A mathematical model has been developed to determine the amount of tritium that permeates the cooling circuit of a tritium breeding blanket containing the liquid eutectic alloy 17Li-83Pb. This model, which has been applied to phase 2A of the International Tokamak Reactor/Next European Torus project, is used to predict the effect of the operating conditions of the blanket, as well as those of a spray tower employed as a tritium recovery unit, and the kinetic parameters for the permeation and desorption processes. The results of this theoretical study indicate that the amount of permeated tritium proved to be not very different for the maximum [10.82 kPa1/2 · m3(mol · T)−1] and minimum [0.7 kPa1/2 · m3(mol · T)−1] values of Sievert's constant (Ks) existing in literature. This amount, moreover, can be reduced to 0.1 to 0.01 g/day of tritium by the presence of small oxide barriers (a permeation reduction factor of α ≅ 100) on the cooling tubes and by the easy operating conditions of the spray tower, which include a droplet diameter of 0.5 mm; a tritium pressure of 0.13 kPa at 673 K; and a residence time of 0.5 s.