A method of producing a purified argon product (174, 195) in a cryogenic air separation unit integrated with a pressure swing adsorption system, the method comprising the steps of: separating argon from an oxygen-argon containing stream within a lower pressure column of the cryogenic air separation unit using an argon rectification column arrangement (56, 90) disposed within the lower pressure column, the separation of the argon from the oxygen-argon containing stream producing an impure argon stream having between about and 4% and 25% of oxygen impurities; warming the impure argon stream to a temperature between about 200K and 300K in an argon recovery heat exchanger (152, 173) against a purified argon stream, a waste stream and a stream of purified, compressed air; pressurizing the warmed impure argon stream; purifying the warmed, pressurized impure argon stream by introducing the warmed, pressurized impure argon stream into the pressure swing adsorption system, the pressure swing adsorption system comprising an adsorbent bed (162, 164) having an adsorbent configured for adsorbing the oxygen impurities to produce the purified argon stream and the waste gas stream, wherein the adsorbent bed is subjected to an alternating cycle having an on-line phase where the impure argon stream is purified within the adsorbent bed to produce the purified argon stream, and an off-line phase where the adsorbent contained in the adsorbent bed is regenerated and produces the waste gas stream; and recycling the waste gas stream from the pressure swing adsorption system back to the argon rectification column arrangement disposed within the lower pressure column; wherein the argon rectification column arrangement comprises a partition wall having a top section, a bottom section, a first surface, and a second surface opposite the first surface, the partition wall disposed within an outer shell of the lower pressure column; a plurality of mass transfer elements disposed adjacent to the first surface of the partitioned wall; an inlet disposed proximate the bottom section of the partition wall for receiving an ascending argon-oxygen containing vapor stream; an outlet disposed proximate the top section of the partition wall for withdrawing an ascending argon-rich vapor; an inlet disposed proximate the top section of the partition wall for receiving a down-flowing liquid reflux stream; an outlet disposed proximate the bottom section of the partition wall for withdrawing a descending oxygen rich liquid stream; and wherein the impure argon stream is an argon vapor stream comprised of all or a portion of the ascending argon-rich vapor exiting the argon rectification column arrangement. separating argon from an oxygen-argon containing stream within a lower pressure column of the cryogenic air separation unit using an argon rectification column arrangement (56, 90) disposed within the lower pressure column, the separation of the argon from the oxygen-argon containing stream producing an impure argon stream having between about and 4% and 25% of oxygen impurities; warming the impure argon stream to a temperature between about 200K and 300K in an argon recovery heat exchanger (152, 173) against a purified argon stream, a waste stream and a stream of purified, compressed air; pressurizing the warmed impure argon stream; purifying the warmed, pressurized impure argon stream by introducing the warmed, pressurized impure argon stream into the pressure swing adsorption system, the pressure swing adsorption system comprising an adsorbent bed (162, 164) having an adsorbent configured for adsorbing the oxygen impurities to produce the purified argon stream and the waste gas stream, wherein the adsorbent bed is subjected to an alternating cycle having an on-line phase where the impure argon stream is purified within the adsorbent bed to produce the purified argon stream, and an off-line phase where the adsorbent contained in the adsorbent bed is regenerated and produces the waste gas stream; and recycling the waste gas stream from the pressure swing adsorption system back to the argon rectification column arrangement disposed within the lower pressure column; wherein the argon rectification column arrangement comprises a partition wall having a top section, a bottom section, a first surface, and a second surface opposite the first surface, the partition wall disposed within an outer shell of the lower pressure column; a plurality of mass transfer elements disposed adjacent to the first surface of the partitioned wall; an inlet disposed proximate the bottom section of the partition wall for receiving an ascending argon-oxygen containing vapor stream; an outlet disposed proximate the top section of the partition wall for withdrawing an ascending argon-rich vapor; an inlet disposed proximate the top section of the partition wall for receiving a down-flowing liquid reflux stream; an outlet disposed proximate the bottom section of the partition wall for withdrawing a descending oxygen rich liquid stream; and wherein the impure argon stream is an argon vapor stream comprised of all or a portion of the ascending argon-rich vapor exiting the argon rectification column arrangement.