Numerical and analytical modeling of flow partitioning in partially
saturated fracture networks.
Abstract
Infiltration processes in fractured-porous media remain a crucial, yet
not very well understood component of recharge and vulnerability
assessment. Under partially-saturated conditions flows in fractures,
percolating fracture networks and fault zones contribute to the fastest
spectrum of infiltration velocities via preferential pathways.
Specifically, the partitioning dynamics at fracture intersections
determine the magnitude of flow fragmentation into vertical and
horizontal components and hence the bulk flow velocity and dispersion of
fracture networks. In this work we derive an analytical solution for the
partitioning processes based on smoothed particle hydrodynamics
simulations and laboratory studies. The developed transfer function
allows to efficiently simulate flow through arbitrary long wide aperture
fracture networks with simple cubic structure via linear response theory
and convolution of a given input signal. We derive a non-dimensional
bulk flow velocity ($\widetilde{v}$) and dispersion
coefficient ($\widetilde{D}$) to characterize the
system in terms of dimensionless horizontal and vertical time scales
$\tau_m$ and $\tau_0$. The
dispersion coefficient is shown to strongly depend on the horizontal
time scale and converges towards a constant value of $0.08$ within
reasonable ranges for the fluid and geometrical parameters, while the
non-dimensional velocity exhibits a characteristic
$\widetilde{v} \sim
\tau_m^{-1/2}$ scaling. Given that hydraulic
information is often only available at limited places within
(fractured-porous) aquifer system, such as boreholes or springs, our
study intends to provide a rudimentary analytical concept to potentially
reconstruct internal fracture network geometries from external boundary
information, e.g., the dispersive properties of discharge (groundwater
level fluctuations).