Influence of Particle Size Characteristics and Swelling of Solid Particles in Porous Media on Pore-Scale Flow Field Characteristics of Groundwater
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摘要: 地下水孔隙尺度流场特征的研究对于深入理解地下水渗流、溶质运移具有重要意义.目前固体颗粒粒径特征不同时介质微观结构对孔隙尺度流场的影响尚不清楚.基于迭代重排算法构建了固体颗粒粒径分布特征、膨胀程度不同的多孔介质，基于此研究了固体颗粒平均粒径、粒径方差及膨胀作用对地下水流场特征的影响.结果表明，在介质孔隙率相同的条件下，固体颗粒平均粒径、粒径方差对多孔介质中流速的非均质性、速度概率密度分布等流场特征影响较小.而在同一介质中，当固体颗粒膨胀引起孔隙率减小时，平均粒径较小幅度的变化就会对以上流场特征产生显著影响.例如当固体颗粒膨胀程度增强时，粒径小幅度的增大，就会导致流场中优势流区和不流动区比例同时大幅度增加，流场非均质性显著增强，流速概率密度分布更加发散.Abstract: The study of groundwater pore-scale flow field characteristics is of great significance for the in-depth understanding of groundwater seepage and solute transport. However, the effect of the microstructure of porous media with different particle size characteristics on the pore-scale flow field is yet unclear. This paper constructs porous media with different particle size distribution characteristics and swelling degrees of solid particles using an iterative rearrangement algorithm. On this basis, the effects of the average particle size, particle size variance and solid particle swelling degrees on the characteristics of groundwater flow field are investigated. The results show that under the condition of the same porosity of the porous media, the mean particle size and particle size variance of solid grains have less influence on the flow field characteristics such as the heterogeneity and probability density distribution of flow velocity in porous media. However, in the same medium, when the expansion of solid particles causes a reduction in porosity, a smaller change in average particle size can have a significant effect on the above flow field characteristics. For example, when the expansion degree of solid particles increases, a slight increase in particle size will lead to a large rise in the proportion of the dominant flow area and the stagnant region at the same time, a significant enhancement in the heterogeneity of flow field, and a significant growth in the divergence degree of the flow velocity probability density distribution.
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图 1 基于迭代重排算法构建的多孔介质模型（灰色为孔隙部分，白色为固体颗粒）
孔隙率n=0.45，平均粒径$ \stackrel{-}{d} $=2 mm，粒径方差$ {\sigma }_{d} $=0.5 mm
Fig. 1. Porous media model constructed by iterative rearrangement algorithm (grey is the pore fraction, white is the solid particle)
图 2 固体颗粒平均粒径不同的多孔介质中粒径概率密度分布
Fig. 2. Particle size probability density distribution of porous media with different solid particle mean sizes
图 3 固体颗粒膨胀程度不同时多孔介质的孔隙率
Fig. 3. The porosity of porous media with varying solid particle expansion degrees
图 4 不同分选度的多孔介质中固体颗粒粒径概率密度分布
Fig. 4. The probability density distribution of particle size in porous media with different solid particle sorting degrees
图 5 固体颗粒平均粒径不同的多孔介质中流速概率密度分布
Fig. 5. Probability density distribution of flow velocity in porous media with different mean particle sizes
图 6 不同膨胀程度的多孔介质中主流方向平均流速为1 m/d的流场分布
Fig. 6. Flow field distribution of porous media with different solid expansion degrees, the average fluid flow velocity in all porous media is 1 m/d
图 7 固体颗粒膨胀程度不同的多孔介质中流速概率密度分布
a.半对数坐标图；b.常数坐标图.图a、图b中的虚线分别为不流动区、优势流区的归一化速度标准值
Fig. 7. The probability density distribution of flow velocity in porous media with different swelling degrees of solid grains
图 8 固体颗粒膨胀程度不同的多孔介质中不流动区（$ {u}_{x}/{\stackrel{-}{u}}_{x} $ < 0.01）局部分布图
Fig. 8. The local distribution of stagnant regions ($ {u}_{x}/{\stackrel{-}{u}}_{x} $ < 0.01) in porous media with different solid particle expansion degrees
图 9 固体颗粒粒径方差不同的多孔介质中流速概率密度分布
Fig. 9. Probability density distribution of flow velocity in porous media with different solid grain size variances
表 1 固体颗粒平均粒径不同的多孔介质中流场属性参数
Table 1. The property parameters of flow field in porous media in which the mean particle sizes are different
平均半径$ \stackrel{-}{R} $（mm） 孔隙率
$ n $$ {\stackrel{-}{u}}_{x} $
（m/d）$ {u}_{x.\mathrm{m}\mathrm{a}\mathrm{x}} $
（m/d）边界层长度
（mm）优势流区平均占比
（%）不流动区平均占比（%） 变异系数
CVu0.23 0.51 10 90.861 15 068.38 0.28 3.07 0.947 1 9.086 4 0.28 3.07 0.947 0.1 0.908 63 0.28 3.07 0.947 0.46 0.49 10 94.377 10 205.31 0.39 3.28 0.973 1 9.442 7 0.39 3.28 0.972 0.1 0.943 6 0.39 3.28 0.973 0.74 0.49 10 98.608 6 680.92 0.45 3.56 0.994 1 9.866 4 0.45 3.56 0.994 0.1 0.986 66 0.45 3.56 0.994 
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表 2 固体颗粒膨胀程度不同的多孔介质中的流场属性参数
Table 2. Flow field property parameters in porous media with different solid grain swelling degrees
膨胀效果
$ {T}_{i} $孔隙率
$ n $平均半径$ \stackrel{-}{R} $(mm) $ {\stackrel{-}{u}}_{x} $
(m/d)$ {u}_{\mathrm{m}\mathrm{a}\mathrm{x}}/{\stackrel{-}{u}}_{x} $ 优势流区占比
(%)不流动区占比
(%)变异系数
CVu速度概率密度峰值(%) $ {T}_{1}=0 $ 0.508 0.740 10 9.91 0.48 3.48 1.01 7.21 1 9.92 0.49 3.48 1.02 0.1 9.90 0.48 3.48 1.01 $ {T}_{2}= $0.138 0.489 0.755 10 11.13 0.78 4.89 1.07 6.97 1 11.13 0.78 4.88 1.07 0.1 11.13 0.78 4.88 1.07 $ {T}_{3}= $0.197 0.469 0.770 10 13.40 1.24 5.88 1.15 6.69 1 13.34 1.24 5.88 1.15 0.1 13.33 1.24 5.89 1.15 $ {T}_{4}= $0.243 0.449 0.785 10 16.90 1.85 6.77 1.25 6.32 1 17.00 1.84 6.77 1.25 0.1 17.00 1.84 6.77 1.25 $ {T}_{5}= $0.285 0.427 0.800 10 20.00 2.60 8.10 1.38 5.84 1 20.03 2.60 8.09 1.38 0.1 20.03 2.60 8.09 1.38
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表 3 固体颗粒粒径分选度不同的多孔介质流体流速变异函数
Table 3. Variation function of fluid flow velocity in porous media with different solid particle sorting degrees
多孔介质 $ C{V}_{u} $ $ C{V}_{{u}_{x}} $ $ C{V}_{{u}_{y}} $ $ {\sigma }_{d1}= $0.18 mm 1.069 0.978 0.610 $ {\sigma }_{d2}= $0.24 mm 1.079 0.984 0.623 $ {\sigma }_{d3}= $0.30 mm 1.043 0.957 0.591
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