Study of the solubility of CO2, H2S and their mixture in the ionic liquid 1-octyl-3-methylimidazolium hexafluorophosphate: Experimental and modelling

J. Chem. Thermodynamics 65 (2013) 220–232

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Study of the solubility of CO2, H2S and their mixture in the ionic liquid 1-octyl-3-methylimidazolium hexafluorophosphate: Experimental and modelling Mohammadali Safavi a, Cyrus Ghotbi a,⇑, Vahid Taghikhani a, Amir Hossein Jalili b, Ali Mehdizadeh b a

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran Gas Science Department, Gas Research Division, Research Institute of Petroleum Industry (RIPI), National Iranian Oil Company (NIOC), P.O. Box 14665-137, West Blvd., Azadi Sport Complex, Tehran, Iran b

a r t i c l e

i n f o

Article history: Received 13 February 2013 Received in revised form 3 May 2013 Accepted 20 May 2013 Available online 28 May 2013 Keywords: Acid gas Ionic liquid Gas solubility Gas separation Modelling

a b s t r a c t New experimental results are presented for the solubility of carbon dioxide, hydrogen sulfide in the ionic liquid 1-octyl-3-methylimidazolium hexafluorophosphate ([C8mim][PF6]) at temperatures range from (303.15 to 353.15) K and pressures up to about 2 MPa. The solubility of the mixture of CO2/H2S in [C8mim][PF6] under various feed compositions were also measured at temperatures of (303.15, 323.15 and 343.15) K and the pressure up to 1 MPa. The solubility of carbon dioxide and hydrogen sulfide increased with increasing pressure and decreased with increasing temperature and the solubility of H2S is about three times that of CO2 in the particular ionic liquid studied. The measured data were correlated using extended Henry’s law included Pitzer’s virial expansion for the excess Gibbs energy, and the generic Redlich–Kwong cubic equation of state proposed for gas/ionic liquid systems. The correlations from the two models show quite good consistency with the experimental data for CO2/IL and H2S/IL binary mixtures within experimental uncertainties. For CO2/H2S/IL ternary mixtures, the RK model shows better correlation with the experimental values. We also studied the effect of cation alkyl chain length on the CO2 and H2S solubility by comparison of the experimental data of this study with those of previous reports. As the cation alkyl chain length became longer, the solubility of CO2 and H2S increased in the ionic liquid. Additionally, the influence of the anion on the solubility is studied by comparing the solubility of CO2 and H2S in [C8mim][PF6] with those in [C8mim][Tf2N]. As a result, CO2 and H2S have higher solubility in the IL with [Tf2N] as the anion. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The presence of acid gases (COS, H2S, and CO2) and other impurities require the natural gas to undergo a gas treatment process to make it suitable for downstream use. Several factors may affect selection of the treatment process such as composition and pressure of the natural gas, type and amounts of the trace components, and the desired quality of marketable natural gas. Based on different physical and chemical processes, some of the available technologies for acid gas separation from gas streams are: membrane technology, adsorption, physical absorption and chemisorptions. Among these methods used to separate and purify gases, the gas-liquid absorption method is one of the most powerful and efficient techniques. Chemical and physical absorption are widely used technologies in the natural gas, petroleum, and chemical ⇑ Corresponding author. Tel.: +98 21 66005819; fax: +98 21 66022853. E-mail address: [email protected] (C. Ghotbi). 0021-9614/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jct.2013.05.038

industries for acid gas removal. A solvent can be used in acid gas absorption processes to dissolve preferentially more CO2 and/or H2S than the other stream gas constituents. The most common solvents for acid gas absorption are aqueous solutions of primary, secondary, tertiary, hindered amines, and formulated amine mixtures [1]. Commercial use of alkanolamine solutions associated with some disadvantages such as transfer of water into the gas stream during the desorption stage and degradation of alkanolamines to form corrosive by products, and high energy consumption during regeneration, as well as insufficient carbon dioxide/hydrogen sulfide capture capacity which make the process economically expensive [2,3]. Ionic liquids (ILs) also known as liquid salts and liquid electrolytes are composed entirely of ions and are liquid at room temperature. The low melting points of ILs are due to the high degree of asymmetry between their organic cation and inorganic or organic anion [4]. At least one ion has a delocalized charge and one component is organic, which prevents the formation of a stable crystal lattice [4]. An extremely low vapour pressure (e.g., ca. 1010 Pa at

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T = 298 K for [C4mim][PF6] [5] compared to 3 kPa at T = 298 K for H2O [6]) due to the Columbic attraction between the ions of ILs is one of the extraordinary properties of these liquids. The uses of ILs in reaction and separation media for environmental work [8–12], in oil and fuel desulfurization processes [13–15] and for separation and capture of acid gases [16–18] are some of the most interesting and foreseeable applications of ILs. It is important to consider that the applications of ILs will be affected by phase behaviour and other properties of ILs with solids, liquids and gases, which are necessary in the design of extraction and separation processes [19]. Although, interests in commercial use of ILs in the chemical industries are expanding rapidly, its commercialisation is hampered by a lack of physicochemical property data, particularly for mixtures of ILs with ordinary gases and liquids. Among different applications of ILs, interest in exploring the possibility of using ILs for the absorption of acid gases (CO2 and H2S) from sour gases and fixation and sequestration of CO2, which is regarded as the most important greenhouse gas, are two main of the areas of current researches [7,16–26,2]. The solubility of acid gases at various temperatures and pressures in ILs is one of the most important properties needed for the evaluation of ILs as a gas separation medium and for the design and operation of gas sweetening processes. In addition, useful information about interaction between gases and ILs will be obtained by investigation of gas solubility in ILs [19]. For such purposes, the solubility of carbon dioxide in a variety of ILs has been studied at low and high pressures in the past few years. A comprehensive review has been presented by Soriano et al. [27] about works on CO2 + IL systems. It should be mentioned that many CO2 + IL systems studies have focused on imidazoliumbased ILs. Some of these solubility studies which are related to imidazoluim as one of the most interesting cation group and three main anion groups namely: [BF4], [PF6], [Tf2N] are summarised in table 1. In order to increase the solubility of CO2 in ILs the effect of many different parameters have been investigated such as cation

types, size of alkyl chain of the cation, fluorination of alkyl chains on the cation, different anion types, degree of fluorination of the anion, and various attempts to increase CO2 solubility without fluorination [19,28,29,36,53,59–66]. One conclusion drawn from these studies is that the solubility of CO2 is greater in ILs with anions having –CF3 groups such as [BF4], [PF6] and [Tf2N]; due to CO2-philic feature of the fluoroalkyl group, i.e. more fluorinated anions result in more solubility of CO2 in ILs. Unlike CO2, H2S + IL systems have not been studied widely and experimental data for solubility of H2S in ILs are not as versatile as those for CO2. The first report regarding H2S and ILs was provided by Jou and Mather [67]. They report the solubility of H2S in 1-butyl-3-methylimidazolium hexafluorophosphate ([C4mim][PF6]) at temperatures from (298.15 to 403.15) K and pressures up to 9.6 MPa. Pomelli et al. [68] reported the solubility of H2S in different [C4mim]+ based ILs with different anions and in a series of [Tf2N] ILs with different cations at 298.15 K and 1400 kPa, using a medium pressure NMR technique. According to their results the interaction energy between H2S and the anion part of the ILs is the main factor responsible for the high solubility of hydrogen sulfide in ILs. Heintz et al. [18] measured the solubility of CO2 as well as a mixture of N2/H2S in a polymeric ammonium polyether-based IL with chloride anion in the temperature range from (300 to 500) K and pressures up to (0.23 and 3.0) MPa for H2S and CO2, respectively. Shiflett and Yokozeki [26] reported the phase equilibrium VLLE measurements of binary mixtures of H2S and CO2 with [C4mim][PF6] at temperatures from (273.6 to 342.2) K for H2S and at T = (283.1 and 293.0) K for CO2 and ternary mixture of H2S/CO2/ [C4mim][PF6] at T = (296 and 322) K and pressures up to 0.55 MPa. They also reported experimental solubility data of H2S in [C4mim][MeSO4] at T = (296 and 315) K and pressures up to 0.8 MPa [69]. The remaining data concerning the solubility of H2S in ILs have been produced in our laboratory at temperatures ranging from (303.15 to 353.15) K and pressures up to about 2.0 MPa. This includes the solubility of H2S in [C4mim][PF6], [C4mim][BF4], and [C4mim][Tf2N] [25], the solubility of H2S in [C6mim][PF6],

TABLE 1 Experimental CO2 solubility data in imidazolium-based ILs. Ionic liquid

Low pressures data

High pressures data

[C2mim][Tf2N]

Kim et al. [30] Jacquemin et al. [40] Camper et al. [41] Cadena et al. [53] Anthony et al. [33] Jacquemin et al. [39] Baltus et al. [42]

Schilderman et al. [31] Shin et al.[21]

[C4mim][Tf2N]

[C6mim][Tf2N]

[C8mim][Tf2N] [C2mim][BF4] [C4mim][BF4]

[C6mim][BF4] [C8mim][BF4] [C2mim][PF6] [C4mim][PF6]

[C6mim][PF6] [C8mim][PF6]

Kim et al. [30] Shiflett and Yokozeki [23] Muldoon et al. [36] Baltus et al. [42] Costa Gomes [54] Baltus et al. [42] Jalili et al. [58] Kim et al. [30] Shiflett and Yokozeki [37] Anthony et al. [33] Jacquemin et al. [40] Chen et al. [51] Cadena et al. [53] Husson-Borg et al. [57] Kim et al. [30] Chen et al. [51] Chen et al. [51] Kim et al. [30] Shiflett and Yokozeki [37] Cadena et al. [53] Anthony et al. [19] Jacquemin et al. [39] Kim et al. [30] This work.

Lee and Outcalt [32] Aki et al. [28] Oh and Lee [34] Shin et al. [21] Kumelan et al. [35] Aki et al. [28] Shin et al.[21] Ren et al. [55] Aki et al. [28] Shin et al. [21] Soriano et al. [56] Kroon et al. [38] Aki et al. [28] Costantini et al. [44] Blanchard et al. [43] Gutkowski et al. [52] Shariati et al. [20] Aki et al. [28] Shariati et al. [45] Kumelan et al. [47] Kamps et al. [48] Liu et al. [49] Zhang et al. [50] Blanchard et al. [43] Shariati and Peters [46] Blanchard et al. [43]

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[C6mim][BF4], and [C6mim][Tf2N] [70], the solubility and diffusion of H2S and CO2 in 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate ([HOC2mim] [BF4]) [71], the solubility and diffusion of H2S and CO2 in 1-ethyl-3-methylimidazolium ethylsulfate ([C2mim][EtSO4]) [72], the solubility of H2S in [HOC2mim]+-based ILs containing [PF6], [OTf], and [Tf2N] anions [73], [C2mim]+based ILs containing [PF6] and [Tf2N] anions [74] and most recently solubility of CO2, H2S and their mixture in the ionic liquid [C8mim][Tf2N] [58]. All the data obtained have been used to estimate Henry’s law constants and or diffusion coefficients at different temperatures. In the present work, we measured the solubility of CO2, H2S and binary mixture of (CO2 + H2S) in [C8mim][PF6]. The objective is to find out the potential of ILs for the separation of CO2 and H2S from natural gas and also for the separation of H2S and CO2 gases from each other in the gaseous streams containing them. According to literature [26,58,69,75–79], the presence of CO2 in a mixture may affect the solubility of the other gases and change the selectivity for gas separations. Thus, the measurement and investigation of the solubility of gas mixtures in ILs are necessary. Furthermore, in the light of previous studies [25,70], the large difference in Henry’s law constants of CO2 and H2S in ILs suggests the selective capturing and separation of these gases may be feasible using ionic liquids. The solubility of CO2 and H2S in the [C8mim][PF6] have been reported in the low to medium pressure range (up to about 2.0 MPa) at temperatures from (303.15 to 353.15) K. The solubility of the mixture of CO2/H2S in [C8mim][PF6] under various feed compositions were also measured at temperatures of (303.15, 323.15 and 343.15) K and the pressure up to 1 MPa. Values of the solubility determined are used to estimate zero pressure Henry’s law constants and partial molar thermodynamic functions of solution of H2S and CO2 at different temperatures. Correlation equations for the obtained Henry’s law constants with temperature are presented here. Also the solubility of CO2/H2S mixtures in [C8mim][PF6] is investigated in this study to explore the facility of separation of these gases from each other. The solubility data obtained are modelled by using two distinct correlation equations, i.e. the extended Henry’s law combined with the Pitzer activity coefficient model for electrolytes [80,81] and a generic Redlich– Kwong type EoS proposed by Shiflett and Yokozeki for gas/ionic liquid systems [16,17,23,24,26,37]. The two models are compared with each other through comparison of the predicted results with those of experimental data. The experimental results obtained in this work are also compared with the corresponding data for [C8mim][Tf2N], [C4mim][PF6], reported in the literature.

2. Experimental s 2.1. Materials Hydrogen sulfide and carbon dioxide (c.p. grade 0.9995 mass fraction purity) were supplied by Roham Gas Company. The

specifications of the chemicals used in this work are listed in table 2. The 1-octyl-3-methylimidazolium hexafluorophosphate [C8mim][PF6] was prepared by an anion exchange reaction using 1-octyl-3-methylimidazolium chloride [Omim][Cl] and potassium hexafluorophosphate by a method reported in [82]. The latter compound was obtained by treating N-methylimadazole with hexyl chloride as described by Huddleston et al. [83]. A mixture of containing 8.21 g of 1-methylimidazole (0.1 mol) and 16.33 g of n-octyl chloride (0.11 mol) was refluxed for 29 h at 100 °C. The reaction mixture was then washed with ethyl acetate to remove un-reacted starting materials. The oily product obtained was then heated at 70 °C for 7 h at reduced pressure to remove the residual water. The yield of the reaction/purification processes was 80%. The product was specified by spectroscopic investigations (1H NMR (300 MHz, CDCl3, 25 °C) d (106) = 0.47 (3H, t, NCH2(CH2)6CH3), 0.89 (10H, m, NCH2CH2(CH2)5CH3), 1.54 (2H, m, NCH2CH2(CH2)5CH3), 3.75 (3H, S, NCH3), 3.95 (2H, t, NCH2(CH2)6 CH3), 7.27 (1H, d, H-4),7.50(1H, d, H-5), 10.12 (1H, S, H-2)). A suspension of 9.22 g of 1-octyl-3-methylimidazolium chloride (40 mmol) and 8.10 g of potassium hexafluorophosphate (44 mmol) in deionised water (25 mL) was magnetically stirred at room temperature for 24 h. After completion of the reaction, the upper aqueous phase was washed with CH2Cl2 (2  20 mL). The loaded CH2Cl2 solutions were combined with the organic phase and dried over anhydrous MgSO4. After filtration, the solvent was removed using a rotary evaporator and the product was then heated at reduced pressure for 7 h at 70 °C to remove residual water. The amount of final product was 12.22 g, which corresponds to a yield of 89.8%. The product was specified by spectroscopic investigations (1H NMR (300 MHz, CDCl3, 25 °C): d (106) = 0.88 (3H, t, NCH2(CH2)6CH3), 1.30 (10H, m, NCH2CH2(CH2)5CH3), 1.87 (2H, m, NCH2CH2(CH2)5CH3), 3.91 (3H, S, NCH3), 4.14 (2H, t, NCH2(CH2)6CH3),7.32 (1H, d, H-5), 7.33 (1H, d, H-4), 8.46 (1H, S, H-2)). The water content of the ionic liquids was carefully determined before the solubility measurements by a Mettler model DL-37 Karl–Fischer volumetric titrator. In all cases, the water mass fraction was found to be below (1 ± 0.1)104. The IL was evacuated at least 24 h at elevated temperature (about 343 K) to pressures below 0.1 kPa by a vacuum pump to remove trace amounts of water and volatile impurities.

2.2. Apparatus and procedure The experimental apparatus of Jalili et al. [58] was used here to measure pure and mixed gas solubility in ionic liquids. Figure 1 shows schematic diagram of the experimental set up. The experimental setup is based on the pressure drop method that has been used in most experimental studies in the literature and described in previous publications [39,40,70–74]. The most accurate PVT data presented by the National Institute of Standards and Technology (NIST) for pure compounds [6] was used to calculate compressibility factors of H2S and CO2 gases, which were needed for

TABLE 2 Provenance and purity of the chemicals used in this work. Compound

Source

Potassium hexafluorophosphate 1-Methylimidazole Octyl chloride Ethyl acetate Dichloromethan Magnesium sulfate Carbon dioxide Hydrogen sulfide

Aldrich Sigma–Aldrich Aldrich Sigma–Aldrich Sigma–Aldrich Sigma–Aldrich Roham gas company Roham gas company

Mass fraction purity (as receive) >0.995 >0.99 >0.99 >0.998 >0.998 >0.995 >0.9995 >0.9995

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Vacuum Pump PT3

C3 V3

PT2

V6

PT4

V8

PT5

GC

V10

C2 V2

V9

V5

V12

PT1

V1

V11 C4

C1

V7 V4

Air Bath Acid Gas Scrubber

V13

Equilibrium Cell

He

H2S

Magnetic Bar

CO2

30°C180

Magnetic Stirrer

FIGURE 1. Apparatus for the measurement of the solubility of pure and mixtures of CO2 and H2S acid gases in liquids: C1 to C3, CO2, H2S, and He gas containers, respectively; C4, gas mixture container; PT1 to PT5, pressure transmitters; V1 to V13, valves; GC, gas chromatograph.

solubility calculations. A detailed description of the experimental apparatus and procedure can be obtained from our previous publication [58]. The apparatus consists of a high pressure equilibrium cell equipped with a magnetic bar, three gas containers (C1 to C3) for introducing known amounts of CO2, H2S, and He into the gas mixture container (C4), a magnetic stirring system at the bottom of the equilibrium cell to facilitate heat and mass transfer inside the cell and an air bath. The volumes of different compartments of the setup were measured and pre-calibrated using a calibrated bulb of known volume [58]. A pre-weighed amount of the ionic liquid (10 to 15) g was introduced into the equilibrium cell and the system was evacuated with valves V8, V11, and V13 open. Then the valves to the vacuum pump (V8 and V10) and the equilibrium cell (V13) were closed and a known amount of first gas component (CO2 or H2S) was introduced into the gas mixture container (C4) from the pure gas containers (C1 or C2) through valves V9 and V10 (check valve). Before the next gas component was charged to the equilibrium cell, the whole system except for pure gas containers (C1–C3) and gas mixture container (C4) was evacuated again and the procedure for first gas was repeated. Afterwards, the valve to equilibrium cell (V13) was opened so that the ionic liquid could be in contact with gas mixture inside the equilibrium cell. When the pressure change in equilibrium cell became negligible in 12 h or more, the vapour phase was sampled and was introduced into a gas chromatograph for composition analysis. For the calibration of chromatograph, the mixed gas composition was determined by the same procedure as described above but without the ionic liquid. The equilibrium composition of the liquid phase was determined using mass balances. The total numbers of moles ngas of H2S and/or CO2 injected into the equilibrium cell can be calculated from:

ngas ¼

  V gc Pi Pf ;  RT gc Z i Z f

ð1Þ

where, V gc denotes the volume of the gas container (C1 or C2), Z i and Z f are the compressibility factors corresponding to the initial and final pressures P i and Pf , respectively, in the gas container before and after transferring H2S or CO2 and T gc is the temperature of the gas container. The most accurate PVT data presented by National Institute of Standards and Technology (NIST) for pure compounds [6] was used to calculate compressibility factors of H2S and CO2 gases.

3. Correlation and modelling of experimental data Two correlation methods were applied to the experimental results obtained in this work. The first method used was the extended Henry’s law, which takes into account the non-ideality of the solute, CO2 or H2S, in the liquid IL phase by the Pitzer activity coefficient model

K h;mi ðT; PÞami ðT; mi Þ ¼ fi ðT; PÞ ði ¼ 1; 2Þ;

ð2Þ

in which K h;mi ðT; PÞ is the molality-scale Henry’s law constant of the ith solute (CO2 or H2S) in the IL at temperature T and pressure P. ami ðT; mi Þ is the activity of the ith gas solute in the liquid phase (IL), which is related to the molality mi of the gas solute and activity coefficient ci through equation (6):

ami ðT; mi Þ ¼

mi c mo i

ði ¼ 1; 2Þ;

ð3Þ

where mo = 1 mol  kg1. The relation between K h;mi ðT; PÞ and ð0Þ Henry’s law constant at zero pressure, K h;mi ðTÞ, is expressed as [84]: ð0Þ

K h;mi ðT; PÞ ¼ K h;mi ðTÞ exp

 1  Vi P ði ¼ 1; 2Þ; RT

ð4Þ

where the exponential term is known as the Poynting correction. The activity coefficient of solute, ci in the IL was calculated using the Pitzer virial expansion for the excess Gibbs energy (molalityscale) [80,81]:

ln ci ¼ 2 

 m 2 mi i  b2 þ 3   b3 o m mo

ði ¼ 1; 2Þ:

ð5Þ

Here b2 and b3 are the dimensionless parameters describing binary and ternary interactions between gas molecules in the solvent, respectively. These parameters depend on temperature. The fugacity of the pure gas (H2S or CO2), fi0 ðT; PÞ is the product of the total pressure P and fugacity coefficient /i ðT; PÞ of the pure gas

fi0 ðT; PÞ ¼ /i ðT; PÞP

ði ¼ 1; 2Þ:

ð6Þ

ð0Þ Henry’s law constant on the molality scale, K h;mi ðTÞ, is related ð0Þ Henry’s law constant on the mole fraction scale, K h;xi ðTÞ, by

  M solv ð0Þ ð0Þ K h;mi ðTÞ=MPa ¼ K h;xi ðTÞ=MPa  ; 1000

to

ð7Þ

where, Msolv is the molar mass of the solvent. According to our previous studies [70–74] and those made by Maurer and co-workers

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[35,47,48], the Pitzer activity coefficient model for electrolytes has been selected due to its simplicity and good correlative accuracy. The second model studied was the one proposed by Shiflett and Yokozeki [23,24,37] which is a generic Redlich–Kwong (RK) type of cubic equations of State (EoS) with a simple modification in order to be applicable to gas/ionic liquid binary systems. In this method, which is a conventional approach, the non-ideality of gas solute in the liquid IL phase as well as in the gas phase is both taken into account by the fugacity coefficient of each component calculated from the RK cubic EoS. The RK EoS is given in the following form [23,24,37]

P¼

RT aðTÞ  ; V  b VðV þ bÞ

aðTÞ ¼ 0:427480

b ¼ 0:08664

ð8Þ

R2 T 2c aðTÞ; Pc

ð9Þ

RT c ; Pc

ð10Þ

where Pc and Tc are the critical pressure and critical temperature of pure components, respectively, and V is the molar volume. The mathematical form of aðTÞ is represented by equation (11) [23,24,37]

Prausnitz and co-workers have shown how it is possible to ð0Þ determine K h;x in a wide temperature range using gas chromatogð0Þ raphy [85]. The K h;x , for a gaseous solute in a solvent, is given by:

f ð0Þ K h;x =MPa ¼ lim ; x!0 x

ð12Þ

where f is the fugacity of solute in the gas phase and x is its mole fraction in the ionic liquid. Since ionic liquids have a negligible vapour pressure, so the fugacity of the gas in the gas phase is assumed to be equal to that of the pure gas. At constant temperature, an extrapolation of the experimental data for the solubility of CO2 and H2S in [C8mim][PF6] give Henry’s law constant of these gases in [C8mim][PF6] at zero pressure. Figures 2 and 3 show the extrapolation according to equation (12) for CO2/[C8mim][PF6] and H2S/ [C8mim][PF6] systems, respectively. Table 5 lists the numerical values of mole fraction-scale Henry’s ð0Þ law constants at zero pressure K h;x at each temperature T for the solubility of H2S and CO2 in the IL studied in this work along with their standard deviations. The fugacity coefficients were calculated using SUPERTRAPP developed by NIST for pure compounds and ð0Þ mixtures [86]. The K h;x values obtained showed good correlation with temperature by the following equation: 1   X ð0Þ ln K h;x =MPa ¼ Ai ðT=KÞi :

ð13Þ

i¼1

aðTÞ ¼

63  k X kk T 1 ; r  Tr

ð11Þ

k¼0

here Tr = T/Tc is the reduced temperature and kk s are simply adjustable parameters obtained by fitting equations (8) through (11) to experimental solubility PTx data for the systems of interest (next section). 4. Results and discussion 4.1. Experimental solubility of the pure gases The results of solubility measurement of the single gases carbon dioxide and hydrogen sulfide solubility in the ionic liquid [C8mim][PF6] at temperatures of (303.15, 313.15, 323.15, 333.15, 343.15, 353.15) K and pressures up to about 2.0 MPa are summarized in tables 3 and 4, respectively. In these tables, the solubility is expressed as mole fraction of solute. Both tables also report the experimental uncertainty of the mole fraction of the dissolved gas. The experimental uncertainties for the solubility pressure and the temperature were 0.001 MPa and 0.05 K, respectively.

The parameters obtained Ai of equation (13) are summarized in table 6. The deviation between experimental and correlated Henry’s law constants by means of equation (13) is within experið0Þ mental uncertainties for K h;x and given in table 5. The Henry’s law constants are compared with each other in figure 4 as a function of temperature. Equation (12) implies that a large value of the Henry’s law constant corresponds to low solubility, while a small ð0Þ value of K h;x indicates high gas solubility. It can be observed that the solubility of hydrogen sulfide and carbon dioxide in [C8mim][PF6] decreases by increasing the temperature and that their solubility behaviour is typical of that of physical solvents [25], therefore obeying the Henry’s law. Figure 4 also shows the effects of anion and the length of alkyl on the CO2 and H2S solubility. As can be seen in figure 4, CO2 and H2S have higher solubility in the IL with [Tf2N] as the anion. This suggests that CO2 and H2S could be associated with [Tf2N] more strongly than with [PF6] [33]. For [C4mim][PF6] and [C8mim][PF6], increasing the alkyl chain length on the imidazolium cation results in an increase of solubility of CO2 and H2S. These results are consistent with those reported in literature for the solubility of CO2 in imidazolium-based ILs [20,28,43,46,64]. The same conclusion has also

TABLE 3 Mole fraction of carbon dioxide, x2, in [C8mim][PF6] at temperature T as a function of pressure P. P/MPa

x2

P/MPa

x2

P/MPa

x2

T/K = 303.15 0.1287 0.2925 0.4889 0.7205 0.9777 1.2204 1.4573

0.0294 ± 0.0004 0.0705 ± 0.0009 0.1148 ± 0.0015 0.1652 ± 0.0021 0.2176 ± 0.0028 0.2675± 0.0034 0.3149 ± 0.0041

T/K = 313.15 0.1349 0.3090 0.5178 0.7637 1.0374 1.2997 1.5335

0.0281 ± 0.0003 0.0661 ± 0.0006 0.1074 ± 0.0010 0.1553 ± 0.0015 0.2080 ± 0.0020 0.2600 ± 0.0025 0.3071 ± 0.0030

T/K = 323.15 0.1418 0.3252 0.5455 0.8050 1.0932 1.3647 1.6185

0.0263 ± 0.0004 0.0623 ± 0.0011 0.1012 ± 0.0017 0.1471 ± 0.0025 0.1960 ± 0.0033 0.2443 ± 0.0042 0.2961 ± 0.0051

T/K = 333.15 0.1484 0.3406 0.5719 0.8442 1.1479 1.4324 1.6985

0.0249 ± 0.0005 0.0592 ± 0.0012 0.0962 ± 0.0020 0.1404 ± 0.0029 0.1874 ± 0.0039 0.2355 ± 0.0049 0.2875 ± 0.0060

T/K = 343.15 0.1547 0.3554 0.5970 0.8816 1.1963 1.4996 1.7755

0.0238 ± 0.0005 0.0565 ± 0.0011 0.0920 ± 0.0019 0.1349 ± 0.0027 0.1824 ± 0.0037 0.2271 ± 0.0046 0.2804 ± 0.0057

T/K = 353.15 0.1605 0.3695 0.6203 0.9178 1.2455 1.5578 1.8501

0.0231 ± 0.0005 0.0546 ± 0.0011 0.0895 ± 0.0018 0.1308 ± 0.0027 0.1777 ± 0.0036 0.2239 ± 0.0046 0.2752 ± 0.0056

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M. Safavi et al. / J. Chem. Thermodynamics 65 (2013) 220–232 TABLE 4 Mole fraction of hydrogen sulfide, x2, in [C8mim][PF6] at temperature T as a function of pressure P. P/MPa

x2

P/MPa

x2

T/K = 303.15 0.0845 0.1923 0.3268 0.4885 0.6542 0.9002 1.1117 1.3165 1.5749

0.0672 ± 0.0014 0.1408 ± 0.0029 0.2412 ± 0.0050 0.3366 ± 0.0069 0.4138 ± 0.0086 0.5087 ± 0.0106 0.5905 ± 0.0123 0.6501 ± 0.0135 0.6972 ± 0.0145

T/K = 313.15 0.0944 0.2125 0.3650 0.5527 0.7401 1.0261 1.2811 1.5274 1.8618

0.0623 ± 0.0017 0.1327 ± 0.0035 0.2284 ± 0.0061 0.3189 ± 0.0086 0.3949 ± 0.0106 0.4880 ± 0.0131 0.5584 ± 0.0151 0.6200 ± 0.0167 0.6750 ± 0.0182

T/K = 333.15 0.1114 0.2515 0.4432 0.6760 0.9101 1.2781 1.6137 1.9584

0.0522 ± 0.0013 0.1185 ± 0.0027 0.2033 ± 0.0047 0.2865 ± 0.0066 0.3585 ± 0.0082 0.4461 ± 0.0103 0.5143 ± 0.0118 0.5740 ± 0.0132

T/K = 343.15 0.1157 0.2676 0.4803 0.7345 0.9912 1.3997 1.7702

0.0516 ± 0.0010 0.1138 ± 0.0022 0.1921 ± 0.0038 0.2717 ± 0.0053 0.3410 ± 0.0067 0.4253 ± 0.0083 0.4928 ± 0.0096

7.5 7

(f /MPa)/(x)

6.5 6 5.5 5 4.5 4 3.5 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

P /MPa FIGURE 2. Influence of the total pressure on the ratio of the fugacity of CO2 to the mole fraction of that gas in the ionic liquid [C8mim][PF6]: experimental results, , T = 303.15 K; D, 313.15 K; j, 323.15 K; s, 333.15 K; +, 343.15 K; , 353.15 K; —, linear fit.

4

(f /MPa)/(x)

3.5 3 2.5 2 1.5 1 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

P /MPa FIGURE 3. Influence of the total pressure on the ratio of the fugacity of H2S to the mole fraction of that gas in the ionic liquid [C8mim][PF6]: experimental results, , T = 303.15 K; D, 313.15 K; j, 323.15 K; s, 333.15 K; +, 343.15 K; , 353.15 K; —, linear fit.

been made by Yunus [87] for the solubility of CO2 in pyridinium based ionic liquids with [Tf2N] anion. Almantariotis et al. [64,65] have demonstrated that for the [Cnmim][Tf2N] ionic liquids, the gas solubility increases when the alkyl chains of the imidazoli-

P/MPa

x2

T/K = 323.15 0.1037 0.2344 0.4049 0.6151 0.8262 1.1543 1.4501 1.7415

0.0591 ± 0.0012 0.1260 ± 0.0027 0.2152 ± 0.0046 0.3022 ± 0.0064 0.3761 ± 0.0079 0.4666 ± 0.0098 0.5361 ± 0.0113 0.5977 ± 0.0126

T/K = 353.15 0.1239 0.2869 0.5156 0.7902 1.0693 1.5141 1.9226

0.0463 ± 0.0005 0.1027 ± 0.0012 0.1749 ± 0.0020 0.2539 ± 0.0030 0.3188 ± 0.0037 0.4030 ± 0.0047 0.4672 ± 0.0055

um cations increase from 2 to 8 carbon atoms and the rise is less important for longer alkyl chains, especially above eight carbon atoms. This trend is also reported for the solubility of CO2 in [Cnmim][BF4] family with alkyl chains containing 4, 6 or 8 carbon atoms [51]. The above mentioned trends in solubility are a consequence of the variations in molecular interactions of ILs with CO2 and H2S which originate from the variations in the chemical constituents, shapes and sizes of ILs. Based on their results, Aki et al. [28] attributed this behaviour to entropic rather than enthalpic reasons, where increasing the cation alkyl chain length of the ionic liquid will decrease the molar density of the imidazolium ionic liquid [88,89]. The similar behaviour was found for the molar density of the pyridinium ionic liquids with alkyl chains from 4 to 12 carbon atoms [87]. As the molar density of the IL decreases, the free volume of the IL increases for the absorption of CO2 and H2S to take place via a space filling mechanism [43]. The hypothesis is supported by the decrease in the molar density values of the ionic liquids from [C4mim][PF6] to [C8mim][PF6] [88–91], and the increase of entropy values from [C4mim][PF6] to [C8mim][PF6]. The observed trend in molar densities may be due to weaker interaction between the anion and cation [92,93], which increases from [C4mim][PF6] to [C8mim][PF6]. However, different trends for the variation of the solubility of the gases with the length of the alkyl chain on the cation of the other ionic liquids have also been reported [65]. The solubility variation with temperature, expressed in Henry’s law constant, provides the means to calculate the thermodynamic properties of solvation [39,40,70–74]. The Henry’ law constants can be exactly converted to the Gibbs energy of solvation, Dsol G1 x corresponding to the change in Gibbs energy when the solute is transferred, at constant temperature, from the pure perfect gas state at the standard pressure to the standard state of infinite dilution of the solute in the solvent [39]: ð0Þ

Dsol G1 x

¼ RT ln

K h;x P0

!

;

ð14Þ

where P0 is the standard state pressure. Enthalpic and entropic contributions to the solvation process of CO2 and H2S in the IL can be also estimated from the temperature dependence of the Henry’s law constants. The partial molar enthalpy of solvation indicates the strength of interactions between the dissolved gas and the IL, while the partial molar entropy illustrates the level of ordering that takes place in the gas/IL mixture [33]. These properties can be obtained by taking the corresponding partial derivatives of the Gibbs energy with respect to temperature using the following equations:

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M. Safavi et al. / J. Chem. Thermodynamics 65 (2013) 220–232

TABLE 5 ð0Þ 1 1 Henry’ law constant K h;x , Gibbs energy Dsol G1 x , enthalpy Dsol H x and entropy Dsol Sx of solvation of CO2 and H2S in [C8mim][PF6] at temperature T. T/K

K h;x =MPa

Dsol G1 x =kJ  mol

303.15 313.15 323.15 333.15 343.15 353.15

4.19 ± 0.01 4.72 ± 0.01 5.30 ± 0.01 5.89 ± 0.01 6.45 ± 0.01 6.93 ± 0.01

9.38 10.06 10.72 11.37 11.99 12.60

303.15 313.15 323.15 333.15 343.15 353.15

1.22 ± 0.02 1.44 ± 0.02 1.72 ± 0.02 1.95± 0.02 2.14 ± 0.01 2.55 ± 0.01

6.44 7.09 7.73 8.35 8.96 9.55

ð0Þ

1

1

Dsol H1 x =kJ  mol

1 Dsol S1  mol x =J  K

11.45 10.92 10.38 9.82 9.24 8.64

68.71 67.00 65.29 63.58 61.87 60.17

13.55 13.07 12.57 12.05 11.52 10.97

65.97 64.39 62.82 61.24 59.67 58.10

1

CO2/[C8mim][PF6]

H2S/[C8mim][PF6]

TABLE 6 Numerical values of the parameters A1, A0, A1, B0, B1, B2, C0, C1, D0, and D1 in equations (13), (17) and (19). A1

A0

A1

B0

B1

2321.12

14.907

0.0116

99.0611 188.999

9.1004

1799.98

0.0022

B2

C0

C1

D0

D1

CO2/[C8mim][PF6] 0.0621 0.00141

0.19898

19.759

0.04108

13.6651

H2S/[C8mim][PF6] 1.2831 0.00292

0.08484

3.1155

0.04147

11.4585

TABLE 7 Experimental VLE data, mole fractions in liquid phase x and gas phase y at temperature T and pressure P for CO2/H2S/[C8mim][PF6] ternary mixtures. Feed

a

CO2 3.3 ± 0.1 8.1 ± 0.1 10.7 ± 0.1 11.3 ± 0.3 15.4 ± 0.3 24.3 ± 0.4 11.2 ± 0.2 20.6 ± 0.4 35.1 ± 0.5 3.3 ± 0.1 7.7 ± 0.1 10.3 ± 0.2 11.0 ± 0.2 15.4 ± 0.3 24.3 ± 0.4 11.5 ± 0.3 20.3 ± 0.4 34.6 ± 0.6 3.2 ± 0.1 8.1 ± 0.2 10.4 ± 0.3 10.7 ± 0.3 15.6 ± 0.4 24.0 ± 0.4 11.4 ± 0.2 20.2 ± 0.4 34.2 ± 0.5 a b

H2S

IL

13.4 ± 0.4 31.4 ± 0.5 43.0 ± 0.7 12.4 ± 0.3 16.9 ± 0.4 25.6 ± 0.5 2.8 ± 0.1 4.9 ± 0.1 8.1 ± 0.1 13.0 ± 0.3 32.0 ± 0.5 43.2 ± 0.6 12.0 ± 0.2 16.6 ± 0.4 25.6 ± 0.5 2.8 ± 0.2 5.1 ± 0.1 8.3 ± 0.1 13.1 ± 0.3 31.2 ± 0.5 42.7 ± 0.6 11.8 ± 0.3 16.6 ± 0.3 25.7 ± 0.5 2.7 ± 0.1 5.0 ± 0.1 8.7 ± 0.1

83.3 ± 0.5 60.5 ± 0.6 46.3 ± 0.8 76.3 ± 0.6 67.7 ± 0.7 50.0 ± 0.9 85.9 ± 0.3 74.5 ± 0.5 56.8 ± 0.6 83.8 ± 0.4 60.2 ± 0.6 46.5 ± 0.8 77.1 ± 0.4 68.0 ± 0.7 50.1 ± 0.9 85.8 ± 0.5 74.6 ± 0.5 57.1 ± 0.7 83.7 ± 0.4 60.7 ± 0.7 46.9 ± 0.9 77.5 ± 0.6 67.8 ± 0.7 50.3 ± 0.9 85.9 ± 0.3 74.9 ± 0.5 57.0 ± 0.6

T/K

P/MPa

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

0.1266 0.3944 0.6809 0.2287 0.3476 0.6947 0.1403 0.2914 0.6305 0.1493 0.4814 0.8134 0.2556 0.4005 0.8092 0.162 0.3262 0.7072 0.1716 0.5522 0.9442 0.282 0.4527 0.9172 0.177 0.3597 0.781

Calculatedb

Measured 100  xH2 S

100  xIL

100  yH2 S

100  xH2 S

100  xIL

100  yH2 S

8.0 ± 0.1 22.1 ± 0.3 33.0 ± 0.4 7.7 ± 0.1 11.1 ± 0.2 20.6 ± 0.3 1.8 ± 0.1 3.4 ± 0.1 6.5 ± 0.1 6.6 ± 0.1 20.0 ± 0.3 30.3 ± 0.5 6.6 ± 0.1 9.8 ± 0.2 18.5 ± 0.4 1.3 ± 0.1 2.9 ± 0.1 5.9 ± 0.1 6.0 ± 0.1 17.5 ± 0.2 26.9 ± 0.4 5.8 ± 0.1 9.1 ± 0.1 16.0 ± 0.3 1.2 ± 0.2 2.3 ± 0.1 5.6 ± 0.1

91.2 ± 0.1 75.5 ± 0.3 63.3 ± 0.6 89.2 ± 0.2 84.1 ± 0.2 70.8 ± 0.3 95.4 ± 0.1 90.8 ± 0.1 81.1 ± 0.3 92.6 ± 0.1 77.9 ± 0.3 66.5 ± 0.5 90.8 ± 0.1 86.2 ± 0.2 73.6 ± 0.3 96.0 ± 0.1 91.8 ± 0.1 83.5 ± 0.1 93.4 ± 0.1 80.5 ± 0.2 70.0 ± 0.4 92.0 ± 0.1 87.4 ± 0.1 76.3 ± 0.3 96.5 ± 0.1 93.0 ± 0.1 84.7 ± 0.2

70.1 ± 0.5 68.6 ± 0.5 70.2 ± 0.6 40.2 ± 0.5 41.0 ± 1.0 37.8 ± 0.5 12.1 ± 0.8 11.9 ± 0.5 11.8 ± 0.6 73.3 ± 1.0 73.1 ± 0.7 73.1 ± 0.5 42.4 ± 0.9 42.0 ± 0.5 40.6 ± 0.5 14.7 ± 0.5 14.8 ± 0.8 13.5 ± 1.0 74.8 ± 0.5 73.3 ± 0.5 74.8 ± 1.0 44.3 ± 0.5 42.5 ± 0.5 44.5 ± 0.5 14.5 ± 0.7 15.9 ± 0.5 15.1 ± 0.6

7.7 ± 0.1 21.1 ± 0.5 32.6 ± 0.6 7.7 ± 0.1 11.5 ± 0.2 20.5 ± 0.5 1.7 ± 0.2 3.2 ± 0.1 6.5 ± 0.1 6.5 ± 0.1 19.3 ± 0.4 29.5 ± 0.5 6.5 ± 0.1 9.9 ± 0.2 18.3 ± 0.3 1.4 ± 0.1 2.9 ± 0.1 5.9 ± 0.1 5.7 ± 0.1 16.9 ± 0.3 26.7 ± 0.5 5.6 ± 0.1 8.7 ± 0.2 16.6 ± 0.3 1.2 ± 0.1 2.5 ± 0.1 5.5 ± 0.1

91.5 ± 0.2 76.5 ± 0.1 63.7 ± 0.8 89.2 ± 0.2 84.0 ± 0.3 70.8 ± 0.6 95.5 ± 0.2 90.9 ± 0.2 81.0 ± 0.3 92.8 ± 0.1 78.6 ± 0.5 67.2 ± 0.7 90.9 ± 0.2 86.1 ± 0.2 73.9 ± 0.4 96.0 ± 0.1 92.0 ± 0.1 83.2 ± 0.3 93.6 ± 0.1 81.2 ± 0.3 70.2 ± 0.5 92.1 ± 0.1 87.6 ± 0.3 76.3 ± 0.6 96.5 ± 0.1 92.9 ± 0.1 84.8 ± 0.3

71.4 ± 0.2 70.2 ± 0.3 70.7 ± 0.2 39.7 ± 0.6 39.7 ± 0.7 38.0 ± 0.6 13.3 ± 0.3 12.5 ± 0.3 11.8 ± 0.2 73.0 ± 0.6 73.7 ± 0.8 73.8 ± 0.5 42.5 ± 0.9 41.9 ± 0.5 40.9 ± 0.3 14.0 ± 1.0 14.5 ± 0.6 13.5 ± 0.7 75.4 ± 0.3 73.9 ± 0.4 74.8 ± 0.5 44.7 ± 0.6 43.5 ± 0.8 43.4 ± 0.5 14.8 ± 0.4 15.2 ± 0.5 15.4 ± 0.7

Concentration units in mole%. Calculated by RK EoS.

Dsol H1 x

" !#   ð0Þ K h;x @ Dsol G1 2 @ x ; ¼ RT ¼ T ln @T @T T P0 2

" !# ! ð0Þ ð0Þ K h;x K h;x @  R ln ln @T P0 P0   1 Dsol H1 x  Dsol Gx : ¼ T

ð15Þ

Dsol S1 x ¼ RT

ð16Þ

It is worth mentioning that the pressure range considered in this work is not high enough to cause Henry’s law constant to be a strong function of pressure [25,74]. Therefore, one would not expect large errors if one ignores this pressure dependency. The values for the partial molar Gibbs energy, enthalpy and entropy of solvation are given at temperatures from (303.15 to 353.15) K for CO2/[C8mim][PF6], H2S/[C8mim][PF6] in table 5, respectively.

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M. Safavi et al. / J. Chem. Thermodynamics 65 (2013) 220–232

12.0

0 -2

10.0

ΔsolH∞x /kJ mol -1

-4

K (0) h,x / MPa

8.0

6.0

-6 -8 -10 -12

4.0

-14 2.0

-16 300

310

320

330

340

350

360

T/K 0.0 300

310

320

330

340

350

-50

360

T/K

-55

ΔsolS∞x /J mol -1K-1

FIGURE 4. Comparison between Henry’s law constants as a function of temperature for the solubility of H2S and CO2 in different ILs: d, H2S + [C8mim][Tf2N] (Ref. [60]); j, H2S + [C8mim][PF6] (this work); N, H2S + [C4mim][PF6] (Ref. [61]); s, CO2 +, [C8mim][Tf2N] (Ref. [60]); h, CO2 + [C8mim][PF6] (this work); D, CO2 + [C4mim][PF6] (Ref. [53]).

18

-60

-65

16

-70

ΔsolG∞x /kJ mol -1

14

300

315

330

345

360

T/K 12 FIGURE 6. Enthalpy (upper plot) and Entropy (lower plot) of solvation of hydrogen sulfide; j, and carbon dioxide; s, in [C8mim][PF6] as a function of temperature.

10

2.0

8

1.8

6

1.4

315

330

345

360

T/K FIGURE 5. Gibbs energy of solvation of hydrogen sulfide j, and carbon dioxide s, in [C8mim][PF6] as a function of temperature.

As can be observed in figure 5, the Gibbs energy of solvation, for both CO2 and H2S, increases with temperature in a similar manner. In figure 6, the variation with temperature of the enthalpy and entropy of solvation for the systems investigated are depicted. Both of the gases have negative enthalpies of solvation corresponding to an exothermic solvation which means that the solvation is thus favoured at lower temperatures. More negative values were calculated for the system involving hydrogen sulfide indicating that the interaction of H2S is more energetic than CO2 with [C8mim][PF6] [58,74]. For the entropy of solvation, all the values are negative and the variations with temperature of the entropy values are positive. The more negative values for CO2 entropy indicate a higher ordering degree as CO2 dissolved in [C8mim][PF6], but the difference is not so high to carry out further analysis indicating that

P / MPa

4 300

1.6

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.1

0.2

0.3

0.4

0.5

x2 FIGURE 7. Solubility of CO2 in [C8mim][PF6]: experimental results, , T = 303.15 K; D, 313.15 K; j, 323.15 K; s, 333.15 K; +, 343.15 K; , 353.15 K; —, correlation by Pitzer’s model.

the energetic effect is more important than the entropic effect [39,94].

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M. Safavi et al. / J. Chem. Thermodynamics 65 (2013) 220–232

TABLE 8 Critical temperature Tc, critical pressure Pc and parameters k0, k1, k2 and k3 in equation (11) for pure component used for the RK EoS.a.

a

Compound

Molar mass/(g  mol1)

Tc/K

Pc/MPa

k0

k1

k2

k3

CO2 H2S [C8mim][PF6]

44.010 34.082 340.29

304.13 373.10 800.14

7.377 9.000 1.404

1.00049 0.99879 1

0.43866 0.33206 0.11919

0.10498 0.049417 0

0.06250 0.0046387 0

The critical parameters for [C8mim][PF6] was estimated with the method proposed by Valderrama et al. [99,100].

2.0

8

1.8

7 1.6

6

K (0) h,x / MPa

P / MPa

1.4 1.2 1.0 0.8

5 4 3

0.6

2

0.4

1

0.2 0.0 0.0

0.2

0.4

0.6

0 300

0.8

x2

310

320

330

340

350

360

T/K

FIGURE 8. Solubility of H2S in [C8mim][PF6]: experimental results, , T = 303.15 K; D, 313.15 K; j, 323.15 K; s, 333.15 K; +, 343.15 K; , 353.15 K; –, correlation by Pitzer’s model.

FIGURE 9. Henry’s law constants of H2S and CO2 in [C8mim][PF6] plotted against temperature: experimental results, s, H2S + [C8mim][PF6]; e, CO2 + [C8mim][PF6]; solid curve = correlation by equation (13); dashed curve = calculated from the RK EoS.

TABLE 9 Binary interaction parameters l12, l21, m12, m21, s12 and s21 of RK EoS in equations (22)-(24).a. System (1)/(2)

l12

l21

m12 = m21

s12 = s21/K

CO2/[C8mim][PF6] H2S/[C8mim][PF6]

0.19255 0.27844

0.16330 0.22195

0.19365 0.20855

44.877 94.985

100 90 80

CO2/H2S : 1/4

Determined by non-linear least squares analysis using the solubility data of this study.

TABLE 10 Comparison between average relative deviations (ARD%) and maximum relative deviations (MRD%) calculated from experimental mole fractions by the two models considered in this work. Pitzer model

RK equation

System

ARD%

MRD%

ARD%

MRD%

CO2/[C8mim][PF6] H2S/[C8mim][PF6] CO2/H2S/[C8mim][PF6]

1.77 2.27 8.61

5.3 5.9 10.8

1.83 2.36 2.55

8.5 6.4 8.6

100.y H2S (Calculated)

a

70 60 50 CO2/H2S : 1/1

40 30 20 CO2/H2S : 4/1

10 0

4.2. Simultaneous solubility of both gases in [C8mim][PF6] The solubility of the mixture of CO2/H2S in [C8mim][PF6] under various T, P, and feed compositions were also measured to evaluate the feasibility of the CO2/H2S gas separation by the selective absorption method. Three levels were selected for the molar ratios of carbon dioxide to hydrogen sulfide in the feed, i.e. CO2/H2S  4/ 1, 1/1, and 1/4. Special care was taken when preparing the CO2/H2S gas mixtures to prevent the H2S from condensing. The saturation vapour pressure for H2S at T = 298 K (2.0173 MPa) is lower than that of CO2 at 298 K (6.4342 MPa). Therefore, the total pressure for the three feed gas mixtures was set below 2.0 MPa to prevent

0

10

20

30

40

50

60

70

80

90

100

100.y H2S (Measured) FIGURE 10. Comparison of measured experimental and calculated VLE data for the ternary CO2/H2S/[C8mim][PF6] system. Measured and calculated H2S vapour phase compositions are compared for various experimental conditions (see table 7). Symbols: D: T = 303.15 K; d: 323.15 K; h: 343.15 K.

the H2S from condensing. All measurements were carried out at temperatures of (303.15, 323.15, and 343.15) K and pressures less than 1.0 MPa. The experimental results for the H2S/CO2/[C8mim][PF6] ternary system are summarized in table 8. Discussions

M. Safavi et al. / J. Chem. Thermodynamics 65 (2013) 220–232

about modelling and gas separation feasibility are presented in the next section. 4.3. Correlation and modelling of experimental data As mentioned earlier, two correlation methods, the models of Pitzer and RK, were used to correlate the new experimental solubility data. In case of the Pitzer model, the partial molar volume of gas solute i at infinite dilution, V 1 i , was considered as a function of absolute temperature T defined by equation (17) [95,96]: 1

3 V1 i ðTÞ=ðcm  mol Þ ¼ B0 þ B1 ðT=KÞ þ B2 ðT=KÞ; 3

V1 i

ð17Þ

1

where is in (cm  mol ) and T is in K. The parameters of equation (17) can be realised based on experimental data of the volumetric properties of the gas solute and ionic liquid mixtures. But, such data are available for few systems only [28,43,95,97]. In the case that the experimental volumetric data are not available the experimental results for the gas solubility were used to determine the partial molar volumes of gas solutes at infinite dilution and interaction parameters between gas molecules in the ionic liquids [35,47,58,95,96]. In order to obtain corresponding values of such properties, solubility data were fitted to equation (18) which is derived from substitution of equations (3)-(5) in equation (2). Then, V1 i of gaseous solutes in [C8mim][PF6] and the binary interaction parameters were obtained by using linear regression.

ln

fi0 ðT; PÞ V 1P ð0Þ ¼ ln K h;xi ðTÞ þ i þ 2  mi  b2 þ 3  m2i  b3 RT mi

ði ¼ 1; 2Þ: ð18Þ

The obtained parameters B0 , B1 and B2 of equation (17) are presented in table 6. As mentioned before, b2 and b3 are parameters that describe binary and ternary interactions, respectively and considered as a function of temperature, defined by equations (19a) and (19b):

b2 ðTÞ ¼ C 0 þ

C1 ; T=K

ð19aÞ

b3 ðTÞ ¼ D0 þ

D1 : T=K

ð19bÞ

The fitted parameters C0 and C1 of equation (19a) and D0 and D1 of equation (19b) are presented in table 6 for each of the systems studied. The correlation results revealed that the influence of temperature on the binary and ternary parameters has to be taken into account. Also, ternary parameter (b3 ) has a considerable effect on the accuracy of correlation for the systems studied in this work. As mentioned earlier, the limited amount of the volumetric data for gas solute and ionic liquid systems is a main obstacle to accurately determine the parameters of equation (17). If the appropriate volumetric data are not available, it will be possible to neglect the Poynting correction for low pressure systems similar to those studied in this work. On the other hand, the partial molar volume of the gas at infinite dilution and the interaction parameters has influence on each other [95]. Therefore, fitting of experimental solubility data, without considering V 1 i , will result in a new set of interaction parameters which is different from those obtained by equation (18). However, both sets of interaction parameters have the same order of magnitude, while few parameters are required to correlate the experimental data in comparison to the case considering V 1 i . The new resulting parameters for binary interactions, C0 and C1 of equation (19a), are 0.26871 and 33.765 for CO2/[C8mim][PF6] system and (0.02276 and 20.394) for the H2S/[C8mim][PF6] system. Also, the new sets of fitted parameters D0 and D1 of equation (19b) are (0.09954, 34.470) and

229

(0.03839, 10.616) for the CO2/[C8mim][PF6] and H2S/[C8mim] [PF6] systems, respectively. For CO2/H2S/[C8mim][PF6] ternary mixtures, when all parameters for interactions between CO2 and H2S in the liquid phase (for example, bH2 S; CO2 ) are neglected, the model allows to predict the solubilities of both CO2 and H2S simultaneously in [C8mim][PF6]. However, the deviation between experimental and such predicted results was significant. In order to improve the correlation accuracy of the Pitzer’s model, the binary interaction parameter between the CO2 and H2S (b2;CO2 H2 S = b2;H2 SCO2 ) was considered (equation (21)):

b2;CO2 H2 S ¼ b2;H2 SCO2 ¼ 0:50082 þ 137:361=TðKÞ:

ð20Þ

In the case that CO2 and H2S are simultaneously dissolved in the ionic liquid, the fugacity in the vapour phase is calculated from the virial equation of state that was truncated after the second virial coefficient. This is a reasonable approximation as in the experiments the highest total pressure is less than 2 MPa [98]. For comparison with the correlations made by the Pitzer model for mole fraction of CO2 and H2S gas solutes, dissolved in the solvent IL at the specified temperature and pressure, the experimental solubility data in tables 3 and 4 are depicted in figures 7 and 8 as a function of temperature. It can be seen that there is quite good agreement between the correlated results and the observed experimental results in tables 3 and 4. In case of the RK model, we need the critical properties of pure compounds that were extracted from the NIST database for CO2 and H2S [6] and were estimated by the modified Lydersen–Joback–Reid method proposed by Valderrama and coworkers [99,100] for the ionic liquid [C8mim][PF6]. The parameters k0 through k3 for CO2 and H2S were taken from Ref. [26], which were obtained by Shiflett and Yokozeki from the corresponding vapour pressure data and those of the IL were obtained through analysis of PTx solubility data for each of the three systems investigated in this work. The parameters k0 through k3 together with the critical constants are presented in table 8 for each pure compound. The parameters a and b (equations (9) and (10)) were modelled by the modified van der Waals–Berthelot mixing rule proposed by Yokozeki [101] for general N-component mixtures as follows:

aðTÞ ¼

N X ðai aj Þ1=2 fij ðTÞð1  kij Þxi xj ;

ð21Þ

i;j¼1

b¼

N 1X ðbi þ bj Þð1  mij Þð1  kij Þxi xj ; 2 i;j¼1

fij ðTÞ ¼ 1 þ

kij ¼

sij T

ð22Þ

ð23Þ

;

lij lji ðxi þ xj Þ ; lji xi þ lij xj

ð24Þ

where sij ¼ sji , sii ¼ 0, mij = mji, mii = 0 and kii ¼ 0. The parameters ai and bi are defined similar to equations (9) and (10):

ai ðTÞ ¼ 0:427480

bi ¼ 0:08664

R2 T 2ci ai ; Pci

RT ci : Pci

ð25Þ

ð26Þ

There are four binary interaction parameters in this model: lij, lji, mij, and sij , which were obtained for each binary pair using non-linear regression analyses of experimental PTx data for CO2/ [C8mim][PF6], H2S/[C8mim][PF6] binary systems. The numerical

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M. Safavi et al. / J. Chem. Thermodynamics 65 (2013) 220–232

5

4.00

(a) CO2/H2S Feed ratio

3.95

CO2/H2S Selectivity

CO2/H2S Selectivity

1/4 1/1

3.90

4/1

3.85

3.80

4.5 T=303.15 K T=323.15 K T=343.15 K

4

3.5

3.75 3

3.70 0

10

20

30

40

50

60

70

80

90

0

100

10

30

40

50

60

70

80

90

100

Mole Percent of [C8mim][PF6]

Mole Percent of [C8mim][PF6] 4.5

20

FIGURE 12. Plot of calculated selectivity defined by equation (29) vs. [C8mim][PF6] mole per cent at T = (303.15, 323.15, and 343.15) K, P = 0.1 MPa, and CO2/H2S = 1/4 feed ratio.

(b)

4

CO2/H2S Feed ratio

3.6

1/1

3

1/4

2.5 2

1 2

3

4

5

6

7

FIGURE 11. (a) Calculated selectivity defined by equation (29) vs. [C8mim][PF6] mole per cent with three different CO2/H2S mole ratios at T = 303.15 K and P = 0.1 MPa. (b) Selectivity plots without ionic liquid [C8mim][PF6] as a function of total pressure.

ði ¼ 1; 2; 3Þ;

ð27Þ

where, xi and yi are liquid and vapour mole fraction of the ith spe^ L and / ^ V stand for the fugacity coefficient of the ith species, and / i i cies in the liquid and vapour phase, respectively. The simultaneous solubility of both gases in the IL was predicted by using those binary interaction parameters were obtained for each binary system. The average of relative deviations, ARD%, defined by equation (29) together with the maximum relative deviations (MRD%) of correlated mole fractions by using each of the models studied, are summarized and compared with each other in table 10 for a number of N data points.

ARD% ¼

   xexp i  exp : xi

N  cor 100 X  xi

N

i¼1



4/1

3.3

3.2

ð28Þ

3 0

10

20

30

40

50

60

70

80

90

100

Mole Percent of [C8mim][PF6] 3.6

(b)

3.5

CO2/H2S Feed ratio 1/4

3.4

CO2/H2S Selectivity

values of the binary interaction parameters are summarized in table 9. The expression for fugacity coefficient /i of the ith species for the RK EoS, which is needed for the phase equilibrium calculation, is given in refs 23, 24, and 38. The equilibrium solubility for the binary and ternary systems of (IL + CO2 + H2S) can be obtained by applying the fundamental criterion for phase equilibrium:

^V yi / i

1/1

3.4

3.1

P / MPa

¼

CO2/H2S Feed ratio

3.5

1.5

^L xi / i

(a)

4/1

CO2/H2S Selectivity

CO2/H2S Selectivity

1/4

3.5

1/1

3.3

4/1

3.2 3.1 3 2.9 2.8 2.7 0

10

20

30

40

50

60

70

80

90

100

Mole Percent of [C8mim][PF6] FIGURE 13. Calculated selectivity defined by equation (29) vs. [C8mim][PF6] mole per cent with three different CO2/H2S mole ratios at T = 343.15 K (a) P = 0.1 MPa and (b) P = 1 MPa.

M. Safavi et al. / J. Chem. Thermodynamics 65 (2013) 220–232

According to table 10, the Pitzer model correlates the solubility data of CO2 and H2S in [C8mim][PF6] with a slightly higher accuracy than the RK EoS. In the case of CO2/H2S/[C8mim][PF6] ternary system, the RK EoS shows the higher correlation accuracy. It must be noted here that the values of the critical constants, Tc and Pc, of the ILs estimated by different methods have a negligible effect on the correlation accuracy of the RK EoS [58]. For example in the case of [C8mim][PF6], the values of Tc and Pc change respectively from 800.1 K and 1.40 MPa using the method of Valderrama et al. [99] (method I) to 533.4 K and 1.49 MPa by using the group contribution method due to Shen et al. [102] (method II). In this case the values of ARD% change from 1.71% by using method I to 1.96% when method II is employed for the CO2/[C8mim][PF6] binary system, and they change from 2.36% by using method I to 2.44% using method II for H2S/[C8mim][PF6] binary system. The RK EoS was also used for the direct calculation of Henry’s law constant on a mole fraction scale. Details of calculations are given in Ref. [103]. The resulting Henry’s constants from the RK EoS are presented and compared with the experimental results and those values calculated from equation (13) in figure 9. The calculated Henry’s constants agree with the experimental results within an average deviation of 1.8% and 1.7% for the CO2/[C8mim][PF6] and H2S/[C8mim][PF6] systems, respectively. Figure 10 presents the comparison of measured and calculated values for H2S mole% in the vapour phase (CO2 mol% = 100 to H2S mol%) under various T, P, and feed composition conditions; see table 7. The model calculations and experimental data are in very good agreement. To investigate the possibility of CO2/H2S separation by the absorptive method using [C8mim][PF6] ionic liquid, the RK EoS was used to calculate the gaseous selectivity aA=B , which is the ability to separate gases A and B in the gas phase. These factors are defined as follows [26,69]

aA=B ¼

yA =xA : yB =xB

ð29Þ

Here we denote CO2 as A and H2S as B, the CO2/H2S selectivity in the gas phase (aA/B) has been computed according to present EoS model at T = (303.15, 323.15, and 343.15) K and the results are summarized in figures 11–13. Figure 11a shows the CO2/H2S selectivity (aA=B ) as a function of the ionic liquid [C8mim][PF6] mole per cent for ternary mixtures with different CO2/H2S mole ratios (4/1, 1/1 and 1/4) at T = 303.15 K and P = 0.1 MPa. As observed, the selectivity (aA=B ) remains relatively constant at about 3.82 to 3.86 for all cases with increasing ionic liquid concentration. In figure 11b, the selectivity without [Omim][PF6] at T = 303.15 K is plotted as a function of pressure for the same CO2/H2S feed ratios (4/1, 1/1, and 1/4). The effect of the ionic liquid addition on the selectivity enhancement can be understood from the comparison between figures 11a and b. According to figure 11a, the selectivity of the ternary system includes the ionic liquid with the feed ration of 4/1 (CO2/H2S) is about 3.8, while the corresponding case without the ionic liquid has a selectivity of about 1.2 [26,58]. As the CO2/H2S feed ratio decreases from 4:1 to 1:4, the improvement in selectivity with the ionic liquid vs. no ionic liquid also decreases. The effect of temperature on the selectivity was studied by calculating the selectivity at temperatures (303.15, 323.15 and 343.15) K and the results are shown in figure 12. As can be seen, an increase in temperature leads to a decrease in the selectivity (the selectivity decreases by increasing temperature). The behaviour as shown in figure 12 exists at all CO2/H2S feed ratios and all pressures from (0.1 to 1.0) MPa. Also, the selectivity characteristics at a higher temperature (343.15 K) and pressures (0.1 and 1 MPa) are shown in figure 13. The general behaviour as shown in figure 13a is similar to the case in figure 11a. Figure 13b shows

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that as the CO2/H2S feed ratio decreases from 4:1 to 1:4, the selectivity decreases by increasing pressure. The most important fact to consider at higher temperatures (343.15 K) is that, at high CO2/H2S feed ratios (1:1 and 4:1) without the ionic liquid, no (vapour + liquid) equilibria exists [26,58] and the gas separation cannot be accomplished using traditional distillation methods. Therefore, the separation of CO2 and H2S is only possible with the addition of the ionic liquid. 5. Conclusions New experimental data for the solubility and thermodynamic functions of solutions of carbon dioxide and hydrogen sulfide gases in ionic liquid 1-octyl-3-imidazolium hexafluorophosphate, not previously reported in the literature, have been measured and presented in this work. The solubility of these gases was measured as a function of temperature over the range of (303.15 to 353.15) K using an accurate isochoric saturation method [58,74,80–83]. The solubility of H2S is higher than that of CO2 in [C8mim][PF6]. Negative enthalpies (exothermic processes) and entropies of solvation were calculated for the systems investigated. The solubility of both gases in the IL studied in this work is of a physical nature. It has been shown that the solubility of both CO2 and H2S gases in [Cnmim][PF6] ILs increases by increasing the number of carbons in the alkyl substituent of the methylimidazolium cation ring. The solubility data for the CO2/H2S/[C8mim][PF6] ternary system can best be correlated by means of the generic Redlich–Kwong cubic equation of state proposed for gas/ionic liquid systems. The addition of the ionic liquid makes feasible the separation of CO2 and H2S from each other especially at high temperatures where the traditional distillation procedure fails to work. Acknowledgements We are thankful to the research council of the Research Institute of Petroleum Industry (RIPI) and also to the Research and Development of the National Iranian Oil Company (NIOC) for their support of this work. We also are very grateful to Prof. Gerd Maurer for his useful comments and kind guidance in correlating experimental data using Pitzer model. References [1] A.L. Kohl, R.B. Nielsen, Gas Purification, fifth ed., Gulf Publishing Company, Texas, 1997. [2] D. Camper, J.E. Bara, D.L. Gin, R.D. Noble, Ind. Eng. Chem. Res. 47 (2008) 8496– 8498. [3] F. Karadas, M. Atilhan, S. Aparicio, Energy Fuels 24 (2010) 5817–5828. [4] J.S. Wilkes, P. Wassercheid, T. Welton (Eds.), Ionic Liquids in Synthesis, WileyVCH Verlag, 2002. [5] B. Markus, S. Dietrich, Mol. Phys. 108 (2010) 211–214. [6] NIST Scientific and Technical Databases, Thermophysical Properties of Fluid Systems. (accessed May 2012). [7] E.D. Bates, R.D. Mayton, I. Ntai, J.H. Davis, J. Am. Chem. Soc. 124 (2002) 926– 927. [8] A. Berthod, M.J. Ruiz-Angel, S. Carda-Broch, J. Chromatogr. A 1184 (2008) 6– 18. [9] X. Li, J. Zhao, Q. Li, L. Wang, S.C. Tsang, Dalton Trans. 19 (2007) 1875–1880. [10] C. Jork, C. Kristen, D. Pieraccini, A. Stark, C. Chiappe, Y.A. Beste, W. Arlt, J. Chem. Thermodyn. 37 (2005) 537–558. [11] X. Li, W. Wu, L. He, H. Li, H. Sui, Energy Fuels 22 (2011) 5224–5231. [12] A.J. Walker, N.C. Bruce, Chem. Commun. 22 (2004) 2570–2571. [13] D. Zhao, R. Liu, J. Wang, B. Liu, Energy Fuels 22 (2008) 1100–1103. [14] J. Wang, D. Zhao, K. Li, Energy Fuels 23 (2009) 3831–3834. [15] R. Schmidt, Energy Fuels 22 (2008) 1774–1778. [16] M.B. Shiflett, A. Yokozeki, Energy Fuels 24 (2010) 1001–1008. [17] A. Yokozeki, M.B. Shiflett, Energy Fuels 23 (2009) 4701–4708. [18] Y.J. Heintz, L. Sehabiague, B.I. Morsi, K.L. Jones, D.R. Luebke, H.W. Pennline, Energy Fuels 23 (2009) 4822–4830. [19] J.L. Anthony, E.J. Maginn, J.F. Brennecke, J. Phys. Chem. B 106 (2002) 7315– 7320. [20] A. Shariati, C.J. Peters, J. Supercrit. Fluids 34 (2005) 171–176. [21] E.K. Shin, B.C. Lee, J.S. Lim, J. Supercrit. Fluids 45 (2008) 282–292.

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JCT 13-76