Linking flow and structure in heterogenous porous and karstic networks

The sound quantification of the flow distribution in heterogenous groundwater systems is
a cornerstone for the prediction of solute dispersion and solute travel times with implications
for the assessment of the vulnerability and management of groundwater resources.  
A broad distribution of flow velocities leads to a broad distribution of mass transfer times,
which is at the root of non-Fickian transport features such as strong tailings of solute breakthrough curves.
The relation between the medium structure and the distribution of flow rates and flow velocities
is a missing link that would allow to estimate solute dispersion directly from the hydraulic medium
properties. While the structure-flow relation is well known for simple stratified
and composite medium geometries, it remains an open question for flow in heterogeneous pore,
fracture and karst networks. To decipher this relation, we analyze flow rate and velocity statistics
across heterogeneous networks of different connectivities and conductance distributions. We quantify
the average flow in terms of the effective conductivity and the full statistics in terms of the
probability density function of flow rates and flow velocities, which are the key quantities for
the prediction of solute transport. The analysis of the conditional flow statistics reveals that
flow in random networks is organized in distinct substructures of different hydraulic
behaviors. These structures can be delineated using percolation theory. The flow distribution can
then be quantified by the interaction between these structures using a random aggregation approach.