# Advancing biogas purification: A systematic numerical study of MOF performance under humid conditions

Justyna Rogacka, Patryk Pakula, Bartosz Mazur, Lucyna Firlej, Bogdan Kuchta

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Justyna Rogacka, Patryk Pakula, Bartosz Mazur, Lucyna Firlej, Bogdan Kuchta. Advancing biogas purification: A systematic numerical study of MOF performance under humid conditions. Chemical Engineering Journal, 2024, 486 (19), pp.150097. 10.1016/j.cej.2024.150097. hal-04889794

HAL Id: hal-04889794

https://hal.science/hal-04889794v1

Submitted on 21 Mar 2025

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>
# Advancing biogas purification: A systematic numerical study of MOF performance under humid conditions

Justyna Rogacka<sup>a, b, *</sup>, Patryk Pakuła<sup>a</sup>, Bartosz Mazur<sup>a</sup>, Lucyna Firlej<sup>a, c</sup>, Bogdan Kuchta<sup>a, d, *</sup>

<figure><img src="image_3.png" /></figure>

Check for
updates

## ARTICLE INFO

### Keywords:

Biogas Purification

Adsorption

MOFs

Water

Gas Separation Efficiency

Computational Screening

## ABSTRACT

The adsorption of gases in nanopores represents a promising engineering tool applicable for gas storage and separation. This study provides a comprehensive evaluation of metal-organic frameworks (MOFs) for biogas purification, with a specific focus on their performance under humid conditions. Beginning with 22 structures identified in the literature as potential top sorbents, we employ numerical simulations of adsorption and kinetic selectivity to identify the best-performing MOFs. The research reveals that the presence of water significantly impacts the biogas separation process due to water clustering, which notably affects CO₂ adsorption. The simulations also indicate variations in regenerability and selective adsorption among the initially selected MOFs in wet conditions. These findings underscore the effectiveness of high-throughput numerical screening in identifying materials with specific properties and ensuring stable performance under varying environmental conditions.

## 1. Introduction

The crucial role of efficient and environmentally friendly energy sources in our rapidly changing world is indisputable. Biogas, one of renewable energy sources, plays a pivotal role in this arena. However, purifying biogas remains a challenging task for scientists and engineers. Among various technologies and materials considered for this task, adsorption in nanoporous sorbents appears to be the most promising approach. In particular, metal-organic frameworks (MOFs) have shown exceptional sorption capabilities due to their tunable porous structure and high surface area [1–4]. Numerous experimental and numerical screening studies have been conducted to identify the most effective MOFs for CH₄/CO₂ separation [5–9]. The very large variety of obtained conclusions is partially due to the complex nature of the separation process, the specific conditions under which each study was conducted, and differences in the MOFs’ synthesis and characterization. Although prior studies have contributed valuable insights to the problem, a need for more comprehensive analysis of separation process and its efficacy persists, to reconcile experimental inconsistencies and determine the MOFs structures that will remain effective under the broadest range of

conditions. The presented results not only serve as a practical guide but also offer new fundamental insights into modeling methodologies, particularly regarding the quality of the employed force fields. This holistic approach aims to address the existing gaps in the literature, providing a more nuanced understanding of biogas purification through adsorption in MOFs.

From this perspective, the impact of water on the separation performance of nanoporous sorbents appeared as a major aspect of biogas separation/purification that requires further understanding, although this problem was already largely addressed in the literature.

Keskin et al. suggest that the interaction of MOFs with water is a critical issue for the separation process [10]. In fact, all industrial CO₂ separation processes deal with humid gas streams. On the other hand, the behavior of MOFs in hydrated conditions varies widely: from materials that irreversibly degrade under mildly humid conditions to those that remain stable even in boiling water. Unless a MOF is stable under long-term exposure to low-temperature steam and its separation characteristics for CO₂ are not decreasing in the presence of water vapor, it will be suitable for CO₂ separation from wet gas mixtures. The authors also note a lack of data regarding the multicomponent adsorption of any

<footnote><sup>a</sup> Department of Micro, Nano and Bioprocess Engineering, Faculty of Chemistry Wroclaw University of Science and Technology, Wroclaw, Poland</footnote>

<footnote><sup>b</sup> Department of Chemistry University of Manchester, Manchester M13 9PL, UK</footnote>

<footnote><sup>c</sup> Charles Coulomb Laboratory, University of Montpellier, CNRS, Montpellier, France</footnote>

<footnote><sup>d</sup> MADIREL, CNRS, Aix-Marseille University, 13288 Marseille, France</footnote>

<footnote>* Corresponding author at: Department of Micro, Nano and Bioprocess Engineering, Faculty of Chemistry Wroclaw University of Science and Technology, Wroclaw, Poland.</footnote>

<footnote>E-mail addresses: justyna.rogacka@pwr.edu.pl (J. Rogacka), bogdan.kuchta@pwr.edu.pl (B. Kuchta).</footnote>
gas mixtures in MOFs and conclude that such information would be
beneficial to better target the most promising materials for real
applications.

Erucar et al. [11] used molecular simulations to examine the effects of the presence of water in natural gas and flue gas mixtures on the adsorptive properties of the top promising MOFs identified among 54,808 MOF structures. The work determined the CO₂ selectivity, working capacity, adsorbent performance score (APS), and percent of regenerability (R%). The top-performing MOFs were selected by considering adsorption of ternary CO₂/CH₄/H₂O and CO₂/N₂/H₂O mixtures, and comparing it with that computed for binary CO₂/CH₄ and CO₂/N₂ mixtures in dry conditions. The study showed that the selectivity of MOFs that have strong affinity toward water is barely affected by addition of water into binary CO₂/CH₄ and CO₂/N₂ mixtures, but their APS and R% parameters significantly decrease.

Altintas et al. [12] analyzed a large number of adsorbent selection metrics (such as selectivity, APS, R%, and the separation potential (ΔQ)) to identify numerically the most promising MOFs for CO₂ separation from flue and landfill gas. The authors also investigated the adsorption of binary (CO₂/N₂ and CO₂/CH₄) and ternary mixtures (CO₂/N₂/CH₄) to provide a more realistic performance testing of MOF adsorbents but did not analyze the influence of water presence on the separation process.

The effect of water on the CO₂/N₂ separation by ZIF-68 and ZIF-69 was studied by Liu et al. [9]. For both ZIFs, the presence of water significantly influences the adsorption selectivity only if the amount of water in the bulk phase is above 5 %. Moreover, at low pressure, the selectivity of CO₂ over N₂ does not depend on the presence of water. At high pressures, because of competitive adsorption of H₂O over CO₂ and N₂, both CO₂ and N₂ the loadings decrease, but to a different degree. In consequence in both ZIFs the CO₂/N₂ selectivity increases. The paper also highlights the importance of electrostatic interactions in achieving high selectivity and underlies the need to correctly account for these interactions in force fields used in simulations.

Jiang et al. [13] show that in some cases (for instance in charged square-octahedron topology MOFs) the selective adsorption of CO₂ from syngas increases in the presence of even a trace amount of water, as H₂O enhances the adsorption of CO₂.

Using ab initio simulations Tan et al. [14] showed that in M-MOF-74 (M = Mg, Co, or Ni) the presence of water impacts the competitive co-adsorption of CO₂ with other small molecules (NH₃, SO₂, NO, NO₂, N₂, O₂, and CH₄). Specifically, the presence of water displaces CO₂ adsorption sites from the vicinity of metal sites in the MOFs, leading to faster CO₂ desorption rates and lowering the kinetic barrier associated with the exchange reaction between H₂O and CO₂.

The effect of water on CO₂ adsorption capacity in zeolite 13X in highly humid flue gas streams was experimentally studied by Li et al. [15]. The authors show that water adsorbs in 13X much stronger than CO₂ (and many other polar adsorbents); therefore, it displaces (replaces) CO₂ from the adsorption sites and reduces the adsorbent's capacity to capture CO₂.

Very often flue gas contains almost as much H₂O as CO₂. Such high humidity level poses additional challenges to the adsorption system [16]. In the case of zeolitic sorbents, while it is possible to control the location of the water loaded zone in the adsorbing bed, high water levels require unreasonably deep vacuum levels to regenerate the adsorption column. Not all zeolites can be regenerated in this way. As water is a potent absorber of microwaves, the desorption of water assisted by microwave radiation may occur at lower temperature. The results suggest that in general, for wet CO₂/N₂ mixtures, microwave-assisted vacuum desorption of CO₂ could be more efficient than column regeneration without microwave radiation.

Joos et al. [17] found that in zeolite 13X the high concentration of H₂O (near its saturation loading) reduces its CO₂ adsorption capacity by an order of magnitude. It is mainly due to the strong permanent dipole of H₂O molecule (~6.17 × 10⁻³⁰ Cm in gas phase and ~ 1 × 10⁻²⁹ Cm in the liquid phase,[18] that efficiently competes for coordination sites at

the sodium cations with CO₂ molecules having much weaker quadrupole
moment (~14.27 × 10⁻⁴⁰ Cm², [19]). The authors conclude that in all
materials showing high selectivity for CO₂ adsorption (so, showing
distribution of charges over the adsorption scaffold), the presence of
H₂O will strongly reduce the capacity of materials to adsorb CO₂.

Finally, in the case of numerical screening of MOF for efficient biogas separation and purification, the choice of MOF structures database is crucial [20]. Each computational-ready database is prepared in a specific way that aims at removing the coordinates of guest molecules (hydrogens, oxygens, metals, metal-O complexes, or bulky halogen groups), that can remain in the samples used for experimental structure determination. [20]. The presence (or absence) of these structural elements can be considered as critical factors that influences gas uptakes. This conclusion was drawn after comparison of simulated CH₄, H₂, and CO₂ uptakes in MOF structures from two commonly used databases, CoRE DB [21] and CSDSS DB [22].

The primary objectives of this work consist then in identifying in a unified way the best performing MOFs for biogas purification. The applied methodology consists in numerical simulations of adsorption (Monte Carlo and Molecular Dynamics), and analysis of key separation parameters, in particular adsorption capacity, separation ability and kinetic selectivity, in dry and wet conditions. We also aim at understanding the separation mechanisms in the presence or absence of water. The present analysis exploits information from two sources: (i) our studies and (ii) the data available in the literature. For that we extended and deepened previous numerical screening study and analysis of experimental data which lacked details and consistency of approach. It's crucial to note that the referenced screening studies used diverse interaction models and examined various physical quantities to identify the top-performing material. This diversity in approach and methodology, while providing a broad perspective, also increases the level of complexity of the problem and renders the comparison of the evaluated materials very difficult. By consolidating models and calculated properties, we aim at providing a unified, comprehensive, and more nuanced evaluation of the performance of various materials in biogas impurity separation. This will lead, we believe, to a more accurate identification of the optimal material for CO₂/CH₄ separation.

## 2. Methodology

The methodology employed in this study involves conducting numerical simulations of a model biogas adsorption in a group of materials obtained from three distinct publications focused on screening of MOFs structures in search of those performing the optimal CO₂/CH₄ separation [23–25]. The best-performing materials from each screening were selected, resulting in a total of 22 structures.

### 2.1. Materials

In the case of numerical screening for materials presenting desired
properties, both correct structure of the modeled system and an
adequate model of inter- and intramolecular interactions (at the atomic
level) are equally important.

Table 1 gathers structural information for 22 structures studied in the present work: largest cavity diameter (LCD), pore limiting diameter (PLD), mass density, available surface area (ASA), non-available surface area (NASA), helium void fraction (HVF), and the type of metal sites (open or not). These data were taken either from the CORE-MOF database [21] or calculated with the Zeo++ program [26].

For all structures the sizes of pore vary significantly. The LCD ranges from 3.68 Å (GUPJEG01) to 9.53 Å (KEVWUF). Similarly, the PLD varies from 1.12 Å (ZUQVAI) to 6.67 Å (PARHEW). Therefore, although a priori all selected structures have been designed in the literature as having large potential for biogas separation and purification, we expect large variations in individual performances. See Table 2..

The mass density of the structures also spans over a broad range,
<caption>**Table 1**</caption>

Structural information for 22 structures studied in the present work (largest cavity diameter (LCD), pore limiting diameter (PLD), mass density, available surface area (ASA), non-available surface area (NASA), helium void fraction (HVF), and the type of metal sites (open or not)).

<table><thead><tr><th>Structure</th><th>LCD<br>Å</th><th>PLD<br>Å</th><th>Density<br>g/cm³</th><th>ASA<br>m²/g</th><th>NASA<br>m²/g</th><th>HVF<br>-</th><th>All Metals</th><th>Open Metal Sites</th></tr></thead><tbody><tr><td>ABIXOZ</td><td>6.23</td><td>4.05</td><td>1.92</td><td>977</td><td>0</td><td>0.59</td><td>Mo, Co</td><td>Mo,Co</td></tr><tr><td>CEHWIX</td><td>3.78</td><td>3.30</td><td>1.55</td><td>0</td><td>189</td><td>0.47</td><td>Ni</td><td>Ni</td></tr><tr><td>FARZEE</td><td>4.36</td><td>4.31</td><td>1.37</td><td>865</td><td>0</td><td>0.24</td><td>Ni</td><td>Ni</td></tr><tr><td>FIGXAU</td><td>3.75</td><td>2.83</td><td>2.04</td><td>0</td><td>104</td><td>0.51</td><td>Er</td><td>Er</td></tr><tr><td>GUPJEG01</td><td>3.68</td><td>3.36</td><td>1.55</td><td>118</td><td>0</td><td>0.39</td><td>Mn</td><td>No OMS</td></tr><tr><td>HAWWUZ</td><td>6.86</td><td>6.21</td><td>1.03</td><td>2474</td><td>0</td><td>0.69</td><td>Nd</td><td>No data</td></tr><tr><td>HISFUM</td><td>4.53</td><td>3.82</td><td>1.48</td><td>333</td><td>0</td><td>0.33</td><td>Na</td><td>Na</td></tr><tr><td>IFOSIG</td><td>4.26</td><td>3.62</td><td>1.59</td><td>416</td><td>77</td><td>0.57</td><td>Zr, Ce</td><td>No OMS</td></tr><tr><td>ISAYUW</td><td>4.59</td><td>4.54</td><td>1.41</td><td>894</td><td>0</td><td>0.23</td><td>Cu</td><td>No OMS</td></tr><tr><td>KEVWUF</td><td>9.53</td><td>4.20</td><td>1.04</td><td>2100</td><td>0</td><td>0.71</td><td>La</td><td>La</td></tr><tr><td>KURSOH</td><td>5.22</td><td>4.60</td><td>1.19</td><td>940</td><td>0</td><td>0.51</td><td>Zn</td><td>No OMS</td></tr><tr><td>LENROM</td><td>4.83</td><td>4.28</td><td>1.41</td><td>909</td><td>0</td><td>0.24</td><td>Zn</td><td>No data</td></tr><tr><td>LOFZUB (AIPO)</td><td>8.37</td><td>3.57</td><td>1.46</td><td>952</td><td>0</td><td>0.55</td><td>Al</td><td>No OMS</td></tr><tr><td>LUCDIW</td><td>8.52</td><td>6.17</td><td>0.82</td><td>2782</td><td>0</td><td>0.72</td><td>Ce</td><td>Ce</td></tr><tr><td>OJONOQ</td><td>6.44</td><td>5.38</td><td>1.50</td><td>1243</td><td>0</td><td>0.66</td><td>Er</td><td>Er</td></tr><tr><td>PARHAS</td><td>6.91</td><td>6.38</td><td>0.70</td><td>3203</td><td>0</td><td>0.68</td><td>Ca</td><td>Ca</td></tr><tr><td>PARHEW</td><td>7.39</td><td>6.67</td><td>0.63</td><td>3796</td><td>0</td><td>0.71</td><td>Ca</td><td>Ca</td></tr><tr><td>QOKCID</td><td>4.31</td><td>3.86</td><td>1.71</td><td>254</td><td>0</td><td>0.37</td><td>Zn</td><td>Zn</td></tr><tr><td>RUVBER</td><td>6.05</td><td>5.68</td><td>1.14</td><td>1258</td><td>0</td><td>0.58</td><td>Cd</td><td>No OMS</td></tr><tr><td>SOMSIY</td><td>6.00</td><td>5.71</td><td>1.30</td><td>1183</td><td>0</td><td>0.58</td><td>Ga</td><td>No OMS</td></tr><tr><td>TIFHAT</td><td>8.78</td><td>5.31</td><td>0.90</td><td>1959</td><td>0</td><td>0.65</td><td>Nd</td><td>No OMS</td></tr><tr><td>ZUQVAI</td><td>4.87</td><td>1.12</td><td>1.53</td><td>0</td><td>239</td><td>0.00</td><td>Cr, Na</td><td>No data</td></tr></tbody></table>

<caption>**Table 2**</caption>

Composition of the model mixtures representing dry and wet biogas used in the simulations.

<table><thead><tr><th rowspan="2">Component</th><th>Full biogas</th><th>Full biogas with water (0.1 mol. %)</th><th>Full biogas with water (5 mol. %)</th></tr><tr><th>mol. %</th><th>mol. %</th><th>mol. %</th></tr></thead><tbody><tr><td>CO<sub>2</sub></td><td>30.0</td><td>30.0</td><td>30.0</td></tr><tr><td>CH<sub>4</sub></td><td>60.0</td><td>60.0</td><td>60.0</td></tr><tr><td>H<sub>2</sub>S</td><td>3.00</td><td>3.00</td><td>1.00</td></tr><tr><td>N<sub>2</sub></td><td>4.00</td><td>3.95</td><td>3.00</td></tr><tr><td>O<sub>2</sub></td><td>3.00</td><td>2.95</td><td>1.00</td></tr><tr><td>H<sub>2</sub>O</td><td>-</td><td>0.10</td><td>5.00</td></tr></tbody></table>

from 0.63 g/cm³ (PARHEW) to 2.04 g/cm³ (FIGXAU). The available surface area which is one of the major parameters determining the gas adsorption capacity varies from almost zero in several MOFs (CEHWIX, FIGXAU, and, in particular, ZUQVAI), to 3796 m²/g (PARHEW). The non-available surface area (NASA) is generally low (the highest value is smaller than 240 m²/g (ZUQVAI).

The helium void fraction (HVF), the second structural parameter strongly influencing the gas storage capacity, ranges from 0.24 (in FARZEE, ISAYUW, LENROM, and ZUQVAI) to 0.72 (LUCDIW). ZUQVAI structure, for which ASA is close to zero and HVF is small, is then supposed to show low or no uptake of any gas. Similar conclusion can be advanced for CEHWIX showing no ASA.

The metal clusters in selected MOFs contain a large variety of metals (Mo, Co, Ni, Er, Mn, Nd, Na, Zr, Ce, La, Zn, Cd, Ga, and Ca). Some of them, such as Mo, Co, Ni, Er, Na, La, and Ce, are additionally open metal sites, and potentially could enhance the selectivity of gas adsorption. GUPJEG01, KURSOH, LOFZUB, RUVBER, SOMSIY, and TIFHAT do not have open metal sites.

The choice of metal in the MOF structure is important not only from the point of view of adsorption efficacy and selectivity, but also for the safety, cost, and technology reasons. Metals such as Zn, Al, and Ni are often preferred due to their relative abundance, low cost, and lower toxicity compared to other metals. From this perspective, Zn-based MOFs like QOKCID and KURSOH, and Al-based materials like LOFZUB (aluminophosphate – AlPO), could be safer and more economical

options for large-scale application. Moreover, some metals (like Ni in CEHWIX) can form open metal sites, which can enhance the selective adsorption from gas mixtures whereas MOFs with metals that do not form open metal sites (like Mn in GUPJEG01) might have limited selectivity.

Furthermore, while more abundant and less toxic elements are generally preferred, the specific requirements of the biogas separation process might necessitate the use of less common metals. For example, the presence of La (in KEVWUF) and Nd (in OJONOQ and TIFHAT), more expensive and less abundant metals, usually leads to the structures with high surface areas and large pore sizes, potentially enhancing gas adsorption and separation.

Therefore, the choice of metal in MOFs to be applied in biogas separation needs also to be optimized to balance separation performance, cost, safety, and production considerations, and requires separated analysis.

In summary, although the MOFs studied in the present work were chosen from the ones previously selected for their potential performance in biogas separation, they all exhibit a wide range of structural and physical properties defining efficacy of adsorption process, with significant variations in pore size, density, surface area, voids fraction, and the presence of open metal sites. These variety of sorbent properties is suitable/necessary, as a specific choice of efficient material for biogas separation would depend not only on adsorbent properties, but also on the exact nature of the biogas mixture and the conditions under which the separation process is conducted.

## 2.2. Molecular simulations

All simulations of adsorption were performed using Grand Canonical Monte Carlo (GCMC) method. The simulations were conducted at three temperatures, 273 K, 298 K, and 303 K, in a wide range of pressures (0.01 bar –10 bar) usually applied in the industrial swing-adsorption processes.

The isotherms of adsorption were simulated for three types of situations: (i) single component (CO₂, CH₄, N₂, O₂, and H₂S) adsorption, (ii) binary mixtures adsorption (CO₂/CH₄ 50 mol %/50 mol %), CO₂/CH₄ (25 mol %/75 mol %), H₂S/CH₄ (50 mol %, /50 mol %), H₂S/CO₂ (50 mol %/50 mol %), and H₂S/N₂ (50 mol %/50 mol %), (iii) full biogas

<footnote>*No OMS – no open metal sites.</footnote>
adsorption, in dry or wet conditions. The enthalpy of adsorption was calculated for all biogas components. The minimization of wet systems' energy provided information about the interactions between water and the MOF structure, which is essential for understanding the impact of water on the separation efficacy in industrial process.

All simulations were performed using state-of-the-art RASPA [27] simulation code. To describe the gas-gas interactions between different molecules (CO₂, CH₄, H₂S, N₂, and O₂) the TraPPE forcefield was employed [28]. For water molecules, the TIP4P model optimized for capturing the hydrogen-bonding capabilities of water was used [29]. The interactions within the MOF structures were modeled using a hybrid approach: (i) the UFF (Universal Force Field) was used for the metal clusters, and (ii) the Dreiding forcefield was applied for the organic linkers [30,31]. The charges on the atoms within the MOFs were calculated using the PACMOF machine learning script [32]. The Lennard-Jones potential was used to describe gas-sorbent interaction, the approach which is widely accepted for simulating van der Waals (VdW) forces [25,33-36]. The Lorentz-Berthelot mixing rules were applied to calculate the interactions between different types of atoms. The VdW interactions were cut-off at the distance of 12 Å. Electrostatic interactions were calculated using the Ewald summation technique, computationally efficient for systems with periodic boundary conditions. The Monte Carlo moves implemented to explore the phase space effectively consisted in molecules' translation, rotation, insertion/deletion, identity change, and swap moves. To ensure system equilibration the equilibration runs (minimum 50 000 cycles for single component adsorption; between 75 000 and 500 000 cycles for remaining systems (two components or more)) were first executed. The production runs that followed consisted in minimum 250 000 cycles for single component adsorption simulations, and between 250 000 and 500 000 cycles for remaining systems (two components or more).

The simulations of molecules' diffusion through the sorbent were performed using Molecular Dynamics simulation procedure implemented in RASPA code. The simulations were run in the NVT ensemble with the time step of 0.025 fs. Five independent runs were performed to average the value of the diffusion coefficient calculated from the mean-square displacement (MSD) graphs. The production runs were started from previously equilibrated configurations for a total of 1 ms to ensure adequate statistical sampling.

The Einstein relation was used to calculate the self-diffusion coefficients [1]:

$$D_{self}^{*} = \frac{1}{6N} \lim_{i \to \infty} \left\{ \frac{d}{dt} (r_n(t) - r_n(0))^2 \right\} \quad (1)$$

where $D_{self}^{*}$ – self-diffusion coefficient, $r_n(t)$ – position of the n-th molecule at the time t, $r_n(0)$ – initial coordinates of the n-th molecule, N – the number of particles simulated in the system.

The selectivity for component A relative to component B of a given gas mixture is defined as follows:

$$S = \left( \frac{x_A}{x_B} \right) \cdot \left( \frac{y_B}{y_A} \right) \quad (2)$$

where $x_A$ and $x_B$ are the molar fractions of components A and B in the adsorbed phase and $y_A$ and $y_B$ are the molar fractions of components A and B in the bulk phase, respectively.

The kinetic selectivity CO₂/CH₄ is defined as:

$$D = \frac{D_{self}^{*} CO_{2}}{D_{self}^{*} CH_{4}} \quad (3)$$

where $D_{self}^{*}$CO₂ and $D_{self}^{*}$CH₄ are the self-diffusion coefficients for CO₂ and CH₄, respectively. molecule.

The regenerability percentage (R%) was calculated using the formula:

$$R\% = \left( \frac{\Delta N_{CO_2}}{N_{CO_2}} \right) \cdot 100\% \quad (4)$$

where $\Delta N_{CO₂}$ represents the working capacity, defined as the difference between the amount of CO₂ adsorbed at a pressure of 5.6 bar and the amount desorbed at 0.56 bar; $N_{CO₂}$ is the amount of CO₂ adsorbed at 5.6 bar [37].

All selectivity coefficients were calculated for the binary and biogas mixtures, in dry and wet conditions. We use them as the key performance indicators along this study.

### 3. Results and discussion

#### 3.1. Enthalpy of adsorption

To evaluate the strength of sorbents interactions with the components of biogas and with water molecules, the enthalpies of their adsorption were calculated, for each selected MOF. The results are shown on Fig. 1 and Fig. 2. For most of the materials CO₂, H₂S, and H₂O have the highest enthalpies of adsorption, above 30 kJ/mol. Such high values are mainly due to the high affinity of MOFs metal clusters for these gases. If the MOF structure contains open metal sites or exposed metal cations, the adsorption enthalpies for CO₂ are high because of the strong metal – CO₂ quadrupole electrostatic interactions. As the molecules of H₂O and H₂S can additionally form hydrogen bonds with appropriate functional groups (like –OH, –NH₂, etc.), MOFs containing them will have higher affinities for these molecules.

The size and shape of the pores can also affect the enthalpy of adsorption. If a gas molecule fills well/fits well to a pore, its interaction with the sorbent will be stronger and the enthalpy of its adsorption - higher. This is known as a confinement effect.

On the other hand, too high enthalpies of adsorption mean more energy required to regenerate the material through pressure, temperature, or vacuum swing processes (pressure swing adsorption (PSA), temperature swing adsorption (TSA), or vacuum swing adsorption (VSA)). From this point of view materials like KURSOH, ISAYUW, RUVBER, TIFHAT, and SOMSIY, for which enthalpies remains below 30 kJ/mol, would be more appropriate for actual applications.

The analysis of water adsorption revealed that 12 over 22 studied structures are hydrophilic (with enthalpy of water adsorption above 40.7 kJ/mol, red line on Fig. 2); the remaining 10 structures are hydrophobic. This will have a considerable impact on the adsorption isotherms.

#### 3.2. Diffusion coefficients

Fig. 3 presents the self-diffusion coefficient $D_{self}^{*}$, calculated separately for all components of biogas (CH₄, CO₂, H₂S, N₂, and O₂), in all selected MOFs, at 298 K. $D_{self}^{*}$ is a measure of rapidity of gas molecules movement through the adsorbing material. Its value is influenced by both geometric factors (size and shape of the moving molecules, the accessibility of sorbent pores, their size, shape, and interconnectivity), and type of gas-sorbent interaction, and vary with the temperature.

The calculated self-diffusion coefficients spread over a wide range of values. For most of the structures (17 over 22) the self-diffusion coefficients for all gases are small, from ~ 6 x 10⁻¹⁰ cm²/s to ~ 2 x 10⁻⁷ cm²/s. No diffusion was observed in ZUQVAI (for any of studied gases) which has PLD = 1.6 Å. For FIGXAU (PLD = 2.83 Å) CH₄ and H₂S do not diffuse, as these molecules have larger VdW diameter (3.8 Å and 3.6 Å, respectively). The MOFs QOKCID (ABIXOZ) have the highest kinetic selectivity coefficient of 3.44 (2.10) for CH₄, indicating their strong affinity for this molecule.

Materials GUJPEG01, HISFUM, ISAYUW, KURSOH, QOKCID, RUVBER, SOMISY have 1-D pore channels where diffusion occurs only in x direction. In CEHVIX diffusion is also unidirectional but in y
<figure><img src="image_4.png" /><figcaption>Fig. 1. Enthalpy of adsorption for CH$_{4}$, CO$_{2}$, H$_{2}$S, N$_{2}$, and O$_{2}$ molecules, in the selected 22 MOF structures.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 2. Enthalpy of water adsorption in the selected 22 MOF structures. The rectangles are colored by the strength of affinity towards water, from dark orange (strongly hydrophobic) to dark blue</figcaption></figure>

**Fig. 2.** Enthalpy of water adsorption in the selected 22 MOF structures. The rectangles are colored by the strength of affinity towards water, from dark orange (strongly hydrophobic) to dark blue (strongly hydrophilic). The red line marks the value of 40.7 kJ/mol. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

direction. In LENROM diffusion occurs in 2 directions (x, y). For other materials diffusion occurs in all directions (x, y, z).

Comparison of self-diffusion coefficients (Fig. 3) and geometric selectivity parameters (Table 1) allows to identify correlations between these values. MOFs with smaller pore limiting diameter (PLD < 3.6 Å) like CEHWIX, GUJPEG01, and LOFZUB have lower CH$_{4}$ and H$_{2}$S self-diffusion coefficients; still, small linear molecules of CO$_{2}$, N$_{2}$ and O$_{2}$ move freely through them. Such behavior is not suitable from the industrial separation process perspective, where the free flow of methane and the retention/adsorption of CO$_{2}$ are prospected. Therefore, ABIXOZ, KURSOH, LENROM, QOKCID, TIFHAT seem to be more appropriate for this purpose, although the self-diffusion coefficients in these structures are much lower. HISFUM and IFOSIG, which have higher densities and more open metal sites, show lower self-diffusion coefficients, as these

structures provide more opportunities for the gases to be trapped in MOF's adsorption sites, and to be delayed in their movement.

CO$_{2}$ and H$_{2}$S (and in some cases, CH$_{4}$) are gases which show the slowest diffusion through almost all studied structures. At the same time their enthalpies of adsorption are the highest. It means that the molecule spends more time close to the highly adsorbing sites and their average motion through the sorbent is slowed down.

The relationship between the geometrical properties of the MOFs and their selectivity is more complex. Larger PLDs and LCDs generally lead to slower self-diffusion coefficients, but not necessarily to higher selectivity. Therefore, for all structures we also calculated the kinetic selectivity coefficient, which is as the ratio of the self-diffusion coefficients of CO$_{2}$ and CH$_{4}$ (see Table S1 in electronic Supporting information, SI). Higher kinetic selectivity coefficient for a particular gas indicates that
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Self-diffusion coefficients for single CH₄, CO₂, H₂S, N₂, and O₂ molecules moving through in 21 of the selected 22 MOF structures, at 298 K. The molecules do not diffuse through ZUQVAI structure (not shown.).</figcaption></figure>

this gas is selectively adsorbed by the given MOF. For example, PARHAS and PARHEW exhibit similar geometrical properties (refer to Table 1), but they demonstrate distinct selectivity for CH₄, with kinetic selectivity coefficients of 1.14 and 0.92, respectively. Consequently, PARHAS is the preferred choice for the separation of CO₂ from CH₄/CO₂ mixtures.

### 3.3. Adsorption of individual biogas components

Fig. 4 shows, as examples, isotherms of biogas components adsorption (CH₄, CO₂, H₂S, N₂, and O₂), in 3 MOFs: KURSOH, LUCDIF, and TIFHAT, in the pressure range from 0.01 to 10 bar, and at three temperatures: 273 K, 298 K, and 303 K. The isotherms for the remaining 19

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Isotherms of (a) CH₄, (b) CO₂, (c) H₂S, (d) N₂, and (e) O₂ molecules adsorption in three selected MOFs: KURSOH, LUCDIF, and TIFHAT at 273 K (blue triangles), 298 K (green squares) and 303 K (red circles). The isotherms for the remaining 19 structures are provided in SI. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
structures are provided in SI (Fig. S1). The shape of isotherms and the adsorbed amount depend strongly on the type of gas and varies for different MOFs.

For all studied MOFs the CO₂ isotherms show a steep increase of the adsorbed amount at very low pressures (the Henry's region), indicating strong interactions between the gas molecules and the MOFs scaffold. The saturation is reached typically at the pressures between 2 and 4 bars, lower than the pressures used in PSA processes (usually, above 4 bars) [38]. The isotherms of H₂S have similar shapes, but the adsorbed amount is generally higher than that of CH₄ (usually, almost double). The amounts of adsorbed N₂ and O₂ increase at slower rates. In fact, these gases have lower polarizability, and the quadrupole moment much smaller than CO₂ and H₂S, and interact weaker with the MOF frameworks.

Experimental results for single gas isotherms for HISFUM and LOFZUB [39,40] show reasonably good agreement with our simulation results, considering the limitations inherent to universal force field approach. However, in both cases the simulated values are slightly overestimated. For HISFUM, at 1 atm and 298 K, the experimental CO₂ uptake is 1.33 mol/kg, whereas our simulations yielded 2.11 mol/kg at similar conditions (1.12 bar and 298 K). For LOFZUB (STA-7), the experimental uptake at 298 K for CO₂ is 6.5 mol/kg while our simulations show 8.1 mol/kg at 303 K. The presence of open metal sites in HISFUM, tends to enhance its affinity for guest molecules during simulations, resulting in higher uptake values. Regarding LOFZUB, although it is included in the Core-MOF database, it belongs technically to the AIPO structures database. In both cases applying universal force fields lead to inaccuracies in predicted uptake values.

HAWWUZ, KEVWUF, LUCIDW, PARHAS, PARHEW, and TIFHAT are better sorbents of CO₂ than other selected structures (at 10 bar and 273 K the adsorbed amount is larger than 15 mol/kg). They all have mass density between 0.63 g/cm³ and 1.04 g/cm³, similar void fraction (0.65 – 0.72), and surface accessible for adsorption above 1950 m²/g. It suggests that these are preferential parameters for high CO₂ uptake. GUPJEG01, QOKCID, and ZUQVAI show lower amounts of gas adsorbed CO₂ (less than 2.5 mol/kg), because of much smaller adsorbing surface and higher mass density.

As anticipated, the quantity of adsorbed gas typically decreases with an increase in temperature. However, the rate of this decline is continuous on the strength of the interactions between the gas and the sorbent. Specifically, it is more pronounced for gases with lower adsorption enthalpies in each MOF.

For all structures we also calculated the volumetric density of CO₂ adsorption at specific (p,T) conditions (298 K and 1.12 bar). The relationship between CO₂ uptake and its volumetric density (Fig.S36) suggests that materials with higher uptake values tend to have higher volumetric densities, indicating their potential efficiency in storing CO₂ per unit volume. KEVWUF, OJONOQ, and PARHAS exhibit the highest volumetric densities, implying that they are potentially more efficient for applications requiring high CO₂ adsorption capacity. On the other hand, materials with lower uptake values such as ZUQVAI and TIFHAT have simultaneously lower volumetric densities, suggesting a limited ability to adsorb CO₂ under the given conditions.

### 3.4. Adsorption isotherms for binary mixtures of biogas components

The simulation of the binary gas mixture adsorption brings an additional information about the competitive adsorption of the biogas components in the MOFs. We focused here on the following binary mixtures: (i) CO₂/CH₄ (50 mol. %/50 mol. %), (ii) CO₂/CH₄ (25 mol. %/75 mol. %), (iii) H₂S/CH₄ (50 mol. %/50 mol. %), (iv) H₂S/CO₂ (50 mol. %/50 mol. %), and (v) H₂S/N₂ (50 mol. %/50 mol. %).

The binary isotherms of CO₂/CH₄ (50 mol. %/50 mol. %), CO₂/CH₄ (25 mol. %/75 mol. %), H₂S/CH₄ (50 mol. %/50 mol. %), and H₂S/CO₂ (50 mol. %/50 mol. %) in three selected MOFs: ABIXOZ, KURSOH, and PARHEW at 298 K are shown on Fig. 5. They show that for given sorbent

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Isotherms of CO₂/CH₄ (50 mol. %/50 mol. %), CO₂/CH₄ (25 mol. %/75 mol. %), H₂S/CH₄ (50 mol. %/50 mol. %), and H₂S/CO₂ (50 mol. %/50 mol. %) in three selected MOFs: (1st line) ABIXOZ, (2nd line) KURSOH, and (3rd line) PARHEW at 298 K. CO₂ - dark red, CH₄ - dark blue, H₂S - dodger blue, N₂ - green, O₂ - purple. The isotherms for the remaining 19 structures and all temperature studied (273 K, 298 K, 303 K) are provided in SI. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

the amount of adsorbed gas (CH₄, CO₂ or H₂S) depends not only on the pressure but also on the composition of the gas mixture. For example, for equal molar mixture of CO₂ and CH₄, CO₂ is preferentially adsorbed, reflecting the stronger electrostatic (dipole-driven) interactions between CO₂ and the MOFs than CH₄-MOFs interactions. Even when the concentration of CH₄ is three times higher than that of CO₂, the adsorbed amount of CH₄, although slightly higher, remains negligible comparing to the amount of adsorbed CO₂. The same preferential adsorption of CO₂ over CH₄ from binary CO₂/CH₄ mixture was observed in all studied MOFs, and at all temperatures, with one exception: in TIFHAT, at 298 the amounts of both adsorbed gases are similar (see Fig. S32 in SI).

The binary isotherms also vary among the MOFs. MOFs with a higher accessible surface area (ASA) such as HAWWUZ, KEVWUF, LUCIDW, PARHAS, PARHEW, and TIFHAT exhibit higher total adsorbed amounts for both gases in the mixture. Conversely, those with the lowest accessible surface area (GUPJEG01, QOKCID, and HISFUM) show the lowest total adsorption. This observation aligns with the findings from single gas adsorption results.

Fig. 5 also shows that separation of CO₂ and H₂S from CO₂dipol/H₂S gas mixture cannot be achieved in the MOF studied here. For IFOSIG, PARHAS and 6 other MOFs (see Figs. S12–S33 in SI) the CO₂ and H₂S uptakes are almost identical. Both gases have similar enthalpies of adsorption in studied sorbents (see Fig. 1). The MOFs: The electrostatic interaction of H₂S with the MOFs is also strong, because its large dipole moment (3.2x10⁻³⁰ C·m).

The binary H₂S/N₂ isotherms (Fig. S12–S33 in SI) show similar features as CO₂/CH₄ isotherms. H₂S interacts much stronger with the MOFs than N₂, therefore its total adsorption is higher. This is probably due to the polarity of H₂S molecule (N₂ is nonpolar). This H₂S property should be exploited when designing sorbent for effective removal of H₂S and N₂ impurities from the biogas.

### 3.5. Simulated adsorption isotherms for full biogas

The simulations of full biogas were conducted in both dry and wet conditions. (0.1 % and 5 % humidity of the raw gas, respectively).

In the dry biogas simulation (Fig. 6), despite the complexity and variability of sorption/separation properties across different MOFs, we
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Simulated isotherms of full biogas adsorption in dry conditions, for six selected MOFs: ABIXOZ, KURSOH, LOFZUB, PARHEW, RUVBER and TIFHAT. The isotherms of each component are drawn separately.</figcaption></figure>

identified three types of behaviors.

(i) Materials such as ABIXOZ and LOFZUB preferentially adsorb CO₂, and small (but non-negligible) amounts of H₂S. This preference may be attributed to the specific enthalpies of adsorption and the structural characteristics of these MOFs, which allow for much stronger interactions with CO₂ and H₂S molecules (enthalpy of adsorption being much higher than for other molecules).

(ii) Materials KURSOH and RUVBER, preferentially adsorb CO₂, but small amounts of CH₄ and H₂S are also adsorbed. The amounts of CH₄ and H₂S are equal, indicating similar interactions with the MOF structures. The values of adsorption enthalpies of CO₂, CH₄ and H₂S are also similar to each other.

(iii) The third type of materials, represented by PARHEW and TIFHAT, still preferentially adsorb CO₂, but the second strongly adsorbed component is CH₄ (instead of H₂S).

From an application standpoint, the first type of material is most suitable, as it allows removing two significant impurities of raw biogas, CO₂ and H₂S while letting CH₄ to pass freely through the structure.

We repeated the full biogas simulations in slightly wet conditions (0.1 mol%, Fig. 7) maintaining water partial pressure in the range from 0.00001 to 0.01 bar, (experimental water condensation pressure at 298 K is equal 0.0314 bar, for simulation model the saturation pressure is 0.0455 bar). Similar three types of adsorptions from mixture were observed.

In highly hydrophilic structures, even the smallest amount of water added to biogas immediately condenses inside the pores, leaving less space for adsorption of biogas components. This phenomenon is particularly pronounced in materials like ABIXOZ and PARHEW, where

the elevated enthalpy of water adsorption triggers water condensation even at lowest pressures. However, other hydrophilic MOFs (such as KURSOH and LOFZUB) show minimal water adsorption, akin to N₂ and O₂, with the adsorbed amount close to 0.01 mol/kg. This suggests that ABIXOZ and PARHEW have specific structural features or chemical properties that reduce their affinity for water, possibly due to weaker water-MOF electrostatic interactions, a lack of suitable adsorption sites, or a presence of linkers containing functions of specific hydrophilicity (–OH, –NH₂, –COOH, and -SO₃H that increase hydrophilicity, –CH₃, -CF₃, -C₂F₅, aromatic linkers, alkyl chains, -SiH₃ that decrease it). Such property would be appreciated in cases where minimal water adsorption is desired, to favor more selective and efficient separation of other gases from the mixture. The understanding of this nuanced behavior, including the immediate condensation of water in highly hydrophilic structures, requires separate study.

When the water content in biogas increases up to 5 mol%, the adsorption characteristics change drastically (Fig. 8). The hydrophilic MOFs, particularly those with an enthalpy below 40.7 kJ/mol such as KURSOH, LOFZUB, RUVBER, and TIFHAT, do not adsorb water up to pressures of 1–3 bars. They preferentially adsorb of CO₂ instead, KURSOH and LOFZUB showing the highest CO₂ uptakes. Such a property is extremely interesting from an industrial perspective: the raw biogas would not have to be dried before entering the separation process. The ability to selectively adsorb CO₂ while leaving water largely not adsorbed could streamline the purification process, reducing both operational/installation complexity and, energetical cost of the process. The low partial pressure of water in this case, ranging from 0.0005 to 0.5 bar, further emphasizes the potential of hydrophilic structures in handling moisture-laden gas streams.

It should be noted that in industrial biogas upgrading or natural gas processing, a desiccant or drying layer is often integrated at the inlet of
<figure><img src="image_10.png" /><figcaption>Fig. 7. Simulated isotherms of for full biogas adsorption in slightly wet conditions (0.1 mol %) for six selected MOFs: ABIXOZ, KURSOH, LOFZUB, PARHEW, RUVBER and TIFHAT. The isotherms of each component are drawn separately.</figcaption></figure>

the adsorptive system to prevent an excessive moisture in the input gas. These solutions typically employ silica gel, activated alumina, or molecular sieves. [41–44].

### 3.6. Regeneration of the sorbent

In industrial setups, where raw biogas is never perfectly dry before entering the separation process, understanding the dynamics of adsorption/desorption process in the presence of water is crucial. Therefore, we also focus on analysis of the performance of the selected MOFs in the presence of varying water concentration.

Fig. 9 (top) compares the regenerability ratio (see Eq. 4) for all selected MOFs, for CO₂ adsorbed from binary CO₂/CH₄ (25 mol. %/mol. 75 %) mixture, and from biogas, in dry and wet conditions.

The regenerability of the structures varies in a wide range. TIFHAT and PARHEW show high regenerability in all conditions, suggesting their robustness and potential for efficient CO₂ capture and release. These structures also show small slope of the CO₂ adsorption isotherms, in each condition (Fig. 9, bottom). ABIXOZ, CEHVIX, FIGXAU, LOFZUB, OJONOQ and ZUQVAI show significantly lower or negative regeneration ratios, indicating potential challenges in the material regenerability. It happens because the maximum CO₂ uptake is reached below the desorption pressure used for R% calculations (5.56 bar). In KEVWUF, LUCIDW, PARHAS and PARHEW a small amount of water increases the regenerability of the sorbent.

The introduction of higher amount (5 mol.%) of water in the biogas drastically decreases the regenerability of all hydrophilic MOFs. The regenerability of ABIXOZ, already negative in the presence of 0.1 mol.% water, further decreases. Similarly, the regenerability of FARZEE and HAWWUZ showing positive regenerability in dry and slightly wet conditions significantly decreases when water content increases. In highly

hydrophilic MOFs (like ABIXOZ and PARHEW), the presence of even a small amount of water (0.1 %) drastically reduces regenerability. These results indicate strong interactions between MOF's scaffolds and water molecules, often at the expense of CO₂ adsorption.

For hydrophobic MOFs (FARZEE, KURSOH, and ZUQVAI), although the regenerability is also affected by the presence of water, its impact on possibility of regenerating the structures is not as severe as for hydrophilic MOFs.

### 3.7. Selectivity

We have also meticulously evaluated the selectivity of CO₂/CH₄ adsorption under various conditions (from binary mixtures, from dry and wet biogas with different water concentrations). The data showed on Fig. 10a-c reveal three distinct selectivity patterns vs. pressure.

#### (i) Conditions-independent selectivity.

In ABIXOZ, FARZEE, HAWWUZ, IFOSIG, KEVWUF, KURSOH, LUCIDW, OJONOQ, and ZUQVAI, the selectivity remains stable in the whole range of studied pressures and humidity conditions. These MOFs have generally the highest enthalpies of CO₂ adsorption, making the CO₂ less susceptible to changes of environmental parameters.

#### (ii) Conditions-dependent selectivity.

The selectivity of GUJPEG01, ISAYUW, LENROM, PARHAS, PARHEW, RUVBER, and TIFHAT varies depending on the humidity conditions. Interestingly, the trend is often opposite for binary and full biogas mixtures. The observed variations may be due to more complex architecture of adsorption sites in these MOFs, leading to intricate
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Simulated isotherms of full biogas adsorption in wet conditions (5 mol %) for six selected MOFs: ABIXOZ, KURSOH, LOFZUB, PARHEW, RUVBER and TIFHAT. The isotherms of each component are drawn separately.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** (top) The regenerability % of the selected 22 MOF structures with respect to CO₂ adsorption for four input gas mixtures: (i) binary CO₂/CH₄ (25 mol. %/75mol. %), in blue, (ii) dry biogas, in red, (iii) biogas with 0.1% water, in yellow, (iv) biogas with 5% water, in green. The negative values were cut off at -10 (we assumed that the structure cannot be regenerated).</figcaption></figure>

interactions with the components of the gas mixture and delicate balance between the adsorbent amount of each of them. This balance may be consequence of competition between electrostatic interactions of quadrupole moment of CO₂ and dipole moment of water with charges distributed over the MOFs' structures. The detailed analysis of the

selectivity mechanism needs further study.

(iii) Selectivity enhanced in specific conditions.

LOFZUB, HISFUM, and SOMISY show higher CO₂ selectivity from
<figure><img src="image_13.png" /><figcaption>Fig. 9. (continued).</figcaption></figure>

biogas either in dry or slightly humid (0.1 mol.% H₂O) conditions. This could be due to their hydrophobic nature, which allows them to preferentially adsorb CO₂ over CH₄ and H₂O, thereby enhancing their selectivity under specific humidity conditions.

FIGXAU is a unique case showing large selectivity fluctuations. This is primarily due to the extremely low CH₄ uptake (excluded geometrically, LCD<sub>FIGXAU</sub> = 3.75 Å), which result in largely overestimated selectivity values. Similar phenomena affect the selectivity calculations for ABIXOZ, FARZEE, IFOSIG, HAWWUZ, KURSOH, LUCIDW, and OJONOQ, at the lowest and highest studied pressures.

The selectivity of ZUQVAI, TIFHAT, and LENROM is below 10, in all analysed conditions. Although designated as such in the previous works

[23,24], they should not be considered as potential sorbents for CO₂/CH₄ separation.

Excluding the above-mentioned outliers, the selectivity in the studied MOFs generally ranges from 100 to 250. Materials with higher CO₂ uptake (higher than 7 mmol/g, like FIGXAU, HAWWUZ, KEVWUF, LOFZUB, PARHAS and PARHEW) could be potentially interesting separation materials because of their elevated working capacity. For industrial applications, particularly in swing-adsorption processes, at pressures above 4 bars and minimal humidity presence (0.1 % H₂O), the most promising materials are ISAYUW, HISFUM, LENROM, LOFZUB, QOKCID, and RUVBER. LOFZUB and QOKCID are excellent candidates for efficient gas separation, with selectivity values (in dry conditions)
<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Selectivity values for CO₂/CH₄ adsorption as a function of pressure. a) selectivity range 0–50, b) selectivity range 0–200, c) selectivity range 0–720 or 0–80000. (i). Circle - binary mixture (CO₂/CH₄ = 0.25 / 0.75), (ii) triangle - dry biogas (CO₂/CH₄ = 0.3 / 0.6), (iii) square - biogas + 5 % H₂O (CO₂/CH₄ = 0.3 / 0.6), (iv) cross - biogas + 0.1 % H₂O (CO₂/CH₄ = 0.3 / 0.6). Color bar is scaled with respect to the CO₂ uptake, from zero (blue) to 15 mol/kg (dark red). Results with an estimation error higher than 20 % are not shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

around 100 and 50, respectively. In wet conditions the selectivity generally decreases, but the slope of this variation seems to be water content independent. However, it is important to remember that at higher water concentration the actual uptakes of CO₂ and CH₄ are small, and the uncertainties of selectivity values are high.

### 3.8. Density maps

To get more intuitive insight in distribution of biogas components adsorbed in selected MOFs, we also calculated their 2D and 3D distribution inside simulation cell. As example, Figs. 11 and 12 provide
<figure><img src="image_15.png" /><figcaption>Fig. 10. (continued).</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 11. Density maps for CO₂, H₂O and H₂S at 2.23 bar for: (a) input gas containing 5 % of water, (b) input gas containing 0.1 % of water (dark red – high density, dark blue – low density of adsorbed molecules), (c) unit cell of KURSOH structure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

density maps (for CO₂, H₂O, and H₂S) for respectively monoclinic KURSOH and triclinic TIFHAT structures, calculated using home-made post-processing code and RASPA outputs.

In KURSOH, when the water concentration in the biogas is low (0.1 mol.%, which corresponds to a partial pressure of 0.00223 bar), H₂O molecules are barely adsorbed (Fig. 11b, middle line). On the contrary, CO₂ and H₂S are adsorbed strongly in the channels formed along monoclinic axis of the structure.

When water concentration increases up to 5 mol.% (partial pressure of 0.1115 bar), clustering of water at random places is observed (Fig. 11a, left panel). As at 298 K the experimental vapor (saturation) pressure of water is approximately 0.0317 bar (for simulation model the saturation pressure is 0.0455 bar), condensation of water molecules

within the MOF channels is observed. It indicates that at these thermodynamic p,T conditions water-water interactions (via hydrogen bonding) are stronger than the interactions between water molecules and the MOF framework, inducing the formation of stable clusters. Water clustering and the resulting occupation of the pore space can have dramatic consequences for MOF's performance in situations where moisture content is high. In MOFs which are less polar or less hydrophilic than KURSOH (see Fig. 2), the water-MOF interactions are stronger than water-water interactions, which prevents the formation of water clusters. Moreover, water organization depends on the geometry and size of the MOFs' pores. If the size of voids channels does not restrict cluster formation, lines of water running in the structures can be observed, unless the presence of other biogas components modify
<figure><img src="image_17.png" /><figcaption>**Fig. 12.** Density maps for CO₂ and H₂O adsorbed from wet input gas (5 %) at two pressures: (a) before H₂O condensation, p = 1.12 bar (b) after H₂O condensation, p = 2.28 bar (dark red – high density, dark blue – low density of adsorbed molecules), (c) TIFHAT structure, (d) 3D map of H₂O density distribution in TIFHAT at p = 2.28 bar (yellow – high density, purple – low density of adsorbed molecules). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

geometric and energetic landscape of the pores interior available for adsorption.

The distribution of adsorbed CO₂ does not changes significantly when the water content in the adsorbed gas increases, only its adsorbed quantity slightly diminishes (Fig. 11a and 11b, projections along x axis).

For H₂S, under slightly humid condition (0.1 mol.% of water, Fig. 11b), the distribution of molecules is comparable to that of CO₂ distribution. When the humidity of the input gas increases, adsorption of H₂S decreases and becomes negligible (therefore, not shown on Fig. 11a).

Fig. 12 provides a visual representation of CO₂ and H₂O distribution in TIFHAT (Fig. 12c), a slightly hydrophilic MOF (with enthalpy of water adsorption below 40.7 kJ/mol). In humid conditions (5 mol.% of water, Fig. 12a), at 1.12 bar (before the H₂O condensation) the distribution of CO₂ is relatively uniform, with few regions of higher density. The presence of H₂O seems to not significantly alter the CO₂ adsorption. At 2.28 bar, (after the H₂O condensation) the situation changes dramatically. The water fills almost all available space (see Fig. 12b and Fig. 12d), whereas CO₂ molecules concentrate in few adsorption sites within the pore.

## 4. Conclusions

This study provides a dependable and multifaceted comparison of performances of MOFs identified in the previous study reported in the literature, recognized as top candidates for biogas purification in wet conditions. The key strength and the best guarantee of the quality and consistency of the study is the consistent application of the same procedure for the best sorbent selection across all MOFs structures previously chosen based on non-uniform criteria.

The study has examined various parameters crucial for effective biogas component separation through adsorption, including structural factors, adsorption enthalpy, kinetic selectivity, regenerability, and, most importantly, stability of adsorption performance under variable humidity conditions. The structural parameters of the optimal structure determined in the present study coincide with general requirements for high efficacy nanoporous sorbents: high pore volume fraction (HVF above 0.6), high surface accessible for adsorption (ASA > 1900 m²/g.), and low mass density of the structure (between 0.6 and 1.2 g/cm³).

High enthalpies of adsorption, although suitable for high uptake of

the adsorbed gases, also imply significant energy expense to regenerate the material in any industrial process. Consequently, the structures with moderate adsorption energies (below 30 kJ/mol) like KURSOH, ISAYUW, RUVBER, TIFHAT, and SOMSIY, are deemed suitable for practical applications.

While CO₂/CH₄ selectivity in the studied MOFs is generally high (between 100 and 250), for industrial processes favoring free flow of methane through the structures and retention of other biogas components, ABIXOZ, KURSOH, LENROM, QOKCID, and TIFHAT appears more appropriate choice of sorbent, despite not having the highest CH₄ self-diffusion coefficients. CO₂ and H₂S diffusion rates are generally slow across all studied structures.

The impact of water on MOFs capacity to selectively adsorb biogas components is particularly essential. In general, at low water pressures clusters tend to form in the MOF pores. In highly hydrophilic materials, water quickly fills the entire structure even at low pressures. As higher water concentration the CO₂ and CH₄ uptakes become reduced, and the selectivity of structures generally decreases. Both factors contribute to high uncertainty of actual uptake/separation determination. These findings underscore the need for designing MOFs that can operate in real-world scenarios where moisture level is a variable process parameter.

In summary we show that while the MOFs-based membranes present a promising way for adsorption-based biogas purification/separation, the performance of the material itself is contingent upon a myriad of factors, including both environmental and intrinsic material properties. In such situation screening for MOFs' adsorption performance in variable humidity conditions, where one needs to discover complex patterns, optimize predictions, and provide more accurate and interpretable insights into the factors influencing MOFs separation capacity may be a complex procedure. Very often it requires application of special approaches, using machine learning algorithms. They are more efficient in optimizing models, identifying patterns, making predictions and, in particular, in extracting the most relevant features from the raw data affecting separation performance and stability. They also allow the models to adapt and improve in the process of continuous learning, as new data becomes available. In fine, such enhanced analysis and conclusions will better guide the synthesis of new structures with the desired properties.
CRediT authorship contribution statement

**Justyna Rogacka:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Formal analysis, Data curation, Conceptualization. **Patryk Pakula:** Writing – original draft, Validation, Software, Methodology, Investigation, Data curation. **Bartosz Mazur:** Validation, Software, Methodology, Conceptualization. **Lucyna Firlej:** Writing – review & editing, Writing – original draft, Validation, Supervision, Formal analysis. **Bogdan Kuchta:** Writing – review & editing, Validation, Supervision, Formal analysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgements

J.R. is supported by the Polish National Agency for Academic Exchange (decision no. BPN/BEK/2022/1/00053/DEC/1). B.K., B.M., L.F are supported by the National Science Centre (NCN), Poland (grant no. 2022/45/B/ST8/02028). Calculations have been carried out in Wroclaw Center for Networking and Supercomputing (http://www.wcscr.pl), grant no. 33.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cej.2024.150097.

References

[1] C. Janiak, J.K. Vieth, MOFs, MILs and more: concepts, properties and applications for porous coordination networks (PCNs), New J. Chem. 34 (2010) 2366, https://doi.org/10.1039/c0nj00275e.

[2] J. Canivet, A. Fateeva, Y. Guo, B. Coasne, D. Farrusseng, Water adsorption in MOFs: fundamentals and applications, Chem. Soc. Rev. 43 (2014) 5594–5617, https://doi.org/10.1039/c4cs00078a.

[3] I. Senkovska, S. Kaskel, Ultrahigh porosity in mesoporous MOFs: promises and limitations, Chem. Commun. 50 (2014) 7089, https://doi.org/10.1039/c4cc0524d.

[4] G. Avci, S. Velioglu, S. Keskin, High-throughput screening of MOF adsorbents and membranes for H2 purification and CO2 capture, ACS Appl. Mater. Interfaces 10 (2018) 33693–33706, https://doi.org/10.1021/acsami.8b12746.

[5] J.-R. Li, J. Sculley, H.-C. Zhou, Metal-organic frameworks for separations, Chem. Rev. 112 (2012) 869–932, https://doi.org/10.1021/cr200190s.

[6] T. Watanabe, S. Keskin, S. Nair, D.S. Sholl, Computational identification of a metal organic framework for high selectivity membrane-based CO2/CH4 separations: Cu (hfipbb)(H2hfipbb)0.5, PCCP 11 (2009) 11389, https://doi.org/10.1039/b918254n.

[7] C. Altintas, S. Keskin, Molecular simulations of MOF membranes and performance predictions of MOF/POLYMER mixed matrix membranes for CO 2 /CH 4 separations, ACS Sustain. Chem. Eng. 7 (2019) 2739–2750, https://doi.org/10.1021/acssueschemeng.8b05832.

[8] S. Keskin, D.S. Sholl, Assessment of a Metal–Organic framework membrane for gas separations using atomically detailed calculations: CO 2, CH 4, N 2, H 2 mixtures in MOF-5, Ind. Eng. Chem. Res. 48 (2009) 914–922, https://doi.org/10.1021/ie8010885.

[9] B. Liu, B. Smit, Molecular simulation studies of separation of CO2/N2, CO2/CH4, and CH4/N2 by ZIFs, J. Phys. Chem. C 114 (2010) 8515–8522, https://doi.org/10.1021/jp101531m/ASSET/IMAGES/LARGE/JP-2010-01531M_0008.JPEG.

[10] S. Keskin, T.M. van Heest, D.S. Sholl, Can metal-organic framework materials play a useful role in large-scale carbon dioxide separations? ChemSusChem 3 (2010) 879–891, https://doi.org/10.1002/cssc.201000114.

[11] I. Erucar, S. Keskin, Unlocking the effect of H2O on CO2 separation performance of promising MOFs using atomically detailed simulations, Ind. Eng. Chem. Res. 59 (2020) 3141–3152, https://doi.org/10.1021/acs.iecr.9b05487.

[12] C. Altintas, G. Avci, H. Daglar, A. Nemati Vesali Azar, S. Velioglu, I. Erucar, S. Keskin, Database for CO2 separation performances of MOFs based on computational materials screening, ACS Appl. Mater. Interfaces 10 (2018) 17257–17268, https://doi.org/10.1021/ACSAMI.8B04600/SUPPL_FILE/AM8B04600 SI 002.XLSX.

[13] J. Jiang, Charged soc metal-organic framework for high-efficacy H2 adsorption and syngas purification: atomistic simulation study, AIChE J 55 (2009) 2422–2432, https://doi.org/10.1002/AIC.11865.

[14] K. Tan, S. Zuluaga, Q. Gong, Y. Gao, N. Nijem, J. Li, T. Thonhauser, Y.J. Chabal, Competitive coadsorption of CO2 with H2O, NH3, SO2, NO, NO2, N2, O2, and CH4 in M-MOF-74 (M = mg CO, ni): the role of hydrogen bonding, Chem. Mater. 27 (2015) 2203–2217, https://doi.org/10.1021/ACS.CHEMMATER.5B00315/SUPPL_FILE/CM5B00315 SI 001.PDF.

[15] G. Li, P. Xiao, P. Webley, J. Zhang, R. Singh, M. Marshall, Capture of CO2 from high humidity flue gas by vacuum swing adsorption with zeolite 13X, Adsorption 14 (2008) 415–422, https://doi.org/10.1007/S10450-007-9100-Y/METRICS.

[16] P.A. Webley, J. Zhang, Microwave assisted vacuum regeneration for CO2 capture from wet flue gas, Adsorption 20 (2014) 201–210, https://doi.org/10.1007/S10450-013-9563-Y/TABLES/2.

[17] L. Joos, J.A. Swisher, B. Smit, Molecular simulation study of the competitive adsorption of H2O and CO2 in zeolite 13X, Langmuir 29 (2013) 15936–15942, https://doi.org/10.1021/LA403824G/SUPPL_FILE/LA403824G SI 001.PDF.

[18] A. Morozenko, I.V. Leontyev, A.A. Stuchebrakov, Dipole moment and binding energy of water in proteins from crystallographic analysis, J. Chem. Theory Comput. 10 (2014) 4618–4623, https://doi.org/10.1021/CT500358R/ASSET/IMAGES/CT-2014-00358R M009.GIF.

[19] The quadrupole moment of the carbon dioxide molecule, Proc. R. Soc. Lond. A 273 (1963) 275–289, https://doi.org/10.1098/RSPA.1963.0088.

[20] H. Daglar, H.C. Gulbalkan, G. Avci, G.O. Aksu, O.F. Altundal, C. Altintas, I. Erucar, S. Keskin, Effect of metal-organic framework (MOF) database selection on the assessment of gas storage and separation potentials of MOFs, Angew. Chem. 133 (2021) 7907–7916, https://doi.org/10.1002/ANGE.202015250.

[21] Y.G. Chung, E. Haldoupis, B.J. Bucior, M. Haranczyk, S. Lee, H. Zhang, K. D. Vogiatzis, M. Milisavljevic, S. Ling, J.S. Camp, B. Slater, J.I. Siepmann, D. S. Sholl, R.Q. Snurr, Advances, updates, and analytics for the computation-ready, experimental metal-organic framework database: CoRE MOF 2019, J. Chem. Eng. Data 64 (2019) 5985–5998, https://doi.org/10.1021/acs.jedc.9b00835.

[22] P.Z. Moghadam, A. Li, S.B. Wiggin, A. Tao, A.G.P. Maloney, P.A. Wood, S.C. Ward, D. Fairen-Jimenez, Development of a Cambridge structural database subset: a collection of metal-organic frameworks for past, present, and future, Chem. Mater. 29 (2017) 2618–2625, https://doi.org/10.1021/ACS.CHEMMATER.7B00441/SUPPL_FILE/CM7B00441 SI 004.XLSX.

[23] H. Demir, C.J. Cramer, J.I. Siepmann, Computational screening of metal–organic frameworks for biogas purification, Mol. Syst. Des. Eng. 4 (2019) 1125–1135, https://doi.org/10.1039/C9ME00095J.

[24] J. Glover, E. Besley, A high-throughput screening of metal–organic framework based membranes for biogas upgrading, Faraday Discuss. 231 (2021) 235–257, https://doi.org/10.1039/D1FD00005E.

[25] J. Rogacka, A. Seremak, A. Luna-Triguero, F. Formalik, I. Matito-Martos, L. Firlej, S. Calero, B. Kuchta, High-throughput screening of metal – organic frameworks for CO2 and CH4 separation in the presence of water, Chem. Eng. J. 403 (2021) 126392, https://doi.org/10.1016/j.cej.2020.126392.

[26] T.F. Willems, C.H. Rycroft, M. Kazi, J.C. Meza, M. Haranczyk, Algorithms and tools for high-throughput geometry-based analysis of crystalline porous materials, Microporous Mesoporous Mater. 149 (2012) 134–141, https://doi.org/10.1016/J.MICROMESO.2011.08.020.

[27] D. Dubbeldam, S. Calero, D.E. Ellis, R.Q. Snurr, RASPA: molecular simulation software for adsorption and diffusion in flexible nanoporous materials, Mol. Simul. 42 (2016) 81–101, https://doi.org/10.1080/08927022.2015.1010082.

[28] B.L. Eggimann, A.J. Sunnarborg, H.D. Stern, A.P. Bliss, J.I. Siepmann, An online parameter and property database for the TriaPPE force field, Mol. Simul. 40 (2014) 101–105.

[29] T.J. Dick, J.D. Madura, Chapter 5 A Review of the TIP4P, TIP4P-EW, TIP5P, and TIP5P-E Water Models, Annu Rep Comput Chem 1 (2005) 59–74. 10.1016/S1574-1400(05)01005-4.

[30] A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations, J. Am. Chem. Soc. 114 (1992) 10024–10035, https://doi.org/10.1021/ja00051a040.

[31] S.L. Mayo, B.D. Olafson, W.A. Goddard, DREIDING: a generic force field for molecular simulations, J. Phys. Chem. 94 (1990) 8897–8909, https://doi.org/10.1021/j100389a010.

[32] S. Kancharlapalli, A. Gopalan, M. Haranczyk, R.Q. Snurr, Fast and accurate machine learning strategy for calculating partial atomic charges in metal-organic frameworks, J. Chem. Theory Comput. 17 (2021) 3052–3064, https://doi.org/10.1021/ACS.JCTC.0C01229/SUPPL_FILE/CT0C01229 SI 005.XLS.

[33] T.J.H. Vlugt, E. García-Pérez, D. Dubbeldam, S. Ban, S. Calero, Computing the heat of adsorption using molecular simulations: the effect of strong coulombic interactions, J. Chem. Theory Comput. 4 (2008) 1107–1118, https://doi.org/10.1021/ct700342k.

[34] V. Finsy, S. Calero, E. García-Pérez, P.J. Merkling, G. Vedts, D.E. De Vos, G. V. Baron, J.F.M. Denayer, Low-coverage adsorption properties of the metal–organic framework MIL-47 studied by pulse chromatography and Monte Carlo simulations, PCCP 11 (2009) 3515, https://doi.org/10.1039/b822247a.

[35] J. Rogacka, L. Firlej, B. Kuchta, Modeling of low temperature adsorption of hydrogen in carbon nanopores, J. Mol. Model. 23 (2017), https://doi.org/10.1007/s00894-016-3202-y.
[36] J. Rogacka, F. Formalik, A.L. Triguero, L. Firlej, B. Kuchta, S. Calero, Intermediate states approach for adsorption studies in flexible metal-organic frameworks, PCCP 21 (2019), https://doi.org/10.1039/c8cp06817h.

[37] Z. Qiao, K. Zhang, J. Jiang, In silico screening of 4764 computation-ready, experimental metal-organic frameworks for CO2 separation, J Mater Chem A Mater 4 (2016) 2105–2114, https://doi.org/10.1039/C5TA08984K.

[38] A.-M. Banu, D. Friedrich, S. Brandani, T. Düren, A multiscale study of MOFs as adsorbents in H2 PSA purification, Ind. Eng. Chem. Res. 52 (2013) 9946–9957, https://doi.org/10.1021/ie4011035.

[39] I. Deroche, L. Gaberova, G. Maurin, P. Llewellyn, M. Castro, P. Wright, Adsorption of carbon dioxide in SAPO STA-7 and AlPO-18: grand canonical Monte Carlo simulations and microcalorimetry measurements, Adsorption 14 (2008) 207–213, https://doi.org/10.1007/S10450-007-9098-1/METRICS.

[40] D. Senthil Raja, J.H. Luo, C.Y. Wu, Y.J. Cheng, C.T. Yeh, Y.T. Chen, S.H. Lo, Y. L. Lai, C.H. Lin, Solvothermal synthesis, structural diversity, and properties of alkali metal-organic frameworks based on V-shaped ligand, Cryst. Growth Des. 13

(2013) 3785–3793, https://doi.org/10.1021/CG400801S/SUPPL_FILE/CG400801S SI 002.CIF.

[41] A.E. Kabeel, Adsorption-desorption operations of multilayer desiccant packed bed for dehumidification applications, Renew Energy 34 (2009) 255–265, https://doi.org/10.1016/J.RENENE.2008.04.011.

[42] J.H. Park, J.N. Kim, S.H. Cho, J.D. Kim, R.T. Yang, Adsorber dynamics and optimal design of layered beds for multicomponent gas adsorption, Chem. Eng. Sci. 53 (1998) 3951–3963, https://doi.org/10.1016/S0009-2509(98)00196-1.

[43] J.A. Shamim, W.L. Hsu, K. Kitaoka, S. Paul, H. Daiguji, Design and performance evaluation of a multilayer fixed-bed binder-free desiccant dehumidifier for hybrid air-conditioning systems: part I – experimental, Int. J. Heat Mass Transf. 116 (2018) 1361–1369, https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2017.09.051.

[44] P. Gandhidasan, A.A. Al-Farayedhi, A.A. Al-Mubarak, Dehydration of natural gas using solid desiccants, Energy 26 (2001) 855–868, https://doi.org/10.1016/S0360-5442(01)00034-2.