A method for producing power and argon is provided by providing a residual gas stream, purifying the residual gas stream in a front-end purification unit to remove carbon dioxide, thereby forming a purified residual gas stream, and introducing the purified residual gas stream to a cold box, wherein the purified residual gas stream is cooled and expanded within the cold box to produce power and then fed to a distillation column system for separation therein, thereby forming an argon-enriched stream and optionally a nitrogen-enriched stream and/or an oxygen-enriched stream, wherein the residual gas stream is sourced from a retentate stream of a cold membrane having oxygen, nitrogen, carbon dioxide, and argon.