Modeling two-phase flow in heterogeneous porous media: part 1, the case
of low interfacial tension
A fractional flow formulation is proposed to model two-phase flow in
heterogenous porous media in the case of low interfacial tension. The
proposed formulation overcomes the limitations of the fractional flow
approach that arise from saturation discontinuity. The total velocity is
calculated with two terms. A total mobility term multiplied by the
non-wetting phase potential which is a smooth term over the
computational domain. The second term is the buoyancy term that
represents the density contrast between the two phases. The proposed
formulation is verified with the Buckely--Leverett analytical solution.
Two other numerical examples are presented in 2D and in 3D. The examples
show the applicability of the model in anisotropic and in heterogenous
porous media and demonstrate the low mesh dependency of the model.