TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The solvent comprises at least one of hexane, cyclohexane, heptane, toluene (methylbenzene), chloroform (trichloromethane) or methyl isobutyl ketone. Preferred Method: The first temperature is carried out at 260-330 degrees C. The first temperature is maintained for 30 minutes to 90 minutes. The feedstock of (c) is cooled to a temperature of 30-150 degrees C. The cooled feedstock is acidified to a pH of 4-5. The second temperature is carried out at 40-100 degrees C. The acidified composition is held at the second temperature of 15-45 minutes. The third temperature is carried out at 110-130 degrees C. The solvent extraction composition is held at the third temperature for 25-35 minutes. The step of separating the extraction composition into at least an organic phase and an aqueous phase is accomplished by at least one of centrifugation and gravity separation. The method further comprises: repeating the steps (f)-(h) on at least one of the aqueous phase and if present a solids phase of at least once; pretreating the feedstock prior to heating to the first temperature by heating the feedstock to a pretreatment temperature of 80-220 degrees C and holding at the pretreatment temperature for 5-60 minutes to produce a pretreated feedstock; removing water from the feedstock following heating; and storing the pretreated feedstock after the pretreatment and before heating to the first temperature. The pretreated feedstock is stored for a period of 1 day to 1 year. EXAMPLE - Algal paste (400 g) was placed in a reactor (600 ml). The reactor was ramped to 260 degrees C for 30 minutes. The reactor was held at 260 degrees C for 30 minutes and then cooled to room temperature for 30 minutes. The amount of gas produced during the hydrothermal treatment was determined from the headspace volume, temperature and pressure using the ideal gas law. Analysis of the gas produced revealed that it was 97% carbon dioxide. The pH of the algal paste following hydrothermal treatment was 8.5. Following hydrothermal treatment, the pH of the material was adjusted to either pH 3-6 using 16.4 wt.% of sulfuric acid. The acidified material was heated to 60 degrees C and held at that temperature of 30 minutes with constant mixing. Following acidification, an amount of solvent (heptane) equal to the amount of water present was added to form a solvent extraction composition which was heated to 70 degrees C. The solvent extraction composition was then held at 70 degrees C for 30 minutes with constant mixing. After 30 minutes, the mixing was stopped and the composition allowed to phase separate at room temperature. The organic phase containing the solvent and oil was decanted. The solvent was removed from the organic phase by evaporation under vacuum to obtain an oleaginous composition.