Refrigeration duty in a carbon dioxide purification unit (CPU) operating at elevated pressure and sub-ambient temperature can be provided in at least a first part by indirect heat exchange against at least latent heat of at least one liquid first refrigerant, preferably carbon dioxide liquid(s) produced in the CPU, thereby typically evaporating the liquid(s), and a second part by indirect heat exchange with sensible heat energy alone of a second refrigerant. The second refrigerant may be nitrogen gas imported from an integrated cryogenic air separation unit (ASU) or carbon dioxide liquid exported from the CPU, cooled and returned to the CPU. One advantage is that total power consumption of the CPU and an integrated ASU is reduced.