Two-phase flow in correlated pore-throat random porous media

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 epsilon, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter e, 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 epsilon. 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 epsilon. For a smaller epsilon, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter e and the increase of the network size L-nz. E has a minimum as L increases up to the maximum no matter what the values of P, M and epsilon. The E similar to 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.