Modeling the Phase Behavior of Carbon Dioxide ... - ACS Publications

Article pubs.acs.org/jced

Modeling the Phase Behavior of Carbon Dioxide Solubility in Deep Eutectic Solvents with the Cubic Plus Association Equation of State Reza Haghbakhsh and Sona Raeissi* School of Chemical and Petroleum Engineering, Shiraz University, Mollasadra Avenue, Shiraz 71345, Iran S Supporting Information *

ABSTRACT: The thermodynamic modeling of a new generation of solvents, deep eutectic solvents (DESs) is investigated. Because hydrogen bonding is a dominant molecular interaction, the cubic plus association (CPA) equation of state (EoS) was chosen for modeling. This is the first study to model DES density and carbon dioxide solubility using CPA. Fifteen different DESs were chosen which have density data, as well as CO2 solubility data, available in the literature over wide temperature and pressure ranges. To date, this is the most extended and global databank of DESs which has been employed in relation to a complex EoS. The density data were used to optimize the CPA parameters. The CPA EoS proved to be capable of accurately modeling pure DES densities. The validity of the optimized CPA parameters was further validated with literature density data of mixtures of DES + water, which were estimated successfully by a purely predictive procedure. To calculate CO2 solubility in DES, all the possible association schemes of CO2 were investigated. It was concluded that the inert (no-association) scheme for CO2 was the most accurate (AARD% = 6.2), while at the same time being the simplest with fewer fitting parameters. The induced association (solvation) scheme (AARD% = 7.1) is also suitable.

1. INTRODUCTION Nowadays, green chemistry is one of the most important issues in the chemical industries because it aims to preserve the environment and to reduce the negative influences of human involvement.1 The importance of the green chemistry concept in the 1990s has led to many studies dedicated to the proposal of new media, for example, suitable for chemical/enzymatic catalysis, electrochemical processes, biomass conversion, or as green solvents.2 The ideal green solvent is one which is safe for both the human being and the environment, and its use and manufacture are both sustainable.3 Among the first principle green solvents were ionic liquids (ILs); organic salts consisting of large asymmetric organic cations and either an organic or inorganic anion. ILs were considered the first potentially good alternatives to organic solvents because of their nonvolatility, thermal stability, high solvation properties, and possibility to be used at room temperature.2 But they are challenged with a few drawbacks that have prevented them from becoming the ideal green solvent candidate. These include cost, difficult synthesis, and the necessity of high purity since the presence of impurities can seriously affect their physicochemical properties. In addition, the “‘green aspect”’ of these solvents still requires investigation due to possible toxicity and very low biodegradability, which have been reported in the literature.2 To overcome these limitations while maintaining the advantageous properties of ILs, a new generation of solvents has been introduced: deep eutectic solvents (DESs). Deep eutectic solvents are formed by mixing a halide salt (typically ammonium or phosphonium salts) with a hydrogen© XXXX American Chemical Society

bond donor (HBD). DESs, like ionic liquids, have a melting point close to room temperature. A study by Shahbaz et al.2 also indicated low volatilities for DESs, although higher than some common ionic liquids. Meanwhile, unlike most ionic liquids, DESs are biodegradable, cheap, and easy to prepare.3 The foundation of DESs was laid in 2003 when Abbott et al.5 reported low melting mixtures of urea and choline chloride which are liquid at room temperature, terming them “deep eutectic solvents”. Abbott’s fundamental work inspired other researchers to investigate the unusual properties of DESs. In the past few years, different HBDs of natural and synthetic origin have been used in combination with halide salts to form new DESs.4,6−10 Various applications of DESs have also been investigated by now. DESs can be used as media in the field of catalysis,11 such as applications in base-catalyzed reactions,11 acid-catalyzed reactions,12 transition-metal-catalyzed reactions,13 and biocatalysis.14 Another interesting application is the use of DESs as media in dissolution and separation processes,15 for example, the use of DESs as solvents for dissolving CO2 and metal oxides,7 usage in drug solubilization,16 and purification of biodiesels.17 Although DESs consist predominantly of ionic species, they have interesting solvent properties for dissolving CO2. Such dissolution can have great potential for a wide variety of Special Issue: In Honor of Cor Peters Received: May 25, 2017 Accepted: August 18, 2017

A

DOI: 10.1021/acs.jced.7b00472 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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chemical industries.15 Because of this, recently a number of researchers have experimentally investigated the thermodynamic behavior of mixtures of CO2 with different DESs as solvents.18−26 To have a comprehensive investigation of DESs, in addition to experimental measurements, thermodynamic modeling of the phase behavior is essential. Because of the short time since DESs have been introduced, they are still novel and only a few thermodynamic models have been investigated to date. Different properties of DESs and their mixtures, such as density,23,24,27−32 viscosity,22,23,30−32 surface tension,23,33 heat capacity,34−37 refractive index,30 etc. have been measured in the literature, and often in these studies, some simple correlations and semiempirical equations were fit to the experimental data to model DES behavior. Such methods describe the dependence of the mentioned physical properties on temperature and pressure within the measured temperature and pressure ranges. Similarly, CO2 solubility in DESs has been modeled thermodynamically in only a few studies.18,22,38−40 Zubeir et al.22 used the Peng−Robinson (PR) equation of state (EoS), coupled with the van der Waals-2 (vdw2) mixing rule, to model the solubility of CO2 in three different DESs (tetramethylammonium chloride, tetraethylammonium chloride, or tetrabutylammonium chloride with lactic acid). They considered the DES as a pseudopure component, which together with CO2, made a binary mixture. Ali et al.,18 having prepared and measured the solubility of CO2 in different DESs (phosphonium- and ammonium-based DESs with different HBDs), used the PR EoS coupled with the vdw1 mixing rule to model their results. They also considered a DES as a psudo-component and calculated the necessary critical properties of the psudocomponent using the Lydersen−Joback−Reid mixing method.41 Zubeir et al.39 applied the PC-SAFT EoS, for the first time, to describe the phase behavior of DESs with CO2 at temperatures from 298.15 to 318.15 K and pressures up to 2 MPa. They used two different modeling strategies for their PCSAFT modeling. The first strategy was a pseudopure component approach, in which the DES pseudopure component parameters were optimized by fitting to DES density data. The second strategy was an individual-component approach, in which the DES was considered to consist of two individual components; the HBA and HBD. The purecomponent parameters of the HBA and HBD were adjusted by fitting to the density of aqueous solutions containing only the individual compounds of the DES.39 Dietz et al. used the pseudocomponent approach in the PC-SAFT EoS to model carbon dioxide solubilities in a number of hydrophobic DESs. They used only the liquid density data to obtain the PC-SAFT parameters of the DESs.40 Lloret et al. used the soft-SAFT EoS to estimate carbon dioxide solubility in four tetra-alkyl ammonium chloride-based DESs. Their proposed model was successful and had good agreement with experimental values.38 However, all of the reviewed studies have the common problem of lack of generality. Each model was used to model only the few DESs of concern in the study, mostly complementing their own measured data. Therefore, these models suffer from generality; that is, they cannot be used to estimate carbon dioxide solubility in different types of DESs, or over wide ranges of temperatures and pressures. In this study, a much more extended data bank of DESs is used than any other study to this date, in order to investigate the modeling ability of a complex EoS, thus making the procedure more generalized and global than former methods.

Densities of DESs are calculated accurately by the Cubic Plus Association EoS, and on the basis of these calculations, the optimized CPA parameters of DESs are presented. Furthermore, densities of mixtures of DES + water are estimated by a purely predictive procedure to check the validity of the optimized CPA parameters. In the final step, the behavior of carbon dioxide solubility in different DESs is investigated using the powerful model of CPA over wide ranges of pressures and temperatures. Up until now, there were no CPA models available in the literature on DES physical properties nor solubility, while the CPA EoS is one of the best choices for modeling systems which involve hydrogen bonds. Hydrogen bonding, is of course, the basis of the DES mixture network.

2. THEORY 2.1. The Cubic Plus Association (CPA) Equation of State. The CPA equation of state was proposed by Kontogeorgis et al.,42,43 P=

∂ ln g ⎞ RT a 1 RT ⎛ − − ⎜1 + ρ ⎟ V−b V (V + b) 2 V ⎝ ∂ρ ⎠ ×

∑ xi ∑ (1 − X A ) i

i

(1)

Ai

which consists of two parts; the classical term which is the wellknown Soave−Redlich−Kwong (SRK) EoS, plus a new association term. For the classical term, which is called the physical term, the SRK EoS is commonly used while other cubic EoSs can be used as well, for example, the PR EoS. In eq 1, a and b are the energy parameter and the covolume parameter of the SRK EoS, respectively.44 The energy parameter follows exactly the Soave-type temperature-dependency, and is defined as42 a(T ) = a0[1 + c1(1 −

Tr )]2

(2)

Ai

X is the major term of the association part of CPA, which indicates the extent of association bonds occurring in the system and is defined as the fraction of A-sites of component i which are not bonded with other molecules’ sites. XAi is itself a function of the important parameter ΔAiBi, which is called the association strength and describes the strength of association bonds between the two involved sites of the molecules. XAi and ΔAiBi can be calculated by44−46 1 1 + ρ ∑j xj ∑ B X BjΔAiBj

(3)

⎤ ⎡ ⎛ ε AiBj ⎞ ΔAiBj = g (ρ)⎢exp⎜ ⎟ − 1⎥bijβ AiBj ⎦ ⎣ ⎝ RT ⎠

(4)

XAi =

j

g(ρ) is a simplified and commonly used form of the radial distribution function, which is defined by Elliot et al.47 as follows, g(ρ) =

1 1 − 1.9η

(5)

and

η=

1 bρ 4

(6)

In this study, the Michelsen−Hendriks formulation43 has been used to calculate the association interactions. This mathematB



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Table 1. DESs Investigated in This Study for Density, And the Temperature, Pressure and Density Ranges of Each

a

DES

temp range (K)

pressure range (MPa)

density range (kg/m3)

Ndpa

density AARD%

ref

ChCl + urea (1:2) ChCl + ethylene glycol (1:2) ChCl + glycerol (1:2) ChCl + lactic acid (1:2) ChCl + phenol (1:2) ChCl + phenol (1:3) ChCl + phenol (1:4) TEAC + levulinic acid (1:3) TEAB + levulinic acid (1:3) TBAC + levulinic acid (1:3) TBAB + levulinic acid (1:3) TMAC + lactic acid (1:2) TEAC + lactic acid (1:2) TBAC + lactic acid (1:2) TBAC + lactic acid (1:3)

293.15−363.15 298.15−638.15 283.15−368.15 298.15−363.15 293.2−318.2 293.2−318.2 293.2−318.2 293.15−343.15 293.15−343.15 293.15−343.15 293.15−343.15 293.15−318.15 293.15−318.15 293.15−318.15 293.15−318.15

0.1−50 0.1−50 0.1−50 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

1210.7−1155.4 1076.7−1132.4 1149.5−1205.6 1138.1−1179.3 1084.3−1099.5 1079.5−1094.8 1076.3−1091.8 1062.29−1097.41 1139.74−1177.35 998.91−1034.53 1064.68−1100.89 1127.4−1144.2 1095.8−1112.4 1008.0−1025.1 1031.9−1049.8 Total

72 112 196 14 6 6 6 11 11 11 11 6 6 6 6 480

0.17 0.35 0.15 0.19 0.01 0.07 0.10 0.10 0.10 0.20 0.21 0.17 0.09 0.13 0.17 0.20

31, 52 28, 53−56 18, 27, 28, 32, 54, 56, 57 23 37 37 37 34 34 34 34 39 39 39 39

Ndp is the number of data points.

effects on carbon dioxide, all of the possible association schemes of carbon dioxide are investigated. The case of solvation is also considered for carbon dioxide in addition to the other association schemes. In this study, the pseudopure-component approach was chosen to model the different DESs. This approach has been used successfully with most of the more complex EoS modeling studies involving DESs in the literature.38−40 In this manner, the whole of the DES mixture, consisting of the hydrogen-bond donor (HBD) and hydrogen-bond acceptor (HBA) molecules is considered as one pseudopure component. Generally the CPA EoS, as introduced through eqs 1−6, consists of three physical parameters (a0, b, and c1) together with the two associative parameters of association volume (β) and association energy (ε). These five parameters are commonly optimized based on vapor pressure and liquid density data for each compound over a wide range of temperatures. However, because of the very strong interactions between the molecules within DESs, they have insignificant vapor pressures, which are very difficult to measure. Therefore, in the optimization process to obtain the CPA parameters, only liquid densities of the DESs were considered. The CPA parameters of the DES pseudopure components are optimized based on eq 8 as the objective function.

ical method can significantly reduce the computational time. A very important step in CPA calculations is the specification of an appropriate association scheme. The association scheme actually indicates the type and number of association sites for each compound, which are required to calculate the value of XAi for the associating compounds. Different association schemes have been proposed by Huang and Radosz for some general categories of compounds.48,49 Within a mixture, each constituting component has its own association scheme. It is also commonly observed that in some mixtures, only one component can have association bonds while the other component(s) of the mixture act as inerts with respect to association. In such cases, only self-association bonds occur among the associating component molecules, while the other components do not get involved in association bonds. Folas et al.50 proposed the new idea of solvation which occurs in some mixtures containing associative components and inerts. They claimed that, for example, mixtures of an olefinic or aromatic compound with a polar associative compound, such as alcohol or water, can be considered to have solvation between their molecules. Solvation means that when such inert nonassociating compounds are mixed with polar associating compounds, the polar compounds affect the inert compounds and result in an induced hydrogen-bond between the polar and inert compounds. Such induced hydrogen-bonds occur only between inert and polar compounds and not as self-associating bonds between inert molecules.44,50 In the case of solvation, only one association bond between the polar and inert compound has been considered, and the cross association volume parameter between the polar and inert compound (βij) must be fitted. The cross association energy parameter of εij is defined as the half of the association energy parameter of the polar compound (i).

εij =

εi 2

2⎞ ⎛ Np ⎛ calc ρi − ρiexp ⎞ ⎟ ⎜ ⎜ ⎟ OF = min ∑ ⎜ ⎟⎟ ⎜ ρiexp ⎠⎠ ⎝ i ⎝

(8)

in which ρexp and ρcalc are the experimental and the CPAi i calculated liquid densities, respectively, and Np is the number of data points.

3. INVESTIGATED DESs In this study, for the purpose of generality, it was the goal to investigate all of the DES systems for which experimental carbon dioxide solubility data are available in literature. However, there is a restriction to the incorporation of all available DES systems in this study, because density data of the pure DES are also required to obtain the necessary CPA parameters. The resulting database consists of 15 different DESs. Table 1 presents each investigated DES and its density

(7)

Carbon dioxide is an inert compound which does not have the potential to self-associate. In most of the studies on CPA, carbon dioxide has been considered as an inert compound, while in some studies,51 it was considered as a molecule with either a 2B, 3B, or 4C association scheme. In this study, because of the unknown intermolecular behavior of DESs and their C



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Table 2. Temperature, Pressure and Carbon Dioxide Solubility Ranges of the Investigated DESs in This Study

a

DES

temp range (K)


CO2 solubility range (mole fraction)

Ndpa

ref

ChCl + urea (1:2) ChCl + ethylene glycol (1:2) ChCl + glycerol (1:2) ChCl + lactic acid (1:2) ChCl + phenol (1:2) ChCl + phenol (1:3) ChCl + phenol (1:4) TEAC + levulinic acid (1:3) TEAB + levulinic acid (1:3) TBAC + levulinic acid (1:3) TBAB + levulinic acid (1:3) TMAC + lactic acid (1:2) TEAC + lactic acid (1:2) TBAC + lactic acid (1:2) TBAC + lactic acid (1:3) total

303.15−343.15 303.15−343.15 303.15−343.15 303.26−348.23 293.15−323.15 293.15−323.15 293.15−323.15 303.15−333.15 303.15−333.15 303.15−333.15 303.15−333.15 298−318 298−318 298−318 298−318

0.299−9.51 0.236−6.323 0.187−6.347 0.829−8.568 0.099−0.5202 0.1044−0.5142 0.1082−0.5291 0.0661−0.5854 0.0687−0.5878 0.0632−0.5916 0.0702−0.5864 0.093−1.993 0.094−1.993 0.093−1.992 0.094−1.993

0.013−0.253 0.006−0.216 0.005−0.285 0.0248−0.0995 0.0024−0.0208 0.0029−0.0212 0.0027−0.0213 0.0028−0.034 0.003−0.0324 0.004−0.0453 0.0038−0.0432 0.0023−0.0618 0.00311−0.07612 0.0056−0.1551 0.0054−0.1403

52 40 40 39 20 20 20 28 28 28 26 45 47 48 40 521

19, 20 21 24 23 25 25 25 26 26 26 26 39 39 39 39


range over the given temperature and pressure domains. A total of 480 density data have been collected from the mentioned literature sources over wide ranges of pressures and temperatures. Table 2 presents the carbon dioxide solubility literature references for the investigated DESs, and the corresponding temperature and pressure ranges. In total, 521 carbon dioxide solubility data, which also include high-pressure conditions, are involved in this study.

Table 3. Calculated Critical Properties and Acentric Factors of the Investigated Pseudo-component DESs in This Study

4. RESULTS AND DISCUSSION The critical properties of DES pseudocomponents are necessary for thermodynamic modeling using EoSs. Group contribution models are suitable approaches because unlike correlations, they can calculate the critical properties with no requirement of experimental data as input. The latest version of the modified Lydersen−Joback−Reid method, as proposed by Valderrama and Rojas,58 together with the Lee-Kesler mixing rules for the various HBD to HBA ratios, as recommended by Knapp et al.,59,60 have been used to calculate the critical properties and acentric factors of the investigated pseudocomponent DESs. The Modified Lydersen−Joback−Reid method was chosen for DESs because it has demonstrated very good accuracies for estimating the critical properties of molecules with high molecular mass,54,61 and DESs do indeed have moderate to high molecular masses. Furthermore, the salts which are used to synthesize the DESs are similar to ionic liquids in terms of ionic nature,54 and the success of this group contribution method with ionic liquids encourages its use for DESs. Table 3 shows the calculated results for the DESs investigated in this study. The detailed equations and calculation steps corresponding to this table are presented as Supporting Information. The next step is to determine appropriate association schemes for the investigated compounds. In almost all of the published studies in the literature, the DES pseudocomponent has been successfully considered with two association sites of type 2B, and for CO2, induced association (solvation) is considered in the presence of DES.38−40 Because of the successful results of the literature studies, we have also considered the DESs to have two association sites of type 2B. However, in the case of CO2 associations within a DES environment, which are less understood, we have investigated

DES

Tc (K)

pc (MPa)

ω

ChCl + urea (1:2) ChCl + ethylene Glycol (1:2) ChCl + glycerol (1:2) ChCl + lactic acid (1:2) ChCl + phenol (1:2) ChCl + phenol (1:3) ChCl + phenol (1:4) TEAC + levulinic acid (1:3) TEAB + levulinic acid (1:3) TBAC + levulinic acid (1:3) TBAB + levulinic acid (1:3) TMAC + lactic acid (1:2) TEAC + lactic acid (1:2) TBAC + lactic acid (1:2) TBAC + lactic acid (1:3)

644.44 602.00 680.67 668.77 621.91 622.81 623.52 583.04 596.13 622.90 633.84 619.53 629.71 685.56 687.05

5.0149 4.1661 3.4183 4.0215 4.6285 5.0176 5.2768 4.9958 5.0535 3.7013 3.7418 4.3564 4.6018 3.2077 3.5518

0.6167 0.8747 1.1780 0.8553 0.5248 0.4999 0.4853 0.6224 0.6124 0.6887 0.6833 0.7348 0.7554 0.8438 0.8639

all of the possible association schemes of carbon dioxide in the presence of different DESs. On the basis of the study of Tsivintzelis et al.,51 the association schemes of 2B, 3B, and 4C, as well as no association (inert), can be considered for carbon dioxide in mixtures with water, alcohols, glycols, and hydrocarbons. This idea has also been investigated here, and all of these schemes are investigated. As mentioned before, because of the very low, and thus mostly unavailable vapor pressures of DESs, the CPA parameters were optimized based on only the liquid densities of the DESs. The results of the optimized CPA parameters, based on the DES density data of Table 1, are reported in Table 4. The AARD% values of calculated liquid densities of the investigated DESs were calculated by eq 9, and reported in Table 1. AARD% =

1 Np

Np

∑ i

ρicalc − ρiexp ρiexp

100 (9)

where the parameters of this equation are the same as those defined in eq 8. All of the density errors presented in this study D



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Table 4. Optimized CPA Parameters of the Investigated Pseudo-component DESs in This Study, and the Estimated Errors

a

DES (2B)a

a0 (bar.L2/mol−2)

b (L/mol)

C1

ε (bar·L/mol)

β

AARD% in ρ

ChCl + urea (1:2) ChCl + ethylene glycol (1:2) ChCl + glycerol (1:2) ChCl + lactic acid (1:2) ChCl + phenol (1:2) ChCl + phenol (1:3) ChCl + phenol (1:4) TEAC + levulinic acid (1:3) TEAB + levulinic acid (1:3) TBAC + levulinic acid (1:3) TBAB + levulinic acid (1:3) TMAC + lactic acid (1:2) TEAC + lactic acid (1:2) TBAC + lactic acid (1:2) TBAC + lactic acid (1:3) water (4C)49 carbon dioxide (inert)51

28.31000 29.28000 26.53000 25.04000 19.69000 24.33000 24.31000 21.89000 21.91000 17.76000 17.53000 26.63000 23.58000 17.81000 20.09000 1.22777 3.50790

0.0657 0.0733 0.0829 0.0795 0.0837 0.0838 0.0824 0.0981 0.0992 0.1176 0.1177 0.0752 0.0891 0.1163 0.1062 0.0145 0.0272

0.1160 0.8350 0.8100 0.1130 0.0880 0.1110 0.1110 0.1090 0.1100 0.1130 0.1120 0.1150 0.1100 0.1120 0.1090 1.1800 0.7602

0.5458 0.5456 0.5585 0.5205 0.4961 0.5278 0.5364 0.4927 0.4960 0.4667 0.4533 0.5244 0.5147 0.4562 0.4795 0.0250

1001.70 1001.70 1018.30 982.10 1056.60 977.60 985.70 959.70 953.70 919.70 916.20 1006.70 979.70 924.30 945.60 140.36

0.17 0.35 0.15 0.19 0.01 0.07 0.10 0.10 0.11 0.20 0.21 0.17 0.09 0.13 0.17

All of the five CPA parameters have been adjusted using density data.

Figure 1. Comparison of estimated liquid densities by the CPA EoS with the experimental data for all of the investigated DESs in this study.

Table 5. Temperature, Pressure, Density and DES Mole Fraction Ranges of the Investigated Mixtures of DES + Water and the Values of AARD% of the Predicted Mixture Liquid Densities Using the CPA EoS DES

temprange (K)


DES mole fraction range

density range (kg/m3)

Ndpa

%AARD

ref

ChCl + urea (1:2) ChCl + ethylene glycol (1:2) ChCl + glycerol (1:2)

293.15−363.15 283.15−363.15 283.15−363.15

0.1−50 0.1−50 0.1−50

0−1 0−1 0−1

965.0−1205.8 965.0−1130.6 965.0−1202.4

682 781 808

1.43 1.70 1.87

52, 62 28, 33, 56 32, 56, 57

2271

1.68

total a


E



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Table 6. CPA Parameters of Carbon Dioxide Based on the Different Association Schemes51 CO2

a0 (bar·L2/mol−2)

b (L/mol)

c1

ε (bar·L/mol)

β

AARD% in Psat

AARD% in ρliq

2B 4C 3B inert

2.6911 3.1404 3.0558 3.5079

0.0273 0.0284 0.0281 0.0272

0.5560 0.6914 0.6703 0.7602

78.12 39.23 51.68

0.0568 0.0297 0.0411

0.05 0.05 0.05 0.20

0.10 0.11 0.11 0.8

Table 7. Comparison of the AARD% Values of Carbon Dioxide Solubility in Four Selected DESs, for All of the Possible Association Schemes of Carbon Dioxide, as Well as CO2-Solvation with DESs CPA (CO2 (2B)) DES ChCl ChCl ChCl ChCl total a

+ + + +

urea (1:2) ethylene glycol (1:2) glycerol (1:2) lactic acid (1:2)

CPA (CO2 (4C))

CPA (CO2 (3B))

CPA (CO2 (inert))

kij = 0

with kij

kij = 0

with kij

kij = 0

with kij

kij = 0

with kij

70.0 73.8 100.9 289.1 128.1

15.4 3.7 12.4 15.2 11.9

80.4 100.3 121.8 279.6 140.2

15.8 3.7 11.8 15.1 11.9

69.9 87.4 111.5 283.5 132.4

15.8 3.7 11.8 15.1 11.9

26.9 46.2 9.2 198.5 66.4

11.6 4.8 5.2 4.8 7.0

CPA (solvation)a 13.0 10.4 9.4 4.4 9.6

The values of the binary interaction parameters and the solvation parameters are presented in the Supporting Information.

were calculated based on the entire density data. In this way, the total AARD%, as presented in Table 1, is the average AARD % for all of the 480 density data points. The results of Table 1 indicate that the calculated liquid densities by the CPA EoS are in good agreement with the corresponding experimental values for all of the investigated DESs. Furthermore, to check the trend and the qualitative behavior of the calculated liquid densities by CPA, Figure 1 shows the behavior of density with respect to temperature at atmospheric pressure for all of the investigated DESs. It is obvious that the CPA EoS calculates acceptable trends, and has good agreement with experimental data in the estimation of DES liquid densities. However, to have a more comprehensive investigation on the optimized CPA parameters of the studied DESs, we have also collected density data of mixtures of DESs with water over wide ranges of pressures and temperatures, and compared them with the corresponding densities calculated by the CPA. Table 5 presents the available literature liquid density data of mixtures of DES + water, and the calculated results. As shown in this table, the CPA EoS with the optimized parameters of Table 4 can predict liquid densities of the mentioned mixtures with errors of less than 2%. The total AARD% of Table 5 is the average AARD% for all of the 2271 mixture density data points. In the calculation of these densities, no binary interaction coefficients were considered between water and DES, so the reported results are purely predictive. Therefore, because of the acceptable results of CPA, even at high pressure and temperature conditions, and most especially by considering that they are predictions involving no optimizations on the binary mixtures, it can be concluded that the determined CPA parameters of the DESs are trustworthy for calculations. These parameters were also used to estimate the solubilities of carbon dioxide in the investigated DESs. For the association scheme, in addition to the solvation scheme of carbon dioxide which is common in the literature for carbon dioxide + DES systems, in this study the association schemes of 2B, 3B, 4C, and no association (inert) have also been investigated. Table 6 presents the CPA parameters of carbon dioxide based on the different association schemes. Because only the first four DESs presented in Table 2 have literature solubility data available over a wide pressure and temperature range, these four systems have been considered in this study as the “test” systems to investigate the idea of other

association schemes of carbon dioxide in mixtures with DESs. If these four systems show much better results using new association schemes of carbon dioxide rather than the commonly used association scheme of solvation, then the scheme(s) can be tested on the rest of the DESs of Table 2, which have solubility data available only in limited pressure and temperature ranges. To have a quantitative comparison between the different models, the AARD% for carbon dioxide solubility is used, as defined by eq 10, 1 AARD% = Np

Np

∑ i

xicalc − xiexp 100 xiexp

(10)

where xexp and xcalc are the experimental and CPA-calculated i i carbon dioxide solubility, respectively, and Np is the number of data points. All of the solubility AARD% values presented in this study were calculated based on the entire solubility data. Table 7 presents the AARD% values of the calculated carbon dioxide solubilities (based on eq 10) in the selected DESs. Two general CPA modes are considered for all of the possible association schemes of carbon dioxide: with and without binary interaction parameters between carbon dioxide and the DES. Binary interaction coefficients were considered to have a linear relationship with temperature, in the form of eq 11, for all of the association schemes.

k12 = k 0T + k1

(11)

where k12 is the binary interaction coefficient, T is the temperature in Kelvin, and k0 and k1 are the constants, whose values are reported in Table S1 of the Supporting Information. Table 7 shows that if carbon dioxide solubility is predicted, that is, without the use of any binary interaction parameters, and the different carbon dioxide association schemes are compared to one another, the association schemes of 2B, 3B, and 4C have similar errors, as opposed to the inert association scheme. However, when optimized binary interaction coefficients are considered in the models, all of the association schemes have acceptably low errors. In these cases, the association schemes of 2B, 3B, and 4C have no significantly improved errors with respect to the inert and the solvation association schemes in prediction (without binary interaction coefficient) and correlation (considering a binary interaction F



Article

the 521 solubility data points corresponding to all of the DESs. A total AARD% value of 6.2% for all of the investigated data in this study shows the very good agreement with experimental data of the CPA model by the inert association scheme. The CPA, with the commonly used association scheme of solvation, also gives good results. The total AARD% value of the latter model was 7.1%, which is slightly higher than CPA in the inert mode (6.2%). The binary interaction coefficients were considered to have a linear relationship with temperature for all of the association schemes, in the form of eq 11. The values of the constants of the binary interaction parameter equation are given in Table S2 of the Supporting Information. It is interesting to note that the CPA with the inert association scheme, and using only one adjustable parameter (binary interaction coefficient), has even slightly better results than the CPA with the solvation association scheme which has one further adjustable parameter (cross association volume). The values of the fitted binary interaction coefficients and the cross association volume parameters are presented in Table S2 of the Supporting Information. To have a comparison with similar literature studies, the calculated results of Zubeir et al.39 using the PC-SAFT EoS by the pseudocomponent approach on carbon dioxide solubility in the last four DESs of Table 8 are considered. For most, our model had smaller errors using both the inert and the solvation association schemes (The values of total AARD% for the last four DESs of Table 2 calculated by Zubeir et al., were 3.6, 3.5, 4.3, and 4.5%, respectively). It should be noted that Zubeir et al.39 presented the errors for three separate sets of temperatures for each DES. But in this work, we have combined the errors of all the three temperature sets, also giving weight to the number of data in each set, and reported the “total” AARD% for each DES, that is, over the number-averaged data of all the three temperatures sets, in order to have the same meaning, and thus be comparable to the AARD% of this work as given in Table 8. This shows the higher accuracy of the CPA results with respect to PC-SAFT for these investigated DESs. However, it is important to mention that both of the inert and solvation association schemes of the CPA have a greater number of fitted parameters with respect to the PC-SAFT modeling carried out by Zubeir et al.39 Figure 2 shows and compares the trends of the CPAestimated carbon dioxide solubilities with the two association schemes of inert and solvation for six random DESs at different pressures and temperatures. As seen in this figure, the CPA estimates a correct trend with respect to the experimental data with both the inert and solvation association schemes of carbon dioxide, over wide ranges of pressures and temperatures.

coefficient). The inert association scheme shows very small errors, both in the prediction and the correlation modes. This association scheme shows a significant superiority with respect to the other models, even giving better results than the solvation association scheme, while it even has less optimized parameters. Therefore, as a final conclusion, the association schemes of 2B, 3B, and 4C were excluded for further investigations of carbon dioxide solubility in the remaining DESs. Only the association schemes of inert and solvation are investigated for these DESs (rows 5 to 15 of Table 2). The total AARD% in Table 7 means the average AARD% for all of the 171 solubility data points corresponding to the four mentioned DESs. Table 8 presents the AARD% values of estimated carbon dioxide solubility by CPA for all of the investigated DESs in this Table 8. Comparison of the AARD% Values of the Estimated Carbon Dioxide Solubilities in All of the Investigated DESs in This Study by the CPA EoS Based on the Inert and the Solvation Association Schemes for Carbon Dioxide DES ChCl + urea (1:2) ChCl + ethylene glycol (1:2) ChCl + glycerol (1:2) ChCl + lactic acid (1:2) ChCl + phenol (1:2) ChCl + phenol (1:3) ChCl + phenol (1:4) TEAC + levulinic acid (1:3) TEAB + levulinic acid (1:3) TBAC + levulinic acid (1:3) TBAB + levulinic acid (1:3) TMAC + lactic acid (1:2) TEAC + lactic acid (1:2) TBAC + lactic acid (1:2) TBAC + lactic acid (1:3) Total

CPA (kij = 0) (inert CO2)

CPA with kij (inert CO2)

CPA (solvation)a

26.9 46.2

11.6 4.8

13.0 10.4

9.2 198.5

5.2 4.8

9.4 4.4

211.4 181.7 182.0 95.4

7.2 4.3 5.7 8.8

7.3 3.7 4.5 9.0

108.1

17.0

19.3

60.1

9.4

9.5

69.3

7.9

8.0

118.3

3.9

3.8

144.2

2.4

2.4

64.1

2.8

2.7

76.1

1.9

1.7

96.5

6.2

7.1

a

The values of the binary interaction parameters and the solvation parameters are presented in the Supporting Information.

study. In this table, the two association schemes of inert, as a newly introduced association scheme of this study for solubility in DESs, and the commonly used scheme of solvation, have been compared with one another. As can be seen in this table, the CPA with the inert association scheme of carbon dioxide does not have acceptable errors when used in the predictive mode (without binary interaction parameters). This was to be expected, because in a mixture of carbon dioxide and DES, various strong molecular interactions are probably at play, while the CPA only considers the hydrogen-bonds in addition to the weak van der Waals forces. However, by incorporating binary interaction coefficients, the CPA with an inert association scheme shows very good results for all of the investigated DESs. The total AARD% in this table is the average AARD% for all of

5. CONCLUSIONS In this study, the CPA EoS has been chosen as a powerful thermodynamic model for the first time, to model the challenging phase behavior of deep eutectic solvents. Both the density of DESs and the solubility of carbon dioxide in the DESs have been investigated. Fifteen different DES + CO2 systems were investigated, for which not only carbon dioxide solubility data, but also pure DES density data were available in the open literature. Both the density data and the carbon dioxide solubility data cover a wide range of pressures and temperatures. The DES has been considered as a pseudo component with two association sites (2B). On the basis of the density data, the CPA parameters of the DESs were obtained by G



Article

Figure 2. Comparison of the CPA-estimated carbon dioxide solubilities in six different DESs at different temperatures and pressures by the two association schemes of inert and solvation for carbon dioxide. (Experimental data (■), CPA with solvation scheme for CO2 (−−−), CPA with inert association scheme for CO2 without kij (···), CPA with inert association scheme for CO2 with kij (−·− )).

optimization and these fitted parameters were then used to predict the densities of DES + water mixtures at different temperature and pressure conditions. The results showed good accuracy in the purely predicted densities of DES + water mixtures, without considering any binary interaction coefficients. In the next step, the different possible association schemes of 2B, 3B, 4C, solvation, and inert, were considered for carbon dioxide in order to estimate the solubility of carbon dioxide in DESs. Four different CO2 + DES systems, which had data available over wide pressure and temperature ranges, were chosen as the test systems. The results showed that the carbon dioxide association schemes of 2B, 3B, and 4C have no significant superiority over the inert or solvation association schemes. Carbon dioxide, with an inert association scheme, has been introduced here. It has been shown as a successful scheme for carbon dioxide, which shows even better results than the solvation scheme for all of the investigated DESs in this study. This association scheme is simpler than the solvation association scheme, involving only one fitted parameter, which is less than the two fitted parameters of the solvation association scheme. The investigation of the trends of the results as a function of pressure at different temperatures also indicates very good agreement with the experimental data for

both of the association schemes. As a result, when modeling the solubility of carbon dioxide in DESs by the CPA EoS, both the inert and solvation association schemes are recommended for carbon dioxide. The calculated results show that the CPA EoS is a suitable model to handle mixtures involving DESs.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00472. Values of the fitted binary interaction parameters of the CPA for different association scheme of CO2 and investigated DESs; detailed procedure for the calculation of critical properties and acentric factors of the investigated DESs (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +98 71 36133707. Fax: + 98 71 36474619. E-mail: [email protected]. ORCID

Reza Haghbakhsh: 0000-0002-8942-3119 H



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Sona Raeissi: 0000-0001-9427-7948 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The authors are grateful to Shiraz University for providing research facilities for this research.

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