Method for purifying a mixture containing carbon dioxide at a low temperature to produce a carbon-dioxide rich fluid, wherein: i) the carbon-dioxide rich mixture is cooled in a first brazed aluminium plate-fin heat exchanger, consisting of wave mats separated by plates, and the cooled mixture condenses at least partially in the first exchanger and is sent to a first phase separator, ii) the cooled mixture or at least one fluid derived from the cooled mixture is sent to a purification step comprising a distillation step and/or at least two successive partial condensation steps, iii) the purification step produces a carbon dioxide-depleted gas which heats up again the first exchanger, iv) the purification step produces a carbon-dioxide rich liquid which is expanded, then sent to a second heat exchanger where it is heated, the gas of the first phase separator is sent to the second exchanger to heat the carbon-dioxide rich liquid by cooling and condensing at least partially in the second exchanger, the second exchanger carrying out an indirect heat exchange between the carbon-dioxide rich liquid and the gas of the first phase separator, and v) the carbon-dioxide rich liquid vaporises at least partially in the second exchanger and the vaporised gas formed is heated in the first exchanger in order to form a carbon-dioxide rich gas, that can be the end product of the method and wherein the second heat exchanger is a shell and tube exchanger, characterised in that the second exchanger carries out only an indirect heat exchange between the carbon-dioxide rich liquid which is heated in the shell and the gas of the first phase separator which heats the carbon-dioxide rich liquid by cooling in the tubes. i) the carbon-dioxide rich mixture is cooled in a first brazed aluminium plate-fin heat exchanger, consisting of wave mats separated by plates, and the cooled mixture condenses at least partially in the first exchanger and is sent to a first phase separator, ii) the cooled mixture or at least one fluid derived from the cooled mixture is sent to a purification step comprising a distillation step and/or at least two successive partial condensation steps, iii) the purification step produces a carbon dioxide-depleted gas which heats up again the first exchanger, iv) the purification step produces a carbon-dioxide rich liquid which is expanded, then sent to a second heat exchanger where it is heated, the gas of the first phase separator is sent to the second exchanger to heat the carbon-dioxide rich liquid by cooling and condensing at least partially in the second exchanger, the second exchanger carrying out an indirect heat exchange between the carbon-dioxide rich liquid and the gas of the first phase separator, and v) the carbon-dioxide rich liquid vaporises at least partially in the second exchanger and the vaporised gas formed is heated in the first exchanger in order to form a carbon-dioxide rich gas, that can be the end product of the method and wherein the second heat exchanger is a shell and tube exchanger, characterised in that the second exchanger carries out only an indirect heat exchange between the carbon-dioxide rich liquid which is heated in the shell and the gas of the first phase separator which heats the carbon-dioxide rich liquid by cooling in the tubes.