Diffusion in the rock matrix: An important factor in radionuclide retardation?

Abstract

This paper discusses migration of radionuclides in the bedrock surrounding a repository. Currently available models use either a surface reaction or a bulk reaction concept to describe the retardation of migrating nuclides. The first model assumes that the nuclide reacts only with the surface of the fissures. This implies that the rock matrix is not utilized as a sink. The other model implies that the whole bulk of the rock is accessible to the nuclides. The paper analyzes the accessibility of the rock matrix to the radio‐nuclides. The transport mechanisms are shown to be flow of water and nuclides in the fissures and transport of nuclides from the water in the fissures into water in the microfissures of the rock by pore diffusion. The diffusion of the nuclides into the rock matrix and their sorption onto the surfaces of the microfissures are the main mechanisms retarding migration from a repository. The diffusivity of the nuclide may be as important as its sorption equilibrium constant. Diffusivities in the pores and microfissures in such dense rocks as granite under confining pressure of hundreds of bars can be expected to be 6–20% of the diffusivity in water. These data are obtained from electrical resistivity measurements of saltwater‐filled granites. Porosity of such granites varies from 0.4 to 0.9%. The apparent diffusivities in the granites will then vary between 0.25 · 10−12/Kdρp and 10 · 10−12/Kdρp m2/s, where Kdρp is the volume equilibrium constant. This varies from the porosity of the rock for nonsorbing species to up to and over 104. For a 100‐year contact time a nonsorbing nuclide can be expected to penetrate tens of meters of the rock matrix and a strongly sorbing nuclide with Kdρp larger than 104 will penetrate a few millimeters. The diffusion into the rock matrix can enhance the retardation by many orders of magnitude as compared to retardation by surface reaction in fissures only. The retardation may, on the other hand, be many orders of magnitude smaller than the maximum value that could be obtained if all the rock matrix were accessible. This depends very much on the fissure widths and spacings.

Field investigation into unsaturated flow and transport in a fault: model analyses

“…Matrix diffusion has been identified as a key mechanism for retarding the radionuclide transport in both unsaturated and saturated fractured rock (e.g., Bodvarsson et al, 2001;Neretnieks, 1980Neretnieks, , 2002. The enhancement of the fracture (fault) -matrix interface area (or effective matrix-diffusion coefficient) seems to be common for matching field-scale solute transport observations, as suggested by this study and previous studies (Shapiro, 2001;Neretnieks, 2002;Liu et al, 2003a).…”

“…While effects of matrix diffusion on solute transport in saturated fractured rocks have been intensively investigated (e.g., Neretnieks, 1980Neretnieks, , 2002Moreno et al, 1997;Ostensen, 1998;Jardine et al, 1999;Shapiro, 2001;McKenna et al, 2001;Meigs and Beauheim, 2001), studies of these effects in unsaturated fractured rock are relatively limited in the literature. Compared with saturated systems, the effects of matrix diffusion in unsaturated systems are more complex, owing to the involved multiphase flow processes and the corresponding fracture-matrix interaction mechanisms.…”

Strategy for experimental validation of waste package performance assessment

“…For very large fracture spacings (i.e., where matrix diffusion between fractures do not interact), Neretnieks [178] derived the following solution to the coupled differential equations: Note that because the flow equations for unsaturated flw are non-linear, they are not subject to a simple solution analogous to Eq. 9 [181].…”

“…5, no distinction is made between adsorption and ion-exchange. Using the above relationships, Neretnieks [178] set up differential equations describing the conservation of mass during fracture flow and matrix diffusion of radionuclides with additional provision for nuclide decay.…”

Modeling conservative tracer transport in fracture networks with a hybrid approach based on the Boltzmann transport equation

“…Although transport in fractured rock often involves more complicated retardation processes such as diffusive exchanges with the rock matrix [Neretnieks, 1980], investigation of conservative tracer transport is the logical starting point for evaluating new approaches to transport models.…”