Solution and upscaling of compositional and immiscible displacements in composite media

The scale of heterogeneities in reservoirs is often smaller than the grid s ize used in large-scale reservoir simulations. Relative permeabilities have the foremost effect on fluid flow and small-scale fractional flow must be upscaled to the,grid size in flow simulations. Thus, systems with fractiona l flow heterogeneities, i.e. relative permeability variations, have to be s olved and effective relative permeability functions determined. In this pap er, benchmark analytical solutions are developed for a system consisting of two media in series where each medium is characterized with a different se t of relative permeabilities, residual saturations and porosities. The anal ytical solutions show a significant discontinuity in the saturation and con centration profiles at the interface of the two media. Numerical results us ing several weighting schemes are compared against the analytical solutions for two-phase immiscible and partially miscible systems. It is shown that single-point upstream weighting requires about 100 grid blocks to capture t he discontinuity at the interface, whereas third-order TVD weighting requir es much fewer. Lastly, the validity of the JBN method and harmonic averagin g for determination of effective relative permeabilities and overall pressu re drop is tested. Both the JBN method and harmonic averaging cannot reprod uce the pressure drop across the composite media prior to water breakthroug h.