The invention relates to a blood processing device using extra-corporealcirculation and comprising a filter (2) with a semipermeable membrane (5); ablood circuit (7, 3, 6); a dialysate circuit comprising the secondary filterchamber (4) and at least one drainage line (8) for a flow of spent fluid to bedischarged from the filter into a drain (9); a first bag (11) in fluidcommunication with the drainage line; at least one first gravimetric weighingmeans (21) linked to the first bag, means for controlling the active fluidflow on the drainage line (31, 32, 33); a control unit (41) connected to thefirst gravimetric weighing means and the fluid flow control means; a secondbag (12) in fluid communication with the drainage line, wherein the controlunit can receive the weight signals from the first gravimetric weighing meansand control the control means to fill one of the bags with fluid while theother bag is emptied of fluid, and vice versa. The invention further relatesto a disposable drainage line for use in the processing device.