A CRRT apparatus comprising a filtration unit (2), a blood circuit (17), a blood pump (21), a dialysate line (13) and one or more lines (8; 51; 57; 58; 63; 69; 67; 74) to transfer a respective solution into blood; a fluid source for each of said one or more lines, wherein said solution comprises at least one buffer agent in the form of bicarbonate or bicarbonate precursor. A control unit (12) is configured to receive a patient prescription and to determine a parameter (Jbuffer_load/BW) indicative of a steady state acid-base balance in the blood of the patient who has to undergo a CRRT blood treatment, wherein said parameter is determined as a function of the concentration of said buffer agent in said fluid source and as a function of the estimated or calculated patient systemic steady state concentration of bicarbonate and/or bicarbonate precursors.