Two-phase flow in correlated pore-throat random porous media
Tian Ju-Ping (田巨平)a, Yao Kai-Lun (姚凯伦)b
a Department of Physics, Wuhan Institute of Science and Technology, Wuhan 430073, China; b Department of Physics Huazhong University of Science and Technology, Wuhan 430074, China; CCAST (World Laboratory), Beijing 100080, Chinab International Center for Material Physics, Chinese Academy Science, Shenyang 110015, China
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 Ninv(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 Lnz. E has a minimum as Lnz increases up to the maximum no matter what the values of P, M and $\varepsilon$. The E～Lnz 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.
Received: 10 June 2001
Revised: 09 December 2001
Accepted manuscript online:
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