Multiscale smoothed particle hydrodynamics model development for
simulating preferential flow dynamics in fractured porous media
Abstract
We present our new multiscale pairwise-force smoothed particle
hydrodynamics (PF-SPH) model for the characterization of flow in
fractured porous media. The fully coupled multiscale PF-SPH model is
able to simulate flow dynamics in a porous and permeable matrix and in
adjacent fractures. Porous medium flow is governed by the
volume-effective Richards equation, while the flow in fractures is
governed by the Navier–Stokes equation. Flow from a fracture to the
porous matrix is modeled by an efficient particle removal algorithm and
a virtual water redistribution formulation to enforce mass and momentum
conservation. The model is validated by (1) comparison to a finite
element model (FEM) COMSOL for Richards-based flow dynamics in a
partially saturated medium and (2) laboratory experiments to cover more
complex cases of free-surface flow dynamics and imbibition into the
porous matrix. For the laboratory experiments, Seeberger sandstone is
used because of its well-known homogeneous pore space properties. The
saturated hydraulic conductivity of the permeable matrix is estimated
from a pore size and grain size distribution analysis. The developed
PF-SPH model shows good correlation with the COMSOL model and all types
of laboratory experiments. We employ the proposed model to study
preferential flow dynamics for different infiltration rates. Here, flow
in fracture is associated with the term “preferential flow”, providing
rapid water transmission, while flow within the adjacent porous matrix
enables only slow and diffuse water transmission. Depending on the
infiltration rate and water inlet location, two cases can be
distinguished: (1) immediate preferential/fracture flow or (2) delayed
preferential flow. In the latter case, water accumulates at the surface
first (ponding), then the fracture rapidly transmits water to the bottom
system outlet. For the immediate fracture flow response, ponding only
occurs once the fracture is fully saturated with water. In all cases,
preferential flow is much more rapid than diffuse flow even under
saturated porous medium conditions. Furthermore, infiltration dynamics
in rough fractures adjacent to an impermeable or permeable matrix for
different infiltration rates are studied as well. The simulation results
show a significant lag in arrival times for small infiltration rates
when a permeable porous matrix is employed, rather than an impermeable
one. For higher infiltration rates, water rapidly flows through the
fracture to the system outlet without any significant delay in arrival
times even in the presence of the permeable matrix. The analysis of the
amount of water stored in permeable fracture walls and in a fracture
void space shows that for small infiltration rates, most of the injected
water is retarded within the porous matrix. Flow velocity is higher for
large infiltration rates, such that most of the water flows rapidly to
the bottom of the fracture with very little influence of matrix
imbibition process