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A numerical model for the simulation of the degasification process in a vacuum tank degasser is introduced. The model calculates the evolution of hydrogen and nitrogen concentration during the process as function of initial concentrations, vacuum pressure and argon injection flow rate. Governing equations are derived from mass transfer considerations, without solving the detail of the fluid dynamics in the vessel. A numerical model was implemented to solve the resulting set of first order nonlinear ordinary differential equations. Results may be obtained in a few seconds in a typical personal computer, which makes the code suitable for on-line application. Model free parameters were calibrated with an extensive database which compiled measurements of hydrogen and nitrogen concentrations performed during plant trials under a wide range of operating conditions. The comparison of calibrated model results and measurements constitutes a good validation of the model. Simulations were carried out in order to analyze the efficiency of the process under different operative conditions. Results showed how the modifications in the pressure reduction strategy (and argon injection strategy) may affect the final concentration of gases and the risk of excessive foaming. The model proved to be a robust and versatile tool and is susceptible of being adapted to take into account other effects of interest during vacuum degassing (slag foaming, emulsification, temperature evolution, etc).