This paper reviews recent work on the development of mathematical models for the transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments.

Firstly, general multi-dimensional numerical models for the flow of water and the transport of dissolved radionuclides through permeable media are described. Their use in assessing the importance of possible transport pathways is illustrated by examples of flow in rocks with high permeability fracture zones.

Secondly, recent advances in the description of flow and transport through fractured rock masses are considered. The results of field experiments are used to examine the characteristics of single fractures such as transmissivity, the proportion taking flow and the diffusion of ions into the surrounding rock. In addition, network models are used to examine the connectivity, flow and hydrodynamic dispersion through fracture systems and to assess how well transport can be modelled by an equivalent permeable medium model. The fracture systems are defined by probability distributions for the orientations, lengths and hydraulic apertures of fractures together with information about the number of fractures per unit volume. It is found that, providing the region size is much bigger than the mean fracture length, the permeability is constant, but that hydrodynamic dispersion is not adequately modelled by a diffusion-like term.

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