Many physical and chemical processes dominate the transport of radionuclides in groundwater. With diffusion only, the basic model cannot be conservative against the cylinder model, with respect to the diffusive mass flux from the waste surface and to the distance that the contaminant can reach. Even though the mass flux from the waste into rock is lower than to the fracture because of lower porosity, the larger waste surface exposed to the rock matrix and the greater matrix sorption can result in greater release rate to the matrix. Radioactive decay enhances mass release from the cylinder. Mass transfer and transport from a cylindrical waste solid are studied in the cylindrical geometry by assuming molecular diffusion in the rock matrix parallel to, as well as perpendicular to the fracture, without advection. Transverse dispersion merges plumes released from individual waste forms in a repository. Neglecting radioactive-decay precursors results in overly optimistic estimates of concentration in the fracture in early times. For multiple more » parallel fractures, the single-fracture model is still applicable for moderate overlap of concentration fields inside the rock matrix. Though enhancing early-time transport, longitudinal dispersion in the fracture may be neglected for long-term evaluations by assuming greater advection and fracture apertures than actual values. Back diffusion is observed after the release period in the vicinity of the fracture entrance. Matrix diffusion and radioactive decay make contaminant stay within some distance away from the source releasing contaminant for a finite period of time.
Sorption and radioactive decay with no precursors are included. In the basic model, one-dimensional advection in a single planar fracture of infinite extent is coupled with diffusion in the rock matrix perpendicular to the fracture.
Comparison of the present cylindrical model with previous planar models, wherein contaminant was assumed to be released only into the fracture and diffusion in the rock matrix was assumed to be one-dimensional perpendicular to the fracture plane, shows that the cylindrical model is more conservative than the planar models with respect to the mass transfer from the source into the fracture and with respect to the far-field transport, provided that diffusion is dominant in the fracture.
Numerical results are shown for (1) the diffusive mass fluxes from the cylindrical waste solid into the fracture and into the rock matrix, (2) the diffusive mass flux across the rock/fracture interface, and (3) the instantaneous concentration isopleths in the fracture and in the rock matrix. The problem was first proposed and solved analytically by Chambre. In the paper are presented more » the derivation of an analytical solution for the time-dependent mass transfer from the cylinder for low-flow conditions and computer-code implementation and numerical results. The purposes of this study are (1) to predict the diffusive mass flux from a cylindrical waste solid into a planar fracture and the surrounding rock matrix for the low-flow conditions wherein near-field mass transfer is expected to be controlled by molecular diffusion and (2) to investigate the effects of cylindrical geometry and of multidimensional matrix diffusion including diffusion in the directions parallel to the fracture plane. This paper presents the numerical results of an analytical study for mass transfer and transport of radionuclides released from a cylindrical waste solid into water-saturated fractured porous rock.