Modelling Selective CO2 Absorption and Validation via Photosynthetic Bacteria and Chemical Adsorbents for Methane Purification in Anaerobic Fermentation Bioreactors

This study delves into advanced methane purification techniques within anaerobic fermentation bioreactors, focusing on selective CO2 absorption and comparing photosynthetic bacteria (PNSB) with chemical adsorbents. Our investigation demonstrates that MgO-Mg(OH)2 composites exhibit remarkable CO2 selectivity over CH4, substantiated through rigorous bulk and surface modelling analyses. To address the challenges posed by MgCO3 shell formation on MgO particles, hindering CO2 transport, we advocate for the utilisation of MgO-Mg(OH)2 composites. In on-site experiments, these composites, particularly saturated MgO-Mg(OH)2 solutions (S2), achieved an astonishing 100% CO2 removal rate within a single day while preserving CH4 content. In contrast, solid MgO powder (S3) retained a mere 5% of CH4 over a 10 h period. Although PNSB (S1) exhibited slower CO2 removal, it excelled in nutrient recovery from anaerobic effluent. We introduce a groundbreaking hybrid strategy that leverages S2’s swift CO2 removal and S1 PNSB’s nutrient recovery capabilities, potentially resulting in a drastic reduction in bioreactor processing time, from 10 days when employing S1 to just 1 day with the use of S2. This represents a remarkable efficiency improvement of 1000%. This pioneering strategy has the potential to revolutionise methane purification, enhancing both efficiency and sustainability. Importantly, it can be seamlessly integrated into existing bioreactors through an additional CO2 capture step, offering a promising solution for advancing biogas production and promoting sustainable waste treatment practices.


Introduction
As a naturally occurring and renewable energy source, biogas, which consists mainly of carbon dioxide-methane (CO 2 -CH 4 ) mixtures, has emerged as an alternative fuel to natural gas. However, the presence of CO 2 can reduce the heating value and generate greenhouse gases. Therefore, the effective separation of CO 2 and CH 4 in biogas streams through targeted CO 2 reduction is critical for the practical application of biogas.
Various separation techniques have been developed to solve the problem, such as absorption, membrane separation, cryogenic separation, and adsorption [1]. While the photosynthetic bacteria system offers the advantage of simultaneous CO 2 capture and methane content enhancement [2], it is essential to acknowledge that its economic viability can be compromised by challenges in cultivation techniques [3,4]. The current materials and methods are less cost-and time-effective and should be redesigned based on this research finding. adsorption capacity. The adsorption of CH 4 is anticipated to remain minimal due to the restricted interaction between CH 4 and the surface OH-group on the Mg(OH) 2 surface. The current study suggests using MgO-Mg(OH) 2 composite as chemical absorbents for CO 2 and CH 4 separation in biogas, in light of these insights. While admitting the inherent constraints in CH 4 adsorption brought on by the weaker interaction with the Mg(OH) 2 surface, the interweaving of both materials offers the possibility of increased CO 2 capture efficiency. Additionally, the use of CO 2 by microalgae or anaerobic photosynthetic bacteria is a rapidly expanding technology for energy conservation. In order to upgrade the methane gas produced by a pig farm, we conducted our research in photobioreactors employing purple non-sulphur bacteria (PNSB) and composite materials made of MgO-Mg(OH) 2 [26].
This study started by simulating the selective absorption of CO 2 over CH 4 by MgO-Mg(OH) 2 composites using both bulk thermodynamic and surface Density Functional Theory (DFT)-based modelling. The results from the modelling establish the groundwork for the later experimental validations. For validation purposes, both biological and chemical experimental methodologies were used. First, biological PNSB was introduced as an absorption agent (S1), which is renowned for its cutting-edge capabilities in wastewater treatment and bioresource recovery. The second method involves chemical absorption utilising two substances: an aqueous solution of MgO-Mg(OH) 2 (S2) and solid MgO powder (S3). On-site sampling was conducted at the anaerobic fermentation methane outlet of a pig manure solid-liquid separation-free bioreactor. Methane gas produced from the anaerobic fermentation of solid-liquid separated free livestock waste was passed through a desulphurization tower and subsequently injected into the bioreactor, allowing for a 10-day shaken culture experiment. To compare the adsorption effects of the biological and chemical techniques, variations in CO 2 and CH 4 were continually measured throughout the observation time. The findings of the experiments were compared to those predicted by the models, and both biological and chemical methods underwent careful analysis. In the end, a synergistic strategy combining PNSB (S1) and MgO-Mg(OH) 2 aqueous solution (S2) is suggested.

Methodology
This study employs a combination of modelling prediction and experimental validation methods to investigate CO 2 selectivity in the S1, S2, and S3 systems.

Theoretical Calculations
For computer modelling, two techniques are utilised: (1) bulk thermodynamic calculations using the commercial software FactSage (Centre for Research in Computational Thermochemistry, Montreal, Canada) [27] and (2)  In our thermodynamic modelling, we utilised the Equilib module from FactSage [27] to compute the chemical equilibria involving CO 2 (gas) and CH 4 (gas) in conjunction with MgO and Mg(OH) 2 . The calculations incorporated thermodynamic data for all relevant compounds, as provided in the FactPS and FToxid databases. These calculations were conducted at a temperature of 25 • C and a pressure of 1 ATM.

DFT Calculations of CO 2 and CH 4 Absorption on MgO and Mg(OH) 2 Surfaces
In order to investigate the surface absorption of CO 2 /CH 4 on MgO and Mg(OH) 2 , a projector augmented wave (PAW) method [30,31] was adopted as a plane-wave basis set to describe the electron-core interaction. The kinetic energy cutoff for the plane-wave expansion was set at 500 eV. The van der Waals contribution was taken into account using the DFT+D3 correction technique developed by Grimme et al. [32]. The total energy convergence was set as 1.0 × 10 −6 eV, and the force on each individual atom was minimised to be smaller than 0.01 eV/Å for geometry optimisation and total energy calculations. The value for smearing was fixed to 0.01 eV. Monkhorst−Pack [33] K-points mesh was used for sampling the Brillouin zone, with the K-points number (N K ) being adjusted to keep (N K × L) and with L being the lattice constant equal to~45 Å for structural relaxations and 75 Å for electronic calculations, respectively. The previously published [34] optimised MgO and Mg(OH) 2 crystalline structures were used in this work. MgO and Mg(OH) 2 were both cleaved in the most stable (001) orientation in order to examine their adsorption of CO 2 and CH 4 [35,36]. To make sure that the interaction force between the layer planes was sufficiently small, the vacuum between them was 20 Å thick. MgO slabs are composed of six layers of the 3×3 expansion of the MgO unit cell. The adsorbate molecule and top 3 layers were free to relax, while the bottom 3 layers remained fixed in their bulk placements. Mg(OH) 2 slabs are composed of three layers of the 4×4 expansion of the Mg(OH) 2 unit cell. The adsorbate molecule and top two layers were free to relax while the bottom layer was held in its bulk position.
The adsorption energy E ad of the adsorbate molecule X (X = CO 2 or CH 4 ) on the MgO and Mg(OH) 2 surface is defined as E ad = E surface+X − E X − E surface , where E surface+X is the total energy of the surface and adsorbate molecule, E X is the energy of the adsorbate molecule CO 2 or CH 4 , and E surface is the total energy of the surface. A lower value of E ad denotes the stronger molecule's adsorption on the surface. The charge of an atom was defined as the difference between the valence charge and the Bader charge. The Bader charge was calculated using the Bader scheme of charge density decomposition [37,38].

Materials and Reagents
Chemicals with a purity of over 95% and 200 mL drip bottles with sealed caps were procured from Nihon Shiyaku Industries Ltd. (Osaka, Japan). The PNSB used in the study consisted of Rhodospirillum, Rhodopseudomonas, and Rhodomicrobium, which constitute the major microbial communities provided by the Food Research Institute. Rhodopseudomonas palustris makes up the majority of the bacterial communities among them. The components of the bacterial growth medium are detailed in Table 1. In our earlier study, we reported on the synthesis and characterisation of MgO-Mg(OH) 2 composites [25].

Separation Measurement of S1, S2, and S3 Systems, Respectively
Dry heat sterilisation was applied to a 200 cc drip bottle over the course of six hours in an oven set to 160 • C. Three different types of separation experiments were carried out in a SAN-C301 biological safety cabinet from San-Hsiung Technology Co., Ltd. (Kaohsiung City, Taiwan): (1) introducing S1, comprising 100 mL of PNSB liquid with a cell concentration of 106 cells/mL, into each of the five sterilised bottles or bioreactors, (2) introducing S2, consisting of 20 g of MgO powder and 100 mL of H 2 O, into each of the five bioreactors, and (3) adding S3, including 20 g of magnesium oxide only, into each of the five bioreactors, once the bioreactors have cooled down. Three distinct types of bottles were agitated at 150 rpm, serving as photobioreactors for biogas purification. Subsequently, each of the five duplicate bottles was filled with gas via the methane vent from the Central Livestock Farm. Following this, each bottle was promptly sealed using a rubber stopper and secured with an aluminium cover. These bioreactors were then placed within a growth chamber set to maintain a temperature of 25 • C, operating under a 16/8 h light/dark cycle with a light intensity of 3000 lux.
To determine the concentrations of CO 2 and CH 4 , we employed Shimadzu GC-8A GC-TCD (Shimadzu Scientific Instruments (Taiwan) Co., Ltd., Taipei City, Taiwan) equipped with a Shimadzu SUS column (4 × 3.0 × 3.0 m) packed with Porapax Q50/80 mesh material. The injection temperature, detector temperature, and oven temperature were set at 150 • C, with the oven temperature held at 45 • C. Helium served as the carrier gas. The concentration of CH 4 and CO 2 was determined using a calibration curve established via a standard gas mixture (55% CH 4 , 20% CO 2 , and 25% He) obtained from Jing De Gases Co., Ltd. (Kaohsiung City, Taiwan) Table 2 calculates and summarises the chemical reactions for equilibrium CO 2 and CH 4 absorption in S2 and S3 systems. The calculated products, which might not be achieved because of unfavourable kinetics, are thermodynamic equilibrium products.

Bulk Thermodynamic Calculations
As can be observed from Table 2, when MgO reaches the equilibrium reaction with H 2 O, it can completely transform into Mg(OH) 2 , as shown in Equation (1). Equations (2) and (3) demonstrate that an equal amount of MgCO 3 was created by MgO and Mg(OH) 2 with a 100% reaction consuming the same amount of CO 2 . However, neither MgO nor Mg(OH) 2 are anticipated to react with CH 4 . Even though Equations (2) and (3) predict that MgO and Mg(OH) 2 can absorb 100% of the CO 2 , kinetic restrictions may prevent their implementation. For instance, the production of MgCO 3 shells around the core MgO particles greatly slows down the CO 2 absorption process [6]. Contrarily, physical adsorption attributed to structural advantages or electrostatic interaction may have a considerable impact, even though Equations (4) and (5) predict 0% CH 4 absorption by MgO and Mg(OH) 2 . The following in-depth analysis of the surface absorption of CO 2 /CH 4 on MgO and Mg(OH) 2 surfaces is therefore required.

Surface DFT Calculations
The optimised configurations for MgO and Mg(OH) 2 with adsorbed CO 2 and CH 4 are shown in Figure 1. The attractive/repulsive interaction between molecules was not taken into account when estimating the adsorption energy in this simulation because only one adsorbate molecule was introduced to the surface. According to our preliminary research, the adsorption energy of the adsorbate molecule on the top of the lattice oxygen of MgO (Figure 2a) was the highest among the four potential adsorption sites, i.e., the two-fold bridge, the four-fold hollow, on the top of the oxygen anion, and on the top of the magnesium cation. However, among the three potential adsorption sites-the two-fold bridge, the four-fold hollow, and the top of the hydrogen cation-the adsorbate molecule's adsorption energy was the highest on top of the four-fold hollow of Mg(OH) 2 . This is consistent with earlier findings [39,40].
As can be observed from Table 2, when MgO reaches the equilibrium reaction with H2O, it can completely transform into Mg(OH)2, as shown in Equation (1). Equations (2) and (3) demonstrate that an equal amount of MgCO3 was created by MgO and Mg(OH)2 with a 100% reaction consuming the same amount of CO2. However, neither MgO nor Mg(OH)2 are anticipated to react with CH4. Even though Equations (2) and (3) predict that MgO and Mg(OH)2 can absorb 100% of the CO2, kinetic restrictions may prevent their implementation. For instance, the production of MgCO3 shells around the core MgO particles greatly slows down the CO2 absorption process [6]. Contrarily, physical adsorption attributed to structural advantages or electrostatic interaction may have a considerable impact, even though Equations (4) and (5) predict 0% CH4 absorption by MgO and Mg(OH)2. The following in-depth analysis of the surface absorption of CO2/CH4 on MgO and Mg(OH)2 surfaces is therefore required.

Surface DFT Calculations
The optimised configurations for MgO and Mg(OH)2 with adsorbed CO2 and CH4 are shown in Figure 1. The attractive/repulsive interaction between molecules was not taken into account when estimating the adsorption energy in this simulation because only one adsorbate molecule was introduced to the surface. According to our preliminary research, the adsorption energy of the adsorbate molecule on the top of the lattice oxygen of MgO (Figure 2a) was the highest among the four potential adsorption sites, i.e., the two-fold bridge, the four-fold hollow, on the top of the oxygen anion, and on the top of the magnesium cation. However, among the three potential adsorption sites-the two-fold bridge, the four-fold hollow, and the top of the hydrogen cation-the adsorbate molecule's adsorption energy was the highest on top of the four-fold hollow of Mg(OH)2. This is consistent with earlier findings [39,40].  Table 3 lists the adsorption properties for CH4 and CO2 on the MgO and Mg(OH)2 surface. MgO and Mg(OH)2 exhibit strong and weak adsorption to CO2, respectively. The of the PDOSs for the two atoms overlap between −5.0 and 0 eV. The strong hybridisation stabilises the CO2 molecule on the MgO surface. There is also hybridisation between the O of Mg(OH)2 and the C of CO2 since their PDOSs share some peaks. However, as can be seen in Figure 2b, the overlap is slight. Therefore, the weak hybridisation results in a low adsorption energy of CO2 on the Mg(OH)2 surface.   In conclusion, the adsorption energies computed in Table 3

Measurements of Selective CO2 Capture over CH4 in S1, S2, and S3 Systems
The dynamic changes in CO2 concentration seen in photobioreactors are shown in Figure 4 using biological S1 and chemical S2/S3 approaches. Over a 10-day period at 150 rpm, S1 (photosynthetic bacteria) and S3 (MgO solid powder) consistently reduce CO2 concentration, while S2 completely eliminates CO2 on the first day. Figure 5 displays changes in the observed CH4 concentration over time in photobioreactors. S1 and S2 both  Table 3 lists the adsorption properties for CH 4 and CO 2 on the MgO and Mg(OH) 2 surface. MgO and Mg(OH) 2 exhibit strong and weak adsorption to CO 2 , respectively. The adsorption energy difference is 0.525 eV. Contrarily, CH 4 exhibits weak adsorption on both MgO and Mg(OH) 2 . The adsorption energy difference is 0.015 eV. This means that MgO has a strong attraction to CO 2 , while Mg(OH) 2 has a mild one. An interwoven composite with alternate layers of MgO and Mg(OH) 2 is anticipated in order to improve CO 2 adsorption, which employs a mechanism similar to that of the Namib Desert beetle. Additionally, a composite comprised of MgO and Mg(OH) 2 would have little impact on the adsorption of CH 4 because of CH 4 's modest affinity for both of these substances. This suggests that CO 2 and CH 4 in the biogas might be separated. The distance from CO 2 to the MgO surface is shown in Figure 1; it is 1.517, which is more than the C-O bond length of 1.43 mm [41]. This demonstrates that the adsorbed CO 2 does not chemically react with MgO to form carbonate; therefore, the adsorption can be assumed to be strong physical adsorption. Since the distance between CO 2 and the Mg(OH) 2 surface is significantly longer than the length of the C-O bond, it is likely due to weak physical adsorption. CH 4 is farther away from MgO and Mg(OH) 2 surface than CO 2 . Perhaps the steric effect is involved here. This agrees with the average angle depicted in  Table 3 shows that the CO 2 molecule accepts a charge of 0.40, indicating that MgO donated 0.40 electrons to the CO 2 molecule. The CO 2 may become polarised as a result of MgO's transfer of electrons to it. The fact that MgO and Mg(OH) 2 both gave very few electrons to CH 4 molecules points to a weak interaction with the surface. As a result, CH 4 can be regarded as being weakly physically adsorbed by MgO and Mg(OH) 2 . Figure 2 displays the projected density of states (PDOSs) of the atoms for CO 2adsorbed MgO and Mg(OH) 2 . The significant hybridisation between the O of CO 2 and Mg of MgO, as well as between the C of CO 2 and O of MgO, is observed in Figure 2a. The peaks of the PDOSs for the two atoms overlap between −5.0 and 0 eV. The strong hybridisation stabilises the CO 2 molecule on the MgO surface. There is also hybridisation between the O of Mg(OH) 2 and the C of CO 2 since their PDOSs share some peaks. However, as can be seen in Figure 2b, the overlap is slight. Therefore, the weak hybridisation results in a low adsorption energy of CO 2 on the Mg(OH) 2 surface.    In conclusion, the adsorption energies computed in Table 3

Measurements of Selective CO2 Capture over CH4 in S1, S2, and S3 Systems
The dynamic changes in CO2 concentration seen in photobioreactors are shown in Figure 4 using biological S1 and chemical S2/S3 approaches. Over a 10-day period at 150 rpm, S1 (photosynthetic bacteria) and S3 (MgO solid powder) consistently reduce CO2 concentration, while S2 completely eliminates CO2 on the first day. Figure 5 displays changes in the observed CH4 concentration over time in photobioreactors. S1 and S2 both In conclusion, the adsorption energies computed in Table 3  3.3. Measurements of Selective CO 2 Capture over CH 4 in S1, S2, and S3 Systems The dynamic changes in CO 2 concentration seen in photobioreactors are shown in Figure 4 using biological S1 and chemical S2/S3 approaches. Over a 10-day period at 150 rpm, S1 (photosynthetic bacteria) and S3 (MgO solid powder) consistently reduce CO 2 concentration, while S2 completely eliminates CO 2 on the first day. Figure 5 displays changes in the observed CH 4 concentration over time in photobioreactors. S1 and S2 both show a negligible drop in CH 4 during a 10-day period at 150 rpm. However, S3 (the introduction of MgO solid powder in the photobioreactor) causes the CH 4 reduction to fluctuate, which is consistent with the results of our DFT simulation shown in Table 3 (−0.173 eV for CH 4 /MgO adsorption). The simulation indicates that the adsorption energy of CH 4 on the MgO surface is stronger than that of CH 4 on Mg(OH) 2 , providing an explanation for the observed fluctuations in CH 4 concentration when MgO solid powder is solely added. The abundant MgO surface sites in S3 contribute to the varying CH 4 concentration.
Additionally, the CO 2 -phobic (Mg(OH) 2 ) and CO 2 -philic (MgO) model [25,34], which is modelled after the water collection system used by the Namib Desert beetle [24], is responsible for the quick elimination of CO 2 through the use of S2, where MgO-Mg(OH) 2 particles are used due to metastable chemical equilibrium, as in the current study, the solubility of MgO is 0.0086 g/100 mL at 30 • C. We did not look at the early phases of the reaction because the effectiveness of our suggested method for purifying methane was the focus of our work. Neshat et al. [2] only observed a slight reduction in CO 2 levels after three days and a 10% decline after ten days when employing purple photosynthetic bacteria for CO 2 fixation from biogas, a significantly slower process compared to our combined approach utilising photosynthetic bacteria and adsorption.  In contrast to adsorbents that are only utilised for methane purification, PNSB demonstrated the potential for concurrent nutrient recovery and biogas upgrading from anaerobic digested wastewater. The S2 method and S1 for waste water treatment and resource recovery can be coupled to expedite the CO 2 separation from CH 4 process.

Conclusions
This study presents a comprehensive analysis of methane purification in anaerobic fermentation bioreactors, with a particular emphasis on selective CO 2 absorption. We systematically evaluated the efficacy of chemical adsorbents (S2 and S3) and photosynthetic bacteria (PNSB) for CO 2 capture and methane purification, employing a combination of modelling and experimental techniques.
Our investigation initially demonstrated the selective CO 2 over CH 4 behaviour in MgO and Mg(OH) 2 systems through bulk thermodynamic equilibrium modelling. Al-though it could not predict CH 4 absorption on MgO, the surface DFT modelling results confidently predicted excellent CO 2 selectivity for MgO-Mg(OH) 2 composites, a prediction substantiated by on-site measurements. PNSB (S1) exhibited commendable CO 2 removal, achieving a 40% reduction over 10 days. In contrast, the S2 (MgO-Mg(OH) 2 composite) showed remarkable speed, achieving complete CO 2 removal within a single day while retaining 100% of the original CH 4 content in the biogas. In contrast, S3 (solid MgO powder) was less effective, preserving only 5% of CH 4 after a 10 h reaction. Consequently, S2 demonstrated an unparalleled CO 2 removal speed, outperforming PNSB by a factor of 10.
Drawing from these results, we propose an innovative hybrid method that leverages the rapid CO 2 removal capability of S2 and the superior nutrient recovery attributes of S1 PNSB. This approach holds the potential to revolutionise methane purification in anaerobic fermentation bioreactors, enhancing both efficiency and sustainability. Moreover, it can be seamlessly integrated into existing bioreactors with the addition of an adsorption module, making it highly practical.

Data Availability Statement:
The datasets used and/or analysed during the current study are available from the corresponding author upon reasonable request.