Abstract: We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, 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 structure varies with the correlation parameter $\varepsilon$, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter $\varepsilon$, the greater the deviation of the normalized size distribution of the invaded throat N_inv(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter ε. The velocity distribution $f(\alpha)$ of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large $\alpha$) is longer for a larger correlation parameter $\varepsilon$. For a smaller $\varepsilon$, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter $\varepsilon$ and the increase of the network size L_nz. E has a minimum as L_nz increases up to the maximum no matter what the values of P, M and $\varepsilon$. The E～L_nz curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.

Key words: correlation parameter, fractal dimension, sweep efficiency, scaling function