On the theoretical calculation of tortuosity in porous media and its experimental validation
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摘要: 多孔介质孔隙连通的定量表征与拓扑连通重构是揭示流体渗透规律的几何方法，而理论工作的滞后严重制约了新的几何建模方法产生。迂曲度是连接渗透率与几何结构的关键载体之一，其理论模型一直没有突破。结合Hagen-Poiseuille与Darcy公式，推导了毛细管迂曲度的普适表达式及颗粒构成孔道的迂曲度公式。针对低渗介质，结合毛细管压力公式，获得了含饱和度的迂曲度公式。引入迂曲度分维，获得基于实验解析的分形影响系数表达式。对于分叉毛细管孔道，建立分叉模型，分析了迂曲度特征，得到了基于能量优化准则的母孔、子孔几何关系。以低渗盐岩渗透为例，验证了迂曲度理论公式的适用性与可靠性，研究结果为多孔介质求解迂曲度提供了一种新的思路。Abstract: The quantitative characterization of connectivity of pore geometry and its reconstruction of topological connectivity are two important methods to describe the laws of fluid seepage in porous media.However, the lag of theoretical work severely restricts the emergence of new geometric modeling methods.The tortuosity is one of the key carriers connecting permeability and geometric structure, and its theoretical model has not been broken through.First, combining the Hagen-Poiseuille equation and Darcy formulas, the universal expression of the tortuosity for capillary model and the pore model composed by the particles are derived.Then for the low permeability medium, combined with the formula of capillary pressure, the tortuosity expression correlated to the saturation is obtained.Furthermore, the fractal dimension of tortuosity is introduced to explain the new term of fractal coefficient based on experimental analysis.Considering the bifurcated capillary channel, a bifurcation model was established to analyze the tortuosity characteristics and the geometric relationship between the mother and sub-holes based on the energy optimization criterion was obtained.Taking the salt rock as an example, the applicability and reliability of the theoretical formula of tortuosity are verified, and the research results provide a new idea for calculating the tortuosity of porous media.
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Key words:
- porous media /
- seepage /
- tortuosity /
- fractal dimension /
- bifurcated capillary
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图 2 长径比和迂曲度分维与分形影响系数的关系
Figure 2. Fractal coefficient influenced by the aspect ratio and fractal dimension of tortuosity
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