A Steady-State Approach to Upscale relative Permeabilities and it's Application in 2D

We present a model for efficient direct upscaling of two-phase relative permeabilities by solving a series of steady state, two-phase problems. The developed numerical model simulates steadystate multiphase flow in 2 and 3D in heterogeneous reservoirs with account for viscous, capillary and gravity forces at a given external pressure drop. It is used to compute effective properties for a synthetic heterogeneous reservoir. The presented examples show the dependence of effective relative permeabilities and residual oil saturation on the magnitude of the pressure drop applied to the boundaries of the flow domain. The convergence of the effective relative permeabilities towards the viscous limit functions is analyzed in 1 and 2D.