Modelling the transport of contaminants in groundwater as a branching stochastic process

Environmental management problems regarding the protection of the environment from potential pollution, the remediation of contaminated sites, the design and operation of repositories for radioactive and toxic wastes, entail the extensive use of mathematical models for the prediction of the transport of contaminants along natural and artificial pathways. 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 this paper we present a probabilistic approach based on the Kolmogorov and Dmitriev theory of stochastic branching processes: a feature of this approach is its flexibility that allows for a detailed description of the elementary processes which may occur during the transport. Several numerical examples are presented to illustrate the capabilities of the method in dealing with practical issues such as adsorption-desorption effects in the hose rock, anistropy 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