An apparatus for separation of a flow containing at least 95 mol % of carbon dioxide and also at least one impurity lighter than carbon dioxide by distillation comprises a heat exchanger (20), a distillation column (30), expansion means (V3), means for sending the flow to be cooled in the heat exchanger, means for sending the cooled flow to be separated in the distillation column, means for withdrawing at the bottom of the column a liquid flow containing at least 99 mol % of carbon dioxide, means for sending at least a portion (12) of the liquid flow to be cooled in the heat exchanger to form a subcooled liquid (3), means for sending at least a portion of the subcooled liquid to the expansion means to produce a two-phase flow, a phase separator (40) for separating the two-phase flow to form a gas and a liquid, means for sending at least a portion (14) of the liquid from the phase separator to be vaporized in the heat exchanger and means for taking a portion (4) of the liquid from the phase separator.

In a process for separating a mixture containing hydrogen and carbon dioxide, the mixture is compressed to form a compressed mixture, the compressed mixture is separated by partial condensation and/or distillation generating a first CO2-depleted stream, the first CO2-depleted stream is separated by permeation through a membrane system to form a residue of the membrane system which is depleted in hydrogen and carbon dioxide and a portion of the residue is recycled, after expansion, to the compressor to be compressed therein.