MODELING THE TRANSPORT OF CONTAMINANTS IN GROUNDWATER AS A BRANCHING STOCHASTIC-PROCESS

Environmental management problems regarding the protection of the envi ronment from potential pollution, the remediation of contaminated site s, the design and operation of repositories for radioactive and toxic wastes, entail the extensive use of mathematical models for the predic tion of the transport of contaminants along natural and artificial pat hways. One of the most significant potential pathways for the return o f hazardous substances from contaminated sites and waste disposals to the biosphere is the flow of groundwater in the subsurface. Many mathe matical models have been developed to simulate the behaviour of ground water systems under various physical conditions. A few different appro aches to the problem have been proposed, ranging from the commonly use d advection-dispersion approach to the more recent transport theory ap proach proposed by Williams. In this paper we present a probabilistic approach based on the Kolmogorov and Dmitriev theory of stochastic bra nching processes: a feature of this approach is its flexibility that a llows 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, anistr opy and inhomogeneity in the spatial characteristics of the medium, va riation of the transport parameters with time. In particular, the adso rption-desorption process is described by introducing a kind of partic le which plays a role very similar to that of the precursors in nuclea r reactor physics. (C) 1997 Elsevier Science Ltd.