Supercritical Fluid Extraction of Fucoxanthin from the Diatom Phaeodactylum tricornutum and Biogas Production through Anaerobic Digestion

Phaeodactylum tricornutum is the marine diatom best known for high-value compounds that are useful in aquaculture and food area. In this study, fucoxanthin was first extracted from the diatom using supercritical fluid extraction (SFE) and then using the extracted diatom-like substrate to produce bioenergy through anaerobic digestion (AD) processes. Factors such as temperature (30 °C and 50 °C), pressure (20, 30, and 40 MPa), and ethanol (co-solvent concentration from 10% to 50% v/v) were optimized for improving the yield, purity, and recovery of fucoxanthin extracted using SFE. The highest yield (24.41% w/w) was obtained at 30 MPa, 30 °C, and 30% ethanol but the highest fucoxanthin purity and recovery (85.03mg/g extract and 66.60% w/w, respectively) were obtained at 30 MPa, 30 °C, and 40%ethanol. Furthermore, ethanol as a factor had the most significant effect on the overall process of SFE. Subsequently, P.tricornutum biomass and SFE-extracted diatom were used as substrates for biogas production through AD. The effect of fucoxanthin was studied on the yield of AD, which resulted in 77.15 ± 3.85 LSTP CH4/kg volatile solids (VS) and 56.66 ± 1.90 LSTP CH4/kg VS for the whole diatom and the extracted P.tricornutum, respectively. Therefore, P.tricornutuman can be considered a potential source of fucoxanthin and methane and both productions will contribute to the sustainability of the algae-biorefinery processes.


Introduction
Diatoms are unicellular photosynthetic eukaryotes that are commonly found in marine ecosystems and moist terrestrial habitats. They contribute to about 20-25% of global carbon dioxide fixation through photosynthesis and play an important role in the global silicon cycle [1,2]. In addition, they are a part of the base of marine trophic networks worldwide and contribute to at least 20% of annual primary productivity, which is equivalent to tropical forests [3,4]. Among the organic molecules produced by diatoms, fatty acids or avoids all the problems associated with the use of inhibitory organic solvents by facilitating the valorization of extracted microalgae through AD.
In this study, we performed supercritical carbon dioxide (SCO 2 ) extraction of fucoxanthin from the diatom P. tricornutum and AD of the extracted microalga under microalgae biorefinery frame. We also studied the effects of factors such as temperature, pressure, and co-solvent concentration on variables such as the total extraction yield, fucoxanthin purity, and recovery. Finally, the biochemical composition of P. tricornutum and methane yields before and after the SFE process were studied to determine how the use of a green extraction system affects methane production. In this study, we performed supercritical carbon dioxide (SCO2) extraction of fucoxanthin from the diatom P. tricornutum and AD of the extracted microalga under microalgae biorefinery frame. We also studied the effects of factors such as temperature, pressure, and co-solvent concentration on variables such as the total extraction yield, fucoxanthin purity, and recovery. Finally, the biochemical composition of P. tricornutum and methane yields before and after the SFE process were studied to determine how the use of a green extraction system affects methane production.

Effects of Pressure and Temperature on the Yield of Fucoxanthin from P. tricornutum
Total extraction yields for each operating conditions (temperature of 30 °C and 50 °C and pressure of 20, 30, and 40 MPa) are summarized in Figure 1. The results are expressed as the percentage of g extract per g dry weight of P. tricornutum, and the values were obtained at the end of extraction (60 min). This extraction time was established as optimal in previous studies on carotenoids from microalgae [30] and was considered profitable for minimizing its operational costs in the process. In general, total extraction yields were slightly affected by the combination of pressure and temperature factors. The highest total yields were without significant differences (p < 0.05) between them, if arranged from the highest to the lowest value, at the highest pressure and temperature (40 MPa at 50 °C, 3.14 ± 0.03%), followed by 30 MPa at 30 °C and 30 MPa at 50 °C (3.05 ± 0.05% and 3.00 ± 0.09%), respectively. On the other hand, the lowest extraction yields, which in turn did not have significant differences (p < 0.05) between them, were obtained at 20 MPa at 30 °C (2.55% w/w) together with the condition of 40 MPa at 30 °C and 20 MPa at 50 °C, which were 2.61 and 2.73% w/w, respectively ( Figure 1).
As shown in Table 1   The results are expressed as the percentage of g extract per g dry weight of P. tricornutum, and the values were obtained at the end of extraction (60 min). This extraction time was established as optimal in previous studies on carotenoids from microalgae [30] and was considered profitable for minimizing its operational costs in the process. In general, total extraction yields were slightly affected by the combination of pressure and temperature factors. The highest total yields were without significant differences (p < 0.05) between them, if arranged from the highest to the lowest value, at the highest pressure and temperature (40 MPa at 50 • C, 3.14 ± 0.03%), followed by 30 MPa at 30 • C and 30 MPa at 50 • C (3.05 ± 0.05% and 3.00 ± 0.09%), respectively. On the other hand, the lowest extraction yields, which in turn did not have significant differences (p < 0.05) between them, were obtained at 20 MPa at 30 • C (2.55% w/w) together with the condition of 40 MPa at 30 • C and 20 MPa at 50 • C, which were 2.61 and 2.73% w/w, respectively ( Figure 1).
As shown in Table 1 and the operating conditions, increasing the pressure at constant temperature increases the CO 2 density from 0.890 to 0.988 g/mL for pressures of 20-40 MPa at 30 • C and from 0.784 to 0.923 g/mL for pressures of 20-40 MPa at 50 • C. Under these conditions of increased pressure, the total extraction yield ( Figure 1) was slightly improved without significant differences (p < 0.05) for 30  and it could be due to the volatility of the extracts under these SFE conditions, or the component solubility is lowered as the polarity and/or the molecular weights of the solutes are increased [19].  Table 1 also shows the purity, calculated as mg fucoxanthin extracted by SFE per g of total extract, and recovery, calculated as the percentage of the weight of fucoxanthin extracted by conventional extraction per grams of biomass as the reference weight of this pigment (equal to 9.82 ± 0.70 mg/g biomass) from of P. tricornutum. The different temperature and pressure conditions had a significant effect on these fucoxanthin variables, according to Tukey's test. Particularly, the highest fucoxanthin purity and recovery were reached for a pressure of 30 MPa at 30 • C (60.62 ± 0.40 mg/g and 18.82 ± 0.12% w/w, respectively), being significant (p < 0.05) for the rest of the processes. Under these conditions, the density and superficial CO 2 velocity were 0.948 g/mL and 0.401 mm/s, respectively, being the second-highest density and lowest superficial velocity, exceeded only by 30 • C and 40 MPa, whose values were 0.988 g/mL and 0.384 mm/s. However, in this treatment, the purity and recovery of fucoxanthin were not the highest. As shown in Table 1, the values of the superficial CO 2 velocities were in the range of 0.384-0.484 mm/s, indicating slight variation, because the mass flow rate (3.62 g CO 2 /min) and the area of the extraction vessel (1589 cm 2 ) were constant, the variations were only due to the density of CO 2 that depends on temperature and pressure.
At low temperatures, the purity was higher than that at high temperatures under the same pressure values. This tendency was similar for fucoxanthin recoveries except for 40 MPa and 50 • C, which was approximately two-fold higher than that at 40 MPa and 30 • C. In contrast, at low pressure and under both temperature conditions, fucoxanthin purity and recovery were the lowest.
The particle size distribution is another important parameter in SFE as it directly affects the porosity and physical properties of the extraction bed. The particle diameter is inversely proportional to the total extraction yield [31,32]. On the other hand, a reduction in the final particle diameter increases the surface-to-volume ratio of the substrate [33]. The mean particle size of the Phaeodactylum tricornutum powder was D P = 0.074 ± 0.004 mm, which is considered an ultrafine powder. Crampon et al. [34] reported that the smaller the particle, the faster the kinetics of the extraction, thus higher the yields. The disintegration of cells is essential in the recovery of intracellular products from algae.
The effect of temperature on extraction yield is more complex than that of pressure. This behavior is known as "crossover pressure" and is defined as the point where the vapor pressure of the compounds in the extract is more pronounced than the effect of solvent density over the solubility of the compounds [35,36]. The crossover region is a phenomenological observation that is supported by a relevant number of experimental studies. This phenomenon refers to the regions of temperature and pressure in the near-critical fluid state where the solute solubility decreases with an isobaric increase in temperature [37].
The effect of temperature on solubility is complex, and the crossover of the solubility isotherm occurs when pressure is considered as a variable. This phenomenon is affected by solvent density and solute vapor pressure. The vapor pressure increases when temperature and solubility increase; on the contrary, density and solvent power decrease. Consequently, solubility decreases because the density of the solvent is the dominant factor. After passing the crossover area, and when the temperature is increased, the vapor pressure of the solute becomes a dominant factor, and the solubility increases. However, this contrasting behavior is often attributed to solvent density and solute vapor pressure [38].
Foster et al. [39] reported that crossover pressure is a phenomenological observation that appears to reflect a characteristic of the solute-solvent system. Furthermore, it is also of fundamental significance in providing a direct indicator of the reliability and consistency of experimental solubility data. As a consequence, it may also be used to introduce a phenomenological constraint on thermodynamic models proposed to describe solutesupercritical fluid phase equilibria. This means that, at pressures lower than the crossover pressure, the effect of CO 2 density is more relevant, whereas for pressures higher than the crossover pressure, the effect of vapor pressure at the determined temperature is more relevant for increasing the extraction yield. This is a common behavior for carotenoids obtained by SFE from vegetable matrices [37].
Fabrowska et al. [40] extracted carotenoids and phenolic compounds from the freshwater macroalgae Cladophora glomerata by optimization of the same parameters included in our study (temperature, pressure, and % ethanol as a co-solvent). The extraction yields were less than our yields without the use of extractants such as 0.6-0.9% w/w. The higher value of carotenoids recovery, represented with fucoxanthin as a majority, was 6.17 ± 0.24 mg/g of the extract under~30 MPa and 50 • C, being similar conditions, except for the temperature. Ruiz-Domínguez et al. [41] used a Box-Behnken design with desirability function to determine the bioactive composition from the microalga Isochrysis galbana by SFE, and the parameters studied were pressure , temperature (40-60 • C), and co-solvent (0-8% ethanol) with a CO 2 flow rate of 7.2 g/min for 120 min. The extraction yield without the presence of ethanol was in a similar range (from 1.09% to 2.28% w/w), and the highest was 2.28 ± 0.11% w/w under 40 MPa at 50 • C. They also determined total carotenoids recovery (included fucoxanthin) with an optimum value of 16.61 ± 0.74% at 40 MPa and 50 • C without co-solvent and 77.93 ± 2.87% at 30 MPa, 60 • C, and 8% v/v ethanol. Roh et al. [42] extracted fucoxanthin and polyphenols from the brown macroalga Undaria pinnatifida using SCO 2 and ethanol as co-solvent. The highest yields of fucoxanthin in the presence of ethanol were at~20 MPa at~50 • C with a value of fucoxanthin recovery much lower than our results (approximately 0.00753 µg fucoxanthin per g freeze-dried sample). Therefore, our results showed that an increase in pressure (from 20 to 30 MPa) at a constant temperature (30 • C) increased the solvating power of carbon dioxide as supercritical fluids favoring fucoxanthin extraction. However, the temperature is a sensitive factor at high ranges, as it can degrade the targeted compound even though it can increase the solubility of this component [43].
Although all results of yield and recovery of fucoxanthin might be improved, the optimal conditions of pressure and temperature for the highest purity and recovery of fucoxanthin were 30 MPa and 30 • C and were selected for evaluating the behavior under ethanol as an extractant by SFE.

Effects of Ethanol as a Co-Solvent Factor on the Yield of Fucoxanthin from Phaeodactylum tricornutum
Many studies have reported that the use of ethanol as an extractant improves the yields of fucoxanthin due to its polarity and affinity with carotenoid molecules [44,45]. The optimal pressure and temperature for the highest purity and recovery of fucoxanthin along with the presence of co-solvent were used for evaluating the effect on the extraction process. Figure 2 shows the total extraction yield obtained under different concentrations of ethanol from 10% to 50% v/v. Here, the co-solvent improved the extraction yield, being at 30% v/v of ethanol, the highest value was obtained with 24.41% w/w, followed by 20% v/v of co-solvent with a value of 14.28% w/w. However, the lowest value was obtained at 10% and 50% v/v of ethanol, with 5.65% and 5.18% w/w of total extraction yields, respectively.
Mar. Drugs 2022, 20, x 6 of 20 along with the presence of co-solvent were used for evaluating the effect on the extraction process. Figure 2 shows the total extraction yield obtained under different concentrations of ethanol from 10% to 50% v/v. Here, the co-solvent improved the extraction yield, being at 30% v/v of ethanol, the highest value was obtained with 24.41% w/w, followed by 20% v/v of co-solvent with a value of 14.28% w/w. However, the lowest value was obtained at 10% and 50% v/v of ethanol, with 5.65% and 5.18% w/w of total extraction yields, respectively. In general, the effect of co-solvent was significant; 30% v/v ethanol improved total yield to 8-fold higher than that using 30 MPa, 30 °C, and only carbon dioxide as a solvent. Many studies have reported that SFE is an excellent technique for the selective extraction of bioactive compounds such as carotenoids from various microalgae [16,43,46]. As a general rule, the extraction improves when SCO2 is used, whereas the presence of co-solvent or extractant such as ethanol enhances the efficiency of the supercritical process but disparages the selectivity [16].
On the other hand, Table 2 shows fucoxanthin purity and recovery under 30 MPa and 30 °C at different percentages of co-solvent. Different superscripted alphabets (a-c) indicate significant differences (p < 0.05) and the data are expressed as mean ± standard deviation (n = 3, SD ≤ 5%).
The highest values with no significant differences in fucoxanthin purity were 85.03 ± 7.67 mg/g and 74.73 ± 2.45 mg/g extract using 40 and 50% v/v of ethanol, respectively. In general, the effect of co-solvent was significant; 30% v/v ethanol improved total yield to 8-fold higher than that using 30 MPa, 30 • C, and only carbon dioxide as a solvent. Many studies have reported that SFE is an excellent technique for the selective extraction of bioactive compounds such as carotenoids from various microalgae [16,43,46]. As a general rule, the extraction improves when SCO 2 is used, whereas the presence of co-solvent or extractant such as ethanol enhances the efficiency of the supercritical process but disparages the selectivity [16].
On the other hand, Table 2 shows fucoxanthin purity and recovery under 30 MPa and 30 • C at different percentages of co-solvent. Different superscripted alphabets (a-c) indicate significant differences (p < 0.05) and the data are expressed as mean ± standard deviation (n = 3, SD ≤ 5%).
The highest values with no significant differences in fucoxanthin purity were 85.03 ± 7.67 mg/g and 74.73 ± 2.45 mg/g extract using 40 and 50% v/v of ethanol, respectively. However, the lowest purity was 13.75 ± 0.65 mg/g extract at 30% v/v of co-solvent despite the extraction yield being higher in this condition.
The highest fucoxanthin recovery with significant differences among others was 66.60 ± 6.00% w/w under 40% v/v of ethanol, whereas the lowest was 12.69 ± 1.14% w/w using 10% v/v of ethanol. The fucoxanthin purity and recovery reached the maximum value under the same conditions of 30 MPa, 30 • C, and 40% v/v ethanol. As reported by Gómez-Loredo et al. [47], an increasing concentration of co-solvent could induce a decrease in the purity and recovery of fucoxanthin as other compounds that were the part of the extract could transfer with this carotenoid. At times, up to a certain value, the addition of co-solvent has no further effect. This could happen at 50% v/v ethanol where fucoxanthin purity and recovery begin to decrease.
Extraction of fucoxanthin from different natural sources using conventional solvent, pressurized liquid extraction, or supercritical fluids extraction has been reported. For example, Conde et al. [48] showed ethanol concentration (0.5-10% v/v) as a significant factor in the supercritical CO 2 extraction process from the macroalgae Sargassum muticum. The improvement in ethanol concentration resulted in total yields up to 3 times higher, radical scavenging capacity up to 2.5 times higher, and fucoxanthin extraction yield up to 90 times higher, thus reaching approximately 12 mg fucoxanthin/100 mg dry biomass under 20 MPa at 30 • C and 10% v/v ethanol. Gilbert-López et al. [49] compared MAE and PLE as green techniques for the extraction of bioactive compounds from P. tricornutum. The total yield (23.95% w/w), fucoxanthin purity, and its recovery (32.29 mg/g extract and 54.41% w/w, respectively) were the highest under 50 • C and 100% ethanol using PLE. Our results of fucoxanthin purity and recovery are higher than these results, although the P. tricornutum strain described by Gilbert-López et al. [49] reached up to 1.5-times higher concentration of fucoxanthin by conventional extraction than our results (maceration in acetone during 24 h at room temperature was around of 59.5 ± 4.7 mg/g extract). All results corroborated that P. tricornutum is an important source of bioactive compounds such as fucoxanthin and is better than other species such as macroalgae. Table 3 presents the physicochemical characterization of the diatom P. tricornutum and supercritical-fluid-extracted P. tricornutum. As shown, most of the analyzed parameters have maintained similar values in both groups. Only metal content, which increased in all cases after SFE, and the P T -P 2 O 5 parameter decreased by four times after SFE. It should be highlighted that the metal content reached non-toxic or inhibiting concentrations. The maintenance of nutrients such as nitrogen (N-TKN) or phosphorous (P T -P 2 O 5 ) in the diatom P. tricornutum is essential for the microorganisms responsible for performing AD.

Biochemical Composition and the Effects of SFE on AD Using P. tricornutum
The comparison of the biochemical composition of P. tricornutum biomass and other strains is presented in Table 4. Biogas production from microalgae depends on their biochemical composition and other factors such as operating conditions, cell wall nature, C/N ratios and ammonia release, and sodium in marine species [50][51][52]. The analysis of the biochemical composition may help in the comprehension of the methane yields obtained. The best theoretical methane yields obtained are for lipids, followed by proteins and carbohydrates, with values 1.014 L CH 4 /g VS, 0.851 L CH 4 /g VS, and 0.415 L CH 4 /g VS, respectively [51]. These values could be accurate considering the composition of the specific microalga species.
Generally, the exhausted diatom has the lowest macronutrient content due to the extraction process, highlighting the decrease in lipid and protein content by more than half. The biochemical composition of pretreated P. tricornutum markedly decreased with the extraction of 68.99% and 60.19% of lipids and proteins, respectively, until the values of 5.01 ± 0.01% and 14.41 ± 0.62% w/w, respectively, were obtained. However, only 29.15% of carbohydrates were extracted. On the other hand, the protein content differed significantly (p ≤ 0.05) among the strains, followed by lipid and carbohydrate contents. The protein content ranged from 38.8 ± 0.11% to 26.95 ± 0.05% w/w (excluding P. tricornutum after SFE) with P. tricornutum F&M-M4 showing the highest value (Table 4). For carbohydrate content, all strains showed similar values with slight differences. Particularly, the carbohydrate content of P. tricornutum in our study was higher (18.80 ± 1.12% w/w) than the P. tricornutum carbohydrate content (16.91 ± 1.61% w/w) reported by Di Lena et al. [53]. P. tricornutum F&M-M4 had the highest lipid content, followed by a diatom described by Bernaerts et al. [54] (17.1 ± 0.9% w/w). In the case of extracted P. tricornutum, the lipid content was significantly decreased compared with the initial content in the biomass before extraction because especially the lipid fraction was recovered through supercritical CO 2 -extraction technology.
Globally, such results have confirmed P. tricornutum as complete and nutritive biomass; hence, it is important in aquaculture feeds and food applications [5,9,10,55]. Nevertheless, the biochemical compositions of P. tricornutum found in previous studies are variable and highly dependent on strains, culturing conditions, and growth stages [54,56]. Table 4. Biochemical composition of the diatom P. tricornutum before and after supercritical fluid extraction compared with the composition reported in previous studies.

Strain/Diatom
Proteins (% w/w) * Sum of storage polysaccharides (SPS) and cell wall polysaccharides (CWPS). Note: Different superscripted alphabets (a-e) indicate significant differences (p < 0.05) and the data are expressed as mean ± standard deviation (n = 3, SD ≤ 5%). Nucleic acids and ash account for the percentage left to make 100% wt of proximal composition.

Lipids
As shown in Table 4, our supercritical-fluid-extracted P. tricornutum or exhausted biomass was rich in proteins, carbohydrates, and to a lesser extent in lipids. This could be used in different integrated processes in algae biorefinery. Hence, in our study, the production of bioenergy in the form of biogas was evaluated.

BMP of Diatom P. tricornutum and Extracted P. tricornutum by SFE
Typically, the yield of biogas obtained by AD is associated with the biochemical composition and VS content of the biomass used as a substrate. Particularly, the AD of microalgae can be affected by different factors such as low C/N ratio, thick cell walls banking on the microalgal genus, and high concentrations of sodium for marine species [50,52,58].
P. tricornutum is the only species in the genus Phaeodactylum, which is rich in bioactive compounds such as fucoxanthin and fatty acids [10,55]. However, this genus has a silicious wall, one of the main drawbacks when considering the microalgae for AD that could affect the results of this process. When intracellular compounds of interest such as fucoxanthin are extracted by SFE from microalgae, the action of temperature, pressure, and the use of ethanol as a co-solvent can be considered as a pretreatment. SFE helps in the extraction of fucoxanthin, but the breakage of cell structures also favors the release of other compounds, which facilitates the action of microorganisms that perform the hydrolytic steps of AD. After SFE, the cell wall and structure breaks to some extent, and the remaining compounds and cell material are released into the surrounding environment, which can be used as substrates to feed anaerobic microorganisms [59].
The methane yields obtained for the whole P. tricornutum and the extracted diatom were 77.2 ± 3.85 LSTP CH 4 /kg VS and 56.7 ± 1.90 LSTP CH 4 /kg VS, respectively (Figure 3). algae can be affected by different factors such as low C/N ratio, thick cell walls banking on the microalgal genus, and high concentrations of sodium for marine species [50,52,58].
P. tricornutum is the only species in the genus Phaeodactylum, which is rich in bioactive compounds such as fucoxanthin and fatty acids [10,55]. However, this genus has a silicious wall, one of the main drawbacks when considering the microalgae for AD that could affect the results of this process. When intracellular compounds of interest such as fucoxanthin are extracted by SFE from microalgae, the action of temperature, pressure, and the use of ethanol as a co-solvent can be considered as a pretreatment. SFE helps in the extraction of fucoxanthin, but the breakage of cell structures also favors the release of other compounds, which facilitates the action of microorganisms that perform the hydrolytic steps of AD. After SFE, the cell wall and structure breaks to some extent, and the remaining compounds and cell material are released into the surrounding environment, which can be used as substrates to feed anaerobic microorganisms [59].
The methane yields obtained for the whole P. tricornutum and the extracted diatom were 77.2 ± 3.85 LSTP CH4/kg VS and 56.7 ± 1.90 LSTP CH4/kg VS, respectively (Figure 3). In both cases, a methane yield of around 55 LSTP CH4/kg VS was obtained in less than 10 h, highlighting the fast biodegradability of the substrate and microbial activity at the beginning of AD. Caporgno et al. [60] obtained methane yields of 257 ± 8 mL of CH4/g VS and 180 ± 6 mL of CH4/g VS, respectively, for P. tricornutum after lipid extraction for biodiesel production with traditional solvents such as hexane and methanol/hexane mixture. Zhao et al. [26] obtained the yield of 339 ± 13 mL of CH4/g VS for the lipid-extracted microalgal biomass using hexane and evaporating it after the extraction at 105 °C in a hood. Studies on the AD of P. tricornutum are limited, and the methane yields reported by Caporgno et al. In both cases, a methane yield of around 55 LSTP CH 4 /kg VS was obtained in less than 10 h, highlighting the fast biodegradability of the substrate and microbial activity at the beginning of AD. Caporgno et al. [60] obtained methane yields of 257 ± 8 mL of CH 4 /g VS and 180 ± 6 mL of CH 4 /g VS, respectively, for P. tricornutum after lipid extraction for biodiesel production with traditional solvents such as hexane and methanol/hexane mixture. Zhao et al. [26] obtained the yield of 339 ± 13 mL of CH 4 /g VS for the lipid-extracted microalgal biomass using hexane and evaporating it after the extraction at 105 • C in a hood. Studies on the AD of P. tricornutum are limited, and the methane yields reported by Caporgno et al. [60], Zhao et al. [26], Frigon et al. [61], or Zamalloa et al. [62] could not be compared with the yields obtained in the present study because the extraction methods were not the same, nor did the extracted compounds include fucoxanthin, and the extraction of different compounds can affect AD methane yields differently.
In addition, a high or low concentration of a co-solvent (as a remainder) at the end of the extraction process of added high-value products can increase methane production when they are biodegradable. In our study, the methane yield obtained for the whole diatom was higher (77.2 ± 3.85 LSTP CH 4 /kg VS) than that obtained for the extracted diatom (56.7 ± 1.90 LSTP CH 4 /kg VS), resulting in a 26.6% reduction in the methane yield obtained from the whole microorganism. However, from the environmental and economic point of view, through the AD of the extracted P. tricornutum, biogas was obtained, which could reduce the energy costs for fucoxanthin extraction by SFE and/or contribute to the reduction in the costs of growing new microalgal biomass conferring the circularity to the process. Table 5 shows the characterization of the effluents or digests obtained after BMP assays of the microalgae P. tricornutum and the supercritical-fluid-extracted P. tricornutum. Conductivity was stable in both microalgae, with values around 17.75 to 18.14 mS/cm in all effluents obtained and loads assayed. The pH in these effluents increased with the second load in the BMP assays of both diatoms. The pH values obtained in the second load of the supercritical-fluid-extracted P. tricornutum were 9.05 ± 0.02, which are especially high for an anaerobic system, for which the optimal pH range is from 6.7 to 7.5, close to neutral ranges. In anaerobic processes and at this pH, VFA and ammonia almost dissociate.   Figure 4 shows the values of T-Alk measured in the effluents obtained after the BMP assays of diatom P. tricornutum and supercritical-fluid-extracted P. tricornutum.

Characteristics of Effluents after AD
T-Alk is an important parameter for AD systems. T-Alk gives anaerobic systems the capacity to cope with pH fluctuations. Most anaerobic reactors have T-Alks between 1500 and 5000 mg CaCO 3 /L, although values above 5000 mg CaCO 3 /L found in some reactors exhibited a slightly negative effect on the process [63]. In the present study, T-Alk values of the effluents were high, 9678 ± 90 mg CaCO 3 /L and 10,098 ± 105 mg CaCO 3 /L for the first and the second loads assayed with P. tricornutum and 9815 ± 115 and 10,300 ± 95 mg CaCO 3 /L for the first and second loads with supercritical-fluid-extracted P. tricornutum, respectively. This increase in T-Alk could be responsible for the increase in ammonia concentration. The initial growth of ammonia in the media can increase buffer capacity [64]; however, the high concentrations of ammonia can inhibit methanogenesis. solids, VS: volatile solids, N-NH4+: ammoniacal nitrogen, TKN: total Kjeldahl Nitrogen, DL: Detection Limit, Phaeodactylum Tricornutum (P. tricornutum). Figure 4 shows the values of T-Alk measured in the effluents obtained after the BMP assays of diatom P. tricornutum and supercritical-fluid-extracted P. tricornutum. T-Alk is an important parameter for AD systems. T-Alk gives anaerobic systems the capacity to cope with pH fluctuations. Most anaerobic reactors have T-Alks between 1500 and 5000 mg CaCO3/L, although values above 5000 mg CaCO3/L found in some reactors exhibited a slightly negative effect on the process [63]. In the present study, T-Alk values of the effluents were high, 9678 ± 90 mg CaCO3/L and 10,098 ± 105 mg CaCO3/L for the first and the second loads assayed with P. tricornutum and 9815 ± 115 and 10,300 ± 95 mg CaCO3/L for the first and second loads with supercritical-fluid-extracted P. tricornutum, respectively. This increase in T-Alk could be responsible for the increase in ammonia concentration. The initial growth of ammonia in the media can increase buffer capacity [64]; however, the high concentrations of ammonia can inhibit methanogenesis.
In anaerobic digesters, ammonium and free ammonia are in equilibrium, and free ammonia, a form of nitrogen, is more dangerous for these systems. Free ammonia concentrations are usually higher at higher pH and temperatures, reaching an inhibitory concentration of 150 mg N-NH3/L [65]. In the present study, N-NH4 + concentration increased from 1472 ± 60 to 1653 ± 50 mg/L when moving from the first load to the second load in the reactors digesting P. tricornutum. On the other hand, N-NH4 + concentrations were almost constant for the first and second loads of the extracted P. tricornutum, with values of 1265 ± 5 and 1290 ± 10 mg/L for the first and second load assayed, respectively ( Figure  5A). In anaerobic digesters, ammonium and free ammonia are in equilibrium, and free ammonia, a form of nitrogen, is more dangerous for these systems. Free ammonia concentrations are usually higher at higher pH and temperatures, reaching an inhibitory concentration of 150 mg N-NH 3 /L [65]. In the present study, N-NH 4 + concentration increased from 1472 ± 60 to 1653 ± 50 mg/L when moving from the first load to the second load in the reactors digesting P. tricornutum. On the other hand, N-NH 4 + concentrations were almost constant for the first and second loads of the extracted P. tricornutum, with values of 1265 ± 5 and 1290 ± 10 mg/L for the first and second load assayed, respectively ( Figure 5A). The values obtained for the whole diatom P. tricornutum were high and close to inhibitory values obtained in anaerobic environments, between 1500 and 3000 mg N-NH4 + /L [66]. Inhibitory concentration values can be higher in an adapted process; some studies have shown the tolerance of microalgae to ammonia concentrations between 1500-7000 mg N-NH4 + /L [67]. Factors such as the origin of the inoculum, temperature, and types of substrates may affect this wide range of inhibitory concentrations of N-NH4 + [65].
The N-TKN ( Figure 5B) present in the effluents obtained after the first and second load of the diatom P. tricornutum were higher than that obtained after the first and second load of the supercritical-fluid-extracted P. tricornutum, obtaining values of 2013 ± 25 mg/L The values obtained for the whole diatom P. tricornutum were high and close to inhibitory values obtained in anaerobic environments, between 1500 and 3000 mg N-NH 4 + /L [66]. Inhibitory concentration values can be higher in an adapted process; some studies have shown the tolerance of microalgae to ammonia concentrations between 1500-7000 mg N-NH 4 + /L [67].
Factors such as the origin of the inoculum, temperature, and types of substrates may affect this wide range of inhibitory concentrations of N-NH 4 + [65]. The N-TKN ( Figure 5B) present in the effluents obtained after the first and second load of the diatom P. tricornutum were higher than that obtained after the first and second load of the supercritical-fluid-extracted P. tricornutum, obtaining values of 2013 ± 25 mg/L and 2169 ± 25 mg/L for the first and second loads of the whole P. tricornutum, respectively. These values were lower for the extracted P. tricornutum, 1720 ± 10 and 1812 ± 15 mg/L for the first and second loads, respectively. These values could be responsible for a 39.8% reduction in proteins, which decreased from 36.20% to 14.41% (w/w) for the diatom P. tricornutum due to SFE, as described in Section 2.3 and Table 4. Figure 6 shows the VFA evolution in each load studied for the diatom P. tricornutum and supercritical-fluid-extracted P. tricornutum. VFAs in the effluents after the BMP assays showed a decreasing trend at the end of the second load, decreasing values from 195 ± 5 mg C/L to 87 ± 5 mg C/L for the non-extracted diatom and from 190 ± 10 mg C/L to 154 ± 5 mg C/L for the supercritical-fluid-extracted P. tricornutum. The decrease in acidity was an indicator of the presence of an adequate amount of methanogenic bacteria. Finally, it seems that metal content provided by the own diatom does not apparently affect the AD process. The use of microalgae (including diatoms) in co-digestion with rich carbon substrates is common for obtaining adequate nutrients and metal balance for the anaerobic system [68].

Biomass and Chemicals
The diatom Phaeodactylum tricornutum (CIB-41 from CIBNOR (https://www.cibnor.gob.mx/) La Paz, Mexico) was obtained from the Mexican Company "Microalgas Oleas de México S.A." (Guadalajara, Mexico). The diatom was cultured in F/2 culture medium as reported previously by Guillard [69] and harvested at the end of the exponential phase. The microalga (diatom) was provided freeze-dried (freeze-dry system Labconco Freezone 18 L Benchtop Freeze Dry System, Kansas, MO, USA), packed in vacuum-sealed plastic bags and then was stored at 4 ± 2 °C in the dark until use. All solutions used in this study were of analytical grade except for the standard solutions and chromatographic solvents. For supercritical fluid extraction, carbon dioxide and ethanol were purchased from Indura Air Products Group (Santiago, Chile) and Sigma-Aldrich (Santiago, Chile), respectively. Bovine Serum Albumin (BSA) (as the standard in protein analy- Figure 6. Concentrations of volatile fatty acids (VFA) obtained in the effluents after biochemical methane potential (BMP) assays (first load and second load) for the diatom P. tricornutum and supercritical-fluid-extracted P. tricornutum.
Finally, it seems that metal content provided by the own diatom does not apparently affect the AD process. The use of microalgae (including diatoms) in co-digestion with rich carbon substrates is common for obtaining adequate nutrients and metal balance for the anaerobic system [68].

Biomass and Chemicals
The diatom Phaeodactylum tricornutum (CIB-41 from CIBNOR (https://www.cibnor. gob.mx/, accessed on 22 November 2021) La Paz, Mexico) was obtained from the Mexican Company "Microalgas Oleas de México S.A." (Guadalajara, Mexico). The diatom was cultured in F/2 culture medium as reported previously by Guillard [69] and harvested at the end of the exponential phase. The microalga (diatom) was provided freeze-dried (freeze-dry system Labconco Freezone 18 L Benchtop Freeze Dry System, Kansas, MO, USA), packed in vacuum-sealed plastic bags and then was stored at 4 ± 2 • C in the dark until use. All solutions used in this study were of analytical grade except for the standard solutions and chromatographic solvents. For supercritical fluid extraction, carbon dioxide and ethanol were purchased from Indura Air Products Group (Santiago, Chile) and Sigma-Aldrich (Santiago, Chile), respectively. Bovine Serum Albumin (BSA) (as the standard in protein analysis) and glucose (as the standard in carbohydrate determination) were acquired from Sigma-Aldrich (Santiago, Chile). For fucoxanthin identification and quantification, a standard of >99% purity (Sigma-Aldrich, Santiago, Chile) was used. Ethyl acetate, acetonitrile, and ultrapure (MilliQ) water were of chromatographic grade (Sigma-Aldrich, Santiago, Chile) for high-performance liquid chromatography (HPLC).

Determination of Particle Size Distribution of the P. tricornutum Freeze-Dried Biomass
The particle size distribution of lyophilized diatom powder was determined using an electromagnetic sieve shaker (CISA Sieving Technologies, BA200N model, Barcelona, Spain). Eight sieves with ISO 3310-1 (ASTM E11) sizes of 10,12,16,18,35,60,120, and 230 were used. After 15 min shaking, the material retained in each sieve and the bottom pan was weighed. The mean particle diameter (Dp) of the P. tricornutum powder was determined according to ASABE [70] using Equation (1).
where D P is the mean particle diameter (mm); d i is the diameter of the sieve opening i (mm); d i+1 is the diameter of the sieve opening above sieve i (mm); W i is the retained mass (g); and n is the total number of fractions. The samples were kept in sealed plastic bags in a refrigerator till further analysis.

SFE
The SFE experiments were performed using a commercial SFE unit (Spe-ed SFE Helix, Applied Separations, Allentown, PA, USA), which was described in detail by Salinas et al. [71]. The aim of this experiment was to evaluate the effect of extraction conditions such as the temperature of 30 • C and 50 • C; the pressure of 20, 30, and 40 MPa; and the concentration of ethanol as a co-solvent from 10% to 50% v/v on the extraction yield, fucoxanthin purity, and fucoxanthin recovery from the P. tricornutum biomass. Initially, different temperature and pressure conditions were evaluated using the freeze-dried biomass to optimize temperature and pressure parameters. For each extraction assay, 2.0 g of P. tricornutum biomass was packaged in a 24 mL extraction vessel (nominal volume), with the dimensions of 0.56 inch (1.4224 cm) of internal diameter and 5.9 inches (14.986 cm) of internal height (ASI Part Number 6414/7975; Applied Separations, Allentown, PA, USA), occupying a volume of 2.54 mL, resulting in a bed density of 0.787 g/mL, which is approximately 10.6% of the total volume of the extraction vessel. The empty space of the extraction vessel was filled with 1.0 mm glass beads. The extraction vessel containing the biomass was assembled into the heated jacket at a selected temperature and kept for 15 min until the desired temperature was stabilized. CO 2 was pumped until the desired pressure was reached, and the system was maintained for 10 min (static time) and the total time of extraction was set at 60 min according to a previous report on the extraction of carotenoids (xanthophyll) from microalgae [30]. The CO 2 flow rate was measured using an electronic flow meter installed at the exit of the sample collection flask. After the static time, the outlet valve of the bed was opened, and the micrometric valve was adjusted to reach a CO 2 flow rate of 2 L/min that corresponds to a mass flow rate of 3.62 g/min. At this mass flow rate, superficial CO 2 velocities (U: mm/s) through the extraction vessel were calculated according to the temperature (30 • C and 50 • C) and pressure (20, 30, and 40 MPa) of each treatment.
A factor that critically affects the cost of SFE processes for solid substrates is the extraction time [72], which in turn affects extraction yield that depends on substrate pretreatment, particle size (Dp), CO 2 temperature (T), pressure (P), and superficial velocity (U) [73]. This flow of CO 2 during 60 min corresponds to a ratio of solvent to feed (S/F) of 108.6. The effect of operative conditions on the yield and extraction of fucoxanthin was expressed in terms of the total yield of extract and fucoxanthin purity and recovery from P. tricornutum, respectively. These variables were calculated using the following Equations (2)-(4): Total Yield (%) = (We/Wb) × 100 (2) Purity (mg/g) = Wc/We Recovery (%) = (Wc/Wt) × 100 (4) where We is the weight of the extract (g), Wb is the weight of biomass (g); Wc is the weight of the fucoxanthin extracted (mg), and Wt is the reference weight of the fucoxanthin from conventional extraction (mg). This value was calculated on the basis of the initial content of fucoxanthin pigment in the diatom, expressed as mg of extract per gram of dry weight of P. tricornutum (equals to 9.82 ± 0.70 mg/g). Each experimental condition was replicated three to five times, and standard deviation (SD) was calculated for each value.

Fucoxanthin Quantification by HPLC
Fucoxanthin was extracted from 50 mg of supercritical fluids extracts, and methanol (0.05% w/v BHT) was added in all samples. The aliquots were filtered (Ø = 0.22 µm filter) and transferred into an amber vial for chromatographic analysis. Subsequently, fucoxanthin was separated and identified using the HPLC system, model 7100 (Merck Hitachi LaChrom, Tokyo, Japan) equipped with three pumps (flow rate of 1 mL/min), and a UV-Vis detector was used at 450 nm. The samples (20 µL) were injected into a capillary column (C18, 250 mm × 4.6 mm, 5 µm, Restek, Bellefonte, PA, USA). The mobile phase consisted of solvent A (ethyl acetate) and solvent B (acetonitrile:water 90:10). The gradient procedure was 100% solvent B for 10 min; 50% solvent B for 4 min; 40% solvent B for 2 min; and 100% solvent B for 1 min. Fucoxanthin was identified by comparing the retention times with that of the reference standard. Fresh standard solutions (1ppm to 20 ppm of fucoxanthin) were prepared and injected to generate the standard fucoxanthin curve. The calculation of the free fucoxanthin concentration in the samples was performed using the standard curve that was found to be linear over the required range (1-25 µg/mL; R 2 = 0.9971). All analyses were performed in triplicate.

Characterization of Biochemical Composition
The characterization of biochemical composition was performed from the original biomass, the whole P. tricornutum, and the exhausted biomass. The exhausted biomass was a unique sample composed of a mixture resulting from the biomass pool after all SFE extractions studied. The protein content of P. tricornutum was analyzed colorimetrically using a microplate reader (Synergy HTX Multi-Mode microplate reader, software Gen5 2.0, BioTek Instruments, Winooski, VT, USA) and BSA solutions for the standard curve (0.0−2.0 mg/mL) by following the Lowry method [74]. The results are expressed as the percentage of total proteins with respect to their dry biomass (% w/w). Total carbohydrate content was determined according to the modified protocols of Dubois et al. [75] and Geresh et al. [76] using a series of glucose solutions as the standard (0.0−1.0 mg/mL). The biomass used for carbohydrate measurement was subjected to acid hydrolysis for cell rupture. Briefly, 20 mg of the dry biomass was incubated in 5 mL of 2.5 M HCl for 3 h at 100 • C (Spectroquant Thermoreactor TR 320, Merck, Darmstadt, Germany). This mixture was neutralized with 5 mL of 2.5 M NaOH to obtain the microalgal extract. Finally, aliquots of 278 µL of extract, 167 µL of phenol solution (5% w/v), and 1000 µL of concentrated sulfuric acid were incubated for 30 min at room temperature, and the absorbance of these samples was measured at 483 nm using the microplate reader. The results are expressed as the percentage of total carbohydrates with respect to the dry biomass (% w/w). Total lipids were obtained according to the method of Axelsson et al. [77]. The dry biomass of P. tricornutum (~20 mg) was resuspended in chloroform:methanol (2:1, v/v) by manually shaking the tube vigorously for a few seconds or until the biomass was dispersed in the solvent system. Finally, 0.73% (w/v) NaCl water solution was added to produce a 2:1:0.8 system of chloroform:methanol:water (v/v/v). The previous evaporation with N 2 was performed using Flexivap Workstation (Glas-Col 109A YH-1, Terre Haute, IN, USA). Lipid content was expressed as the percentage of total lipids with respect to the biomass (% w/w). Proteins, total carbohydrates, and total lipids are expressed as the average of a triplicate (n = 3), and the data are expressed as mean ± SD.

Analytical Methods
The parameters pH, conductivity, total alkalinity (T-Alk), total solids, volatile solids (VS), mineral solids, total chemical oxygen demand (TCOD), soluble chemical oxygen demand, and volatile fatty acids (VFA) were determined according to the Standard Methods of the APHA et al. [78]. A Shimadzu model TOC-VCSH carbon analyzer was used for the determination of total organic carbon by the catalytic oxidation of total carbon present in the sample to CO 2 and detection by infrared spectrophotometry. Metal content was determined by flame photometry [78] with a Perkin-Elmer A Analyst 300 atomic absorption spectrophotometer. The methodology proposed by the US Department of Agriculture and the US Composting Council [79] was used for the determination of ammoniacal nitrogen (N-NH 4 + ), total Kjeldahl nitrogen (N-TKN), and phosphorus (P-P 2 O 5 ) content. Volatile fatty acids (VFA) such as acetic, propionic, butyric, isobutyric, valeric, and isovaleric acids were determined using a Hewlett-Packard HP-5890 gas chromatograph equipped with a 15 m × 5.3 × 10 −4 m (i.d.) Nukol-silica semi-capillary column and a flame ionization detector. Table 6 summarizes the main characteristics of the inoculum used for the biochemical methane potential (BMP) tests. The inoculum used was a baker's yeast vinasse obtained from La Golondrina plant, the municipal water company (EMACSA), Córdoba, Spain. The AD of P. tricornutum was assessed by performing BMP assays in batches. The 1.2 L reactors or digesters were maintained at mesophilic temperature (35 ± 2 • C) using a thermostatic water bath (LAUDA RTM 20) and were continuously agitated at 200 rpm. An inoculum-to-substrate ratio was maintained at 4 (on a VS basis). A total of 5.7 g inoculum of VS was added in each reactor using an effective volume of 1000 mL. The headspace of each flask was flushed with nitrogen to displace O 2 and promote AD conditions. The CH 4 produced was measured using a 1 L Boyle-Mariotte reservoir connected to each digester. NaOH solution (6N) was used assuming that the non-captured gas from biogas was methane. The volume of CH 4 was measured by water displacement. All methane volumes and yields were measured under standard temperature and pressure conditions (STP): 0 • C and 1 atm.

Anaerobic Inoculum and BMP
Before the experiments, the biomass was activated with GAL solution, a mixture of glucose (50 g/L), lactic acid (21 mL/L), and sodium acetate (25 g/L) with a TCOD concentration of 86,900 ± 75 mg O 2 /L and a pH of 7.05 ± 0.01. The experiments were performed in duplicate. Subsequently, the two digesters were fed with diatom P. tricornutum and the other two digesters with the extracted P. tricornutum (after the-SFE) to obtain CH 4 yields from both substrates.

Statistical Analysis
The Statgraphics Centurion XVIII ® Statistics software (StatPoint Technologies, Inc., Warrenton, VA, USA) was used for data elaboration and statistical analysis using a significance level of 95%. One-way analysis of variance, together with Tukey's test, was used for group extracts based on statistically significant differences. The effect of each factor and its statistical significance for each response variable were analyzed. A p-value of <0.05 was considered statistically significant. All experiments were performed in triplicate (n = 3), and the data are expressed as the mean ± SD.

Conclusions
In this study, we evaluated the use of P. tricornutum as biomass in the algae biorefinery concept using SFE, a green method, and biogas production to close the loop in a circular schedule. Fucoxanthin was the first valuable molecule to be recovered due to its many possible health benefits and high food market value. The best operating SFE parameters for the extraction yield, purity, and recovery of fucoxanthin from P. tricornutum by SFE were assessed. These optimal conditions were 30 MPa pressure at 30 • C and 30% v/v ethanol for extraction yield and 30 MPa pressure at 30 • C and 40% v/v of the extractant for fucoxanthin purity and recovery. Fucoxanthin recovery improved by 3.5 times at 30 MPa and 30 • C in the presence of ethanol, the most significant variable of SFE. Moreover, the diatom P. tricornutum was confirmed to be a potentially valuable natural resource for nutritional or nutraceutical purposes due to its good biochemical composition. The use of P. tricornutum and extracted diatom for AD enhanced the benefit of obtaining bioenergy in the form of biogas, obtaining methane yields of 77.15 ± 3.85 LSTP CH4/kg VS and 56.66 ± 1.90 LSTP CH4/kg VS for the whole diatom and the extracted P. tricornutum, respectively, in addition to fucoxanthin extraction; thus, implying its use a circular economy strategy, minimizing the potential costs associated with SFE as a costly pretreatment process for biogas production.
Based on our findings, P. tricornutum can be a useful candidate to diversify its multipurpose use from biotechnological and bioactive applications to sustainable energy production, playing a key role in the "algae biorefinery" concept.