To date, the complexity of fractured porous media still precludes the direct
incorporation of small-scale features into field-scale modelling. These features,
however, can be instrumental in shaping and triggering coarsening
instabilities and other forms of emergent behaviour which need to be considered
on the field-scale. Here we develop numerical simulation methods
for this purpose and demonstrate their improved performance in single-and
two-phase flow simulations with models of fractured porous media.
Material discontinuities in fractured porous media strongly influence single-and
multi-phase fluid flow. When continuum methods are used to model
transport across such interfaces, they smear out jump discontinuities of concentration
or saturation. To overcome this drawback, we “explode” hybrid
finite-element node-centred finite-volume models along these introducing
complementary finite-volumes along the material interfaces. With this embedded
discontinuity discretization we develop a transport scheme that realistically
represents the dependent variable discontinuities arising at these
interfaces. The main advantage of this new scheme is its ability to honour
the flow effects that we know that these discontinuities have in physical
experiments.
We have also developed a new time-stepping control scheme for the transport
equation. It allows the user to specify the volume fraction of the model
in which he/she is prepared to relax the CFL condition. This scheme is applied
in a study of the impact of fracture pattern development on solute
transport. These two-dimensional simulations quantify the effect of the
fractures on macro-scale dispersion in geomechanically generated fracture
geometries, as opposed to stochastically generated ones. Among other insights,
the results indicate that fracture density, fracture spacing, and the
fracture-matrix flux ratio control anomalous mass transport in such media.
We also find that it is crucial to embed discontinuities into large-scale
models of heterogeneous porous media.