A method of producing a purified liquid argon product comprising the steps of: separating argon from oxygen in an argon column within a cryogenic air separation plant, wherein the argon column is configured to produce a liquid argon stream having oxygen impurities; introducing a portion of the liquid argon stream having oxygen impurities into an adsorbent bed; adsorbing the oxygen impurities from the liquid argon stream in an adsorption process having an adsorbent to produce a purified liquid argon stream constituting the purified liquid argon product; subjecting the adsorbent bed to an alternating cycle having an on-line phase where oxygen impurities are adsorbed from the portion of the liquid argon stream having oxygen impurities within the adsorbent bed and an off-line phase where the adsorbent contained in the adsorbent bed is regenerated; indirectly exchanging heat from the adsorbent bed to a coolant stream during the on-line phase of the alternating cycle to the adsorbent bed at a reduced temperature that is sufficient to prevent vaporization of the liquid argon stream and the liquid argon product stream terminating the step of introducing a portion of the liquid argon stream having oxygen impurities into the adsorbent bed during the off-line phase of the alternating cycle; draining the adsorbent bed of residual liquid argon contained in the adsorbent bed during the off-line phase of the alternating cycle to produce a residual liquid argon stream; directing the residual liquid argon stream into the argon column or a low pressure column of the cryogenic air separation plant as a liquid or a vapor or a mixture of liquid and vapor; regenerating the adsorbent by removing the oxygen impurities from the adsorbent; refilling the adsorbent bed with purified liquid argon product; and re-subjecting the adsorbent bed to the on-line phase of the alternating cycle. separating argon from oxygen in an argon column within a cryogenic air separation plant, wherein the argon column is configured to produce a liquid argon stream having oxygen impurities; introducing a portion of the liquid argon stream having oxygen impurities into an adsorbent bed; adsorbing the oxygen impurities from the liquid argon stream in an adsorption process having an adsorbent to produce a purified liquid argon stream constituting the purified liquid argon product; subjecting the adsorbent bed to an alternating cycle having an on-line phase where oxygen impurities are adsorbed from the portion of the liquid argon stream having oxygen impurities within the adsorbent bed and an off-line phase where the adsorbent contained in the adsorbent bed is regenerated; indirectly exchanging heat from the adsorbent bed to a coolant stream during the on-line phase of the alternating cycle to the adsorbent bed at a reduced temperature that is sufficient to prevent vaporization of the liquid argon stream and the liquid argon product stream terminating the step of introducing a portion of the liquid argon stream having oxygen impurities into the adsorbent bed during the off-line phase of the alternating cycle; draining the adsorbent bed of residual liquid argon contained in the adsorbent bed during the off-line phase of the alternating cycle to produce a residual liquid argon stream; directing the residual liquid argon stream into the argon column or a low pressure column of the cryogenic air separation plant as a liquid or a vapor or a mixture of liquid and vapor; regenerating the adsorbent by removing the oxygen impurities from the adsorbent; refilling the adsorbent bed with purified liquid argon product; and re-subjecting the adsorbent bed to the on-line phase of the alternating cycle.