Prediction of Liquid–Liquid Equilibria for Biofuel Applications by

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Prediction of Liquid
Liquid Equilibria for Biofuel Applications by Quantum Chemical Calculations Using the Cosmo-SAC Method† Mitesh R. Shah and Ganapati D. Yadav* Department of Chemical Engineering, Institute of Chemical Technology (ICT), Matunga, Mumbai 400019, India

bS Supporting Information ABSTRACT: Currently, there is a great interest in the production of biofuels such as biodiesel, bioethanol and biobutanol. These processes involve liquid
liquid equilibria, which are important for the overall design of the process. However, suitable experimental data are often scarce. The Cosmo-SAC model provides a method to predict liquid
liquid equilibrium data from quantum chemical calculations without any experimental data. Hence, it can be used to provide initial estimates where experimental data are not available. In this work, we have evaluated the Cosmo-SAC model for the liquid
liquid equilibria involved in biodiesel production and bioalcohol extraction using ionic liquids, and we have compared it with the currently available experimental data.

1. INTRODUCTION In the past few years, there has been great concern about the limited availability of fossil fuels, as well as the fluctuating crude oil prices. Hence, there is an increased emphasis on developing alternative fuels such as biodiesel and bioalcohols. Bioalcohols, which are derived from waste biomass, and bioglycerol, which is obtained as a byproduct from biodiesel production, also provide important and renewable starting materials for the production of value-added chemicals. With the increasing importance of biodiesel and bioalcohols, there is a need to investigate the various aspects of the process design of the biodiesel and bioalcohol production processes. In the biodiesel production process, one encounters several liquid
liquid equilibria (LLE). The systematic study, prediction, and correlation of these equilibria is necessary for efficient process design of biodiesel production. However, experimental data for such equilibria are scarce. This is further complicated by the fact that biodiesel itself consists of a series of different compounds. Hence, equilibrium data for all of these compounds are required for process design, and this information is generally not available. In the past couple of years, however, there has been significant interest in this area. Andreatta et al.,1 Negi et al.,2 and Barreau et al.3 have reported experimental data for ternary LLE for the glycerol
methanol
methyl oleate system. Oliviera et al.4 have reported binary LLE data for water
fatty acid ester systems. The same group has also reported binary LLE data for water
fatty acid systems.5 In a subsequent work, Oliviera et al.6 have also compared common thermodynamic models for LLE involved in biodiesel production. Despite these works, the experimental data available are still limited. Hence, there is still a need for new models for prediction of LLE involved in biodiesel production where experimental data are not available. In the case of the production of bioalcohols, an important problem is the recovery of bioalcohols from the fermentation broths. Because of the limited tolerance of the microorganisms to alcohols, the concentration of alcohols in the fermentation broths must be maintained at a low level. The recovery of alcohols by a conventional process such as distillation requires the vaporization of all of the water present in the solution, which r 2011 American Chemical Society

is energy-intensive. An alternative is to carry out LLE using ionic liquids. Several ionic liquids are available that are insoluble in water but still dissolve significant quantities of ethanol and butanol. Hence, they provide excellent candidates for extraction of bioalcohols from fermentation broths. However, experimental data are very scarce.7 Conventional predictive methods such as UNIFAC are also not applicable, because the corresponding parameters for ionic liquids are not available. Hence, there is a need to develop methods to predict the phase equilibria of ionic liquids with bioalcohols. The Cosmo-SAC model8,9 provides a method to predict LLE using quantum chemical calculations without any experimental data. It can predict LLE data over the entire composition range and at different temperatures. It can also handle multicomponent systems that are typical of the separations involved in biodiesel production and biobutanol separation. Furthermore, it does not rely on any parameters derived from single-component or binary data such as UNIFAC. Therefore, it can also be applied to new compounds, such as ionic liquids. For the above reasons, the application of the Cosmo-SAC model to the phase equilibria encountered in biodiesel production and bioalcohol separation is investigated in this work. The predictions of the Cosmo-SAC model are compared with the available experimental data. The results of the quantum chemical calculations for additional molecules in the form of “Cosmo” files are provided to the general scientific community for application to systems where experimental data are not available.

2. THE COSMO-SAC METHOD 2.1. Introduction. The Cosmo-SAC method uses quantum chemical calculations for the determination of thermodynamic Special Issue: Ananth Issue Received: July 7, 2011 Accepted: October 10, 2011 Revised: September 30, 2011 Published: October 10, 2011 13066

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activity coefficients. It involves two steps. The first step involves quantum chemical calculations to produce a “Cosmo” file, which is unique for each compound. This step may be called the Cosmo solvation calculation. The next step involves calculation of the activity coefficients from the “Cosmo” files. No interaction parameters are required. Therefore, once the “Cosmo” file for a particular compound is computed, any mixture of the compound can be investigated without any further quantum chemical calculations. The Cosmo-SAC method is a re-implementation of the Cosmo-RS method that has been studied in more detail in the literature.10
14 Several papers have also been published with the Cosmo-RS method involving ionic liquids.15
18 However, Cosmo-RS requires the use of proprietory software for the second step mentioned above. On the other hand, Cosmo-SAC is available in the open domain. Several versions of the CosmoSAC model have been proposed.8,9,19 In this work, the version proposed in 20079 has been used, unless specified otherwise. 2.2. The Cosmo Model. As mentioned previously, the first step consists of the quantum chemical calculations. This is based on the Cosmo model as proposed by Klamt et al.20 Please note that the “Cosmo model” includes just the quantum chemical calculations and is different from the “Cosmo-SAC model”, which mainly involves the determination of activity coefficients from the Cosmo results. The Cosmo model belongs to a class of dielectric continuum models. According to this approach, the solute is placed in a dielectric continuum of the solvent. As a result of the charge distribution on the solute, the adjacent solvent also gets polarized. This leads to the development of screening charges in the solvent corresponding to the charges on the solute. In the Cosmo model, the solute surface is divided into small segments and the screening charges corresponding to these segments are calculated by quantum chemical calculations. These screening charges, along with the areas of the various segments, are then stored in a file called the “Cosmo file” and are used subsequently in the determination of activity coefficients. In addition to the screening charges and areas of the segments, the Cosmo file also provides the surface area and the volume of the cavity formed by the solute. This is only a simplistic description of the Cosmo model. For more details, the reader is directed to the original paper of Klamt and Sch€u€urmann20 and the book by Klamt.21 2.3. The Cosmo-SAC Model. Once the screening charges are computed, the activity coefficient of the solute must be calculated using them. This is done using the Cosmo-SAC model. The details of the derivation of the Cosmo-SAC model are beyond the scope of this paper and have been described very well in the original references.8,9,19 However, a brief description and the equations are provided in this section. 2.3.1. Sigma Profiles. The quantum chemical calculations provide a three-dimensional (3D) distribution of the screening charges over the molecular surface. In the Cosmo-SAC model, this 3D charge distribution is projected to a two-dimensional (2D) histogram. This is done by calculating the probability of finding a segment having a screening charge density σ. This probability distribution is known as the sigma profile, and it is unique for a particular molecule. Thus, we have Ai ðσÞ pi ðσÞ ¼ Ai

density σ. Ai(σ) is the total surface area with a surface charge density σ, and Ai is the total surface area of the cavity formed by the solute. For most compounds, the screening charge density falls between
0.025 e/Å2 and 0.025 e/Å2. In order to calculate the sigma profile, this interval is partitioned into 50 parts and the histogram (weighted by the area of each segment) of the averaged charge density is computed at each 0.001 e/Å2 increment. The above equation gives the sigma profile for a single solute. The sigma profile of a mixture is given by a weighted average of the sigma profiles of the individual components. Thus, we have

∑i xi Ai pi ðσÞ pS ðσÞ ¼ ∑i xi Ai

ð2Þ

In the Cosmo-SAC method, the interactions between segments are based on segments of the same area. But the Cosmo quantum chemical calculations result in segments of different surface areas. Hence, the screening charge densities from the Cosmo file σ* must be averaged. The resulting “apparent” surface charge density over a segment of standard size must be used in the sigma profile calculation. The “apparent” surface charge density σm of a segment m is given by ! " !# 2 2 rn2 reff dmn  σn 2 exp
fdecay 2 2 2 rn þ reff rn þ reff n " !# σm ¼ ð3Þ 2 2 rn2 reff dmn 2 exp
fdecay r 2 þ r 2 2 n rn þ reff n eff

∑

∑

where rn is the radius of segment n (rn = [Ai(σ/n)/π]1/2), dmn the distance between segments m and n, reff the effective radius, which is an empirical parameter (reff = 1.52 Å), and fdecay an empirical parameter (fdecay = 3.57). The above procedure may be followed for the calculation of sigma profiles of non-hydrogen bonding compounds. In the case of hydrogen-bonding compounds, it is necessary to construct separate sigma profiles for the hydrogen-bonding atoms and the non-hydrogen-bonding atoms.9 This is done by considering only the segments corresponding to the hydrogen-bonding or nonhydrogen-bonding atoms while computing the corresponding sigma profiles. The hydrogen-bonding and non-hydrogen-bondnhb ing sigma profiles are then denoted as σhb m and σm , respectively. To make this approach more general, in the case of nonhydrogen bonding compounds, the sigma profile of the entire hb molecule is treated as σnhb m and σm is set to zero. 2.3.2. Activity Coefficient Calculation. According to the Cosmo-SAC model, the activity coefficient of component i is given by the following equations: lnðγi Þ ¼ ni

nhb, hb

pi ðσ sm Þ½lnðΓsS ðσsm ÞÞ
lnðΓsi ðσsm ÞÞ þ lnðγSG ∑s ∑ i Þ σ m

ð4Þ   ln ΓtS ðσ tm Þ ¼
ln

"

nhb, hb

∑s ∑σ n

pS ðσ sn ÞΓsS ðσ sn Þ

 #
ΔWðσ tm , σ sn Þ exp RT

t ¼ nhb, hb

ð1Þ

" nhb, hb   ln Γti ðσ tm Þ ¼
ln

∑s ∑σ

where the subscript i refers to a pure component i, and pi(σ) is the probability of finding a segment having a surface charge

n

pi ðσ sn ÞΓsi ðσ sn Þ exp

 #
ΔWðσ tm , σ sn Þ RT

t ¼ nhb, hb 13067

ð5Þ

ð6Þ

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Industrial & Engineering Chemistry Research ΔWðσ tm , σ sn Þ

¼ fpol

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! 0:3aeff 3=2 ðσ tm þ σ sn Þ2
chb ðσ tm , σ sn Þðσ tm
σ sn Þ2 2ε0

ð7Þ chb ðσtm , σsn Þ ¼ chb if s ¼ t ¼ hb, σ tm 3 σ sn < 0 ¼ 0 otherwise lnðγSG i Þ

!   ϕi ϕ z θi ¼ ln þ qi ln þ li
i 2 xi ϕi xi

xi qi ; xj qj

θi ¼

∑j

ri ¼

Vi ; r

qi ¼

ϕi ¼

xi ri xj rj

∑j

Ai q

z li ¼ ðri
qi Þ
ðri
1Þ 2

∑j xj lj

ð8Þ

ð9Þ ð10Þ

ð11Þ ð12Þ

where ni is the total number of segments in component i (ni = Ai/aeff), aeff an empirical parameter representing the standard surface segment area (aeff = πreff2 = 7.25 Å2), fpol an empirical parameter ( fpol = 0.64), ε0 the permittivity of a vacuum (ε0 = 2.395  10
4 (e2 mol)/(kcal Å)), chb another empirical parameter (chb = 3484.42 (kcal/mol)(Å4/e2)), Vi the total volume of the cavity formed by a molecule of component i (obtained from the Cosmo file), r the standard volume parameter (r = 66.69 Å3), q the standard area parameter (q = 79.53 Å2), and z the coordination number (z = 10). The superscripts hb and nhb refer to quantities pertaining to the hydrogen-bonding and non-hydrogen-bonding components, respectively. Equations 4
12 are solved to obtain the activity coefficient of a particular component in a liquid mixture. Equations 5 and 6 are solved iteratively. The remaining equations are solved by simple substitution.

3. COMPUTATIONAL DETAILS As mentioned previously, the Cosmo-SAC method consists of two steps, viz, the quantum chemical calculation to generate the “Cosmo” file and the determination of the activity coefficient from the Cosmo file. The quantum chemical calculations may be carried out using molecular modeling software such as Dmol3,22 Gaussian,23 or Gamess-US.24,25 Of these, Dmol3 and Gaussian are proprietory. However, Gamess-US is freely available, making this method truly an open source method. In this work, we have used the Dmol3 module in the Accelrys Materials Studio suite, because it was available and is convenient to use. The quantum chemical calculations involve two steps. The first step involves geometry optimization of the molecule to its lowest energy configuration using density functional theory. In order to carry out the optimization, the GGA/VWN-BP functional setting and the DNP v4.0.0 basis set are used as proposed by Mullins et al.26 Here, GGA represents the generalized gradient approximation, and VWN-BP represents the Becke
Perdew version of the Volsko
Wilk
Nusair functional. The convergence criteria for energy, maximum force, and maximum displacement are set to 1.0  10
6 Ha, 0.002 Ha/Å, and 0.005 Å, respectively.

In the case of flexible molecules, the exact conformation of the molecule used for geometry optimization may be important. In order to see whether the effect of various conformations is significant, we have computed the sigma profiles for two different conformations of methyl oleate; a straight chain conformation and a conformation bent at the double bond. However, we obtained almost identical sigma profiles. Hence, we have assumed that the conformation of the molecule does not have a significant effect on the sigma profile in the case of the molecules considered in this work. Also, in all calculations for the fatty acid esters, we have used straight-chain conformations, which are expected to have the lowest energy. After the geometry optimization, the optimized molecular structure is used to carry out an energy calculation in Dmol3 to determine the screening charges on the molecule. In order to generate the “Cosmo” file simultaneously, it is necessary to insert the corresponding Cosmo keywords in the corresponding input file before running the energy calculation. An example of such an input file is provided in the Supporting Information. Detailed step-by-step instructions for the quantum chemical calculations using Dmol3 can also be found in the paper by Mullins et al.26 and the website maintained by the Liu research group.27 The website of the Liu research group also provides a basic code for calculation of activity coefficients for binary systems using an older version of Cosmo-SAC. It also provides the “Cosmo” files for several common compounds. The code provided by the Liu group has been used as a starting point for our own code. The “Cosmo” files for glycerol, ethanol, 1-butanol, and the fatty acids used in this work have also been taken from their database. We have generated the “Cosmo” files for water, ionic liquids, and fatty acid esters, and these have been provided in the Supporting Information. Once the “Cosmo” file has been created, the sigma profile is generated from the “Cosmo” file. In the case of compounds containing hydrogen-bonding groups, two sigma profiles have been generated; one for the hydrogen-bonding atoms and another for the rest of the molecule. In the “Cosmo” file, each segment is associated with a particular atom. In order to calculate the hydrogen-bonding sigma profile, only the segments corresponding to the hydrogen bonding atoms are considered while computing the sigma profile. Similarly, only the segments corresponding to the non-hydrogen-bonding atoms are considered while computing the non-hydrogen-bonding sigma profile. This can be readily done by introducing an IF
THEN statement in the FORTRAN code. In the case of ionic liquids, the Cosmo solvation calculation of the entire molecule (consisting of both cation and anion) is computationally very intensive. It also results in erroneous results, as reported by Yang et al.28 Two alternative approaches have been suggested in the literature.14,29 The first method is called the metafile approach, and the second method is called the electroneutral mixture approach. Both of these methods have been reasonably successful in prediction of LLE using the Cosmo-RS method, which is similar to the Cosmo-SAC method used in this work.14,29 We provide a brief description of these methods in the next two paragraphs. In the metafile approach, the quantum chemical calculations for the cation and anion are carried out separately. The sigma profile of the molecule is then computed by addition of the sigma profiles of the individual ions. While Banerjee et al.29 generated a single sigma profile, in this work, we have generated two sigma profiles: one for the hydrogen-bonding component and another for the rest of the molecule. This was done via the addition of the 13068

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Industrial & Engineering Chemistry Research corresponding sigma profiles of the hydrogen-bonding and the non-hydrogen-bonding components of the individual ions, respectively. Similarly, in the electroneutral approach, the quantum chemical calculations for the cation and anion are carried out separately. The cation and anion are then considered as separate components. Thus, a three-component mixture involving an ionic liquid is treated as a four-component mixture. The mole fractions of the four components are calculated assuming complete dissociation of the ionic liquid. The thermodynamic activities of the four components are then calculated using the Cosmo-SAC method. The thermodynamic activity of the ionic liquid is obtained as the product of the thermodynamic activities of the cation and the anion. This is a result of the assumption that the chemical potential of the ionic liquid is the sum of the chemical potentials of the cation and the anion, as suggested by Diedenhofen et al.14 Note that an additional advantage of the metafile and electroneutral mixture approaches is that the sigma profiles of a large number of ionic liquids are computed using a smaller number of Cosmo calculations. For example, by carrying out the Cosmo calculations for 10 cations and 10 anions, we can carry out calculations for 100 ionic liquids. The same calculations made by assuming a single ionic liquid molecule would require 100 Cosmo calculations. In order to calculate the sigma profiles, the atoms corresponding to the hydrogen-bonding component must be selected. In the case of methanol and ethanol, the OH groups are considered as the hydrogen-bonding component of the molecule. For the esters, the two oxygen atoms are considered to be the hydrogen-bonding component, and for water, the entire molecule is considered to be the hydrogen-bonding component. In order to calculate the sigma profiles of fatty acids, the OH and carbonyl groups of the acid are considered to be the hydrogen-bonding component. In order to calculate the sigma profiles of the bis(trifluoromethylsulfonyl)imide [Tf2N] anion, the oxygen and nitrogen atoms are considered as the hydrogen-bonding component. In the case of the 1-hexyl-3-methylimidazolium [hmim] cation, the determination of the atoms involved in hydrogen bonding is not simple. Fuller et al.30 have reported that the C
H group at the 2-position on the imidazole ring is involved in hydrogen bonding in the case of the 1-ethyl-3-methylimidazolium ([emim]) cation, which is similar to the [hmim] cation. Hence, this group is taken as the hydrogen-bonding component. This is also consistent with the fact that the H atom of this group has the maximum screening charge in the [hmim] ion, according to the Cosmo file. Once the sigma profiles have been generated, the activity coefficients are calculated from the sigma profiles using eqs 4
12. Finally, the Rachford
Rice algorithm31 is used to compute the tie lines of the ternary LLE. A brief flowchart of the Rachford
Rice algorithm is provided in the Supporting Information.

4. RESULTS AND DISCUSSION 4.1. Biodiesel. Biodiesel is produced by transesterification of triglycerides from oils or fats with methanol or ethanol to produce the corresponding fatty acid esters (biodiesel) and glycerol. An excess of alcohol is generally required to drive the reaction to completion. Once the reaction is complete, the reaction mixture splits into two phases, viz, a glycerol-rich phase and an ester-rich phase. The excess alcohol distributes itself between these two

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phases and must be recovered. Hence, the LLE of glycerol
alcohol
fatty acid ester systems are important. Furthermore, the ester-rich phase may be washed with water after alcohol recovery to remove the residues of alcohol, glycerol, catalyst, and soaps. As a result, some dissolved water may remain in the final ester-rich or biodiesel phase. This water must be removed to achieve the specifications of commercial biodiesel. Hence, the solubility of water in the fatty acid esters is important. Finally, if the initial oils or fats contain free fatty acids, these get converted to soap by the base catalyst and may be later recovered from the ester-rich phase using acidified water. Hence, the LLE of the fatty acid
water system is also important. In the background of the above discussion, the ternary equilibria of glycerol
alcohol
fatty acid ester systems and the solubilities of water in fatty acid esters and free fatty acids have been predicted using Cosmo-SAC in this work. 4.1.1. Ternary Liquid
Liquid Equilibria for Glycerol
Alcohol
Fatty Acid Ester. In the case of ternary LLE for glycerol
alcohol
fatty acid ester systems, experimental data for two systems are available in the literature, viz, glycerol
methanol
methyl oleate and glycerol
ethanol
methyl laurate. Tie-line data are available for the first system, whereas only cloud-point data are available for the second system. Figures 1 and 2 show the tie-line behavior of the glycerol
methanol
methyl oleate system. Figure 1 shows the comparison of the experimental data reported by Andreatta et al.1 with the Cosmo-SAC predictions for various temperatures. Figure 2 shows the comparison of experiments with various other models as reported by Oliveira et al.6 Of the models evaluated by Oliveira et al.,6 only UNIFAC,32 PSRK,33 PR-MHV2,6,34
37 and SRKMHV26,34
37 are predictive in nature, while the SRK34 and CPA-EoS38 use interaction parameters and, hence, are mainly correlative in nature. In addition to the ternary diagrams, the root-mean-square error (ΔxRMS) is reported in Table 1. The root-mean-square error is defined as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u ðxpred
xexpt Þ2 ð13Þ ΔxRMS ¼ t ndat nph ncomp ðndat  nph  ncompÞ

∑ ∑ ∑

where xpred is the predicted mole fraction, xexpt the experimental value of the mole fraction, ndat the number of tie lines, nph the number of phases (nph = 2), and ncomp the number of components (ncomp = 3). For the methyl oleate system, it can be seen that the CosmoSAC predictions are in very good agreement with the experimental data over the entire composition range and also over a wide range of temperature. It can be seen that the accuracy of the Cosmo-SAC method is much higher than the other predictive models, even though it does not use any interaction parameters or experimental data. From the ternary diagram, it can be seen that the CPA-EoS model also performs reasonably well. However, it uses interaction parameters and, hence, is mainly correlative in nature. Figures 3 and 4 show the cloud point data for the glycerolethanol-methyl laurate system, as reproduced by Oliveira et al.,6 along with the predictions of the various models. Figure 3 shows the comparison of experimental data with Cosmo-SAC, and Figure 4 has been reproduced from Oliveira et al.6 and shows the results of other predictive models. It can be seen that, even for this system, the Cosmo-SAC results are in excellent agreement with the experimental data. The plait point is also correctly predicted. In comparison, 13069

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Figure 1. Liquid
liquid equilibria (LLE) for the methyl oleate + methanol + glycerol system. Gray squares, solid lines, experimental data (from ref 1). Red triangles, dashed lines, Cosmo-SAC predictions. (a) 313.2 K, (b) 333.2 K, and (c) 373.2 K.

Figure 2. LLE for the methyl oleate + methanol + glycerol system at 333 K, as reproduced from Oliveira et al.6 Black solid lines, experimental data; blue and dashed-dotted line, UNIFAC; red and dashed line, SRK; pink and dotted line, PSRK; green and dashed-dotted line, PR-MHV2; gray and dashed line, SRK-MHV2; and dark pink and solid line, CPA EoS.

Figure 4 shows that the other predictive models perform only moderately well and overpredict the plait point. Once again, the CPA-EoS model also performs reasonably well. But, as previously mentioned, it cannot be used for outright predictions, because it uses interaction parameters.

4.1.2. Solubility of Water in Fatty Acids. The solubility of water in various fatty acids over a wide range of temperature has been calculated using Cosmo-SAC. The results are then compared with the experimental data available in the literature5 and the predictions of the other predictive models, as reported by Oliveira et al.6 13070

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The deviation of the predictions of the various models from the experimental data are reported in the form of the percentage absolute average deviation in Table 2. The Cosmo-SAC results have been calculated in this work while the results for the other models have been taken from Oliveira et al.6 It can be seen that the predictions of the Cosmo-SAC are moderately good for all fatty acids except heptanoic acid, while the other models perform badly for many of the compounds. Table 1. LLE for the Methyl Oleate + Methanol + Glycerol System ΔxRMSa temperature, T (K) Cosmo-SAC UNIFAC PSRK PR-MHV2 SRK-MHV2 313

0.03

0.097

0.116

0.102

0.04

333

0.008

0.053

0.284

0.079

0.03

373

0.005

a

Root-mean-square errors for the predictive models, obtained from Oliveira et al.6 and using the Cosmo-SAC method.

Figure 3. Cloud point data and predictions for the methyl laurate + ethanol + glycerol system. Black filled circles, experimental cloud point data;6 red filled triangles and dashed lines, Cosmo-SAC predictions.

4.1.3. Solubility of Water in Fatty Acid Esters. The solubility of water in various fatty acid esters encountered in biodiesel over a wide range of temperature has been calculated using Cosmo-SAC. The results are then compared with the experimental data available in the literature,4 and the predictions of the other predictive models as reported by Oliveira et al.6 The deviation of the various models from the experimental data are reported in the form of percentage absolute average deviation in Table 3. It can be seen that the Cosmo-SAC method, UNIFAC, and PSRK perform moderately well in predicting the solubilities. 4.2. Bioalcohols. As mentioned previously, ionic liquids are suitable for the removal of bioalcohols from fermentation broths by liquid
liquid extraction. Hence, two systems involving ionic liquid, alcohol, and water are investigated here. The first system involves 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([hmim][Tf2N]), along with 1-butanol and water. The second involves [hmim][Tf2N], ethanol, and water. 4.2.1. Ternary LLE of [hmim][Tf2N]
Butanol
Water. The ternary tie-line behavior for the [hmim][Tf2N]
butanol
water system has been predicted using Cosmo-SAC. The results of the Cosmo-SAC calculations using the metafile and the electroneutral mixture approaches are compared with the experimental data of Chapeaux et al.7 in Figure 5. In addition to the ternary diagrams, the root-mean-square error (ΔxRMS), as defined in eq 13, is also reported in Table 4. It can be seen that, for both the metafile and electroneutral approaches, the model overpredicts the solubility of water in butanol whereas it underpredicts the solubility of water in the ionic liquid. However, the model correctly predicts that both butanol and the ionic liquid are not soluble in water at all compositions. From the root-mean-square errors, it can also be seen that the electroneutral mixture approach performs marginally better than the metafile approach. Note that, although the predictions of the Cosmo-SAC method are not in complete agreement with the experimental data, they have been obtained without any parameters derived from experimental data. It should also be mentioned that Simoni et al.39 have reported better agreement with experiments using UNIQUAC40 and NRTL.41 However, their predictions were carried out using parameters derived from binary LLE and VLE data.

Figure 4. Cloud point data and predictions for the methyl laurate + ethanol + glycerol system as reproduced from Oliveira et al.6 Black filled circles, experimental cloud point data; blue and dashed-dotted line, UNIFAC; red and dashed line, SRK; pink and dotted line, PSRK; green and dashed-dotted line, PR-MHV2; gray and dashed line, SRK-MHV2; and dark pink and solid line, CPA EoS. 13071

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Table 2. Solubilities of Water in Fatty Acids % Absolute Average Deviation in Solubility Cosmo-SAC UNIFAC PSRK PR-MHV2 SRK-MHV2 pentanoic acid

30.1

8.2

4.6

49

hexanoic acid

24.3

26.4

26.8

107

heptanoic acid

78.6

58.1

50.8

180

106

octanoic acid

17.3

79.6

317

187

nonanoic acid

15.7

65.9

52.1

217

124

decanoic acid

12.3

64.6

39

271

150

102

19.7 57.1

Table 3. Solubilities of Water in Fatty Acid Esters % Absolute Average Deviation in Solubility Cosmo-SAC UNIFAC PSRK PR-MHV2 SRK-MHV2 methyl laurate methyl myristate

15.3 14.2

28.3 28.7

9.1 7.8

536 673

185 291

methyl palmitate

29.2

15.8

11.3

613

225

methyl stearate

42.1

8.3

22.7

739

322

methyl oleate

29.0

86.9

23.8

973

767

Table 4. LLE for the [hmim][Tf2N] + 1-Butanol + Water System: Root-Mean-Square Errors (ΔxRMS) for the Metafile, Electroneutral, and the Modified Cosmo-SAC Methods

In order to improve the results obtained by Cosmo-SAC, a further refinement of the Cosmo-SAC model similar to that proposed by Hsieh et al.19 is used. In the discussion of the Cosmo-SAC model in the previous sections, the sigma profile was divided into a hydrogen-bonding and non-hydrogen-bonding component. The enhanced interaction between the hydrogen-bonding segments was taken into account using a single empirical parameter (chb), which was independent of the type of atoms involved in hydrogen bonding. Hsieh et al.19 have proposed that the sigma profile of the hydrogen-bonding component may be further divided into different parts, depending on the type of the atoms involved in hydrogen bonding and different values of the empirical parameter chb may be used for interaction between the different types of hydrogen bonding segments. Thus, we have divided the molecules into four parts: the non-hydrogen-bonding part, the hydrogen-bonding part consisting of the water molecule, the hydrogen-bonding part consisting of the OH group, and the hydrogen-bonding part consisting of the other atoms involved in hydrogen bonding. This is referred to as the modified Cosmo-SAC model. Different values of the empirical parameter chb are used by replacing eq 8 in Section 2.3.2 with the following equation: chb ðσtm , σsn Þ

Figure 5. LLE for the [hmim][Tf2N] + 1-butanol + water system. Gray squares, thick solid lines, experimental data;7 red triangles, dashed lines, Cosmo-SAC metafile predictions; magenta diamonds, thin solid lines, Cosmo-SAC electroneutral mixture predictions; and blue diamonds, dashed-dot lines, modified Cosmo-SAC predictions.

¼ chb if s ¼ t ¼ hb, σtm 3 σsn < 0 if s ¼ t ¼ OH, σ tm 3 σ sn < 0 ¼ chb ¼ chb if s ¼ hb, t ¼ OH, σ tm 3 σsn < 0 if s ¼ hb, t ¼ W, σtm 3 σsn < 0 ¼ chb if s ¼ OH, t ¼ W, σtm 3 σsn < 0 ¼ chb
OH
W if s ¼ W, t ¼ W, σtm 3 σsn < 0 ¼ chb
W
W ¼0 otherwise

ð14Þ In the above equations, the subscript W refers to the water molecule, OH refers to the OH group in the alcohol, and hb refers

ΔxRMS for Cosmo-SAC metafile

electroneutral mixture

modified version

0.077

0.067

0.031

to the hydrogen bonding part of the sigma profile other than the water and alcohol groups. Thus, separate empirical parameters chb
W
W and chb
OH
W are used for the hydrogen-bonding interaction between water segments, and the segments of water and OH groups, respectively. The parameter chb
W
W is determined from the solubility of water in the ionic liquid and the parameter chb
OH
W is determined from the solubility of water in butanol using the value of chb
W
W determined before. The values obtained are chb
W
W = 3710 (kcal/mol)(Å4/e2) and chb
OH
W = 4000 (kcal/mol)(Å4/e2). The empirical parameters for the remaining hydrogen-bonding interactions are set to the value chb = 3484.42 (kcal/mol)(Å4/e2), as in the original Cosmo-SAC model. In this manner, interaction parameters have been introduced in the Cosmo-SAC model and binary LLE has been used to determine these parameters. The predicted results of this modified Cosmo-SAC model are shown in Figure 5. The root-mean-square error ΔxRMS, as defined in eq 13, is also reported in Table 4. It can be seen that the results of the modified Cosmo-SAC model are better than those of the original Cosmo-SAC model. 4.2.2. Ternary LLE of [hmim][Tf2N]
Ethanol
Water. The ternary tie-line behavior for the [hmim][Tf2N]
ethanol
water system has been predicted using Cosmo-SAC. The results of the Cosmo-SAC calculations using the metafile and the electroneutral mixture approaches have been compared with the experimental data reported by Chapeaux et al.7 in Figure 6. Also, the comparison of UNIQUAC,40 NRTL,41 and e-NRTL42 with experimental data, as carried out by Simoni et al.,43 has been reproduced from the original paper in Figure 7. It can be seen that none of the 13072

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in fatty acids and fatty acid esters have been considered. The Cosmo-SAC model performs exceedingly well for the ternary systems and it is also moderately successful in predicting the solubility in the case of the binary systems. In the case of the extraction of bioalcohols from ionic liquids, two systems have been considered, viz, [hmim][Tf2N]
butanol
water and [hmim][Tf2N]
ethanol
water. For these systems, the performance of Cosmo-SAC is not very good but comparable to other models.

’ ASSOCIATED CONTENT

bS

Figure 6. LLE for the [hmim][Tf2N] + ethanol + water system. Gray squares, black solid lines, experimental data;7 red triangles, dashed lines, Cosmo-SAC metafile predictions; and blue diamonds, blue solid lines, Cosmo-SAC electroneutral mixture predictions.

Supporting Information. Section S1 contains a sample input file for the “Cosmo” calculation in the Dmol3 module of Accelrys Materials Studio. Section S2 contains a flowchart for the Rachford
Rice algorithm for the calculation of tie lines of ternary LLE. Section S3 contains results of the quantum chemical calculations in the form of “Cosmo” files for water, [hmim] cation, [Tf2N] anion, and various fatty acid esters. Section S4 contains experimental and predicted data for the methyl oleate + methanol + glycerol system, whereas Section S5 contains experimental and predicted data for the [hmim][Tf2N] + 1-butanol + water system. (PDF) This information is available free of charge via the Internet at http://pubs.acs.org/.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: +91 22 3361 1001. Fax: +91 22 3361 1002/1020. E-mail: [email protected]. Notes †

Institute of Chemical Technology (ICT) was formerly the University of Mumbai, Institute of Chemical Technology (UICT), which is now a separate university.

Figure 7. LLE for the [hmim][Tf2N] + ethanol + water system, as reproduced from Simoni et al.43 Comparison of the experimental data with the predictions of the NRTL, UNIQUAC, and eNRTL models.

models can successfully predict the experimental data. However, the Cosmo-SAC results using the metafile approach are comparable to eNRTL and are only slightly worse than UNIQUAC and NRTL. This is despite the fact that no experimental data has been used for Cosmo-SAC while the UNIQUAC, NRTL, and eNRTL models predict the ternary data on the basis of parameters derived from binary data. It can also be seen that the electroneutral mixture approach for Cosmo-SAC leads to a very small two phase region and poor predictions.

5. CONCLUSION The Cosmo-SAC model has been evaluated for prediction of the various phase equilibria involved in the production of biodiesel and the extraction of bioalcohols from fermentation broths by ionic liquids. In the case of biodiesel, ternary phase equilibria of glycerol, alcohol, and fatty acid esters, and water solubility

’ ACKNOWLEDGMENT M.R.S. acknowledges the support from University Grants Commission, India in the form of the Dr. D. S. Kothari postdoctoral fellowship. G.D.Y. acknowledges support from R.T. Mody Distinguished Professor Endowment and DST, GOI as the J.C. Bose National Fellow. This paper is dedicated to Professor M.S. Ananth, Director, IIT-Madras, on the occasion of his 65th birthday. ’ NOMENCLATURE Ai = total surface area of the cavity formed by the solute (Å2) Ai(σ) = total surface area with charge density σ (Å2) aeff = standard surface segment area (empirical parameter) (Å2) chb = empirical parameter in the Cosmo-SAC model ((kcal/ mol)(Å4/e2)) dmn = distance between segments m and n (Å) fdecay = empirical parameter in the Cosmo-SAC model fpol = empirical parameter in the Cosmo-SAC model ni = total number of segments in component i ncomp = number of components ndat = number of tie lines nph = number of phases pi(σ) = sigma profile of component i pS(σ) = sigma profile of mixture q = standard area parameter; q = 79.53 Å2 r = standard volume parameter; r = 66.69 Å3 13073

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Industrial & Engineering Chemistry Research rn = radius of segment n (Å) reff = effective radius (an empirical parameter in the Cosmo-SAC model) (Å) T = temperature (K) Vi = total volume of the cavity formed by a molecule of component i (Å3) xexpt = experimental value of the mole fraction xi = mole fraction of component i xpred = the predicted mole fraction ΔxRMS = root-mean-square error in mole fraction z = coordination number; z = 10 Greek Symbols

γi = activity coefficient of component i ε0 = permittivity of vacuum; ε0 = 2.395  10
4 e2 mol/(kcal Å) σm = screening charge density of segment m (e/Å2) Superscripts

hb = hydrogen bonding component nhb = non-hydrogen bonding component

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