The assessment of waste repositories are based on predictive models that are able to forecast the migration of contaminants within groundwater. The heterogeneity and stochasticity of the media in which the dispersion phenomenon takes place, renders classical analytical- numerical approaches scarcely adequate in practice. Furthermore, these approaches are computationally intensive and limited to small scale applications. In this paper, the contaminant transport is described by the linear Boltzmann integral transport equation and solved by means of a Monte Carlo particle tracking based approach. The governing parameters of the stochastic model are calibration on a small-scale analysis based on the Discrete Fracture Network simulation. The proposed approach is very flexible and computationally efficient. It can be adopted as an upscaling procedure and to predict the migration of contaminants through fractured media at scale of practical interest.