金毅, 黄欢, 宋慧波,等.分形毛细管束中溶质对流-扩散传质行为研究[J].河南理工大学学报（自然科学版）,2025,44(4):124-133.

JIN Y, HUANG H, SONG H B, et al. Advection-diffusion mass transfer behavior of solutes transfer in fractal capillary bundles [J]. Journal of Henan Polytechnic University (Natural Science) , 2025, 44(4): 124-133.

分形毛细管束中溶质对流-扩散传质行为研究

金毅1,2,3, 黄欢1, 宋慧波1,2,3, 郑军领1, 董佳斌1,2, 董文浩1

1.河南理工大学 资源环境学院，河南 焦作  454000；2.煤炭安全生产与清洁高效利用省部共建协同创新中心，河南 焦作  454000；3.中原经济区煤层（页岩）气协同创新中心，河南 焦作  454000

摘要:探明煤层气在煤储层中的运移规律对煤层气高效开发和产能评估至关重要。煤层气在储层通道中的运移隶属对流、扩散的耦合，受限于孔隙结构复杂形貌，而传统连续介质理论难以准确表征孔隙结构多尺度分形特征对对流-扩散耦合输运过程的控制性作用。  目的 为了深入阐释复杂多尺度孔隙结构中煤层气对流-扩散耦合传质的内在机理。方法 首先，依托分形拓扑理论构建分形毛细管束模型，以定量表征孔隙结构的几何异质性与拓扑连通性；其次，结合经典Taylor-Aris方程，推导耦合孔隙结构尺度不变特征的溶质对流-扩散数学传质方程；最后，借助格子Boltzmann方法模拟分形毛细管束中溶质的对流-扩散过程，并阐释了孔隙结构分形特征对溶质输运的影响机制。结果 结果表明，对流-扩散数学传质方程可精准预测溶质有效扩散系数，具有较好的适配性；管道弯曲度分形维数、缩放间隙度、最大管径等孔隙结构特征参数制约着溶质对流-扩散行为。具体地，管道弯曲度分形维数反比于有效扩散系数，而缩放间隙度和最大管径与有效扩散系数呈良好正相关关系，并以控制流体流速的形式影响溶质对流-扩散过程。结论 研究结果可为煤储层中煤层气复杂运移规律研究提供理论与方法参考，进而为煤层气产能精准预测及储层压裂改造方案的优化提供理论支撑与决策支持。 

关键词:对流-扩散;毛细管束;分形拓扑;有效扩散系数;格子Boltzmann方法

doi: 10.16186/j.cnki.1673-9787.2023040005

基金项目:国家自然科学基金资助项目（41972175）；河南省高校科技创新团队项目（21IRTSTHN007）；河南省高校基本科研业务费专项资金（NSFRF220204）；河南省科技攻关计划项目（232102320351）

收稿日期:2023/04/04

修回日期:2023/06/20

出版日期:2025/06/19

Advection-diffusion mass transfer behavior of solutes transfer in fractal capillary bundles

Jin Yi1,2,3, Huang Huan1, Song Huibo1,2,3, Zheng Junling1, Dong Jiabin1,2, Dong Wenhao1

1.School of Resources and Environment， Henan Polytechnic University， Jiaozuo  454000， Henan， China；2.Collaborative Innovation Center of Coal Work Safety and Clean High Efficiency Utilization， Jiaozuo  454000， Henan， China；3.The Collaborative Innovation Center of Coalbed Methane （Shale Gas） of Central Plains Economic Region， Jiaozuo  454000， Henan， China

Abstract:It is very crutial to explore the migration law of coalbed methane in coal reservoir for its efficient development and productivity evaluation. The migration of coalbed methane in reservoir channels belongs to the coupling of advection and diffusion， which is constrained by the intricate morphological complexity of pore structures. However， the conventional continuum-based theories fail to rigorously characterize the governing influence of multiscale fractal features of pore structures on coupled advective-diffusive transport processes.  Objectives To fuether elobrate the intrinsic mechanisms of coupled advection-diffusion mass transfer of coalbed methane in complex multiscale pore structures， this study employs a systematic approach. Methods Firstly， the fractal capillary bundle model is constructed based on the fractal topology theory to quantitatively characterize the geometric heterogeneity and topological connectivity of pore structures； secondly， building upon the classical Taylor-Aris equation， the mathematical mass transfer equation for solute advection-diffusion is derived， incorporating the scale-invariant characteristics of pore structures；finally， the lattice Boltzmann method is employed to simulate the advection-diffusion process of solutes in fractal capillary bundles， elucidating the influence mechanism of fractal characteristics of pore structures on solute transport. Results The results show that the advection-diffusion mathematical mass transfer model can accurately predict the effective diffusion coefficient of solute and has good adaptability. The pore structure characteristic parameters such as fractal dimension of pipe tortuosity， scaling lacunarity and maximum pipe diameter restrict the solute advection-diffusion behavior. Specifically， the fractal dimension of pipe tortuosity is inversely proportional to the effective diffusion coefficient， while the scaling lacunarity and the maximum pipe diameter have a good positive correlation with the effective diffusion coefficient， and affect the solute advection-diffusion process in the form of controlling the fluid flow rate. Conclusions The research results can provide theoretical and methodological references for the study of the complex migration laws of coalbed methane in coal reservoirs， and further provide theoretical and decision support for the accurate prediction of coalbed methane production capacity and the optimization of reservoir fracturing and modification schemes. 

Key words: advection-diffusion; capillary bundle; fractal topology; effective diffusion coefficient; lattice Boltzmann method