A stochastic model for underground transport of radionuclides

Several environmental management applications rely on mathematical models for the numerical simulation of contaminant transport in groundwater. The performance assessment of a high-level radioactive waste repository, for example, requires, an extensive use of simulation models. This is due to the fact that the regulations concerning the licensing and operation of these facilities require that the safety functions be guaranteed over very long periods of time and quite extensive spatial scales. In these conditions, no significant tests nor monitoring can be performed and one must rely on predictive models for the assessment. One of the most significant potential pathways for the return of hazardous substances from contaminated sites and waste disposals to the biosphere is the flow of groundwater in the subsurface. Many mathematical models have been developed to simulate the behaviour of groundwater systems under various physical conditions. A few different approaches to the problem have been proposed, ranging from the commonly used advection-dispersion approach to the more recent transport theory approach proposed by Williams. 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 given hydrogeological medium. Several numerical examples are presented to illustrate the capabilities of the method in dealing with adsorption-desorption effects in the host rock, anisotropy and inhomogeneity in the spatial characteristics of the medium, variation of the transport parameters with time. In particular, the adsorption-desorption process is described by introducing a kind of particle which plays a role very similar to that of the precursors in nuclear reactor physics. (author)