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在二次采油和三次采油中都存在一种粘性指进现象，它对采收率有很大影响。本工作 设计了一台改进型Ｈｅｌｅ－Ｓｈａｗ Ｃｅｌｌ模型，能模拟采油过程中的这种指进现象，它和油田开采有许多 类似之处。应用分维几何的基本原理，以排出率（Ｓｅ）为目标函数，对随机的复杂的分枝形状图形进行 了数学处理，研究了时间（ｔ）和 Ｓｅ的分枝数目（Ｎ）的影响．结论是在该条件下，分枝数的变化率 （ｄＮ／ｄｔ）对Ｓｅ的影响很大，在粘性指进发展的前、中期，Ｓｅ与 ｔ的关系可用一个数学公式描述： Ｓｅ＝ ０．６０８＋ －０． １６ｔ~０.２４，这一结论对研究聚合物驱油机理，提高采收率有一定的意义。
In both secondary and tertiary recovery, there is a viscous fingering phenomenon that has a significant impact on recovery. In this work, an improved Hele-Shaw Cell model was designed to simulate this fingering in the oil recovery process. It has many similarities with oilfield development. By applying the basic principle of fractal geometry and taking the discharge rate (Se) as the objective function, the random and complicated branch shapes are mathematically treated, and the influence of time (t) and the number of branches (N) of Se is studied. The conclusion is that under this condition, the rate of change of branch number (dN / dt) has a great influence on Se. Before and during the development of viscosity index, the relationship between Se and t can be described by a mathematical formula: Se = 0. 608 + -0. 16t ~ 0.24. This conclusion is of great significance for studying the mechanism of polymer flooding and enhancing oil recovery.