Viscous Fingering in Correlated Site-Bond Square Lattice

A new porous media model with correlated sites-bonds has been
constructed. Taking into account both the pore and throat geometries, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF's structure varies with the correlation parameter ε and the viscous ratio M. The sweep efficiency E decreases along with the increase of the correlation parameter ε and the lattice size R_ls. The surface fractal D_s gradually increases as the correlation parameter ε increases, whatever the viscous ratio M is. Also, D_s gradually increases as M increases whatever ε is. These mean that not only the viscosity ratio but also the topology and the geometry of the porous media have a strong effect on the displacement process, the VF's structure, the sweep efficiency and the surface pattern.