逾渗集团中的分形粘滞指进

The Fractal Viscous Fingering in Percolation Cluster

构造了具有不同逾渗概率的逾渗集团。在逾渗集团中,认为侯道半径分别服从 Rayleigh 分布和 Beta分布,采用超松驰技术,模拟了逾渗集团中的粘滞指进。计算了粘滞指进分维,结果表明,增加逾渗概率,降低粘滞比可增加指进的分维。在粘滞比趋于无穷的极限情形下,指进的分维和 DAL 的结果吻合。孔隙介质的几何拓扑很强地影响驱替过程和粘滞指进的结构。驱扫效率主要依赖网格的尺寸和粘滞比。

The Percolation clusters with varying occupy probability were constructed in this paper. Viscous fingering (VF) in percolation cluster, based on the assumption that bond radii are Rayleigh and Beta distribution, is investigated by means of successive over-relaxation technique. The fractal dimension for VF in percolation cluster is calculated. The result shows that it can increase fractal dimension of VF as increase of percolation probability or reduce of viscous ratio. VF’s fractal dimension of porous media in the limit viscous ratio →∞ is found to be identical with the DLA. We have found that the topology and the geometry of the porous medium has strong effect on the displacement processes and the structure of the VF. 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.