Carbon Capture from Biogas by Deep Eutectic Solvents: A COSMO Study to Evaluate the Effect of Impurities on Solubility and Selectivity

: Deep eutectic solvents (DES) are compounds of a hydrogen bond donor (HBD) and a hydrogen bond acceptor (HBA) that contain a depressed melting point compared to their individual constituents. DES have been studied for their use as carbon capture media and biogas upgrading. However, contaminants’ presence in biogas might affect the carbon capture by DES. In this study, conductor-like screening model for real solvents (COSMO-RS) was used to determine the effect of temperature, pressure, and selective contaminants on ﬁve DES’ namely, choline chloride-urea, choline chloride-ethylene glycol, tetra butyl ammonium chloride-ethylene glycol, tetra butyl ammonium bromide-decanoic acid, and tetra octyl ammonium chloride-decanoic acid. Impurities studied in this paper are hydrogen sulﬁde, ammonia, water, nitrogen, octamethyltrisiloxane, and decamethylcyclopentasiloxane. At inﬁnite dilution, CO 2 solubility dependence upon temperature in each DES was examined by means of Henry’s Law constants. Next, the systems were modeled from inﬁnite dilution to equilibrium using the modiﬁed Raoults’ Law, where CO 2 solubility dependence upon pressure was examined. Finally, solubility of CO 2 and CH 4 in the various DES were explored with the presence of varying mole percent of selective contaminants. Among the parameters studied, it was found that the HBD of the solvent is the most determinant factor for the effectiveness of CO 2 solubility. Other factors affecting the solubility are alkyl chain length of the HBA, the associated halogen, and the resulting polarity of the DES. It was also found that choline chloride-urea is the most selective to CO 2 , but has the lowest CO 2 solubility, and is the most polar among other solvents. On the other hand, tetraoctylammonium chloride-decanoic acid is the least selective, has the highest maximum CO 2 solubility, is the least polar, and is the least affected by its environment. upgrading systems. The fundamental understanding of the solvents and their behavior under various temperatures, pressures, and inﬂuences from contaminants show that a complex web of variables exists that must be considered when choosing a DES for any application. It has been shown that the polarity of a solvent, its size, and its constituents are factors contributing to solubility, but the main determinant is the HBD selection. The signiﬁcance of the varied contaminant concentrations is providing a method to model the accumulation that occurs within recycled solvent, where not all contaminants will be purged through the regeneration process. This study is a glimpse into the potential lifetime of the solvent, and how each solvent will be suited for a speciﬁc feed gas composition. The results show that the DES are affected by these contaminants in varying degrees in order of most to least, as follows: ChCl:U, ChCl:EG, N4Cl:EG, N4Br:DA, and N8Br:DA. This trend is the same for polarity and the reverse of alkyl chain length, and also suggests the order in which the length of time the solvents will be able to operate


Introduction
Anaerobic digestion (AD) is the process of breaking down organic substances in anoxic conditions by bacteria [1]. Organic macro-molecules such as fats, carbohydrates, and proteins are digested into micro-molecules during AD, which results in a nutrient-rich solid for plants (fertilizer) and biogas [2]. This process occurs naturally in landfills, but also in a controlled environment in equipment called anaerobic digestors. The feedstock for AD are materials that are otherwise considered waste, such as agricultural waste, manure, organic waste from animal processing plants, food waste, and many others [3,4]. The growing adoption of AD offers a new approach to these waste streams which supports a recycle economy that increases market efficiency and bolsters the renewable energy industry as the globe shifts towards green fuel.
During AD, several reactions occur, but the process can be categorized into four stages: hydrolysis, acidogenesis, acetogenesis, and methanogenesis. During hydrolysis, long-chain polymers like cellulose are hydrolyzed into fermentable forms like glucose.

Composition of Biogas
The standard percent ranges of biogas composition used in this study have been listed in Table 1. The variance of the composition depends upon several factors surrounding the AD process, such as temperature, retention time, kinetics, and feed stock composition [30]. Table 1 shows the components studied with their respective abbreviations for the investigation and their industrial compositions.  Table 2 lists the five common DES considered for this study, including choline chlorideurea, choline chloride-ethylene glycol, tetra butyl ammonium chloride-ethylene glycol, tetra butyl ammonium bromide-decanoic acid, and tetra octyl ammonium chloride-decanoic acid, along with their components and component mixing ratios. The solvents studied are termed quaternary ammonium salts due to the structure of the HBD. The quaternary ammonium salts are relatively cheap, safe for the environment, and naturally derived [16,36,37]. The specific solvents were chosen as an attempt to represent a large range of their class by means of carbon chain length of the quaternary ammonium salts and commonly paired HBDs.

COSMO Simulation
COSMO is a quantum modeling software that determines thermodynamic properties using density functional theory (DFT). To determine the thermodynamic properties, the HBAs and HBDs are modeled using TurboMoleX software. The impurities are selected from the COSMO library. HBAs and HBDs are then mathematically evaluated for their natural geometrical lowest energy state and conformers. COSMO was then used for all thermophysical property calculations. TurboMoleX ® was used to generate all molecular sigma profiles, conformers, and data not already found in the included database. TZVP (tri-zeta-valence-polarized) settings were used with default numerical grid of m3 and BP86 functions. COSMOThermX ® was used for all thermodynamic property calculations. These properties were used to calculate sigma profile of the molecules, where charge density is plotted with charge of the molecule. Here, the molecule is differentiated into charge density segments, with each segment representing areas with charge density ranging from −0.3 to +0.3 e/Å 2 . The charge density segments are plotted to form the sigma profiles. The data from the sigma profiles are used to model microscopic molecular surface charge interactions between analytes, then a statistical thermodynamic procedure is carried out to derive macroscopic thermodynamic properties from the generated information [38]. The base values generated are chemical potentials of the systems' constituents, these are then applied to thermodynamic calculations of Henry's Law coefficient and activity coefficients. Determination of the solubility and selectivity of the systems was carried out by COSMO-RS, whose results are based upon the chemical potential generated by COSMO-RS.

Sigma Profiles of DES's, Polar, and Non-Polar Molecules
A sigma profile is a distribution function that relates the surface area of a molecule to the charge density of the surface [39]. In this study, sigma profiles are used to understand the electrostatic interactions between DES and selected polar and nonpolar molecules. The sigma profiles explain the trends of solubility and selectivity for a DES-based extraction. To generate these profiles, COSMO creates incremental segments of the studied molecule, which are then organized based upon surface charge density. The area under these sigma profile curves gives the total surface area of the studied molecule. Peaks between ±0.0082 e/Å 2 charge density indicate that the molecule readily undergoes van der Waals interactions [39,40]. Peaks outside of this range indicate hydrogen bonding as the preferred interaction due to polarity [40].
Sigma profiles are useful for determining how molecules will interact in a solventsolute system. From a range of sigma profiles, appropriate solvents may be identified for a given molecule based on how the charge densities between the two profiles align. A highly polar solvent that has significant charge density in the HBA region (−0.0082 e/Å 2 ) could be expected to have a high affinity for a solute that shows a significant charge density in the HBD region (+0.0082 e/Å 2 ). The same is true for two molecules that have significant charge densities in the non-polar region of the sigma profile (±0.0082 e/Å 2 ). This logic can be used to determine if an impurity will have a lesser or higher affinity than a solute, giving rise to competition for the solvents' binding sites.
In Figure 1, the sigma profiles of each DES are displayed. The order of the solvents from the most to the least polar and, therefore, most available for hydrogen bonding to least available, are as follows: ChCl:U > ChCl:EG > N4Cl:EG > N4Br:DA > N8Br:DA. The peaks between 0.015 and 0.002 e/Å 2 are from the halogens associated with each solvent. It is observed that by changing the HBD groups as with the tetrabutylammonium variants, the sigma structure is significantly altered, which lends to the notion of DES properties being highly tunable [16,41]. Sigma profiles of non-polar gases can be seen in Figure 2. For the non-polar gases, the key difference in the sigma profiles of the molecules is the charge density distribution of CO2 vs. N2 vs. CH4. N2 and CH4 have most of their area concentrated around the zerox-axis compared to CO2. CO2 is considered a non-polar gas, since the distribution of the charges for CO2 are weighted between ±0.0082 e/Å 2 . However, CO2 can be influenced by its environment to make it behave more like a polar molecule and participate in hydrogen bonding or behave more like a non-polar molecule and participate in van der Waals in- Sigma profiles of non-polar gases can be seen in Figure 2. For the non-polar gases, the key difference in the sigma profiles of the molecules is the charge density distribution of CO 2 vs. N 2 vs. CH 4 . N 2 and CH 4 have most of their area concentrated around the zero-x-axis compared to CO 2 . CO 2 is considered a non-polar gas, since the distribution of the charges for CO 2 are weighted between ±0.0082 e/Å 2 . However, CO 2 can be influenced by its environment to make it behave more like a polar molecule and participate in hydrogen bonding or behave more like a non-polar molecule and participate in van der Waals interactions. The potential for this behavior can be seen in the sigma profile as the charge density is concentrated closely to the ±0.0082 e/Å 2 boundary. It is also understood that CO 2 contains two polar bonds, but the linear structure of the molecule creates a net-zero dipole moment. However, in a polar environment such as CO 2 in water, it behaves as an acid gas. Sigma profiles of non-polar gases can be seen in Figure 2. For the non-polar gases, the key difference in the sigma profiles of the molecules is the charge density distribution of CO2 vs. N2 vs. CH4. N2 and CH4 have most of their area concentrated around the zerox-axis compared to CO2. CO2 is considered a non-polar gas, since the distribution of the charges for CO2 are weighted between ±0.0082 e/Å 2 . However, CO2 can be influenced by its environment to make it behave more like a polar molecule and participate in hydrogen bonding or behave more like a non-polar molecule and participate in van der Waals interactions. The potential for this behavior can be seen in the sigma profile as the charge density is concentrated closely to the ±0.0082 e/Å 2 boundary. It is also understood that CO2 contains two polar bonds, but the linear structure of the molecule creates a net-zero dipole moment. However, in a polar environment such as CO2 in water, it behaves as an acid gas. Regarding polar gases, only gases reported as impurities of biogas are selected for this study. There exist large variations in profiles among this group, as seen in Figure 3. The most notable impurity is water, which reaches the farthest among the other gases on the charge density and is relatively symmetric, which concludes its adaptability in assuming the roles as a Lewis acid or base. Acetone has a large peak near the 0 e/Å 2 yet behaves as a Lewis base due to the considerable peak beyond 0.01 e/Å 2 . H 2 S is relatively evenly dispersed along the x-axis, suggesting it can participate in both van der Waals interactions and hydrogen bonding depending upon its environment. SO 2 is heavily concentrated around the boundaries of ±0.0082 e/Å 2 , and as such, would be expected to have lower solubility among the less polar DES. Ammonia is a weak base, and this is indicated in the large peaks near the HBA region (−0.0082 e/Å 2 ) but is capable of hydrogen donating interactions, as seen in the trailing area in the positive region of the plot as it extends to nearly 0.03 e/Å 2 . drogen bonding or van der Waals interactions. Due to this and the generated sigma profiles, it stands to reason that a DES containing significant amounts of a polar or non-polar contaminant may change the level of solubility of CO2 within that system. For example, when considering the relatively polar profile of ChCl:U, it could be reasoned that if it were to accumulate strong polar molecules like water then the effect of hydrogen bond affinity for CO2 would be enhanced. Thus, resulting in a higher selectivity for CO2 than CH4 in this particular solvent.

Selectivity for CO2 over CH4 by DES in Infinite Dilution
Considering the valuable product of biogas upgrading is methane, the selectivity of a solvent to solvate is of significant importance. The selectivity of CO2 over CH4 was first studied for various DES at infinite dilution by Henry's Law calculations and presented in As discussed previously, CO 2 can be influenced by its environment to partake in hydrogen bonding or van der Waals interactions. Due to this and the generated sigma profiles, it stands to reason that a DES containing significant amounts of a polar or nonpolar contaminant may change the level of solubility of CO 2 within that system. For example, when considering the relatively polar profile of ChCl:U, it could be reasoned that if it were to accumulate strong polar molecules like water then the effect of hydrogen bond affinity for CO 2 would be enhanced. Thus, resulting in a higher selectivity for CO 2 than CH 4 in this particular solvent.

Selectivity for CO 2 over CH 4 by DES in Infinite Dilution
Considering the valuable product of biogas upgrading is methane, the selectivity of a solvent to solvate is of significant importance. The selectivity of CO 2 over CH 4 was first studied for various DES at infinite dilution by Henry's Law calculations and presented in Figure 4. Henry's Law constants are used to study the solubility of CO 2 vs. CH 4 for a pure DES regarding the first molecules of gas and how they selectively enter the DES and are only valid at low concentrations of gases in the DES. At room temperature and at infinite dilution, the largest selectivity of 4.7 can be observed in ChCl:U. Here, approximately 4.7 moles of CO 2 are expected to be absorbed per mole of CH 4 . The least selective solvent in this model is N8Br:DA at approximately 1.75. The remaining solvents show a slight trend up from N8Br:DA. The data follows a rational trend of selectivity to size, with the smallest DES molecular constituents displaying the highest selectivity. However, this does not explain the dramatic increase in selectivity between ChCl:EG and ChCl:U, considering they are nearly the same mass (Table 2) and considering the selectivity is molar-based. This behavior could be explained from sigma profiles. Figure 1 shows ChCl:U as being the most likely to participate in hydrogen bonding of the five solvents and N8Br:DA as most likely to participate in van der Waals interactions. As previously mentioned, CO 2 can become polarized in a polar environment, which makes it much more likely to bind with ChCl:U than methane. In a relatively non-polar environment like N8Br:DA, both molecules will behave non-polar and bind closer to a 1:1 ratio. The values for simulated vs. experimental solubilities of CO 2 in ChCl:U at 5.6 MPa and 303.15 K are reported as 5.7 and 3.56 (mol/kg), respectively. The difference was reported to be caused by poorly optimized DES structures [42]. Xie et al. and Ji et al. report experimental solubilities of CO 2 in ChCl:U at 308.2 K and 0.651 and 0.678 p/MPa respectively, as 0.05 and 0.045 mole fraction, respectively. The solubility parameters were studied in this paper at a highest-pressure condition of 0.6 MPa and 25 • C, and for ChCl:U, the solubility of CO 2 at these conditions is 0.074. The discrepancies between experimental and calculated values could be attributed by the limitations of COSMO to fully model all solvation phenomena that occur, such as hole theory, induced polarity of solutes, and induced conformers of analytes. The selectivity appears to be mostly influenced by the polarity of the DES at room temperature. Similar observation was found in the literature, where Slupek et al. [10] compared the sigma profiles of their studied DES with solutes and determined that the overlapping regions between the two plots suggested interaction compatibility.
are nearly the same mass (Table 2) and considering the selectivity is molar-based. This behavior could be explained from sigma profiles. Figure 1 shows ChCl:U as being the most likely to participate in hydrogen bonding of the five solvents and N8Br:DA as most likely to participate in van der Waals interactions. As previously mentioned, CO2 can become polarized in a polar environment, which makes it much more likely to bind with ChCl:U than methane. In a relatively non-polar environment like N8Br:DA, both molecules will behave non-polar and bind closer to a 1:1 ratio. The values for simulated vs. experimental solubilities of CO2 in ChCl:U at 5.6 MPa and 303.15 K are reported as 5.7 and 3.56 (mol/kg), respectively. The difference was reported to be caused by poorly optimized DES structures [42]. Xie et al. and Ji et al. report experimental solubilities of CO2 in ChCl:U at 308.2 K and 0.651 and 0.678 p/MPa respectively, as 0.05 and 0.045 mole fraction, respectively. The solubility parameters were studied in this paper at a highest-pressure condition of 0.6 MPa and 25 °C, and for ChCl:U, the solubility of CO2 at these conditions is 0.074. The discrepancies between experimental and calculated values could be attributed by the limitations of COSMO to fully model all solvation phenomena that occur, such as hole theory, induced polarity of solutes, and induced conformers of analytes. The selectivity appears to be mostly influenced by the polarity of the DES at room temperature. Similar observation was found in the literature, where Slupek et al. [10] compared the sigma profiles of their studied DES with solutes and determined that the overlapping regions between the two plots suggested interaction compatibility. The selectivity thus far has been discussed at 25 °C, however, temperature of the biogas could be as high as 55 °C depending on mesophilic or thermophilic microorganisms. Therefore, the effect of temperature on selectivity at infinite dilution is of practical interest. Figure 5 has shown the effect of temperature on Henry's Law constant, which is analogous to selectivity. Due to the unit of the Henry constant, the lower values are associated with higher solubility. With the increase of temperature, the Henry's Law constant increases. Interestingly, for the same HBA (e.g., ChCl), exceptional deviations in Henry's Law constant can be found for different HBD (e.g., urea versus ethylene glycol). This is probably due to the smaller HBA chain lengths that might have a naturally smaller affinity for CO2 [41]. However, the induced polarity phenomena have a stronger impact on the solubility The selectivity thus far has been discussed at 25 • C, however, temperature of the biogas could be as high as 55 • C depending on mesophilic or thermophilic microorganisms. Therefore, the effect of temperature on selectivity at infinite dilution is of practical interest. Figure 5 has shown the effect of temperature on Henry's Law constant, which is analogous to selectivity. Due to the unit of the Henry constant, the lower values are associated with higher solubility. With the increase of temperature, the Henry's Law constant increases. Interestingly, for the same HBA (e.g., ChCl), exceptional deviations in Henry's Law constant can be found for different HBD (e.g., urea versus ethylene glycol). This is probably due to the smaller HBA chain lengths that might have a naturally smaller affinity for CO 2 [41]. However, the induced polarity phenomena have a stronger impact on the solubility outcome. This is due to CO 2 being naturally non-polar, as seen in Figure 2. Thus, the magnitude of the dipole moment of a solvent will determine the affinity CO 2 will have for it.
Clean Technol. 2021, 3, FOR PEER REVIEW 8 outcome. This is due to CO2 being naturally non-polar, as seen in Figure 2. Thus, the magnitude of the dipole moment of a solvent will determine the affinity CO2 will have for it.

Effect of Pressure on Selectivity and Solubility of CO2 in Various DES
Selectivity of CO2 over CH4 in various DES at infinite dilution provides valuable information on how polarity of DES and solute affect the selectivity. However, Henry's Law is only valid for infinite dilution, which might be misleading for carbon capture from biogas, as CO2 concentration in biogas is often high. Therefore, Raoult's Law might provide more accurate information of the solubility and selectivity. In this study, modified Raoult's Law calculations are used to determine the maximum solubilities for a pure solvent by studying the last molecules to enter the system at any concentration. Understanding the effect pressure has on a system and how its constituents behave away from ideality is crucial to its design parameters. Figure 6 investigates the last molecules entering the system at equilibrium. It provides total saturation values for CO2 on the left axis and selectivity of CO2 vs. CH4 on the right axis at varying partial pressures in 40% increments, since this falls within the composition range for both CO2 and CH4, as shown in Table 1. The first observation in this Figure 6 is the increase in solubility of CO2 with increased pressure, regardless of solvent. The next is the same trend being seen in Figure 4 with respect to the solvent ordering of selectivity. This trend becomes significantly more pronounced when the system is closer to saturation. For example, the selectivity of ChCl:U at 1 bar is nearly 25 in Figure 6 compared to the Henry's Law calculations which were 4.7 in Figure  4. A possible explanation for this could be due to the solvent matrix becoming more of a polar environment as the holes fill with CO2 and CH4 has to squeeze into the smaller polarized spaces in order to occupy the solvent, which is not energetically favorable. The negative slopes of the selectivity analysis are due to the increase in pressure, as the molecules are forced into solvent, they become less selective. The more drastic change occurs within ChCl:U as the influence of polarity is overcome by the force of pressure, resulting in a non-linear relationship unlike the other less acidic solvents. The total capacity for CO2 varies significantly between pressures, and the resulting trends of the bars suggest that the effect on the solvents also vary significantly. As discussed previously, the order of solvents in their ability to solvate CO2 and the gaps in capacities are explained through alkyl-chain lengths [16], HBD selection, and the resulting polarity of these combinations with little effect from the halogens. The results here further confirm this by segregating the solvents into 3 visible groupings regarding solubility of CO2 of N8Br:DA and N4Br:DA, N4Cl:EG and ChCl:U, and ChCl:EG. The most significant finding from this grouping is the relative effects on solubility between HBA chain length and associated

Effect of Pressure on Selectivity and Solubility of CO 2 in Various DES
Selectivity of CO 2 over CH 4 in various DES at infinite dilution provides valuable information on how polarity of DES and solute affect the selectivity. However, Henry's Law is only valid for infinite dilution, which might be misleading for carbon capture from biogas, as CO 2 concentration in biogas is often high. Therefore, Raoult's Law might provide more accurate information of the solubility and selectivity. In this study, modified Raoult's Law calculations are used to determine the maximum solubilities for a pure solvent by studying the last molecules to enter the system at any concentration. Understanding the effect pressure has on a system and how its constituents behave away from ideality is crucial to its design parameters. Figure 6 investigates the last molecules entering the system at equilibrium. It provides total saturation values for CO 2 on the left axis and selectivity of CO 2 vs. CH 4 on the right axis at varying partial pressures in 40% increments, since this falls within the composition range for both CO 2 and CH 4 , as shown in Table 1. The first observation in this Figure 6 is the increase in solubility of CO 2 with increased pressure, regardless of solvent. The next is the same trend being seen in Figure 4 with respect to the solvent ordering of selectivity. This trend becomes significantly more pronounced when the system is closer to saturation. For example, the selectivity of ChCl:U at 1 bar is nearly 25 in Figure 6 compared to the Henry's Law calculations which were 4.7 in Figure 4. A possible explanation for this could be due to the solvent matrix becoming more of a polar environment as the holes fill with CO 2 and CH 4 has to squeeze into the smaller polarized spaces in order to occupy the solvent, which is not energetically favorable. The negative slopes of the selectivity analysis are due to the increase in pressure, as the molecules are forced into solvent, they become less selective. The more drastic change occurs within ChCl:U as the influence of polarity is overcome by the force of pressure, resulting in a non-linear relationship unlike the other less acidic solvents. The total capacity for CO 2 varies significantly between pressures, and the resulting trends of the bars suggest that the effect on the solvents also vary significantly. As discussed previously, the order of solvents in their ability to solvate CO 2 and the gaps in capacities are explained through alkyl-chain lengths [16], HBD selection, and the resulting polarity of these combinations with little effect from the halogens. The results here further confirm this by segregating the solvents into 3 visible groupings regarding solubility of CO 2 of N8Br:DA and N4Br:DA, N4Cl:EG and ChCl:U, and ChCl:EG. The most significant finding from this grouping is the relative effects on solubility between HBA chain length and associated HBD. N4Br:DA and N8Br:DA have relatively similar capacities for CO 2 that are significantly higher compared to N4Cl:EG. N4Br:DA finds a maximum ratio of approximately 1.9 over the CO 2 solubility of N4Cl:EG, where the alkyl chain lengths are the same but the HBD are different. However, N8Br:DA only finds a maximum approximate ratio of 1.08 over the CO 2 solubility of N4Br:DA, which displays a difference in alkyl chain length but the same HBD.
Clean Technol. 2021, 3, FOR PEER REVIEW 9 HBD. N4Br:DA and N8Br:DA have relatively similar capacities for CO2 that are significantly higher compared to N4Cl:EG. N4Br:DA finds a maximum ratio of approximately 1.9 over the CO2 solubility of N4Cl:EG, where the alkyl chain lengths are the same but the HBD are different. However, N8Br:DA only finds a maximum approximate ratio of 1.08 over the CO2 solubility of N4Br:DA, which displays a difference in alkyl chain length but the same HBD. Figure 6. Effect of pressure on selectivity of CO2 vs. CH4 and solubility of CO2 at equilibrium and 25 °C for each DES. Y-axis 1 is the solubility and y-axis 2 is the selectivity. The dotted lines coincide with y-axis 2 and the bars coincide with y-axis 1. The partial pressure is the same for CO2 and CH4.

Effect of Impurities on CO2 Solubility in Various DES
Effect of selected impurities on CO2 solubility of various DES at different temperatures under 3.6 bar pressure conditions are studied by solubilities. Analysis was performed on each DES to determine how the presence of contaminants within the feed gas, captured by the solvent, would affect the absorptive capacity for CH4 and CO2. This was performed on a wide range of contaminants found in Table 1 over three temperatures (25,37, and 55 °C) at ambient pressure and three mole fractions of contaminant within the solvent (1, 3, and 5 mol%). The solubilties were normalized to show the deviation from the maximum solubility of CO2 and CH4 at DES, with no contaminants.
Of the five DES, ChCl:U is the most affected to the presence of all the impurities within biogas, as can be seen in Table 3. With the increase of ammonia in biogas, the maximum solubility of CO2 and CH4 increase in ChCl:U. For instance, the values for CO2 at 37 °C are 1.01 and 1.03 for ammonia in ChCl:U at 1 and 5 mol%, respectively. However, the presence of all other contaminants decrease the maximum solubility of both CO2 and CH4 in ChCl:U. All contaminants produce a change greater than 5% from the base case, with the octa and deca siloxane compounds inciting the greatest changes. This finding is significant, as Jiang et al. [43] report an average concentration of siloxanes in untreated biogas reaching up to 2000 mg m 3 . It is observed that change in temperature produces minimal effect

Effect of Impurities on CO 2 Solubility in Various DES
Effect of selected impurities on CO 2 solubility of various DES at different temperatures under 3.6 bar pressure conditions are studied by solubilities. Analysis was performed on each DES to determine how the presence of contaminants within the feed gas, captured by the solvent, would affect the absorptive capacity for CH 4 and CO 2 . This was performed on a wide range of contaminants found in Table 1 over three temperatures (25, 37, and 55 • C) at ambient pressure and three mole fractions of contaminant within the solvent (1, 3, and 5 mol%). The solubilties were normalized to show the deviation from the maximum solubility of CO 2 and CH 4 at DES, with no contaminants.
Of the five DES, ChCl:U is the most affected to the presence of all the impurities within biogas, as can be seen in Table 3. With the increase of ammonia in biogas, the maximum solubility of CO 2 and CH 4 increase in ChCl:U. For instance, the values for CO 2 at 37 • C are The solvents with the HBD of ethylene glycol (in Supplementary Information Tables S1 and S2) show a positive effect from every contaminant except H 2 O, H 2 S, and SO 2 . The other contaminants show asymmetry with a weighted area around the HBA region, whereas H 2 O, H 2 S, and SO 2 are significantly more symmetrical regarding sigma profiles. A notable difference between the two DES with these HBD groups is the response to the contaminants at varying concentrations. At lower concentrations of the contaminants (1 mol%), N4Cl:EG is much more affected in terms of maximum CO 2 and CH 4 solubility compared to its ChCl:EG counterpart, but the opposite is true at higher concentrations. For example, at 25 • C, the CO 2 maximum solubility increases by 4% when octa makes up 1 mole percent of N4Cl:EG, however there is virtually no change when these same conditions are met for ChCl:EG as a value of 1 is reported. The trend found in ChCl:U between the temperature change and solubility change is not present in either of these DES.
The solvents with the HBD decanoic acid (N4Br:DA and N8Br:DA, Tables S3 and S4, respectively) show negative effects from all contaminants except siloxanes. Here, CH 4 solubility increases with the presence of octa and deca but CO 2 decreases with their presence. For these two DES, another similar trend follows regarding CO 2 and CH 4 solubility. The solubility varies little with contaminant mole percent, with nearly all changes being within 2%, with the exception of H 2 O and ammonia for N8Br:DA and H 2 O, ammonia, deca, and octa for N4Br:DA. At 1% contamination presence, the solubility of CO 2 in both DES start above 1 with higher solubility and decrease with increasing percentages of contaminant. Another trend to note is the slightly less negative effect the contaminants have upon N4Br:DA than N8Br:DA, whose main difference is their alkyl chain length.

Conclusions
The results of this study contain important preliminary data regarding the implementation of DES in biogas upgrading systems. The fundamental understanding of the solvents and their behavior under various temperatures, pressures, and influences from contaminants show that a complex web of variables exists that must be considered when choosing a DES for any application. It has been shown that the polarity of a solvent, its size, and its constituents are factors contributing to solubility, but the main determinant is the HBD selection. The significance of the varied contaminant concentrations is providing a method to model the accumulation that occurs within recycled solvent, where not all contaminants will be purged through the regeneration process. This study is a glimpse into the potential lifetime of the solvent, and how each solvent will be suited for a specific feed gas composition. The results show that the DES are affected by these contaminants in varying degrees in order of most to least, as follows: ChCl:U, ChCl:EG, N4Cl:EG, N4Br:DA, and N8Br:DA. This trend is the same for polarity and the reverse of alkyl chain length, and also suggests the order in which the length of time the solvents will be able to operate before regeneration is necessary, from least to most. The pressure study suggests the ideal operating environment is closer to atmospheric pressure considering selectivity but not for solubility. The selectivity at ambient temperature and pressure (STP) and infinite dilution are 4.7, 2.4, 2.2, 2.0, and 1.7 mol CO 2 /mol CH 4 for ChCl:U, ChCl:EG, N4Cl:EG, N4Br:DA, and N8Br:DA, respectively. However, the selectivity at STP and finite dilution conditions are 25.9, 13.6, 12.3, 11.1, and 9.7 mol CO 2 /mol CH 4 . For ChCl:U, the absorbance was decreased by the presence of deca at STP and 1, 3, and 5 mole % by 0.91, 0.81, and 0.74 respectively, from a normalized value of 1. The changes in the presence of CH 4 at STP and 1, 3, and 5 mole % are 1.00, 0.96, and 0.92, respectively. These solvents have been shown to behave differently to each other when subjected to differing environmental factors such as temperature and pressure. All of these factors point to high tunability and complexity for these solvents.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/cleantechnol3020029/s1, Table S1: Normalized values for solubility of CO 2 and CH 4 at various mole percentages in ChCl: EG and at varying temperatures. The values are normalized to fresh solvent solubilities of respective CO 2 and CH 4 ., Table S2: Normalized values for solubility of CO 2 and CH 4 at various mole percentages in N4Cl: EG and at varying temperatures. The values are normalized to fresh solvent solubilities of respective CO 2 and CH 4 ., Table S3: Normalized values for solubility of CO 2 and CH 4 at various mole percentages in N4Br: DA and at varying temperatures. The values are normalized to fresh solvent solubilities of respective CO 2 and CH 4 ., Table S4: Normalized values for solubility of CO 2 and CH 4 at various mole percentages in N8Br: DA and at varying temperatures. The values are normalized to fresh solvent solubilities of respective CO 2 and CH 4 .