The fracture network in fractured coal is the main channel of coal seam gas flow. Not only the geometric topology properties (such as fractal characteristics) of a single fracture but also the connection topology properties (interconnection characteristics between fractures) of the fracture network have an important impact on the fluid flow in fracture networks. In this study, the connection topology properties of the fracture network in the fractured coal are explored based on the complex network theory for the first time. The property parameters such as the fracture node degree, the clustering coefficient, and the average path length are analyzed. It shows that the average clustering coefficient of the fracture network in fractured coal is larger, and the average path length is smaller. The connection property of the fracture network in the fractured coal presents a typical “small-world” clustering model. Further, by considering the fractal characteristics of the single fracture and the clustering characteristics of the fracture network, an improved clustered fractal discrete fracture network (DFN) model is developed. Then, based on the lattice Boltzmann method, the permeability properties of the generated clustered fractal DFNs are analyzed. The results show that the permeability of DFNs is positively correlated with the average clustering coefficient of fracture network, and negatively correlated with the fractal dimension of fracture. Therefore, the topological clustering characteristics of fracture networks and the fractal characteristics of fractures cannot be ignored in describing the fluid flow in the fracture network, and our clustered fractal DFN model provides a new idea for guiding the optimization design in DFN engineering.

裂隙煤中的裂隙网络是煤层瓦斯流动的主要通道。不仅单个裂缝的几何拓扑性质（如分形特征），而且裂缝网络的连接拓扑性质（裂缝之间的互连特征）对裂缝网络中的流体流动都有重要影响。本研究首次基于复杂网络理论探讨了裂隙煤中裂隙网络的连接拓扑特性。分析了断裂节点度、聚类系数、平均路径长度等属性参数。表明裂隙煤中裂隙网络的平均聚类系数较大，平均路径长度较小。裂隙煤中裂隙网络的连通特性呈现出典型的“小世界”聚类模型。进一步，考虑单裂缝的分形特征和裂缝网络的聚类特征，提出了改进的聚类分形离散裂缝网络（DFN）模型。然后，基于格子玻尔兹曼方法，分析了生成的聚类分形DFN的渗透特性。结果表明，DFNs的渗透率与裂缝网络的平均聚类系数呈正相关，与裂缝的分形维数呈负相关。因此，在描述裂缝网络中流体流动时，不能忽视裂缝网络的拓扑聚类特征和裂缝的分形特征，而聚类分形DFN模型为指导DFN工程的优化设计提供了新的思路。