE experiment for water-alcohol-ether systems at 1 atmosphere pressure. These systems are reported in Table 4.1 for which the predictions of phase equilibria were carried out by the equilibrium approach and the flash approach.

The initial guess of feed mole fractions is taken as the average mole fraction of the three phases of the component in consideration. Saturation pressure is calculated by Antoine equation. Antoine constants are reported in Table 4.2. Antoine equation is given by

where:

P^sat is the saturation pressure in mmHg t is °C

The prediction of phase equilibria involves the calculation of activity coefficients for every compound in both liquid phases. COSMO-SAC calculation was done to predict activity coefficients. The parameters for COSMO-SAC are given in Table 4.3. The representative outcome of COSMO calculation is o-profile that is a two-dimensional representation of three-dimensional charge distribution among molecules. The representative o-profile of water + ethanol + hexane is shown in Figure 4.4. From o-profile, it is evident that hexane is nonpolar, that is, its peak lies between -0.0084 e/A² and 0.0084 e/A². But ethanol and water have segments lying in nonpolar as well as hydrogen bond donor and acceptor regions.

Predicted tie lines of Systems 1, 2 and 3 of Table 4.1 and Figure 4.5a-c have fewer slopes as compared to experimental tie lines. At the lower part of the phase envelope, water molecules mainly contribute to hydrogen bonding as compared to ethanol. The presence of more amount of ethanol as compared

Phase Equilibria in Ionic Liquid Facilitated Liquid-Liquid Extractions

TABLE 4.2

Antoine Constants

104

Source: Rao, Y. V. C. Chemical Engineering Thermodynamics, Hyderabad, University Press (India) Pvt. Ltd, 2003.

TABLE 4.3

COSMO-SAC Parameters

Source: Lin, S.-T. and Sandler, S. I. Ind. Eng. Chem. Res., 41, 899-913, 2002.

FIGURE 4.4

c-profile of water + ethanol + hexane. (a in e/A²).

Application of COSMO-SAC in Complex Phase Behavior

105

FIGURE 4.5

Comparison of VLLE from experiments and predictions for (a) water + ethanol + hexane,

(b) water + ethanol + heptane, (Continued)

106

Phase Equilibria in Ionic Liquid Facilitated Liquid-Liquid Extractions

FIGURE 4.5 (Continued)

Comparison of VLLE from experiments and predictions for (c) water + ethanol + cyclohexane,

(d) water + ethanol + toluene, (Continued)

Application of COSMO-SAC in Complex Phase Behavior

107

FIGURE 4.5 (Continued)

Comparison of VLLE from experiments and predictions for (e) water + 1-propanol + 1-pentanol,

(f) water + 1-propanol + di-n-propyl ether, (Continued)

FIGURE 4.5 (Continued)

Comparison of VLLE from experiments and predictions for (g) water + 2-propanol + diisopropyl ether. N.B. For all the ternary diagrams the following notations will be used: (O) liquid phase experimental data, (A) vapor phase experimental data, (?) liquid phase predicted by equilibrium relation, (x) vapor phase predicted by equilibrium relation, (?) liquid phase predicted by flash relation and (•) vapor phase predicted by flash relation.

to water in the organic phase results in higher predicted points in the organic phase than the corresponding experimental values. The deviations are low near the base of the aqueous phase where the concentrations of ethanol and hexane/heptane/cyclohexane are very low. As the concentrations of ethanol and water become equal or come close to each other, the deviation increases. This is seen at the upper part of the ternary diagram in Figure 4.5a-c. The trend in the organic phase is maintained even when ethanol concentration is increasing and the corresponding solvent concentration is decreasing giving an RMSD of 14.59%, 14.23% and 11.17%, respectively. The deviation in the aqueous phase towards the plait point is higher. Near the plait point, the composition of water is almost half to that of ethanol; thus, ethanol is responsible for contributing towards hydrogen bonding. RMSD in the aqueous phase for the three systems are 12.38%, 11.77% and 8.93%, respectively. In the original COSMO-SAC model, hydrogen bonding is not correctly accounted for when the predicted mole fractions of water and ethanol are closer. The hydrogen bonding correction for COSMO-SAC will be discussed in Chapter 5. These lower the area of the binodal curve as compared to the experimental phase envelope.

For System 4 of Table 4.1 and Figure 4.5d, in the aqueous phase, the mole fraction of water is always greater than ethanol. Hydrogen bonding is mainly contributed by water; thus, predicted mole fraction of water is much higher, while that of ethanol is lower. The organic phase follows the same trend as observed in previous three systems. Thus, the concentrations of ethanol and water make the tie line slope negative, although it is positive by experimental data. Nevertheless, COSMO-SAC predicts a closer phase envelope corresponding to experimental tie lines. NRTL, UNIQUAC and UNIFAC predict much bigger phase envelopes (Gomis et al., 2008).

In System 5 of Table 4.1 and Figure 4.5e, in the aqueous phase, the composition of water is closer to unity, thus making contribution in hydrogen bonding resulting in accurate prediction with an RMSD of only 0.76%. Predicted tie lines merge with the corresponding experimental tie lines but due to the presence of three similar polar components, organic phase compositions vary (RMSD of 12.57%), resulting in a bigger phase envelope. Hydrogen bonding contribution will be visible here most as all the compounds (water, 1-propanol and 1-pentanol) have hydrogen bonding acceptor segments (due to the presence of oxygen atoms) and hydrogen bonding donor segments (due to the presence of hydrogen atoms bonded with oxygen atom). Both cross and self-hydrogen bonding are visible in this system. The mole fraction of water in the aqueous phase is near to unity for all the tie lines making water a dominant contributor of hydrogen bonding in this phase. As a result mainly cross hydrogen bonding is visible here and RMSD is very less. In the organic phase, three species are present with comparable mole fractions. Thus, hydrogen bonding is present among all type of species. The present method of hydrogen bonding calculation cannot take into account all such combinations and give higher RMSD.

Systems 6 and 7 of Table 4.1 and Figure 4.5f and g have ethers (di-n-propyl ether and diisopropyl ether, respectively) as solvents. The ternary diagrams of these systems are shown below.

Ether's а-profile lies in the nonpolar region as well as in the hydrogen bond acceptor region (Figure 4.6).

The aqueous phase prediction via the equilibrium approach is somewhat accurate. The RMSD calculated using the equilibrium approach for Systems 6 and 7 for the aqueous phase are 2.04% and 4.72%, respectively, whereas using the flash approach are 2.45% and 5.61%, respectively. In the organic phase, at lower mole fraction of ether (or higher mole fraction of water), the predicted data (both by equilibrium approach and flash approach) are near the experimental points, but at higher ether mole fraction, deviations are bigger. Because total polar segments of ether are in the acceptor region, then at comparable mole fractions, that is, near the plait point, there will be a deficiency of donor segments. But COSMO-SAC cannot take into account these extra segments and generate the same amount of donor and acceptor segments. For that reason, the phase envelope predicted by the equilibrium approach is slightly higher than that predicted by the flash approach, although the RMSD in the organic phase by the equilibrium approach (8.7% and 10.66%) are much lower than the flash approach (14.06% and 24.27%). The split values, a and p, of these systems are reported in Table 4.4. It is seen that both parameters lie between 0 and 1 which implies Equations 4.35 through 4.37 are satisfied.

FIGURE 4.6

о-profile of water + 1-propanol + di-n-propyl ether (o in e/A²).

TABLE 4.4

Splits for Systems 6 and 7

The quaternary system was plotted via the pseudo-ternary (cyclohexane and isooctane are taken together) approach in four different ternary diagrams (Figure 4.7a-d) as described in literature (Pequenfn et al., 2010). As both cyclohexane and isooctane are nonpolar, hydrogen bonding characteristics in both

FIGURE 4.7 (Continued)

Comparison of pseudo-ternary VLLE from experiments and predictions for water + ethanol + cyclohexane + isooctane. (c) M = 0.6 and (d) M = 0.8.

liquid phases follow Systems 1, 2 and 3 of Table 4.1. The prediction of a phase envelope agrees well with experimental points, with the RMSD of 7.09% in the organic phase and 6.23% in the aqueous phase. This is smaller than that of Systems 1, 2 and 3 of Table 4.1. In all the cases, vapor phase deviations are less than 7%.

Quaternary systems are plotted using the following notation:

M = 0.2, 0.4, 0.6, 0.8 are reported in literature (Pequenfn et al., 2010). (O) liquid phase experimental data, (A) vapor phase experimental data, (?) liquid phase predicted by equilibrium relation and (x) vapor phase predicted by equilibrium relation.

The RMSD values are tabulated in Tables 4.5 and 4.6. While Table 4.5 shows the RMSD values for all the eight systems predicted via the equilibrium relation, Table 4.6 gives the RMSD values for Systems 6 and 7 via the flash relation. In both predictions, average RMSD in the organic phase (10.67% for equilibrium- and 19.17% for flash-based algorithm) is much higher as compared to the aqueous phases, 7.45% (equilibrium based) and 4.03% (flash based) and the vapor phases, 3.26% (equilibrium based) and 5.84% (flash based), indicating that there are interactions in the organic phase.

The ternary water-ethanol-entrainer systems form an azeotrope inside the distillation column. From the experimental isothermal bimodal curve and the vapor line, a ternary azeotrope is clearly visible for hexane, heptane and cyclohexane entrainers. For water-ethanol-hexane system (System 1), the azeotrope appears between 13th and 14th tie lines because from 1st to 13th tie lines, the vapor lines come above the liquid-liquid tie line and for 14-20th, it comes under the liquid-liquid tie line. From experimental data, the vapor phase coincides with the liquid tie line between 13th and 14th tie lines and an azeotrope is formed. From the equilibrium approach of VLLE computation, the azeotrope formation appears at the 6th tie line. VLLE computation predicts a bigger phase envelope but undermines the azeotropic composition. The predicted composition for a ternary azeotrope is x₁ (water) = 0.1642, x₂ (ethanol) = 0.1870 and x₃ (hexane) = 0.6489. Liquid composition for the water-rich phase is x₁ (water) = 0.8439, x₂ (ethanol) = 0.1548 and x₃ (hexane) = 0.0013 and for the organic phase is x₁ (water) = 0.0286, x₂ (ethanol) = 0.1909 and x₃ (hexane) = 0.7805. For water-ethanol-heptane system (System 2), the azeotrope formation exactly mimics the experimental data and lies within 10th and 11th tie lines. From numerical interpolation, the composition is determined as

TABLE 4.5

RMSD by Equilibrium Prediction* (Equations 4.28 and 4.29)

'Systems 1-8 are as reported in Table 4.1.

TABLE 4.6

RMSD (%) by Flash Prediction (Equations 4.31 through 4.38)

'Systems 6 and 7 are as reported in Table 4.1.

x₁ (water) = 0.2545, x₂ (ethanol) = 0.3975 and x₃ (heptane) = 0.3479, with the aqueous phase composition as x₁ (water) = 0.5166, x₂ (ethanol) = 0.4544 and x₃ (heptane) = 0.0290 and the organic phase composition x₁ = 0.0711, x₂ = 0.3684 and x₃ = 0.5605. From the experimental VLLE data of water-ethanol- cyclohexane system (system 3), the azeotrope lies between 9th and 10th tie lines (Gomis et al., 2005). However, the computational approach undermines the experimental findings and the azeotrope lies at the 8th tie line with a composition of x₁ (water) = 0.1945, x₂ (ethanol) = 0.2797 and x₃ (cyclohexane) = 0.5258. A homogeneous azeotrope is formed for water-ethanol-toluene system (System 4) at the 7th tie line which is very near to the plait point. The composition at the azeotrope is determined at x₁ (water) = 0.3438, x₂ (ethanol) = 0.4066 and x₃ (toluene) = 0.2496. No azeotropic distillation is observed for water- 1-propanol-1-pentanol and water-alcohol-ether systems (System 5, 6 and 7). Quaternary systems are reported as pseudo-ternary systems combining cyclohexane and octane. Thus, the pseudo-ternary diagram will not give hints of the formation of azeotropes. The tetrahedral representation of quaternary VLLE data reveals that equilibrium vapor phases lie outside sectional planes containing liquid phases (Pequenin et al., 2010). Thus, this system does not form a heterogeneous azeotrope. A complete list of the predicted composition of the azeotropic mixture and the liquid composition at the organic and the aqueous phases is given in Table 4.7.

Because VLLE is important for designing chemical equipment and because experiments are time consuming, a predictive method is necessary to describe the phase behavior of azeotrope-forming systems. The COSMO-SAC model predicts activity coefficients and phase compositions based on a quantum chemical coupled with statistical mechanical calculations. The resulting phase envelope follows a similar trend as observed via the NRTL, the UNIQUAC and the UNIFAC models. The average RMSD obtained for all the eight systems using the equilibrium approach was 8.11%. In the same manner, the overall RMSD obtained for two systems using flash calculation is 11.81%.

TABLE 4.7

Comparison between Predicted and Experimental Azeotropic Compositions