Thermodynamic modeling of solubility of hydrogen ...

Journal of Molecular Liquids 229 (2017) 591–598

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Thermodynamic modeling of solubility of hydrogen sulfide in ionic liquids using Peng Robinson-Two State equation of state Abolfazl Shojaeian Department of Chemical Engineering, Hamedan University of Technology, Hamedan, Iran

a r t i c l e

i n f o

Article history: Received 20 October 2016 Received in revised form 30 November 2016 Accepted 2 December 2016 Available online 8 December 2016 Keywords: Ionic liquids Peng Robinson-Two State equation of state (PRTS EoS) Solubility of H2S Association models

a b s t r a c t In this work, a simple association equations of state, namely Peng Robinson-Two state (PR-TS) association model is applied to model the PVT behavior of pure ionic liquids and solubility of H2S in 12 various imidazolium-based ionic liquids. This equation of state consists of two terms, the Peng-Robinson (PR) equation of state as cubic term for non-specific energy contribution and two-state association model (TSAM) for association energy contribution. First, to obtain the parameters of the PR-TS EoS for pure components, the experimental liquid density of different pure ionic liquids at various temperatures and pressures are correlated and the percent absolute average deviation between the calculated and experimental densities of ionic liquids is about 0.24%. For pure H2S two association schemes are considered as in the presence or not of association behavior. Then, the parameters of the model for these two schemes are correlated by simultaneously optimization of vapor pressure and liquid density data. Following successful application of the model for the pure components the PR-TS EoS is applied to predict the vapor-liquid equilibrium (VLE) of the several H2S + IL binary mixtures with this assumption that in binary mixtures present cross-association or self-association interaction. For binary systems in first approach only one interaction parameter is used and in second approach two binary interaction parameters are applied. The results of the VLE calculation of the H2S + IL systems show that the best accuracy with AAD = 3.40% is obtained when H2S is considered as non-association component and is used two binary interaction parameters for modeling the binary systems. In overall, the results of the present model for pure and binary systems comprise H2S and ILs are in very good agreement with experiments. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Hydrogen sulfide (H2S) as one of the acid gases, usually existing or can be produced in several industries such as natural gas processing, petroleum refining, syngas production, landfill management, pulp and paper industry and coal gasification. H2S is a toxic and corrosive component and must be removed from gas streams because of operational, economics and environmental problems. To remove undesirable gases such as H2S from gas stream mixtures, various industrial processes have been used such as physical/chemical sorption, membrane separation, molecular sieves and carbamation techniques. At present, the most preferred H2S removal processes are gas absorption processes using alkanolamine-based aqueous solvents as the amine-based process is used for sweetening over 95% of natural gas streams in the United States [1–6]. In overall, the alkanolamines present several disadvantages such as volatility, toxicity, degradation, transfer of water into the gas stream during desorption stage, and high energy consumption, which makes the process economically expensive [7]. To overcome these drawbacks, the attention of many researchers have been attracted toward to use of ionic liquids (ILs) as a new class

http://dx.doi.org/10.1016/j.molliq.2016.12.001 0167-7322/© 2016 Elsevier B.V. All rights reserved.

of solvents in the past two decades. Ionic liquids are organic salts that are in liquid form below 100 °C even at the room temperature (RTILs). The unique properties of ionic liquids like negligible vapor pressure, thermal and chemical stability, a wide liquid temperature range, nonflammable, tunable nature and good gas solubility are representing them as green solvents and interesting candidates for a variety of applications. The negligible vapor pressure of ILs present them desirable as an alternative to volatile organic compounds (VOCs) which introduce several health, environmental, and economic concerns in numerous industrial applications [8,9]. The knowledge about the thermodynamic properties data such as solubility of H2S into solvents has a key role in the designing, simulating and operating of many chemical processes for example natural gas refinery units [10,11]. Therefore, a few years ago several researchers focused on the equilibrium solubility of H2S in ILs especially on experimental measurements. As a first attempt to experiment in this area, Jou and Mather [12] determined H2 S solubility in 1butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) at five temperatures in the range of 298.15–403.15 K and pressures up to 9.6 MPa. Afterward, Pomelli et al. [13] Reported experimental data for solubility of H2S in [bmim]-based ILs with different anions

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A. Shojaeian / Journal of Molecular Liquids 229 (2017) 591–598

at 298 K and 1400 kPa. Heintz et al. [14] attempted to measure the solubility and transfer coefficient of CO2 and a mixture of N2/H2S in ammonium-based ILs from 300 to 500 K and pressures up to 3.0 MPa. Shiflett and Yokozeki [15] reported the phase equilibrium VLLE measurements of binary mixtures of H2 S and CO2 with [bmim][PF6] at temperatures from (273.6 to 342.2) K for H2S and at 283.1 K and 293.0 K for CO2 and ternary mixture of H2 S/CO 2 / [bmim][PF6] at 298.15 K and 333.15 K and pressures up to 6.5 MPa. Subsequently, Shiflett et al. [16] published the solubility of H2S in [bmim][MeSO 4] at 298–318 K and pressures up to 0.75 MPa and phase behavior of CO2/H2S/[bmim][MeSO4] ternary system. Jalili et al. as a research group at Research Institute of Petroleum Industry (RIPI), published a series experimental data of the solubility of H2S in various types of ionic liquids at temperatures from 303 K to 353 K and pressures up to 3.0 MPa. These publications dealt with the solubility of H2S in [bmim][PF6], [bmim][BF4], and [bmim][Tf2N] [17], the solubility of H2S in [hmim][PF6], [hmim][BF4], and [hmim][Tf2N] [18], the solubility of H2S and CO2 in [HOemim] with [PF6], [OTf] and [Tf2N] anions [19,20], the solubility and diffusion of H2S and CO2 in [HOemim][BF4] [21] and [emim][EtSO4] [19], the solubility of H2S in [emim][PF6] and [emim][Tf2N] [22], the solubility of single gases H2S and CO2 as well as their binary mixtures in [omim][Tf2N] [23] and [omim][PF6] [24] and finally, the solubility of CO2 and H2S gases in [emim][eFAP] [25] and most recently in [emim][OTf] [26]. An accurate estimation of the phase behavior of H2S + IL systems over a wide range of operational conditions is crucial if ionic liquids are to be used as solvent. On the other hand, experimental works are time-consuming, expensive and in some cases dangerous. Therefore, some researchers attempted to model the solubility of hydrogen sulfide in ionic liquids using different methods such as conductor-like screening model for real solvents (COSMO-RS) [27], machine learning approach [28–33] and equation of state [15,16, 34–37]. As examples for COSMO-RS method and machine learning approach, recently, a comprehensive review of the solubility of gases such as H 2 S in ionic liquids has been made by Lei et al. [27] in terms of experimental and modeling. In that work, the authors applied the COSMO-RS to model the various gas solubilities in ILs. Faúndez et al. [30] applied an artificial neural network (ANN) model to train the network and to predict the solubility of hydrogen sulfide in twelve binary H2S + IL mixtures. Also, Zhao et al. [33] proposed a new model using an extreme learning machine (ELM) intelligence algorithm and the number of fragments for solubility of H2S in ionic liquid. Equation of state (EoS) is a powerful tool in accurate representation of thermodynamic properties of pure fluids in a wide range of temperature and pressure. It can also be applied for calculation of thermodynamic properties of the mixtures using proper mixing rule. In the past few years, some researchers are modeling these types of systems using various equations of state. In the following as equation of state approach, Shiflett et al. [15,16] studied the vapor–liquid–liquid equilibrium phase behavior of H2S + IL binary mixtures using a generic Redlich–Kwong equation of state. Carvalho and Coutinho [34] used the Flory-Huggins model coupled with PengRobinson EoS to evaluate the nonideality of NH 3 , SO 2 and H2 S + imidazolium and pyridinium ionic liquid solutions. Faúndez et al. [35] used modified Peng-Robinson equation of state for correlating the solubility data and a flexible thermodynamic consistency method is applied to analyze 80 isothermal P-x data for H2S + IL binary mixtures. Lelovell et al. [36] presented a study of the solubility of NH3, SO 2 and H2 S in a number of imidazolium-based ionic liquids using the soft-SAFT equation of state with relatively simple models. Also, Rahmati-Rostami et al. [37] model the solubility of hydrogen sulfide in 6 imidazolium ionic liquids using the SAFT-VR and PCSAFT EoSs. They studied the influence of the polar contribution and the effect of self and cross-associating interactions on the calculation of those mixtures when applied both equations.

Recently, in a previous work [3] we developed the Peng-Robinsontwo-state equation of state (PR-TS EoS) based on cubic-two-state (CTS) concept [38] and used to describe the phase behavior of carbon dioxide in pure 1-butyl-3-methylimidazolium acetate ([bmim][acetate]) and mixtures with methyl diethanolamine (MDEA). As following, in the present work, the PR-TS EoS is extended and applied for representation of the solubility of H2S in various ionic liquids for the first time. To achieve this purpose, firstly, the PVT behavior of pure H2S and various pure ionic liquids are correlated and parameters of PR-TS EOS for these components are optimized. In this work, the ionic liquid is considered as neutral molecules, due to strong electrostatic interactions [39,40], with possess associating interactions [41]. Then, by using the mixing and combining rules the phase behavior of H2S + IL systems are explored. 2. Thermodynamic modeling The cubic-two-state equation of state (CTS EoS) based on cubic plus association (CPA) EoS [42], consists of two major contributions. A cubic equation of state as the non-specific (physical) contribution and the other contribution due to association as following A ¼ Ans þ Aas

ð1Þ

where, A is the Helmholtz energy and the subscripts ns and as refer to non-specific and association contributions, respectively. In this work, the Peng-Robinson (PR) equation of state [43] is used as the physical term, while the two-state association model (TSAM) is applied to describe the association contribution. Therefore, the pressure expression of the CTS EoS, namely Peng-Robinson-Two-State (PR-TS) equation of state has the following form X x j υij f ij ðT Þ X RT aðX; T Þ j 3 P ðX; v; T Þ ¼ xi 2 − −RT v−bðX Þ v½v þ bðX Þ þ bðX Þ½v−bðX Þ X i 4 x j υij f ij ðT Þ5 v vþ j

ð2Þ f ij ðT Þ ¼ e−Eij =RT −1

ð3Þ

where a and bdenote the characteristic parameters, P, v, T and R are the pressure, molar volume, temperature and gas constant, respectively. Also, Eij and υij are the association energy and association characteristic volume between species i and j, respectively. For pure compounds, b is the temperature independent parameter and temperature following of the a(T) is expressed by h pffiffiffiffiffiffiffiffiffiffii2 aðT Þ ¼ a0 1 þ c1 1− T=T c

ð4Þ

Table 1 Properties for all substances involved in this study.

[bmim][PF6] [bmim][BF4] [bmim][Tf2N] [omim][Tf2N] [hmim][Tf2N] [hmim][PF6] [hmim][BF4] [emim][EtSO4] [HOemim][PF6] [HOemim]Tf2N] [hemim][BF4] [emim][OTF] H2S

TC, K

PC, MPa

ω

Mw, g·mol−1

719.4 632.3 1265 1311.9 1287.3 764.9 679.1 1067.5 766.9 1297.5 691.9 992.3 373.1

1.73 2.04 2.76 2.1 2.39 1.55 1.79 4.046 2.02 3.307 2.467 3.584 9.0

0.7917 0.8489 0.2656 0.4453 0.3539 0.8697 0.9258 0.3744 1.0367 0.5172 1.1643 0.3255 0.1

284.2 226.02 419.3 475.4 447.3 312.2 254.08 236.29 272.1 407.3 214 260.2 34.081


593

Table 2 The parameters of the PR-TS EoS for pure ILs and Absolute Average Deviation (AAD%1) of liquid density. ILs

T, K

P, MPa

a0, Pa·m6·mol−2

b × 106, m3·mol−1

c1

−E11/R, K

υ11 × 106, m3·mol−1

AAD%a

N

Ref.

[bmim][Tf2N] [hmim][Tf2N] [omim][Tf2N] [bmim][BF4] [hmim][BF4] [bmim][PF6] [hmim][PF6] [emim][EtSO4] [HOemim][PF6] [HOemim]Tf2N] [hemim][BF4] [emim][OTF] Total

298.15–328.2 298.15–333.15 293.15–393.15 293.15–393.15 288.15–323.15 298.15–398.15 293.15–393.15 283.15–353.15 303.15–353.15 303.15–353.15 293.15–338-15 293.15–393.15

0.1–59.1 0.1–59.59 0.1–30 0.1–10 0.1 0.7–40 0.1–10 0.1–35 0.1 0.1 0.1 0.1–35

0.0424 0.0729 0.1025 6.402 6.791 1.906 4.498 0.0120 3.047 0.0380 3.869 5.804

272.2 305.1 337.0 174.3 201.1 196.8 225.6 179.3 162.5 236.8 143.6 172.8

39.10 31.44 27.03 1.187 0.8500 5.819 2.537 72.464 2.568 37.368 1.271 0.5707

2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600

0.564 0.682 0.692 0.019 0.022 0.021 0.030 0.0182 0.0806 0.3626 3.995 0.194

0.24 0.32 0.47 0.18 0.01 0.29 0.23 0.10 0.04 0.04 0.02 0.47 0.24

168 163 96 77 36 45 77 261 11 11 10 91 1046

[45] [45] [48] [47] [50] [52] [47] [49] [20] [20] [51] [46]

a

N

exp exp AAD% ¼ ð100=NÞ∑ jðρcal i −ρi Þ=ρi j. i¼1

where Tc is the critical temperature. The parameters a and b for a mixture are calculated by one-fluid van der Waals mixing and combining rules as aðX; T Þ ¼

XX i

aij ðT Þ ¼ bðX Þ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ai ðT Þa j ðT Þ 1−kij

XX i

bij ¼

xi x j aij ðT Þ

ð5Þ

j

xi x j bij

ð6Þ ð7Þ

j

bi þ b j 1−lij 2

In overall, thea0, b, c1, Eii and υiiare adjustable parameters of the present model for pure compounds. For non-associating compounds, Eii =υii = 0 and the model reduces to the cubic Peng-Robinson equation of state. The CTS model uses a simple association term that once coupled with a cubic equation of state, which can form a volume polynomial equation. Also, this volume polynomial shows a characteristic similar to the cubic equation of states that have one or three root(s). The Reynoso-Lopez et al. [44] showed that the CTS EoS always has one or three root(s) greater than co-volume parameter. Therefore, this association model is very simpler than CPA and SAFT type models.

ð8Þ 3. Results and discussion

where, kij and lij in Eqs. (6) and (8) are the binary interaction parameters so that kij = kji and lij = lji. The association energy (Eij) and association characteristic volume (υij) for the cross association mixtures are calculated using the following combining rules Eij ¼

Eii þ Ejj 2

ð9Þ

υij ¼

pffiffiffiffiffiffiffiffiffiffi υii υjj

ð10Þ

Fig. 1. Liquid density vs. temperature diagram at 0.1 MPa. Symbols show the experimental data; (■)[bmim][Tf2N], (×)[hmim][Tf2N], (◇)[omim][Tf2N], (♦)[bmim][BF4], (Δ) [hmim][BF4]. Solid lines are the PR-TS EoS correlations.

3.1. Pure components The properties of pure fluids are important when using the equation of state models for prediction of phase behavior of pure and mixture systems. Therefore, in Table 1 the critical temperature, critical pressure, acentric factor and molecular weight of pure H2S and ILs which are used in this work are given. Using the data in Table 1 and experimental liquid density of pure ILs [20,45–52] the parameters of the PR-TS EoS (a0, b, c1, Eii and υii) for pure components are correlated at a wide range of temperatures and

Fig. 2. Density vs. Pressure diagram for the [emim][EtSO4] ionic liquid. Symbols show the experimental data; (♦) 283.15 K, (▲) 293.15 K, (●) 303.15 K, (■) 313.15 K, (*) 323.15 K, (×) 333.15 K, (◇) 343.15 K, (Δ) 353.15 K. Solid lines are the PR-TS EoS correlations.

594


Table 3 Pure parameters of PR-TS EoS for H2S and Absolute Average Deviation (AAD%) of saturated vapor pressure (P), liquid density (ρl) and vapor density(ρv).

H2S H2S a b

Scheme

a0, Pa·m6.mol−2

b × 106, m3·mol−1

c1

υ11 × 106, m3·mol−1

E11/R, K

AAD% P

AAD% ρl

AAD% ρvb

Ref.

Assoc.a non assoc.a

0.3898 0.5037

27.16 27.88

0.1853 0.5285

1.755 0

1096.4 0

0.399 0.066

1.72 3.37

1.20 1.64

[57] [57]

Assoc. denote association. Predicted vapor density.

and vapor pressure data of the phase equilibrium diagram by using the following objective function:

pressures as following objective function

OF ¼

exp N ρcal 100 i −ρi ∑ exp N ρi i¼1

!2 ð11Þ

Table 2 presents the PR-TS model parameters and percent of absolute average deviation (AAD%) between experiment and calculated liquid densities for different pure family of ionic liquids. Also, in this work, for reduction of the adjustable parameters of pure ionic liquids, the association energy parameter for pure ionic liquids is fixed to 2600 K and therefore four parameters are adjusted for PR-TS model. This value is obtained from the correlated results using the five-parameter PR-TS EoS that show the association energy parameter is very close to 2600 K, which is consistent with the typical value of association energy parameter reported in the literature [3,38]. The PR-TS EoS results for temperature density fitting are shown in Fig. 1 for [Cnmim] [Tf2N] and [Cnmim] [BF4] ionic liquids family at 0.1 MPa. The influence of the pressure on the behavior of density is represented in Fig. 2 for [emim] [EtSO4] ionic liquid from 0.1 MPa up to 35 MPa at different temperatures from 283.15 up to 353.15 K. As it can be seen from Figs. 1–2, the results of the PR-TS model are in good agreement with experimental data. For association behavior of hydrogen sulfide, Cabaleiro-Lago concluded from ab-initio calculations that in H2S clusters there is a low tendency for self-association [53]. Also Pecul estimated the H 2 S-H 2 S hydrogen binding energy to be between − 3766 and − 6276 J·mol− 1 , that is very lower than a typical hydrogen bond value of − 25.000 J·mol − 1 [54]. Therefore, some contributions with equations of state have been published using non-association and association with various types of the association site for H 2 S [55,56]. Hence, in this work we have chosen two schemes for H2S, association and non-association schemes. All the parameters for H 2 S are fitted by simultaneous optimization of the liquid density

OF ¼

# " exp exp N cal N cal X 100 P i −P i Xρi −ρi þ P exp ρexp N i i i¼1 i¼1

ð12Þ

where N is the number of data points and superscript of “cal” and “exp” denote the calculated and experiment. In the following, by using the obtained parameters the vapor density of H2S are predicted. The adjustable parameters with the percentage Absolute Average Deviation (AAD%) between experimental and PR-TS calculated results for H2S with two different schemes are given in Table 3. According to the Table 3, the PR-TS with 5 adjustable parameters (association scheme) demonstrates the better results for liquid and vapor density and shows the poorer results for vapor pressure respect to PR-TS with 3 adjustable parameters (non-association scheme). In overall, for pure H 2S correlation the PR-TS with 5 parameters shows the better results. 3.2. Binary mixtures As mentioned in pervious section, due to the weak association behavior of H2S, this molecule can be considered as association or non-association component. Considering the non-association behavior for H2S leads to the using of the simple non-association EoSs respect to the association behavior with using the complex association EoSs for modeling the phase behavior of systems consist of H2S. Also, the PR-TS EoS with five adjustable parameters reduces to simpler cubic PR EoS with three adjustable parameters. So, if results of the consideration of the H2S as non- association component is acceptable therefore it is an advantage that can be used the simple models with the low adjustable parameters. Moreover, the phase behavior of binary systems can be presented by using the correlation of one or more binary interaction parameters that the lower binary adjustable parameters show the predictability of the model. Therefore, According to the above criteria and using

Table 4 The binary interaction parameters and Absolute Average Deviation (AAD%1) for solubility of H2S in various ILs. H2S with association scheme

H2S with non-association scheme

System

Fit. I AAD%

Fit. II AAD%

Fit. III AAD%

H2S+[bmim][PF6] H2S+[bmim][BF4] H2S+[bmim][Tf2N] H2S+[omim][Tf2N] H2S+[hmim][Tf2N] H2S+[hmim][PF6] H2S+[hmim][BF4] H2S+[emim][EtSO4] H2S+[HOemim][PF6] H2S+[HOemim]Tf2N] H2S+[hemim][BF4] H2S+[emim][OTF] Total

9.12 5.13 3.95 11.59 7.45 3.44 5.59 9.89 6.29 8.18 4.80 10.27 7.78

6.56 3.55 3.91 9.49 3.49 3.40 4.65 2.96 3.35 5.24 2.22 1.85 5.11

8.17 4.58 2.40 9.40 6.25 3.57 4.76 11.12 5.01 6.51 3.37 10.15 5.47

a

N

exp exp AAD% ¼ ð100=NÞ∑ jðP cal i −P i Þ=P i j. i¼1

kij

Fit. IV lij

0.0259 0.0213 −0.0968 −0.1080 −0.0612 −0.0324 −0.0457 0.5216 −0.3650 0.0259 0.1061 0.0244

0.0189 0.0261 0.0038 0.0295 0.0229 −0.0097 0.0213 0.1387 −0.0088 0.0305 0.0203 0.0489

AAD%a

N

Ref.

6.41 3.18 2.30 7.27 1.39 3.41 4.04 5.71 1.97 3.18 3.05 4.36 3.40

81 42 44 47 57 34 33 36 47 41 51 36 636

[12,17] [17] [17] [23] [23] [58] [58] [19] [20] [20] [21] [26]


595

Fig. 3. Ratio of calculated pressure to the experimental pressure at different temperatures in the H2S + IL binary systems. (a) based on Fit. I; (b) based on Fit. II; (c) based on Fit. III; (d) based on Fit. IV.

the pure parameters that are obtained in the previous section, solubility of H2S in various ionic liquids at different temperatures and pressures is investigated by four different approaches. In first approach, namely “Fit. I” H2S is considered as an association specie and only one binary interaction parameter (kij) is used and in second approach (Fit. II), similarly H2S is assumed as an association component however two binary interaction parameters (kij , lij) are fitted. In thirst and fourth approaches (Fit. III and Fit. IV) H2S is applied as non-association specie, but in Fit. III one binary interaction parameter is used and at Fit. IV two binary interaction parameters are correlated to describe the VLE behavior of binary mixtures. It should note be that, ILs are generally considered as association and nonvolatile components due to very low volatility in order to perform VLE calculations for binary systems. The binary interaction parameters are determined by minimizing the following objective function in various approaches

OF ¼

exp N cal 100 X P i −P i N i¼1 P exp i

ð13Þ

where N is the number of data points for each binary mixture. The binary interaction parameters that are independent of temperature with the deviation between experimental pressure data and results of the present model as AAD% for various H2S + IL binary systems for four different approaches are listed in Table 4. The results show that the AAD% of PR-TS model with two binary interaction parameters are smaller than the AAD% by one binary interaction parameter. However, considering the H2S as non-association specie shows the better results compared to considering the association

scheme for H2S. It means that the PR-TS with 3 adjustable parameters for H2S shows the better results respect to the PR-TS with 5 adjustable parameters, so that even the addition of one more adjustable binary interaction parameter in Fit. 2 respect to Fit. 3 has not created significant changes in the results. In overall, we can conclude from the results of the different approaches that for PR-TS model the Fit IV that considered non-association behavior for H2S component and used two binary interaction parameters based on Eqs. (6) and (8) shows the best results for VLE description of H2S + IL binary systems. For comparison, Fig. 3 shows the pressure deviation, Pcal/Pexp, obtained by different four fitting approaches for the all binary systems that are studied in this work at temperature range from 298.15 K to 403.15 K. As one can see, the Fig. 3-d (Fit. IV results) shows the lower deviation between other figures. In overall, Fig. 3 shows that the deviation of the pressure at high temperatures is more than that at low temperatures. Also, an under-correlation (Pcal/Pexp b 1) is observed at high temperatures. This phenomenon may be due to using of the temperature independent binary interaction parameters for representation of the phase behavior of the binary systems or due to this fact that the vapor pressure of the ionic liquids increase and it becomes significant at high temperatures. A similar scheme is plotted in Fig. 4 that shows the deviation based on the ratio of calculated pressure to the experimental pressure versus the H2S mole fraction in liquid phase for all binary systems and four fitting methods. It can be seen that for four methods at high concentration of H2S in liquid phase the most of the points are below the horizontal line which means the results of the model are under-correlated. Also, Figs. 3-d and 4-d show the better deviation from the other subfigures, which means that fit IV shows the best results. Figs. 5 and 6 present the results of the pressure versus mole fraction of H2S in liquid phase for the H2S+[bmim][Tf2N] and H2S+[hmim][Tf2N]

596


Fig. 4. Ratio of calculated pressure to the experimental pressure at different mole fraction of H2S in the H2S + IL binary systems. (a) based on Fit. I; (b) based on Fit. II; (c) based on Fit. III; (d) based on Fit. IV.

binary systems at different temperatures, respectively. Similarly, Figs. 7 and 8 demonstrate the phase behavior of H2S+[bmim][BF4] and H2S+ [HOemim][PF6] binary systems at different temperatures and pressures. The calculated pressures of PR-TS model in Figs. 5–8 are based on the Fit. IV and show a good accuracy of the calculated results with the experiments for these systems at different temperatures with independent temperature binary interaction parameters. Also, it must be mentioned

that as shown in Figs. 5-8 the results of the model for some isotherm not show an adequate trend.

Fig. 5. Comparison between experimental solubility data [17] and calculated PR-TS model (based on Fit. IV) for H2S+[bmim][Tf2N] system. Symbols show the experimental data; (●) 303.15 K (■) 313.15 K, (♦) 323.15 K, (▲) 333.15 K, (*) 343.15 K and solid lines represent correlated results (PR-TS based on Fit IV).

Fig. 6. Comparison between experimental solubility data [23] and calculated PR-TS model (based on Fit. IV) for H2S+[hmim][Tf2N] system. Symbols show the experimental data; (●) 303.15 K (■) 313.15 K, (♦) 323.15 K, (▲) 333.15 K, (*) 343.15 K, (□) 353.15 K and solid lines represent correlated results (PR-TS based on Fit IV).

4. Conclusion Peng Robinson-Two State equation of state (PR-TS EoS) based on CPA concept is applied for modeling the vapor–liquid equilibrium of


597

binary interaction parameters is used (Fit. III) and finally H2S is non-association specie and two binary interaction parameters are applied (Fit. IV). The results of the present model for these four fitting methods show that the considering H2S as an non-association specie show better results than assuming the association scheme for H2S. Also the results of the fitting two binary interaction parameters show higher accuracy than one interaction parameter. In overall, the results of the present model for pure and binary systems are in very good agreement with experiments and the Fit. IV shows the best results with AAD% = 3.40 for H2S + IL binary systems. List of symbols

Fig. 7. Comparison between experimental solubility data [17] and calculated PR-TS model (based on Fit. IV) for H2S+[bmim][BF4] system. Symbols show the experimental data; (●) 303.15 K (■) 313.15 K, (♦) 323.15 K, (▲) 333.15 K, (*) 343.15 K and solid lines represent correlated results (PR-TS based on Fit IV).

the pure and binary ionic liquid systems. Ionic liquids in this work are considered as neutral molecules, due to strong electrostatic interaction with associating interactions. In beginning, the model is used to correlate the liquid density of 12 pure ionic liquids with N1000 data points in the wide range of temperatures and pressures. The correlation of the pure ionic liquids densities with total AAD% = 0.24 show that the results of the present model are in good agreement with experimental data. Due to the weak association behavior of H2S, it is considered as two different behaviors: association and non- association specie. The parameters of PR-TS model for pure H2S are correlated on saturated vapor pressure and liquid density and obtained pure parameters is used to predict the vapor density without any additional adjustable parameters. Following successful application of the model for the pure components, using one or two temperature independent binary interaction parameter(s), the PR-TS EoS is applied to predict the vapor-liquid equilibrium of the several binary H2S + IL mixtures. In other hands, four fitting methods are used for modeling the phase behavior of binary systems as; H2S is association specie and one binary interaction parameter is used (Fit. I), H2S is association specie and two binary interaction parameters are correlated (Fit. II), H2S is non-association specie and one

Fig. 8. Comparison between experimental solubility data [20] and calculated PR-TS model (based on Fit. IV) for H2S+[HOemim][PF6] system. Symbols show the experimental data; (●) 303.15 K (■) 313.15 K, (♦) 323.15 K, (▲) 333.15 K, (*) 343.15 K, (□) 353.15 K and solid lines represent correlated results (PR-TS based on Fit IV).

a a0 b c Eij fij kij N OF P R v υij T X xi

attraction parameter (Pa·m6·mol−2) parameter in the physical energy term a van der Waals co-volume parameter (m3·mol−1) parameter in the physical energy term a association energy between sites i and j Meyer function independent temperature binary interaction parameter number of data points objective function for parameter adjusting pressure gas constant molar volume association characteristic volume of the pair interaction i-j temperature vector of mole fractions mole fraction of the substance i

Greek letters ρ

mass density (kg·m−3)

Subscripts and superscripts exp cal c i, j v l

experimental calculated critical dummy index vapor liquid

Abbreviations AAD absolute average deviation CPA cubic plus association CTS cubic two-state EoS equation of state ILs ionic liquids VLE vapor-liquid equilibria VLLE vapor-liquid-liquid equilibria SRK Soave-Redlich-Kwong equation of state PR Peng-Robinson equation of state TSAM two-state association model PR-TS Peng Robinson-Two State equation of state [cnmim] 1-cn-3-methylimidazolium [HOemim] 1-(2-hydroxyethyl)-3- methylimidazolium [hemim] [emim] 1-ethyl-3-methylimidazolium [bmim] 1-butyl-3-methylimidazolium [hmim] 1-hexyl-3-methylimidazolium [omim] 1-octyl-3-methylimidazolium [Tf2N] bis(trifluoromethylsulfonyl)imide [BF4] tetrafluoroborate [PF6] hexafluorophosphate

598


[EtSO4] ethylsulfate [MeSO4] methylsulfate [OTf] trifluoromethanesulfonate

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