Processes and systems for extracting and purifying sorghum waxes from sorghum-based feedstocks

Abstract

This invention generally relates to processes and systems for extracting and purifying sorghum waxes from sorghum-based feedstocks. In a first aspect, the invention relates to a process that introduces the sorghum-based feedstock to a supercritical carbon dioxide (SC-CO2) extractor, extracts a wax-rich fraction from the sorghum-based feedstock using pure SC-CO2, and extracts a phenolic-rich fraction from the sorghum-based feedstock using SC-CO2 and at least one cosolvent. In a second aspect, the invention relates to a SC-CO2 extractor that includes a high-pressure vessel, a high-pressure CO2 pump that delivers SC-CO2 to the high-pressure vessel, and a cosolvent pump that delivers at least one cosolvent to the high-pressure vessel.

Description

CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 PROCESSES AND SYSTEMS FOR EXTRACTING AND PURIFYING SORGHUM WAXES FROM SORGHUM-BASED FEEDSTOCKS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of and priority to U.S. Provisional Patent Application No. 63 / 629,966 filed on November 24, 2023, and incorporates the provisional application by reference in its entirety into this document as if fully set out at this point. BACKGROUND OF THE INVENTION 1. Field of the Invention.

[0002] The subject matter disclosed herein relates to processes and systems for extracting and purifying sorghum waxes from sorghum-based feedstocks. 2. Description of the Related Art.

[0003] Sorghum is the fifth most produced cereal crop worldwide after wheat, maize, rice, and barley, with 58.7 metric tons of production annually. Grain sorghum is covered with a pericarp-testa layer called bran (approximately 7% of the whole grain), which contains non- starch polysaccharides, phenolic compounds, and a coating wax that could potentially be a source of natural wax.

[0004] Grain sorghum has a higher wax-to-grain ratio than other cereals (between 0.1% and 0.4% (w / w), depending on the variety, kernels’ physical state, and extraction methods). Sorghum wax contains primary long-chain alcohols (policosanols) and phytosterols, which manifest a broad range of health-promoting features, including increasing muscle endurance and plasma cholesterol-lowering properties. The surface (bran) wax from sorghum has a high melting point (84-87°C) owing to its unique composition, as aldehydes (48-55%), and policosanols (37-44%) are the dominant ingredients. Due to the relatively high melting point,CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 sorghum bran waxes are a potential alternative to commercial carnauba wax. Sorghum grain also has a total lipid content of between about 3% and 4% (w / w). Over 90% of sorghum oil is triacylglycerols, with 15% total saturated, 35% monounsaturated, and 50% polyunsaturated fatty acids, where oleic, linoleic, and palmitic acids are the major fatty acids.

[0005] Moreover, grain sorghum contains high-value health-promoting phenolic compounds, namely phenolic acids and anthocyanins. Specifically, ferulic and protocatechuic acids are the primary phenolic acids present in sorghum, where coumaric, syringic, gallic, vanillic, hydroxybenzoic, caffeic, and cinnamic acids exist in relatively small amounts. However, phenolic acids, flavonoids, and condensed tannins are mostly concentrated in the pericarp layer of grain sorghum. Sorghum bran could serve as a critical source of anthocyanins, and it has been shown to provide anti-cancer activities. Among sorghum varieties, sorghum with a black pericarp is famous for containing the highest amount of 3-deoxyanthocyanins, which are more resistant to oxidation than other anthocyanidins, and are rare compounds in nature. Specifically, black sorghum bran showed higher antioxidant activity compared to blueberries. Moreover, the oxidative resistance of 3-deoxyanthocyanins makes them potential natural food colorants.

[0006] Sorghum bran, with its high-value lipids and phenolic compounds, is an underutilized food processing byproduct. Grain sorghum brans are often discarded by decortication during milling and used as cheap sources of feedstock or animal feed. Therefore, there is a great potential to recover high-value compounds, i.e., phytochemicals and waxes, from grain sorghum bran to increase their utilization in various food and pharmaceutical applications.

[0007] In addition, the growing awareness of environmental issues and accompanying demand for cleaner energy production means that new incentives are being put in place toCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 utilize industrial wastes and side products at maximum efficiency. One of the objectives of the 2030 Agenda for Sustainable Development is to guarantee access to inexpensive, reliable, and sustainable energy. Biofuels present sustainable and renewable options to traditional fuels, offering the benefit of reduced carbon and greenhouse gas emissions. According to the Renewable Fuel Association (“RFA”), a total of 103,228 million liters of fuel ethanol was produced worldwide in 2021. In 2023, the United States was the largest fuel ethanol producer at 53%, followed by Brazil (28%), the European Union (5%), and India (5%). The production of bioethanol presents a promising market for corn and sorghum cultivated in the United States. While corn has been the most preferred cereal for bioethanol production in both the European Union and the United States, sorghum (Sorghum bicolor (L.) Moench) is also incorporated into bioethanol production alongside corn in the United States. The RFA reported that 36 million kg of sorghum was used in bioethanol production in October 2021. In 2023, the United States used 134 million metric tons of corn and 1.1 million metric tons of sorghum for bioethanol production. The RFA states that a standard dry mill ethanol plant increases the value of each bushel (25.4 kg) of processed corn by almost $2 and helps in cutting down carbon emissions, equivalent to removing 12 million cars from the road annually.

[0008] Decreasing production costs is imperative to improving the competitiveness and sustainability of biofuels compared to fossil fuels. A viable strategy involves the valorization of co-products and side streams derived from biofuel productions. With recent investments in research and infrastructure, biofuel production is anticipated to increase, which consequently would increase biofuel side-streams. Such bioethanol side-streams have potential uses in food, cosmetic, specialty chemicals (e.g., pharmaceuticals), and biodiesel industries if adequate extraction / purification systems are implemented. For agro-industrial sourced bioethanol production, fine flour is obtained from grains through dry milling and proceeds to a liquefactionCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 process, where it is mixed with water, enzymes, and other ingredients to transform starch into glucose through saccharification. The produced glucose is converted into ethanol through fermentation. As the ethanol is purified by distillation and dehydration, the remaining semi- solid mass (stillage) is centrifuged to obtain technical oil. As the bioethanol side-streams are centrifuged to remove these oils, the remaining bulk (wet distillers grain) is dried to obtain dried distillers grains with solubles to use as animal feed.

[0009] During the process of converting grains into ethanol, grain-to-ethanol fermentation produces a lipid-rich biofuel side-stream known by several names, including bioethanol side-stream, lipids, lipid slurry (LS) , technical corn oil, and distillers’ corn oil, as a co-product. Based on data from January 2020 through March 2024, the RFA indicated a monthly byproduct yield of 166,234 metric tons of bioethanol side-stream. In 2023, over 2 million tons of bioethanol side-stream were produced as a byproduct of bioethanol production in the United States. The biofuel side-stream of ethanol formation has a fatty acid composition comparable to that of commercial corn oil. Like grain sorghum, bioethanol side-streams from corn contain a variety of phytochemicals and bioactive compounds, such as phytosterols, squalene, tocopherols, lutein, beta-carotene, polyphenols, anthocyanins, and bioactive peptides. This bioethanol side-stream has a more complex matrix than commercial oil due to the presence of proteins, amino acids, waxes, and other valuable compounds. Bioethanol side- streams are also rich in triacylglycerols, free fatty acids, and plant sterols. Fermenting sorghum and corn together further complicates the bioethanol side-stream, adding value to the byproduct. On the other hand, the complexity of bioethanol side-stream poses a significant challenge for extraction, hindering its efficient utilization in biodiesel, food, or cosmetics industries.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0010] Previous efforts to extract wax from sorghum have produced relatively low yields (around 1-3% w / w). Moreover, wax-rich lipids and phytochemicals have been traditionally extracted from grain sorghum using toxic organic solvents like hexane, acetone, chloroform, petroleum ether, or methanol. Methanolic extraction (either pure, acidic, or aqueous methanol) is traditionally accepted to extract phenolic compounds from plants, probably due to its favorable polarity for an optimal phenolic extraction. Unfortunately, the toxicity of these solvents impedes their food applications. For sorghum bran and / or bioethanol side-stream oils to be sustainable sources of lipids to the industries for food, cosmetics, biofuel, etc., there is an unresolved need to develop a green and sustainable method for fractionating lipids from such complex matrices. SUMMARY OF THE INVENTION

[0011] Accordingly, the invention relates to improved processes and systems for recovering sorghum wax from a sorghum-based feedstock. This invention also relates to selectively extracting triacylglycerols from a bioethanol lipid slurry to purify sorghum wax. The inventive food-grade extraction processes and systems separate the waxes and phytochemicals from sorghum bran or from lipid slurries in bioethanol facilities using green, sustainable valorization approaches. With the drive toward cleaner energy production, the inventive process improves the economic and environmental impact of biofuel production by recovering high-value compounds and other useful products from grain sorghum bran and from biofuel side-streams.

[0012] In general, in a first aspect, the invention relates to a process for recovering sorghum wax from a sorghum-based feedstock. The process introduces the sorghum-based feedstock to a supercritical carbon dioxide (SC-CO2) extractor, extracts a wax-rich fractionCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 from the sorghum-based feedstock using pure SC-CO2, and extracts a phenolic-rich fraction from the sorghum-based feedstock using SC-CO2and at least one cosolvent.

[0013] In an embodiment, the wax-rich fraction includes one or more of fatty acids, policosanols, and phytosterols.

[0014] In an embodiment, the step of extracting the wax-rich fraction from the sorghum-based feedstock is performed at a predetermined wax-extraction temperature between about 20°C and about 100°C.

[0015] In an embodiment, the step of extracting the wax-rich fraction from the sorghum-based feedstock is performed at a predetermined wax-extraction pressure between about 20 MPa and about 40 MPa.

[0016] In an embodiment, the predetermined wax-extraction temperature is about 60°C and the predetermined wax-extraction pressure is about 40 MPa.

[0017] In an embodiment, the phenolic-rich fraction includes phenolic acid, 3- deoxyanthocyanin, or both.

[0018] In an embodiment, the step of extracting the phenolic-rich fraction from the sorghum-based feedstock is performed at a predetermined phenolic-extraction temperature between about 20°C and about 100°C.

[0019] In an embodiment, the step of extracting the phenolic-rich fraction from the sorghum-based feedstock is performed at a predetermined phenolic-extraction pressure between about 20 MPa and about 40 MPa.

[0020] In an embodiment, the predetermined phenolic-extraction temperature is between about 30°C and about 40°C, and the predetermined phenolic-extraction pressure is about 40 MPa.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0021] In an embodiment, the predetermined phenolic-extraction temperature is about 60°C and the predetermined phenolic-extraction pressure is about 30 MPa.

[0022] In an embodiment, the step of extracting the phenolic-rich fraction involves introducing to the sorghum-based feedstock the mixture of the SC-CO2and the cosolvent in a ratio of about 1:4.5 (feedstock : cosolvent / SC-CO2).

[0023] In an embodiment, the sorghum-based feedstock is a sorghum bran, a sorghum- based bioethanol lipid slurry, or a corn / sorghum-based bioethanol lipid slurry.

[0024] In an embodiment, the concentration of the cosolvent used in the step of extracting the phenolic-rich fraction is between about 5 vol.% and about 40 vol.% with reference to the mixture of the SC-CO2 and the cosolvent.

[0025] In an embodiment, the process includes a step of extracting an oil-rich fraction from the sorghum-based feedstock before the step of extracting the wax-rich fraction, optionally at a predetermined oil-extraction temperature of between about 35°C and about 75°C and at a predetermined oil-extraction pressure of between about 8 MPa and about 40 MPa, where the oil-rich fraction optionally includes triacylglycerols.

[0026] In an embodiment, the process includes a step of collecting purified sorghum wax from the wax-rich fraction by dissolving the wax-rich fraction in ethanol, precipitating the sorghum wax from the wax-rich fraction, and drying the sorghum wax.

[0027] In general, in a second aspect, the invention relates to a SC-CO2 extractor for recovering sorghum wax from a sorghum-based feedstock. The extractor includes a high- pressure vessel configured to extract a wax-rich fraction and a phenolic-rich fraction from the sorghum-based feedstock, a high-pressure CO2pump configured to deliver SC-CO2to the high- pressure vessel, and a cosolvent pump configured to deliver at least one cosolvent to the high- pressure vessel.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0028] In an embodiment, the high-pressure CO2pump is configured to pressurize CO2gas to produce the SC-CO2.

[0029] In an embodiment, the high-pressure vessel is further configured to extract an oil-rich fraction from the sorghum-based feedstock. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The above and other objects and advantages of this invention may be more clearly seen when viewed in conjunction with the accompanying drawing wherein:

[0031] Figure 1 is a schematic diagram of a SC-CO2 extractor for cosolvent-modified SC-CO2 extraction in accordance with an illustrative embodiment of the invention disclosed herein.

[0032] Figure 2 is a schematic diagram of a SC-CO2 extractor for cosolvent-modified SC-CO2 extraction in accordance with another illustrative embodiment of the invention disclosed herein.

[0033] Figure 3 depicts a flowchart for a process of recovering sorghum wax from a sorghum-based feedstock in accordance with an illustrative embodiment of the invention disclosed herein.

[0034] Figure 4 depicts extraction curves of sorghum bran lipids at different pressures and temperatures with a CO2flow rate of 3.6 g / min (measured at ambient conditions) in accordance with an illustrative embodiment of the invention disclosed herein.

[0035] Figure 5 depicts crude lipid and wax yields obtained with pure SC-CO2extraction at different pressures and temperatures after 3 hours and Soxhlet extraction using hexane after 6 hours in accordance with an illustrative embodiment of the invention disclosed herein.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0036] Figure 6 depicts Differential Scanning Calorimetry (“DSC”) thermograms of purified waxes extracted by SC-CO2and hexane in accordance with an illustrative embodiment of the invention disclosed herein.

[0037] Figure 7 graphically illustrates total phenolics (GAE: gallic acid equivalent) and flavonoids (CAE: catechin equivalent) contents obtained with ethanol-modified and ethanol- water-modified SC-CO2at different pressures and temperatures in accordance with an illustrative embodiment of the invention disclosed herein.

[0038] Figure 8 depicts the relative compositions of phenolic acids, taxifolin, and apigenin extracted by different solvents in accordance with an illustrative embodiment of the invention disclosed herein.

[0039] Figure 9 depicts the relative compositions of 3-deoxyanthocyanins extracted by different solvents in accordance with an illustrative embodiment of the invention disclosed herein.

[0040] Figure 10A depicts response surface plots of the crude oil yield in view of pressure-temperature (at 4 hours) in accordance with an illustrative embodiment of the invention disclosed herein.

[0041] Figure 10B depicts response surface plots of the crude oil yield in view of time- temperature (at 24 MPa) in accordance with an illustrative embodiment of the invention disclosed herein.

[0042] Figure 10C depicts response surface plots of the crude oil yield in view of time- pressure (at 55°C) in accordance with an illustrative embodiment of the invention disclosed herein.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0043] Figure 10D depicts response surface plots of the crude oil yield in view of pressure-temperature (at 4 hours) in accordance with an illustrative embodiment of the invention disclosed herein.

[0044] Figure 10E depicts response surface plots of the crude oil yield in view of time- temperature (at 24 MPa) in accordance with an illustrative embodiment of the invention disclosed herein.

[0045] Figure 10F depicts response surface plots of the crude oil yield in view of time- pressure (at 55°C) in accordance with an illustrative embodiment of the invention disclosed herein.

[0046] Figure 11A depicts a corn / sorghum-based post-fermentation lipid slurry before SC-CO2 fractionation at optimized conditions in accordance with an illustrative embodiment of the invention disclosed herein.

[0047] Figure 11B depicts the corn / sorghum-based post-fermentation lipid slurry of Figure 11B after the SC-CO2 fractionation at optimized conditions.

[0048] Figure 11C depicts a wax-rich fraction (i.e., spent lipid slurry) that remained in the vessel after the SC-CO2 fractionation of Figure 11B.

[0049] Figure 12 depicts DSC thermograms of crude oil and wax-rich fractions obtained after SC-CO2 extraction at 35°C, 40 MPa, and 4.1 hours in accordance with an illustrative embodiment of the invention disclosed herein.

[0050] Figure 13A depicts DSC (melting) patterns of commercial carnauba, candelilla, paraffin, and beeswaxes, overlayed with lipid slurry (LS) in unscaled y-axis ranges in accordance with an illustrative embodiment of the invention disclosed herein.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0051] Figure 13B depicts DSC (melting) patterns of commercial carnauba, candelilla, paraffin, and beeswaxes, overlayed with LS in scaled y-axis ranges in accordance with an illustrative embodiment of the invention disclosed herein.

[0052] Figure 14A depicts DSC patterns of the commercial waxes, LS, and the LS- derived waxes overlayed as unscaled in accordance with an illustrative embodiment of the invention disclosed herein.

[0053] Figure 14B depicts DSC patterns of the commercial waxes, LS, and the LS- derived waxes overlayed as scaled in accordance with an illustrative embodiment of the invention disclosed herein.

[0054] Figure 14C depicts DSC patterns of 2nd order P-spline basis systems with 101 basis functions and lambda of 1 in accordance with an illustrative embodiment of the invention disclosed herein.

[0055] Figure 14D depicts DSC patterns of regenerated DSC curves using the P-splines in accordance with an illustrative embodiment of the invention disclosed herein.

[0056] Figure 15 depicts a flow chart of the modeling procedure in accordance with an illustrative embodiment of the invention disclosed herein.

[0057] Figure 16 depicts a Scree plot of the 10 FPC explaining the cumulative variance in accordance with an illustrative embodiment of the invention disclosed herein.

[0058] Figure 17A depicts mean function in accordance with an illustrative embodiment of the invention disclosed herein.

[0059] Figure 17B depicts the first four FPCs in accordance with an illustrative embodiment of the invention disclosed herein.

[0060] Figure 18 depicts mean function with the addition and subtraction of FPC1 in accordance with an illustrative embodiment of the invention disclosed herein.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0061] Figure 19A depicts FPCS plots in 2D (total of 63.4% variation), where the lowercase letters next to the sample codes denote replicates, and the run conditions are provided in Table 8 in accordance with an illustrative embodiment of the invention disclosed herein.

[0062] Figure 19B depicts FPCS plots in 3D (total of 75.1% variation), where the lowercase letters next to the sample codes denote replicates, and the run conditions are provided in Table 8 in accordance with an illustrative embodiment of the invention disclosed herein.

[0063] Figure 20A depicts unscaled DSC patterns of LS-derived wax 18 selected by FPCA as the closest alternatives to the commercial carnauba wax in accordance with an illustrative embodiment of the invention disclosed herein.

[0064] Figure 20B depicts scaled DSC patterns of the LS-derived wax 18 of Figure 20A.

[0065] Figure 20C depicts unscaled DSC patterns of LS-derived wax 12 selected by FPCA as the closest alternatives to the commercial beeswax in accordance with an illustrative embodiment of the invention disclosed herein.

[0066] Figure 20D depicts scaled DSC patterns of the LS-derived wax 12 of Figure 20C.

[0067] Figure 20E depicts unscaled DSC patterns of LS-derived wax 2 selected by FPCA as the closest alternatives to the commercial paraffin wax in accordance with an illustrative embodiment of the invention disclosed herein.

[0068] Figure 20F depicts scaled DSC patterns of the LS-derived wax 2 of Figure 20E.

[0069] Figure 20G depicts unscaled DSC patterns of LS-derived wax 17 selected by FPCA as the closest alternatives to the raw LS in accordance with an illustrative embodiment of the invention disclosed herein.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0070] Figure 20H depicts scaled DSC patterns of the LS-derived wax 17 of Figure 20G.

[0071] Figure 21A depicts actual vs predicted FPCS with XGB for FPCS1 in accordance with an illustrative embodiment of the invention disclosed herein.

[0072] Figure 21B depicts actual vs predicted FPCS with XGB for FPCS2 in accordance with an illustrative embodiment of the invention disclosed herein.

[0073] Figure 21C depicts actual vs predicted FPCS with XGB for FPCS3 in accordance with an illustrative embodiment of the invention disclosed herein .

[0074] Figure 21D depicts actual vs predicted FPCS with XGB for FPCS4 in accordance with an illustrative embodiment of the invention disclosed herein.

[0075] Figure 22A depicts validation run V1 and the predicted curves estimated by the XGB-advised FPC model at 14.5 MPa, 45°C, 2.7 hours in accordance with an illustrative embodiment of the invention disclosed herein.

[0076] Figure 22B depicts validation run V2 and the predicted curves estimated by the XGB-advised FPC model at 32 MPa, 45°C, 2.8 hours in accordance with an illustrative embodiment of the invention disclosed herein.

[0077] Figure 22C depicts validation run V3 and the predicted curves estimated by the XGB-advised FPC model at 16 MPa, 65°C, 3 hours in accordance with an illustrative embodiment of the invention disclosed herein.

[0078] Figure 22D depicts validation run V4 and the predicted curves estimated by the XGB-advised FPC model at 32 MPa, 65 °C, 3 hours in accordance with an illustrative embodiment of the invention disclosed herein.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 DETAILED DESCRIPTION

[0079] While this invention is susceptible to embodiment in many different forms, there are shown in the drawings and will herein be described hereinafter in detail some specific embodiments of the invention. It should be understood, however, that the present disclosure is to be considered an exemplification of the principles of the invention and is not intended to limit the invention to the specific embodiments so described.

[0080] The inventive system and process is directed to a sequential pure supercritical carbon dioxide (SC-CO2) and ethanol / water-modified SC-CO2 extraction technique for extracting both wax-rich lipids and phenolic compounds from sorghum bran in a single process. SC-CO2 poses several advantages as a solvent for lipid extraction and fractionation. First, the density of CO2 can be easily controlled by changing temperature and pressure, which means solvent selectivity can be tuned to extract a specific class of compounds. SC-CO2 can, therefore, be used to separate lipids with different solubilities effectively. As an environmentally friendly solvent, SC-CO2is also a green alternative to petroleum-based solvents used in traditional lipid extraction from cereals and grains. Unlike toxic organic solvents such as hexane, chloroform, or petroleum ether, SC-CO2is a non-toxic, recyclable, readily available, and highly diffusive solvent that can be employed to extract lipids and waxes from grains, seeds, and animal tissues. CO2possesses a mild critical point of 7.4 MPa and 31°C and leaves no solvent residues, making it a highly practical solvent. Properties of SC-CO2may also be tuned by changing pressure and temperature, allowing for selective extraction or fractionation of specific compounds from complex matrices.

[0081] In one aspect, as depicted in Figure 1, a SC-CO2extractor 100 for recovering sorghum wax from a sorghum-based feedstock includes a high-pressure vessel 102, a high- pressure CO2pump 104 that is configured to deliver SC-CO2to the high-pressure vessel 102,CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 and a cosolvent pump 106 that delivers at least one cosolvent (e.g., from a cosolvent container 108) to the high-pressure vessel 102. The high-pressure CO2pump 104 is driven by an air compressor 110 and pressurizes CO2gas received from a CO2cylinder 112 that is positioned downstream from the high-pressure pump. In one embodiment, the CO2cylinder 112 includes a heating jacket 114 and a needle valve 116 for releasing the CO2gas. As depicted in Figure 2, a pressure gauge 118 and a pre-chiller 120 can be used to measure pressure and lower temperatures of the CO2 gas before it is received in the high-pressure CO2 pump 104. The SC- CO2 is optionally heated by a pre-heater 122 before delivery to the high-pressure vessel 102. A plurality of check valves 124 regulates delivery of the SC-CO2 and the cosolvent to the high- pressure vessel 102.

[0082] As depicted in Figure 1, the SC-CO2 extractor 100 includes a thermal isolation chamber 126 disposed about the high-pressure vessel 102 and a temperature controlling unit 128 in communication with the high-pressure vessel 102 to control temperatures for the extraction steps. The SC-CO2 extractor 100 may also include a pressure controller 130 in communication with the high-pressure vessel 102 to manage pressures therein.

[0083] A rupture disk 132 upstream of the high-pressure vessel 102 protects the SC- CO2 extractor 100 from over pressurization or potentially damaging vacuum conditions. A second needle valve 134, a micro-metering valve 136, or both is used to control the movement of fractions from the high-pressure vessel 102. A second temperature controller 138 may be used to manage temperatures at the second needle valve 134, the micro-metering valve 136, or both. At lab scale, fractions of wax-rich lipids and phenolic compounds may be collected in one or more vials 140 on a cold trap 142, where fluid movement is optionally monitored using a flow meter 144. It will be appreciated that different components may be used to collect fractions when the SC-CO2extractor 100 is scaled up for large-scale production.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0084] In another aspect, the inventive system and process is directed to an optimized green method based on a sequential SC-CO2and ethanol / water-modified SC-CO2extraction. High-value lipophilic and hydrophilic compounds in sorghum-based feedstock can be recovered by a sequential SC-CO2and cosolvent-modified SC-CO2approach in a single run. In one embodiment, as depicted in Figure 3, a process 200 for recovering sorghum wax from a sorghum-based feedstock involves a step 202 of introducing the sorghum-based feedstock to an SC-CO2 extractor 100, a step 204 of extracting a wax-rich fraction from the sorghum-based feedstock using pure SC-CO2, and a step 206 of extracting a phenolic-rich fraction from the sorghum-based feedstock using SC-CO2 and at least one cosolvent. Step 202 may be performed by introducing the sorghum-based feedstock to the high-pressure vessel 102 of the SC-CO2 extractor 100. The sorghum-based feedstock in one embodiment is a sorghum bran, such as a milled black sorghum bran, white sorghum bran, waxy white sorghum bran, sumac sorghum bran, burgundy sorghum bran, or waxy burgundy sorghum bran. The sorghum bran may contain a small part of endosperm / germ, as stated by the manufacturer. In another embodiment, the sorghum-based feedstock is a sorghum-based bioethanol lipid slurry or a corn / sorghum- based bioethanol lipid slurry. In one embodiment, between about 30% and 100% (w / w) sorghum-based feedstock is introduced into the high-pressure vessel 102, based on the weight of the overall feedstock introduced to the high-pressure vessel 102; the overall feedstock may also include, for example, a corn-based feedstock. Optionally, a plurality of glass beads is introduced to the high-pressure vessel 102 with the sorghum-based feedstock to avoid compacting of the feedstock.

[0085] Turning to step 204, the pure SC-CO2used to extract the wax-rich fraction may be introduced to the high-pressure vessel 102 before step 202, after step 202, or contemporaneous with step 202, and the SC-CO2is optionally pre-heated by pre-heater 122CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 before it is introduced to the high-pressure vessel 102. Although Figures 1 and 2 depict a system for pressurizing CO2gas using a high-pressure CO2pump before the resulting SC-CO2is introduced to the high-pressure vessel 102, it will be appreciated that SC-CO2may otherwise be obtained or may be stored in its supercritical state without the need for further pressurization. The wax-rich fraction that is extracted from the sorghum-based feedstock may include esters of long-chain carboxylic acids and alcohols, as well as other long-chain nonpolar compounds (i.e., hydrocarbons, aldehydes) that can provide elevated melting point and water-repelling characteristics. In various embodiments, the wax-rich fraction includes one or more of fatty acids, policosanols, and phytosterols, while the phenolic-rich fraction includes phenolic acid, 3-deoxyanthocyanin, or both.

[0086] The step 204 of extracting the wax-rich fraction may involve steps of obtaining a predetermined wax-extraction temperature and obtaining a pre-determined wax-extraction pressure. The predetermined wax-extraction temperature may be obtained using the temperature controlling unit 128 and may range between about 20°C and about 100°C (and any range or value therebetween, including without limitation between about 30°C and about 90°C, more particularly between about 35°C and about 80°C, and alternatively between about 40°C and about 70°C, more particularly between about 50°C and about 60°C). In one embodiment, the predetermined wax-extraction temperature is 60°C. Suitable pre-determined wax- extraction pressures include pressure between about 8 MPa and about 40 MPa (and any range or value therebetween including, but not limited to, between about 10 MPa and about 40 MPa, more particularly between about 30 MPa and about 40 MPa). In one embodiment, the pre- determined wax-extraction pressure is about 40 MPa. In at least one embodiment, a relatively high predetermined wax-extraction temperature (e.g., from 60°C to 100°C) is combined with a relatively high predetermined wax-extraction pressure (e.g., 40 MPa) for the wax-richCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 fraction extraction step. The wax-extraction pressures may be controlled to maintain the pre- determined wax-extraction pressures using the pressure controller 130.

[0087] Step 204 of extracting the wax-rich fraction may also be performed for a pre- determined wax-extraction time ranging between about 0.5 hours and about 5 hours, more particularly between about 2 hours and about 6 hours, more particularly about 3 hours. The wax-rich fraction may be collected in one or more vials 140 or containers for removal from the SC-CO2 extractor 100. Optionally, additional steps are performed to recover sorghum wax from the wax-rich fraction. In one such embodiment, the wax-rich fraction is dissolved in ethanol, sorghum wax is allowed to precipitate from the wax-rich fraction, and the sorghum wax is then collected and dried.

[0088] As a nonpolar solvent, SC-CO2 cannot effectively extract polar compounds such as phenolic compounds. To extract phenolic compounds in the phenolic-rich fraction extraction step 206, at least one cosolvent may be added to modify the solvating power of SC-CO2. The cosolvent may be stored in the cosolvent container 108 and may be combined with the SC-CO2 before entering the high-pressure vessel 102 or may be introduced to the high-pressure vessel 102 before, after, or contemporaneous with the SC-CO2. The combination of SC-CO2 and at least one cosolvent enables the extraction and fractionation of both polar and nonpolar compounds from the sorghum-based feedstock. Suitable cosolvents include ethanol, water, and mixtures of ethanol and water (e.g., 1:1, v / v ethanol-water mixture). Other suitable cosolvents include Generally Recognized as Safe (GRAS) substances, as defined determined by the United States Food and Drug Administration. The concentration of the cosolvent used for extracting the phenolic-rich fraction may be between about 5 vol.% and about 40 vol.%, with reference to the total mixture of the cosolvent and the SC-CO2. It will be understood that, as used herein, a range of X vol.% to Y vol.% will be interpreted to include the disclosure of each discreteCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 integer value between X and Y (e.g., X, X+1, X+2….Y-1, Y). To extract the phenolic-rich fraction in step 206, the ratio of the sorghum-based feedstock to the mixture of the cosolvent and the SC-CO2in the high-pressure vessel 102 may be about 1:4.5 (feedstock : cosolvent / SC- CO2).

[0089] The step 206 of extracting the phenolic-rich fraction from the sorghum-based feedstock may be performed by obtaining a predetermined phenolic-extraction temperature and a predetermined phenolic-extraction pressure. The predetermined phenolic-extraction temperature may be between about 20°C and about 100°C (and any range or value therebetween including, but not limited to, between about 40°C and about 60°C, alternatively between about 30°C and about 40°C). The predetermined phenolic-extraction temperature may be obtained using the temperature controlling unit 128. Suitable predetermined phenolic- extraction pressures include between about 20 MPa and about 40 MPa (and any range or value therebetween including, but not limited to, between about 30 MPa and about 40 MPa). The phenolic-extraction pressures may be controlled to maintain the predetermined phenolic- extraction pressures using the pressure controller 130. Where the predetermined phenolic- extraction pressure is about 40 MPa, suitable predetermined phenolic-extraction temperatures include, without limitation, between about 30°C and about 40°C. Where the predetermined phenolic-extraction pressure is about 30 MPa, suitable predetermined phenolic-extraction temperatures include, without limitation, about 60°C.

[0090] Step 204 of extracting the wax-rich fraction may also be performed for a pre- determined wax-extraction time ranging between about 0.5 hours and about 5 hours, more particularly between about 2 hours and about 6 hours, more particularly about 3 hours. The wax-rich fraction may be collected in one or more vials 140 or containers for removal from the SC-CO2extractor 100.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0091] Step 206 of extracting the phenolic-rich fraction from the sorghum-based feedstock may be performed for a pre-determined phenolic-extraction time ranging between about 0.5 hours and about 5 hours, more particularly between about 2 hours and about 3 hours. In one embodiment, the pre-determined phenolic-extraction time is about 3 hours. The phenolic-rich fraction may be collected in one or more vials 140 or containers for removal from the SC-CO2extractor 100.

[0092] The process 200 for recovering sorghum wax from the sorghum-based feedstock optionally include a step of extracting an oil-rich fraction from the sorghum-based feedstock before the step of extracting the wax-rich fraction from the sorghum-based feedstock. This optional step may be performed in the high-pressure vessel 102 or before the sorghum- based feedstock is introduced to the high-pressure vessel 102. By extracting lipids such as triacylglycerol from the sorghum-based feedstock in the oil-rich fraction, a purified sorghum wax product is obtainable from the wax-rich fraction. Once collected, the crude oil-rich fraction can be used as a feedstock for biodiesel production, while the wax-rich fraction can be used for food and non-food applications. The step of extracting the oil-rich fraction may be performed at a predetermined oil-extraction temperature between about 35°C and about 75°C (and any range or value therebetween, including about 55°C) and at a predetermined oil-extraction pressure between about 8 MPa and about 40 MPa (and any range or value therebetween). In one embodiment, the crude oil content in the oil-rich fraction is maximized and wax content therein is minimized at a predetermined oil-extraction temperature of about 35°C and a predetermined oil-extraction pressure of about 40 MPa. Suitable predetermined oil-extraction times for performing the optional oil-rich fraction extraction include between about 2 hours and about 6 hours (and any range or value therebetween). In one embodiment, the predetermined oil-extraction time is 4 hours.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0093] The inventive system and process allow for the development of effective extractions for an extensive array of compounds of interest (both hydrophilic and hydrophobic), which has the potential to be scaled up for large-scale production. The fractions obtained could be (i) a sustainable source of high-value wax, (ii) a health-promoting phenolic extract for developing functional foods with high antioxidant activity, and (iii) natural colorings for the food industry. These fractions are recovered from a bioethanol production waste stream without the use of petroleum-based chemicals. Recovered sorghum wax from the wax-rich fraction has tunable properties (e.g., a customizable melting point). This wax can also be an alternative to carnauba wax and is useful for food and non-food coating applications (e.g., by car wax producers or in drug coatings), water barrier applications, and oleogel applications. EXAMPLES

[0094] The process and system for extracting sorghum wax from a sorghum-based feedstock is further illustrated by the following examples, which are provided for the purpose of demonstration rather than limitation. EXAMPLE I

[0095] In this Example, several tests were performed to compare the inventive SC-CO2 extraction method with conventional solvent extraction techniques. The results revealed that wax and phenolic compounds were successfully extracted from black sorghum bran in a single run by neat and ethanol / water-modified SC-CO2 consecutively.

[0096] Materials.

[0097] Milled black sorghum bran (Tx430 variety) was obtained in a particle size that passed through a 60-mesh sieve (250 µm), and it was used as-is for the extractions. The bran contained 7.7 ±0.2% (wet basis) moisture content as determined by keeping the bran at 105°C until a constant weight was reached. Each of the following chemicals was also obtained for thisCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 test: liquid CO2(99.99% purity) with a dip tube, N2(99.9% purity), butylated hydroxyl toluene, ferulic acid, potassium hydroxide, hexane, methyl tert-butyl ether, 5α-cholestane, aluminum chloride, 1-octacosanol, apigenin, caffeic, trans-p-coumaric, and trans-cinnamic acid, methanol, pyridine, bis- (trimethylsilyl)-trifluoroacetamide with 1% trimethylchlorosilane (“BSTFA”), Folin-Ciocâlteu’s phenol reagent, sodium carbonate, taxifolin, oleic, linoleic and palmitic acid.

[0098] Wax-Rich Lipid Extraction Using Pure SC-CO2.

[0099] As depicted in the process schematic diagram of Figure 1, SC-CO2 extractions were performed using a lab-scale SC-CO2 extractor (SFT-120) equipped with a cosolvent pump. The high-pressure pump for CO2 was equipped with an internal thermoelectric cooling module; therefore, an additional cooling bath was not used prior to the pump. First, the cylindrical stainless-steel vessel (100 mL) was filled with 18 g milled black sorghum bran and 60 g glass beads mixture. Glass beads (3 mm in diameter) were included to avoid compacting of the bran and consequent channeling during extraction. The vessel was sealed with glass wool from both ends to prevent the stainless-steel frits from clogging. Then, the system was flushed with CO2 to eliminate any air in the vessel. Subsequently, the temperatures of the needle and micrometering valves were set to 80°C to prevent freezing owing to the Joule Thompson effect during the continuous flow of CO2. Next, the vessel was heated to the set temperature (40- 80°C) and pressurized to the set pressure (10-40 MPa). After a static extraction time of 20 minutes, the flow rate of CO2 was adjusted to 3.6 g / min (measured at ambient conditions).

[0100] A sequential pure SC-CO2and ethanol / water-modified SC-CO2extraction was carried out for all samples. First, the nonpolar fraction, i.e., wax-rich lipid fraction, was extracted using pure SC-CO2at 30-40 MPa and 40-60°C for 3 hours. Next, phenolic compounds were extracted by introducing cosolvents, i.e., pure ethanol (100%) or ethanol-CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 water (50%, v / v) mixture, into the vessel, where the pressure and temperature were set to 30- 40 MPa and 40-60°C for another 3 hours, respectively. Ethanol and water were selected due to their GRAS status. The cosolvent concentration in the vessel was kept constant at 15% (w / w) throughout the extraction based on the preliminary experiments. The extracted fractions were continuously collected in 40 mL brown glass vials kept in an ice bath. The moisture residue in the lipid extracts was removed under vacuum at 50°C. Finally, the samples were flushed with nitrogen and stored in a freezer at -20°C until further analysis. The total lipid yield was calculated according to Equation 1:

[0101] Total lipid yield (%) = [Total lipid extract (g) / Dry sample used (g)] x 100 (Equation 1).

[0102] Total wax was fractionated from the lipid extract by dissolving the extract in ethanol to make a 10 mg / mL solution, sonicating for 5 minutes, and heating in a water bath at 91°C until the extract was fully dissolved. Then, the solution was kept at 4°C for 24 hours to precipitate the waxy compounds, which were collected by centrifugation at 3220 g for 10 minutes. Finally, the waxy compounds were dried at 50°C under a stream of nitrogen. The resulting wax yields were calculated according to Equation 2:

[0103] Wax fraction (%) = [Sediment at 4°C (g) / Total extract (g)] x 100 (Equation 2).

[0104] Conventional Technique 1: Soxhlet Extraction of Lipids from Sorghum Bran.

[0105] Total lipids in milled black sorghum bran were extracted by a Soxhlet apparatus. Black sorghum bran (5 g) was wrapped in a filter paper (Whatman® Grade 2, 125 mm diameter), which was placed in a cellulose extraction thimble and fit in a Soxhlet apparatus attached to a flask containing 175 mL of hexane. The solvent was refluxed for 6 hours toCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 recover all the lipids in the sample. After 6 hours of extraction, the residue solvent was evaporated overnight at 50°C in a conventional oven.

[0106] Conventional Technique 2: Solvent Extraction of Phenolic Compounds from Sorghum Bran.

[0107] Total phenolic extraction was carried out using fresh samples by soaking 1 g of milled black sorghum bran into 45 mL of 80% methanol (v / v) for 1 hour at 50°C. The suspension was centrifuged at 3220 g and 4°C for 10 minutes. The supernatant was collected, and the residue was resuspended in 80% methanol for a second extraction period for 1 hour at 50°C. The suspension was centrifuged under the same conditions, and the supernatants were pooled. The extract solution was analyzed for total phenolic content (“TPC”) and total flavonoid content (“TFC”).

[0108] Phenolic extraction was also performed with the same solute to solvent ratio (w / v) used in the SC-CO2 extraction. Briefly, 1 g of black sorghum bran was suspended in 4.5 mL 80% methanol (v / v) for 1 hour at 50°C; the residue was separated by a centrifuge and at 3220 g and 4°C for 10 minutes. The same steps were repeated for a second time as described previously, and the pooled extract was analyzed for its TPC and TFC.

[0109] Analysis of Wax-Rich Lipid Extraction Yields.

[0110] The effects of pure SC-CO2 conditions in the first part of the inventive SC-CO2 extraction method, namely, pressure (10-40 MPa) and temperature (40-100°C), on the wax- rich lipid yields were investigated at a constant CO2 flow rate of 3.6 g / min (measured at ambient conditions). In preliminary experiments, a lipid yield of 5.2% (w / w dry basis) was obtained at 10 MPa and 40°C (ρ = 628.6 kg / m3), which was the lowest yield attained in this study. Based on these preliminary data, two pressure values (30 MPa and 40 MPa) and temperature values (40°C and 60°C) values were chosen to investigate further the effects ofCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 pressure and temperature on the extraction yield and composition. The pure SC-CO2extraction time of 3 hours was decided based on the extraction curves presented in Figure 4. Approximately 95% of the lipids were collected in the first 2 hours of the pure SC-CO2extraction at all the SC-CO2conditions investigated.

[0111] Figure 5 demonstrates the crude lipid and corresponding wax yields extracted using pure SC-CO2at various pressures and temperatures after 3 hours, as well as the yield from Soxhlet extraction using hexane after 6 hours (Conventional Technique 1). Crude lipid extraction yields with different capital letters and wax yields with different lowercase letters in Figure 5 are significantly different (p < 0.05).

[0112] For pure SC-CO2 extraction, the total lipid yields varied between 5.5-6.2% (w / w dry basis), where the highest crude lipid yield was achieved at 40 MPa and 60°C (ρ = 890.1 kg / m3) as 6.2% (w / w dry basis). Although the total lipid yields were lower at 30 MPa and 60°C (ρ = 829.7 kg / m3) (5.9%, w / w dry basis) and 40 MPa and 40°C (ρ = 957.7 kg / m3) (5.5%, w / w dry basis), the differences were statistically insignificant (p > 0.05). It is established that both the temperature and pressure of SC-CO2 dictate its solvating power. The density of SC-CO2 (ρ), and therefore its solvating power, is determined by the operating conditions. In other words, each compound requires a specific range of absolute density of SC-CO2 for optimal extraction. Previous literature has not shown that increasing pressure up to 40 MPa results in a significant increase in the wax yield from grain sorghum by SC-CO2. These results may not have been previously observed due to the difficulties in maintaining the operating conditions (e.g., the flow rate of CO2) at this high pressure.

[0113] Compared to the pure SC-CO2extraction (which had a highest crude lipid yield of 6.2%, w / w dry basis, p < 0.05), the conventional hexane extraction provided a significantlyCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 higher crude lipid yield (7.5%, w / w dry basis). However, the hexane extraction time was 6 hours, while SC-CO2extraction was carried out only for 3 hours.

[0114] Fractionation of crude extracts was performed for all the samples obtained via the SC-CO2and hexane extractions to quantify waxes and observe the potential effects of temperature and pressure on the wax yield. As shown in Figure 4, wax yields (0.2-0.3% w / w in dry bran) did not significantly differ from each other under the applied SC-CO2conditions (p > 0.05). However, the conventional hexane extraction led to a higher wax yield of 0.9% (w / w). SC-CO2 and hexane extractions differ from each other in many aspects, including their chemistry, density, diffusivity, etc. SC-CO2 has a limited affinity for slightly polar solutes, which might explain the lower wax yield of SC-CO2 as opposed to hexane. Sorghum wax mainly consists of long-chain alcohols (32-34%), fatty aldehydes (21-32%), and wax esters (4- 13%). Hexane can recover glycolipids and phospholipids to a certain extent, while SC-CO2 cannot.

[0115] Differential Scanning Calorimetry (“DSC”) Analysis to Characterize Thermal Behavior of the Wax Fractions.

[0116] Melting points were measured for each of the obtained extracts using a differential scanning calorimeter. During the DSC analysis, each sample underwent a linear temperature program, and the heat flow rate into the sample was continuously monitored. In an aluminum pan, ∼3 mg sample was weighed was each extract. The sample was then heated from 20°C to 105°C at 10°C / min, held at 105°C for 1 minute, and cooled to -10°C at 10°C / min and held for 1 minute; then the sample was heated to 105°C for a second time at a rate of 10°C / min.

[0117] The DSC curves of purified waxes from the SC-CO2 and hexane extractions are shown in Figure 6. The reported DSC thermograms are of the second heating cycle. The waxCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 fractions obtained using SC-CO2showed broad melting peaks at 52°C and 57°C, whereas hexane-extracted wax fractions had two major melting peaks at 45°C and 87°C. Sorghum wax has been previously reported to have relatively high melting points, up to 84.9°C, which is comparable with the melting point of the commercial carnauba wax. The high melting point behavior of sorghum wax is attributed to its paraffin, alcohol, and aldehyde fractions, where sorghum waxes were extracted using hexane or petroleum ether. Lower melting points observed for sorghum wax have been attributed to higher concentrations of free fatty acids, mono-, di-, and triacylglycerol in SC-CO2-extracted lipids compared to extracts obtained using hexane. Even though the signal was quite weak in the present tests, Figure 6 shows a peak-like formation at 86°C on the DSC curve of the SC-CO2-extracted wax. This might have resulted from the relatively low fatty alcohol content of the SC-CO2-extracted waxes.

[0118] Analysis for Fatty Acid Composition of the Crude Lipids.

[0119] The fatty acid composition was determined using an Agilent® 6890N Network Gas Chromatograph system equipped with a 5973 inert mass selective detector and 7683 series Agilent® autosampler. The fatty acid profiles of crude lipids extracted by SC-CO2 and by hexane are given in Table 1.

[0120] Table 1. Fatty Acid Composition of Sorghum Bran Lipids Extracted by SC-CO2 and Hexane* c nt

[0121] The solvent type slightly altered the fatty acid composition, where oleic (C18:1) and linoleic (C18:2) acids constituted approximately 75% of the fatty acids present in the SC-CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 CO2and hexane extracts. The lipids extracted by SC-CO2contained oleic and linoleic acids of 51.4 and 23.1%, respectively. Extracts obtained using hexane had a lower rate of oleic acid (46.6%) but a higher rate of linoleic acid (29.8%). Furthermore, the palmitic acid (C16:0) ratio was higher in the lipids extracted by SC-CO2compared to hexane, which could be due to the higher solubility of short-chain saturated fatty acids in SC-CO2. For example, palmitic acid (23.0 * 10-3 kg / kg CO2) is known to have a higher solubility than stearic acid (4.1 * 10-3 kg / kg CO2) in SC-CO2 at the same conditions (27.4 MPa and ~45°C). Similarly, the solubility of oleic acid is known to be higher than linoleic acid in SC-CO2. These solubilities could have contributed to the higher percentages of palmitic and oleic acids in the lipids extracted via SC- CO2. On the other hand, stearic acid (C18:0) content in the extracts did not change significantly with the different extraction methods.

[0122] Analysis for Phytosterols and Policosanol Content.

[0123] Phytosterols and policosanols were also determined using the Agilent® 6890N network Gas Chromatograph system described above. Briefly, an internal standard of 50 μL of 5α-cholestane (2.5 mg / mL) was mixed with a 0.1 g sample. The mixture was saponified with 4 mL of 1 N potassium hydroxide in methanol at 40°C for 1 hour, and then kept at room temperature (23°C) for 18 hours. Next, 2 mL of deionized water was added. Subsequently, methyl tert-butyl ether / hexane (50:50, v / v) was added to extract the unsaponifiable fraction. The upper layer was collected and dried under nitrogen at room temperature (23°C). The dried samples were dissolved in 0.3 mL of pyridine and silylated with 1 mL of BSTFA at 50°C for 30 minutes. Finally, the silylated samples (1 μL) were eluted in a DB-17HT capillary column (30 m × 0.25 mm I.D., 0.15 μm film thicknesses). Helium was used as the carrier gas with a constant flow rate of 0.5 mL / min. The inlet and mass spectroscopy interface temperatures were set to 270°C and 300°C, respectively. The initial oven temperature was set to 100°C, held forCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 5 minutes, then raised to 250°C at 25°C / min, held for 1 minute, then increased to 290°C at a ramping rate of 3°C / min, and kept at 290°C for 40 minutes. The collected data were analyzed with ChemStation software (G1701DA version D.00.00), and compounds were identified based on the NIST (v.02) library, NIST Chemistry Webbook, and published data in the literature. Policosanol quantification was performed using a relative response factor, which was determined by comparing the area and concentration of the 1-octacosanol standard to the area and concentration of the 5α-cholestane internal standard.

[0124] The phytosterol and policosanol contents of the SC-CO2-extracted and hexane- extracted sorghum bran lipids are given in Table 2. Table 2. Phytosterol and Policosanol Composition of Sorghum Bran Wax Extracted by CO2and Hexane*

[0125] Total phytosterols extracted by SC-CO2was 26.5 ±0.5 mg / g crude lipid, in which β-sitosterol (61%, w / w) was the major compound, followed by campesterol (23%, w / w) and stigmasterol (16%, w / w). On the other hand, hexane exaction resulted in 21.8 ± 0.6 mg of total phytosterols per gram of crude lipid, which was significantly lower than the one obtained via SC-CO2(p < 0.05). The phytosterol composition of hexane-extracted lipids was similar to that of the SC-CO2.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0126] Total policosanols extracted by SC-CO2and hexane were 25.1 ± 0.5 and 45.7 ± 0.5 mg / g crude lipid, respectively. Policosanols encompass up to 46% (w / w) of the sorghum wax, with octacosanol (C28) and triacontanol (C30) being the major components. As shown in Table 2, octacosanol was the dominant policosanol in both extraction methods, though hexane almost doubled SC-CO2in octacosanol recovery. Moreover, the triacontanol content of the hexane-extracted crude lipid was significantly higher than that of SC-CO2(p < 0.05). However, there was no statistical difference between the two methods in tetracosanol (C24) and hexacosanol (C26) contents (p > 0.05). Lower recovery of the long-chain policosanols (octacosanol and triacontanol) could be explained by the fact that the solvating power of SC- CO2 diminishes with increasing molecular weights for homologous series.

[0127] Analysis of Total Phenolic Content (“TPC”) and Total Flavonoid Content (“TFC”).

[0128] TPC determination was performed by diluting the collected extract to 1:10 (v / v) with deionized water, where an aliquot of 100 μL was placed in a 10 mL glass test tube. Then, a 500 μL of 0.2 N Folin-Ciocâlteu reagent was added to the sample. Lastly, a 400 μL of 0.7 M sodium carbonate solution was added, and the mixture was incubated for 2 hours in a dark environment at room temperature (23°C). The absorbance was measured by a spectrophotometer at 760 nm. The TPC was calculated based on a gallic acid standard curve prepared prior to the experiments at the concentrations of 12.5-200 ppm (R2= 0.99). Deionized water was used as a blank. The results were presented as mg GAE per 100 g dry sample.

[0129] TFC was measured by an aluminum chloride colorimetric method where the extract was diluted to 1:10 (v / v) with deionized water, and an aliquot of 1 mL was placed in a 10 mL glass test tube containing 4 mL of deionized water. The test tube was added with 0.3 mL of 5% NaNO2, incubated for 5 minutes, and 0.3 mL of 10% AlCl3was then added to theCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 solution and rested for another 1 minutes. Then, 2 mL of 1 M NaOH was added to the solution, and the volume was adjusted to 10 mL with deionized water. Lastly, the absorbance was measured by the spectrophotometer described above at 510 nm. The TFC was calculated based on a catechin standard curve prepared prior to the experiments at concentrations of 10-100 ppm (R2= 0.99). Deionized water was used a blank, and results were presented as CAE per 100 g dry sample.

[0130] Repetitive aqueous methanolic extraction from the sorghum bran in 1:45 (w / v) solute-to-solvent ratio resulted in a TPC of 3,064 ± 185 mg GAE / 100 g dry bran. Also, the TFC of the extracts obtained with the same method and solute-to-solvent ratio was 2,044 ± 28 mg CAE / 100 g dry bran. However, aqueous methanol extraction at the same solute-to-solvent ratio as in the cosolvent-modified SC-CO2 (≈1:4.5) resulted in considerably lower TPC and TFC yields as 290 ± 19 mg GAE / 100 g dry bran and 197 ± 13 mg CAE / 100 g dry bran, respectively.

[0131] Figure 7 presents the total phenolics (GAE) and flavonoids (CAE) extracted by ethanol- and ethanol-water-modified SC-CO2 at various temperatures and pressures. Total phenolic yields with different capital letters and total flavonoid yields with different lowercase letters are significantly different (p < 0.05). The highest TPC and TFC yields were achieved at 40 MPa and 40^C using 15% (w / w) ethanol-water-modified SC-CO2 as 150 ± 3 mg GAE / 100 g dry bran and 99 ± 4 mg CAE / 100 g dry bran, respectively. The lower yield with ethanol- water-modified SC-CO2 could be due to lower 3-deoxyanthocyanin recovery, a subgroup of flavonoids. TPC and TFC yields obtained using ethanol-water-modified SC-CO2 were 49 ± 4 mg GAE / 100 g dry bran and 29 ± 1 mg CAE / 100 g dry bran, respectively, at 30 MPa and 60°C.

[0132] Ethanol-water-modified SC-CO2surpassed ethanol-modified SC-CO2under all conditions in total phenolic and flavonoid yields. The lowest yields obtained with ethanol- water-modified SC-CO2were still significantly higher than the highest yields achieved byCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 ethanol-modified SC-CO2, implying that 50% (v / v) ethanol-water mixture was more effective than pure ethanol as a cosolvent to extract phenolic compounds. This could be explained by the higher polarity of water against ethanol. Water might have also caused swellings on the solute material, which improved the diffusivity of the solvents. However, water does not have good solubility in SC-CO2, limiting the mass transfer properties. Therefore, a further increase in the ratio of water in ethanol above 50% did not provide higher TPC and TFC yields (data not shown).

[0133] The extraction temperature of 40°C resulted in higher TPC and TFC than 60°C under both pressures (30 and 40 MPa) when ethanol-water was used as the cosolvent, as shown in Figure 7. In other words, increasing the extraction temperature reduced both TPC and TFC significantly (p < 0.05). Extraction pressure displayed a significant effect only for TPC at 40°C, where the TPC was higher at 40 MPa than at 30 MPa (p < 0.05). In the case of pure ethanol as the cosolvent, 30 MPa and 60°C resulted in the highest yields for both TPC and TFC (p < 0.05) (see Figure 7). For the TPC yield, the only significant difference was observed at 60°C with ethanol as the cosolvent, where increasing the pressure from 30 MPa to 40 MPa reduced the yield by approximately half. However, increasing the pressure at 40°C did not significantly affect the TPC and TFC yields (p > 0.05). Furthermore, TPC and TFC yields suggest an interaction effect between temperature and pressure as the solvating power of the solvent mixture depends on temperature and pressure. At constant pressures, having the highest TPC and TFC yield achieved at lower temperatures might be due to the lower solvent density of the solvation complex at higher temperatures.

[0134] Phenolic Compounds Analysis.

[0135] Phenolic acids were determined using a UFLC Shimadzu® (SPD-20AV UV / Vis detector) to analyze the samples, where the samples (10 µL injection volume) wereCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 separated using a Waters® Symmetry C18 column (5 µm, 4.6 x 250 mm) at 28°C with a flow rate of 0.65 mL / min. The mobile phase consisted of 1% formic acid in water (Solvent A) and acetonitrile (Solvent B). Starting with 5% Solvent B, the 80-minute elution procedure was as follows: 5 minutes, 5-8% Solvent B; 30 minutes, 8-21% Solvent B; 19 minutes, 21-35% Solvent B; 9 minutes, 35-60% Solvent B; 4 minutes, 60-100% Solvent B; 5 minutes, 100% Solvent B; 0.1 minutes, 100-5% Solvent B; and 7.9 minutes, 5% Solvent B. The compounds were detected at 280 nm and identified using authentic standards.

[0136] Determination of 3-deoxyanthocyanins was performed at 520 nm. The mobile phases were 5% formic acid in water (Solvent C) and methanol (Solvent D). The elution program was as follows: 5% Solvent D, 0-2 minutes; 5-20% Solvent D, 2-10 minutes; 20% Solvent D, 10-15 minutes; 20-30% Solvent D, 15-30 minutes; 30% Solvent D, 30-35 minutes, 30-45% Solvent D, 35-50 minutes; 45% Solvent D, 50-55 minutes; 45-5% Solvent D, 55-65 minutes; and 5% Solvent D, 65-68 minutes. The flow rate was 1 mL / min. The compounds were identified based on authentic standards and published data. The percentages were calculated according to Equation 3:

[0137] Percentage of the compound (%) = [Area under the curve of a specific compound] / [Sum of the areas under the curves of all identified compounds] x 100 (Equation 3).

[0138] The compositions of phenolic acids along with apigenin and taxifolin in the extracts obtained using methanol, ethanol-modified SC-CO2, and ethanol-water-modified SC- CO2are shown in Figure 8. Bars that do not share the same letter are significantly different (p < 0.05). In the methanol extraction, ferulic acid dominated the composition with 43.0%, followed by taxifolin, apigenin, and coumaric acid with 34.3%, 10.3%, and 8.9%, respectively. The composition changed drastically in both modified SC-CO2extractions. Although ferulicCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 acid was still the primary compound by 41.5% in the ethanol-modified SC-CO2extraction, coumaric acid contribution increased to 37.8%. On the other hand, coumaric acid became the most prominent component slightly (37.7%) over ferulic acid (34.6%) in the ethanol-water- modified SC-CO2extraction. It is also noteworthy that caffeic acid content was higher in the extracts obtained with ethanol-modified SC-CO2(5.6%) and ethanol-water-modified SC-CO2(5.9%) compared to methanol (1.6%; p < 0.05). Moreover, the highest concentration of cinnamic acid was achieved with the ethanol-water-modified SC-CO2 extraction by 3.4%, whereas no cinnamic acid was detected when ethanol was used as the cosolvent. Apigenin concentration was significantly lower in the ethanol-water-modified SC-CO2 extracts (1.1%) compared to the ethanol-modified SC-CO2 ones (11.0%). Taxifolin compositions were 34.3%, 20.1%, and 4.3% for methanol, and ethanol-water- modified SC-CO2, and ethanol-modified SC-CO2 extractions, respectively. Taxifolin, also known as dihidroquercetin, is one of the significant flavonols found in sorghum.

[0139] Figure 9 demonstrates 3-deoxyanthocyanin profiles in the extracts, which were obtained by different extraction methods. Bars that do not share the same letter are significantly different (p < 0.05). In methanolic extraction, luteolinidin (49.7%) was the major compound over apigeninidin (41.5%) and 7-metoxyapigeninidin (3.8%). A few minor peaks were unknown, which contributed to 4.8% of the total composition. Different 3-deoxyanthocyanin profiles were observed from ethanol-modified and ethanol-water-modified SC-CO2 extractions. For instance, apigeninidin became the dominant compound in the ethanol-water- (49.4%) and ethanol- (64.2%) modified SC-CO2extractions. Figure 9 also shows that 7- methoxyapigeninidin contribution was raised by increasing ethanol composition, while the unknown compounds almost disappeared (<1%).CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0140] Summary of Results for Example I.

[0141] In summary, wax and phenolic compounds were successfully extracted from black sorghum bran by the inventive SC-CO2process. The highest crude lipid yield of 6.2% (w / w dry basis), which contained ~5% (w / w) high-melting point waxes, was achieved at 40 MPa and 60°C using neat SC-CO2. This yield was slightly lower than the crude lipid yield for conventional hexane extraction (7.5%, w / w dry basis). Fatty acids, policosanols, and phytosterols were successfully recovered by neat SC-CO2. The purified wax fractions containing phytosterols showed high melting points of 57-87°C. For TPC and TFC, yields were greatly affected by temperature, pressure, and cosolvent type during the modified SC-CO2 extractions. The ethanol-water mixture performed better than pure ethanol as a cosolvent for total phenolic and flavonoid extractions. The TPC and TFC yields were maximized at the low temperature (40°C) and high pressure (40 MPa) using 15% ethanol-water (1:1, v / v) modified SC-CO2. At the optimized condition, the major phenolic acid and 3-deoxyanthocyanin were trans-coumaric acid and apigeninidin, respectively. EXAMPLE II

[0142] The study in this Example II aimed to develop a new fractionation method to selectively extract triacylglycerols from a corn / sorghum (3:2, w / w) bioethanol side-stream slurry to purify waxes via SC-CO2. The specific objectives were to (i) optimize the SC-CO2 extraction conditions utilizing response surface methodology for the highest oil yield with minimum wax content, and (ii) characterize the oil- and wax-rich fractions for their composition and melting point.

[0143] Materials.

[0144] Corn / sorghum-based post-fermentation lipid slurry was obtained, where a corn / sorghum ratio of 60 / 40 (w / w) was used as a feed to the fermenter. The slurry was used inCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 the experiments as-is without further processing. The following analytical grade chemicals were separately obtained for this study: liquid CO2(99.99% purity) and N2(99.9% purity), phytosterols, 1-octacosanol, pyridine, BSTFA, mono-, di-, triacylglycerols, alkanes, oleic, linoleic, and palmitic acid.

[0145] Oil-Rich and Wax-Rich Extractions Using Pure SC-CO2.

[0146] A lab-scale SC-CO2extractor (SFT-120) as depicted in Figure 1 was used for lipid fractionation. The SC-CO2 extractor was equipped with a pneumatically driven piston pump (maximum pressure of ~69 MPa and maximum flow rate of 100 mL / min liquid CO2) to compress liquid CO2 from the cylinder pressure, where a compressor was used to provide compressed air to the air piston. The slurry (10 g) was wrapped in two cellulose filter papers (Whatman® #42 filter paper) and placed at the bottom of a 100 mL stainless-steel high-pressure vessel. Additional filter papers were placed on the top and bottom of the vessel. The system was then flushed with CO2 to remove any air from the vessel. The temperature of the needle and micrometering valves was set to 80°C to avoid freezing due to the Joule-Thompson effect during the continuous CO2 flow. Once the vessel temperature reached the set temperature, the system was pressurized using a high-pressure pump. The static extraction (20 minutes) was applied prior to each run. The flow rate for dynamic extractions was constant at 2 L / min (measured at ambient conditions). The extracts and remaining samples in the vessel were weighed gravimetrically and kept at -60°C until further characterization. The crude oil yield was calculated using Equation 4:

[0147] Crude oil yield (%) = [weight of crude extract (g) / weight of slurry used for extraction (g)] x 100 (Equation 4).

[0148] Preliminary experiments were conducted with temperatures of 30-80°C, pressures of 10-40 MPa, flow rates of 1-4 L / min (measured at ambient conditions), and timesCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 of 1-5 hours. A three-level response surface (Box-Behnken) design was created using JMP® Pro to further optimize the process and provide a predictive equation for triacylglycerols extraction from corn / sorghum slurry based on temperature (35-75°C), pressure (8-40 MPa), and time (2-6 hours). Table 3 describes this Box-Behnken design for the SC-CO2extraction. Table 3. Variable Level

[0149] The design involved replicated 12 experimental runs and 6 center points (total 30). As soon as the 30 runs were performed, the data was analyzed. Next, the design was augmented with 8 additional runs to enhance the predictability of the model, where augmented runs were determined by JMP® software. Therefore, the final design was composed of a total of 38 runs. The responses were crude oil (%) and wax (%) yields. To normalize the data, square root transformation was applied to the responses. The collected data were fitted to the following quadratic Equation 5:

[0150] √Y ൌ ^^^+∑ଷ ^ୀ^ ^^^^^^ ^ ∑ଷଶଷ ଷ ^ୀ^ ^^^^^^^ ^ ∑^ୀ^ ∑^ୀ^ା^^^^^^^^^^^(Equation 5),

[0151] ^^^is the linear coefficient, ^^^and ^^^represent independent variables, ^^^^is the quadratic coefficient, and ^^^^is theof interaction.

[0152] Analysis to Determine Wax Yield.

[0153] The total wax content in the extracts was determined by fully dissolving the extracts in ethanol (10 mg / mL) through sonicating for 5 minutes and subsequently heating in a water bath at 91°C. The solutions were then placed in a refrigerator at 4°C for 24 hours to precipitate the waxes. After 24 hours, the solution was vacuum filtered using a Whatman®CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 filter paper #4 (pore size: 20-25 µm). Upon filtration, the filter paper was folded to place in a 40 mL vial, and 20 mL of chloroform was added. The vial was sonicated for 2 minutes and heated in a water bath at 91°C for 30 seconds to dissolve all the material trapped on the filter paper. Lastly, the filter paper in the vial was taken out, the chloroform was evaporated under N2, and the residue was weighed. The wax yields were calculated according to Equation 6:

[0154] Wax yield (%) = [weight of sediment at 4°C (g) / weight of slurry used for extraction (g)] x 100 (Equation 6).

[0155] Model Fitting.

[0156] The results of the augmented Box-Behnken design are shown in Table 4, where SC-CO2 conditions were optimized using two responses, namely, crude oil yield and wax yield.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 Table 4. Experimental variables (temperature, pressure, time) and responses (crude oil and wax yields). R T t P Ti C d Oil Yi ld W Yi ld

[0157] As both responses were subjected to the response surface analysis, determination coefficients (R2) were 0.98 and 0.94 for crude oil and wax yields, respectively. Nonetheless, both responses had a significant lack of fits (p < 0.05). In order to remediate the lack of fits, runs 1, 11, and 17 were reduced, and both the crude oil and wax yields data were normalized by square root transformation. As a result, the predictive power of the model was enhanced, such that the R2of crude oil yield raised to 0.99 with a nonsignificant lack of fit (p = 0.0945), as shown in Table 5. Similarly, R2of wax yield increased to 0.96 with aCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 nonsignificant lack of fit (p = 0.0822), suggesting a stronger fit. Moreover, root mean square errors of the transformed data were calculated as 0.216 and 0.135 for crude oil and wax yields, respectively. The optimum conditions for the maximum crude oil yield and minimum wax yield were determined as 35°C, 40 MPa, and 4.1 hours. The model predicted the responses at the optimized conditions as 46.9 ±4.5% (w / w) and 1.2 ±0.4% (w / w) for crude oil and wax yields, respectively. The run at the optimized conditions (35°C, 40 MPa, and 4.1 hours) resulted in 47.5 ±1.4% crude oil and 1.0 ±0.2% wax, which were not significantly different from the predicted values (p > 0.05), validating the model. Table 5. ANOVA and lack of fit tests of the models for the optimization of crude oil and wax yields. 2

[0158] The coefficients of the independent variables of the responses are presented in Table 6. The only nonsignificant effect to predict the crude oil yield was the temperature*time interaction, which was reduced from Equation 7 (p > 0.05). Similarly, temperature*temperature and time*time interactions were not significant for wax yield; therefore, they were reduced from Equation 8 (p > 0.05).CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0159] √Y1= 2.3854 - 0.1552x1+ 0.1741x2+ 1.0518x3+ 0.0007x12- 0.0043x22- 0.1129x32+ 0.0028x1x2+ 0.0155x2x3(Equation 7), and

[0160] √Y2= 0.7399 - 0.0227x1+ 0.0235x2- 0.1218x3- 0.0008x22+ 0.0007x1x2+ 0.0032x1x3+ 0.0036x2x3(Equation 8),

[0161] where x1is temperature (°C), x2is pressure (MPa), x3is time (h), and Y1and Y2are crude oil yield (%) and wax yield (%), respectively. The coefficient values in Equation 7 and Equation 8 were obtained after the elimination of the nonsignificant terms in Table 6. Table 6. The regression coefficients of the models for the optimization of crude oil and wax yields. re

[0162] Optimization of the SC-CO2 Extraction Conditions.

[0163] Figure 10 depicts surface plots demonstrating the effects of temperature, pressure, and time on crude oil and wax yields obtained via SC-CO2 extractions are depicted. Surface Plot 9A depicts crude oil yield in view of pressure-temperature (at 4 hours), Plot 9B depicts crude oil yield in view of time-temperature (at 24 MPa), Plot 9C depicts crude oil yield in view of time-pressure (at 55°C), Plot 9D depicts wax oil yield in view of pressure- temperature (at 4 hours), Plot 9E depicts wax oil yield in view of time-temperature (at 24 MPa), and Plot 9F depicts wax oil yield in view of time-pressure (at 55°C).CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0164] At first glance, the similarity between Plots 9A and 9D stood out, suggesting that the interaction between temperature and pressure led to similar trends in the yields of crude oil and wax. At low pressures (<20 MPa), the yields were at the lowest, and temperature showed almost no effect. For instance, at low pressures (i.e., 35°C, 8 MPa, 4 hours) (Run 3), crude oil and wax yields were among the lowest, and increasing the temperature to 75°C at 8 MPa and 4 hours (Run 6) demonstrated a decreasing impact on both responses. At low pressures (i.e., 8 MPa) around the critical region (7.3 MPa), it would be expected to observe a reduction in the extractive performance of SC-CO2 as the pressure is expected to be below the crossover pressure. Increasing the temperature lowers the solvent density while increasing the vapor pressure of the solute, but the overall solvating power is reduced as the reduced solvent density is more dominant compared to the increased vapor pressure of the solute. Nonetheless, at pressures above 20 MPa, temperature possessed a huge impact on both crude oil and wax yields (see Plots 9A and 9D). As shown in Table 4 (Run 7 and 8), raising the temperature from 35°C to 75°C at 40 MPa for 4 hours almost doubled the crude oil yield and tripled the wax yield. This was due to the extraction pressure (40 MPa) being above the crossover pressure as the temperature was increased, where the increase in the vapor pressure of the solute was more effective than the reduction in the solvent density, resulting in an increased solvating power of SC-CO2. Coherently, the maximum crude oil and wax extraction yields were observed at 75°C, 40 MPa, and 6 hours as 92% and 5.7%, respectively (Run 18). The testing in Example I illustrated the positive impact of high pressures (>20 MPa) on lipids and, specifically, wax extractions from various raw materials. Therefore, the statistical model suggested operating at the lowest temperature (35°C) in the predetermined range while keeping the pressure at the uppermost bound (40 MPa) to minimize wax yield, since raising the temperature favored the wax extraction considerably. The impact of time alsoCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 depended on temperature and pressure. Plot 9B showed an increase in the crude oil yield with prolonged treatments, irrespective of temperature, as expected. Nevertheless, the time*temperature interaction presented a different story on the wax (Plot 9E). The wax yield peaked at a high temperature (75°C) and long extraction time (6 hours) with 3.0 ±0.6%, which was amongst the highest wax yields achieved throughout the experimental design (Run 5). Thus, the time*temperature interaction provided additional evidence to avoid high temperatures (i.e., 75°C) and prolonged processing (i.e., 6 hours) to minimize wax extraction. Surface Plots 9C and 9F were also strikingly similar in shape. An increase in the pressure (8- 40 MPa) raised both crude oil and wax yields regardless of time. For instance, the crude oil yields at 8 MPa, 2 hours, 55°C (Run 9) and 40 MPa, 2 hours, 55°C (Run 10) were 0.2 ±0.0% and 29.8 ±0%, respectively, which show the tremendous impact of pressure in maximizing the crude oil yield. Moreover, 8 MPa, 6 hours, 55°C and 40 MPa, 6 hours, 55°C resulted in 0.4 ±0.1% and 65.5 ±1.3% crude oil yields, respectively. In addition, the wax amount also increased from 0.1 ±0.0 to 2.8 ±0.2% (Run 11 and 12) at 40 MPa, 6 hours, and 55°C though pressure seems to favor crude oil yield over wax. Therefore, the model suggested the optimized conditions as low temperature (35 MPa) to minimize wax yield, high pressure (40 MPa) to maximize crude oil yield, and average time (4.1 hours) to balance the increasing effect of long time on the wax extraction. The model predicts 46.9 ±3.2% and 1.2 ±0.6% of crude oil and wax yields at the optimized conditions, respectively. The runs at the optimum conditions resulted in 47.5 ±1.4% crude oil and 1.0 ±0.2% wax yields, validating the developed model.

[0165] Differential Scanning Calorimetry (“DSC”) Analysis.

[0166] DSC analysis was performed to measure the melting points of the extracts / fractions. The samples (∼5 mg) were placed in an aluminum pan, heated from 20°C to 105°C at a rate of 10°C / min, held for 1 minute at 105°C, cooled to -10°C at 10°C / min, andCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 held 1 minute at -10°C. The cycle was repeated for a second time, and the thermograms obtained at the second heating cycle were reported.

[0167] Figure 11 depicts the untreated lipid slurry, crude oil fraction, and the wax-rich fraction that remained in the vessel after the SC-CO2extraction at the optimized conditions (35°C, 40 MPa, and 4.1 hours). The untreated corn / sorghum-based post-fermentation lipid slurry was liquid at room temperature (23°C) and mostly homogenous (see Figure 11A). Corn / sorghum-based post-fermentation lipid slurry is a potent source of carotenoids, which explains the yellow-orange color of the material in Figure 11A. The crude oil fraction obtained after the SC-CO2 extraction at the optimum conditions (35°C, 40 MPa, and 4.1 hours) was clear liquid at room temperature (23°C) (see Figure 11B). On the other hand, the wax-rich fraction (i.e., spent lipid slurry) that remained in the vessel after SC-CO2 extraction showed a paste- like, creamy texture (Figure 11C) due to the increase in the concentration of waxes. The untreated lipid slurry contained 5.1 ±0.6% (w / w) wax content, while the wax-rich fractions contained 11.1 ±1.2% (w / w) wax.

[0168] Figure 12 depicts DSC thermograms of the oil fraction and the wax-rich fraction obtained after SC-CO2 extraction at 35°C, 40 MPa, and 4.1 hours. The melting point of the extracted crude oil via SC-CO2 was measured at 17°C. No clear peaks were observed after 17°C, suggesting the high-melting-point waxy compounds were left in the vessel unextracted. Nevertheless, the thermogram of the wax-rich fraction showed multiple melting peaks, indicating a complex matrix. For instance, there was a clear peak at 60°C with two peak-like shoulders at 50°C and 70°C, suggesting multiple compounds contributed to the melting point thermogram. In fact, it is rare to observe defined peaks for natural waxes due to their complex composition of esters, policosanols, and hydrocarbons. Sorghum and corn waxes are composed of fatty alcohols (i.e., octacosanol, triacontanol), aldehydes (i.e., octacosanol, triacontanol),CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 hydrocarbons (i.e., heptacosane, nonacosane) and wax esters in various lengths of carbon chains providing waxes with their unique thermal behaviors. For instance, octacosanol and nonacosane have meting points of 83°C and 63°C, respectively, which might explain the high- temperature peaks (>50°C) in crude slurry and wax-rich fractions in Figure 12. The melting temperatures of such materials are highly affected by the carbon chain length, degree of saturation, and the orientation of the ester bond of the waxes. Therefore, the hilly thermogram between 17-60°C in Figure 12 either resulted from the shorter carbon chain moieties of the waxy compounds or a higher degree of unsaturation since decreasing chain length and increasing degree of unsaturation both lower the melting point. The creaminess of the wax-rich fraction could be explained by the peak at 17°C, indicating that the oil was not fully extracted from the slurry. Prolonged processing would increase the crude oil yield, though it would also convey more waxes.

[0169] Gas Chromatography / Flame Ionization Detector (“GC / FID”) Analysis for Composition of the Lipid Slurry, Crude Oil, and Wax-Rich Fractions.

[0170] GC / FID analysis was performed according using an Agilent® 6890N GC system equipped with an FID detector and a 7683 series Agilent® autosampler. The samples were dissolved in 0.3 mL of pyridine and silylated with 1 mL of BSTFA at 50°C for 30 minutes prior to the injection. Upon silylation, the samples were flushed with nitrogen at room temperature (23°C) until dryness, and 10 mg / mL solutions were prepared in hexane. The samples (1 μL) were injected onto an Agilent® J&W DB-5HT capillary column (30 m × 0.25 mm I.D., 0.1 μm film thickness) at split mode (1:20), with the inlet temperature of 330°C. The flow rate of the carrier gas (helium) was 1 mL / min. The initial oven temperature was set to 120°C and immediately ramped to 240°C at a rate of 15°C / min, then further ramped to 390°C at a rate of 7°C / min, and held for 6 minutes. Data were analyzed with ChemStation softwareCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 (G1701DA version D.00.00), and compounds were identified based on the authentic standards and literature data.

[0171] The GC analysis was conducted to analyze the composition of crude oil and wax-rich fractions obtained after the SC-CO2extraction at the optimized conditions (35°C, 40 MPa, and 4.11 hours). The chromatograms showed the presence of free fatty acids, waxy compounds, wax esters, diacylglycerols, and triacylglycerols. The major free fatty acid compositions were expressed as relative percentages, as shown in Table 7. Table 7. Free fatty acid compositions of the side-stream lipid slurry, crude oil fraction, and wax-rich fraction.* 2) ns (p

[0172] Based on the area under the peaks, the dominant free fatty acids in the oil fraction were linoleic acid, followed by oleic and palmitic acids, whereas in the wax-rich fraction, the ratio of palmitic acid was significantly higher than that of oleic acid, with linoleic acid remaining dominant. The significant change in the free fatty acid content can be explained by their solubilities in SC-CO2. The solubility of the fatty acids in SC-CO2was demonstrated as oleic, linolenic, and palmitic acid in decreasing order. Therefore, oleic acid became the second major free fatty acid in the crude oil fraction as it is dissolved better in SC-CO2. Moreover, triolein was detected amongst the major triacylglycerols present in the crude oil. Triacylglycerols appeared between the retention times of 30-34 min, where the peak at 33.21 min was identified as triolein. Furthermore, long-chain aldehydes, policosanols, and alkanesCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 that appeared in the wax-rich fraction (R.t. of 12-20 min) were notably higher in comparison to the crude oil fraction, as these compounds are waxy components. The compounds that appeared before the triacylglycerols were presumably diacylglycerols (R.t. of 24-25 min) and wax esters (R.t. of 25-30 min). Lipid-soluble phytochemicals such as phytosterols also fall in the same region. Small quantities of phytosterols were also observed. There were some compounds (R.t. of 34-37 min) eluted after triacylglycerols, which are strongly possible to be aldehyde dimers that are unique to sorghum-based bioethanol lipid slurries.

[0173] Summary of Results for Example II.

[0174] In summary, bioethanol side-stream was successfully fractionated into oils and waxes using pure SC-CO2, and the fractions were characterized with GC analysis.

[0175] Corn / sorghum-based post-fermentation lipid slurry was fractionated into crude oil and wax-rich fractions using pure SC-CO2. Additionally, the process was optimized using response surface methodology (augmented-Box-Behnken design), and quadratic equations were generated to predict future operations. Within the ranges tested, the optimized conditions for maximum crude oil yield (46.9%) and minimum wax co-extraction were determined as 35°C, 40 MPa, and 4.1 hours. Operating at the optimized SC-CO2 conditions led to the crude oil and wax yields of 47.5 ±1.4% (w / w) and 1.0 ±0.2% (w / w), respectively, which validated the developed model. It was shown that operating at lower temperatures (i.e., 35°C) was imperative to selectively extract oils (i.e., triacylglycerols and free fatty acids) from the lipid slurry. Low pressures (e.g., 8 MPa) minimized the crude oil and wax yields at any temperature investigated (i.e., 35-75°C), whereas high pressures (e.g., 40 MPa) maximized crude oil and wax yields at high temperatures (e.g., 75°C). Crude oil and wax fractions exhibited major melting points at 17°C and 60°C, respectively. The major compounds in the crude oil fraction were determined as triacylglycerols and free fatty acids, with linoleic acid being the mostCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 abundant constituent, while the wax-rich fraction contained triacylglycerols, long-chain aldehydes, policosanols, and alkanes. Notably, the wax-rich fractions remaining after extraction exhibited complex melting behavior with multiple peaks in their differential scanning calorimetry (DSC) thermograms. The solvating and selective power of SC-CO2is primarily dependent on temperature and pressure. Consequently, each experimental run produced waxes with varying compositions, giving rise to distinct thermal spectra. Overall, this study demonstrated a novel green approach to purify waxes from a bioethanol side-stream lipid slurry. EXAMPLE III

[0176] The following tests were aimed at leveraging advanced data analysis techniques for a process for extracting and purifying sorghum waxes from sorghum-based feedstock. More particularly, this Example III focused on using functional data analysis (FDA) to examine the differential scanning calorimetry (DSC) profiles of SC-CO2-fractionated waxes derived from corn / sorghum-based bioethanol side-stream, also known as lipid slurry (LS). Subsequently, a machine learning algorithm was employed to model the relationship between the processing variables and the extracted features. This combined approach aimed to establish a modern, data-driven framework for transforming bioethanol LS, a significant industrial waste stream, into valuable commercial waxes.

[0177] The rich information contained within an entire DSC thermogram, encompassing multiple peaks and variations, necessitates advanced data analysis techniques to fully capture the complex melting behavior observed in our wax fractions. FDA allows the analysis of the entire DSC thermogram as a single functional data, effectively extracting the maximum information from these complex thermal profiles for a more comprehensive understanding of the wax characteristics. The goal of Example III was to identify alternativeCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 waxes that could potentially replace commercial carnauba, candelilla, beeswax, and paraffin waxes. In addition, the melting features obtained through functional principal components analysis (FPCA) were used with the extreme gradient boosting, also known as XGBoost (XGB), ensemble learning method to predict wax melting profiles based on fractionation pressure (MPa), temperature (°C), and time (hours). The FPCA showed that carnauba wax substitutes were produced by subjecting the LS to 40 MPa and 75°C for 6 hours. Similarly, an alternative to beeswax was obtained using 40 MPa and 55°C for 6 hours. The XGB model was trained and tested for the first four functional principal component scores (FPCS1 to FPCS4) derived from a dataset containing 21 waxes’ DSC curves combined with synthetic data (10 synthetic data points with a noise level of 0.1). The XGB model demonstrated high coefficients of determination (R2): 0.9957 for FPCS1, 0.9944 for FPCS2, 0.9850 for FPCS3, and 0.9856 for FPCS4 in the testing data. Lastly, the final XGB-advised FPC model was validated through a series of four separate randomly generated runs. Thus, an efficient valorization of the side stream LS can be achieved by eco-friendly SC-CO2 along with advanced statistical and machine learning techniques, ultimately reducing time and energy consumption.

[0178] Materials.

[0179] The LS used in the experiments was derived from a post-fermentation process using a 60 / 40 (w / w) ratio of corn to sorghum as feed for the fermenter. The slurry was utilized in its original form. The liquid CO2 (99.99% purity) and N2 (99.9% purity) were purchased from Airgas, Inc. (Fayetteville, AR, USA). Beeswax, paraffin, and candelilla waxes were purchased from Sigma-Aldrich (St. Louis, MO, USA). Carnauba wax was obtained from Modernist Pantry (Eliot, ME, USA).

[0180] SC-CO2Treatment.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0181] The wax fractionation process was carried out in a manner consistent with Examples I and II. Briefly, a laboratory-scale SC-CO2extractor (Supercritical Fluid Technologies, Inc., Newark, DE, USA, SFT-120) was utilized for the extraction process. The extraction setup included a pneumatically driven piston pump with a maximum pressure of approximately 69 MPa and a maximum flow rate of 100 mL / min for compressing liquid CO2from the cylinder pressure. A compressor was used to send compressed air to the air piston. The LS (10 g) was enclosed within two cellulose filter papers (Whatman #42 filter paper) and positioned at the base of a 100 mL stainless-steel high-pressure vessel. Additional filter papers were situated at the top and bottom of the vessel. The system was purged with CO2 to eliminate any air from the vessel. The temperatures of the needle and micrometering valves were adjusted to 80°C to prevent freezing caused by the Joule-Thompson effect. After reaching the desired temperature, the system was pressurized using the high-pressure pump. The static extraction (20 minutes) was conducted before each run. The flow rate for dynamic extractions was kept constant at 2 L / min (measured under ambient conditions). The fractionated waxes were weighed and stored under nitrogen at 4°C for subsequent characterization.

[0182] Experimental Design.

[0183] Briefly, an augmented Box-Behnken design was established using JMP Pro 17 (Cary, NC, USA) to investigate the effects of temperature (35 - 75°C), pressure (8 - 40 MPa), and time (2 - 6 hours) (Table 8). The design consisted of 13 replicated experimental runs and 4 extra runs at the center points (6 center runs), totaling 30. Next, the design was improved with 8 additional runs to increase the predictability of the model. The augmented runs were determined by JMP software. Thus, the final design consisted of a total of 38 runs. The 4 validation runs were also randomly generated by the software.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 Table 8. Three-level augmented Box-Behnken response surface design for the SC-CO2 fractionation. R T t °C P MP Ti h

[0184] Differential Scanning Calorimetry (“DSC”) Analysis.

[0185] The wax extracts obtained via SC-CO2 and commercially available waxes, including carnauba, candelilla, paraffin, and beeswax, were analyzed using a differential scanning calorimeter (Model Diamond, Perkin-Elmer, Norwalk, CT, USA). Each sample (~20 mg) was placed in an aluminum pan and subjected to a heating cycle from 20°C to 105°C at a rate of 10°C / min. The sample was then held at 105°C for 1 min, cooled to -5°C at 10°C / min, and held at -5°C for 1 min. The cycle was repeated a second time, and the resulting thermograms from the second heating cycle were analyzed.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0186] Functional Data Analysis – Spectral Data Preprocessing.

[0187] The modeling procedure was carried out using Python 3.11.5 along with the scikit-learn libraries. Each thermogram, represented as a function of temperature, was first interpolated at a uniform grid size of 632 points. This step ensures that all curves have the same number of data points, facilitating subsequent analysis. Furthermore, each thermogram was centered and scaled using a standard scaler to ensure consistent scaling and dimensionality to mitigate potential biases due to varying curve lengths and baseline offsets:

[00188] ^^ ൌ ^௭ିఓ^ఙ (Equation 9)

[0189] the scaled data point, z is the centered data point, ^^ is the mean of the data, and ^^ is the standard deviation of the data.

[0190] Functional Data Analysis – Basis Expansion.

[00191] DSC samples are denoted by ^^ ൌ ^^^^,^^ଶ,^^ଷ, … ,^^^^^^ୀ^, where n is the number of samples. Each sample is composed of m temperature measurements and described by ^^ ^^ ൌ ൫^^^,^, ^^^,ଶ, ^^^,ଷ, … , ^^^,^൯ ∈ ^^ ௫^, j ൌ 1, 2, 3, … , m. The association between the jthas follows:

[00192] ^^^,^ ൌ ^^^^^^^^ ^ ^^^,^ (Equation 10)

[0193] where εi,jrepresents the noise, and tjis the jthtemperature. The P-spline basis functionto estimate X(t) and is formulated as follows:

[00194] ^^^^^^ ൌ ∑^ ^ୀ^ ^^^∅^^^^^(Equation 11)

[0195] where ∅ is basis functions, K represents the number of basis functions, Ck is the kthcoefficient (also known as the P-spline weights), which is estimated by minimizing the least criterion using the following cost function:

[00196] ^^^^^^^^^\^^^ ൌ ∑^^ ^^^^ െ ∑^^^ଶ^∅^^^^^^൧ (Equation 12)CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0197] The estimated function X(t) was smoothed using a roughness penalty. Another term (γ) called the smoothing parameter was added to further smoothen the function, regulating the roughness of derivatives, known as regularization:

[0198] ^^^^^^^^^^^^^^ ൌ ^^^^^^^^^\^^^ ^ ^^^^^^^^ଶ^^^^ (Equation 13)

[0199] ^^^^^^ ^^^^ ൌ ^^ ଶ ^ଶଶ ^ ^ ^^^^^^ ^^^^ (Equation 14)

[0200] where D2() is the second-order derivative of the function. The volatility of the function increases as the value of ^^^^^^ଶ^^^^ rises. In simpler terms, if the function has sharp turns or rapid changes in its slope, it is considered to have high volatility.

[0201] Functional Data Analysis – Functional Principal Components Analysis.

[0202] The FPCA method was employed to characterize each function using a finite set of eigenfunctions. The mean function is defined as follows:

[0203] ^ത^^ ^ ^^^^^ ൌ^∑^ୀ^ ^^^^^^^(Equation 15)

[0204] algorithm performs eigendecomposition to derive the principal components (also known as harmonics) as follows:

[0205] ^^^^^^, ^^^ ^^^^^^^^^^^^^ ൌ ^^^^^^^^^^ (Equation 16)

[0206] corresponding to the jtheigenfunction (orharmonic). The term ^^^^^, ^^^ is the covariance function, which quantifies the relationshipbetween two random variables, s and t, using the following formula:

[0207] ^^^^^, ^^^ ൌ ^^ି^∑^^ୀ^ ^^^^^^^^^^^^^^^^ (Equation 17)

[0208] Next, the score for the jthprincipal component is then computed as:

[0209] ^^^,^ ൌ ^ ^^^^^^^^^^^^^^^^^^^ (Equation 18)

[0210] where ^^^^^^^ represents the jthharmonic and meets the specified constraints:CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 ଶ

[0211] ^^^^^^^^^^൧^^^^ ൌ 1(Equation 19) ⋯0to recreate the initial estimationfunction, provided that a specific number of harmonics, referred to as "p" is selected:

[00213] ^^^^^^ ൌ ∑^ ^ୀ^ ^^^^^^^^^^ ^ ^ത^^^^^ (Equation 19)

[0214] (FPC1 to FPC4) were selected, capturing a cumulative explained variance ratio of 83.8%.

[0215] The proximity of the LS-derived waxes to the commercial waxes was assessed using the Euclidean distance metric on their functional principal component scores (FPCS). The data set consisted of 21 unique observations for each of the four main components (FPCS1 to FPCS4) together with the four commercial waxes. To enhance robustness, the mean values of the replicated runs (13) were taken as single observations for each principal component, along with the data from 8 non-replicated trials (hence, 21 LS-derived waxes). The Euclidean distances (d) between two samples (A and B) were computed as follows:

[00216] ^^^^^,^^^ ൌ^^^^^^^^^^1^ െ ^^^^^^^^1^^ଶ ^ ^^^^^^^^^2^ െ ^^^^^^^^2^^ଶ ^ ^^^^^^^^^3^ െ ^^^^^^^^3^^ଶ ^ ^^^^^^^^^4^ െ ^^^^^^^^4^^ଶ(Equation 20)

[0217] where A is any LS-derived wax and B is any commercial wax or visa-versa.

[0218] Functional Data Analysis – Machine Learning Algorithm.

[0219] After the FPCA, a machine learning algorithm was used to predict the FPCSs and thus to generate a predicted DSC curve for future applications. The dataset comprised 21 observations for each of the four principal components (FPCS1 to FPCS4), derived from the mean values of replicated experimental runs (13) combined with the nonreplicated augmented runs (8). Synthetic data were generated for each observation to enhance the robustness andCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 predictive performance of the model. Specifically, 10 synthetic data points (noise = 0.1) per observation were generated based on the normal distribution of the original data, resulting in an expanded dataset that provided a more comprehensive representation of the underlying data distribution. An XGBoost (XGB) model was employed to predict the target variables, with a separate model trained for each FPCS. The hyperparameters for the models were optimized by leveraging the Optuna framework, which enabled efficient hyperparameter tuning by employing a hybrid approach that involved Bayesian optimization and the pruning of less promising trials. The expanded dataset was divided into training and testing subsets, with 70% of the data used for model training and the remaining 30% for testing. The model’s performance was evaluated using the mean squared error (MSE) as the error function, which was minimized for each principal component during the training phase:

[0220] ^^^^^^ ൌ ^^ ^∑^ୀ^ ^^^^ െ ^^^^^ଶ(Equation 21)

[0221] Example III.

[0222] DSC Thermograms and Compositions of the LS and Commercial Waxes.

[0223] DSC thermograms of the LS and commercial waxes are depicted in Figure 13. The LS displayed multiple peaks, suggesting a complex structure. Upon initial examination, five distinct peaks were easily identified through visual observation: around 17-18°C, 28-29°C, 40-42°C, 50-51°C, and 57-58°C. In Examples I and II, the composition of the LS was detailed using a GC method. On the other hand, carnauba wax typically melts at temperatures between 82°C and 87°C (85.6°C in Figure 13). The composition mainly involves fatty acid esters (80– 85%), fatty alcohols (10–16%), acids (3–6%), and hydrocarbons (1–3%). Moreover, candelilla wax melted between 56.8-79°C, comprising mainly hydrocarbons (50%), alcohols and sterols (20–29%), free acids (7 – 9%), and triterpenoid esters (12 – 14%). Paraffin wax showed two distinct peaks (at 40.6°C and 59.3°C), unlike the other commercial waxes. In fact, the meltingCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 point of paraffin wax may vary between 50°C and 70°C due to its composition of solid crystalline hydrocarbons, mostly straight-chain alkanes. Finally, beeswax melted at 68.3°C. Beeswax is typically composed of linear monoester (35 – 45%), complex esters (15 – 27%), hydrocarbons (12 – 16%), and free fatty acids (12 – 14%), and it has a reported melting point within the range of 63°C to 70°C.

[0224] With a visual inspection, one could conclude that the LS has a similar melting behavior to paraffin wax, with two peaks at around 40°C and 57°C aligning. Nevertheless, the LS exhibited a wavy pattern as a result of its unrefined composition, unlike the industrially purified paraffin wax. It is important to note that the earliest peak in the LS spectra comes from its oil fraction that is liquid at room temperature (23°C). As the oils were fractionated from the LS, leaving behind the waxy fractions, the composition varied based on the processing conditions. This complexity renders visual observation inefficient.

[0225] Functional Data Analysis.

[0226] The primary step of functional data analysis entails transforming the empirical (raw) data into a functional form. As in the case of DSC, which was recorded as a sequence of discrete data, we needed techniques to retrieve the underlying function from the raw functional data through a variety of basis systems. Among the basis systems, the most relevant ones for chemometric data (i.e., GC, HPLC, DSC) were reported to be the Fourier and spline systems (i.e., P-splines), where Fourier is useful for periodic data, while spline is better for non-periodic data. In the context of DSC, P-splines were utilized to model the original data due to the non- periodic nature of the DSC curves (Figure 14A). In addition, it is crucial to scale the spectral data before applying spline expansion for several reasons. Spectral data can vary significantly in magnitude. Therefore, the normalization of data range in spectral analysis plays a crucial role in ensuring equal variable contribution to spline fitting, enhancing numerical stability,CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 improving the interpretability of spline coefficients, and ensuring consistent regularization (Figure 14B). These factors collectively lead to more accurate and interpretable results. Following the data scaling, second-order basis splines were fitted in 101 knots to approximate the actual DSC curves (Figure 14C). The representation of the data in a compact basis structure is depicted in Figure 14D. Typically, one would expect the spline curves to closely resemble the actual curves, ensuring that the features extracted from the splines accurately represent the real-world data, as observed in Figures 13B to 13D. Following the selection of spline fitting, the subsequent step entailed the application of FPCA to extract the fundamental spectral features capable of representing the main patterns of variation in a collection of functions.

[0227] Functional Principal Components Analysis (FPCA).

[0228] FPCA is a statistical method utilized to represent a set of functions through a series of coefficients (FPCS) associated with eigenfunctions. In contrast to multivariate PCA, FPCA produces principal components represented as curves rather than vectors. The first functional principal component (FPC) is designed to encapsulate the maximum variability among the functions while ensuring that all subsequent FPCs remain orthogonal to one another. The FPCSs, serving as numerical representations of the eigenfunctions, facilitate the creation of clustering and machine-learning algorithms capable of leveraging the predicted FPCSs to estimate a DSC curve. The entire modeling process is illustrated by the flow chart shown in Figure 15.

[0229] Consequently, the FPCA generated a mean function by averaging all DSC curves and then decomposed them into 10 FPC, collectively explaining 97.9% of the variance (Figure 16). Similar to multivariate PCA, the goal is to reduce dimensionality while retaining essential information, such as peaks, shoulders, valleys, and other curvatures in the DSC curves. Although there is no clear “elbow point” in Figure 16, capturing >80% of the varianceCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 is usually considered sufficient to represent the underlying structure of the data while reducing the dimensionality. Hence, the first 4 principal components together account for 83.8% of the total variance in the DSC patterns. Additionally, incorporating additional components (e.g., surpassing 4) would minimally enhance the explained variance. In fact, this comes at the expense of introducing superfluous complexity to the model, most likely constituting noise. Accordingly, the first four FPCs were employed to determine the nearest neighbors and build a predictive model, leveraging their combined variance to explain the underlying patterns.

[0230] Figures 17A and 17B depicts the mean function and the first four FPCs, respectively. The mean function represents the average behavior of all the DSC curves fed into the model. The mean function exhibited peaks at 18.3°C, 31.7°C, and 60.5°C. Moreover, a peak-like structure was discernible in the left wing of the largest peak (within the range from 40°C to 55°C), implying the existence of an undisclosed peak in that vicinity. Furthermore, a subtle swelling pattern was observable between 75°C and 90°C, which was not easily distinguishable. The first FPC explained 37.8% of the variation, and in total, the first two FPCs contributed to more than 60% of the variation in the spectra. The practical advantage of FPCA lies in its potential to manipulate the DSC patterns fed to the model by adding or subtracting specific numbers and combinations of the FPC into the mean function. The term “specific number” of a FPC refers to what was previously denoted as FPCS. Figure 18 was generated to illustrate the mechanism behind curve estimation through the mean and FPCs. A hypothetical curve with FPCS as 1 and the rest of the FPCSs as zero would simply be generated by adding the mean function and one FPC1 together. As demonstrated in Figure 18, the addition of one FPC1 would shift the first peak from 18.3°C to 18.4°C. Similarly, the second and third peaks have shifted from 31.7°C to 32.4°C and from 60.5°C to 61.5°C, respectively. Additionally, adding one FPC1 led to a decrease in the heights of the three peaks (about 0.20, 0.04, and 0.05CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 units in the first, second, and third, respectively). Moreover, the vague concave structure between 75°C and 90°C became more pronounced, as if another peak was vegetating in the region. As expected intuitively, subtracting the FPC1 resulted in modifications that were opposite to adding. Thus, the three peaks shifted towards zero on the x-axis while their heights increased upon the subtraction of FPC1.

[0231] Both clustering and classification play important roles in both traditional multivariate data analysis and functional data analysis. Even though no complex clustering or classification algorithm has been employed, traditional principal component score plots can effectively examine the proximity of the LS-derived waxes to the commercial waxes through a distance metric. Thus, the Euclidean distance metric was used to identify the closest neighbors to the beeswax, carnauba, candelilla, and paraffin wax samples within the dataset. In this context, the findings provide valuable insights into the extent to which LS-derived waxes can closely resemble their commercial counterparts, if any are detected. The 2D plot (Figure 19A) shows that the majority of the LS-derived waxes were clustered in the FPCS1 range of - 4 to 6 and the FPCS2 range of -2 to 3. At first glance, carnauba wax stood out as notably distinct from all the other samples, including the industrial ones, as expected. This was due to its significantly higher maximum peak temperature, rendering it an exceptionally valuable commodity in various industries. Based on the calculated proximity and visual observations in the score plots, it was evident that sample 18 (sample generated at 40 MPa, 75°C, 6 hours) was the only sample with the potential as an alternative to carnauba wax (d= 4.86). The carnauba wax is typically characterized by a major peak at 85.6°C and a quasi-peak at 61.2°C. Similarly, sample 18 displayed a major peak at 80.0°C and a quasi-peak at 63.3°C, confirming the model’s precision in classifying based on the most apparent features and capturing the complexities (Figures 20A and 20B). Consequently, within the specified range of processing levels, the bestCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 approach to approximate the melting behavior of carnauba wax is to process LS at high pressure (40 MPa) and temperature (75°C) for an extended period of time (6 hours).

[0232] Furthermore, beeswax and sample 12 (especially replicate 12a) showed a high degree of overlap. This was especially clear in the 3D score plot (Figure 19B), where the 2D score plot revealed how FPCS1 and FPCS2 tightly separate them. In addition, proximity analysis confirmed that sample 12 (40 MPa, 55°C, and 6 hours) appears to be the most promising alternative to beeswax (d =1.97), on average (Figures 20C and 20D). The major peak for beeswax was at 68.3°C, whereas for sample 12, the peak temperature averaged at 64.2°C (65.9°C in replicate 12a). Furthermore, the model also captured the complexities in the early stages (between 40°C and 60°C) of melting. Such that beeswax showed a protrusion at 54.4°C during the onset of the peak. The same behavior was also observed in sample 12, on average, at a temperature of 51.6°C.

[0233] On the other hand, deciding the closest neighbor for paraffin wax solely based on the score plots can be challenging, considering that paraffin wax is situated at the center of the cluster. The distance analysis suggested sample 2 as the closest neighbor to paraffin wax (d= 3.22). Nevertheless, sample 2 and paraffin wax did not show a convincing similarity, unlike what was observed with carnauba and beeswax (Figures 20E and 20F). This may be due to the gap between the paraffin wax and sample 2 in the FPCS4 (the score is approximately 3.5 times that of sample 2, as shown in Table 9), leading to two possible interpretations: first, the fractionation process may not have produced a pattern that closely resembles paraffin wax. Second, relying only on visual inspections of the principal components score charts could be misleading, especially in high-dimensional spaces, since these visualizations are limited to 3 dimensions. Lastly, the model detected no alternative to candelilla wax. This finding may be attributed to the fact that candelilla wax exhibits a singular peak at a specific location whereCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 the LS-derived waxes failed to demonstrate a comparable similarity. Moreover, the fact that candelilla wax exhibits the second-highest FPCS1 further validates this observation.

[0234] The full potential of the FPCA allows for the extraction of even more comprehensive information. For instance, the raw LS samples looked insulated from the cluster, and sample 17 was placed along with them. This implies that sample 17 is expected to exhibit melting behavior similar to that of the LS. This observation aligns with the fact that processing LS at 8 MPa and 75°C for 2 hours (sample 17) does not induce any alterations in the melting pattern, which is evident in Figures 20G and 20H. The provided information holds particular significance in refining future experimental designs as the ability to discern unpromising processing conditions eventually leads to considerable time and energy savings. Lastly, the 3D score plot indicated that sample 5b stood out as an outlier due to its distance from the cluster and its replicated run (5a), despite appearing to be within the cluster in the 2D score plot. Table 9. The first four FPCSs of the commercial waxes, their closest LS-derived neighbors, and the LS.* 5 9 0 al

[0235] Machine Learning (XGB) Model.

[0236] As previously discussed, the model consisted of two main parts: FDA-based FPCA dimension reduction to represent the DSC curves as scalars and the XGB model as theCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 predictive algorithm. XGB, an ensemble learning method, is a powerful gradient-boosting algorithm known for its efficiency in machine-learning tasks. It leverages regularization to prevent overfitting and parallel processing for speed, making it versatile for handling diverse data types. The algorithm’s wide range of characteristics, including its adaptability, accuracy, and capacity for handling large and varied datasets, bolster its effectiveness in predicting intricate and multifaceted issues. As a result, it is increasing in popularity for tackling challenges related to biomass management and environmental preservation.

[0237] The scatter plots in Figure 21 compare actual and predicted values for the FPCSs. The dashed line (y = x) indicates the point where the predicted and experimental values are equal. Thus, the accuracy of the prediction improves as the dots get closer to this line. Table 10 also reveals the fitting details, as well as the range and optimal hyperparameters for the XGB model. To illustrate, the final FPCS1 model used 1771 decision trees with a learning rate of 0.0230 for gradual model updates at each iteration. A subsample rate of 0.8778 was used to prevent overfitting, meaning approximately 87.7% of the data was randomly sampled for each tree. A maximum depth of 28 was chosen to control the complexity of the trees, while an elastic net regularization was employed with parameters of reg_alpha (L1) and reg_lambda (L2 regularization) set to 0.0840 and 7.0808, respectively. As a result, the final model displayed a training and testing R2of 0.9999 and 0.9957, indicating a strong fit to the experimental data and powerful predictive capability for unseen data. Similarly, testing R2values of 0.9944, 0.9850, and 0.9856 were achieved for FPCS2, FPCS3, and FPCS3, respectively, within their own optimal hyperparameters. For each of FPCS1, FPCS2, FPCS3, and FPCS3, the hypermeters range was as follows: n_estimators: [100, 2000]; learning_rate: [0.01, 0.3]; subsample: [0.1, 1.0]; max_depth: [3, 50]; colsample_bytree: [0.1, 1.0]; reg_alpha: [0.0, 10.0]; reg_lambda: [0.0, 10.0].CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 Table 10. Optimal hyperparameters and the fitting analysis for the XGB model.* Optimal hyperparameters Train Test Train Test 227 4 0 6 .

[0238] The performance of the whole model (XGB-advised FPC) was tested using LS- derived waxes generated at the randomly chosen processing parameters. In other words, the software generated four validation runs on top of the designed experiments (Table 8), namely V1 as 14.5 MPa, 45°C, 2.7 hours; V2 as 32 MPa, 45°C, 2.8 hours, V3 as 16 MPa, 65°C, 3 hours; and V4 as 32 MPa, 65°C, 3 hours. The actual vs. predicted curves were overlayed and are presented in Figure 22. Overall, all the actual thermograms display one major peak alongside two minor peaks at the beginning and the middle of the spectra, all of which were captured by the model within a margin of 1.0°C to 2.5°C. Specifically, the early peaks in the actual spectra occurred between 20.3°C and 21.7°C, whereas the predicted peaks were between 18.1°C and 18.5°C. Additionally, the second peaks in the actual spectra span from 33.1°C to 35°C, which was a broader range than the first peaks, and the predicted peaks ranged fromCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 30.7°C to 31.7°C. Furthermore, the third peak, which was the most prominent feature distinguishing one wax from another, falls within the range of 60.5°C to 62.6°C on the actual curves. Coherently, the predicted curves displayed the major peaks in the range of 59.7°C to 61.8°C.

[0239] It is possible to analyze the model’s response to specific changes in the processing variables by monitoring the shifts in the peaks. For instance, looking closely at the major peaks, the wax obtained at 14.5 MPa and 45°C peaks at 60.5°C (actual V1). As the temperature remained constant at 45°C and the pressure was increased to 32 MPa, the peak temperature slightly rose by 0.7°C to 61.2°C. On the other hand, the predicted major peaks remained the same at 59.7°C (predicted V1 and V2). The behaviors can be explained by Examples I and II, which investigated how pressure and temperature affect extraction efficiency through response surface methodology. Examples I and II illustrated the critical interplay between temperature and pressure levels in determining the degree to which the other variable influences the fractionation efficiency. As such, at lower temperature levels (i.e., < 50°C), increasing pressure has minimally increased the fractionation yield of crude oil from wax. On the other hand, at high temperatures (i.e., > 50°C), pressure has a greater impact on the fractionation process, as pressure and temperature synergistically enhance the dissolution of the lipids in CO2, which, as a result, alters the purity and concentration of the fractions. Therefore, the model may interpret the difference between the major peaks at V1 and V2 as a random fluctuation rather than a systematic one. Furthermore, the difference between V3 (16 MPa and 65°C) and V4 (32 MPa and 65°C) confirms the narrative. Such that, at an elevated temperature of 65°C, increasing the pressure resulted in a shift of the actual peak by 1.1°C, from 61.5°C to 62.6 °C. Simultaneously, the model displayed a shift in the estimated peak from 60.1°C to 61.8 °C. This observation suggests that the model exhibited a more aggressiveCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 response to the pressure elevation at the higher temperature, thus showcasing its volatile sensitivity to varying processing conditions. Coherently, an increase in both pressure and temperature (from V1 to V4) raised both the actual and predicted peaks by 2.1°C, providing further evidence of the model's precision.

[0240] Conclusions.

[0241] This Example III study provided evidence of the potential use of bioethanol LS, a waste material, as a new and innovative source for producing commercial wax analogs while also highlighting the efficiency and practicality of using pure SC-CO2 for such purposes as a green and solvent-free fractionation method. The potential of LS-derived waxes as a substitute for commercial waxes was evaluated based on their melting behaviors using DSC. FPCA showed that it is feasible to obtain a type of wax that could serve as a substitute for carnauba wax under conditions of 40 MPa, 75°C, and 6 hours. Furthermore, the wax extracted at 40 MPa, 55°C, and 6 hours demonstrated significant potential as a substitute for beeswax. The study also demonstrated the effectiveness of combining FPCA with an ensemble learning algorithm, namely XGB, to precisely estimate spectral patterns, specifically DSC, and create a robust predictive model. The findings demonstrated that the byproduct bioethanol side stream LS, which is a significant waste material in a major industry, can be efficiently valorized using an environmentally friendly processing technique based on SC-CO2. Moreover, advanced statistical techniques can effectively guide the development of products with customized characteristics, thus reducing both time and energy consumption.

[0242] For purposes of the instant disclosure, the term “at least” followed by a number is used herein to denote the start of a range beginning with that number (which may be a range having an upper limit or no upper limit, depending on the variable being defined). For example, “at least 1” means 1 or more than 1. The term “at most” followed by a number is used hereinCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 to denote the end of a range ending with that number (which may be a range having 1 or 0 as its lower limit, or a range having no lower limit, depending upon the variable being defined). For example, “at most 4” means 4 or less than 4, and “at most 40%” means 40% or less than 40%. Terms of approximation (e.g., “about”, “substantially”, “approximately”, etc.) should be interpreted according to their ordinary and customary meanings as used in the associated art unless indicated otherwise. Absent a specific definition and absent ordinary and customary usage in the associated art, such terms should be interpreted to be ± 10% of the base value.

[0243] When, in this document, a range is given as “(a first number) to (a second number)” or “(a first number) – (a second number)”, this means a range whose lower limit is the first number and whose upper limit is the second number. For example, 25 to 100 should be interpreted as a range whose lower limit is 25 and whose upper limit is 100. Additionally, it should be noted that where a range is given, every possible subrange or interval within that range is also specifically intended unless the context indicates the contrary. For example, if the specification indicates a range of 25 to 100, such range is also intended to include subranges such as 26 -100, 27-100, etc., 25-99, 25-98, etc., as well as any other possible combination of lower and upper values within the stated range, e.g., 33-47, 60-97, 41-45, 28-96, etc. Note that integer range values have been used in this paragraph for purposes of illustration only, and decimal and fractional values (e.g., 46.7 – 91.3) should also be understood to be intended as possible subrange endpoints unless specifically excluded.

[0244] It should be understood that the exemplary embodiments described above should be considered in a descriptive sense only and not for purposes of limitation. Descriptions of features or aspects within these embodiments should typically be considered as available for other similar features or aspects in other embodiments.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02

[0245] While one or more embodiments have been described with reference to the figures, it will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the scope of the inventive concept as defined by the following claims.

Claims

CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 WHAT IS CLAIMED IS:

1. A process for recovering sorghum wax from a sorghum-based feedstock, the process comprising the steps of: introducing the sorghum-based feedstock to a supercritical carbon dioxide (SC-CO2) extractor; extracting a wax-rich fraction from the sorghum-based feedstock using pure SC-CO2; and extracting a phenolic-rich fraction from the sorghum-based feedstock using a mixture of SC-CO2and at least one cosolvent.

2. The process of Claim 1, wherein the wax-rich fraction comprises one or more of fatty acids, policosanols, and phytosteols.

3. The process of Claim 1, wherein the step of extracting the wax-rich fraction from the sorghum-based feedstock is performed at a predetermined wax-extraction temperature between about 20°C and about 100°C.

4. The process of Claim 3, wherein the step of extracting the wax-rich fraction from the sorghum-based feedstock is performed at a predetermined wax-extraction pressure between about 20 MPa and about 40 MPa.

5. The process of Claim 4, wherein the predetermined wax-extraction temperature is about 60°C and the predetermined wax-extraction temperature pressure is about 40 MPa.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 6. The process of Claim 1, wherein the phenolic-rich fraction comprises phenolic acid, 3- deoxyanthocyanin, or both.

7. The process of Claim 1, wherein the step of extracting the phenolic-rich fraction from the sorghum-based feedstock is performed at a predetermined phenolic-extraction temperature between about 20°C and about 100°C.

8. The process of Claim 7, wherein the step of extracting the phenolic-rich fraction from the sorghum-based feedstock is performed at a predetermined phenolic-extraction pressure between about 20 MPa and about 40 MPa.

9. The process of Claim 8, wherein the predetermined phenolic-extraction temperature is between about 30°C and about 40°C and the predetermined phenolic-extraction pressure is about 40 MPa.

10. The process of Claim 8, wherein the predetermined phenolic-extraction temperature is about 60°C and the predetermined phenolic-extraction pressure is about 30 MPa.

11. The process of Claim 1, wherein the step of extracting the phenolic-rich fraction comprises introducing to the sorghum-based feedstock the mixture of the SC-CO2 and the at least one cosolvent in a ratio of about 1:4.5 (feedstock : cosolvent / SC-CO2).

12. The process of Claim 1, wherein the sorghum-based feedstock is a sorghum bran, a sorghum-based bioethanol lipid slurry, or a corn / sorghum-based bioethanol lipid slurry.CUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 13. The process of Claim 1, wherein the concentration of the at least one cosolvent used in the step of extracting the phenolic-rich fraction is between about 5 vol.% and about 40 vol.% with reference to the mixture of the SC-CO2and the at least one cosolvent.

14. The process of Claim 1, further comprising the step of extracting an oil-rich fraction from the sorghum-based feedstock before the step of extracting the wax-rich fraction.

15. The process of Claim 14, wherein the step of extracting the oil-rich fraction from the sorghum-based feedstock is performed at a predetermined oil-extraction temperature between about 35°C and about 75°C and at a predetermined oil-extraction pressure between about 8 MPa and about 40 MPa.

16. The process of Claim 14, wherein the oil-rich fraction comprises triacylglycerols.

17. The process of Claim 1, further comprising the step of collecting purified sorghum wax from the wax-rich fraction by dissolving the wax-rich fraction in ethanol, precipitating the sorghum wax from the wax-rich fraction, and drying the sorghum wax.

18. A supercritical carbon dioxide (SC-CO2) extractor for recovering sorghum wax from a sorghum-based feedstock, the extractor comprising: a high-pressure vessel configured to extract a wax-rich fraction and a phenolic-rich fraction from the sorghum-based feedstock; a high-pressure CO2pump configured to deliver SC-CO2to the high-pressure vessel; andCUSTOMER NO.22267 PATENT APPLICATION Docket Nos.: P2917PC01 UADA 2024-012-02 a cosolvent pump configured to deliver at least one cosolvent to the high-pressure vessel.

19. The extractor of Claim 18, wherein the high-pressure CO2pump is configured to pressurize CO2gas to produce the SC-CO2.

20. The extractor of Claim 18, wherein the high-pressure vessel is further configured to extract an oil-rich fraction from the sorghum-based feedstock.

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