JIN Y, GUO A Q, DONG J B,et al.Effects of fractal behavior on the permeability in regular self-similar porous media[J].Journal of Henan Polytechnic University(Natural Science) ,2026,45(3):133-142.

doi:10.16186/j.cnki.1673-9787.2023120057

Received:2023/12/09

Revised:2024/05/10

Published:2026/04/28

Effects of fractal behavior on the permeability in regular self-similar porous media

Jin Yi1,2,3, Guo Anqi1, Dong Jiabin1,2, Liu Dandan1, Zhao Jingyan1, Zheng Junling1, Wu Ying1

1.School of Resources and Environment， Henan Polytechnic University， Jiaozuo  454003， Henan， China；2.Henan Key Laboratory of Coal Measure Unconventional Resources Accumulation and Exploitation， Jiaozuo  454003， Henan， China；3.Collaborative Innovation Center of Coal Work Safety and Clean High Efficiency Utilization， Jiaozuo  454003， Henan， China

Abstract: Objectives To investigate the relationship between seepage behavior and the fractal topological structure of the pore spaces， the influence of fractal behavior on permeability was studied.  Methods Based on the fractal topological theory and the construction concept of the Sierpinski carpet， regular self-similar porous media and their series-parallel geometric models were constructed by combining the series-parallel relationships between multiple porous media. A permeability calculation model for regular self-similar porous media and series-parallel media was derived by integrating the particle diameter-permeability relationship in cylinder flow and the permeability scaling law.  Results For porous media in series， the overall permeability k satisfies k=1/(1/k₁×l₁/L+1/k₂×l₂/L） where the total length L=l₁+l₂， and the parameters of the two sub-segments are （k₁，l₁） and （k₂，l₂）； for the parallel case， the permeability model is k=1/（k₁×l₁+k₂×l₂）/L. In addition，there is a power relationship with an exponent of 2 between the scaling lacunarity P and the permeability， and the permeability of cylinder flow with a relative diameter of D/L satisfies k_l=0.14l²(1-D/L)^{2.784 4}.The calculated permeability errors between the second-order and third-order fractal iterations and the simulated values of porous media are 0.051 9 and 0.067 3， respectively； the errors for the V4S2L2Rd， V5S3L2Rd， V6S4L2Rd， and V6S2L2Rd models are -0.040 1， -0.079 1， -0.001 2， and -0.098 0， respectively， indicating that a more complex iterative structure leads to a larger error. Conclusions The permeability of regular fractal porous media can be calculated based on the above relationships and the scaling ratio between the original scale of the pore structure and the target scale.  Conclusions This provides a new idea and method for studying the heterogeneous seepage behavior of complex porous media.

Key words:fractal topological theory;porous media;permeability;flow resistance;series-parallel relationship