Methods and systems for purifying argon from a crude argon stream are disclosed, employing pressure swing adsorption at cold temperatures from 186 C. to 20 C.; more preferably from 150 C. to 50 C.; and most preferably from 130 C. to 80 C. with oxygen-selective zeolite adsorbent. In some embodiments, the oxygen-selective zeolite adsorbent is a 4A zeolite, a chabazite, or a combination thereof.

A pressure swing absorption apparatus, including: at least four beds that each include an absorbent material, wherein the at least four beds are configured to rotate and are grouped such that members of one group only have fluid interconnections with members of another group; and a control system that controls a flow rate of a fluid communication between at least two of the beds by adjusting a phase angle difference between the at least two of the beds.