In this paper we present a model to predict the onset and evolution of segregation during the discharge of binary mixtures of granular materials. The model accounts for the multi-phase and multi-component nature of the granular mixtures, to simulate the main flow regimes occurring in the discharge of silos (funnel and mass flow) and how they affect segregation. The new comprehensive model for segregation follows a continuum Eulerian approach and results from the coupling between an ad-hoc rheology for granular flow and a percolation model for multi-component mixtures. Predictions are compared with independent literature experimental data, for short and tall silos and prove to be quite accurate, after a tuning of the percolation flux sub-model. The larger segregation in short flow paths with smaller amount of fines reported by the experiments is quantitatively predicted. The model also predicts the three phases observed in experiments during the discharge of tall silos. (C) 2016 Elsevier Ltd. All rights reserved.