Migration of Radionuclides in Fissured Rock: Analytical Solutions for the Case of Constant Source Strength

Abstract

An analytical solution is derived for the problem of radionuclide migration in fissured rock, where the rock blocks are modelled as spheres. The solution differs from a previous one mainly in the inlet boundary condition. In the present paper the case of constant source strength is treated instead of a decaying step release. The solution developed here is considerably more complex. Processes that are accounted for are advection and longitudinal dispersion in the fissures, external and internal diffusion into spherical rock blocks, sorption onto the fissure surfaces, and sorption within the matrix and radioactive decay. The solution is obtained in the form of an infinite single integral depending in general on six dimensionless parameters. The steady state solution includes five dimensionless quantities. A comparison with previously published results for a system of parallel fractures is made. It is shown that if the area‐to‐volume ratio of the slabs and the spherical rock blocks is the same, identical breakthrough curves are produced for short and long contact times. In the intermediate range the solution with spherical rock blocks will give earlier breakthrough and higher steady state concentrations. It is shown that the analytical solution for parallel fractures, previously given as an infinite double integral, may be derived as an infinite single integral. The numerical evaluation is thereby considerably simplified. Examples demonstrate the impact of hydrodynamic dispersion and water transport time on radionuclide transport in situations considered to be realistic repository conditions.