Flow equations on a fractal structure

Two-phase flow equations are solved on a fractal Bernasconi lattice including capillary and viscous forces. The recursive structure of the lattice allows the use of a renormalization group approach to calculate flow properties, resulting in a much faster method compared to conventional simulations. The interplay between disorder or heterogeneity in local flow conductance and capillary pressure effects is studied as a function of length scale. Flow related quantities such as water cut curves, saturation profiles, and breakthrough times are found to depend on the size of the system and on disorder strength. As disorder increases larger sizes are needed to get good averaging. It is found that this lattice can be used to get a good approximated solution of the two-phase flow equations in complex anisotropic structures, since it grants considering the effect of anisotropy on flow properties, a condition relevant for a variety of industrial applications.