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首次利用重正化群方法对三维ＷａｒｅｎＲｏｏｔ模型进行了理论研究，求出其临界导通概率（Ｐｃ）值（０．０４２３）及单方向裂缝临界开启概率（Ｐｆｃ）值（７．１８‰），由此求出其分形维数（Ｄｆ）值（０．８７１）。通过对这些参数的分析，探讨了该模型的意义和适用范围，认为对于有裂缝的碳酸盐岩这样的双重介质系统而言：①只要基质岩块的导通概率超过Ｐｃ值，系统趋于整体连通，有较好的开发潜力；②Ｐｆｃ反映系统中开启裂缝所占比例，只要各方向裂缝开启概率大于Ｐｆｃ值，整个系统趋于导通；③Ｄｆ值较低，反映ＷａｒｅｎＲｏｏｔ模型中裂缝很发育，分形充满程度不高，说明该模型适用于裂缝非常发育地区的致密岩性储集层评价。图３参６（陈志宏摘）
For the first time, the renormalization group method is used to study the three-dimensional Waren-Root model, and its critical conduction probability (Pc) value (0.0423) and uni-directional fracture critical open probability (Pfc) value of 7.18 ‰ ), Thereby obtaining its fractal dimension (Df) value (0.871). Through the analysis of these parameters, the significance and scope of this model are discussed. It is considered that in the case of double media systems with fractured carbonate rocks, the system tends to be as long as the conduction probability of the matrix rock exceeds the Pc value The overall connectivity, there is a good potential for development; ② Pfc reflect the proportion of open cracks in the system, as long as the crack initiation probability in all directions is greater than the Pfc value, the entire system tends to conduct; ③ Df value is low, reflecting the Waren Root model cracks The results show that this model is suitable for the evaluation of tight lithologic reservoirs in areas with very developed fractures. Figure 3 reference 6 (Chen Zhihong pick)