Contaminant transport in bidimensional porous media via biased Monte Carlo simulation

One of the most vulnerable spots of nuclear power systems is the hazard posed by the radioactive wastes at the end of the fuel cycle. Currently, the most widely pursued end solution consists of disposing the radioactive wastes in repositories buried in deep geologic formations of presumed high stability. Licensing of such repositories is conditional on the assessment of the reliability of such confinement for quite extensive periods of time ranging from 10 000 to 1 million years. Over such long time scales the repositories may leak, thus releasing contaminants to the surrounding medium. The released contaminant may reach the groundwater and be transported for substantial distances, eventually returning to the biosphere, where it poses a hazard for human health and the environment. In the present paper, we propose a phenomenological model based on the Kolmogorov-Dmitriev theory of branching stochastic processes in which a distributed source releases contaminant which is transported over a bidimensional medium whose physical properties are stochastic in space. The proposed model is implemented within a Monte Carlo scheme which exploits variance reduction techniques