Technological, Ecological, and Energy-Economic Aspects of Using Solidified Carbon Dioxide for Aerobic Granular Sludge Pre-Treatment Prior to Anaerobic Digestion

The technology of aerobic granular sludge (AGS) seems prospective in wastewater bio-treatment. The characteristics as well as compactness and structure of AGS have been proved to significantly affect the effectiveness of thus far deployed methods for sewage sludge processing, including anaerobic digestion (AD). Therefore, it is deemed necessary to extend knowledge on the possibilities of efficient AGS management and to seek viable technological solutions for methane fermentation of sludge of this type, including by means of using the pre-treatment step. Little is known about the pre-treatment method with solidified carbon dioxide (SCO2), which can be recovered in processes of biogas upgrading and enrichment, leading to biomethane production. This study aimed to determine the impact of AGS pre-treatment with SCO2 on the efficiency of its AD. An energy balance and a simplified economic analysis of the process were also carried out. It was found that an increasing dose of SCO2 applied in the pre-treatment increased the concentrations of COD, N-NH4+, and P-PO43− in the supernatant in the range of the SCO2/AGS volume ratios from 0.0 to 0.3. No statistically significant differences were noted above the latter value. The highest unit yields of biogas and methane production, reaching 476 ± 20 cm3/gVS and 341 ± 13 cm3/gVS, respectively, were obtained in the variant with the SCO2/AGS ratio of 0.3. This experimental variant also produced the highest positive net energy gain, reaching 1047.85 ± 20 kWh/ton total solids (TS). The use of the higher than 0.3 SCO2 doses was proved to significantly reduce the pH of AGS (below 6.5), thereby directly diminishing the percentage of methanogenic bacteria in the anaerobic bacterial community, which in turn contributed to a reduced CH4 fraction in the biogas.


Introduction
The methods for sewage sludge processing are well-known and widely implemented on a technical scale. They have been optimized for the most commonly applied wastewater treatment solutions based on the use of suspended conventional activated sludge (CAS) [1]. A novel, alternative, and competitive technology is offered by the use of granular activated sludge (AGS) [2]. The strengths and advantages of this solution have spurred the interest of researchers, operators, and designers, which has consequently led to a growing number of commercial-scale installations [3,4]. The use of AGS has been shown to allow simplifying the technology, increasing the resistance of the biological system to the variability of wastewater composition, shortening the reactor operation cycle, resigning from the need to ensure variable oxygen conditions in order to remove nutrients, and simplifying the methods of excess sludge separation [5]. The AGS-based wastewater treatment systems are now widely accepted as promising and future-proof solutions due to their high level of There are no reports in the world literature on the use of SCO 2 in the AGS pretreatment process prior to AD. Given the characteristics of AGS and the results obtained during CAS disintegration, as well as taking into account the possibility of SCO 2 recovery, it seems justified to verify the possibility of implementing this method for AGS pre-treatment. The main goal of this study was to determine the effect of AGS pre-treatment with SCO 2 on the efficiency of its AD. The impact of this disintegration method on the structure and properties of sewage sludge, changes in the concentration of organic and biogenic compounds in the dissolved phase, taxonomic structure of anaerobic bacteria, and the yield and kinetics of biogas production and methane content were assessed as well. Finally, empirical optimization models were developed, and an energy and economic balance was prepared in order to demonstrate the competitiveness of the pre-treatment technology under study.
water of proteins, which modifies their properties. The extracellular crystals that expand during the freezing process destroy the microbial cells that lie between them. They also cause damage to biomembranes and modify their properties, which leads to the leakage of intracellular substances into the environment [22].
There are no reports in the world literature on the use of SCO2 in the AGS pretreatment process prior to AD. Given the characteristics of AGS and the results obtained during CAS disintegration, as well as taking into account the possibility of SCO2 recovery, it seems justified to verify the possibility of implementing this method for AGS pretreatment. The main goal of this study was to determine the effect of AGS pre-treatment with SCO2 on the efficiency of its AD. The impact of this disintegration method on the structure and properties of sewage sludge, changes in the concentration of organic and biogenic compounds in the dissolved phase, taxonomic structure of anaerobic bacteria, and the yield and kinetics of biogas production and methane content were assessed as well. Finally, empirical optimization models were developed, and an energy and economic balance was prepared in order to demonstrate the competitiveness of the pretreatment technology under study.

AGS and Inoculum of the Anaerobic Sludge (AS)
AGS was cultured under laboratory conditions (23 °C, relative humidity 50%). The CAS from the municipal wastewater treatment plant in Rajgród, Poland (53.99434 N, 22.76847 E) with PE = 2500 served as the inoculum. The average capacity of the treatment plant is 400 m 3 /d, and it operates based on the terrace-flow technology with increased nutrient removal. Prior to granule cultivation, the activated sludge was filtered through a sieve with a mesh diameter of 1.0 mm, which allowed the separation of fine suspensions from a mixture of wastewater and activated sludge and enabled achieving a high organic mass of CAS. The AGS culture process was continued for 120 days in a sequencing batch reactor (SBR) [23]. The reinforced PE reactor was equipped with a stirrer, aerating diffuser, oxygen probe, and discharge valve, which enabled decantation at a ratio of 0.33. The rotational speed of the stirrer was 70 rpm. During aeration, the air was supplied to the reactor by a compressor with a capacity of 550 dm 3 /h, maintaining dissolved oxygen concentration at 2.5 mg/dm 3 . In turn, during the filling, mixing, sedimentation, and  AGS was cultured under laboratory conditions (23 • C, relative humidity 50%). The CAS from the municipal wastewater treatment plant in Rajgród, Poland (53.99434 N, 22.76847 E) with PE = 2500 served as the inoculum. The average capacity of the treatment plant is 400 m 3 /d, and it operates based on the terrace-flow technology with increased nutrient removal. Prior to granule cultivation, the activated sludge was filtered through a sieve with a mesh diameter of 1.0 mm, which allowed the separation of fine suspensions from a mixture of wastewater and activated sludge and enabled achieving a high organic mass of CAS. The AGS culture process was continued for 120 days in a sequencing batch reactor (SBR) [23]. The reinforced PE reactor was equipped with a stirrer, aerating diffuser, oxygen probe, and discharge valve, which enabled decantation at a ratio of 0.33. The rotational speed of the stirrer was 70 rpm. During aeration, the air was supplied to the reactor by a compressor with a capacity of 550 dm 3 /h, maintaining dissolved oxygen concentration at 2.5 mg/dm 3 . In turn, during the filling, mixing, sedimentation, and shutdown phase, the concentration of dissolved oxygen in the reactor was kept below 0.3 mg/dm 3 . The reactor work cycle was 8 h (480 min). The filling and stirring phase lasted 60 min, the aeration phase lasted 270 min, the sedimentation phase lasted 15 min, and the decantation phase lasted 135 min. The reactor was fed with model wastewater composed of: casein peptone (0.452 g/dm 3 ), enriched broth (0.304 g/dm 3 ), CH 3 COONa (0.300 g/dm 3 ), NH 4 Cl (0.242 g/dm 3 ), KH 2 PO 4 (0.032 g/dm 3 ), and K 2 HPO 4 (0.080 g/dm 3 ), as well as NaCl (0.014 g/dm 3 ), CaCl 2 ·6H 2 O (0.015 g/dm 3 ), and MgSO 4 ·7H 2 O (0.004 g/dm 3 ). The mixture of these components ensured the presence of organic carbon, organic nitrogen, ammonium nitrogen, phosphates, and macroelements in the wastewater flowing into the reactor. AGS was produced using the gravimetric selection method as a stress factor. In the first 30 days of the experiment, CAS was adapted to laboratory conditions. Afterward, the exact experiment was performed for the subsequent 90 days, when the gravimetric selection of CAS was successively increased by washing out the slowest sedimenting fractions from the reactor. After 120 days of the experiment, mature granules were obtained, which were used in further research works. Figure 2 shows microscopic images of CAS and AGS.
shutdown phase, the concentration of dissolved oxygen in the reactor was kept below 0.3 mg/dm 3 . The reactor work cycle was 8 h (480 min). The filling and stirring phase lasted 60 min, the aeration phase lasted 270 min, the sedimentation phase lasted 15 min, and the decantation phase lasted 135 min. The reactor was fed with model wastewater composed of: casein peptone (0.452 g/dm 3 ), enriched broth (0.304 g/dm 3 ), CH3COONa (0.300 g/dm 3 ), NH4Cl (0.242 g/dm 3 ), KH2PO4 (0.032 g/dm 3 ), and K2HPO4 (0.080 g/dm 3 ), as well as NaCl (0.014 g/dm 3 ), CaCl2·6H2O (0.015 g/dm 3 ), and MgSO4·7H2O (0.004 g/dm 3 ). The mixture of these components ensured the presence of organic carbon, organic nitrogen, ammonium nitrogen, phosphates, and macroelements in the wastewater flowing into the reactor. AGS was produced using the gravimetric selection method as a stress factor. In the first 30 days of the experiment, CAS was adapted to laboratory conditions. Afterward, the exact experiment was performed for the subsequent 90 days, when the gravimetric selection of CAS was successively increased by washing out the slowest sedimenting fractions from the reactor. After 120 days of the experiment, mature granules were obtained, which were used in further research works. Figure 2 shows microscopic images of CAS and AGS. The inoculum of fermentation reactors was AS from a closed fermentation chamber (CFC) with a capacity of 7300 m 3 from a wastewater treatment plant in Białystok, Poland (53.16903 N, 23.08705E) ( Table 1). The plant operated at a temperature of 35 °C, organic load rate (OLR) of 2.0 gVS/dm 3 ·d, and hydraulic retention time (HRT) of 21 days. Before being used as an inoculum, the anaerobic sludge was adapted to the experimental conditions of 42˚C for 40 days (HRT = 20 days) and an OLR of 1.0 gVS/dm 3 ·d. Table 1 presents the characteristics of CAS, AGS, and AS inoculum.  The inoculum of fermentation reactors was AS from a closed fermentation chamber (CFC) with a capacity of 7300 m 3 from a wastewater treatment plant in Białystok, Poland (53.16903 N, 23.08705 E) ( Table 1). The plant operated at a temperature of 35 • C, organic load rate (OLR) of 2.0 gVS/dm 3 ·d, and hydraulic retention time (HRT) of 21 days. Before being used as an inoculum, the anaerobic sludge was adapted to the experimental conditions of 42 • C for 40 days (HRT = 20 days) and an OLR of 1.0 gVS/dm 3 ·d. Table 1 presents the characteristics of CAS, AGS, and AS inoculum. Experiments were conducted with the use of SCO 2 (Sopel Ltd., Białystok, Poland) in the form of granules 3.0 ± 1.0 mm in diameter. The SCO 2 used sublimes under pressure below 5.13 atm and temperatures over −56.4 • C. Under atmospheric pressure, its sublimation proceeds at a temperature of −78.5 • C, and sublimation enthalpy is 573 kJ/kg, which makes it ca. 3.3 times more efficient than water ice of the same volume. The SCO 2 used in the study is a natural, odorless, tasteless, non-toxic, and non-flammable product approved for contact with foodstuffs [24].

Experimental Stations
Experiments were performed using a jar tester (JLT 6, VELP Scientifica, Milano, Italy). AGS having a temperature of 20 • C was poured into glass reactors in single doses of 200 cm 3 , and then an appropriate dose of SCO 2 was added. The mixture was stirred with a yield of 50 rpm for 20 min. The samples were left for complete SCO 2 sublimation and then subjected to MF when they had reached a temperature of 20 • C. Figure 3 presents the scheme of an experimental station used in this stage.

SCO2
Experiments were conducted with the use of SCO2 (Sopel Ltd., Białystok, Poland) in the form of granules 3.0 ± 1.0 mm in diameter. The SCO2 used sublimes under pressure below 5.13 atm and temperatures over −56.4 °C. Under atmospheric pressure, its sublimation proceeds at a temperature of −78.5 °C, and sublimation enthalpy is 573 kJ/kg, which makes it ca. 3.3 times more efficient than water ice of the same volume. The SCO2 used in the study is a natural, odorless, tasteless, non-toxic, and non-flammable product approved for contact with foodstuffs [24].

Stage 1
Experiments were performed using a jar tester (JLT 6, VELP Scientifica, Milano, Italy). AGS having a temperature of 20 °C was poured into glass reactors in single doses of 200 cm 3 , and then an appropriate dose of SCO2 was added. The mixture was stirred with a yield of 50 rpm for 20 min. The samples were left for complete SCO2 sublimation and then subjected to MF when they had reached a temperature of 20 °C. Figure 3 presents the scheme of an experimental station used in this stage.

Stage 2
Measurements of the volumes of biogas produced were carried out in a set of eudiometers (Hornik Ltd., Poznań, Poland), the scheme and photo of which are provided in Figure 4. A single eudiometer is made of a reactor with a volume of 1000 cm 3 , connected with a joint to a burette with a volume of 600 cm 3 , inside of which there is a thin capillary. The gas comes out of the fermenter via the capillary and flows to the upper part of the burette, from where it can be taken for analysis through the stub pipe with a valve mounted therein. The principle of measurement is that the gas emitted displaces the liquid from the burette, which flows through the hose to the connected equalization tank to equalize the pressure. A total of 200 cm 3 of the inoculum were fed to the reactors, followed by the appropriate amount of AGS. In order to remove oxygen from the reaction chambers, the feedstock and the gaseous phase of the respirometer were purged with compressed nitrogen (N40). Nitrogen was introduced via a rubber hose terminated with a

Stage 2
Measurements of the volumes of biogas produced were carried out in a set of eudiometers (Hornik Ltd., Poznań, Poland), the scheme and photo of which are provided in Figure 4. A single eudiometer is made of a reactor with a volume of 1000 cm 3 , connected with a joint to a burette with a volume of 600 cm 3 , inside of which there is a thin capillary. The gas comes out of the fermenter via the capillary and flows to the upper part of the burette, from where it can be taken for analysis through the stub pipe with a valve mounted therein. The principle of measurement is that the gas emitted displaces the liquid from the burette, which flows through the hose to the connected equalization tank to equalize the pressure. A total of 200 cm 3 of the inoculum were fed to the reactors, followed by the appropriate amount of AGS. In order to remove oxygen from the reaction chambers, the feedstock and the gaseous phase of the respirometer were purged with compressed nitrogen (N40). Nitrogen was introduced via a rubber hose terminated with a stone diffuser placed below the surface of the mixture of inoculum and feedstock for 3 min. The initial OLR was 5.0 gVS/dm 3 [25]. Respirometers were placed in a temperature control cabinet with a hysteresis of ±0.5 • C. Measurements were conducted at 42 • C. The volume of emitted biogas was read out every day until its production ceased. Measurements of biogas composition were carried out at the end of the process. stone diffuser placed below the surface of the mixture of inoculum and feedstock for 3 min. The initial OLR was 5.0 gVS/dm 3 [25]. Respirometers were placed in a temperature control cabinet with a hysteresis of ±0.5 °C. Measurements were conducted at 42 °C. The volume of emitted biogas was read out every day until its production ceased. Measurements of biogas composition were carried out at the end of the process.

Analytical Methods
Contents of TS, VS, and MS were determined with the gravimetric method. Contents of TS in the sludge were determined by drying it to a constant weight at 105 °C, then burning it at 550 °C. The loss after combustion was the VS, according to PN-EN 15935:23022-01 [26]. Total carbon (TC) content was determined using high-temperature decomposition with infrared detection of TOC in a multi-NC 3100 analyzer (Analytik Jena, Jena, Germany). Contents of total nitrogen (TN), ammonia nitrogen, orthophosphates, and COD in the sludge supernatant were determined with the spectrophotometric method after previous mineralization using a Hach DR6000 spectrometer (Hach, Loveland, CO, USA). The supernatant was obtained by AGS centrifugation in an MPW-251 laboratory centrifuge (MPW Med. Instruments, Warsaw, Poland) at a rotational speed of 5000 rpm for 10 min. The potentiometric method was used to determine pH. Biogas composition was controlled at the end of the process using a DP-28BIO gas analyzer (Nanosens, Wysogotowo, Poland).

Molecular Methods
The FISH method was deployed to identify the consortia of anaerobic microorganisms. Four molecular probes were used for hybridization, namely a universal probe for EUB338 bacteria and ARC915 archaea and a specific probe for Methanosarcinaceae MSMX860 and Methanosaeta MX825. The samples were analyzed under an epifluorescence microscope with a 100× objective and 1000× total magnification (Nikon, Tokyo, Japana). The population numbers of microorganisms of the tested species were calculated from cells stained with DAPI using Image Processing and Analysis in Java (ImageJ) software

Analytical Methods
Contents of TS, VS, and MS were determined with the gravimetric method. Contents of TS in the sludge were determined by drying it to a constant weight at 105 • C, then burning it at 550 • C. The loss after combustion was the VS, according to PN-EN 15935:23022-01 [26]. Total carbon (TC) content was determined using high-temperature decomposition with infrared detection of TOC in a multi-NC 3100 analyzer (Analytik Jena, Jena, Germany). Contents of total nitrogen (TN), ammonia nitrogen, orthophosphates, and COD in the sludge supernatant were determined with the spectrophotometric method after previous mineralization using a Hach DR6000 spectrometer (Hach, Loveland, CO, USA). The supernatant was obtained by AGS centrifugation in an MPW-251 laboratory centrifuge (MPW Med. Instruments, Warsaw, Poland) at a rotational speed of 5000 rpm for 10 min. The potentiometric method was used to determine pH. Biogas composition was controlled at the end of the process using a DP-28BIO gas analyzer (Nanosens, Wysogotowo, Poland).

Molecular Methods
The FISH method was deployed to identify the consortia of anaerobic microorganisms. Four molecular probes were used for hybridization, namely a universal probe for EUB338 bacteria and ARC915 archaea and a specific probe for Methanosarcinaceae MSMX860 and Methanosaeta MX825. The samples were analyzed under an epifluorescence microscope with a 100× objective and 1000× total magnification (Nikon, Tokyo, Japana). The population numbers of microorganisms of the tested species were calculated from cells stained with DAPI using Image Processing and Analysis in Java (ImageJ) software developed by the National Institutes of Health and Laboratory for Optical and Computational Instrumentation (LOCI, University of Wisconsin, Madison, WI, USA) [27].

Computation Methods
The biogas production rate (r) and reaction rate constants (k) were determined in all experimental variants based on test data obtained with the non-linear regression method using Statistica 13.3 PL software (Statsoft, Inc., Tulsa, OK, USA). A non-linear regression iterative method was used, in which the function is replaced by a linear differential with respect to the determined parameters in each iterative step. The contingency coefficient ϕ2 was adopted as a measure of the curve's fit to the test data. It was assumed that the model was fitted to the experimental points where the value of this coefficient did not exceed 0.2 (Statistica 13.3 PL package (Statsoft, Inc., Tulsa, OK, USA)).
The net energy output (E nout ) was calculated using Equation (3): where: E out(Vx) -the energy output in n-variant (Wh); E out(V1) -the energy output in V1 (Wh).
The net energy gain (E net ) was calculated from Equation (4): where: E nout -the net energy output (Wh); E s -the specific energy input (Wh).
The energy value (EV) was computed using Equation (5): where: Enet-the net energy gain (Wh); EP-energy price (EUR/Wh)-the energy price was adopted as the mean from 2020 to the first half of 2022 based on Eurostat data [29].
The SCO 2 value (SCO 2 V) was computed from Equation (6): where: M SCO2 -mass of SCO 2 (kg); CPP-price of EU Carbon Permits (EUR/kg)-the price of EU Carbon Permits was adopted as the mean from 2020 to the first half of 2022 based on Trading Economics data [30].

Statistical and Optimization Methods
All experimental variants were conducted in triplicate. The statistical analysis of the results was carried out with the Statistica 13.3 PL package (Statsoft, Inc., Tulsa, OK, USA). The Shapiro-Wilk test was used to verify the hypothesis regarding the distribution of every researched variable. The ANOVA test was performed to establish the significance of differences between variables. Levene's test was used to check the homogeneity of variance in groups, and Tukey's HSD test was used to determine the significance of differences between the analyzed variables. Differences were found significant at α = 0.05.
Empirical equations were elaborated using stepwise regression with multiple regression. Key predictors of changes in the values of the estimated parameters were identified in model systems. Model fit to empirical data was verified by means of the determination coefficient (Statistica 13.3 PL package (Statsoft, Inc., Tulsa, OK, USA)).

Stage 1
Investigations conducted so far have proved that damage to CAS cell structures triggered by the treatment with SCO 2 may increase the concentration of dissolved COD, proteins, molecular material, orthophosphates, and ammonia nitrogen in the supernatant [25]. These phenomena contribute to the increased turbidity of the supernatant and improve CAS susceptibility to dehydration [31]. Effective CAS disintegration has also been proved by means of FTIR spectroscopy [21]. The increase in COD concentration is claimed to be related to the breaking of CAS structures followed by the degradation of single cells of microorganisms [32]. Analogous effects were observed in the present study during AGS pre-treatment using SCO 2 . In the case of the non-pre-treated sludge (V1), the COD concentration in the supernatant was 152 ± 14 mgO 2 /dm 3 ( Figure 5). In variants V2-V4, the COD concentration was observed to increase successively from 334 ± 15 mgO 2 /dm 3 (V2) to 437 ± 16 mgO 2 /dm 3 (V4). A further increase in the SCO 2 dose caused no statistically significant (p > 0.5) changes in the COD concentrations in the supernatant ( Figure 5), which reached 442 ± 15 mgO 2 /dm 3 (V5) and 450 ± 13 mgO 2 /dm 3 (V6).
Machnicka et al. (2019) [21] observed a correlation between the SCO 2 /CAS ratio and COD concentration in the supernatant. Pre-treatment caused the COD concentration to increase from 63 mgO 2 /dm 3 in the raw sludge to 205 mgO 2 /dm 3 in the sludge pretreated at the SCO 2 /CAS ratio of 1:0.25. Increasing SCO 2 /CAS to 1:1 caused an increase in COD concentration to 889 mgO 2 /dm 3 [21]. Additionally, Zawieja (2018) [33] noted a significant COD increase in the supernatant. At SCO 2 /CAS ratios ranging from 0.05/1.0 to 0.75/1.0, they observed changes in the COD concentration ranging from 119 mgO 2 /dm 3 to 296 mgO 2 /dm 3 [33]. Another research [25] demonstrated a proportional increase in the COD concentration in a dairy CAS supernatant along with an increase in the SCO 2 /CAS volume ratio to 0.3. In crude CAS, the COD concentration was at 400.5 ± 23.8 mg/dm 3 . The highest COD values, falling within a narrow range of 490.6 ± 12.9 to 510.5 ± 28.5 mg/dm 3 , were noted at SCO 2 /CAS ratios ranging from 0.3 to 0.5 [25]. Stabnikova et al. (2008) [34] demonstrated an almost two-fold increase in COD concentration in the supernatant in their study investigating the effect of the freezing/thawing process on food waste.  [21] observed a correlation between the SCO2/CAS ratio and COD concentration in the supernatant. Pre-treatment caused the COD concentration to increase from 63 mgO2/dm 3 in the raw sludge to 205 mgO2/dm 3 in the sludge pre-treated at the SCO2/CAS ratio of 1:0.25. Increasing SCO2/CAS to 1:1 caused an increase in COD concentration to 889 mgO2/dm 3 [21]. Additionally, Zawieja (2018) [33] noted a significant COD increase in the supernatant. At SCO2/CAS ratios ranging from 0.05/1.0 to 0.75/1.0, they observed changes in the COD concentration ranging from 119 mgO2/dm 3 to 296 mgO2/dm 3 [33]. Another research [25] demonstrated a proportional increase in the COD concentration in a dairy CAS supernatant along with an increase in the SCO2/CAS volume ratio to 0.3. In crude CAS, the COD concentration was at 400.5 ± 23.8 mg/dm 3 . The highest COD values, falling within a narrow range of 490.6 ± 12.9 to 510.5 ± 28.5 mg/dm 3 , were noted at SCO2/CAS ratios ranging from 0.3 to 0.5 [25]. Stabnikova et al. (2008) [34] demonstrated an almost two-fold increase in COD concentration in the supernatant in their study investigating the effect of the freezing/thawing process on food waste. In turn, Bailey et al. (2011) [35] reported a 15% increase in COD concentration when freezing/thawing excess municipal sewage sludge.
Damage caused by SCO2 to the cellular structure of microorganisms triggers the release of enzymes contained in their protoplasts, whose hydrolytic activity results in the degradation of organic compounds of nitrogen and phosphorus and consequently in increased concentrations of ammonia nitrogen and orthophosphates in the supernatant [36]. In the present study, an increase in the SCO2 dose was accompanied by increasing concentrations of N-NH4 + and P-PO4 3− . In V2, the N-NH4 + concentration reached 155 ± 8.4 mg/dm 3 and that of P-PO4 3− reached 66.5 ± 3.5 mg/dm 3 . In the supernatant of raw AGS, the respective values were 81.5 ± 3.1 mg N-NH4 + /dm 3 and 62.2 ± 2.2 mg P-PO4 3− /dm 3 ( Figure  5). The applied SCO2 dose had a significant effect on the N-NH4 + and P-PO4 3− concentrations determined in variants V1-V4, which were observed to ultimately increase to 274 ± 9.3 mg/dm 3 and 75.7 ± 1.9 mg/dm 3 , respectively ( Figure 5). In the subsequent variants, the increase in their concentrations was no longer statistically significant (p > 0.5) ( Figure 5).
In the study conducted by Zawieja (2019) [37], the N-NH4 + concentration in the supernatant of crude CAS approximated 43 mg/dm 3 and increased successively along with an increasing SCO2 dose, reaching ca. 102 mg/dm 3 at the SCO2/CAS volume ratio of Damage caused by SCO 2 to the cellular structure of microorganisms triggers the release of enzymes contained in their protoplasts, whose hydrolytic activity results in the degradation of organic compounds of nitrogen and phosphorus and consequently in increased concentrations of ammonia nitrogen and orthophosphates in the supernatant [36]. In the present study, an increase in the SCO 2 dose was accompanied by increasing concentrations of N-NH 4 + and P-PO 4 3− . In V2, the N-NH 4 + concentration reached 155 ± 8.4 mg/dm 3 and that of P-PO 4 3− reached 66.5 ± 3.5 mg/dm 3 . In the supernatant of raw AGS, the respective values were 81.5 ± 3.1 mg N-NH 4 + /dm 3 and 62.2 ± 2.2 mg P-PO 4 3− /dm 3 ( Figure 5). The applied SCO 2 dose had a significant effect on the N-NH 4 + and P-PO 4 3− concentrations determined in variants V1-V4, which were observed to ultimately increase to 274 ± 9.3 mg/dm 3 and 75.7 ± 1.9 mg/dm 3 , respectively ( Figure 5). In the subsequent variants, the increase in their concentrations was no longer statistically significant (p > 0.5) ( Figure 5). In the study conducted by Zawieja (2019) [37], the N-NH 4 + concentration in the supernatant of crude CAS approximated 43 mg/dm 3 and increased successively along with an increasing SCO 2 dose, reaching ca. 102 mg/dm 3 at the SCO 2 /CAS volume ratio of 0.75/1.0 [37]. In another study [25], the pre-treatment of dairy CAS with SCO 2 increased N-NH 4 + concentration in the supernatant from 155.2 ± 10.2 mg/dm 3 in the crude sludge to 185.9 ± 11.1 mg/dm 3 in the sludge pre-treated at the SCO 2 /CAS volume ratio of 0.5. Likewise, an increasing SCO 2 dose caused the P-PO 4 3− concentration to increase from 198.5 ± 23.1 to 300.6 ± 35.9 mg/dm 3 [25]. In their experiment with freezing/thawing mixed sewage sludge, Montusiewicz et al. (2010) [38] reported an increase in the N-NH 4 + concentration in the supernatant from 94.0 mg/dm 3 in the non-conditioned sludge to 130.9 mg/dm 3 as well as an over two-fold increase in P-PO 4 3− concentration from 86.4 mg/dm 3 in the control sample to 185.2 mg/dm 3 . In another study, this method of conditioning municipal CAS resulted in a 1.5-fold to 2.5-fold increase in the P-PO 4 3− concentration in the supernatant [39]. An expected technological outcome of pre-treatment is the increased effectiveness of methane fermentation [40]. Undoubtedly, the disintegration of complex macromolecules of the biomass, followed by the efficient transfer of organic compounds to the dissolved phase, increases substrate availability to anaerobic bacteria [41].

Stage 2 3.2.1. Biogas and Methane Production
The biogas yield of raw AGS (V1) was 309 ± 21 cm 3 /gVS (Figures 6 and 7). The r value was 47.7 cm 3 /d, and the CH 4 concentration in the biogas produced was 68.84 ± 2.2% ( Table 2). The highest yields of biogas and methane were obtained in V4, i.e., 476 ± 20 cm 3 /gVS and 341 ± 13 cm 3 /gVS, respectively. The rate of the process reached 113.3 cm 3 /d biogas, and CH 4 concentration was at 71.58 ± 1.7% (Figures 6 and 7). Compared to V1, an increase in biogas and CH 4 production yield in this variant reached 54.05 ± 3.5% and 60.18 ± 2.4%, respectively. The subsequent variants brought about an AD yield reduction and a significant decrease in CH 4 concentration, whose values reached 430 ± 21 cm 3 /gVS biogas and 271 ± 10 cm 3 /gVS CH 4 (63.03 ± 1.3%) in V5, as well as 427 ± 22 cm 3 /gVS biogas and 196 ± 12 cm 3 /gVS methane in V6 (45.80 ± 2.1%) (Figures 6 and 7).  [42] demonstrated that the potential of biogas production from AGS was 1.8-fold lower than from CAS. At the applied OLRs ranging from 2.0 to 6.0 gVS/cm 3 ·d, these authors observed that biogas productivity decreased along with increasing OLR, i.e., from 408.9 cm 3 /gVS at OLR 2 gVS/cm 3 ·d to 318.5 cm 3 /gVS at OLR 6 gVS/cm 3 ·d, and that the CH 4 concentration in the biogas ranged from 56.7 to 59.5% [42]. In turn, Cydzik-Kwiatkowska et al. (2022) [43] applied the ultrasound pre-treatment of AGS to boost biogas production. In the case of AGS not subjected to ultrasonic disintegration, they found no significant differences in the biogas yield and the CH 4 content of biogas in the analyzed OLR range from 1.0 to 3.0 gVS/cm 3 ·d. The biogas yield approximated 375 cm 3 /gVS, and the CH 4 concentration in the biogas ranged from 56.7 ± 0.4 to 57.5 ± 0.6%. Biogas production was observed to increase significantly along with the extension of the disintegration process. Regardless of OLR, after 0.5, 4.0, and 8.0 min of disintegration, the biogas yield was ca. 400 cm 3 /gVS, 420 cm 3 /gVS, and 455 cm 3 /gVS, respectively [43]. Zawieja (2019) [37] investigated the effect of pre-treatment using SCO 2 on the course of methane fermentation of modified sewage sludge. At the SCO 2 to excess sludge volume ratio of 0.55/1, this author achieved a biogas yield of 620 cm 3 /gVS. In the case of prepared sludge, the CH 4 content of the biogas approximated 78% [37]. In turn, Nowicka et al. (2014) [44] used SCO 2 for the disintegration of municipal CAS prior to AD. In the most effective variant, biogas yield was 49% higher compared to raw CAS [44].

pH and FOS/TAC
The use of SCO 2 caused a decrease in the pH value of AGS (Table 3). In V1, the pH reached 7.80 ± 0.1 and successively decreased to 6.93 ± 0.1 in V4. A further increase in the SCO 2 dose in the subsequent experimental variants reduced the pH value of AGS to 6.42 ± 0.1 in V5 and 6.31 ± 0.1 in V6. During CO 2 sublimation, its part dissolves in the supernatant. CO 2 is well soluble in aqueous solutions, and its solubility at a temperature of 25 • C reaches 2900 mg/dm 3 [45]. Its sublimation results in the formation of carbonate ions (CO 3 2− ), bicarbonate ions (HCO 3 − ), and hydrogen ions (H + ), leading to pH reduction [46], which in turn negatively affects the outcomes of methane fermentation expressed by biogas and methane yields [38]. Hence, the pH values measured in digesters were a consequence of initial conditions after pre-treatment with SCO 2 . In the control sample in V1, the pH value measured in digesters decreased from 7.48 ± 0.1 to 7.01 ± 0.1 after AD (Table 3). In V2-V4, the pH ranged from 7.12 ± 0.1 to 7.36 ± 0.1 and decreased after AD to values ranging from 6.75 ± 0.1 to 6.86 ± 0.1 (Table 3). In V5 and V6, in which the pre-treatment contributed to environment acidification, pH values measured in digesters decreased drastically after AD, i.e., from 6.93 ± 0.1 to 6.44 ± 0.1 in V5 and from 6.89 ± 0.1 to 6.30 ± 0.1 in V6 (Table 3). This pH decrease was reflected in the population of methanogens and, consequently, in CH 4 yield. In another study [37], the pH of digesters was also observed to decrease upon sludge pre-treatment with SCO 2 , which resulted in diminished AD yield. It is all the more important that the pH value in an anaerobic digester is a key factor determining process stability [47]. The FOS/TAC ratio was sustained at the optimal level in all experimental variants. Its lowest value was determined in V6, i.e., 0.40 ± 0.02, and its highest value was sustained in V1, i.e., 0.42 ± 0.04 (Table 3). These differences were not statistically significant (p > 0.5). The FOS/TAC ratio is a value describing the ratio of the volatile organic acid to the alkaline buffer capacity. It is often applied to assess process stability in anaerobic digesters. According to literature data [48,49], the FOS/TAC values of a stable AD process range from 0.2 to 0.6. The FOS/TAC values exceeding 0.6 are indicative of operating conditions inappropriate for anaerobic microorganisms and contribute to biogas yield decline [48].

Bacterial Community Structure
This part of the study analyzed the effect of experimental variants on the taxonomic structure of the population of anaerobic bacteria (Table 4). In V1, the prevailing taxonomic group was Bacteria (EUB338), accounting for 69 ± 10% of the anaerobes population (Table 4). In turn, methanogenic archaea (ARC915) accounted for 24 ± 6%, Methanosarcinaceae (MSMX860) accounted for 10 ± 4%, and Methanosaeta (MX825) accounted for 5 ± 2% (Table 4). In the subsequent variants, again, Bacteria (EUB338) turned out to be the prevailing consortium of microorganisms, with their percentage in the population of anaerobes ranging from 68 ± 10% in V6 to 70 ± 11% in V2, regardless of SCO 2 dose (Table 4). In V2-V4, the contribution of Archaea (ARC915) in the population of anaerobes ranged from 24 ± 4 to 25 ± 11%, that of Methanosarcinaceae (MSMX860) ranged from 11 ± 4 to 12 ± 5%, and that of Methanosaeta (MX825) ranged from 8 ± 3 to 9 ± 4% (Table 4). In V5 and V6, the contribution of Archaea (ARC915) diminished to 19 ± 9% and 18 ± 8%, respectively. The contribution of Methanosarcinaceae (MSMX860) reached 11 ± 4% in V5 and 10 ± 6% in V6, whereas that of Methanosaeta (MX825) accounted for 7 ± 3% in V5 and for 5 ± 2% in V6 (Table 4). This decrease observed in V5-V6 in the abundance of the selected consortia was due to environment acidification prior to digestion, which influenced environmental conditions as well as the course and effectiveness of the AD process in digesters. After AD, the pH value reached barely 6.44 ± 0.1 in V5 and 6.30 ± 0.1 in V6. Hence, it may be concluded that the changes in the population of methanogens were ascribed to the modification of environmental conditions upon pre-treatment with SCO 2 . Fermentative bacteria may effectively function in a broad range of pH values, i.e., between 4.0 and 8.0, whereas methanogenic bacteria are functionally active in the pH range of 6.5-7.5 [50]. Int. J. Environ. Res. Public Health 2023, 20, x 11 of 23 Figure 6. The course of biogas and methane production processes in experimental variants. Figure 6. The course of biogas and methane production processes in experimental variants.  A study conducted by Bernat et al. (2017) [42] demonstrated that the potential of biogas production from AGS was 1.8-fold lower than from CAS. At the applied OLRs ranging from 2.0 to 6.0 gVS/cm 3 ·d, these authors observed that biogas productivity decreased along with increasing OLR, i.e., from 408.9 cm 3 /gVS at OLR 2 gVS/cm 3 ·d to 318.5 cm 3 /gVS at OLR 6 gVS/cm 3 ·d, and that the CH4 concentration in the biogas ranged from 56.7 to 59.5% [42]. In turn, Cydzik-Kwiatkowska et al. (2022) [43] applied the ultrasound pretreatment of AGS to boost biogas production. In the case of AGS not subjected to ultrasonic disintegration, they found no significant differences in the biogas yield and the CH4 content of biogas in the analyzed OLR range from 1.0 to 3.0 gVS/cm 3 ·d. The biogas yield approximated 375 cm 3 /gVS, and the CH4 concentration in the biogas ranged from 56.7 ± 0.4 to 57.5 ± 0.6%. Biogas production was observed to increase significantly along with the extension of the disintegration process. Regardless of OLR, after 0.5, 4.0, and 8.0 min of disintegration, the biogas yield was ca. 400 cm 3 /gVS, 420 cm 3 /gVS, and 455 cm 3 /gVS, respectively [43]. Zawieja (2019) [37] investigated the effect of pre-treatment using SCO2 on the course of methane fermentation of modified sewage sludge. At the SCO2 to excess sludge volume ratio of 0.55/1, this author achieved a biogas yield of 620 cm 3 /gVS. In the case of prepared sludge, the CH4 content of the biogas approximated 78% [37]. In turn, Nowicka et al. (2014) [44] used SCO2 for the disintegration of municipal CAS prior to AD. In the most effective variant, biogas yield was 49% higher compared to raw CAS [44].  Methanosaeta (MX825) 5 ± 2 8 ± 3 8 ± 3 9 ± 4 7 ± 3 5 ± 2

Empirical Models and Correlations
One of the ways to assess the effectiveness of pre-treatment processes is to analyze concentrations of selected indicators in the dissolved phase of the organic substrate undergoing disintegration [51]. Usually, this assessment is made based on monitoring concentrations of organic compounds [52]. In some cases, it is possible to develop reliable correlations and models to estimate AD efficiency based on the presence of organic compounds in the dissolved phase [53]. For this reason, carrying out this type of assessment is useful from a practical point of view, as it reduces the need to conduct more advanced measurements in order to determine the effectiveness of the applied pre-treatment methods.
In variants from V1 to V4, very strong positive correlations were found between the concentrations of COD (Figure 8a), N-NH 4 + (Figure 8b), and P-PO 4 3− (Figure 8c) in the dissolved phase and biogas production yield. The coefficients of determination reached R 2 = 0.8755, R 2 = 0.9472, and R 2 = 0.953, respectively. The higher SCO 2 doses tested in V5 and V6 resulted in negative correlations between concentrations of the monitored indicators in the dissolved phase and biogas yield, i.e., R 2 = 0.6799 for COD, R 2 = 0.6858 for N-NH 4 + , and R 2 = 0.7385 for P-PO 4 3− (Figure 8). Similar phenomena were observed for the concentrations of COD (Figure 8a  In V1-V4, strong negative correlations were noted between pH values after AD and yields of biogas (R 2 = 0.8205) (Figure 8d) and CH 4 (R 2 = 0.8305) (Figure 8d), as well as a strong correlation between the Archaea percentage in the population of anaerobic bacteria and CH 4 yield (R 2 = 0.8381) (Figure 8e). A strong correlation was also found between pH value and Archaea percentage, with a determination coefficient reaching R 2 = 0.8026 (Figure 8f). In variants V1-V4, the taxonomic structure of the population of fermentative bacteria was similar, whereas an increase in biogas and CH 4 yields was due to increased availability and improved biodegradability of the substrate after pre-treatment. In variants V5-V6, availability and biodegradability were similar to those noted in V4, as indicated by concentrations of the indicators tested in the dissolved phase, whereas high applied SCO 2 doses decreased the pH value, thereby inhibiting the populations of methanogenic bacteria. These changes were indicated by strong correlations noted between Archaea and CH 4 yield as well as between pH value and Archaea. Methanogenic bacteria are sensitive to changes in the environment and require neutral pH for their optimal metabolic activity [54].
The results achieved in variants V1-V4 allowed presenting a correlated surface effect of COD and N-NH 4 + concentrations in the supernatant (Figure 9a The multiple regression method was deployed to develop empirical equations for biogas and methane yield estimation. Variants V1-V4 were considered in the estimation because of the revealed linear correlations. It was found that biogas and methane yields were statistically significantly (p < 0.5) affected by such dependent variables as COD and N-NH4 + concentrations in the dissolved phase as well as the SCO2/AGS volume ratio. The postulated model of biogas yield (8) is characterized by an estimation error of ±13.446 and reflects ca. 96.69% of changes in the process of biogas production (R 2 = 0.9669). The me- The multiple regression method was deployed to develop empirical equations for biogas and methane yield estimation. Variants V1-V4 were considered in the estimation because of the revealed linear correlations. It was found that biogas and methane yields were statistically significantly (p < 0.5) affected by such dependent variables as COD and N-NH 4 + concentrations in the dissolved phase as well as the SCO 2 /AGS volume ratio. The postulated model of biogas yield (8) is characterized by an estimation error of ±13.446 and reflects ca. 96.69% of changes in the process of biogas production (R 2 = 0.9669). The methane yield model (9) reflects ca. 98.04% changes in the process of its production (R 2 = 0.9804) with an estimation error of ±7.6996. where: BIOGAS-biogas yield, cm 3 /gVS; METHANE-methane yield, cm 3 /gVS; COD-COD concentration in the supernatant, mgO 2 /dm 3 ; N-NH 4 + -N-NH 4 + concentration in the supernatant, mg/dm 3 ; SCO 2 /AGS-volume ratio of SCO 2 to AGS.

Energy and Economic Balance
The assessment of energetic effectiveness is extremely important to the evaluation of process viability, especially on a large scale [55]. Considering the production yield of methane and its energy value per volume reaching 9.17 Wh/dm 3 , the highest gross energy gain was achieved in V4, i.e., 218.49 ± 1.6 Wh (Table 5). In the control variant (V1), the gain was only 136.48 ± 1.5 Wh. Energy consumption for the pre-treatment was found to be proportional to SCO 2 dose and ranged from 0.64404 Wh in V2 to 3.22018 Wh in V6 (Table 5). Positive net energy gains were obtained in variants V2-V4. The gain increased from 13.45 ± 1.4 Wh in V2 to 80.08 ± 1.5 Wh in V4. In the subsequent variants, the net energy gains were observed to decrease drastically, reaching 34.59 ± 1.7 Wh in V5 and −14.11 ± 1.6 Wh in V6 (Table 5). When converted per tons of TS, the optimal variant produced net energy gain at 1047.85 ± 20 Wh/MgTS (Table 5). In V1-V4, very strong positive correlations were found between the SCO 2 /AGS mass ratio and net energy gain (R 2 = 0.9643) (Figure 10a). The use of this type of pre-treatment to intensify methane fermentation could be even more advisable if a closed CO 2 circuit was applied in the following cycle: biogas production-biogas enrichment-SCO 2 production-sludge disintegration-digestion-biogas production. It is an important argument that affects the improvement in the economic and technological viability of fermentation processes and provides a solution for reducing CO 2 emissions to the atmosphere, being necessary from the environmental protection standpoint. The estimated economic analysis demonstrated a feasible profit ranging from 144.99 EUR/tonTS in V2 to 554.05 EUR/tonTS in V4 (Table 6). Very strong positive correlations were found in V1-V4 between the SCO 2 /AGS mass ratio and profit (R 2 = 0.9925) (Figure 10b). Energy sustainability is one of the critical parameters that need to be analyzed to ensure the successful application of pre-treatment processes [56]. Balasundaram et al. (2022) [57] made a critical assessment of the energetic effectiveness of various energy-consuming techniques of sewage sludge pre-treatment. They demonstrated that the conventional heat pre-treatment of sludge (∼5% TS) ensured 244 cm 3 CH 4 /gTS, which could yield a positive energy balance at 2.6 kJ/kg TS, and that the microwave pre-treatment allowed generating only 178 cm 3 CH 4 /gTS, yielding a negative energy balance at −15.62 kJ/kg TS. In turn, the ultrasound pre-treatment of sewage sludge prior to AD required sludge thickening to achieve a positive energy balance [58]. Therefore, the proposed pre-treatment method with the use of SCO 2 seems very promising. SCO 2 /AGS-volume ratio of SCO 2 to AGS; ρ AGS -specific density of AGS; M AGS -mass of AGS; V AGS -volume of AGS; ρ SCO2 -density of SCO 2 ; V SCO2 -volume of SCO 2 ; M SCO2 -mass of SCO 2 ; P SCO2 -generator power SCO 2 ; W SCO2 -efficiency of SCO 2 generator; E s -specific energy input; Y methane -methane yield; CV methane -methane calorific value; E out -energy output; E nout -net energy output; E net -net energy gain.

Conclusions
The present study demonstrated a proportional increase in COD, N-NH 4 + , and P-PO 4 3− concentrations in the supernatant, along with increasing doses of SCO 2 within the applied SCO 2 /AGS volume ratios ranging from 0.1 to 0.3. The higher SCO 2 dose tested had no significant effect upon increasing concentrations of the analyzed indicators in the dissolved phase.
The highest unit biogas yield, I.e., 476 ± 20 cm 3 /gVS, was achieved in the variant with an SCO 2 /AGS volume ratio of 0.3. Methane yield in this variant reached 341 ± 13 cm 3 /gVS. Increasing the SCO 2 dose caused no significant changes in the volumes of biogas and methane produced. Optimization procedures demonstrated COD and N-NH 4 + concentrations, as well as the SCO 2 /AGS ratio, to be the significant predictors of changes in the values of the estimated parameters, i.e., biogas and methane yields.
The study proved that applying SCO 2 doses higher than 0.3 contributed to a significant decrease in the pH value of AGS and environment acidification, thereby directly affecting a reduction in the percentage of methanogenic bacteria in the anaerobic bacterial community, which ultimately decreased the CH 4 content of the biogas produced.
The energetic analysis demonstrated the highest net energy gain, reaching 1047.85 ± 20 kWh/tonTS, in the variant with the SCO 2 /AGS volume ratio of 0.3. In turn, the economic analysis proved the feasibility of achieving a profit of 554.05 EUR/tonTS in this variant. The use of SCO 2 from the produced biogas could significantly improve the energy balance. Its production via technologies dedicated to biogas upgrading and its application for sewage sludge pre-treatment correspond with the idea of material recycling and directly inscribe into the assumptions of the circular economy. This approach also supports the idea of reducing carbon dioxide emissions through its sequestration and use in a closed cycle. Funding: The manuscript was supported by research project no. 2020/04/X/ST8/00211 financed by the National Science Center and by Project financially supported by the Minister of Education and Science in the range of the program entitled "Regional Initiative of Excellence" for the years 2019-2023, project no. 010/RID/2018/19, amount of funding: 12,000,000 PLN.