From Multi-Porosity to Multiple-Scale Permeability Models of Natural Fractured Media

Classical dual-porosity models and homogenization approaches fail to represent the permeability scaling, the high flow channeling and the broad variability observed in natural fractured media. More critically, most modeling frameworks cannot restitute simultaneously the permeability increase with scale and the persistence of channeling. In fact, channeling enhances the impact of bottlenecks, reduces permeability, and increases permeability variability with scale. It is the case of percolation theory but also of more advanced large-range correlated theories including power-law scaling of some of the fracture properties including their length or their mutual distances.

More generally, we show with extensive numerical studies on 3D Discrete Fracture Networks (DFNs) that hydraulic behaviors come from a number of local and global fracture characteristics. The concept of effective properties like effective permeability itself appears quite weak and should be replaced by new modeling frameworks. We propose three alternative approaches combining the specificies of fracture flow and transport of DFNs and the simplicity of continuum approaches:

1- Discrete dual porosity media for high flow localization in a subset of the fracture network.

2- Structured Interacting Continua for highly organized diffusive processes in poorly connected fracture structures.

3- Multiple-scale permeability models for hierarchically structured fractured media with 3D concurrent fracture percolating networks.

These different approaches can be combined and specified with a limited number of parameters. They are also efficient in representing the potentially large hydraulic impact of minor modification of the fracture network geometry and local connectivity.