Relation between pressure and fractional flow in two-phase flow in porous media

We study average flow properties in porous media using a two-dimensional network simulator. It models the dynamics of two-phase immiscible bulk flow where film flow can be neglected. The boundary conditions are biperiodic, which provide a means of studying steady-state flow where complex bubble dynamics dominate the flow picture. We find fractional flow curves and corresponding pressure curves for different capillary numbers. In particular, we study the case of the two phases having equal viscosity. In this case we find that the derivative of the fractional flow with respect to saturation is related to the global pressure drop. This result can also be expressed in terms of relative permeabilities or mobilities, resulting in an equation tying together the mobilities of the two phases.