A new model for describing the transport of radionuclides through fractured rock

A new model of radionuclide transport in fractured rock is developed based upon an analogy with neutron transport. The reason for introducing such a new model is to explain the scale-dependence of the dispersion length which arises when the classical advective-dispersive model is used to interpret experiments on groundwater flows. The new model associates travel along a fracture with an effective mean free path, and the distribution of fractures at a branching point, with a pseudo-scattering process. It is shown, using a ''backward-forward'' model of transport, and for more complicated rock structure, that the concentration obeys a generalised Telegrapher's equation and thereby predicts a wave front to the concentration cloud, as expected physically. The general form of the equation is discussed and exact solutions are obtained for some simple cases in infinite media. Numerical results are given to illustrate differences between classical advective-dispersive theory and the Telegrapher's equation. A moments method is developed and it is shown that the classical dispersion coefficient depends strongly on time during the early stages of development. (Author)