NOVELTY - Obtaining an oleaginous composition from biomass comprises: obtaining an feedstock; heating and cooling the feedstock; acidifying the cooled feedstock to a pH of 3 to less than 6 to produce an acidified composition; heating the acidified composition; adding a volume of a solvent equal in volume to the water in the acidified composition to produce a solvent extraction composition; heating and separating the extraction composition into at least an organic phase and an aqueous phase; removing the organic phase from the aqueous phase; and removing the solvent from the organic phase.    USE - The method is useful for obtaining an oleaginous composition from biomass, where the biomass includes an aquatic microorganism, preferably photo synthetic alga or a photosynthetic bacterium (all claimed), and the oleaginous composition includes e.g. hydrocarbons, lipids, waxes, fatty acyls including free fatty acids, fatty esters and fatty amides, glycerolipids, glycerophospholipids, sphingolipids, sterols, terpenes, saccharolipids, polyketides, carotenoids and chlorophylls.    ADVANTAGE - The method is economical.    DETAILED DESCRIPTION - Obtaining an oleaginous composition from biomass, comprises: (a) obtaining an feedstock comprising the biomass and water; (b) heating the feedstock in a closed reaction vessel to a first temperature of 250-360 degrees C and holding at the first temperature for 0-90 minutes; (c) cooling the feedstock at ambient temperature to 150 degrees C; (d) acidifying the cooled feedstock to a pH of 3 to less than 6 to produce an acidified composition; (e) heating the acidified composition to a second temperature of 40-150 degrees C, and holding the acidified composition at the second temperature for 0-45 minutes; (f) adding a volume of a solvent equal in volume to the water in the acidified composition to produce a solvent extraction composition, where the solvent is sparingly soluble in water, but oleaginous compounds are at least substantially soluble in the solvent; (f) heating the solvent extraction composition in closed reaction vessel to a third temperature of 60-150 degrees C and holding at the third temperature for 15-45 minutes; (g) separating the solvent extraction composition into at least an organic phase and an aqueous phase; (h) removing the organic phase from the aqueous phase; and (i) removing the solvent from the organic phase to obtain an oleaginous composition. An INDEPENDENT CLAIM is included for the oleaginous composition comprising: a calcium content of less than 30 ppm, a magnesium content of less than 20 ppm, a manganese content of less than 20 ppm, a phosphorus content of less than 20 ppm, a sodium content of less than 50 ppm and a strontium content of less than 20 ppm, where the composition is obtained from aquatic biomass; or an oil extracted from biomass comprising a microorganism, where the composition has a percent mass fraction with a boiling point of 260-630 degrees C of 5-55% as determined by ASTM protocol D7169-11.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of a process for obtaining an oleaginous composition from biomass.    Heater (103)    Hydrothermal reactor unit (104)    Cooling unit (105)    Outlet flash unit (106)    Heating unit. (107)