2.1.1. Computational Studies

In this investigation, COSMO-RS calculations were carried out using ADF COSMO-RS software (SCM, Netherlands). The geometry optimization of all DESs were performed using the continuum solvation COSMO model at the BVP86/TZVP level of theory. This level of theory was selected due to proven high e fficiency and low computational costs [51]. The list of 23 DESs is presented in Table 2. The main thermodynamic parameters, i.e., the activity coe fficient, excess enthalpy, and Henry's constant were calculated based on previous studies [52,53]. The parameters were determined for model biogas composed of 64.9% of CH4, 31% of CO2, 3% of H2O and 1.04 of H2S, and 0.02% of hexamethyldisiloxane (L2), octamethyltrisiloxane (L3), and octamethylcyclotetrasiloxaan (D4), which represents the typical composition of biogas from wastewater treatment plants and landfills [8,54].



Henry's constant ( *KH*) was applied to systems in thermodynamic equilibrium. The *KH* links the solubility of solute impurities (*i*) to its partial pressure above the mixture (*pvap i* ). *KH* was calculated using Equation (1).

$$K\_H = \frac{1}{\mathcal{V}i\mathcal{P}\_i} \tag{1}$$

where γ*i* is the infinite dilute activity coe fficient of impurities (*i*), and *pvap i* is the vapor pressure of impurities (*i*).

The activity coefficient was calculated using Equation (2) and Equation (3).

$$\ln(\gamma\_i) = \frac{\mu\_i^{\text{solv}} - \mu\_i^{\text{pure}}}{RT} \tag{2}$$

where μ*pi* is the chemical potential of pure impurities (*i*), μ*ji* is the chemical potential of impurities in the liquid phase, *T* is the temperature (K), and the universal gas constant *R* = 8.314 J/mol.

The excess enthalpy of mixtures *H<sup>E</sup>* (kJ/mol) was calculated based on Gibbs-Helmholtz using Equation (3).

$$H^E = -T^2 \frac{\partial \left(\frac{\delta^E}{T}\right)}{\partial T} \tag{3}$$

where *T* is the temperature (K), and *G<sup>E</sup>* is the excess Gibbs free energy (kJ/mol).

2.1.2. Biogas Upgrading Technology Description

The scheme for the biogas upgrading technology described in this paper is presented in Figure 2. The physicochemical properties of DESs are similar to the most commonly used absorbents (i.e., amine or water), therefore, DESs can be applied in existing and currently used absorption installations. In order to better compare the benefits of DESs application in the absorption process, the size of the installations (absorption and desorption column, compressor, pump, blower, dryer, and heat exchangers) and the process streams (inlet biogas stream 813 m<sup>3</sup>/<sup>h</sup> and inlet air stream 403 m<sup>3</sup>/h) was adopted from previous studies [55,56].

**Figure 2.** Scheme for the biogas upgrading technology [55,56].

In the first stage, biogas stream is introduced into Dryer 1. Then, the biogas is passed directly to the heat exchanger, after which biogas is directed into the bottom part of the absorber (813 m<sup>3</sup>/h), which operates at a temperature of 20 ◦C, and pressure of 100 kPa. The biogas stream is introduced at the bottom of the absorber. The DES is introduced at the top of the column. The biogas and DES move through a counter-flow scrubbing column. In the column, the biogas comes into contact with a DES to dissolve the main impurities (L2, L3, D4, CO2, and H2S). This is a process of mass transfer of pollutants from the biogas phase to the liquid DES phase. The upgraded bio-methane is downloaded from the top of the absorber, drained again (Dryer 2), and compressed. The obtained renewable bio-methane can be directly injected into the distribution gas grid at 700 kPa. The biogas purification system also contains the stripper column, which is operated under a temperature of 115–125 ◦C and pressure of 140–170 kPa. Saturated DES from the absorption column is directed into the stripper column where

DES is purged with an inlet air stream (403 m<sup>3</sup>/h). Most of the impurities (L2, L3, D4, CO2, and H2S) are liberated into a concentrated air stream that exits at the top of the stripper column. The impurities stream is directed to the H2S, CO2, L2, L3, and D4 recovery system. The regenerated DES is cooled and returned to the absorber column.

#### 2.1.3. Cost and Economic Analysis

The cost simulations included an estimation of the total annual cost (*TAC*) of the biogas upgrading process. *TAC* included the annual capital investment cost (*ACIC*), and the annual operation and maintenance cost (OC and MC).

The *ACIC* was estimated based on the method of Scholz et al. [57] according to Equation (4).

$$ACIC = TCIC \frac{i(1+i)^n}{(1+i)^n - 1} \tag{4}$$

where *ACIC* is the annual capital investment cost, *TCIC* is the total capital investment cost, *i* is the interest rate (9%), and *n* is the depreciation period (15 years).

The *TCIC* was mainly estimated as the percentage value of the equipment cost (*EC*) [55]. The *EC* was estimated by Guthrie's method [58], according to Equation (5).

$$EC = PEC \left( f\_{mp} + f\_{\text{m}} - 1 \right) \tag{5}$$

where *EC* is the equipment cost, *PEC is*the bare purchased equipment cost, *fmp* the material and pressure correction factor, and *fm* is the module factor, which depends on the size equipment. The values of *fmp* and *fm* were adopted according to the procedure proposed by Scholz et al. [57]. The *EC* of the absorption column, stripper column, blowers, pumps, compressors, and heat exchangers was adopted from other studies [56]. The list of basic parameters for maintenance and operation cost, which consist of operating supply cost, research, and development (R&D) costs, personnel labor cost, utility costs (i.e., electricity cost for heating and cooling, absorbent exchange cost) is presented in Table 3.


**Table 3.** Parameters for operation costs.

The last step of the cost analysis was the estimation of the risk and economic benefits of the project. The financial assessment of the investment was carried out on the basis of the expected energy production, and total costs of the plant. The unit cost (*UC*) of 1 m<sup>3</sup> biogas purification was calculated according to Equation (6) [63].

$$LIC = \left(\frac{\left(\frac{TICI}{n}\right) + \left(\left(TICI \* i\right) + TAC\right)}{APB}\right) \tag{6}$$

where *UC* is the unit cost of 1 m<sup>3</sup> bio-methane, *i* is the interest rate (9%), *n* is the depreciation period (15 years), *APB* is the annual production of bio-methane [m3], and *TAC* is the total annual cost.

The annual amount of cubic meters of upgraded biogas stream was determined according to Equation (7).

$$APB = BF \cdot \% \text{ } \text{CH}\_4 \cdot ML \tag{7}$$

where *BF* is the biogas flow, % *CH*4 is the percentage of methane in biogas, and *ML* is the methane loss.

#### **3. Results and Discussion**

#### *3.1. COSMO-RS Prediction—Pre-Selection of DESs*

The preselection of DESs that are characterized by high solubility of siloxanes, H2S, CO2, H2O, and CH4 was made based on the Henry's constants, activity coe fficients, and excess enthalpy of mixtures that were predicted according to the COSMO-RS method. Water was omitted in the calculations because it was assumed to be removed before the biogas enters the absorption column. All parameters were determined at 20 ◦C and 100 kPa. The calculation results are presented in Table 4.

The activity coe fficient is a thermodynamic parameter that is associated with the a ffinity of siloxanes, H2S, CO2, and CH4 to DESs. This parameter indicates the di fferences in strength among DESs and impurities, which are a result of the dominant interactions. Usually, the activity coe fficient values are given as ln(1/γ), hence these are rather negative (Table 4) [64]. The higher negative values of logarithmic activity coe fficients indicate greater solubility of siloxanes, H2S, and CO2 in DESs. The second main thermodynamic parameter is the excess enthalpy of mixtures ( *H<sup>E</sup>*). *H<sup>E</sup>* is a sensitive measure of the intermolecular interactions between DESs and impurities. The results of H<sup>E</sup> calculated for all DES-impurities models are presented in Table 4. The DES, which is characterized by a higher dissolution capacity of CO2, H2S, and siloxanes has lower values of *H<sup>E</sup>* (higher negative). The third parameter is the Henry's Law constant ( *KH*). The *KH* describes the ratio at the equilibrium of the concentration of impurities in the gas phase to the concentration of impurities in the DES phase, and it combines vapor pressure and solubility, which can be used to estimate the likelihood that a substance will be exchanged between the gas phase and a DES. Lower *KH* indicates a higher concentration of impurities in the DES phase than in the gas phase.

ChCl:U (1:2) and ChCl:OA (1:2) showed lower values for all thermodynamic parameters, relative to all impurities. Slightly higher values were obtained for the rest of the DESs composed of choline chloride such as HBA. This indicates that this type of HBA in DES structures has a major influence on absorption e fficiency. This is in line with the conclusions obtained in previous studies [46]. This can be caused by several factors, including HBA alkyl chain length, di fferent charge density on the ammonium, as well as asymmetry in ChCl ammonium with a hydroxyl group in the longest branch, and theoretically, a type of counter-ion (Cl− or Br−). However, the obtained results indicate that this type of counter-ion in HBA only has a slight e ffect on the ability of DESs to dissolve all impurities. The use of DESs containing ChCl as HBA in the absorption process is preferred because they are characterized by less viscosity compared to DESs composed of quaternary ammonium salts with long alkyl chain length [65].

Principal components analysis (PCA) was used to obtain a better interpretation of all results (the activity coe fficient, excess enthalpy, and Henry's constant). The PCA plot is presented in Figure 3. The numbers on the diagram correspond to the DESs numbers in Table 4. The results indicate that DESs can be divided into three groups. The first group is marked with a yellow circle and contains two DESs (ChCl:U 1:2 and ChCl:OA 1:2) that have the greatest dissolution potential for all impurities. The second group, marked with a green circle, includes DESs that have the potential to e ffectively absorb siloxanes, but they have low CO2 and H2S dissolution potential. These DESs may have potential use for selective siloxane removal, but their solubility is insu fficient in applications that require the comprehensive removal of impurities from biogas. The last group includes DESs that have the lowest absorption potential for all of the tested compounds.


**Table 4.** The logarithmic activity coefficient of siloxanes H2S, and CO2 model at infinite dilution, excess enthalpy of mixtures and Henry's constant of siloxanes

**Figure 3.** Principal components analysis (PCA) plot of all thermodynamic data including the activity coefficient, excess enthalpy and Henry's constant.

Based on the obtained thermodynamic results, only the DESs that showed the greatest dissolution potential for all impurities were adopted for further consideration (ChCl:U 1:2 and ChCl:OA 1:2). In practice, most of the obtained results using COSMO-RS are slightly overestimated, and this fact was more pronounced for temperatures far from room temperature. Due to the fact that all calculations were made for 20 ◦C, it can be concluded that the obtained results are very reliable, because the COSMO-RS model ensures acceptable accuracy (about 5%) with regard to experimental results [66,67].

## *3.2. Molecular Interactions*

After geometric optimization, the absorption efficiency of DESs can be interpreted by molecular interactions. The geometric optimized structures of DESs are presented in Figure 4. Based on molecule-specific characteristics, the charge-related σ-profiles and σ-potential were successfully used to interpret the complex molecular interactions, according to previous studies [68–70].

**Figure 4.** Optimized structures of (**a**) ChCl:OA (1:2), (**b**) ChCl:UA (1:2).
