An acid medium is provided comprising one or more water-soluble oxidized disulfide oil ODSO compounds. The use of such an acid medium is disclosed as a replacement for conventional acids. Embodiments of the present disclosure are directed to an ODSO acid or ODSO acid mixture medium comprising, consisting of or consisting essentially of one or more polar water-soluble ODSO compounds, including polar water-soluble ODSO compounds present in an effluent refinery hydrocarbon stream recovered following catalytic oxidation of mercaptans present in a petroleum feedstream.