A biased Monte Carlo methodology is presented for solving the transport of radionuclide chains through a porous medium in the context of the risk assessment of radioactive waste repositories. It is based on the construction of random walks from an integral equation. This leads to a biased Monte Carlo simulation because it uses the solution of an adjoint reference problem to improve the efficiency of the calculations. The transport of a radionuclide chain is modeled by introducing the notion of a radionuclide "state." The consequence is that only one integral equation has to be considered for the simulation in a continuous - discrete space (r,t;i), where r is the radionuclide position vector, t is time, and i is the radionuclide state. Transport in a random velocity field is also considered by using double randomization techniques.

The methodology is illustrated by numerical results on test problems; the score of the simulations being the quantity of radionuclides transferred, during the mission time, to the upper surface of the geological domain. Validations of the simulations are first realized by comparison with analytical solutions, and the influence of biasing techniques is put in evidence. Finally, simulations conducted simultaneously with the generation of a large number of random velocity fields illustrate the feasibility of the method for the transport of radionuclides in a stochastic medium.