An analytical solution based on Laplace transforms is developed for the problem of radionuclide transport along a discrete planar fracture in porous rock. The solution takes into account advective transport in the fracture, longitudinal hydrodynamic dispersion in the fracture along the fracture axis, molecular diffusion from the fracture into the rock matrix, sorption within the rock matrix, sorption onto the surface of the fracture, and radioactive decay. The longitudinaldispersion-free solution, which is of closed form, is also reported. The initial radionuclide concentrations in both the fracture and the rock matrix are assumed to be zero. A kinetic solubility-limited dissolution model is used as the inlet boundary condition. In addition to the radionuclide concentrations in both the fracture and the rock matrix, the mass flux in fracture is provided. The analytical solution is in the form of a single integral that is evaluated by a Gauss-Legendre quadrature for each point in space and time. As the dissolution rate constant approaches infinity, the inlet boundary condition of the kinetic solubility-limited dissolution model can be replaced by the boundary condition of constant concentration, as is shown by numerical illustration. Restated, the constant concentration boundary condition represents a conservative upper limit to the solubility-limited dissolution rate. Diffusion into the rock matrix enhances the dissolution rate, even though it can also enhance the retardation of solute transport in fracture. This analytical solution has been verified by the results generated from a numerical inversion of the Laplace transforms. The agreement is excellent.
