The present invention relates to methods and apparatus for producing alkyl esters from lipid feed stocks, such as plant oils and/or animal fats, and systems including the same. In an embodiment, the invention includes a process for producing alkyl esters including mixing a lipid feed stock with an alcohol to form a reaction mixture; and contacting the reaction mixture with a catalyst under supercritical conditions for the alcohol, the catalyst comprising an unmodified metal oxide selected from the group consisting of alumina, titania, zirconia, and hafnia, and removing residual free fatty acids from the reaction mixture. Other embodiments are included herein.