COMPUTER SIMULATION OF VISCOUS FINGERING IN SIERPINSKI CARPET
Tian Ju-ping (田巨平)a, Yao Kai-lun (姚凯伦)b
a Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China; Department of Basic Science, Jianghan Petroleum Institute, Jingzhou 434102, China; b International Center for Materials Physics, Academia Sinica, Shenyang 110015, China
Abstract A new method—mapping dilation method is proposed in this paper to construct Sierpinski carpet. Viscous fingering (VF) in Sierpinski carpet, based on the assumption that bond radii are beta distribution, is investigated by means of successive over-relaxation techniques. The topology and the geometry of the porous media have a strong effect on displacement processes. In the Sierpinski network, the VF pattern of porous media in the limit M→∞ is found to be similar to the diffusion-limited-aggregation pattern. The fractal dimension for VF in fractal space is calculated and the fractal dimension D can be reasonably regarded as a useful parameter to evaluate the sweep efficiencies and oil recoveries. We have also found that the geometry of the porous medium also has strong effects on the displacement processes and the structure of the VF. Moreover, we find that the sweep efficiency of the displacement processes mainly depends upon the length of the network system and also on the viscosity ratio M. This shows that the current method can be used to solve VF problems in complex structures if the structures are self-similar, or they can be reduced to a self-similar structure.
Received: 12 December 1997
Accepted manuscript online:
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