河南理工大学学报（自然科学版）2026，Vol.45Issue(3)：133-142,10.DOI:10.16186/j.cnki.1673-9787.2023120057
规则自相似多孔介质中分形行为对渗透率的影响
Effects of fractal behavior on the permeability in regular self-similar porous media
摘要
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 po-rous media and series-parallel media was derived by integrating the particle diameter-permeability relation-ship in cylinder flow and the permeability scaling law.Results For porous media in series,the overall per-meability 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 kl=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,re-spectively,indicating that a more complex iterative structure leads to a larger error.Conclusions The perme-ability of regular fractal porous media can be calculated based on the above relationships and the scaling ra-tio 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.关键词
分形拓扑理论/多孔介质/渗透率/流阻/串并联关系Key words
fractal topological theory/porous media/permeability/flow resistance/series-parallel relation-ship分类
数理科学引用本文复制引用
金毅,郭安琪,董佳斌,刘丹丹,赵静妍,郑军领,吴影..规则自相似多孔介质中分形行为对渗透率的影响[J].河南理工大学学报（自然科学版）,2026,45(3):133-142,10.基金项目
国家自然科学基金资助项目(41972175,42502167) （41972175,42502167）
河南省高校科技创新团队项目(21IRTSTHN007) （21IRTSTHN007）
河南省高校基本科研业务费专项项目(NSFRF220204,NSFRF220427) （NSFRF220204,NSFRF220427）
