Simulations are presented for two-dimensional Eden growth into fractal networks. We find that the fractal dimension of the Eden cluster, d,, does not have a simple behavior when the cluster grows into the structure of a fractal network. We also find that d, depends strongly on the minimal path between two arbitrary points in the network backbone and on the number of paths that appear between these two points at each scale.
One of the most important topics in the study of processes of oil recovery is the displacement of fluids in porous media and in particular the capillary displacement process. The Eden model [l] is the simplest description for this class of processes. It is a good method to simulate capillary displacement processes when the pores are all of the same size. Porous media have a self-similar structure (pore surface and volume), for a range of scales [2-41. In this paper we model the porous medium using percolating and regular fractals. In this form, we can analyze the dependence of the fractal dimension of the Eden cluster, EC, on the fractal structure of the media. In particular, we study the case when the native fluid is fully incompressible and therefore trapping zones appear during the displacement process [5].
In 1985 Family and Vicsek, and Bunde et al. [6-81, studied the case when the native fluid is fully compressible using a spreading percolation method. They found that the fractal dimension of the Eden cluster coincides with the value of the fractal dimension of the percolating cluster.
In 1987 Oxaal et al.
[9] performed computer simulations on percolating clusters at the percolation threshold p, using the Eden model, for the fully incompressible case, and obtained fractal Eden clusters (d, = 1.5). Using the same percolating clusters they constructed micromodels of porous media and performed experiments of displacement of fluids into it. They obtained that the experimental results agree completely with the Eden simulations at very low flow rates.
Meir and Aharony (MA) [lo] in 1989 obtained analytically, for the fully incompressible case, that the fractal dimension of the EC, d,, depends on the