In this study, a new approach to estimate the effective permeability of the fracture network is proposed. New functional expressions are derived considering laminar fluid flow through fracture networks. Effective permeability of the fracture network is expressed as a function of topological connectivity, statistical branch segment length distributions, maximum, and minimum branch segment lengths. It is observed that the statistical cumulative branch segment length distribution of fracture networks can follow both fractal and multi-fractal patterns. Hence, analytical expressions of effective permeability are proposed considering both fractal and multi-fractal distribution of branch segment lengths. Obtained expressions are validated using numerical simulation results from past studies. It is observed from derived expressions that, effective permeability of fracture networks increases non-linearly with increasing topological connectivity and fractal dimensions of statistical branch segment length distributions. However, the non-linearity in the relationship is mainly governed by the scaling exponent and scaling coefficient of the fracture network. With increasing scaling exponent and scaling coefficient, non-linearity in the relation between effective permeability and topological connectivity increases. It is observed from the derived relation that, effective permeability of a fracture network is more sensitive to longer branch segments compared to the shorter branch segments. Effective permeability of fracture networks increases rapidly with increase in length of the branch segments. Hence it is interpreted, longer branch segments in fracture networks play a critical role in determining the effective permeability of the fractured reservoir.

在这项研究中，提出了一种估算裂缝网络有效渗透率的新方法。考虑到流过裂缝网络的层流，得出了新的函数表达式。裂缝网络的有效渗透率表示为拓扑连通性，统计分支段长度分布，最大和最小分支段长度的函数。可以看出，裂缝网络的统计累积分支段长度分布可以遵循分形和多分形模式。因此，提出了同时考虑分支段长度的分形和多分形分布的有效渗透率的解析表达式。使用过去研究的数值模拟结果对获得的表达式进行了验证。从派生表达式可以看出，裂缝网络的有效渗透率随着拓扑连通性和统计分支段长度分布的分形维数的增加而非线性增加。但是，关系中的非线性主要由裂缝网络的缩放指数和缩放系数决定。随着缩放指数和缩放系数的增加，有效渗透率和拓扑连接性之间的非线性关系增加。从推导的关系可以看出，与较短的分支段相比，裂缝网络的有效渗透率对较长的分支段更敏感。裂缝网络的有效渗透率随分支段长度的增加而迅速增加。因此，它被解释为