Linear Response Concept Combining Advection and Limited Rock Matrix Diffusion in a Fracture Network Transport Model

Abstract

This paper presents the conceptual and mathematical basis of a model for transport of nuclides in the geosphere between the near field of a radioactive waste repository and high‐conductivity fractures that are assumed to be closely connected to the biosphere. The geosphere is modeled as a network of fractures that are mapped onto a network of channels. The balance equations and boundary conditions on the scale of a single rectangular channel are given. The effects of one‐dimensional matrix diffusion in addition to advection, linear sorption in the fractures and the rock matrix, and radioactive decay are considered. A hierarchical linear response concept using Laplace transformation techniques is developed for solution of the balance equations (1) on the scale of a channel network, (2) in the individual channels, and (3) in the rock matrix adjacent to the channels. Examples with unlimited and limited matrix diffusion and for additional rock layers are discussed.