Invasion percolation between two wells in continuous media

Invasion percolation between two wells was studied in continuous media consisted of overlapping disks and spheres. The invasion percolation between injection and extraction wells occurs when a fluid injected through the injection well invades less pressurized neighboring pores until it reaches the extraction well. Attention was paid to whether the probability distribution of the invading mass m and the fractal dimension of the clusters of invaded pore particles remain similar to those of the lattice model. Our results indicated that the power α characterizing the probability distribution via P(m) ∝m −α was considerably larger than that of the lattice model for a reduced volume density η = η c of pore particles, η c being the percolation critical density, and that it converged to the value for the lattice model for p e = 0 as η was increased, where p e is the pressure of an extraction site for the lattice model. The fractal dimension of the invaded clusters was found to be similar to that of the ordinary lattice percolation clusters generated at the percolation threshold. The scaling of the invaded clusters was also examined, and it held in both two and three dimensions.