Radionuclide transport in fractured porous media - Analytical solutions for a system of parallel fractures with a flux-type boundary condition

An analytical solution is developed for the problem of radionuclide transport in a system of planar parallel fractures situated in a porous rock matrix. The flux at the inlet boundary of a fracture is assumed to decrease exponentially with time. The solution considers the following processes: (a) advective transport in the fractures, (b) mechanical dispersion and molecular diffusion along the fractures, (c) molecular diffusion from a fracture to the porous matrix, (d) adsorption onto the fracture wall, (e) adsorption within the porous matrix, and (f) radioactive decay. The solution is based on the Laplace transform method. The general transient solution is in the form of a double integral that is evaluated using composite Gauss-Legendre quadrature. A simpler transient solution that is in the form of a single integral is also presented for the case that assumes negligible longitudinal dispersion along the fractures. A few examples are given to illustrate the effect of various fracture spacings and groundwater velocities, a 1% penetration distance, and the effect of neglecting the longitudinal dispersion in the fractures.