Determination of SO2 solubility in ionic liquids: COSMO-RS and modified Sanchez-Lacombe EOS

Accepted Manuscript Determination of SO2 solubility in ionic liquids: COSMO-RS and modified Sanchez-Lacombe EOS

Farshad Gholizadeh, Amin Kamgar, Mohamad Roostaei, Mohammad Reza Rahimpour PII: DOI: Reference:

S0167-7322(18)33880-7 doi:10.1016/j.molliq.2018.09.137 MOLLIQ 9743

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

1 August 2018 13 September 2018 29 September 2018

Please cite this article as: Farshad Gholizadeh, Amin Kamgar, Mohamad Roostaei, Mohammad Reza Rahimpour , Determination of SO2 solubility in ionic liquids: COSMORS and modified Sanchez-Lacombe EOS. Molliq (2018), doi:10.1016/ j.molliq.2018.09.137

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ACCEPTED MANUSCRIPT Determination of SO2 solubility in Ionic Liquids: COSMO-RS and modified Sanchez-Lacombe EOS

Farshad Gholizadeh1, Amin Kamgar2, Mohamad Roostaei2, Mohammad Reza Rahimpour2

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1- Department of chemical engineering, shiraz university of technology, shiraz 71555 -313, Iran

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2- Department of chemical engineering, Shiraz University, Shiraz 71345, Iran

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Abstract:

With more stringent standards regarding the emission of greenhouse gases, capturing or removal

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of these detrimental pollutants has become of significant importance in industrial plants. In this presented investigation,   - modified Sanchez–Lacombe equation of state and COSMO-RS-Lei

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and COSMO-RS-ADF models have been employed in order to estimate the solubility of sulfur dioxide (SO 2 ) in different ionic liquids (ILs) as chemical sorbents with different cations and

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anions. The experimental data of Imidazolium, Pyridinium, Guanidinium and Ammonium based ionic liquids such as experimental data of density and the amount of SO 2 solubility into ionic

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liquids in a wide range of temperature and pressure have been obtained from the literature. The characteristic parameters of the   - modified Sanchez–Lacombe EOS have been adjusted by

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applying a database including 580 experimental data points of ILs density for 4 SO2 /IL systems. In order to confirm the accuracy of the mentioned models, the phase equilibrium (PTx) diagrams

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of the SO 2 /ILs systems have been drawn and predicted data are compared with experimental data. According to the figures and also reported tables which contain the amount of calculated errors, It can be claimed that presented models in this study are capable to predict the amount of SO2 solubility into ionic liquids within the value of AARD% around 5% , 63% and 62% for   modified Sanchez–Lacombe EOS, COSMO-RS-Lei and COSMO-RS-ADF respectively.

Keywords: Solubility, Sulfur Dioxide, Ionic liquids,   - modified Sanchez–Lacombe EOS, COSMO RS model

ACCEPTED MANUSCRIPT

1. Introduction More than 20 percent of the energy demand of the worldwide is supplied from natural gas and it is worthwhile to mention that more than 50 percent of the household energy consumption

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is from natural gas[3; 11]. For optimal usage of natural gas in industrial plants or home

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consumption, a series of pretreatment processes such as dehydration is necessary to achieve a higher quality. There are non-hydrocarbon gases such as carbon dioxide (CO 2 ), sulfur dioxide

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(SO2 ), hydrogen sulfide (H2 S) and other gaseous compounds as the impurity in natural gas. Corrosion in pipelines, lower heating value of natural gas, increasing the size of gas transmission

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lines and more cost for the pipelines, reduction in capacity compressor stations and reduce the economic value of natural gas are the main harms of existing such impurities[1; 17; 18].

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Furthermore, the burning of fossil fuels in power plants and motor vehicles releases greenhouse gases such as CO 2 and SO 2 into the atmosphere cause the greenhouse effect and global warming

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which is one of the most significant concerns of scientists in the last century. Therefore, capturing or removal of such harmful gases from natural gas and atmosphere is one of the most

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important steps in order to design the relative equipment and exploitation of fossil fuels. Common technologies are applied for the SO 2 capture on the industrial scale like utilizing

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different chemical absorbents. With more stringent standards regarding the emission of greenhouse gases, capturing or removal of these detrimental pollutants has become of significant

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importance in industrial plants. One method that has recently been considered as a high efficiency method is SO 2 removal by using ionic liquids (ILs) as appropriate solvents. ILs are

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known as green sorbent and environmental benignity because of some unique properties in comparison with other chemical solvents such as high stability, being in a liquid phase at low temperatures, low vapor pressure and non-volatility[4; 7; 23]. It is also noteworthy that SO2 absorption into ILs is a totally reversible process in the ambient condition because of adjustable ability of cations and anions[6]. Some valuable experimental researches have been done for SO2 capture using ILs recently. Anderson et al. in 2006, studied amount of SO 2 absorption in Imidazolium and Pyridinium based ILs with bis (trifluoromethylsulfonyl) imide ([Tf2 N]) anion part in the temperature range 298.15-313.15 k and different pressure up to 4 bar. They reached high SO 2 absorption capacity to 85 mole percent and showed that SO 2 absorption is a

ACCEPTED MANUSCRIPT physisorption process based on the excess Gibbs and enthalpy[2]. Jiang et al. in 2007, investigated SO 2 absorption in several Imidazolium based ILs at temperature range 298.15318.15 k and 1 bar. They examined selectivity of ILs in order to capture SO 2 and CO 2 and presented that the selectivity of ILs for SO 2 absorption is more than CO 2 [13]. Huang et al. in 2008 synthesized Guanidinium based room temperature ionic liquids (RTIL) and investigated their ability to capture SO 2 and Ammonia gases. It was realized that SO 2 absorption in ILs is an

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exothermic process with enthalpy equal to -21 to -37 kJ/mol and the reversibility of the process

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was proved[10]. Shiflett and Yokozeki in 2009, studied SO 2 and CO 2 absorption in

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[hmim][Tf2 N] room temperature ILs experimentally and theoretically. They applied the RedlichKwong (RK) equation of state for a ternary system of SO 2 +CO2 +ILs in various conditions of

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temperature, pressure and feed composition[26]. Also in 2010, Shiflett and Yakozeki measured the amount of SO2 solubility in Imidazolium based room temperature ILs in several isothermal

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processes and analyzed the PTx diagram by using the equation of state accurately. Unlike the previous research, it was found that absorption of SO 2 in ILs is chemisorption[24]. Jin et al. in

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2010, synthesized a special kind of ILs as Ammonium and Guanidinium based Task-specific Ionic Liquid (TSIL) to achieve more capacity of SO 2 absorption and compare with normal

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Imidazolium based ILs. It was demonstrated that SO 2 absorption in TSIL is both physisorption and chemisorption processes, while normal ILs absorb SO 2 just physically[14]. In addition to the

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experimental studies, theoretical researches using thermodynamic models such as equations of states (EOS) have been implemented for investigation of gas absorption in ILs. Iguchi et al. in

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2011, applied   - modified Sanchez–Lacombe EOS include temperature-dependent binary interaction parameter, kij, to predict CO2 absorption in ILs which is a vapor-liquid

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equilibrium[12]. Hekayati et al in 2015, carried out a research in order to model absorption of different refrigerant gases in ILs using Sanchez–Lacombe and   - Modified SL EOS. They demonstrated that   - Modified SL EOS is more capable than original SL EOS for modeling refrigerants absorption in ILs[9]. In this study, SO2 solubility into various Imidazolium, Pyridinium, Guanidinium and Ammonium based ILs with different anions have been modeled by using thermodynamic model   - Modified SL EOS and two different types of COSMO-RS model so-called COSMO-RS-Lei and COSMO-RS-ADF. Experimental data of SO 2 solubility in the ILs which have been listed in table1, gathered from the reliable literature.

ACCEPTED MANUSCRIPT Table 1: data source and info of ILs using in this modeling Operation conditions P (bar)

T (k)

No. of data points

Ref.

45

[2; 26]

[hmim][Tf2 N]

0.1-3

282.3-348.1

1-n-hexyl-3-methylpyridin iu m bis(trifluoromethylsulfonyl)imide

[hmpy][Tf2 N]

0.2-3

298.15

11

[2]

1-butyl-3-methylimidazo liu m tetrafluoroborate

[bmim][BF4 ]

0.01-2

298.15

15

[13; 14]

1-butyl-3 methyl imidazoliu m hexafluorophosphate

[bmim][PF6 ]

0.01-2

293.15298.15

11

[13; 14]

0.005-0.3

298.1-348.1

42

[24]

0.005-0.3

298.1-348.1

42

[24]

0.1-2.5

298.15

12

[13]

0.1-2.5

298.15

11

[13]

[bmim][Tf2 N]

0.1-2.5

298.15

10

[13]

[TMG][L]

0.01-1.01

293.15-333.15

15

[14]

[MEA][L]

0.007-1.01

293.15-333.15

15

[14]

[TMGH][BF4 ]

1

292.15-412.15

7

[10]

[bmim][Ac] [bmim][MeSO4 ]

1-ethyl-3-methylimidazoliu m tetrafluoroborate

[emim][BF4 ]

1-hexyl-3-methylimidazoliu m tetrafluoroborate

[hmim][BF4 ]

M

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PT

1-butyl-3-methyl imidazoliu m bis(trifluoromethylsulfonyl) imide

1,1,3,3-tetramethyl guanidinium lactate

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monoethanolaminium lactate

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1,1,3,3-tetramethylguanidiniu m tetrafluoroborate

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1-n-butyl-3-methylimidazoliu m methyl sulfate

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1-n-butyl-3 methylimidazoliu m acetate

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1-n-hexyl-3 methylimidazoliu m bis(trifluoromethylsulfonyl)imide

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Ionic Liquids

2. Thermodynamic modeling In this investigation, the amount of SO 2 solubility in ILs has been determined using phase equilibrium calculation. In the equilibrium state, the fugacity of the components in each phase is equal. Fugacity is calculable term according to the fugacity coefficient. Since the vapor pressure of the ILs is pretty low, it can be assumed that there is no IL in the vapor phase and there is only

ACCEPTED MANUSCRIPT pure SO 2 in this phase with a satisfying precision (The mole fraction of SO 2 in the vapor phase is equal to one). Also, the fugacity coefficient of SO 2 in the vapor and liquid phase is obtained by employing the equation of state.

2.1.   -Modified SL equation of state:

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The SL EOS contains three characteristic parameters which are dependent on the substance

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nature. SL EOS which submitted by Sanchez and Lacombe in 1976 is based on lattice fluid thermodynamic theory that fundamentally retrieved from statistical thermodynamics and is

~

1 

 

US

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defined by Eqs. 1 and 2:

~ 2  P  T  ln 1  ~   1   ~   0 r ~ P P * P

~ 

 *

(1)

(2)

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~ T T  * T

 

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

M

~

Where T * , P * and  * are the characteristic parameters of the SL EOS. The characteristic

PT

parameters of interaction energy (   ), characteristic volume ( v  ) and the segment length ( r ) for

*

RT * v  * P *

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  RT *

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pure substances which are functions of T, P, and  , are defined as below[21; 22]:

MP* r RT *  *

(3)

Where M is the molecular weight of components and R is the universal constant of gases. It is necessary to be considered that in original SL EOS,   is a temperature-independent parameter. According to the original SL EOS, Machida et al. in 2010[19] presented a new correction called

  - Modified SL which expressed temperature dependence of the interaction energy parameter (   ) as:

ACCEPTED MANUSCRIPT  * T    0

T 1  T

(4)

Where  indicates the constant temperature dependence factor of   and  0 is the asymptotic amount of the interaction energy. It should be considered that at the high range of temperature, the value of  0 is equivalent to   . The   - Modified SL will be obtained by replacing Eq (4) in

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original SL EOS. The applied mixing rules in the original SL EOS and   -SL EOS to mixtures (5):



Pij*  1  kij  Pi* Pj*

 i0Ti*  T  P   *  i  Pi 

v*   i0 vi*

j



M

*



ri0 xi   r

rx i  i i r

PT

0 i

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Where the closed-packed volume fraction of component

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respectively is demonstrated by component

i

i

and i , 0

i

i

and

j.

in both pure and mixture state

ri 0 and ri indicate the segment length of

in pure and mixture state, respectively, and also

interaction between component

i

(5)

i

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*

1/ 2

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i



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P *   i j Pij*

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which are the recommended combining rules of Sanchez and Lacombe[22] are presented in Eqs

kij

parameter represents a binary

The relationship of fugacity coefficient of component

is presented as below:

  ~  nr     ~  z  1  nr  ~ ln i   ln z  ri  2 ~  ln(1   )  ( ) ( )n   ~  ( )n  r   ni j  T    ni j   T  0

(6)

ACCEPTED MANUSCRIPT

Where z is the compressibility factor. The phrases including derivatives in the Eq. (6) are demonstrated as:



T



IP

rio nr   ( ) n j  *  v *  vi*   ni v

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N  nr   v*  * *   ( )  2 r  P   P  nj i j ij   *  ni  j 1  

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(7)

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By placing the above expressions in equation (6), a functional relationship will be obtained for

M

fugacity as:

o  2 ~   Z  1   ri * *  ~ ln i   ln Z  ri  ~  ln 1        *  v  vi   T   r  v    rio  ~  v *  * N *  ~  * 2ri   P    j Pij    *  v *  vi*   T   j 1     v









(8)

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CE

PT

ED

o

2.2. COSMO-RS model: The Conductor-like screening thermodynamic Model (COSMO-RS) is based on quantum chemical computations and

also

statistical thermodynamic in order to characterize the

thermodynamic behavior of pure and mixtures of compounds which applies the compounds chemical structures without relying on experimental data[16]. On the other hand, The COSMORS method prepares a link between chemical thermodynamic and quantum chemistry at the molecular scale.

Because of local dual interactions of surface segments in the all molecular

ACCEPTED MANUSCRIPT interactions of COSMO-RS model, the statistical averaging is accomplished in the interacting surface fragment ensemble[8]. In the COSMO-RS models, COSMO-RS-ADF and COSMO-RSLei which have been developed by Lei’s group[8], Pi ( ) indicates probability distributions, also known as sigma-profile, qualifies the composition of the surface segment ensemble[5; 15].

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ps ( ) Which is the sum of Pi ( ) for all components of the system is defined as below:

xi

is mole fraction of component

i

in the mixture.

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ies

Where

(9)

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ps ( )   xi Pi ( )

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In order to measure the dependency of the whole system (S) to the surface of polarity 𝜎, 𝜇𝑠 (𝜎) is expressed.

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aeff  RT  ln  Ps (  ) exp( (s (  )  e( ,   )))d   aeff  RT 

(10)

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M

s ( )  

PT

The chemical potential of compound 𝑖 in system 𝑆 is:

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i  ic,s   Pi ( ) s ( )d

AC

 ic , s 

(11)

Gc , s xi

r q    RT 0 ln ri  1 (1  i  ln r )   2 (1  i  ln q ) r q  

  Gic , s  RT 0  xi ln ri  1 ln(  xi ri )   2 ln(  xi qi ) i i  i 

(12)

(13)

Which 𝑞𝑖 and 𝑟𝑖 indicate the molecular area of compound i and the molecular volume,

ACCEPTED MANUSCRIPT respectively. Also, the total area and volume of all compounds are shown:

r   xi ri i

(14)

q   xi ri

T

i

IP

In this method the gas phase is considered as an ideal, so as the system’s pressure increased

predict gas solubility based on the following equation

(15)

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𝑦𝑖 𝑝 = 𝛾𝑖 𝑥𝑖 𝑝𝑖𝑠𝑎𝑡

CR

above 20 bar, it is get out of ideality and high error of prediction obtained. COSMO-RS method

Activity coefficient in the eq. 15 is obtained based on firstly calculating chemical potential of the

properties.

𝜇𝑥𝑥

is

the

chemical

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solution. The chemical potential 𝜇𝑠𝑖 allows for the prediction of almost all thermodynamic potential

in

the

pure

liquid

substance.

M

For each compound 𝑗 the mole fraction 𝑥𝑗 is varied until the partial pressure of the compound,

(16)

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Pj  Pj0 x j  j

PT

 (  sx   xx )    exp   kT   x s

ED

which is calculated from eq. (9), is equal to the given reference pressure p .

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Vapour pressure of pure compound j is demonstrated with𝑃𝑗0 . Mole fraction and activity coefficient of compound j in liquid is showed with 𝑥𝑗 and 𝛾𝑗 respectively. The basis of calculation is to decreasing the difference between reference pressure and the partial pressure of the compound 𝑃𝑗 according to the equation 9. 𝑥𝑗 will vary, and consequently 𝛾𝑗 is obtained. No longer needing of primary experimental data made this method valuable even if high prediction error is obtained. Quantum calculation of chemical potential and activity coefficient in the consequence may be the exordium of precise prediction.

ACCEPTED MANUSCRIPT 3. Results and discussion: As discussed before, in this investigation, the amount of SO 2 solubility into different ILs based on various cations and anions in a wide range of temperature and pressure have been scrutinized in order to examine the ability of   - SL EOS and COSMO-RS-Lei and COSMO-RS-ADF models. The characteristic parameters of the   - SL EOS for some of the ILs which have not

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been published in the literature, were specified through minimizing the average absolute relative

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deviations (AARDs %) between the calculated and experimental liquid density data which were

 i 1

iexp  ical  100 iexp

(10)

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N

1 AARD%  N

CR

extracted from the reliable literature based on the given objective function as below:

Where  iexp and  ical are the experimental and calculated data of ILs density, respectively. Table

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2 shows the fitted characteristic parameters for the   - SL EOS. Furthermore, the related information to the experimental data of ILs density which have been implemented to fit the

M

characteristic parameters of the EOS, have been reported in table 3. It is noteworthy that the

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amount of characteristic parameters which have been employed from the other reference [9] is

CE

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distinguished by letter b in table 2.

Table 2: Characteristic parameters for the   -modified Sanchez–Lacombe equation of state

1  K 

   j mol 

  cm 3 mol 

r

AARD%

[Bmim][BF4]a

508.27843

8965.851338

1.9026334

80.84264

0.0122

[Bmim][Ac]a

517.65706

9343.819361

2.1785828

71.532881

0.0135

[Bmim][MeSO4]a

462.44365

9169.899617

2.3081209

76.038067

0.0114

[Hmpy][Tf2N]a

278.30885

7395.434297

4.2084522

69.316637

0.0102

SO2a

40.121593

3971.7317

5.5441637

6.6520685

0.2882

AC

Components

ACCEPTED MANUSCRIPT

[Hmim][Tf2N]b

1  K 

 0  j mol 

  cm 3 mol 

r

AARD%

494.573

8389.657

2.126

122.716

0.179

619.495

10599.5

2.681

65.053

0.082

632.075

10617.62

2.175

59.117

0.081

571.575

10074.19

2.919

63.714

0.084

732.084

10066.4

1.642

136.101

0.118

b

[Bmim][PF6]

[Emim][BF4]b b

[Hmim][BF4]

[Bmim][Tf2N]

T

b

IP

a: calculated in this work

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b: extracted from [9]

PMPa

[Bmim][BF4]

0-35

[Bmim][Ac]

0-25

[Bmim][MeSO4]

0-35

0-35

No. of data

Ref.

283-328

171

[20]

298-353

63

[25]

283-333

99

[25]

273-428

249

M

PT

SO2

ED

[Hmpy][Tf2N]

T K 

AN

Components

US

Table 3: Data sources for calculation the characteristic parameters of the EOS

N



AC

1 AARD%  N

CE

The binary interaction parameter (kij), was coordinated by making least the objective function as:

i 1

xiexp  xical  100 xiexp

(11)

Which xiexp and xical are the experimental and calculated data of SO 2 solubility into ILs, respectively. This assumption has been considered that the liquid phase will not be solved into the vapor phase in the VLE calculations, so that the vapor phase is supposed to be pure SO 2 . A first degree polynomial has been applied in order to correct the fitted k ijs for each isothermal and also to determine the dependency of the binary interaction parameter to high temperatures for each ILs/SO 2 system which is quite predictable because of the nearly wide temperature range of the experimental data of SO 2 solubility in ILs. The binary coefficients of the mentioned first

ACCEPTED MANUSCRIPT degree polynomial and also the amount of AARD% between experimental and calculated mole fractions of SO 2 in the ILs using   -SL EOS from Eq. (11) have been reported in table 4. Based on the table 4 and the reported value of AARD%, it is clear that the   - SL EOS is capable to predict the solubility data of SO 2 accurately within about 1.99124 AARD%. Table 4: Binary interaction parameter correlation parameters for the EOS

a

[Bmim][PF6]

-0.115170898

[Emim][BF4]

-0.17453125

[Hmim][BF4]

-0.116484375

[Bmim][Tf2N]

-0.176796875

[Bmim][BF4]

-0.181806878

1.4165

0.000888794

1.217

AN

ED

[Bmim][MeSO4]

0 0

1.3669 0.8988 1.3816 1.8478

-0.224930907

-0.00044887

4.4124

-0.204206753

-0.00021264

1.9924

-0.04296875

0

3.3878

Ave.

1.99124

CE

PT

[Hmpy][Tf2N]

0

5.61E-05

M

[Bmim][Ac]

AARD%

0.000636178

CR

-0.128069706

US

[Hmim][Tf2N]

IP

b

T

K ij  a  b T

ILs

In addition, for endorsing the EOS, the calculated data has been compared with experimental

AC

data of SO 2 solubility into ILs as a function of pressure (bar) at various temperatures (k) in Figs1-4. As observed in the above mentioned figures, the PTx diagrams have been illustrated for four of the binary ILs/SO 2 mixtures. Repeatedly, the accuracy of the   - SL EoS to estimate the amount of SO 2 solubility in ILs such as [Bmim][MeSO 4 ], [Bmim][Ac], [Bmim][Tf2 N], [Hmim][ Tf2 N] is determined obviously according to the mentioned Figures.

AN

US

CR

IP

T

ACCEPTED MANUSCRIPT

Fig. 1-4, all are so2 solubility in 1) [HMIM][Tf2N], 2) [BMIM][Tf2n], 3) [BMIM][AC], 4)

M

[BMIM][MESO4]

ED

It mentioned that the remarkable feature of COSMO-RS model has no requirement to rely on experimental data which has attracted abundant attention recently. That is the reason why we

PT

were able to model more binary systems IL/SO 2 by COSMO-RS compare with the   - SL EoS in this paper. COSMO-RS-Lei and COSMO-RS-ADF models have been applied in order to

CE

predict the amount of SO 2 solubility into various Imidazolium, Pyridinium, Guanidinium and Ammonium based ILs. In fig 5 the estimated value of SO 2 solubility in [BMIM][BF4 ] IL has

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been drawn as a function of pressure (bar) at temperatures 298.15 and 293.15 o C using COSMORS-Lei and COSMO-RS-ADF models.

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Fig. 5, SO2 solubility in [BMIM][BF4] Table 5: total calculated errors in this modeling COSMO-RSLei

[HMIM][Tf2N] [BMIM][BF4] [BMIM][AC] [EMIM][BF4] [BMIM][BF4] [BMIM][PF6] [HMIM][BF4] [BMIM][MeSO4] [BMIM][Tf2N] [HMPY][Tf2N] [TMGH][BF4] [TMGHPO][BF4] [TMGHPO2][BF4] [TMGH][Tf2N] [TMGHB2][Tf2N] [TMG][L] Over all

3.14 11.82 2.9 1.74 9.92 1.54 4.08 3.1 9.9 5.35

95.54 25.96 89.07 31.17 32.67 32.17 34.93 57.79 51.97 43.98 42.82 60.78 69.35 60.98 68.85 78.33 63.71

95.63 42.52 63 28.05 45.03 32.87 35.57 62.77 52.8 46.81 49.45 65.69 73.03 62.09 71.14 86.73 62.86

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Temperature Range (K)

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COSMO-RSADF

NO. Point

283.15--348.1 298.15K 283.15-348.1 298.15 293.15-298.15 293.15-298.15 298.15 283.15-348.2 298.15 298.15 292-412 293-413 293-412 293-412 293-412 293-333 -

48 10 42 12 15 11 11 42 10 11 7 7 7 7 7 15 262

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EOS

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ILs

Further, in fig 6-10 the accuracy of two types of COSMO-RS models has been compared with

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the   - SL EOS in the form of PTx diagram. As obvious from the figures, the precision of the

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EOS is much higher than COSMO-RS-Lei and COSMO-RS-ADF models, although the quantities of binary ILs/SO 2 mixtures modeled by COSMO-RS models are greater. Table 5 is a

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comprehensive table which contains the whole calculated errors for the EOS and two types of COSMO-RS models.

According to table 5 the important subject that why the   - SL EOS is more accurate than COSMO-RS-Lei and COSMO-RS-ADF models, two determinants should be considered in this section. First, despite the fact that in the COSMO-RS models the gas phase has been assumed as an ideal phase, in the   - SL EOS this phase is treated as a real phase. Also as described before, the unique advantage of COSMO-RS model is that it is a priori predictive method independent of experimental data, but it is completely required to extract and employee experimental data to

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on the difference between applied models in this investigation.

Fig. 6-10, all are so2 solubility in 6) [HMPY][Tf2N], 7) [BMIM][BF4], 8) [HMIM][BF4], 9) [EMIM][BF4], 10) [BMIM][PF6]

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4.

Conclusion

In this study,   - SL EOS, COSMO-RS-Lei and COSMO-RS-ADF models were applied in order to

estimate the amount of SO 2

solubility in different Imidazolium, Pyridinium,

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Guanidinium and Ammonium based ionic liquids with various anions in the wide range of

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temperature and pressure. The total number of experimental data was equal to 262 which had been obtained from the reliable literature. The characteristic parameters of the   - SL EOS were

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fitted by minimizing an objective function on experimental data of ILs density and reported in table 2. To prove this claim that the employed models in this investigation have high predicting

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capability, the related results of SO 2 solubility into 16 different ILs were drawn in Figs. 1–10 and the errors between experimental and calculated data were reported in tables 5.The average error

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of   - SL EOS which is within 5%, illustrates its precision and the fact that the EOS can be considered as a reliable equation of state for predicting the solubility of materials (solubility of

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SO2 in Ionic Liquids in this case). The accuracy of the EoS is better than COSMO-RS model obviously but the advantage of the COSMO-RS is the possibility of modeling more systems

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because of no longer needing of any experimental data.

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References :

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[1] D.B. Alvarado, M.F. Asaro, J.L. Bomben, A.S. Damle, and A.S. Bhown, Nitrogen removal from low quality natural gas, in, SRI International, Menlo Park, CA (United States), 1997. [2] J.L. Anderson, J.K. Dixon, E.J. Maginn, and J.F. Brennecke, Measurement of SO2 solubility in ionic liquids, 110 (2006), 15059-15062. [3] R.S. Bhavsar, S.C. Kumbharkar, and U.K. Kharul, Investigation of gas permeation properties of film forming polymeric ionic liquids (PILs) based on polybenzimidazoles, 470 (2014), 494-503. [4] O. Ciocirlan, O. Croitoru, and O. Iulian, Densities and viscosities for binary mixtures of 1-butyl-3methylimidazolium tetrafluoroborate ionic liquid with molecular solvents, 56 (2011), 1526-1534. [5] F. Eckert and A. Klamt, COSMOtherm User’s Manual, version C2. 1, Release 01.05; COSMOlogic GmbH & Co, KG: Leverkusen, Germany (2005).

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[6] R. Fortunato, C.A. Afonso, M. Reis, and J.G. Crespo, Supported liquid membranes using ionic liquids: study of stability and transport mechanisms, 242 (2004), 197-209. [7] K. Ghandi, A review of ionic liquids, their limits and applications, Green. SUSTAIN. Chem. 4 (2014), 44. [8] J. Han, C. Dai, G. Yu, and Z. Lei, Parameterization of COSMO-RS model for ionic liquids, Green. Energ & Environ 3 (2018) 247-265. [9] J. Hekayati, A. Roosta, and J. Javanmardi, Thermodynamic modeling of refrigerants solubility in ionic liquids using original and ϵ*-Modified Sanchez–Lacombe equations of state, 403 (2015), 14-22. [10] J. Huang, A. Riisager, R.W. Berg, and R. Fehrmann, Tuning ionic liquids for high gas solubility and reversible gas sorption, 279 (2008), 170-176. [11] Y.C. Hudiono, T.K. Carlisle, A.L. LaFrate, D.L. Gin, and R.D. Noble, Novel mixed matrix membranes based on polymerizable room-temperature ionic liquids and SAPO-34 particles to improve CO2 separation, 370 (2011), 141-148. [12] M. Iguchi, H. Machida, Y. Sato, and R.L. Smith Jr, Correlation of supercritical CO2–ionic liquid vapor–liquid equilibria with the ε*‐modified Sanchez–Lacombe equation of state, 7 (2012), S95-S100. [13] Y.-Y. Jiang, Z. Zhou, Z. Jiao, L. Li, Y.-T. Wu, and Z.-B. Zhang, SO2 gas separation using supported ionic liquid membranes, 111 (2007), 5058-5061. [14] M. Jin, Y. Hou, W. Wu, S. Ren, S. Tian, L. Xiao, and Z. Lei, Solubilities and thermodynamic properties of SO2 in ionic liquids, 115 (2011), 6585-6591. [15] A. Klamt, Conductor-like screening model for real solvents: a new approach to the quantitative calculation of solvation phenomena, 99 (1995), 2224-2235. [16] A. Klamt and G. Schüürmann, COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient, J. Chem. Soc., Perkin Trans. 2 (1993), 799805. [17] P. Li, K. Pramoda, and T.-S. Chung, CO2 separation from flue gas using polyvinyl-(room temperature ionic liquid)–room temperature ionic liquid composite membranes, 50 (2011), 9344-9353. [18] K.A. Lokhandwala, M. Ringer, H. Wijmans, and R.W. Baker, Nitrogen removal from natural gas using membranes, in: Proceedings of the Natural Gas Conference, Federal Energy Technology Center (FETC), Houston, Texas, March, 1999. [19] H. Machida, Y. Sato, and R.L. Smith Jr, Simple modification of the temperature dependence of the Sanchez–Lacombe equation of state, 297 (2010), 205-209. [20] D. Matkowska and T. Hofman, High-pressure volumetric properties of ionic liquids: 1-butyl-3methylimidazolium tetrafluoroborate,[C4mim][BF4], 1-butyl-3-methylimidazolium methylsulfate [C4mim][MeSO4] and 1-ethyl-3-methylimidazolium ethylsulfate,[C2mim][EtSO4], 165 (2012), 161-167. [21] I.C. Sanchez and R.H. Lacombe, An elementary molecular theory of classical fluids. Pure fluids, 80 (1976), 2352-2362. [22] I.C. Sanchez and R.H. Lacombe, Statistical thermodynamics of polymer solutions, 11 (1978), 1145-1156. [23] P. Scovazzo, J. Kieft, D.A. Finan, C. Koval, D. DuBois, and R. Noble, Gas separations using non hexafluorophosphate [PF6]− anion supported ionic liquid membranes, 238 (2004), 57-63. [24] M.B. Shiflett and A. Yokozeki, Chemical absorption of sulfur dioxide in room-temperature ionic liquids, 49 (2009), 1370-1377.

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[25] S.p. Stevanovic, A. Podgoršek, A.A. Pádua, and M.F. Costa Gomes, Effect of water on the carbon dioxide absorption by 1-alkyl-3-methylimidazolium acetate ionic liquids, 116 (2012), 14416-14425. [26] A. Yokozeki and M.B. Shiflett, Separation of carbon dioxide and sulfur dioxide gases using roomtemperature ionic liquid [hmim][Tf2N], 23 (2009), 4701-4708.

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Determination of the solubility of SO 2 in different Ionic Liquids

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  -modified Sanchez–Lacombe, COSMO-RS (Lei, ADF) models capability are compared A wide range of experimental data are used to optimize the parameters.

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  -Modified Sanchez–Lacombe showed higher accuracy than COSMO-RS models.

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