Invasion percolation in correlated porous media

Correlated 2-D porous structure models are generated using fractional Brownian motion (fBm) and invasion percolation simulations are applied on these lattices to investigate the influences of existing correlations on the structural properties of percolation clusters. It is found that as the fractal dimension of an fBm lattice decreases, the cluster gets more compact but a similar displacement pattern is followed for all lattices with different fractal dimensions. The fractal dimension of the displacement front decreases with decreasing fractal dimension as well. The results also show that the dynamics of the invasion process depends on the fractal dimension of the fBm lattice. This dependency is clarified.