Six series of solute transport experiments were conducted with an objective to compare scale decency of fractional dispersion coefficient (D_f) in space fractional advection–dispersion equation (s-FADE) with that of dispersion coefficient (D) in advection–dispersion equation (ADE) at three flow rates. The experiments were performed in a 2.5 m × 0.1 m × 0.6 m (length × width × height) sandbox filled with a homogeneous or heterogeneous soil. The parameters of the s-FADE and ADE were estimated using an inverse method. The results indicated that the scale dependency of D_f was significantly less than that of D in the heterogeneous soil. The maximum variations of D_f and D for the heterogeneous soil were observed at the flow rate of 200 cm³ min^–1, in which the ratios of the maximum D_f and D to the minimum ones were 6.009 and 39.039, respectively. However, in the homogeneous soil, the scale dependency of D_f was relatively similar to that of D. In this soil, the ratios of the maximum D_f and D to the minimum ones were 3.109 and 5.041, respectively, which were observed at the flow rate of 548 cm³ min^–1. Contrary to D_f and D, the v values of the s-FADE and ADE for both soils varied in relatively similar ranges at the flow rates studied. Also, the fractional differentiation order (α) of the s-FADE described properly the heterogeneity degrees of the soils used. In a nutshell, the s-FADE is an efficient solute transport model to explain the solute transport process in natural porous media with different heterogeneity degrees.

中文翻译：

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分数弥散系数的比例依赖性实验研究

进行了六个系列的溶质运移实验，目的是比较空间分数对流-弥散方程（s-FADE）中分数弥散系数（D _f）与对流-弥散方程（ADE）中弥散系数（D）的比例衰减）的三个流量。实验是在装有均质或非均质土壤的2.5 m×0.1 m×0.6 m（长×宽×高）沙箱中进行的。使用逆方法估计s-FADE和ADE的参数。结果表明，在非均质土壤中，D _f的尺度依赖性明显小于D。D _f和的最大变化在200 cm ³ min ^–1的流速下观察到非均质土壤的D，其中最大D _f和D与最小D之比分别为6.009和39.039。然而，在均质土，规模依赖性d _˚F相对类似的d。在这种土壤中，最大_Df和D与最小D之比分别为3.109和5.041，这在548 cm ³ min ^–1的流速下观察到。与D _f和D相反，在研究的流速下，两种土壤的s-FADE和ADE的v值在相对相似的范围内变化。同样，s-FADE的分数微分阶数（α）正确描述了所用土壤的异质度。简而言之，s-FADE是一种有效的溶质运移模型，用于解释具有不同异质度的天然多孔介质中的溶质运移过程。