Modified UNIFAC-Lei Model for Ionic LiquidâCH4 Systems - Industrial

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Thermodynamics, Transport, and Fluid Mechanics

Modified UNIFAC-Lei Model for Ionic Liquid-CH4 Systems Gangqiang Yu, Chengna Dai, and Zhigang Lei Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00986 • Publication Date (Web): 24 Apr 2018 Downloaded from http://pubs.acs.org on April 25, 2018

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Industrial & Engineering Chemistry Research

Modified UNIFAC-Lei Model for Ionic Liquid-CH4 Systems

Gangqiang Yu, Chengna Dai, and Zhigang Lei* State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Box 266, Beijing, 100029, China

ABSTRACT: The modified UNIFAC-Lei model (Mod. UNIFAC-Lei) is proposed for the first time for ionic liquid (IL) - methane (CH4) systems over a wide temperature and pressure range. The group binary interaction parameters were obtained by correlating the experimental solubility data of CH4 both from the literature and measured in this work. The CH4 solubility in common pure ILs and mixed ILs at temperatures down to 243.15 K was measured to determine unknown solubility data at low temperatures. The Mod. UNIFAC-Lei model can be used to predict CH4 solubility in both pure and mixed ILs at either high or low temperatures. Moreover, it is interesting to find that cations and anions in complementary IL pairs ([C1][A1] + [C2][A2] or [C2][A1] + [C1][A2]) with equimolar amounts can be freely exchanged. A low temperature is favorable for increasing both the solubility of CH4 and the selectivity of CH4 to CO2 in ILs.

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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INTRODUCTION In recent years, the consumption of natural gas as a fuel has become economically

attractive. Natural gas primarily consists of CO2 and CH4, whereas the presence of CO2 can reduce the energy content and combustion efficiency of methane and even increase the corrosion of pipelines in case of the presence of water.1 There is also a high level of CO2 in synthetic natural gas (SNG).2 Therefore, a systematic investigation of CO2 removal from either natural gas or SNG is needed as a significant task to obtain methane with high purity. Several approaches have been developed to achieve successful CO2/CH4 separation, e.g., membrane purification, solvent absorption, and adsorption on porous materials.3 For adsorption, there are three major types of solid adsorbents as follows: zeolites,4 activated carbons,5,6 and metal–organic frameworks (MOFs).7,8 Zeolites exhibit high selectivity in separation processes but are rapidly saturated in the case of water vapor in feed gas, leading to the decreased CO2 adsorption capacity.9 In addition, a high temperature is required for a zeolite regeneration process, which requires a high energy consumption with high quality. Recently, MOFs have achieved satisfactory CO2 removal capacities at low concentrations, but the presence of humidity is a severe limitation because the availability and adsorption of H2O can weaken CO2 absorption.10,11 However, compared to zeolites or MOFs, activated carbons show low adsorptive selectivity for CO2/CH4.12 Several effective, economical and traditional chemical absorbents (e.g., monoethanolamine (MEA), diethanolamine (DEA), and N-methyldiethanolamine (MDEA)13-15) have been widely used for over 60 years in chemical industries for CO2 absorption.16 However, the major disadvantages are as follows: 1) organic liquid absorbents exhibit high corrosivity for pipelines and equipment, requiring special

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construction materials, especially for the regeneration of absorbents at high temperature (at least 100 °C);16 and 2) the high temperature required for solvent regeneration leads to very high energy consumption.17,18 The Rectisol process with methanol as an effective physical absorbent operating at low temperature has also been extensively used to capture CO2 due to the relatively simple regeneration of absorption process. However, high solvent loss occurs due to the high volatility of methanol.19 Thus, the development of a more suitable alternative absorbent to replace conventional organic solvents is urgent for CO2 separation from natural gas. In the last two decades, ionic liquids (ILs) as a relatively new type of solvents have received increasing concern and attention,20-22 and have been widely applied in chemical reactions,23,24 new material preparations,25,26 biomass dissolution,27,28 and gas separation due to their unique properties, such as low melting points, ultralow vapor pressure, wide liquid temperature range, high stability, and tunable structures.29-34 In addition, physical and chemical properties can be freely fine-tuned by choosing an appropriate combination of cation and anion. To date, much literature has reported the work on CO2 capture and separation using ILs.35-39 In this work, ILs were used to separate CO2 and CH4. A number of solubility data for CO2 in ILs, even at low temperatures down to 228 K, have been published. At 243.2 K, the solubility of CO2 can reach a 0.7 mole fraction even at low pressure (14 bar).40 However, solubility data for CH4 in common ILs are very limited, involving approximately 350 data points in total for CH4-IL systems to date.41-48 Furthermore, no solubility data for CH4 in ILs at low temperatures (below 273.2 K) have been published. Therefore, in this work, the solubility of CH4 in several common ILs at temperatures from

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243.15 to 353.15 K and pressures up to 80 bar was measured to fill the gap in solubility data at low temperatures. However, it is extremely difficult and time-consuming to obtain CH4 solubility with sufficient precision in all ILs through experiments. Thus, to achieve a thorough understanding of the separation of CO2 from CH4 using ILs, the predictive thermodynamic models related to IL-CH4 systems over a wide temperature and pressure range are necessary. Currently, predictive thermodynamic models are mainly divided into two types: (1) equations of state (EOS) models including cubic EOS (e.g., Peng-Robinson (PR)49 and (Redlich-Kwong) RK50 EOSs ), GCNLF EOS (group contribution nonrandom lattice-fluid equation of state), 51 GC EOS (group contribution equation of state),52 and SAFT-based EOS (statistical associating fluid theory-based equation of state) like PC-PSAFT (perturbed chain statistical associating fluid theory) EOS;53 and (2) activity coefficient models including UNIFAC (universal quasichemical functional-group activity coefficients)-based models, COSMO (conductor-like screening model)-based models, and excess Gibbs energy models like NRTL.54 For the EOS models, one of the main advantages is that they can disclose the dependence of phase volume on pressure. But some critical parameters of ILs are required in the EOS models, which can only be obtained indirectly with great uncertainty. This limits the predictive power and potential for engineering application of these models. For the activity coefficient models like NRTL, the IL pair is considered as a single molecule in the solution, which leads to a lot of intermolecular interaction parameters having to be predetermined. Two widely used and convenient predictive models for predicting the thermodynamic properties (e.g., vapor-liquid equilibria, liquid-liquid equilibria, vapor pressures, and gas solubility) of

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systems with ILs are the COSMO-RS55,56 and UNIFAC-Lei models.57,58 However, the COSMO-RS model only provides a qualitative description of the thermodynamic behavior of systems containing ILs, and is treated as an extremely powerful tool for fast solvent pre-screening without support for a large amount of experimental data.59-61 However, the UNIFAC-Lei model can give quantitative predictions with high accuracy for systems containing ILs, e.g., IL-CO2, IL-H2, and IL-CO systems, and thus has been widely applied by many authors. However, when the UNIFAC-Lei model was used for IL-CH4 systems, CH4 solubility in ILs could not be predicted well, especially at low temperatures. Thus, a main objective of this work is to propose a modified UNIFAC-Lei model (named as Mod. UNIFAC-Lei) that can be applied to predict CH4 solubility at either high or low temperatures in both pure and mixed ILs. The modification was completed from two aspects as follows: 1) two additional group interaction parameters (bnm and cnm) were introduced to describe the influence of temperature on the residual contribution to activity coefficients; and 2) an empirical exponential62 was used for the relative van der Waals volume due to the large difference among group volumes in the calculation of a combinatorial contribution to activity coefficients. Thus, the aim of this work is to address the fundamental issues on the Mod. UNIFAC-Lei model related to IL-CH4 systems by doing the following: 1) obtaining the group parameters of the Mod. UNIFAC-Lei model between the CH4 and ILs groups (i.e., [MIM][BF4], [MIM][PF6], and [MIM][Tf2N]) by correlating the experimental data that have been measured in this work and also exhaustively collected from the literature over a wide temperature range of 243-353 K and a pressure range of 5-80 bar; 2) determining whether the

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group parameters of the Mod. UNIFAC-Lei model can be extrapolated to predict the solubility of CH4 in binary mixtures of ILs from low to high pressures; 3) checking whether the free exchange law between cations and anions can be used for complementary IL pairs ([C1][A1] + [C2][A2] or [C2][A1] + [C1][A2]); and 4) exploring the structure–property relationship for CH4 solubility and selectivity in pure and mixed ILs. The meanings of abbreviations and the structures for the cations and anions of ILs used throughout this article are listed in Supporting Information Table S1. 2.

Mod. UNIFAC-Lei MODEL 2.1. Model Description. In the Mod. UNIFAC-Lei model for gas-IL systems, the IL

molecule was divided into several functional groups in the same manner as in the Orig. UNIFAC-Lei model, where the skeleton of cations and anions is treated as an entire functional group,57,58 and the activity coefficient is determined using the sum of the combinatorial term and residual term

ln γ i = ln γ iC + ln γ i R

(1)

where ln γ i C represents the combinatorial contribution to activity coefficient, which is R caused by different sizes and shapes of groups, and ln γ i represents the residual

contribution, which is essentially due to the energetic interaction between groups. The combinatorial part ln γ i C was represented empirically for a better description of systems involving molecules with significantly different sizes:

ln γ iC = 1 − Vi ' + ln V 'i − 5qi (1 − '

Vi V + ln( i )) Fi Fi

(2)

where the parameter Vi was obtained empirically using the modified 0.7-term of relative van der Waals volumes (ri) for various groups as follows: 6


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Vi ' =

ri 0.7 ∑ r j 0.7 x j

(3)

j

Meanwhile, the calculations for all other parameters in ln γ iC in the Mod. UNIFAC-Lei model is the same as in the Orig. UNIFAC-Lei model using the following equations: Vi =

ri ∑ rj x j

Fi =

j

qi ∑ qjx j

(4)

j

ri = ∑ v Rk ; qi = ∑vk(i )Qk (i ) k

k

(5)

k

where the group parameter Rk and Qk can be obtained using the van der Waals group volumes and surface areas Vk and Ak, which can be obtained using Bondi’s correlation or the COSMO-RS model.57,58 The values of Rk and Qk in the Mod. UNIFAC-Lei model are the same as those in the Orig. UNIFAC-Lei model, and can be found in our previous works.63 R The residual contribution ln γ i is expressed as

m

ln γ iR = ∑ vk(i) (ln Γk − ln Γ(i) k )

(6)

k =1

ln Γ k = Qk [1 − ln(∑θm −ψ mk ) − ∑ ( m

m

θmψ km )] ∑θnψ nm

(7)

n

where the group area fraction θm and the group mole fraction Xm are expressed by the following equations:

Q X θm = m m ; X m = ∑ Qn X n n

∑v x ∑∑v x (i) m i

i

(i) k i

i

(8)

k

To acquire a better description of the temperature dependence and the real phase behavior in the wide temperature region, the group interaction parameter ψnm in the Mod. UNIFAC-Lei model is expressed as a function of temperature:

ψ nm = exp( −

anm + bnmT + cnmT 2 ) T

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(9)


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where three parameters (anm, bnm, and cnm) are used to describe the influence of temperature. However, in the Orig. UNIFAC-Lei model, the group interaction parameter ψnm is expressed as ψnm = exp(−anm / T) using only one parameter (anm). 2.2. Procedure of Estimation of Mod. UNIFAC-Lei Model Group Interaction Parameters. For the CH4 (1) + IL (2) binary system, the gas-liquid equilibrium (GLE) at low and medium pressures is described as

y1Pφ1 (T , P, y1 ) = x1γ 1P1S

(10)

where y1 and x1 are the mole fractions of CH4 in gas and liquid phases, respectively; φ 1 (T , P , y 1 )

is the gas-phase fugacity coefficient of CH4 calculated using the

Peng-Robinson (PR) equation of state; P and T are the system pressure and temperature, s

respectively; P1 is the saturated vapor pressure of CH4, which can be obtained by the extrapolated Antoine equation as proposed by Fogg and Gerrard;64 and γ1 is the activity coefficient of CH4 in the liquid phase, which can be calculated using the UNIFAC-Lei model (Mod. or Orig.). Notably, the gas phase can be regarded as a pure CH4 component (i.e., y1 = 1) due to the negligible vapor pressure of ILs. The minimized average relative deviation (ARD) was used as an objective function (OF) to obtain the group binary interaction parameters (anm, amn, bnm, bmn, cnm, and cmn) between the CH4 and ILs groups:

 1 N xcal − xexp OF = min  ∑ xexp  N 1

  

(11)

where xexp and xcal are the solubility of CH4 in ILs obtained from experimental measurements and predicted results by the UNIFAC-Lei model (Mod. or Orig.), respectively, and N is the number of data points. 8


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The fitting procedure using the SOLVER function with the optimization algorithm of Newton’s central difference in Microsoft Excel 2014 was used, similar to that used for correlating the group binary interaction parameters of the orig. UNIFAC-Lei model in our previous publications.57,58 The modified group interaction parameters (anm, amn, bnm, bmn, cnm, and cmn) between CH2 and IL groups in the Mod. UNIFAC-Lei model were first obtained by correlating the experimental data of the activity coefficients at infinite dilution for alkanes and cycloalkanes in ILs that were exhaustively collected from the literature.65-72 The modified group interaction parameters (anm, amn, bnm, bmn, cnm, and cmn) between the CH4 and CH2 groups were obtained using the experimental CH4 solubility data in alkanes collected from previous publications.73-75 Finally, the group interaction parameters (anm, amn, bnm, bmn, cnm, and cmn) between the CH4 and IL groups (i.e., [MIM][BF4], [MIM][PF6], and [MIM][Tf2N]) in the Mod. UNIFAC-Lei model were obtained by correlating the experimental CH4 solubility data in ILs collected from the literature and the new experimental data measured in this work. The detailed data for all investigated ILs, data points and corresponding literature are given in Supporting Information Tables S2-S4. Several group parameters (Rk and Qk) concerned in this work are listed in Supporting Information Table S5. The newly obtained group interaction parameters and the available parameters48,57,76 in the Orig. UNIFAC-Lei model are listed in Table 1. 3. EXPERIMENTAL SECTION 3.1. Materials. In this work, the ILs ([EMIM][BF4], [BMIM][BF4], [OMIM][BF4], [BMIM][PF6], [OMIM][PF6], [EMIM][Tf2N], [BMIM][Tf2N], and [OMIM][Tf2N]) were purchased from the Shanghai ChengJie Chemical Co., Ltd. (China), and the details are listed

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in Table 2. It should be mentioned that the original purities of ILs are afforded by the supplier. Before experiments, the ILs were pretreated to remove traces of water and volatile impurities using a vacuum rotary evaporator at 353.2 K for 12 h and to ensure water content less than 400 ppm, as determined by the Karl Fischer titration (KLS701). The gas CH4 (purity >99.95% in mass fraction and pressure of 13 MPa) was purchased from the Beijing Beifen Special Gases Factory (China), and used without further purification. The binary mixtures of ILs ([EMIM][BF4] + [OMIM][Tf2N] and [EMIM][Tf2N] + [OMIM][BF4]) with certain proportions were prepared by an electronic analytical balance with an uncertainty of ± 0.001 g. 3.2. Apparatus and Procedure. The solubility measurements of CH4 in pure and mixed ILs at low temperatures (below 293.2 K) and at high temperatures (above 293.2 K) were performed by the drainage gas-collecting method using a low-temperature equilibrium apparatus, and a high-temperature and high-pressure view-cell apparatus, respectively. The high and low temperatures in the equilibrium apparatus were controlled by electric heating elements and a cooling ethanol bath with a fluctuation of ± 0.1 K, respectively. Furthermore, at low temperatures, the system pressure was measured by a pressure gauge with a range of 0–20.000 MPa; at high temperatures, a pressure gauge with a range of 0–9.999 MPa with a fluctuation of ± 0.001 MPa was used. The details on solubility measurements can be found in our previous publications.77-79 4. RESULTS AND DISCUSSION 4.1. Comparison between the Mod. and Orig. UNIFAC-Lei Models for Predicting the CH4 Solubility in Pure ILs at both High and Low Temperatures. The solubility data for

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CH4 in seven pure ILs (i.e., [BMIM][PF6], [OMIM][PF6], [EMIM][BF4], [BMIM][BF4], [OMIM][BF4], [BMIM][Tf2N], and [OMIM][Tf2N]) with three common anions ([BF4]-, [PF6]-, and [Tf2N]-) and imidazolium-based cations at a wide temperature range from 243.15 to 333.15 K were measured in this work to explore the effect of anions and the length of alkyl side-chains on cations in the GLE of CH4-IL systems. The detailed experimental solubility data are listed in Supporting Information Table S6. The comparison between experimental CH4 solubility data (collected from the literature and measured in this work) and the predicted results from the Mod. and Orig. UNIFAC-Lei models is summarized in Table 3. It can be seen that at high temperatures (above 293.2 K), in most cases, the Orig. UNIFAC-Lei model can give a quantitative prediction of CH4 solubility with the average relative deviations (ARDs) less than 20%. However, at low temperatures, the Orig. UNIFAC-Lei model significantly over-predicts CH4 solubility with the ARDs above 50%. In some cases, the ARDs exceed 100%, indicating that the Orig. UNIFAC-Lei model overestimates the temperature influence on activity coefficients. Thus, it is necessary to modify the Orig. UNIFAC-Lei model. The Mod. UNIFAC-Lei model was improved in the following two aspects: 1) the two additional group interaction parameters (bnm and cnm) were introduced to express the temperature influence on the residual contribution to activity coefficients; and 2) the exponential 0.7 was adopted for the relative van der Waals volume to correct the large group volume difference among CH4, CH2, and IL groups. In this way, the Mod. UNIFAC-Lei can provide a good prediction of CH4 solubility at both high and low temperatures, with the ARDs of 8.61% and 9.23%, respectively. Thus, the Mod. UNIFAC-Lei model is a more suitable and efficient alternative predictive thermodynamic

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model for predicting the phase equilibrium of IL-CH4 systems over a wide temperature and pressure range. The influence of temperature and pressure on the experimental solubility of CH4 in pure ILs is illustrated in Figure 1. As shown, CH4 solubility increases with the decrease in temperature, especially for [BF4]- and [PF6]--based ILs. However, the temperature dependence of [Tf2N]--based ILs is not so obvious, as shown in Figures 1f and 1g. The influence of IL structures on the solubility of CH4 in pure ILs is shown in Figure 2. The CH4 solubility in pure ILs follows the order [EMIM][BF4] < [BMIM][PF6] < [BMIM][BF4] < [OMIM][PF6] < [BMIM][Tf2N] < [OMIM][BF4] < [OMIM][Tf2N] at the same temperature and pressure, indicating that both cations and anions mutually contribute to CH4 solubility. With the same imidazolium-based cation, the [Tf2N]--based ILs exhibit the highest solubility, while the [PF6]--based ILs exhibit the lowest. Moreover, CH4 solubility would increase significantly with the increase in the length of alkyl side-chains on imidazolium-based cations for ILs with the same anion. The reason why the [Tf2N]--based ILs exhibit the highest solubility and the long alkyl side-chains on cations are favorable for increasing CH4 solubility may be that the anion [Tf2N]- and the imidazolium-based cations with long alkyl side-chains have the relatively larger Van der Waals volume than other anions (e.g., [PF6]- and [BF4]-) and cations with short side-chains, leading to the stronger Van der Waals interaction between CH4 and IL. Moreover, the larger Van der Waals volume between cation and anion results in the larger void (or free volume) in IL phase, which facilitates the small CH4 molecules entering. 4.2. Prediction of CH4 Solubility in the Binary Mixtures of ILs. The lever rule is an

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effective method for predicting the solubility of CO2, H2, and CO in mixed ILs.40,73 Herein, the lever rule is extended to estimate the solubility of CH4 in mixed ILs because mixed ILs are sometimes needed in specific separation processes. The lever rule is written as

x1 = X 2 x1,2 + X 3 x1,3

(12)

where x1,2 and x1,3 are CH4 (1) solubility in pure ILs at the same temperature and pressure as determined by the Mod. UNIFAC-Lei model, and X2 and X3 are the mole fractions of IL components in a binary mixture on a CH4-free basis. In principle, three methods (i.e., Orig. UNIFAC-Lei model, Mod. UNIFAC-Lei model, and lever rule) can be used to predict CH4 solubility in mixed ILs. The solubility of CH4 (1) in the binary mixed ILs of [EMIM][BF4] (2) + [OMIM][Tf2N] (3) and [EMIM][Tf2N] (2) + [OMIM][BF4] (3) was measured for different mole fractions (X2 = 0.5, and 0.706 on a CH4-free basis) at temperatures from 243.15 to 353.2 K. The detailed data and the predicted results using these three methods are listed in Supporting Information Table S7. The comparison between experimental data and predicted results is summarized in Table 4. The Orig. UNIFAC-Lei model demonstrates a bad prediction, whereas both the Mod. UNIFAC-Lei model and lever rule provide a good prediction, with the ARDs of 9.16% and 12.11%, respectively. The experimental solubility data of CH4 in four mixed ILs at different temperatures, along with the predicted results from the Mod. UNIFAC-Lei model, are illustrated in Figure 3. The good agreement between experimental data and the predicted results indicates that the Mod. UNIFAC-Lei model can be effectively and efficiently extrapolated from pure to mixed ILs, and the lever rule can also be extended to predict the solubility of CH4 in a binary mixture of ILs.

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Furthermore, it is interesting that the experimental solubility data of CH4 in the binary mixture with equimolar amounts of [EMIM][BF4] and [OMIM][Tf2N] (50%[EMIM][BF4] + 50%[OMIM][Tf2N]) are almost identical to those in the [EMIM][Tf2N] and [OMIM][BF4] mixture with equimolar amounts. The corresponding predicted results from the Mod. UNIFAC-Lei model are also almost identical, since the predicted curves overlap, as shown in Figure 3. The similar conclusion also holds for the viscosity property of mixed ILs in an equimolar amount of complementary pairs, as proposed by Fillion and Brennecke.80 Notably, the free exchange law between cations ([C1] and [C2]) and anions ([A1] and [A2]) can be generalized to other complementary IL pairs ([C1][A1] + [C2][A2] or [C2][A1] + [C1][A2] mixture) in an equimolar amount and are not limited to the IL mixtures investigated in this work. This finding means that we have more choices in the preparation of a binary mixture with the same absorption ability of CH4 using the [C1][A1] + [C2][A2] or [C2][A1] + [C1][A2] mixed ILs. We went a step further to explain the free exchange phenomenon by calculating the free volume and fractional free volume (FFV) for pure and mixed ILs using the COSMO-RS model, as shown in Figure 4. The detailed calculation procedure can be found in our previous publication,57 and the detailed data for free volume and FFV for pure and mixed ILs involved in this work are listed in Supporting Information Table S8. In Figure 4, four pure ILs exhibit different FFV values, whereas the mixtures of 50%[EMIM][BF4] + 50%[OMIM][Tf2N] and 50%[EMIM][Tf2N] + 50%[OMIM][BF4] have identical values for both free volume and FFV, confirming the same CH4 solubility at the same temperature and pressure. 4.3. Structure–property relationship for CH4 solubility and selectivity in ILs. The

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structure–property relationship between the molecular structures of ILs and separation performance (i.e., CH4 solubility and selectivity of CH4 to CO2) can be explored by the Mod. UNIFAC-Lei model. The Henry’s law constants based on the mole fraction are applied to evaluate CH4 solubility in various ILs, as calculated by

H 1 (T ) = lim

x1 → 0

y1 Pφ1 (T , P, y1 ) x1

= lim γ 1 P1S (T ) = γ 1 ∞ P1S (T ) x1 → 0

(13)

where T and P are the system temperature and pressure, respectively; P1S is the saturated vapor pressure of CH4 obtained by the extrapolated Antoine equation, as mentioned above; φ 1 ( T , P , y 1 ) is the fugacity coefficient of CH4 in the gas phase determined by the PR ∞ equation of state; and γ 1 is the activity coefficient of CH4 in ILs at infinite dilution, as

predicted by the Mod. UNIFAC-Lei model. In this work, the experimental Henry’s constants of CH4 (1) in various pure and mixed ILs at various temperatures were determined by

H1 (T , P) ≡ lim

x1 →0

f1L x1

(14)

where f1L is the fugacity of CH4 in the liquid phase by the PR equation of state at a certain temperature and pressure, and x1 is the mole fraction of CH4 in ILs. Moreover, the lever rule was also introduced to calculate the Henry’s law constants for mixed ILs, and it is expressed as

1 1 1 = X2 + X3 H1 H1,2 H1,3

(15)

where H1,2 and H1,3 are the Henry’s law constants for CH4 in individual ILs at the same temperature obtained by the Mod. UNIFAC-Lei model, and X2 and X3 are the mole fractions of IL components in a binary mixture on a CH4-free basis. 15



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Table 5 shows the experimental and predicted Henry’s law constants for CH4 in pure ILs and mixed ILs. The ARDs for CH4 Henry’s law constants between the experimental data and predicted values from the Mod. UNIFAC model in pure ILs and mixed ILs from 243.15 to 353.15 K were only 6.54% and 3.02%, respectively, while the ARD in mixed ILs using the lever rule was 11.89%. This indicates that both the Mod. UNIFAC-Lei model and the lever rule can predict the Henry’s law constants of CH4 in mixed ILs, but the former appears to be more convenient and more accurate. The experimental data and predicted results from the Mod. UNIFAC-Lei model for the Henry’s law constants of CH4 at 333.15 K are illustrated in Figure 5a, and some experimental data were obtained by the linear extrapolation of CH4 solubility using eq. 14 derived from the literature,43,44,48 and others obtained in this work. The Henry’s law constants of CH4 are in the order [EMIM][A] > [BMIM][A] > [HMIM][A] > [OMIM][A] (where the anion [A] stands for [Tf2N]-, [BF4]-, or [PF6]-), indicating that increased alkyl side-chain length in the imidazolium-based cations is favorable for increasing the solubility of CH4. The Henry’s law constants of CH4 in ILs with the same cation are in the order [PF6]- > [BF4]- > [Tf2N]-, similar to that of CO2. It is known that the selectivity of CH4 to CO2 ( SCO2 /CH4 ) in various ILs is the basis of gas separation, and is defined as S CO 2 /CH 4 =

H CH 4 (T ) H CO 2 (T )

(16)

It should be mentioned that here, the selectivity ( SCO2 /CH4 ) is used as an “idealized” selectivity, because the interaction between different types of gases is not considered; this will have a certain impact on real selectivity and should be addressed in future work. The 16


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experimental and predicted selectivities of CH4 to CO2 in both pure and mixed ILs are shown in Figure 5b, and the experimental Henry’s law constants for CO2 in ILs were obtained from the literature.77,79,81-92 Notably, the predicted Henry’s law constants for CH4 were obtained by the Mod. UNIFAC-Lei model, while those for CO2 were obtained using the Orig. UNIFAC-Lei model because of the efficient applicability of the Orig. UNIFAC-Lei model for predicting the binary CO2-IL systems and ternary CO2-IL-IL systems at either high or low temperatures, as confirmed by our previous publication.40 Detailed data on Henry’s law constants and the selectivity of CH4 to CO2 are given in Supporting Information Table S9. Clearly, the predicted selectivities are in good agreement with the experimental data, as shown in Figure 5b. Moreover, the order of selectivity of CH4 to CO2 in ILs is consistent with that of the Henry’s law constants of CH4. Thus, the ILs with a large selectivity of CH4 to CO2 usually corresponds to a small solubility of CH4 and CO2. Thus, mixed ILs are usually adopted to combine the desirable properties of two different ILs to exhibit appropriate selectivity and solubility simultaneously. In addition, both Henry’s law constants and selectivity in mixed ILs are between those in pure ILs. More importantly, either the Henry’s law constants of CH4 or the selectivity of CH4 to CO2 in the binary mixtures of 50%[EMIM][BF4] + 50%[OMIM][Tf2N] and 50%[EMIM][Tf2N] + 50%[OMIM][BF4] were the same. This indicates that anions and cations in the binary mixture of an equimolar amount of complementary IL pairs can be freely exchanged. Evidently, this helps guide the selection of mixed ILs in gas separation. Moreover, simple mixed ILs can be used to replace the complicated chemical synthesis of single ILs.

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To achieve a better understanding of the influence of temperature on separation performance, the selectivity of CH4 to CO2 in ILs at low temperatures was investigated down to 243.15 K. As seen from Figure 6, low temperature is significantly favorable for increasing the selectivity of CH4 to CO2 for all ILs investigated in this work. For the same anions (i.e., [BF4]-, [PF6]-, and [Tf2N]-), the influence of temperature on the selectivity of CH4 to CO2 becomes more obvious for ILs with short alkyl side-chain lengths in the cation, especially at temperatures below 293.15 K. Thus, the ILs with short alkyl side-chain lengths in the cation are more suitable for gas separation at low temperatures. It should be mentioned that, similar to the Orig. UNIFAC-Lei model, the parameters in the Mod. UNIFAC-Lei model obtained in this work can be directly used in commercial simulation programs, such as Aspen Plus, ProII and ChemCAD, to establish rigorous equilibrium (EQ) stage and nonequilibrium (NEQ) stage models for process design, simulation, and optimization. 5. CONCLUSIONS To the best of our knowledge, this is the first work to develop the Mod. UNIFAC-Lei model for IL-CH4 systems, and the corresponding new modified group interaction parameters (anm, amn, bnm, bmn, cnm, and cmn) were obtained by correlating the experimental solubility data for CH4 at both high and low temperatures. The solubility data for CH4 in several common pure and mixed ILs at temperatures from 243.15 to 353.15 K were measured to test the applicability of the Mod. UNIFAC-Lei model. Compared to the Orig. UNIFAC-Lei model, the Mod. UNIFAC-Lei model has stronger predictive power for the solubility of CH4 in both pure and mixed ILs at either high or low temperatures. Moreover, cations ([C1] and [C2]) and anions ([A1] and [A2]) can be freely exchanged in

18


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complementary IL pairs ([C1][A1] + [C2][A2] or [C2][A1] + [C1][A2]) in equimolar amounts without changing the gas solubility and selectivity, due to the same free volume and FFV. Thus, we have more choices to prepare mixed ILs for gas absorption. Furthermore, the structure-property relationship for IL-CH4 systems was studied by means of the combination of experiments and the Mod. UNIFAC-Lei model. The selectivity trend for CH4 to CO2 in different ILs is consistent with that of the Henry’s law constant for CH4. Furthermore, a low temperature is favorable for increasing both the solubility of CH4 and the selectivity of CH4 to CO2 in ILs. Thus, the separation of CO2 from CH4 using ILs as separating agents at low temperatures can be an alternative route in future industrial applications. ■ ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the website. Tables S1-S8; Detailed meanings of abbreviations for all anions and cations of ILs, experimental solubility and selectivity data, and predicted results by the Mod. UNIFAC-Lei model, and the free volume and

FFV data. (.doc file). ■ AUTHOR INFORMATION Corresponding Author *Tel.: +86-1064433695. E-mail: [email protected].

ORCID Zhigang Lei: 0000-0001-7838-7207

Notes The authors declare no competing financial interest.

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■ ACKNOWLEDGMENTS This work is financially supported by the National Natural Science Foundation of China under Grant (Nos. 21476009).

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(85) Chen, Y.; Zhang, S.; Yuan, X.; Zhang, Y.; Zhang, X.; Dai, W.; Mori, R. Solubility of CO2 in imidazolium-based tetrafluoroborate ionic liquids. Thermochim. Acta. 2006, 441, 42-44. (86) Zhang, J.; Zhang, Q.; Qiao, B.; Deng, U. Solubilities of the gaseous and liquid solutes and their thermodynamics of solubilization in the novel room-temperature ionic liquids at infinite dilution by gas chromatography. J. Chem. Eng. Data 2007, 52, 22772283. (87) Jacquemin, J.; Husson ,P.; Majer, V.; Costa Gomes, M. Influence of the cation on the solubility of CO2 and H2 in ionic liquids based on the bis(trifluoromethylsulfonyl)imide anion. J. Solution Chem. 2007, 36, 967-979. (88) Carvalho, P. J.; Alvarez, V. H.; Marrucho, I. M.; Aznar, M.; Coutinho, J. A. P. High pressure phase behavior of carbon dioxide in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and 1-butyl-3-methylimidazolium dicyanamide ionic liquids. J. Supercrit. Fluids 2009, 50, 105-111. (89) Aki, S. N. V. K.; Mellein, B. R.; Saurer, E. M.; Brennecke, J. F. High-pressure phase behavior of carbon dioxide with imidazolium-based ionic liquids. J. Phys. Chem. B 2004, 108, 20355-20365. (90) Kumelan, J.; Kamps, A. P.; Tuma, D.; Yokozeki, A.; Shiflett, M. B.; Maurer, G. Solubility of CO2 in the ionic liquid [hmim][Tf2N]. J. Chem. Thermodyn. 2006, 38, 1396-1401. (91) Costa Gomes, M. F. Low-pressure solubility and thermodynamics of solvation of carbon dioxide, ethane, and hydrogen in 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide between temperatures of 283 K and 343 K. J. Chem. Eng. Data 2007, 52, 472-475. (92) Camper, D.; Bara, J.; Koval, C.; Noble, R. Bulk-fluid solubility and membrane feasibility of Rmim-based room-temperature ionic liquids. Ind. Eng. Chem. Res. 2006, 45, 6279-6283.

27



Table Captions Table 1. Group Interaction Parameters of the Mod. and Orig. UNIFAC-Lei Models Used in This Work.

Table 2. Specifications of ILs Used in This Work.

Table 3. Comparison of the Experimental CH4 Solubility in ILs with the Predicted Results by Orig. and Mod. UNIFAC-Lei Models.

Table 4. Comparison of the Experimental CH4 Solubility in Mixed ILs with the Predicted Results by Lever Rule, and Orig. and Mod. UNIFAC-Lei Models.

Table 5. Henry’s Constant of CH4 in ILs Determined Experimentally (Hexp) and Predicted by the Mod. UNIFAC-Lei Model (Hpred) at Different Temperatures (the Values in Parenthesis Come from Lever Rule as Calculated by eq. 15).

28


Page 28 of 46

Page 29 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 1. Group Interaction Parameters of the Mod. and Orig. UNIFAC-Lei Models Used in This Work Groups m

Mod. UNIFAC-Lei Model n

αmn (K)

αnm (K)

bmn

bnm

cmn (K-1)

Orig. UNIFAC-Lei Model cnm (K-1)

αmn (K)

αnm (K)

CH2

[MIM][Tf2N]

400.88

145.7928

-0.8992

-0.3514

0. 1275 × 10-2

0.2119 × 10-2

400.89b

145.80b

CH2

[MIM][PF6]

692.26

401.54

-0.0135

0.0244

-0.3913× 10-4

-0.5292 × 10-4

692.26b

401.54b

CH2

[MIM][BF4]

1108.51

588.74

0.3722

1.7986

-0.2746 × 10-3

-0.8516 × 10-2

1108.51b

588.74b

CH4

CH2

119.8349

-25.3837

-1.3051

1.5015

0.0000

0.0000

-399.50b

1161.00b

CH4

[MIM][Tf2N]

2588.07

1209.48

6.6426

-5.8431

0.3341 × 10-2

0.9175 × 10-2

2588.07a

434.02a

CH4

[MIM][PF6]

503.03

1201.45

2.3016

2.5710

-0.3008a × 10-2

0.3863 × 10-1

484.75c

1368.40c

CH4

[MIM][BF4]

4193.28

1701.94

0.0677

-0.9328

-0.8058a × 10-2

-0.6219 × 10-2

1799.86c

1153.11c

a

Group binary interaction parameters are from reference.48 bGroup binary interaction parameters are from reference.57 cGroup binary

interaction parameters are from reference.76

29



Page 30 of 46

Table 2. Specifications of ILs Used in This Work Molecular

Puritya

Chloride contenta

Water contenta

Water contents

weight (g·mol-1)

(mass fraction)

(mass fraction)

(mass fraction)

after drying

[EMIM][BF4]

197.97

> 99%

< 200 ppm

< 2000 ppm

200 ppm

[BMIM][BF4]

226.02

> 99%

< 200 ppm

< 1000 ppm

230 ppm

[OMIM][BF4]

282.13

> 99%

< 200 ppm

< 1000 ppm

250 ppm

[BMIM][PF6]

284.18

> 99%

< 200 ppm

< 2000 ppm

340 ppm

[OMIM][PF6]

340.29

> 99%

< 200 ppm

< 2000 ppm

320 ppm

[EMIM][Tf2N]

391.31

> 99%

< 200 ppm

< 1000 ppm

180 ppm

[BMIM][Tf2N]

419.36

> 99%

< 150 ppm

< 1000 ppm

220 ppm

[OMIM][Tf2N]

475.47

> 99%

< 150 ppm

< 1000 ppm

270 ppm

Abbreviation

a

Specifications and purities of ILs afforded by the ILs supplier.

30


Page 31 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Comparison of the Experimental CH4 Solubility in ILs with the Predicted Results by Orig. and Mod. UNIFAC-Lei Models ILs

T range (K)

P range (bar)

ARDs (%) Orig.

Mod.

No. of data points

Refs.

High temperatures (above 293.15 K)

[BMIM][PF6] [OMIM][PF6] [EMIM][BF4] [BMIM][BF4] [BMIM][BF4] [OMIM][BF4] [EMIM][Tf2N] [BMIM][Tf2N] [BMIM][Tf2N] [HMIM][Tf2N] [OMIM][Tf2N] [BMIM][PF6]

293.15-353.15 293.15-353.15 293.15-353.15 293.15-353.15 292.95-343.09 293.15-353.15 313.15-353.15 315.15-453.15 293.15-353.15 333.15-413.25 293.15-353.15 298.15-323.15

4.91-74.21 5.08-66.30 5.46-83.76 5.56-70.12 0.47-0.98 10.27-68.23 5.7-59.07 15.1-161.05 9.96-74.78 14.40-93.00 5.78-62.00 1.00-13.00 Total ARD

17.65 23.75 25.95 33.35 23.94 42.24 9.65 16.93 17.11 13.03 27.28 25.42 21.94

10.16 8.90 7.47 7.77 26.46 9.13 17.75 9.81 9.16 5.40 4.47 20.79 8.61

44 46 50 50 12 48 24 82 40 18 43 38 495

This work This work This work This work 40 This work 47 42 This work 43 This work 41

Low temperatures (below 293.15 K)

[BMIM][PF6] [BMIM][PF6] [OMIM][PF6] [EMIM][BF4] [BMIM][BF4] [OMIM][BF4] [BMIM][Tf2N] [OMIM][Tf2N]

273.15 283.15 258.15-273.15 273.15 258.15-273.15 243.15-273.15 243.15-273.15 243.15-273.15

5.01-59.7 0.19-10.49 10.11-60.19 10.45-64.76 5.36-71.1 5.12-56.9 10.09-71.94 5.76-61.76 Total ARD

40.94 8.56 146.20 107.02 155.65 274.97 65.45 152.36 105.59

11.32 15.18 8.21 7.16 10.16 7.55 15.04 7.20 9.23

13 21 22 9 22 33 36 31 187

This work 41 This work This work This work This work This work This work

31



Page 32 of 46

Table 4. Comparison of the Experimental CH4 Solubility in Mixed ILs with the Predicted Results by Lever Rule, and Orig. and Mod. UNIFAC-Lei Models ARDs (%) ILs

T range (K)

P range (bar)

50% [EMIM][BF4]+ 50% [OMIM][Tf2N] 70.6% [EMIM][BF4]+ 29.4% [OMIM][Tf2N]

293.15-353.15 243.15-273.15

5.79-63.99 6.12-56.76

293.15-353.15

Orig.

Mod.

Level Rule

5.99-65.08

24.49 175.31 33.34

8.82 9.75 12.31

9.57 11.07 10.40

243.15-273.15

7.37-57.85

180.64

9.14

12.58

50% [EMIM][Tf2N]+ 50% [OMIM][BF4]

293.15-353.15

5.23-75.99

36.79

8.73

11.65

243.15-273.15

5.17-57.85

182.84

8.76

9.50

70.6% [EMIM][Tf2N]+ 29.4% [OMIM][BF4]

293.15-353.15

5.53-64.82

18.68

9.25

11.40

243.15-273.15

5.67-57.83

108.15

7.34

20.97

Total ARD

91.77

9.16

12.11

32


Page 33 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 5. Henry’s Constant of CH4 in ILs Determined Experimentally (Hexp) and Predicted by the Mod. UNIFAC-Lei Model (Hpred) at Different Temperatures (the Values in Parenthesis Come from Lever Rule as Calculated by eq. 15) ILs

T (K)

Hexp (MPa)

Hpred (MPa)

RDs (%)

[BMIM][PF6]

353.15 333.15 313.15

174.56 151.36 126.85

182.51 155.27 129.14

4.55 2.58

293.15 273.15

95.25 75.86

104.54 81.88

353.15 333.15

70.34 65.46

77.43 66.46

313.15 293.15

61.83 44.69

55.85 45.76

273.15 258.15

35.22 30.03

36.35 29.83

353.15 333.15

231.19 225.89

223.53 220.59

313.15 293.15

198.86 170.87

206.24 181.00

273.15 353.15

136.33 114.87

148.28 124.53

333.15 313.15

111.92 94.16

114.96 101.45

293.15 273.15

75.95 59.56

85.40 68.59

258.15 353.15

53.68 59.27

56.51 61.86

333.15 313.15

54.75 46.56

54.94 47.33

293.15 273.15

38.31 30.55

39.56 32.07

258.15 243.15

25.19 20.42

26.85 22.06

353.15 333.15

47.56 46.02

48.59 44.49

313.15 293.15

42.11 37.15

40.90 37.75

273.15 258.15

33.64 30.33

34.95 33.01

243.15

26.44

31.11

[OMIM][PF6]

[EMIM][BF4]

[BMIM][BF4]

[OMIM][BF4]

[BMIM][Tf2N]

33


1.81 9.75 7.94 10.08 1.53 9.67 2.39 3.21 0.67 3.31 2.35 3.71 5.93 8.77 8.41 2.72 7.74 12.44 15.16 5.27 4.37 0.35 1.65 3.26 4.98 6.59 8.03 2.17 3.32 2.87 1.62 3.89 8.84 17.66


[OMIM][Tf2N]

50% [EMIM][BF4] + 50% [OMIM][Tf2N]

353.15 333.15

36.66 32.67

29.77 27.43

313.15 293.15

30.85 28.65

25.32 23.39

273.15

22.16

21.59

18.36 2.57

258.15

21.38

20.25

5.29

243.15

18.42

18.87 Total ARD

2.44

52.45

55.43 (52.57)

5.68 (0.23)

46.70 41.93

49.17 (48.81) 43.68 (45.12)

5.29 (4.52) 4.17 (7.61)

38.72 34.83

38.9 (41.45) 34.67 (37.71)

0.46 (7.06) 0.46 (8.27)

32.72 27.12

31.74 (34.76) 28.89 (31.61)

3.02 (6.24) 6.53 (16.55)

78.88 69.43

83.64 (76.76) 74.07 (71.87)

6.03 (2.69) 6.68 (3.51)

63.34 58.91

64.93 (66.54) 56.57 (60.75)

2.51 (5.05) 3.97 (3.12)

49.61 44.49

49.09 (54.43) 43.94 (49.28)

1.05 (9.72) 1.24 (10.77)

37.98 54.45

39.06 (43.75) 55.15 (66.75)

2.84 (15.19) 1.29 (22.59)

47.43 43.09

48.93 (59.9) 43.46 (52.97)

3.16 (26.28) 0.86 (22.94)

38.37 34.66

38.72 (46.11) 34.51 (39.42)

0.86 (20.18) 0.46 (13.73)

32.54

31.58 (34.54)

2.95 (6.14)

28.56

28.74 (29.79)

0.63 (4.31)

53.95 51.57

58.56 (69.02) 52.59 (62.21)

8.54 (27.89) 1.98 (20.63)

45.38 42.88

47.46 (55.71) 43.07 (49.49)

4.58 (22.76) 0.44 (15.42)

38.19 34.97

39.24 (43.52) 36.62 (39.15)

2.75 (13.96) 4.72 (11.96)

33.57

34.08 (34.82) Total ARD

1.52 (3.72) 3.02 (11.89)

353.15 333.15 313.15 293.15 273.15 258.15

70.6% [EMIM][BF4] + 29.4% [OMIM][Tf2N]

243.15 353.15 333.15 313.15 293.15 273.15 258.15 243.15

50% [EMIM][Tf2N] + 50% [OMIM][BF4]

353.15 333.15 313.15 293.15 273.15 258.15

70.6%[EMIM][Tf2N] + 29.4% [OMIM][BF4]

Page 34 of 46

243.15 353.15 333.15 313.15 293.15 273.15 258.15 243.15

34


18.79 16.04 17.93

6.54

Page 35 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure Captions Figure 1. Solubility of CH4 in pure [BMIM][PF6] (a), [OMIM][PF6] (b), [EMIM][BF4] (c), [BMIM][BF4] (d), [OMIM][BF4] (e), [BMIM][Tf2N] (f), and [OMIM][Tf2N] (g) at different temperatures. Lines, results predicted by the Mod. UNIFAC-Lei model; scattered points, experimental data. (■) 353.15 K; (●) 333.15 K; (▲) 313.15 K; (▼) 293.15 K; (□) 273.15 K; ( ) 258.15 K; (∆) 243.15 K.

Figure 2. Solubility of CH4 in seven pure ILs at temperature of 273.15 K. Lines, results predicted by the Mod. UNIFAC-Lei model; scattered points, experimental data. (▲) [EMIM][BF4]; (■) [BMIM][PF6]; (▼) [BMIM][BF4]; (●) [OMIM][PF6]; (★) [BMIM][Tf2N]; (◆) [OMIM][BF4]; (□) [OMIM][Tf2N].

Figure 3. Solubility of CH4 in mixed ILs at 353.15 K (a), 293.15 K (b), 273.15 K (c), and 243.15 K (d). Solid lines, results predicted by the Mod. UNIFAC-Lei model; Scattered points, experimental data. (■) 70.6% [EMIM][BF4] +29.4% [OMIM][Tf2N]; (●) 50% [EMIM] [Tf2N] + 50% [OMIM][BF4]; (▲) 70.6% [EMIM][Tf2N] + 29.4% [OMIM][BF4]; (◆) 50% [EMIM][BF4] + 50% [OMIM][Tf2N].

Figure 4. Free volume Vf (a) and FFV (b) in pure and mixed ILs at 298.15 K calculated by the COSMO-RS model.

Figure 5. Henry’s constant of CH4 (a) and selectivity of CH4 to CO2 (b) in ILs at 333.15 K. (□) Results predicted by the Mod. UNIFAC-Lei model; (●) experimental data coming from literature; (■) experimental data obtained in this work.

35



Figure 6. Influence of temperature on the selectivity of CH4 to CO2 in ILs. Solid lines, results predicted by the Mod. UNIFAC-Lei model; scattered points, experimental data. (a) (■) [BMIM][PF6]; (●) [[EMIM][BF4]; (▲) [OMIM][PF6]; (▼) [BMIM][BF4]; (★) [OMIM][BF4]. (b) (◆) [EMIM][Tf2N]; (●) [BMIM][Tf2N]; (▲) [HMIM][Tf2N]; (■) [OMIM][Tf2N]; (▬) 50% [EMIM][BF4] + 50% [OMIM][Tf2N] or 50% [EMIM] [Tf2N] + 50% [OMIM] [BF4].

36


Page 36 of 46

Page 37 of 46

0.07

(a)

0.06 0.05

x1

0.04 0.03 0.02 0.01 0.00

0

1

2

3

4

5

6

7

8

P/ MPa

0.18

(b)

0.16 0.14

x1

0.12 0.10 0.08 0.06 0.04 0.02 0.00

0

1

2

3

4

5

6

7

P/ MPa

0.05

(c) 0.04

0.03

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.02

0.01

0.00

0

1

2

3

4

5

6

7

P/ MPa

37


8

9


0.12

(d)

0.10

x1

0.08 0.06 0.04 0.02 0.00

0

1

2

3

4

5

6

7

8

5

6

7

8

5

6

7

8

P/ MPa

0.24

(e)

0.21 0.18

x1

0.15 0.12 0.09 0.06 0.03 0.00

0

1

2

3

4

P/ MPa

0.20 0.18

(f)

0.16 0.14 0.12

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 46

0.10 0.08 0.06 0.04 0.02 0.00

0

1

2

3

4

P/ MPa

38


Page 39 of 46

0.27

(g)

0.24 0.21 0.18

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.15 0.12 0.09 0.06 0.03 0.00

0

1

2

3

4

5

6

7

P/ MPa

Figure 1. Solubility of CH4 in pure [BMIM][PF6] (a), [OMIM][PF6] (b), [EMIM][BF4] (c), [BMIM][BF4] (d), [OMIM][BF4] (e), [BMIM][Tf2N] (f), and [OMIM][Tf2N] (g) at different temperatures. Lines, results predicted by the Mod. UNIFAC-Lei model; scattered points, experimental data. (■) 353.15 K; (●) 333.15 K; (▲) 313.15 K; (▼) 293.15 K; (□) 273.15 K; ( ) 258.15 K; (∆) 243.15 K.

39



0.21 0.18 0.15 0.12

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 46

0.09 0.06 0.03 0.00

0

1

2

3

4

5

6

7

8

P/ MPa

Figure 2. Solubility of CH4 in seven pure ILs at temperature of 273.15 K. Lines, results predicted by the Mod. UNIFAC-Lei model; scattered points, experimental data. (▲) [EMIM][BF4]; (■) [BMIM][PF6]; (▼) [BMIM][BF4]; (●) [OMIM][PF6]; (★) [BMIM][Tf2N]; (◆) [OMIM][BF4]; (□) [OMIM][Tf2N].

40


Page 41 of 46

0.12

(a) 0.10

x1

0.08 0.06 0.04 0.02 0.00

0

1

2

3

4

5

6

7

P/ MPa

0.18 0.16

(b)

0.14 0.12

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.10 0.08 0.06 0.04 0.02 0.00

0

1

2

3

4

5

6

P/ MPa

41


7

8


0.14

(c)

0.12 0.10

x1

0.08 0.06 0.04 0.02 0.00

0

1

2

3

4

5

6

4

5

6

P/ MPa

0.18 0.16

(d)

0.14 0.12 0.10

x1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 46

0.08 0.06 0.04 0.02 0.00

0

1

2

3

P/ MPa

Figure 3. Solubility of CH4 in mixed ILs at 353.15 K (a), 293.15 K (b), 273.15 K (c), and 243.15 K (d). Solid lines, results predicted by the Mod. UNIFAC-Lei model; Scattered points, experimental data. (■) 70.6% [EMIM][BF4] +29.4% [OMIM][Tf2N]; (●) 50% [EMIM] [Tf2N] + 50% [OMIM][BF4]; (▲) 70.6% [EMIM][Tf2N] + 29.4% [OMIM][BF4]; (◆) 50% [EMIM][BF4] + 50% [OMIM][Tf2N].

42


0.00

the COSMO-RS model.

43

ACS Paragon Plus Environment [OMIM][Tf2N]

[OMIM][BF4]

70.6% [EMIM][Tf2N] + 29.4% [OMIM][BF4]

70.6% [EMIM][BF4] + 29.6% [OMIM][Tf2N]

50% [EMIM][Tf2N] + 50% [OMIM][BF4]

50% [EMIM][BF4] + 50% [OMIM][Tf2N]

0.14 [OMIM][Tf2N]

[OMIM][BF4]

70.6% [EMIM][Tf2N] + 29.4% [OMIM][BF4]

70.6% [EMIM][BF4] + 29.6% [OMIM][Tf2N]

50% [EMIM][Tf2N] + 50% [OMIM][BF4]

50% [EMIM][BF4] + 50% [OMIM][Tf2N]

[EMIM][Tf2N]

Vf (cm3·mol-1) 30

[EMIM][Tf2N]

[EMIM][BF4]

0

[EMIM][BF4]

FFV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 x

Page 43 of 46 Industrial & Engineering Chemistry Research

35

(a)

25

20

15

10 5

0.16

(b)

0.12

0.10

0.08

0.06

0.04

0.02

Figure 4. Free volume Vf (a) and FFV (b) in pure and mixed ILs at 298.15 K calculated by

4

14

10

8

6 [HMIM][Tf2N]

experimental data obtained in this work.

44

ACS Paragon Plus Environment [BMIM][PF6]

[EMIM][BF4]

[EMIM][Tf2N]

[BMIM][BF4]

70.6% [EMIM][BF4] + 29.6% [OMIM][Tf2N] [OMIM][PF6]

[EMIM][BF4]

[BMIM][PF6]

70.6% [EMIM][BF4] + 29.4% [OMIM][Tf2N] [BMIM][BF4]

[EMIM][Tf2N]

[OMIM][PF6]

50% [EMIM][Tf2N] + 50% [OMIM][BF4] 50% [EMIM][BF4] + 50% [OMIM][Tf2N] 70.6% [EMIM][Tf2N] + 29.4% [OMIM][BF4] [OMIM][BF4]

12

50% [EMIM][Tf2N] + 50% [OMIM][BF4] 50% [EMIM][BF4] + 50% [OMIM][Tf2N] 70.6% [EMIM][Tf2N] + 29.4% [OMIM][BF4] [BMIM][Tf2N]

(b) [BMIM][Tf2N]

16

[OMIM][BF4]

[OMIM][Tf2N]

[OMIM][Tf2N]

0

[HMIM][Tf2N]

HCH4/ MPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 S (CH4/CO2)

Industrial & Engineering Chemistry Research Page 44 of 46

250

200

(a)

150

100

50

Figure 5. Henry’s constant of CH4 (a) and selectivity of CH4 to CO2 (b) in ILs at 333.15 K.

(□) Results predicted by the Mod. UNIFAC-Lei model; (●) experimental data coming from literature; (■)

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30

(a)

25

S (CH4/CO2)

20 15 10 5 0 240

260

280

300

320

340

360

T/ K

50

(b) 40

S (CH4/CO2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30

20

10

0 240

260

280

300

320

340

360

T/ K

Figure 6. Influence of temperature on the selectivity of CH4 to CO2 in ILs. Solid lines, results predicted by the Mod. UNIFAC-Lei model; scattered points, experimental data. (a) (■) [BMIM][PF6]; (●) [[EMIM][BF4]; (▲) [OMIM][PF6]; (▼) [BMIM][BF4]; (★) [OMIM][BF4]. (b) (◆) [EMIM][Tf2N]; (●) [BMIM][Tf2N]; (▲) [HMIM][Tf2N]; (■) [OMIM][Tf2N]; (▬) 50% [EMIM][BF4] + 50% [OMIM][Tf2N] or 50% [EMIM] [Tf2N] + 50% [OMIM] [BF4].

45



Table of Content (TOC) Graphic

ln γ i = ln γ i R + ln γ i C

46


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Modified UNIFAC-Lei Model for Ionic LiquidâCH4 Systems - Industrial

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