  We perform more than 6000 steady-state simulations with a dynamic pore
network model, corresponding to a large span in viscosity ratios and capillary
numbers. From these simulations, dimensionless quantities such as relative
permeabilities, residual saturations, mobility ratios and fractional flows are
computed. Relative permeabilities and residual saturations show many of the
same qualitative features observed in other experimental and modeling studies.
However, while other studies find that relative permeabilities converge to
straight lines at high capillary numbers we find that this is not the case when
viscosity ratios are different from 1. Our conclusion is that departure from
straight lines occurs when fluids mix rather than form decoupled flow channels.
Another consequence of the mixing is that computed fractional flow curves,
plotted against saturation, lie closer to the diagonal than they would
otherwise do. At lower capillary numbers, fractional flow curves have a
classical S-shape. Ratios of average mobility to their high-capillary number
limit values are also considered. These vary, roughly, between 0 and 1,
although values larger than 1 are also observed. For a given saturation and
viscosity ratio, the mobilities are not always monotonically increasing with
the pressure gradient. While increasing the pressure gradient mobilizes more
fluid and activates more flow paths, when the mobilized fluid is more viscous,
a reduction in average mobility may occur.

Fluid Dynamics;Computational Physics