Tritium extraction from the Pb-17Li liquid breeder of a fusion reactor can be efficiently carried out by bubble columns. To this aim, a mathematical model describing the complex fluid-dynamics of a bubble extractor is here presented. The model equations are made dimensionless and, together with the proper boundary conditions, numerically solved by the orthogonal collocation technique. Moreover, in order to better understand the role played by the different parameters in determining the perfomance of a bubble column, a closed solution of the model is obtained by introducing suitable hypotheses. A parametric analysis of the extraction efficiency of a bubble column as a function of the process parameters is carried out and, on this basis, the design of a tritium extraction system from the Pb-17Li breeder of a DEMO-type fusion reactor is proposed.