The main aim of this paper is to reveal effects of fractal features on the formation factors associated with different transport processes in scale invariant pore-fracture networks. Accordingly, we explore a class of deterministic infinitely ramified networks associated with pre-fractal standard Sierpinski carpets (including Sierpinski cubes and inverse Menger sponges). The focus is placed on the effects of network ramification, connectivity, and loopiness on the transport streamline constriction and tortuosity of transmission paths. The differences between the formation factors associated with the diffusibility, electrical conductivity, and hydraulic permeability are elucidated. Explicit expressions for the constrictivity and formation factors of deterministic pre-fractal networks are derived. In this regard, we stress that the electrical formation factor obeys the Archie law only if the random walk in the pre-fractal pore-fracture network is recurrent. We also note that the Archie's exponent can be either equal to, or less than the power-law exponent characterizing the scaling behavior of diffusibility. The notion of the structural formation factor is introduced. The values of scaling exponents characterizing the formation factors associated with different transport properties of the model networks are found to be within the ranges of field observations.

本文的主要目的是揭示分形特征对尺度不变孔隙-裂缝网络中与不同输运过程相关的形成因素的影响。因此，我们探索了一类与前分形标准谢尔宾斯基地毯（包括谢尔宾斯基立方体和逆门格尔海绵）相关的确定性无限分支网络。重点放在网络分枝、连接性和循环性对传输流线压缩和传输路径曲折的影响。阐明了与扩散性、电导率和水力渗透率相关的地层因素之间的差异。导出了确定性前分形网络的收缩性和形成因子的显式表达式。在这方面，我们强调，只有当分形前孔隙裂缝网络中的随机游走是循环的时，电形成因子才符合 Archie 定律。我们还注意到，Archie 的指数可以等于或小于表征扩散性缩放行为的幂律指数。引入结构形成因子​​的概念。发现表征与模型网络的不同传输特性相关的形成因素的比例指数值在现场观测的范围内。引入结构形成因子​​的概念。发现表征与模型网络的不同传输特性相关的形成因素的比例指数值在现场观测的范围内。引入结构形成因子​​的概念。发现表征与模型网络的不同传输特性相关的形成因素的比例指数值在现场观测的范围内。