A Network Model for Diffusion in Media with Partially Resolvable Pore Space Characteristics
A Network Model for Diffusion in Media with Partially Resolvable Pore Space Characteristics
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DOI：
10.1007/s11242-014-0360-1
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发表时间：
2014-07
影响因子：
2.7
通讯作者：
A. Jivkov;Q. Xiong
中科院分区：
文献类型：
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作者：
A. Jivkov;Q. Xiong
提出了一个考虑微观结构的多孔介质中杂质扩散的细观模型。该模型适用于实验获得的孔隙几何数据仅占总孔隙率一小部分的介质。一个细胞复合体，与一个细胞代表的平均孔隙邻域，是用来生成三维图形的网站在细胞中心和债券之间的相邻细胞。将孔隙系统解释为图形的新方法，可以在运输的数学公式中明确区分拓扑（这里是连通性）和物理（这里是扩散）。此外，它允许容易地将动态引入系统，即，由于其他物理机制，如微裂纹或孔堵塞，局部改变拓扑结构。微观结构特征和图形元素之间的映射用于模型构建。该映射是基于粘土的数据，其中实验解析的孔隙系统包括具有大体积分数的未解析孔隙的优选取向的孤立的细长孔隙。已解析系统和“隐藏”系统都被考虑在内。图的几何形状由主长度（在优选方向上的单元大小）和次长度（在优选方向之外的单元大小）描述。这被认为是粘土矿物学不均匀性的代表。分析图，一个专业化的离散外部演算，是用来获得连通性和扩散性形成的网络。由于实验数据不足以确定主长度，因此根据有限的信息确定上限和下限。研究了主细胞大小之间的限制和辅助细胞大小的影响。实验测量的宏观（散装）扩散系数的范围内的研究材料，包括各向异性扩散系数的结果。计算出的扩散系数的变化与主要和次要的长度提供了一个解释在不同的粘土实验测得的系数的变化。
A microstructure-informed meso-scale model for diffusion of foreign species in porous media is proposed. The model is intended for media where the pore geometry data acquired experimentally represent a fraction of total porosity. A cellular complex, with a cell representing the average pore neighbourhood, is used to generate 3D graphs of sites at cell centres and bonds between neighbouring cells. The novel interpretation of pore systems as graphs allows for clear separation between topology (here connectedness) and physics (here diffusion) in the mathematical formulation of transport. Further, it allows for easy introduction of dynamics into the system, i.e., local changes in topology due to other physical mechanisms, such as micro-cracking or blockage of pores. A mapping between microstructure features and graph elements is used for model construction. The mapping is based on data for clays, where the experimentally resolved pore system comprises isolated elongated pores of preferred orientation with a large volume fraction of unresolved pores. Both the resolved and the “hidden” systems are accounted for. The graph geometry is described by a principal length, the cell size in the preferred orientation, and a secondary length, the cell size out of preferred orientation. This is considered as a representation of mineralogical heterogeneity of clays. Analysis on graphs, a specialisation of the discrete exterior calculus, is used to obtain connectivity and diffusivity properties of formed networks. Since the experimental data are not sufficient to determine the principal length, upper and lower limits are determined from the limited information. Effects of the principal cell size between limits and of the secondary cell size are studied. The results are within the range of experimentally measured macroscopic (bulk) diffusivity for the material studied, including anisotropic diffusion coefficients. The variation of calculated diffusivity coefficients with principal and secondary lengths provides an explanation for the variability in experimentally measured coefficients across different clays.