Transport of radionuclides in stochastic media: 1. The quasi-asymptotic approximation

A three-dimensional quasi-asymptotic approximate equation is developed for the transport of radionuelides in a stochastic velocity field. This approximation is derived from an integro-differential equation of transport in stochastic media, commonly encountered in hydrogeology. The quasi-asmptotic equation turns out to be a generalised Telegrapherʹs equation as found by Williams in the particular context of fractured media. We obtain the Telegrapherʹs equation without specifying the causes responsible for the random velocity field. Our model may thus be applied in porous media as well as in fractured media. We give the developments leading to the analytical solution of the three-dimensional Telegrapherʹs equation for constant parameters. This solution is then visualised for a source in the form of a square wave