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We perform more than 6000 steady-state simulations with a dynamic porenetwork model, corresponding to a large span in viscosity ratios and capillarynumbers. From these simulations, dimensionless quantities such as relativepermeabilities, residual saturations, mobility ratios and fractional flows arecomputed. Relative permeabilities and residual saturations show many of thesame qualitative features observed in other experimental and modeling studies.However, while other studies find that relative permeabilities converge tostraight lines at high capillary numbers we find that this is not the case whenviscosity ratios are different from 1. Our conclusion is that departure fromstraight 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 wouldotherwise do. At lower capillary numbers, fractional flow curves have aclassical S-shape. Ratios of average mobility to their high-capillary numberlimit values are also considered. These vary, roughly, between 0 and 1,although values larger than 1 are also observed. For a given saturation andviscosity ratio, the mobilities are not always monotonically increasing withthe pressure gradient. While increasing the pressure gradient mobilizes morefluid and activates more flow paths, when the mobilized fluid is more viscous,a reduction in average mobility may occur.

Pore network modeling of the effects of viscosity ratio and pressure gradient on steady-state incompressible two-phase flow in porous media