[1]牟新竹,陈振乾.多尺度分形多孔介质气体有效扩散系数的数学模型[J].东南大学学报(自然科学版),2019,49(3):520-526.[doi:10.3969/j.issn.1001-0505.2019.03.017]
 Mou Xinzhu,Chen Zhenqian.Mathematical model for effective gas diffusion coefficient in multi-scale fractal porous media[J].Journal of Southeast University (Natural Science Edition),2019,49(3):520-526.[doi:10.3969/j.issn.1001-0505.2019.03.017]
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多尺度分形多孔介质气体有效扩散系数的数学模型()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
49
期数:
2019年第3期
页码:
520-526
栏目:
能源与动力工程
出版日期:
2019-05-20

文章信息/Info

Title:
Mathematical model for effective gas diffusion coefficient in multi-scale fractal porous media
作者:
牟新竹陈振乾
东南大学能源与环境学院, 南京 210096
Author(s):
Mou Xinzhu Chen Zhenqian
School of Energy and Environment, Southeast University, Nanjing 210096, China
关键词:
多孔介质 分形 气体扩散 多尺度
Keywords:
porous media fractal gas diffusion multi-scales
分类号:
TK121
DOI:
10.3969/j.issn.1001-0505.2019.03.017
摘要:
基于毛细管束假设和分形理论,建立了一种计算多孔介质中气体有效扩散系数的数学模型.利用分形几何理论,引入孔隙面积分形维数、孔道迂曲度分形维数以及孔隙连通性等参数定量表征多孔介质中真实的内部结构,构建出多孔介质、多尺度孔隙结构的分形模型,系统地研究了多孔介质中不同尺度孔隙下的气体扩散过程,推导出了分形多孔介质气体有效扩散系数模型,并分析讨论了多孔介质微结构参数对气体有效扩散系数的影响.研究结果表明,气体有效扩散系数随着平面孔隙度的增大而近似呈线性增加,孔隙面积分形维数与气体有效扩散系数呈正相关,而孔道迂曲度分形维数与气体有效扩散系数呈负相关;不同孔隙度情况下,气体有效扩散系数随着孔隙最小/最大直径比的变化趋势不同,孔隙连通性越强的多孔介质,气体有效扩散系数越大.
Abstract:
Based on the capillary hypothesis and fractal theory, a mathematical model for calculating the effective gas diffusion coefficient in porous media was established. By using the fractal geometry theory, the pore area fractal dimension, the tortuosity fractal dimension and the pore connectivity were introduced to quantitatively characterize the real internal structure in the porous media, and the fractal model for the microscopic pore structure in the porous media was established. The gas diffusion in the porous media on different scales was systematically studied. An effective gas diffusion coefficient model for the fractal porous media was derived, and the influence of multi-scale porous media microstructure parameters on the effective gas diffusion coefficient was discussed. The results show that effective gas diffusion coefficient approximates to linearly increase with the increase of porosity, the pore area fractal dimension and the effective gas diffusion coefficient is positive correlation, but the tortuosity fractal dimension is negative correlation with it. In the case of different porosities, the gas effective diffusion coefficient varies with the change of the pore diameter ratio, the effective gas diffusion coefficient increases with the increase of pore connectivity.

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备注/Memo

备注/Memo:
收稿日期: 2018-10-31.
作者简介: 牟新竹(1994—),男,博士生;陈振乾(联系人),男,博士,教授,博士生导师,zqchen@seu.edu.cn.
基金项目: 国家自然科学基金资助项目(51676037).
引用本文: 牟新竹,陈振乾.多尺度分形多孔介质气体有效扩散系数的数学模型[J].东南大学学报(自然科学版),2019,49(3):520-526. DOI:10.3969/j.issn.1001-0505.2019.03.017.
更新日期/Last Update: 2019-05-20