Viscous fingering in fractured porous media

The effect of heterogeneities induced by highly permeable fracture
networks on viscous miscible fingering in porous media is examined using
high-resolution numerical simulations. We consider the planar injection of a
less viscous fluid into a two-dimensional fractured porous medium which is
saturated with a more viscous fluid. This problem contains two sets of
fundamentally different preferential flow regimes; the first is caused by the
viscous fingering and the second is due to the permeability contrasts between
the fractures and rock matrix. We study the transition from a regime where the
flow is dominated by the viscous instabilities, to a regime where the
heterogeneities induced by the fractures define the flow paths. We find that
fractures greatly affect the viscous fingering, even for small permeability
differences between the rock matrix and the fractures. The interaction between
the viscosity contrast and permeability contrast causes channeling of the less
viscous fluid through the fractures and back to the rock. This channeling
stabilizes the displacement front in the rock matrix, and the viscous fingering
ceases for the higher permeability contrast. Several different fracture
geometries are considered, and we observe a complex interplay between the
geometries and unstable flow. While we find that the most important
dimensionless number determining the effect of the fracture network is a
weighted ratio of the permeability of the fractures and the permeability of the
rock matrix, the exact point for the cross-over regime is highly dependent on
the geometry of the fracture network.