  The flow of immiscible fluids inside a porous medium shows non-linearity in
the form of a power law in the rheological properties of the fluids under
steady state flow conditions. However, different experimental and numerical
studies have reported different values for the exponent related to this power
law. Here we explore how the rheological properties of the two-phase flow in
porous media depends on the distribution of the pore sizes and how it affects
the power-law exponent. The pore-size distribution controls fluctuation in the
pore radii and their density in a porous material. We present two approaches,
analytical calculations using a capillary bundle model and numerical
simulations using dynamic pore-network modeling. We observe crossover from a
non-linear to linear rheology when increasing the flow rate where the
non-linear part is highly affected by the pore-size distribution. We have also
carried out the study for different saturations of the two fluids.
