Pattern Structure and Properties of Invasion Percolation in Porous Media

The percolation clusters with varying occupy probability are constructed. Invasion percolation (IP) in percolation cluster is investigated by means of IP algorithm without trapping. The pattern constructions of IP in percolation clusters are obviously different from that of viscous fingering (VF) in percolation clusters. The fractal dimension D_f of IP increases with the increase of the percolation probability P. The geometry and the topology of the porous media have strong effects on the pattern structure of IP. For large M (the node numbers occupied by the injected fluid), the rescaled value is R_g/M^1/D_f, which asymptotically approaches a constant value, and R_g is the gyration radius of IP cluster. Moreover, the chemical dimension D_l and the shortest path exponent d_min are obtained.