COMPUTER SIMULATION OF VISCOUS FINGERING IN SIERPINSKI CARPET

• 来源期刊: 物理学报（海外版）（英文版）
• 学科: 物理学
• 关键词: SIERPINSKI CARPET Sierpinski carpet fractal dimension D porous media sweep efficiency porous medium new method
• 年，卷（期）: 1998,（9）
• 页码范围: 681-687
• 页数: 7页
• 分类号: O4
• 语种: 英文

摘要

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.