Diffusion of a contaminant in fractured porous media

A theoretical model is developed for diffusion from a finite source of buried contaminant through a porous medium containing a fracture that reaches to the atmosphere. Important quantities are shown to be the burial depth, source width and fracture width, the soil porosity, the diffusion coefficients in the soil and the (air-filled) fracture, and the decay constant of a radioactive contaminant. The flux across the soil-air interface is calculated and shown to be greatly increased by the presence of the fracture. The flux is found to increase with fracture width and source width, to decrease with increasing soil porosity and decay constant, and to decrease with increasing ratio of soil diffusion coefficient to air diffusion coefficient.