An apparatus for extracorporeal blood treatment comprising: - a filtration unit having a primary chamber and a secondary chamber separated by a semi-permeable membrane; - a blood withdrawal line connected to an inlet of the primary chamber, - a blood return line connected to an outlet of the primary chamber, said blood lines being configured for connection to a patient cardiovascular system; - a dialysis supply line; - a dialysis effluent line connected to an outlet of the secondary chamber; - a preparation device for preparing a dialysis fluid connected to said supply line and comprising regulating means for regulating the composition of the dialysis fluid, - a control unit connected to the regulating means and programmed for receiving a set value of a parameter for the dialysis fluid in the dialysis supply line, said parameter of the dialysis fluid being at least one chosen in a group including a conductivity of the dialysis fluid, and a concentration of a substance in the dialysis fluid; wherein said control unit is configured for: • receive or calculate a value of a first parameter, the first parameter being chosen in the group including a plasma conductivity, a concentration of the substance in the blood, and a dialysis fluid concentration of the substance at a dialysis treatment in which the substance concentration of the dialysis fluid does not change pre- to post- filtration unit; and characterized in that said control unit is further configured for: • calculate a mass transport of the substance at an instant t of a treatment session as a function of an ultrafiltration flow rate, an elapsed treatment time and of a difference between the value of the first parameter and said set value of the parameter for the dialysis fluid in the dialysis supply line. - a filtration unit having a primary chamber and a secondary chamber separated by a semi-permeable membrane; - a blood withdrawal line connected to an inlet of the primary chamber, - a blood return line connected to an outlet of the primary chamber, said blood lines being configured for connection to a patient cardiovascular system; - a dialysis supply line; - a dialysis effluent line connected to an outlet of the secondary chamber; - a preparation device for preparing a dialysis fluid connected to said supply line and comprising regulating means for regulating the composition of the dialysis fluid, - a control unit connected to the regulating means and programmed for receiving a set value of a parameter for the dialysis fluid in the dialysis supply line, said parameter of the dialysis fluid being at least one chosen in a group including a conductivity of the dialysis fluid, and a concentration of a substance in the dialysis fluid; wherein said control unit is configured for: • receive or calculate a value of a first parameter, the first parameter being chosen in the group including a plasma conductivity, a concentration of the substance in the blood, and a dialysis fluid concentration of the substance at a dialysis treatment in which the substance concentration of the dialysis fluid does not change pre- to post- filtration unit; and • receive or calculate a value of a first parameter, the first parameter being chosen in the group including a plasma conductivity, a concentration of the substance in the blood, and a dialysis fluid concentration of the substance at a dialysis treatment in which the substance concentration of the dialysis fluid does not change pre- to post- filtration unit; and characterized in that said control unit is further configured for: • calculate a mass transport of the substance at an instant t of a treatment session as a function of an ultrafiltration flow rate, an elapsed treatment time and of a difference between the value of the first parameter and said set value of the parameter for the dialysis fluid in the dialysis supply line. • calculate a mass transport of the substance at an instant t of a treatment session as a function of an ultrafiltration flow rate, an elapsed treatment time and of a difference between the value of the first parameter and said set value of the parameter for the dialysis fluid in the dialysis supply line.