THERMODYNAMIC MODELING OF AZEOTROPIC MIXTURES WITH [EMIM][TfO] WITH CUBIC-PLUS-ASSOCIATION AND CUBIC EOSs

Abstract

Ionic liquids (ILs) are organic salts that are liquids at room temperature and have low vapor pressure. These characteristics render ILs potential substitutes of organic solvents and inorganic salts in separation of azeotropic mixtures. This work presents vapor-liquid equilibrium modeling of the azeotropic mixture acetone + methanol + 1-ethyl-3-methylimidazolium-trifluoromethanesulfonate and ethanol + water + 1-ethyl-3-methylimidazolium-trifluoromethanesulfonate with the Cubic-Plus-Association Equation of State (CPA EoS). The azeotropic ternary mixture phase behavior was properly predicted using binary interaction parameters that were adjusted from binary mixture phase equilibrium data. Results show that the CPA EoS provides a better description of experimental data as compared to the Peng-Robinson-Wong-Sandler Equation of State (PRWS EoS).

Keywords:
Cubic-Plus-Association Equation of State; ionic liquids; azeotropic mixtures

INTRODUCTION

Azeotrope formation occurs in a variety of chemical and industrial processes, as in ethanol and methyl acetate production. The most common process to remove components in an azeotrope point is extractive distillation. This consists of the addition of a relatively non-volatile component (entrainer) to increase relative volatility. Although widely used, extractive distillation requires a high energetic burden. Ethanol separation from water is a typical example, since it demands distillation columns in series. Moreover, most of the entrainers are often organic solvents and inorganic salts that cause corrosion and accumulation in the distillation column, hindering recycle. Recently, ionic liquids (ILs) have been used as an alternative to traditional entrainers because they are chemically stable organic salts that remain liquid over a broad temperature range and have a very low vapor pressure. They can also be recycled easily and mixed with the reflux stream without accumulating in the less-volatile components at the top of the distillation column (Orchillés et al., 2007). Phase behavior prediction of ILs in azeotropic mixtures is of great utility to verify if these are able to break the azeotrope point due to all the advantages which come with the use of ILs. A common strategy to describe ILs phase equilibrium is the use of either Gibbs free energy models such as the Non-Random-Two-Liquid (NRTL) (Renon and Prausnitz, 1968) and Universal Quasi Chemical (UNIQUAC) models (Anderson and Prausnitz, 1978) or Gibbs free energy models associated with the Peng-Robinson-Wong-Sandler Equation of State (PRWS EoS) (Peng and Robinson, 1976; Wong et al., 1992). In these models, the strong interactions present in systems such as hydrogen bonding result in deviations from ideal mixture behavior and are taken into account implicitly in the energy parameters. An alternative methodology to describe ILs phase behavior is the use of the Cubic-Plus-Association Equation of State (CPA EoS) (Kontogeorgis et al., 2006). This is a hybrid equation of state that combines the Soave-Redlich-Kwong (SRK EoS) (Soave, 1972) to take into account physical interactions and the association term from the Statistical-Associating-Fluid-Theory (SAFT EoS) (Chapman et al., 1990; Huang and Radosz, 1990) in order to describe hydrogen-bond formation. The CPA EoS has already provided satisfactory results in mixtures with ionic liquids (Maia et. al., 2012).

In this work, we study the vapor-liquid equilibrium of the azeotropic mixtures acetone + methanol and ethanol-water with 1-ethyl-3-methylimidazolium trifluoromethanesulfonate ([emim][TfO]), Figure 1, as entrainer with CPA. Moreover, we define the best association strategy which is able to account for the [emim][TfO] effect on the acetone + methanol and ethanol + water azeotropic mixtures. We decided to study the IL with those components due to the fact that the mixture methanol-acetone is essential for the production of synthetic hydrocarbons via the Fischer-Tropsch process (Wilsak et al., 1986). Moreover, the development of new separation processes for the ethanol-water mixture is important for the energy industry such as in the production of biodiesel and anhydrous alcohol used in automotive engines (Gil et al, 2008).

Figure 1
2D structure of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate.

CPA EoS

The functional form of the CPA EoS can be expressed for mixtures in terms of pressure:

(1) $\begin{array}{c}{P}^{\mathrm{CPA}}=\frac{\mathrm{RT}}{\overline{V}-b}-\frac{a}{\overline{V}(\overline{V}+b)}-\hfill \\ \frac{1}{2}\left(\frac{\mathrm{RT}}{\overline{V}}\right)\left(1+\frac{1}{\overline{V}}\frac{\partial \mathrm{In}g}{\partial (1/\overline{V})}\right)\sum _i{x}_i\sum _{A_i}(1-X_{A_i})\hfill \end{array}$

The pressure due to the associative contribution in Equation (1) is the CPA simplified version (Michelsen, 2006). This associative pressure takes into account site-site interactions due to hydrogen bonding between molecules of the same type (self-association) and different molecular types (cross association). The mole fraction X_Ai of non-bonded molecules at site A is defined by:

(2) $X_{A_1}=\frac{1}{1+(1/\overline{V})\sum _j{x}_j\sum _{B_j}{X}_{B_j}{\Delta }^{A_i{B}_j}}$

The summation is done over all association sites, the association strength Δ_iB_j between the site A in molecule i and site B in molecule j is given by:

(3) ${\Delta }^{A_i{B}_j}=g_{\mathrm{ij}}\left[\exp \left(\frac{{\epsilon }^{A_i{B}_j}}{\mathrm{RT}}\right)-1\right]b_{\mathrm{ij}}{\mathit{\beta }}^{A_i{B}_j}$

where ε^A_iB_j and β^A_iB_j are the association energy and volume, respectively. In Equation (3), the radial distribution is g_ij=1(1-1.9η), with η=b/4V, where b_ij=(b_i+b_j)/2.

The energy parameter in Equation (1) has the Soave temperature dependency form, whereas the parameter b is temperature independent:

(4) $a(T)={\left(a_{0}1+c_1\left(1-\sqrt{T_t}\right)\right)}^2$

where T_r is the reduced temperature, a₀ and c₁ are non-associative parameters to be estimated for pure substances.

Therefore, for pure components, there are three parameters (a_0i, c_1i and b_i) for non-associating components and five (a_0i, c_1i, b, ε^A_iB_j and β^A_iB_j) for associating components. When the CPA EoS is applied to mixtures, the a and b parameters are calculated from the van der Waals mixing rules.

These mixing association parameters are calculated from mixtures of pure components through combination rules. The energy association parameter is calculated with the arithmetic rule and the volume parameter with the geometric rule (Derawi et al., 2003; Wolbach and Sandler, 1998). Different types of association schemes are described elsewhere (Huang and Radosz, 1990).

PARAMETER ESTIMATION

The critical parameters for the ionic liquid [emin][TfO] are available in the literature (Valderrama and Roja, 2009). The parameter of the pure component UNIQUAC model for the ILs and the solvents are available elsewhere (Santiago et al., 2009; Banerjee et al., 2005; Anderson and Prausnitz, 1978). CPA EOS parameters for pure solvents (methanol and acetone) are obtained by minimizing Equation (5) based on deviations between experimental (DIADEM, 2000) and calculated vapor-pressure and saturated-liquid-density data. CPA EOS parameters for [emim][TfO] were adjusted with Equation (6) from liquid density data at 1 bar (Garcia-Miaja et al., 2009; Vercher et al., 2007). The estimation of the vapor pressure has not been made due the lack of data for [emin][TfO] and the really low vapor pressure for ionic liquids in general. In order to analyze the prediction of the CPA EOS, the vapor pressure of this ionic liquid was calculated for a temperature range of 298-600 K and the values were within a range of 0.01-4 bar.

(5) ${\mathrm{FO}}_1={\sum _{i=1}^N\left[\frac{\left|\left.P_{\mathrm{sat}}^{\mathrm{cal}}{}_i-P_{\mathrm{sat}}^{\mathrm{cal}}{}_i\right|\right.}{P_{\mathrm{sat}}^{\mathrm{cal}}{}_i}\right]}^2+{\sum _{i=1}^N\left[\frac{\left|\left.P_{\mathrm{sat}}^{\mathrm{cal}}{}_i-P_{\mathrm{sat}}^{\exp }{}_i\right|\right.}{P_{\mathrm{sat}}^{\exp }{}_i}\right]}^2$

(6) ${\mathrm{FO}}_2={\sum _{i=1}^N\left[\frac{\left|\left.p_L^{\mathrm{cal}}{}_i-p_L^{\exp }{}_i\right|\right.}{P_L^{\exp }{}_i}\right]}^2$

The binary interaction parameters for CPA and PRWS EoS were estimated from the vapor-liquid equilibrium (VLE) data with the following equation:

(7) ${\mathrm{FO}}_3={\sum _{i=1}^N\left[\frac{\left|\left.T^{\mathrm{cal}}{}_i-T^{\exp }{}_i\right|\right.}{P^{\exp }{}_i}\right]}^2+{\sum _{i=1}^N\left|y^{\mathrm{cal}}-y^{\exp }{}_i\right|}^2$

The Particle Swarm Optimization (PSO) (Schwaab et al., 2008) combined with the Simplex algorithms (Nelder and Mead, 1965) were employed to minimize the objective functions.

In order to evaluate the model performance, we define the relative deviation averages as:

(8) $\Delta P\mathrm{(\%)}=(1/N)\sum _{i=1}^N\left|\frac{P_i^{\exp }-P_i^{\mathrm{cal}}}{P_i^{\exp }}\right|\times 100$

(9) $\Delta \mathit{\rho }\mathrm{(\%)}=(1/N)\sum _{i=1}^N\left|\frac{{\mathit{\rho }}_i^{\exp }-{\mathit{\rho }}_i^{\mathrm{cal}}}{{\mathit{\rho }}_i^{\exp }}\right|\times 100$

(10) $\Delta T\mathrm{(\%)}=(1/N)\sum _{i=1}^N\left|\frac{T_i^{\exp }-T_i^{\mathrm{cal}}}{T_i^{\exp }}\right|\times 100$

(11) $\Delta y=(1/N)\sum _{i=1}^N\left|y_i^{\exp }-y_i^{\mathrm{cal}}\right|$

ASSOCIATION SCHEMES

The CPA EoS parameter estimation requires a strategy to define how the components associate. Among the schemes tested the ones that presented better results are illustrated in Figure 2.

Figure 2
Association scheme modified from Chapman et al. (1990).

The nomenclature 2B indicates the association scheme. The 2B scheme is used for components that have a receptor site and a donor electron pair per molecule, such as alcohols. In the second approach, the components with no nomenclature next to them have no self-association but are capable of forming hydrogen bonds with another component that has self-association, for example acetone. This ability to form hydrogen bonds only within the mixture is represented by the association volume of the mixture (β_ij) and by the association energy of the mixture (Kleiner and Sadowski, 2007). The association volume of the mixture is estimated from VLE data and the association energy of mixture is equal to half the association energy of the component that has self-association.

RESULTS AND DISCUSSION

Pure Components

Table 1 shows the CPA EoS pure-component parameters estimated for this study. We observe that the CPA EOS provides excellent correlation for pure components, showing low vapor-pressure and saturated-liquid-density deviations for solvents, and low liquid-density deviations at 1 bar for ILs.

Table 1
CPA parameters for pure components.

Components	a0 (bar.L2.mol-2)	b (L/mol)	c1	εAB (bar.L.mol-1)	βAB∙103	Δρ (%)	∆P (%)
Acetone (2B)	7.79	0.059	1.00	111.7	296.79	0.40	0.1
Acetone	13.93	0.062	0.81	-	-	0.92	0.8
Methanol (2B)	3.77	0.031	0.83	213.4	42.22	1.00	0.7
Ethanol (2B)	7.49	0.048	0.72	231.2	9.42	0.62	0.3
Water (4C)	1.06	0.014	0.55	173.3	68.56	0.3	0.7
[emim][TfO]	64.15	0.163	0.06	-	-	0.03	-
[emim][TfO](2B)	34.45	0.155	0.01	755.6	0.15	0.03	-

Figure 3 summarizes the results for pure density of [emin][TfO] with the strategies explained above.

Figure 3
Different association schemes: [emim][TfO](2B) + Methanol (2B) (solid line) and [emim][TfO] + Methanol(2B) CPA EoS (dashed line). Experimental data (■) (Garcia-Miaja et. al., 2009; Vercher et al., 2007).

Acetone + Methanol + [emim][TfO]

Tables 2 and 3 present binary parameters and relative deviations obtained for the binary mixtures Acetone + Methanol, [emim][TfO] + Acetone and [emim][TfO] + Methanol with the PRWS-NRTL and PRWS-UNIQUAC models, respectively.

The PRWS-NRTL EoS requires four binary parameters in order to describe all binary mixtures and give satisfactory results. The small temperature deviations suggest that the PRWS-NRTL EoS is able to describe those binary mixtures. For the same binary mixtures, the PRWS-UNIQUAC EoS requires three binary parameters. The PRWS-UNIQUAC EoS results for binary mixtures are also in excellent agreement with the experimental data. Table 4 shows that the CPA EoS offers a good prediction of experimental data with two or only one binary interaction parameters.

Table 2
Binary interaction parameters for PRWS-NRTL EoS for binary mixtures

NRTL
	k 12	α 12	τ 12	τ 21	∆T(%)	∆y
Acetone + methanol	0.35	0.30	2.42	-1.38	0.014	0.05
Acetone+[emim][TfO]	0.52	0.09	-11.11	17.30	0.032	-
Methanol+[emim][TfO]	0.46	0.18	-1.83	2.17	0.014	-
Acetone+methanol+[emim][TfO]					0.205	-

Table 3
Binary interaction parameters for PRWS-UNIQUAC EoS for binary mixtures

UNIQUAC
	k 12	u12(K)	u12(K)	∆T (%)	∆y
Acetone + methanol	-0.311	617.0	40.18	0.012	0.06
Acetone+[emim][TfO]	0.671	-412.4	702.86	0.031	-
Methanol+[emim][TfO]	0.723	-452.1	920.09	0.061	-
Acetone+methanol+[emim][TfO]				0.756	-

Table 4
Binary interaction parameters for CPA EoS for binary mixtures

	kij	βij	∆T (%)	∆y
Acetone(2B)+Methanol(2B)	0.07	-	0.11	0.01
Acetone+Methanol(2B)	0.11	1.2	0.06	0.40
Ethanol(2B)+Water(4C)	-0.01	-	0.13	0.93
[emim][TfO]+Acetone	-0.02	-	0.17	-
[emim][TfO] (2B)+Acetone(2B)	0.01	-	0.12	-
[emim][TfO]+Methanol(2B)	-0.06	1.3	0.05	-
[emim][TfO] (2B)+Methanol(2B)	-0.15	-	0.17	-
[emim][TfO] (2B)+Ethanol(2B)	-0.03	-	0.04	-
[emim][TfO] (2B)+Water(4C)	-0.77	-	0.29	-
[emim][TfO]+Ethanol(2B)	-0.09	-	0.13	-
[emim][TfO]+Water(4C)	-0.93	-	1.02	-

For the EOS CPA, we tested different association schemes as observed in Table 4 in order to describe the behavior of binary mixtures. We verified that there is no significant difference between the strategies (See Figures 4 and 5).

Figure 4
Different association schemes: [emim][TfO] (2B) + Acetone(2B) (solid line) and [emim][TfO] + Acetone CPA EoS (dashed line). Experimental data (■) (Orchillés et al., 2007).

Figure 5
Different association schemes: [emim][TfO] (2B) + Methanol (2B) (solid line) and [emim][TfO] + Methanol(2B) CPA EoS (dashed line). Experimental data (■) (Orchillés et al., 2007)

Using the estimated binary parameters, the behavior of the ternary mixture [emim][TfO] + acetone + methanol was predicted varying the mole fraction of the IL. The results in Figures 6 and 7 and Table 5 show an inaccurate description of this mixture's vapor fraction with the PRWS-NRTL and PRWS-UNIQUAC EOSs, especially for larger mole fractions of [emim][TfO]. At low compositions, the PRWS-NRTL EoS provides a better prediction compared with the PRWS-UNIQUAC EoS. However, the PRWS-NRTL EoS poorly describes the ternary mixture with IL mole fractions equal to 0.250 and 0.360. We observe clearly the formation of a double azeotrope, which is not in agreement with experimental data. There is no prediction of a double azeotrope with the PRWS-UNIQUAC EoS, but the overall description of experimental data is very poor.

Figure 6
VLE for Acetone + Methanol + [emim][TfO]. Experimental data (Orchillés et. al., 2007) for X_[emim][TfO]: (♦) 0.055; (▲) 0.125; (■) 0.165; (x) 0.250 and (+) 0.360. PRWS-NRTL EoS for X_[emim][TfO]: 0.30 (dotted line); 0.40 (dashed line); all the other compositions (solid line).

Figure 7
VLE Acetone + Methanol + [emim][TfO]. Experimental data (Orchillés et. al., 2007) for X_[emim][TfO]: (♦) 0.055; (▲) 0.125; (■) 0.165; (x) 0.250 and (+) 0.360. PRWS-UNIQUAC EoS (solid line).

Table 5
Deviation for the ternary mixture Acetone +Methanol + [emim][TfO] for different IL mole fractions

x[emim][TfO]	0.055		0.125		0.165		0.250		0.360
	∆T (%)	∆y	∆T (%)	∆y	∆T (%)	∆y	∆T (%)	∆y	∆T (%)	∆y
UNIQUAC	0.38	0.03	0.88	0.03	0.81	0.03	0.73	0.02	0.70	0.02
NRTL	0.14	0.01	0.12	0.03	0.14	0.03	0.24	0.04	0.42	0.06
CPA (2B)	0.17	0.01	0.17	0.01	0.22	0.01	0.29	0.01	0.30	0.01
CPA (no self association)	0.10	0.01	0.11	0.02	0.09	0.01	0.11	0.01	0.09	0.01

When the ternary mixture is predicted with the CPA EoS, we observe that there is a significant improvement compared with the other EOSs (see Table 5). In the prediction of the ternary mixture containing [emim][TfO], we consider acetone and methanol with the 2B association scheme and the CPA EoS qualitatively predicts the ternary phase behavior, as one can observe in Figure 8. However, this association scheme is not accurate for the data correlation of the mixture, especially for higher mole fractions of [emim][TfO].

Figure 8
Acetone (2B) + Methanol(2B) + [emim][TfO](2B). VLE Experimental data (Orchillés et al., 2007) for X_[emim][TfO]: (●) 0.0; (♦) 0.055; (■) 0.165; (x) 0.250 and (+) 0.360. CPA EoS (solid line).

We can see the improvement in the prediction of the behavior of the ternary mixture considering both acetone and the IL without self-association, as shown in Figure 9. Despite the satisfactory results, it is necessary to point out that the difference between association strategies may be related to the anomalous behavior of acetone, and the absence of terms in the CPA EoS that explicitly account for possible ion formation due to the presence of ILs.

Figure 9
Acetone + Methanol (2B) + [emim][TfO]. VLE Experimental data (Orchillés et al., 2007) for X_[emim][TfO]: (●) 0.0; (♦) 0.055; (■) 0.165; (x) 0.250 and (+) 0.360. CPA EoS (solid line).

Water + Ethanol+ [emim][TfO]

Table 4 shows that the CPA EoS gives a good prediction of VLE of binary mixtures when the ionic liquid is considered to be an associative component. When the ionic liquid is considered to be a non-associative component, the deviation is higher compared to experimental data. This behavior can be seen clearly in Figures 10 and 11.

Figure 10
Different association strategies: [emim][TfO] (2B)+Ethanol(2B) (solid line) and [emim][TfO] + Ethanol. CPA EoS (dashed line). Experimental data (■) (Orchillés et al., 2010).

Figure 11
Different association schemes: [emim][TfO] (2B) + Water (4C) (solid line) and [emim][TfO] + Water(4C) CPA EoS (dashed line). Experimental data (■) (Orchillés et al., 2010).

Using the estimated binary parameters, the behavior of the ternary mixture [emim][TfO] + ethanol + water was predicted varying the mole fraction of the IL. The results in Figures 12 and 13 and in Table 6 show that the best association scheme for this mixture is the one that considers [emin][TfO] to be a 2B component, as expected due to the results from the binary mixture.

Figure 12
Ethanol (2B) +Water (4C) + [emim][TfO]. VLE Experimental data (Orchillés et al., 2010) for X_[emim][TfO]: (●) 0.0; (♦) 0.055; (■) 0.1 and (x) 0.215. CPA EoS (solid line).

Figure 13
Ethanol (2B) +Water (4C) + [emim][TfO] (2B). VLE Experimental data (Orchillés et al., 2010) for X_[emim][TfO]: (●) 0.0; (♦) 0.055; (■) 0.1 and (x) 0.215. CPA EoS (solid line).

Table 6
Deviation for the ternary mixture Ethanol + Water + [emim][TfO] for different IL mole fractions

x[emim][TfO]	0.055		0.1		0.215
	∆T	∆y	∆T	∆y	∆T	∆y
CPA (2B)	0.26	0.03	0.13	0.02	0.05	0.01
CPA (no self association)	0.31	0.04	0.31	0.04	0.63	0.06

When the ternary mixture is predicted considering [emin][TfO] as 2B, a significant improvement in the prediction is observed mainly for higher concentrations of the ionic liquid.

These results show an anomalous behavior of the ionic liquid [emim][TfO], as its association scheme varies according to the other components in the mixture.

CONCLUSIONS

This work shows that the CPA, PRWS-NRTL and PRWS-UNIQUAC EoSs are able to describe binary mixtures [emim][TfO] + Acetone, and [emim][TfO] + Methanol. However, the CPA EoS describes the mixture [emim][TfO] + Acetone better than the PRWS EoS. We observe better predictions of the ternary mixture phase behavior with the CPA EoS, especially for the association scheme in which acetone and [emim][TfO] are non-associative, and can form cross association with methanol. We also observe that results for the ternary mixture [emim][TfO] + Acetone + Methanol are sensitive to the association scheme. This can be attributed to the absence of terms in the CPA EoS that take into account electrostatic interactions, in addition to the anomalous behavior of acetone. The study of the mixture [emim][TfO] + Ethanol + Water with the EOS CPA for two association schemes for the ionic liquid showed that for this specific case the ionic liquid has a 2B association scheme. These results show that the better association scheme for [emim][TfO] depend on the nature of the components of the mixture.

• This is an extended version of the manuscript presented at the VII Brazilian Congress of Applied Thermodynamics - CBTermo 2013, Uberlândia, Brazil.

ACKNOWLEDGEMENT

The authors are grateful to FAPITEC/SE (Fundação de Amparo à Pesquisa e à Inovação Tecnológica do Estado de Sergipe) and COPES/UFS (Coordenação de Pesquisa da Universidade Federal de Sergipe) for the financial support.

NOMENCLATURE

• a₀ =  parameter in the energy term (a) (bar.L².mol^-2)
• b =  co-volume parameter (L/mol)
• c₁ =  parameter in the energy term
• k₁₂=  binary interaction parameter
• g =  radial distribution function
• N =  number of components
• P =  pressure (bar)
• R =  gas constant (bar.L.mol^-1.K^-1)
• T =  temperature (K)
• T_r =  reduced temperature
• u₁₂=  UNIQUAC energy interaction parameter (K)
• V=  Molar volume (L/mol)
• x =  mole fraction in the liquid phase
• X_Ai =  mole fraction of the component not bonded at site A
• y =  mole fraction in the vapor phase

Greek Letters
• =  NRTL dimensionless parameter
• β^AB =  association volume of the mixture (L)
• ∆^AB =  strength of interaction between sites A and B (L.mol^-1)
• ε^AB =  energy of association (bar.L.mol^-1)
• ρ =  molar density (mol/cm³)
• π₁₂=  NRTL energy interaction parameter

Superscripted/Subscripts
• cal =  calculated value
• exp =  experimental values
• i, j =  components
• L =  liquid
• sat =  saturated

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Publication Dates

• Publication in this collection
  Apr-Jun 2018

History

• Received
  15 Jan 2016
• Reviewed
  21 Feb 2017
• Accepted
  07 Mar 2017