Models for incompressible underground flows through naturally fractured formations subjected to high-level nuclear waste contamination are introduced and studied. They consider a chain of contaminants that decay into other species, allowing the monitoring of descendant radioactive species as well. A simulator that describes scenarios of long distance effects in case of leakage from a repository placed in such rock formations was developed. The simulator includes features like high accuracy and slowly increasing time steps in order to handle phenomena of timescale of centuries with detailed description of the transient phase, where few days is the adequate time scale.