A process for cryogenic fractionation of air uses an air fractionation plant (100-400) comprises a rectification column system (10) having a high-pressure column (11) operated at a pressure level of 9 to 14.5 bar, a low-pressure column (12) operated at a pressure level of 2 to 5 bar, and an argon column (13). A recirculating stream is formed using a second top gas or a portion thereof, which is heated, compressed, cooled again, and after partial or complete liquefaction or in the unliquefied state is introduced partially or completely, or in fractions, into the first rectification column (11) and/or into the second rectification column (12).

A system and method of ultra-high purity (UHP) oxygen production from an argon and oxygen producing cryogenic air separation unit incorporating a dedicated methane rejection column or column section having a liquid to vapor (L/V) ratio lower than the L/V ratio in the associated argon rectifier is provided.