Method for purifying a carbon dioxide-rich gas at low temperature in order to produce a carbon dioxide-rich fluid wherein: i) the carbon dioxide-rich gas is cooled and condensed at least partially in a first brazed aluminium plate-fin heat exchanger, formed of wave mats separated by plates, ii) the partially condensed carbon dioxide-rich gas is sent to a first phase separator and a liquid from the first phase separator 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 cooled, then is expanded then is sent to a second heat exchanger which is a shell and tube exchanger, the carbon dioxide-rich liquid being sent to be heated in the shell where it is heated by means of the gas of the first phase separator which condenses in the tubes to form condensed liquid, the exchanger carrying out an indirect heat exchange only between the carbon-dioxide rich liquid and the gas of the first phase separator, 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 vi) the carbon-dioxide rich liquid is cooled before the expansion in a third heat exchanger (9, 109) by indirect heat exchange with the carbon dioxide-depleted gas which is heated in the first exchanger and by heat exchange with the gas vaporised in the second exchanger. i) the carbon dioxide-rich gas is cooled and condensed at least partially in a first brazed aluminium plate-fin heat exchanger, formed of wave mats separated by plates, ii) the partially condensed carbon dioxide-rich gas is sent to a first phase separator and a liquid from the first phase separator 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 cooled, then is expanded then is sent to a second heat exchanger which is a shell and tube exchanger, the carbon dioxide-rich liquid being sent to be heated in the shell where it is heated by means of the gas of the first phase separator which condenses in the tubes to form condensed liquid, the exchanger carrying out an indirect heat exchange only between the carbon-dioxide rich liquid and the gas of the first phase separator, 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 vi) the carbon-dioxide rich liquid is cooled before the expansion in a third heat exchanger (9, 109) by indirect heat exchange with the carbon dioxide-depleted gas which is heated in the first exchanger and by heat exchange with the gas vaporised in the second exchanger.