Radionuclide response functions for the convection-dispersion equation from a point source along the axis of nested cylindrical media

In this report we develop response functions for the mass transport of radionuclides from a small pinhole-sized defect in a waste container located in a cylindrical disposal room. The disposal rooms are considered to be Idled with buffer and backfill materials composed of mixtures of clay and sand or crushed rock. Mass transport of radionuclides released gradually into the room by diffusion through a pinhole can be determined by convolution with the response functions. A model based on the boundary-integral method (BIM) is described here. In this model the room is represented by three coaxial cylinders comprised of buffer, backfill and excavation damage zone, surrounded by the sparsely fractured rock. The main result of the model is the flux integrated over the surface of the excavation damage zone which can serve as the input into a model representing the surrounding geosphere. The integrated flux obtained from the BIM model is compared with the integrated flux obtained from the finite-element code called MOTIF (Chan et al. 1987). The finite-element model consists of coaxial rectangular regions that have the same volume as the respective cylinders in the BIM model. Sample numerical calculations are shown for 129I which is one of longest lived and most readily Teachable radionuclides that would be released from a failed container. The two models give identical results in the absence of groundwater flow, and almost identical results for a range of small groundwater velocities. For very large groundwater velocities the BIM model is conservative (it gives higher integrated fluxes than the MOTIF model), except when the source is near the end of the room towards which the flow is directed. (author)