Flux-dependent percolation transition in immiscible two-phase flows in porous media

Using numerical simulations, we study immiscible two-phase flow in a pore network reconstructed from Berea sandstone under flow conditions that are statistically invariant under translation. Under such conditions, the flow is a state function which is not dependent on initial conditions. We find a second-order phase transition resembling the phase inversion transition found in emulsions. The flow regimes under consideration are those of low surface tension-hence high capillary numbers Ca-where viscous forces dominate. Nevertheless, capillary forces are imminent, we observe a critical stage in saturation where the transition takes place. We determine polydispersity critical exponent tau=2.27 +/- 0.08 and find that the critical saturation depends on how fast the fluids flow.