The invention relates to a cryogenic distillation apparatus for a gas mixture, including a purification apparatus for purifying a gas mixture in a system with a plurality of adsorbant bottles, a column system, a capacity, means for feeding a cryogenic liquid to the capacity, means for feeding a vaporized liquid from the capacity to a column of the system, a vaporizer in the capacity for vaporizing the contained liquid; means for feeding a calorigenic gas to the vaporizer, and means for drawing a liquid from the capacity.

An air separation plant is provided that includes a plurality of air compressors, a plurality of air purification units, and one or more cold boxes. In a first mode of operation, a first air compressor is configured to compress air to a higher pressure than a second air compressor. In a second mode of operation, the second air compressor is configured to compress air to a higher pressure than during the first mode of operation.

A method for operating an air separation plant having a distillation column system, a heat exchanger, and an adsorber, wherein, in a first time period, a first operating mode is carried out and, in a second time period following the first time period, a second operating mode is carried out. In a third time period between the second time period and the first time period, a third operating mode is carried out, in which third operating mode compressed air is at least partially freed of water and carbon dioxide in the adsorber and at least part of said compressed air is cooled in the heat exchanger, an air product is removed from the distillation column system and at least part of said air product is heated in the heat exchanger.