AN ANALYTICAL MODEL FOR RADIONUCLIDE TRANSPORT IN A SINGLE FRACTURE - CONSIDERING NONEQUILIBRIUM MATRIX SORPTION

An analytical solution covering the entire range of sorption properties of rock has been derived for the migration of radionuclides along a discrete fracture in a porous rock matrix. The analysis takes into account the advective transport in the fracture, longitudinal hydrodynamic dispersion in the fracture, molecular diffusion from the fracture into the rock matrix, adsorption within the matrix, and the radioactive decay. For adsorption of radionuclide within the matrix, the effects of no sorption, linear nonequilibrium sorption, and linear equilibrium sorption are integrated into a generic transient analytical solution. Based on certain assumptions, the problem can be formulated into two coupled one-dimensional transport equations: one for the fracture and another for the porous matrix in a direction perpendicular to the fracture axis. The general solution is of a single semi-infinite integral form that can be evaluated by Gaussian quadrature. The results indicate that the assumption of equilibrium sorption within the rock results in underestimation of the concentration profile along the fracture in the early stages of migration. It is worth noting that the concentration profile of the nonequilibrium sorption case is slightly smaller than that of the equilibrium sorption case after a certain time. However, the profiles eventually approach the same value. It is also confirmed that the porosity of rock strongly affects radionuclide transport in a fracture.