TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Process: The cavitation reactor (106) is operated at predetermined temperature and predetermined pressure for predetermined time period to promote beneficial cetane increasing oxygenation reactions and inhibit detrimental cetane decreasing oxygenation reactions. The predetermined temperature is 20-200 degrees C, preferably 40-80 degrees C. The predetermined pressure is 1-30 bars, preferably 5-20 bars. The time period is 3-90 minutes, preferably 8-40 minutes. The cavitation reactor (106) is operated with cooling or heat exchanging apparatus to control temperature inside cavitation reactor (106). The promotion of cetane-increasing reactions is carried out using one or more additional cavitation reactors in series in addition to the cavitation reactor (106). The cavitation is ultrasonic cavitation. The cavitation is provided by one or more spinning rotor, an oscillating magnetic field, hydrodynamic flow of liquid reactants within the cavitation reactor, optic cavitation, or particle cavitation. The liquid hydrocarbon product is separated from light hydrocarbon gases (110), water, catalyst, and oxidation source by phase separation. At least a portion of liquid hydrocarbon product is recycled to cavitation reactor. At least a portion of oxidation source, catalyst and acid is recycled to cavitation reactor. The over-oxidized hydrocarbons are removed from liquid hydrocarbon product to form purified hydrocarbon product. The oxidative increase of cetane number of liquid hydrocarbon is carried out by introducing oxidation source and aqueous mixture containing water and acid to an ultrasonic cavitation reactor, subjecting aqueous mixture and oxidation source to ultrasonic cavitation to obtain pretreated aqueous mixture having hydroxyl groups, introducing pretreated aqueous mixture, liquid hydrocarbon feedstock having initial cetane number, and optionally catalyst to an upgrading reactor and mixing liquid hydrocarbon feedstock, pretreated aqueous mixture and optionally catalyst within the upgrading reactor to oxygenate the liquid hydrocarbon feedstock and to obtain liquid hydrocarbon product having final cetane number which is 20% or more with respect to initial cetane number.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The catalyst comprises iron, nickel, vanadium and/or molybdenum. The inorganic acid comprises sulfuric acid, nitric acid and/or hydrochloric acid.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Property: The liquid hydrocarbon feedstock has boiling point of 150-380 degrees C. Preferred Composition: The liquid hydrocarbon feedstock comprises refinery stream, straight-run petroleum, thermally-cracked hydrocarbon, catalytically-cracked hydrocarbon, hydrocracked hydrocarbon, biodiesel, vegetable oils, animal fats and/or material produced by visbreaking bright stock, used lubricating oil, and/or gas oil having boiling point of 200-500 degrees C. The oxidation source comprises aqueous hydrogen peroxide, organic peroxide, inorganic peroxides and/or ozone, preferably ozone. The acid is organic acid chosen from acetic acid, formic acid, oxalic acid and benzoic acid, or inorganic acid.