Thermodynamic modeling of hydrogen solubility in a series of ionic liquids

Thermodynamic modeling of hydrogen solubility in a series of ionic liquids

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Thermodynamic modeling of hydrogen solubility in a series of ionic liquids Azadeh Kordi, Fatemeh Sabzi* Department of Chemical Engineering, Shiraz University of Technology, Shiraz 71555-313, Iran

article info

abstract

Article history:

In this study, the Perturbed Hard Sphere Chain Equation of State (PHSC EoS) has been

Received 11 April 2018

employed to predict the hydrogen solubility in a series of ionic liquids. As ionic liquids have

Received in revised form

no vapor pressure and no critical parameters and as hydrogen is a light molecule which

23 July 2018

behaves like a perfect gas, simple cubic equations of state cannot be used for modeling of

Accepted 7 August 2018

H2 þ ionic liquid mixture. Three main parameters of non-cubic PHSC EoS, i.e. (r) the

Available online xxx

number of segments per molecule, ðsÞ the distance between two molecules at zero potential and ðεÞ well-depth of potential between two non-bonded units have been calculated

Keywords:

by regression of the experimental Pressure-Volume-Temperature (PVT) data points. The

Hydrogen solubility

hydrogen solubility decreases with increasing temperature in [BMIM][BF4], [BMIM][C8SO4],

PHSC equation of state

[EMIM][EtSO4], [MDEA][Cl], and [N4,1,1,1][Tf2N], but inverse temperature effect is observed in

Ionic liquids

[BMIM], [BMPY], [EMIM] and [HMIM][Tf2N] as well as [BMIM][MeSO4]. The binary interaction parameter which has been obtained from fitting of the equation of state with experimental hydrogen absorption data shows both the usual and the opposite trend of temperature effect as well. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Today, the excessive consumption of fossil materials has been led to entering of toxic gases such as CO2 and CO to the environment. On the other hand, fossil fuels resources, i.e. gas, oil and their derivatives, have been declining over time. Hence, scientists and experts are looking for an alternative to these out of date fuels. Meanwhile, hydrogen as a future energy carrier has opened the door for CO2-free mobility and power generation. The interest in hydrogen has been started by introduction of hydrogen powered fuel cells and by the demand of efficient energy storage for renewable electricity [1,2]. Hydrogen is an excellent candidate to supersede current fuels because of its high energy density and zero emission of

greenhouse gases. It shows the superiority that its combination with atmospheric oxygen produces energy and water as the only by-product. Despite this, there are still some disadvantages that prevent the proceeding of the so-called “hydrogen economy”. The first is the unavailability of this gas in pure form in the earth's crust, then hydrogen must be produced in a usually unsustainable process. The second is the dangers related to its flammable nature and the requirements for its storage and transportation in a compressed way [3]. To meet the storage challenges, a host of associated performance and system necessities should be taken into account. Issues to be considered include operation pressure and temperature, the stability of the storage material, the degree of hydrogen purity imposed by the fuel cell, the reversibility of hydrogen uptake and so on [4]. Hydrogen can

* Corresponding author. E-mail address: [email protected] (F. Sabzi). https://doi.org/10.1016/j.ijhydene.2018.08.055 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Kordi A, Sabzi F, Thermodynamic modeling of hydrogen solubility in a series of ionic liquids, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.08.055

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e1 0

be stored as a compressed gas in high pressure tanks [5,6], as a liquid by absorbing physically and chemically within metal hydrides [7], carbon nanotubes [8] and metal organic frameworks [9] or by storing in an alternative chemical form. In fact the aforementioned requirements are in contradictory to each other and accordingly seems to be unattainable especially with compressed gas and liquid methods. Storing of hydrogen in chemical compounds offers a much wider range of possibilities to meet storage challenges. There is currently growing interest in gas storage by ionic liquids. Ionic liquids known as green solvent are a kind of salt that unlike high-temperature molten salts such as alkaline earth metal salts are liquid at room temperature. Their unique properties such as nonflammability, non-toxicity, high temperature stability and low vapor pressure makes them logical replacement for volatile organic solvents used in liquid membranes for separation processes [10]. Actually, as none of the present hydrogen purification technologies including pressure swing adsorption and cryogenic separation have reached level of industrial sophistication, an extensive amount of research have been carried out for development of supported liquid membranes whose pores are impregnated with ionic liquids (SILM). Then, reliable information on the solubility of hydrogen in ionic liquids is needed for the design and operation of separation processes [11]. The solubility of hydrogen has been investigated in a wide range of imidazolium-based ILs including 1butyl-3-methylimidazolium tetrafluoroborate [BMIM][BF4] [12], 1-butyl-3-methylimidazolium octylsulphate [BMIM] [C8SO4] and 1-ethyl-3-methylimidazoliumethylsulfate [EMIM] [EtSO4] [13], 1-butyl-3- methylimidazolium hexafluoro-phosphate [BMIM][PF6] [14e16], 1-butyl-3-methylimidazolium methyl sulfate [BMIM][MeSO4] [17], 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) amide [BMIM][Tf2N] [18], 1-butyl-1-methylpyrrolidinium bis(trifluoromethyl-sul[19], 1-ethyl-3methylfonyl)amide [BMPY][Tf2N] pyrrolidinium bis(trifluoromethylsulfonyl)amide [Emim] [Tf2N] [20], in 1-hexyl-3- methylpyrrolidinium bis(trifluoromethylsulfonyl)amide [HMIM][Tf2N] [21e23], 2-[2hydroxyethyl(methyl)amino] ethanol chloride [MDEA][Cl] [24] and in butyltrimethylammoniumbis(trifluoromethylsulfonyl) imide [N4,1,1,1][Tf2N] [25]. The prediction of hydrogen solubility in ILs is a fundamental step toward the development of simulation tools to implement in the process calculation prior to industrial applications such as fuel cells and so on. Since the ionic liquids are complex macromolecules and they have no or small vapor pressure and consequently no critical parameters, simple cubic equations of state cannot be used for their modeling. On the other hand, hydrogen is a light gas with small intermolecular forces which cause hydrogen behaves like a perfect gas. Moreover, hydrogen solubility in ionic liquids, in contrast to conventional gases, does not always decreases with temperature. It shows a decreasing trend in a range of temperature and an increasing trend in another range of temperature. Thus, the purpose of this study is to correlate the unusual solubility behavior of hydrogen and to predict the amount of hydrogen sorption in ionic liquids. In this respect, hydrogen gas sorption in ILs has been modeled using Perturbed Hard Sphere Chain (PHSC) equation of state (EoS) in continuity of our previous research done for hydrogen storage in a series of Zn-

based Metal Organic Frameworks (MOFs) [26]. For this purpose, three main parameters of this equation including the number of segments per molecule (r), which is selected based on the size of each molecule relative to methane molecule, the distance between two molecules at zero potential ðsÞ and the well-depth of potential between two non-bonded units ðεÞ have been obtained from laboratory Pressure-VolumeTemperature (PVT) data points using the Differential Evolution (DE) optimization algorithm. One binary interaction parameter along with its corresponding mixing rule has been introduced in the equation of state for the mixture, to show the mutual influence of hydrogen and ionic liquid on each other.

Theory The PHSC equation of state has been established based on the modified Chiew equation of state for hard-sphere chains as the reference term [27] which has been derived from PercusYevick integral-theory and modified by Carnahan-Starling radial distribution function. A van der Waals attractive term has been taken as perturbation part and the Song-Mason method [28] relates the parameters of the equation of state to the intermolecular potential. The general form of PHSC EoS is written as below: 



     P P P ¼ þ rkB T rkB T ref rkB T pert

(1)

       r2 ar P ¼ 1 þ r2 bg dþ  ðr  1Þ g dþ  1  rkB T kB T

(2)

where P is the pressure, T the absolute temperature, r ¼ N V the number density and kB the Boltzmann constant. d is the hard sphere diameter and g(dþ) is pair radial distribution function of hard spheres which are at constant with each other. The three segment-based parameters, a, band r which are interpreted physically, represent the strength of the attractive forced between two non-bonded segments, the van der Waals segment co-volume and the number of single hard spheres per chain molecule, respectively. a and b are functions of temperature and can be correlated in terms of suitable reducing constants as follows [29]: =

2



    2p 3 kB T s εFa 3 ε

(3)



    2p 3 kB T s Fb 3 ε

(4)

Fa

     kB T kB T ¼ 1:8681exp  0:0619 ε ε " 3 #  kB T 2 þ 0:06715exp  1:7317 ε

"   1 #  kB T kB T 2 ¼ 0:7303exp  0:1649 Fb ε ε " 3 #  kB T 2 þ 0:2697exp  2:3973 ε

(5)

(6)

Fa and Fb are the general functions of the reduced temperature as described for macromolecules [30]. The extended

Please cite this article in press as: Kordi A, Sabzi F, Thermodynamic modeling of hydrogen solubility in a series of ionic liquids, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.08.055

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PHSC equation of state for multi-component mixtures by applying one-fluid mixing rule leads to the following equation:

Xm i h Xm P þ þ ¼ 1 þ r ij xi xj ri rj bij gij dij  xi ðri  1Þ gii dij  1 i rkB T r Xm xi xj ri rj aij  kB T ij

  Qii ¼ Qij h; zij ¼

0

  1 Wii ¼ Wij h; zij ¼ rr

The parameters aij and bij are defined as the extension of Eqs. (3) and (4) to mixtures:

I1 ¼ lnð1  hÞ

    2p 3 kB T sij εij Fa aij ¼ 3 εij

In ¼ In1 þ

(8)

    2p 3 kB T sij Fb 3 εij

  sii þ sij 2 

εij ¼ εi εj

12 

1  kij

(11)

The PHSC EoS can better describe the physics of macromolecules such as ionic liquid systems when is written in terms of segment number:

(12)

where Pm

i¼1 Ni ri

rr ¼

4i ¼

Nr ¼

V Ni ri xi ri ¼ Pm Nr j xj rj Xm i¼1

Ni ri

(13)

(14)

(15)

In order to perform the equilibrium calculation with PHSC equation of state, the chemical potential should be written in terms of Helmholtz free energy from pressure-explicit equation of state. Then by differentiation of the Helmholtz free energy with respect to the number of molecules and some mathematical manipulations, the chemical potential of the mixture is obtained as follows [29,31]:   Xm Xm Nr vWij m0 ml ¼ l þ 2ri rr 4 b W þ r 4 4 b c ij ij ij r i¼1 i i¼1 i j kB T kB T vNl   Xm  1 Nr vQii 2rl rr Xm  ðri  1ÞQll  4 1 4 ail  i¼1 i i¼1 i ri vNi kB T   4 r kB T þ ln l r þ1 rl (16) where

0

2 I1 3 zij 1 zij þ I2 þ I3 2 2 h3 h 2h

(18)

(19)

1 hn1 1  n ð1  hÞ1n

(20)

For calculating the solubility of hydrogen gas in ionic liquids, the three pure-component molecular parameters of hydrogen and under-studied ionic liquids, i.e. r, s and ε need to be compiled. The objective function used for optimization of these parameters is OF ¼



Xm  Xm P 1 þ þ ¼ 1 þ rr ij 4i 4j bij gii dij  4i 1  gii dii i rr kB T ri r Xm 4 4 aij  r kB T ij i j

gij drr ¼

Results and discussion

(10) 

Zrr

(9)

The combining rule for s is defined as a consequence of simple arithmetic mean of the hard-sphere diameters without any interaction parameter, while one binary interaction parameters, kij , is introduced in the geometric mean for the energetic parameter: sij ¼

dr z2ij 3 zij 1 r gij  1 þ ¼ lnð1  hÞ þ 2 1  h 4 ð1  hÞ2 rr (17)

(7)

bij ¼

Zrr

exp 1 XNp ri  rcal i exp NP i¼1 ri

(21)

where subscripts cal and exp exhibit the calculated and experimental densities respectively, and NP is the number of data points. Table 1a shows the three characteristic parameters adopted from Bazargani and Sabzi work [32,33]. Table 1b represents the results of optimized parameters for H2 and remained ionic liquids along with their molecular weights and the references which have been used for taking experimental PVT data. In this study, H2 solubility in different ionic liquids has been predicted by PHSC EoS establishing the vapor-liquid equilibrium between the gas phase and ionic liquid þ gas phase. By calculating Eq. (16), the amount of H2 mole fraction that gives equal chemical potential in hydrogen and ionic liquid phases determines H2 solubility in the ionic liquids. By defining the objective function in Eq. (22), the binary interaction parameter, kij has been optimized by fitting the experimental data of absorption of H2 in ionic liquids and in each temperature and pressure according to the flowchart demonstrated in Fig. (1): OF ¼

exp 1 XNp xi  xcal i exp i¼1 NP xi

(22)

After determination of xcal which is the final amount of calculated solubility, the Average Absolute Error (AAE) and

Table 1a e Pure component parameters of PHSC EoS for ILs adopted from other references. Materials [BMIM][BF4] [BMIM][PF6] [BMIM][MeSO4] [BMIM][Tf2N] [HMIM][ Tf2N]

Mw

r

s(Aº)

ε (  1020)

Ref.

226.20 284.20 250.32 419.20 447.42

2.96 3.82 2.44 3.62 2.66

5.27 5.07 5.78 5.70 6.53

1.09 0.97 1.37 1.03 1.32

[33] [33] [33] [33] [32]

Please cite this article in press as: Kordi A, Sabzi F, Thermodynamic modeling of hydrogen solubility in a series of ionic liquids, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.08.055

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Table 1b e Pure component parameters of PHSC EoS for H2 and ILs optimized in this work. Materials H2 [BMIM][C8SO4] [EMIM][EtSO4] [BMPY][Tf2N] [EMIM][ Tf2N] [MDEA][Cl] [N4,1,1,1][Tf2N] [BMIM][C8SO4]

Mw

r

s(Aº)

ε(1020)

Ref.

2.02 348.50 236.29 442.41 391.34 155.62 396.38 2.02

0.46 2.40 3.38 0.92 3.33 4.18 2.83 0.46

4.57 6.85 4.85 3.80 6.29 5.99 5.75 4.57

0.08 1.54 0.79 1.09 1.32 1.74 0.39 0.08

[34] [13] [35] [19] [36] [37] [38] [34]

percentage of Average Absolute Deviation (%AAD) have been also calculated from the difference between calculated and experimental H2 solubility in each ionic liquid according to Eqs. (23) and (24): AAE ¼

1 XNp exp x  xcal i NP i¼1 i

%AAD ¼

(23)

exp 1 XNp xi  xcal i  100 NP i¼1 xexp i

(24)

[BMIM][BF4], [BMIM][C8SO4] and [EMIM][EtSO4] The solubility of hydrogen gas has been measured in 1-butyl3-methylimidazolium tetrafluoroborate [BMIM][BF4] by Jacquemin et al. [12], in 1-butyl-3-methylimidazolium octylsulphate [BMIM][C8SO4] and in another ionic liquid based on alkylsulfate anion, 1-ethyl-3-methylimidazoliumethylsulfate [EMIM][EtSO4] by Jacquemin et al. [13] at a temperature range of 283e343 K and at pressure close to atmospheric. Hydrogen is found to be less soluble in ionic liquid than other gaseous solutes. For example, the mole fraction of carbon dioxide in [BMIM][BF4] is in the order of 8  103 e 16  103 where the mole fraction of hydrogen in the same ionic liquid is in the order of 2  104 e 5  104. The solubility of other gases like ethane, methane, argon, oxygen, nitrogen and carbon monoxide are respectively between carbon dioxide and hydrogen solubility [12]. The modeling of hydrogen solubility in abovementioned ionic liquids have been shown in Fig. (2). Hydrogen solubility usually behaves with temperature in a similar manner for all other conventional gases, i.e. gas solubility decreases with increasing temperature due to the weak interaction of hydrogen gas with ionic liquid. But the variation with temperature of the solubility is inverse at the lower

Fig. 1 e A flowchart showing the method of kij optimization. Please cite this article in press as: Kordi A, Sabzi F, Thermodynamic modeling of hydrogen solubility in a series of ionic liquids, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.08.055

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Table 3 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [BMIM][C8SO4]. Ionic liquid

T(K)

[BMIM][C8SO4] 313.33 323.03 332.87 342.98

P(MPa)

kij

0.08 0.08 0.08 0.10

0.68 0.74 0.80 0.95

AAE (  108) %AAD Ref. 3.13 1.08 4.76 0.58

0.005 0.004 0.010 0.007

[13]

Table 4 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [EMIM][EtSO4]. Ionic liquid Fig. 2 e Prediction of H2 solubility in [BMIM][BF4], [BMIM] [C8SO4] and [EMIM][EtSO4] at different temperatures. Experimental data [12,13].

temperature end. For the sake of easy understanding, the phase behavior of hydrogen in ionic liquids can be explained using the P-T diagram at the critical point of the mixture, since it defines the upper limit of the vapor-liquid region. The extremely light and small size molecule such as hydrogen is highly different from heavy ionic liquid ion pairs. In contrast to ionic liquids with estimated critical temperatures in the range of 500e1500 K, hydrogen has a critical temperature of 33.2 K. This large difference in critical points would result in a temperature range with a negative-sloped bubble-point curve within the low concentrations that hydrogen dissolves in ionic liquids. Then, the temperature coefficient of solubility at constant pressure is positive for gases like hydrogen with so low critical temperature. It is clear that this phenomenon occurs in a certain range of temperatures, pressures and concentrations. Fig. (2) demonstrates that PHSC EoS can satisfactorily predict the inverse temperature effect observed in the systems of H2 þ [BMIM][BF4] and H2 þ [EMIM][EtSO4]. In Tables 2e4 have been reported binary interaction parameters, average absolute errors (AAE) and percentage of average absolute deviations (%AAD). The small amounts of AAE and % AAD show that the PHSC equation of state can predict the

Table 2 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [BMIM][BF4]. Ionic liquid [BMIM][BF4]

T(K)

P(MPa)

kij

278.20 283.29 285.25 288.30 290.37 293.36 298.34 303.41 313.25 323.24 333.17 343.11

0.07 0.07 0.07 0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.08 0.09

0.22 0.21 0.21 0.21 0.21 0.22 0.23 0.24 0.31 0.36 0.47 0.59

AAE (  108) %AAD Ref. 0.19 1.07 1.64 1.26 2.15 1.90 0.90 0.92 1.71 1.89 0.79 0.67

0.012 0.011 0.003 0.011 0.004 0.012 0.103 0.103 0.014 0.012 0.002 0.010

[12]

T(K)

[EMIM][EtSO4] 283.16 292.93 303.39 303.42 316.29 323.29 333.12 343.13 343.13

P(MPa)

kij

0.07 0.08 0.08 0.09 0.09 0.09 0.10 0.09 1.03

0.27 0.21 0.20 0.25 0.26 0.36 0.47 0.56 0.61

AAE (  108) %AAD Ref. 4.06 4.97 1.91 1.54 0.77 1.04 0.82 0.53 0.20

0.010 0.010 0.011 0.010 0.005 0.004 0.004 0.008 0.006

[13]

solubility with good precision. Referring to Eq. (11), it is worth to mention that when kij increases, the interaction between two components involved in the mixture is less than the interaction among components in pure state. In this instance, the binary interaction parameter in the system of H2 þ [BMIM] [C8SO4], Table 3, increases with temperature which depicts the lower solubility at higher temperatures. This parameter initially decreases and then increases in the system of H2 þ [BMIM][BF4], Table 2, and in H2 þ [EMIM][EtSO4], Table 4, showing the inverse trend at the lower temperature end.

[BMIM][PF6] The solubility of hydrogen gas in 1-butyl-3-methylimidazolium hexafluorophosphate [BMIM][PF6] has been obtained by Jacquemin et al. [14] in the temperature interval between 283 and 343 K in steps of approximately 10 K. Hydrogen shows a complex variation of solubility with a maximum near 313 K as exhibited in Fig. (3). Kumelan et al. [15] also measured the solubility of hydrogen gas in this ionic liquid at a temperature range of 313e373 K and at pressure up to 9 MPa. The solubility pressure linearly increases with increasing molality of hydrogen in ionic liquid phase. Hydrogen solubility indicates also an inverse temperature effect, showing increased solubility at higher temperature in contrast to other commonly investigated gas solubility. The experimental and calculated results by PHSC equation of state have been brought in Fig. (4). Barghi et al. [16] reported the measurement of the solubility of H2 in [BMIM][PF6] over the temperature range 298e328 K and for pressure up to 10 MPa. They have presented experimental evidence where the solubility of hydrogen has a decreasing trend with temperature as it is clear in Fig. (5). In comparison, Jacquemin et al. [14] presented an increasing-then-decreasing trend with temperature. It seems that the increase of solubility with temperature

Please cite this article in press as: Kordi A, Sabzi F, Thermodynamic modeling of hydrogen solubility in a series of ionic liquids, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.08.055

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Fig. 3 e Prediction of H2 solubility in [BMIM][PF6] at different temperatures. Experimental data [14].

is limited to certain spaces on the P-T-x-y diagram. The complete explanation of temperature dependency of hydrogen solubility has been discussed from a thermodynamic point of view in previous section and by Raeissi and Peters [18]. The binary interaction parameters obtained for H2 absorption in [BMIM][PF6] [14] along with AAE and %AAD have been presented in Table 5a. The variation of binary interaction parameter, kij, is consistent with temperature dependency of hydrogen solubility, i.e. it is descending when solubility increases and ascending when solubility decreases with temperature. The binary interaction parameters regressed from the experimental data in Refs. [15,16] have been brought in Table 5b. Again the inverse and regular temperature effect is clear in the kij variations.

Fig. 5 e Prediction of H2 solubility in [BMIM][PF6] at 313.05, 333.15, 353.10 and 373.15 K. Experimental data [16].

Table 5a e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [BMIM][PF6]. Ionic liquid [BMIM][PF6]

T(K)

P(MPa)

kij

283.40 293.40 303.39 308.17 313.28 318.16 323.17 333.19 343.12 343.14

0.07 0.07 0.08 0.08 0.08 0.08 0.08 0.09 0.09 0.09

0.46 0.32 0.24 0.26 0.23 0.23 0.26 0.34 0.45 0.44

AAE (  108) %AAD Ref. 0.13 1.86 1.43 0.47 1.69 1.64 1.58 0.67 0.12 0.37

0.008 0.013 0.002 0.009 0.012 0.004 0.010 0.008 0.006 0.001

[14]

[BMIM][MeSO4] The solubility of hydrogen gas in 1-butyl-3-methyllimidazolium methyl sulfate [BMIM][MeSO4] has been reported by Kumelan et al. [17] at temperature range of 293e413 K and pressure higher than 9.3 MPa. As it is evident in Fig. (6), the inverse temperature effect in hydrogen solubility has been again occurred. The binary interaction parameter obtained from the regression of the equation of state along with AAE and %AAD have been reported in Table 6. Small amounts of deviations show the noticeable capability of the PHSC equation of state to correlate the absorption of hydrogen in this ionic liquid. As hydrogen is a small gas molecule which has no strong interaction with ionic liquid, then the kij value is positive and its amount decreases with increasing solubility of hydrogen in [BMIM][MeSO4].

Fig. 4 e Prediction of H2 solubility in [BMIM][PF6] at 313.05, 333.15, 353.10 and 373.15 K. Experimental data [15].

Table 5b e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [BMIM][PF6]. Ionic liquid T(K) [BMIM][PF6]

[BMIM][PF6]

313.05 333.15 353.10 373.15 298.15 308.15 318.15 328.15

P(MPa) 1.69e9.08 1.23e9.01 1.45e9.10 1.08e9.02 0.00e10.81 0.00e9.70 0.00e10.30 0.00e10.49

kij AAE (  102) %AAD Ref. 0.70 0.67 0.64 0.59 0.36 0.41 0.44 0.47

0.01 0.04 0.01 0.01 0.11 0.05 0.03 0.05

1.51 6.66 1.68 1.02 7.80 1.67 4.35 4.21

[15]

[16]

Fig. 6 e Prediction of H2 solubility in [BMIM][MeSO4] at 293.30, 333.15, 373.10 and 413.15 K. Experimental data [17].

Please cite this article in press as: Kordi A, Sabzi F, Thermodynamic modeling of hydrogen solubility in a series of ionic liquids, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.08.055

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Table 6 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [BMIM][MeSO4]. Ionic liquid

T(K)

[BMIM][MeSO4] 293.30 333.15 373.10 413.15

P(MPa)

kij

1.457e8.617 1.125e8.393 1.348e8.873 1.179e8.919

0.50 0.44 0.36 0.28

AAE %AAD Ref. (  102) 0.01 0.02 0.02 0.03

2.53 3.74 3.70 2.65

[17]

[BMIM],[BMPY],[EMIM] and [HMIM][Tf2N] The solubility of hydrogen gas has been measured in 1-butyl3-methylimidazolium bis(trifluoromethylsulfonyl)amide [BMIM][Tf2N] by Raeissi and Peters [18]. Table 7 shows the estimated kij and two kinds of deviation, and the graphical presentation of P-x isotherms has been given in Fig. (7). The experimentally measured mole fraction of H2, indicative of the solubility of hydrogen in 1-butyl-3-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide [BMPY][Tf2N] [19] has been presented in Fig. (8). These two figures compare the calculated mole fraction of H2 with experimental absorption data points which associated with small amounts of deviations depicted in Table 8 confirms the high precision of PHSC equation of state in prediction of hydrogen solubility in ionic liquids. The pressure-composition curves of hydrogen solubility in the above-mentioned ionic liquids are nearly linear but as temperature is increased, the dissolution of hydrogen happens in lower pressures. This is indeed the opposite of temperaturedependency of vast majority of gas solubility in liquids. In fact, at normal temperatures light hydrogen gas behaves like a perfect gas, i.e. the repulsive intermolecular forces dominate attractive ones and consequently there needs higher pressure to force hydrogen to ionic liquid state. The solubility of hydrogen in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulphonyl)amide [EMIM][Tf2N] has been determined by Raeissi et al. [20]. The experimental data points have been brought in Fig. 9 to compare with calculated mole fraction of H2. The hydrogen solubility decreases with temperature in consistency of other conventional gases. The calculated results deviate extremely low from measured solubility data. The binary interaction parameter in Table 9 has also an increasing trend showing the weak interaction of hydrogen molecules with ionic liquid at higher temperatures. Costa Gomes [21], Kumelan et al. [22] and Raeissi et al. [23] have published the solvation of H2 in 1-hexyl-3-methy-

Fig. 7 e Prediction of H2 solubility in [BMIM][Tf2N] at 333.15, 353.15, 373.15, 393.15, 413.15, 433.15 and 453.15 K. Experimental data [18].

Fig. 8 e Prediction of H2 solubility in [BMPY][Tf2N] at 293.20, 333.10, 373.10, 393.15 and 413.20 K. Experimental data [19].

Table 8 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [BMPY][Tf2N]. Ionic liquid T(K)

P(MPa)

[BMPY][Tf2N] 293.20 333.10 373.10 413.20

1.472e8.945 1.443e8.408 1.384e8.325 1.365e8.272

kij AAE (  102) %AAD Ref. 0.91 0.76 0.58 0.37

0.04 0.04 0.04 0.03

2.24 2.61 2.07 1.52

[19]

Table 7 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [BMIM][Tf2N]. Ionic liquid T(K)

P(MPa)

[BMIM][Tf2N] 333.15 353.15 373.15 393.15 413.15 433.15 453.15

2.12e5.16 2.12e735 2.12e7.35 2.12e8.52 2.12e8.52 2.12e9.37 2.12e10.81

kij AAE (  102) %AAD Ref. 0.39 0.36 0.31 0.28 0.23 0.17 0.11

0.13 0.19 0.18 0.21 0.18 0.23 0.36

3.95 5.18 4.86 6.29 5.67 5.42 5.97

[18]

Fig. 9 e Prediction of H2 solubility in [EMIM][Tf2N] at 363.15e453.15 K. Experimental data [20].

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Table 9 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [EMIM][Tf2N]. Ionic liquid

T(K)

[EMIM][Tf2N] 282.98 293.10 303.38 304.35 313.19 323.18 325.15 333.03 343.05

P(MPa)

kij

0.08 0.08 0.08 0.08 0.08 0.04 0.08 0.08 0.09

0.14 0.15 0.16 0.17 0.18 0.30 0.34 0.39 0.45

AAE (  108) %AAD Ref. 2.69 2.10 0.78 2.79 2.53 6.01 6.40 1.26 1.55

0.013 0.012 0.007 0.013 0.004 0.010 0.010 0.010 0.004

[20]

limidazolium bis(trifluoromethylsulfonyl)amide [HMIM][Tf2N] in a wide pressure range and at various temperatures. The hydrogen solubility increases with increasing temperature in Refs. [22] and [23]. This is in contrast to the doubtful decreasing trend introduced by Costa Gomes [21], thus in this study, the results reported in Refs. [22] and [23] have been modeled by PHSC EoS. Figs. (10) and (11) respectively report the measured and calculated results confirming the good agreement of PHSC EoS with experiments. It is worth to mention that the PHSC predictions also capture the inverse temperature trend as well. The binary interaction parameters, AAE and %AAD have been described in Table 10. The binary interaction parameter decreases as solubility increases with temperature.

Table 10 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [HMIM][Tf2N]. Ionic liquid

T(K)

[HMIM][Tf2N] 293.20 333.20 373.15 413.20 [HMIM][Tf2N] 293.15 313.15 333.15 353.15

P(MPa) 1.47e9.81 2.26e9.30 1.59e9.07 1.62e9.50 6.35e12.30 5.76e11.13 5.26e10.15 4.85e9.33

kij AAE (  102) %AAD Ref. 0.39 0.29 0.19 0.10 0.39 0.35 0.29 0.24

0.09 0.11 0.12 0.14 0.14 0.13 0.12 0.11

2.25 2.92 3.14 3.09 3.26 3.04 2.95 2.83

[22]

[23]

Fig. 12 e Prediction of H2 solubility in [MDEA][Cl] at 313.15, 318.15, 323.15, 328.15 and 333.15 K. Experimental data [24].

[MDEA][Cl], and [N4,1,1,1][Tf2N]

Fig. 10 e Prediction of H2 solubility in [HMIM][Tf2N] at 293.20, 333.20, 373.20 and 413.20 K. Experimental data [22].

has been investigated by Zhao et al. [24] at temperature ranging from 313 to 333 K and in a wide range of pressure. In another study the solubility of hydrogen in butyltrimethylammoniumbis(trifluoromethylsulfonyl)imide [N4,1,1,1][Tf2N] has been given by Jacquemin et al. [25]. The hydrogen solubility in two above-mentioned ionic liquids have been predicted using PHSC equation of state and have been demonstrated along with adopted experimental data points in Figs. (12) and (13). Binary interaction parameter, AEE and %AAD which have been optimized using the experimental absorption data have been reported in Tables 11 and 12. As in the case of all conventional gases, the solubility decreases with increasing temperature. The decreasing trend show itself in growing amount of binary interaction parameter with temperature. The very low AAE and quantitative agreement with the experimental data confirms the precision and good performance of PHSC equation of state.

Fig. 11 e Prediction of H2 solubility in [HMIM][Tf2N] at 293.15, 313.15, 333.15 and 353.15 K. Experimental data [23].

Fig. 13 e Prediction of H2 solubility in [N4,1,1,1][Tf2N] at different temperatures. Experimental data [25].

The solubility of H2 in novel alcamine ionic liquid of 2-[2hydroxyethyl(methyl)amino] ethanol chloride [MDEA][Cl]

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Table 11 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [MDEA][Cl]. Ionic liquid T(K) [MDEA][Cl]

313.15 318.15 323.15 328.15 333.15

P(MPa) 1.32e5.44 1.34e5.77 1.59e5.85 1.64e5.88 1.65e5.87

Nomenclature

kij AAE (  102) %AAD Ref. 0.49 0.53 0.60 0.61 0.62

0.04 0.06 0.12 0.09 0.07

0.04 0.07 0.11 0.08 0.07

T(K)

P(MPa)

kij

0.07 0.08 0.08 0.08 0.08 0.09 0.09

0.14 0.15 0.17 0.23 0.29 0.34 0.43

[N4,1,1,1][Tf2N] 282.93 292.61 303.40 313.29 323.16 333.27 343.02

a AAD AAE b d Fa Fb g(dþ)

AAE (  108) %AAD Ref. 0.83 1.60 1.23 1.48 1.10 0.76 1.22

0.000 0.001 0.005 0.001 0.001 0.005 0.002

a

[24]

Table 12 e Binary interaction parameter, average absolute error and average absolute deviation of hydrogen sorption in [N4, 1, 1, 1][Tf2N]. Ionic liquid

9

[25]

Conclusion The PHSC equation of state has been employed to check its capability in capturing the solubility of hydrogen in different ionic liquids. The results of the comparison with the available experimental data show the high precision of the PHSC EoS in predicting the hydrogen gas absorption in ionic liquids. Only one interaction parameter, which is of course dependent on temperature, is sufficient to predict hydrogen solubility in ionic liquids somehow to be in excellent agreement with experimental data. However, hydrogen solubility interestingly does not always show the same behavior over the temperature range with various ionic liquids. In this manner, the hydrogen solubility decreases with increasing temperature in [BMIM][BF4], [BMIM][C8SO4], [EMIM][EtSO4], [MDEA][Cl], and [N4,1,1,1][Tf2N]. In the case of [BMIM][PF6], there is an increasing-then-decreasing trend with temperature which is limited to certain spaces on the P-T-x-y diagram. Inverse temperature effect is observed in [BMIM], [BMPY], [EMIM] and [HMIM][Tf2N] as well as [BMIM][MeSO4]. It seems extreme lightness and small intermolecular forces of hydrogen molecules cause the hydrogen gas showing the characteristic of a perfect gas. It is valuable to mention that the PHSC equation of state can predict this solubility trend well. The variation of binary interaction parameter is also consistent with temperature dependency of hydrogen solubility, i.e. it is ascending when solubility decreases and descending when solubility increases with temperature.

Acknowledgement The authors wish to thank the computer facilities provided by Shiraz University of Technology.

gij(dþ ii ) I kB kij m N Np OF P Q r T V W xi

equation of state parameter reflecting the attractive forces between two non-bonded segments (kPa cm6/ mol2) helmholtz free energy (J/K) average absolute deviation averaged absolute error van der Waals covolume per segment (cm3/mol) hard-sphere diameter (Aº) universal function used to calculate a(T) universal function used to calculate b(T) pair radial distribution function of hard spheres at contact ij-pair radial distribution function of hard spheres in mixtures integrating constant boltzmann's constant (J/mol K) ij-pair interaction parameter number of components number of molecules number of data points objective function pressure (Mpa) parameter in Eq. (16) number of segments per molecule temperature (K) volume of the system (cm3) parameter in Eq. (17) mole fraction

Subscripts and superscripts cal calculated exp experimental i, j, l type of component Greek symbols ε depth of the minimum in the pair potential (J/mol) x parameter in equation (16) and (17) h packing fraction (reduced density) r density (Kg/cm3) s separation distance between segment centers at the minimum of pair potential (Aº) 4 volume fraction m chemical potential

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