Abstract
Fractional À ow of immiscible phases occurs at the pore
scale where grain surfaces and phases interfaces obstruct
phase mobility. However, the larger scale behavior is
described by a saturation-dependent phenomenological
relationship called relative permeability. As a consequence,
pore-scale parameters, such as phase topology and/
or geometry, and details of the À ow regime cannot be
directly related to Darcy-scale À ow parameters. It is well
understood that relative permeability is not a unique
relationship of wetting-phase saturation and rather depends
on the experimental conditions at which it is measured.
Herein we use fast X-ray microcomputed tomography to
image pore-scale phase arrangements during fractional
À ow and then forward simulate the À ow regimes using
the lattice-Boltzmann method to better understand the
underlying pore-scale À ow regimes and their inÀ uence on
Darcy-scale parameters. We ¿ nd that relative permeability
is highly dependent on capillary number and that the Corey
model ¿ ts the observed trends. At the pore scale, while
phase topologies are continuously changing on the scale of
individual pores, the Euler characteristic of the nonwetting
phase (NWP) averaged over a suf¿ ciently large ¿ eld of
view can describe the bulk topological characteristics; the
Euler characteristic decreases with increasing capillary
number resulting in an increase in relative permeability.
Lastly, we quantify the fraction of NWP that À ows through
disconnected ganglion dynamics and demonstrate that
this can be a signi¿ cant fraction of the NWP À ux for
intermediate wetting-phase saturation. Rate dependencies
occur in our homogenous sample (without capillary end
effect) and the underlying cause is attributed to ganglion
À ow that can signi¿ cantly inÀ uence phase topology during
the fractional À ow of immiscible phases.
