Novel Index to Screen and Evaluate Ionic Liquids for CO 2 /CH 4 Separation

: Efficient CO 2 /CH 4 separation for biogas upgrading can be achieved by using ionic liquids (ILs) as absorbents. In this study, a novel index named “relative absorption ability” (RAA) was proposed for the first time to facilitate the screening and evaluation of potential absorbents based on their thermodynamic and kinetic properties for CO 2 /CH 4 separation. Subsequently, the properties of 2009 ILs were predicted with the conductor-like screening model, and the top 10 ILs were screened. Finally, the cost of the screened top two ILs for CO 2 /CH 4 separation was further estimated with process simulation. The results further prove the reliability of the new proposed RAA index in screening and evaluating, and the screened promising ILs can reduce the costs of CO 2 /CH 4 separation by 53.9% and 51.9%, respectively, in comparison to the current commercial technology.


INTRODUCTION
Biogas is a green and safe renewable energy, garnering significant attention owing to its high calorific value (15−30 MJ•N•m −3 ). 1 Typically, CO 2 and CH 4 are the dominant components that exist in the raw biogas, where the presence of CO 2 (up to 47 vol %) notably diminishes its calorific value and affects other properties. 2 Therefore, cost-effective and environmentally friendly technologies for CO 2 /CH 4 separation need to be developed.
Numerous technologies have been developed and commercialized for CO 2 /CH 4 separation, such as absorption, adsorption, and membrane processes. 3Among these, absorption technology is preferred owing to its high efficiency in energy cycle and continuity. 4Specifically, physical absorption technology is favored under conditions of high CO 2 partial pressure, such as in biogas upgrading, and the commonly used physical absorbents include dimethyl ether of polyethylene glycol (DEPG), propylene carbonate (PC), water (H 2 O), methanol, and glymes. 5The physical absorption demands relatively low energy for solvent regeneration, while the investment and the amount of circulated absorbent can be substantial. 6Given these considerations, there is a pressing need to develop high-performance absorbents for the CO 2 / CH 4 separation.
Ionic liquids (ILs) have been proposed for CO 2 /CH 4 separation because of their negligible vapor pressure, high stability, and tunable structures for designing ILs with high CO 2 solubility and selectivity. 7Significant efforts have been devoted to making ILs from the fundamental research into industrial application, where promising ILs have been designed and synthesized. 8However, with over 10 6 categories of ILs, 9,10 it is impractical to experimentally study all target ILs and their properties for technology development. 11Thus, effective indexing or modeling approaches are essential for advancing IL-based technologies in the CO 2 /CH 4 separation.
Previously, CO 2 working capacity, desorption enthalpy, and diffusion coefficients were used as three performance indicators to screen potential ILs for CO 2 separation. 12Later, the indexes of "absorption separation" and "absorption degree", a combination of Henry's constant with the unit of pascal, liquid-side mass-transfer coefficient, and selectivity, were proposed 9,13 to effectively evaluate the separation performance of ILs.In our previous study, 14 the index of "absorption ability", coupled with the liquid-side mass-transfer coefficient, Henry's constant with the unit of Pa•m 3 •mol −1 , and enhancement factor, was proposed to describe the CO 2 mass-transfer flux in aqueous choline-amino acids.However, when separating CO 2 /CH 4 with physical absorption, the CO 2 mass-transfer flux and selectivity are two key factors, 15 which have not been adequately addressed.Furthermore, the chosen IL for CO 2 /CH 4 separation with the arbitrary selection without screening or through the evaluation by the deficiency index is not rigorous, failing to showcase the potential of the IL-based technology.On the other hand, currently, the cost of CO 2 /CH 4 separation is obtained with the detailed process simulation or pilot testing, where several models and parameters as well as complex apparatus and operation are usually needed; 16 while no index is linked to the cost, indicating that the available index might be unreasonable.Therefore, it underscores the need for a novel index bridging the properties of the absorbent with the separation cost to screen and evaluate promising ILs for CO 2 /CH 4 separation.
Once a comprehensive index is established, it can be used to screen and evaluate potential ILs when their properties are available.Considering the huge number of ILs that can be synthesized, a theoretical prediction will be desirable.Here, conductor-like screening model for real solvents (COSMO-RS) can be used to swiftly predict the thermodynamic and kinetic properties of ILs, 16,17 where the molecular structural information is the sole input, and their reliability has been verified in the previous studies for the properties of density, 18 heat capacity, 19 activity coefficient, 20 Henry's constant, 21,22 and viscosity. 23This makes it possible to integrate the prediction of the COSMO-RS with a systematic and efficient index to screen and evaluate the IL candidates.
This study aimed to develop a novel index to screen and evaluate potential ILs for the CO 2 /CH 4 separation.A new index named "relative absorption ability" (RAA) was proposed, considering the molecular weight, density, viscosity, and Henry's constants of CO 2 and CH 4 of ILs, and a generalized linear equation was established to relate the cost of CO 2 /CH 4 separation with the RAA index.Then, the properties of 2009 ILs were predicted with COSMO-RS, and the top two ILs were screened as candidates by using the RAA index.The performance of these two potential ILs for CO 2 /CH 4 separation was simulated using the commercial software Aspen Plus, and the results were compared with the prediction from the established generalized equation for further verification as well as comparison with other absorbents to quantify their potential.

Relative Absorption Ability.
In this study, the performance of H 2 O at 293.15 K is used as the reference because it is a commercial absorbent for CO 2 /CH 4 separation, and the RAA index is proposed and presented in eq 1: Usually, S CO /CH 2 4 can be described as the ratio of Henry's constant of CH 4 to that of CO 2 in the absorbent, 24 and the RAA index can then be expressed as eq 2. (2) k L is an important engineering parameter reflecting the masstransfer resistance of CO 2 in the absorbent, 25 which can be described in eq 3: where D and δ are the diffusion coefficient and mass-transfer distance of CO 2 in the absorbent, respectively.Usually, the δ value is related to the wettability of ILs on the packing materials, 26 which is affected by the operating conditions (the circulated amounts of gas and absorbent) as well as the properties of ILs and packing materials.Considering the similar process and operating conditions, it is assumed that the δ value is the same, and k L is only related to the D value.Meanwhile, the commonly used empirical correlation, i.e., the Wilke−Chang equation, 27 is applied to calculate the D value of CO 2 in ILs, which is illustrated in eq 4: where T represents the temperature, μ is the viscosity, M w is the molecular weight, V m is the molar volume of CO 2 at the boiling point (34.0 cm 3 •mol −1 ), and φ is the solvent interaction parameter with a value of 7.5 for ILs. 12 Based on the definition of Henry's law, 28 K H can be depicted in eq 5: where H is the Henry's constant of gas in the absorbent with the unit of pascal, and ρ is the density of the absorbent.Therefore, the formula of RAA can be obtained with the combination of eqs 1−5, where the corresponding values of H 2 O at 293.15 K are calculated based on the properties from the literature. 29Consequently, we can express the RAA index (as shown in eq 6, derived from both thermodynamic and kinetic properties, and the relationship between the physical properties and the RAA index is established.

Generalized Equation to
Predict Cost from RAA.The cost of CO 2 /CH 4 separation is usually determined by multiple factors, such as absorbent, process, operating conditions, and others, 30 which is strongly related to or can be reflected by the properties of the absorbent.Therefore, it is possible to correlate the cost of the CO 2 /CH 4 separation with the RAA index.The average cost (AC) of CO 2 /CH 4 separation is described in eq 7: where CapEX, OpEX, and Q are the total capital expenditure, total operational expenditure, and total CO 2 /CH 4 capacity during the facility operation, respectively.

B
CapEX includes the total investments in equipment and absorbent, where the absorbent only occupies a small proportion if a stable absorbent like IL is applied. 31Therefore, CapEX can be assumed as a constant in the cost estimation for the same process and equipment.Meanwhile, the utilities, operating and maintenance, local taxes and insurance, and others are included in OpEX, 32 where the power consumptions of the compressor (W comp ), blower (W blow ), and pump (W pump ) are the variables for the same process using different absorbents.The expression of OpEX is described in eq 8: where η represents the efficiency of power utilization.EP is the price of electricity, and C is the constant representing the contribution of factors, except the power consumption.Among the power consumptions, W comp usually occupies the major ratio as is depicted in eq 9: where n is the molar amount, R is the universal gas constant, and Z is the compressibility factor.P 0 and P a are the pressures before and after compression, respectively.In this study, W pump is also viewed as a constant owing to its limited contribution to the total power consumption as well as the marginal effect that comes from the viscosity. 31Additionally, W blow should also be positively related to the Q value.Therefore, for the same CO 2 /CH 4 separation process using different absorbents, eq 7 can be simplified into eq 10 with the consideration of eqs 8 and 9: where C 1 and C 2 are the constants.
Based on the definition of RAA, a small RAA value only reflects a poor CO 2 /CH 4 separation performance, so, it is undesirable to correlate the cost of CO 2 /CH 4 separation with the RAA value directly.Therefore, the ratio of CO is depicted in eq 11.
For the CO 2 /CH 4 separation using the physical absorbent and H 2 O, the value of Q Q / H O absorbent 2 can be described in eq 12: where CO 2 mass-transfer flux (J CO 2 ) can be depicted in eq 13. 14,15 Based on eqs 1,12 and 13, it can be inferred that the value of is equal to that of the reciprocal of RAA, and eq 11 can be converted into eq 14: where A and B are constants.
According to eq 14, the relationship between the value of with the reciprocal of RAA should be linear, and a generalized equation between the RAA index and the cost of CO 2 /CH 4 separation can be established, i.e., the cost can be predicted from RAA.

Systematic Screening and Evaluation.
Based on RAA and the generalized equation between the RAA index and the cost of CO 2 /CH 4 separation combined with the COSMO-RS prediction, a systematic method to screen and evaluate potential ILs for CO 2 /CH 4 separation was proposed, as described below and illustrated in Figure 1.In this study, 293.15K was chosen as the temperature in screening ILs with COSMO-RS, while the screening and evaluating ILs at other temperatures can also be performed similarly.
Step 1: property prediction using COSMO-RS.To calculate RAA at 293.15 K, the values of ρ, μ, H CO 2 , and H CH 4 in 2009 ILs (CO 2 solubility in ILs is dominant by physical interaction) formed by 41 cations and 49 anions, with structures, names, and abbreviations as listed in Tables S1 and S2, were predicted based on the COSMO-RS method, where H CO 2 and H CH 4 were calculated using eq 15: 33 = H yP T P y where x i and y i represent the mole fractions of gas i (CH 4 or CO 2 ) in the liquid and gas phases, respectively.φ i is the fugacity coefficient of gas i (CH 4 or CO 2 ) in the gas phase, and P is the total pressure.γ i is the activity coefficient of gas i (CH 4 or CO 2 ) in ILs, and i is the infinite dilution activity coefficient of gas i (CH 4 or CO 2 ) in ILs, and P i s is the saturated vapor pressure of gas i.Within COSMO-RS, P i s is calculated using Antoine equation, 34 and i is predicted. 21,35It should be mentioned that the expression of eq 15 in COSMO-RS to calculate H i is not rigorous, 36 while the previous study evidenced that eq 15 could be used to predict H and screen ILs reliably. 37

C
Step 2: screening ILs with the RAA index.In this step, ILs were screened using the RAA index, and ILs with RAA greater than one were obtained.Then, the top 10 ILs were screened.
Step 3: cost estimation of the CO 2 /CH 4 separation.To quantify the potential of IL-based technology and further verify the reliability of the RAA index, the techno-economic analysis of CO 2 /CH 4 separation using the screened top 1 and 2 ILs was conducted, and the detailed simulation and estimation are described in the following section.Particularly, the cost of CO 2 /CH 4 separation obtained by running the detailed simulation was compared with that predicted by using the generalized linear equation.
2.4.Process Simulation and Cost Estimation.2.4.1.Process Flow of CO 2 /CH 4 Separation.The commercial software Aspen Plus (V11.0) was utilized for the process simulation of CO 2 /CH 4 separation by using the rate-based approach.CO 2 /CH 4 separation using HPWS was extensively simulated in our previous study, 31 and the process and equipment size as well as the operating conditions were applied for ILs in this study.Figure 2 illustrates the process flow, and Table 1 details the parameters and operating conditions of the absorption/desorption towers.For the purpose of this simulation, it is assumed that the feed-gas only contains CH 4 and CO 2 , as impurities like H 2 S and H 2 O are removed prior to the units of CO 2 /CH 4 separation.Additionally, the raw biogas is 60 vol % CH 4 + 40 vol % CO 2 , and the CH 4 purity in bio-CH 4 after purification is expected to exceed 97 vol %.
2.4.2.Properties of ILs.The critical properties (T c , P c , V c , and Z c ), the acentric factor (ω), and the normal boiling temperature (T b ) of ILs were estimated using the group contribution method. 38Meanwhile, the molar volume, viscosity, surface tension, and heat capacity of the pure ILs were predicted with the COSMO-RS method, and the temperature-dependent parameters of these properties were obtained by the empirical equation correlations.It should be mentioned that the properties of ILs predicted with the COSMO-RS method are only at atmospheric pressure, while it is still reasonable to neglect the pressure effect on their properties under the operating pressure of 8.0 bar owing to the insignificant influence of the pressure. 39Additionally, the temperature-dependent H i in ILs was linearly interpolated according to those predicted by using COSMO-RS.
2.4.3.Cost Estimation.The total annual cost (TAC) includes the annual capital cost (ACC) as well as the operating and maintenance cost (OMC).ACC is calculated by the total capital cost (TCC) with eq 16: where i and n are the interest rate and project life, respectively.In this study, the interest rate is assumed as 0.09, and the project life as well as plant's annual operating time are 15 years and 8600 h, respectively. 31,40CC and OMC were obtained from the equipment cost (EC), which was achieved in our previous study. 40EC was estimated by Guthrie's method 41 as illustrated in eq 17: where f mp is the material and pressure correction factor, f m is the module factor based on the size of the equipment, and PEC is the bare cost of the purchased equipment.Based on the method of Scholz et al., 42 the values of f mp and f m were determined by the type of equipment.
For the absorber, desorber, and flash tank, the costs were obtained using the parameters of height (l) and diameter (d) with eq 18.Meanwhile, eq 19 was used to calculate the cost of the compressor, pump, heat exchange, and turbine, where S represents the characteristics of the equipment, such as electric power and heat exchange area.All of these parameters were obtained from Aspen Plus.
= i k j j j j j y where C 0 is the reference cost, and S 0 , l 0 , and d 0 are the reference size characteristic values for the equipment.is a linear correlation with the reciprocal of RAA, where A and B represent the intercept and slope of the linear equation, respectively.To determine A and B, in this study, DEPG, PC, H 2 O, and 50.0 wt % aqueous choline chloride/urea (ChCl/Urea) (molar ratio = 1:2) were selected, where their properties as well as the corresponding CO 2 /CH 4 separation cost were taken from the literature. 29As shown in Figure 3   It can be seen that all μ values of ILs in Figure 4 are greater than those of traditional absorbents at the same temperature, such as DEPG (7.58 mPa•s), PC (2.77 mPa•s), H 2 O (1.02 mPa•s), and 50.0 wt % aqueous ChCl/Urea (molar ratio = 1:2) (2.84 mPa•s).Usually, a larger μ value leads to a greater CO 2 mass-transfer resistance that is harmful to the CO 2 /CH 4 separation. 21Meanwhile, as depicted in Figure 4c,d 4c,d seem similar, which can be explained that the Henry's constant is proportional to the reciprocal of gas solubility, where the CO 2 and CH 4 solubilities in ILs are closely related to the molar volume (specifically free volume) of ILs. 433.3.IL Screening.In this section, ILs were screened using the RAA index, which was compared with those using other indexes to further highlight the significance of the RAA index.

Generalized Equation for
3.3.1.IL Screening Using RAA.After the prediction of IL properties using COSMO-RS, the RAA values of 2009 ILs at 293.15 K were calculated using eq 6 based on the values of M w , ρ, μ, H   [Emim][TCB], [Mpy][TCB], [Epy][TCB], and [Pmim][TCB] are 4.24, 4.17, 3.82, 3.69, 3.57, 3.38, 3.31, and 2.85, respectively.Therefore, both the cation and anion affect the RAA values, and the effect of the anion may be more significant, where the cyanide anion is promising.On the other hand, it should be mentioned that the high viscosity is a key challenge, limiting the CO 2 /CH 4 separation performance using the physical ILs, 11 while the physical ILs can still achieve the better CO 2 /CH 4   2 and D CO 2 are described in Figure 5, where all ILs are divided into three different regions, (1), (2), and (3) in Figure 5, representing those with better thermodynamic performance, better combination of thermodynamic and kinetic performances, and better kinetic performance, respectively.When S K / CO /CH H,CO 2 are closely related to the CO 2 solubility in the ILs, which is consistent with that the halogen anion plays an important role in the CO 2 solubility in the physical absorption ILs. 44hen D CO 2 was used for the criterion, the top 10 ILs were obtained in the region (3), which is mainly owing to their relatively low viscosity (21.Based on the above results and compared with those in Section 3.3.1, the screening results based on the individual thermodynamic or kinetic properties are obviously different from those obtained by using the RAA index.Therefore, neither thermodynamic nor kinetic properties can be solely used to screen and evaluate the potential ILs for CO 2 /CH 4 separation.On the contrary, the top 10 ILs in region (2) are the same as those obtained by the RAA index.This is reasonable, as RAA is indeed an index considering both the thermodynamic and the kinetic properties.Additionally, to further confirm the contribution of properties on the RAA index, the relationship between M w , ρ, μ, H CO 2 , and H CH 4 in 152 ILs with the RAA index was described using the Pearson correlation coefficient (PCC). 45As shown in Figure S1, the largest absolute PCC value between viscosity and RAA index (PCC = −0.41)was observed, demonstrating its key contribution on the RAA index in the studied conditions.S5, and the temperature-dependent parameters of molar volume, viscosity, surface tension, and heat capacity are described in Table S6.
For the process simulation of CO 2 /CH 4 separation using [Emmim][TCB] and [Empyr][TCB], the vapor phase is assumed to be CO 2 and CH 4 owing to the negligible vapor pressure of ILs.The vapor−liquid equilibrium was described using Henry's law, and the corresponding parameters for Henry's constants of CO 2 and CH 4 in [Emmim][TCB] and [Empyr][TCB] are described in Table 3.Additionally, the parameters of H 2 O for the HPWS technology were taken from the Aspen Plus software.In this study, the HPWS technology was selected as the reference, and the same upgrading process and the size of equipment were employed to evaluate the CO 2 / CH 4 separation performance of [Emmim][TCB] and  [TCB] are applied as the absorbents, i.e., the CO 2 /CH 4 capacities increase 1.66 and 1.48 times, respectively.On the other hand, the loss of CH 4 is also increasing, primarily due to the higher CH 4 solubilities in [Emmim][TCB] and [Empyr][TCB] compared to that of H 2 O. 29 Additionally, as illustrated in Figure 6b, the average energy usage is much lower for the IL-based processes owing to the rapidly increased CO 2 /CH 4 capacity.
Furthermore, the cost of CO 2 /CH 4 separation was also estimated and compared with the HPWS technology.For the cost estimation, the prices of [Emmim][TCB] and [Empyr]-[TCB] were assumed to be 34000 $•ton −1 with industrial-scale production, and ILs were not replaced in the life cycle owing to their low evaporation and degradation losses. 46As shown in Figure 7 mixture, respectively, and their corresponding deviations from those using process simulation are 24.9% and 27.0%.These deviations could be ascribed to the difference in wettability of ILs on the packing materials, i.e., the effects of surface tension of ILs and the different separation conditions (i.e., the composition of feed gas, the amount of IL circulation, and the CO 2 /CH 4 capacity) on the δ value.On the other hand, the above deviations are still acceptable for the industrial application.
Overall, the RAA index demonstrates its reliability in screening and evaluating the absorbents for CO 2 /CH 4 separation, and the selected ILs also show great potential for CO 2 /CH 4 separation.However, our future work will address four important aspects: (1) several factors like separation target, technical process, and operating conditions affect the cost of CO 2 /CH 4 separation, and they should be well considered in a modified RAA index to predict the cost of CO 2 /CH 4 separation; (2) the advantages of the selected [Emmim][TCB] and [Empyr][TCB] on the CO 2 /CH 4 separation cost were estimated based on the properties predicted using the COSMO-RS method, while its reliability and detailed process simulation should be performed according to the experimental data points; (3) the modified RAA index describing the CO 2 separation performance using the chemical ILs will be developed with the consideration of desorption enthalpy; (4) the reliability of RAA index should be further confirmed and optimized according to the experimental or industrialized results.The units of H and T are bar and K, respectively.

CONCLUSIONS
A novel index named "relative absorption ability" (RAA) was proposed to facilitate the screening of promising candidate absorbents for CO 2 /CH 4 separation and the prediction of the cost of CO 2 /CH 4 separation with the RAA index.The two ILs with the highest RAA values were identified as promising candidates among the 2009 ILs.Process simulation and cost estimation for the CO 2 /CH 4 separation using promising candidates were performed.
The cyanide anion of ILs plays an important role in the RAA index, and 1-ethyl-2,3-dimethyl-imidazolium tetracyanoborate ([Emmim][TCB]) and 1-ethyl-1-methyl-pyrrolidinium tetracyanoborate ([Empyr][TCB]) are promising candidates with the highest RAA values.The costs of CO 2 /CH 4 separation using [Emmim][TCB] and [Empyr][TCB] decrease by 53.9% and 51.9% compared to that of H 2 O, respectively, and the deviations between the process simulation and the predictions from RAA are only 24.9% and 27.0%.The detailed analysis in this study confirms the reliability of the RAA index to screen promising absorbents and to predict the cost for CO 2 /CH 4 separation.

Figure 1 .
Figure 1.Methodology was used to screen and evaluate potential ILs for CO 2 /CH 4 separation.

3. 4 .
Cost Estimation of CO 2 /CH 4 Separation.[Emmim][TCB] and [Empyr][TCB] were identified as the top two ILs with the largest RAA, and thus they were selected for the process simulation to evaluate their technical potentials for CO 2 /CH 4 separation and further verify the reliability of RAA.In the process simulation, the values of T c , P c , V c , Z c , T b , and ω of [Emmim][TCB] and [Empyr][TCB] are listed in Table
, the average costs of CO 2 /CH 4 separation using H 2 O, [Emmim][TCB], and [Empyr][TCB] are 0.206, 0.095, and 0.099 $•N•m −3 for the CO 2 /CH 4 mixture, respectively.This means the average costs of CO 2 /CH 4 separation using ILs as the absorbents decrease by 53.9% and 51.9% compared to that of H 2 O, respectively.Therefore, IL-based technology shows great potential for CO 2 /CH 4 separation.On the other hand, as described in Figure 7, the RAA index values of H 2 O, [Emmim][TCB], and [Empyr][TCB] are 1, 4.24, and 4.17, respectively, which is consistent with the trend of CO 2 /CH 4 separation cost.Meanwhile, based on the prediction from the RAA index using the linear equation, the costs of CO 2 /CH 4 separation using [Emmim][TCB] and [Empyr][TCB] are 0.071 and 0.072 $•N•m −3 CO 2 /CH 4

Figure 7 .
Figure 7. Cost estimation using HPWS and IL-based technology for CO 2 /CH 4 separation as well as the corresponding RAA index values (ACC: annual capital cost; OMC: operation and maintenance cost).

G
and operating conditions was proposed in this study, where H 2 O is a widely used physical absorbent for CO 2 /CH 4 separation.
2 /CH 4 separation costs based on an absorbent to that of H 2 O ( 2 ) under the same technical process

Table 1 .
Parameters of the Packed Absorption and Desorption Towers a reliably predict the cost of the CO 2 /CH 4 separation based on the properties of absorbents.In this study, ρ, μ, H CO 2 , and H CH 4 at 293.15 K for 2009 ILs were predicted from COSMO-RS, and the results are summarized in Table S3 and illustrated in Figure 4.The values of ρ, μ, H CH 4 are ranging from 0.83 to 2.10 g•cm −3 , 21.16− 13967.88mPa•s, 4.73−69.43bar, and 66.00−3328.25 bar, respectively, where the values of μ and H a HETP: the height equivalent of a theoretical plate.Industrial & Engineering Chemistry Research https://doi.org/10.1021/acs.iecr.4c01658Ind. Eng.Chem.Res.XXXX, XXX, XXX−XXX D index can 3.2.Predictions of IL Properties Using COSMO-RS.CH 4 change obviously.
value that is beneficial to the CO 2 / CH 4 separation.Additionally, the distributions of H , the H CO 2 values are much smaller than those of values, resulting in a relatively high S CO /CH 2 4

Table 2 .
ILs with the Top 10 RAA Values and Their Properties at 293.15 K