##
Modelling flow and transport in a granitic rock, with focus on the sub metre scale

##### Abstract:

Radionuclide migration in a fractured granitic rock is controlled by a combination of processes, both macroscopic and microscopic. All of these need to be addressed when the safety aspects of high-level radioactive waste repositories are considered. On the repository scale, say 1 km, numerical models have been developed and applied over the last few decades. However, it has been argued that it is the conditions in near field of a deposition hole that are the most critical; a few metres away from the deposition hole it is harder to evaluate if a fast connection to a major fracture or fault is present. This has led to studies of the rock matrix. These studies are mostly experimental and mathematical/numerical models seem to be less applied on the matrix scale.The objective of present project is to develop a conceptual, mathematical and numerical model of flow and transport in a granitic rock matrix and then demonstrate its potential by applying the model to generic but realistic cases.

An illustration of the fracture system on the mm scale is given by Figure 1; the fracture system seen is due to “the high porosity region between grains”. Migration due to advection and diffusion is hence assumed to be due to this system. The length scale of the grains, say 2-3 mm, defines the length scale of the system. Above this length scale one expects a fracture network with a continuous range of length scales. Here we will assume that a power law applies for these length scales.

The key points in the conceptual fracture model are summarized by the following points:

- A “traditional” Discrete Fracture Network (DFN) model is assumed for fractures down to a length scale of 5 mm.
- A grain size DFN (DFN
_{gs}), with the length scale interval 4-5 mm, will represent the high porosity regions between grains. - Fractures smaller than 4 mm are represented as immobile volumes and modelled by the multi rate diffusion model.

The model is tuned to fit four basic cases: permeability of rock samples, through diffusion experiments, dispersion from a point source and the break-through-curve. Resolving the fracture networks, requires computational cells of a scale of 1 mm or smaller. In 3D simulations the total number of cells is then typically 50-100 million cells.

*Figure 1.** Grain size fractures. **The photos cover an area of 2.5 x 2.5 mm.*