Diffusion in Relatively Homogeneous Sand Columns: A Scale-Dependent or Scale-Independent Process?
Diffusion in Relatively Homogeneous Sand Columns: A Scale-Dependent or Scale-Independent Process?
复制标题
DOI：
10.3390/e15104376
复制
发表时间：
2013-10
期刊：
影响因子：
2.7
通讯作者：
Yong Zhang;Hongxia Xu;Xueyan Lv;Jichun Wu
中科院分区：
文献类型：
--
作者：
Yong Zhang;Hongxia Xu;Xueyan Lv;Jichun Wu
溶质在均匀介质中的运移一直被认为是与尺度无关的，可以用二阶对流-弥散方程（ADE）来量化。然而，这项研究，在实验室中，观察到相反的CuSO 4通过相对均匀的石英砂柱的运输表现出子扩散增长的空间尺度。只有在很小的传播距离（约10厘米）和一个相对较短的时间尺度的运输可以近似为正常扩散。这也是唯一的时空尺度，其中的基本概念的“代表性元素体积”（它定义了规模的均匀单元使用的基于ADE的水文模型）是有效的。标准ADE的失败促使我们应用回火稳定的分数阶对流-弥散方程（TS-FADE）来捕获CuSO 4穿透曲线中具有指数截断幂律后期尾部的瞬态异常弥散。结果表明，在TS-FADE模型中的回火参数一般随柱长的增加而减小（可能是由于长保留过程的概率较高），而时间指数（这是一个非局部参数）保持稳定的均匀填充柱。因此，在填充有相对均匀的硅砂的砂柱中的传输是尺度依赖的，并且由此产生的瞬态次扩散可以由TS-FADE模型量化。
Solute transport through homogeneous media has long been assumed to be scale-independent and can be quantified by the second-order advection-dispersion equation (ADE). This study, however, observed the opposite in the laboratory, where transport of CuSO4 through relatively homogeneous silica-sand columns exhibits sub-diffusion growing with the spatial scale. Only at a very small travel distance (approximately 10 cm) and a relatively short temporal scale can the transport be approximated by normal diffusion. This is also the only spatiotemporal scale where the fundamental concept of the “representative element volume” (which defines the scale of homogeneous cells used by the ADE-based hydrologic models) is valid. The failure of the standard ADE motivated us to apply a tempered-stable, fractional advection-dispersion equation (TS-FADE) to capture the transient anomalous dispersion with exponentially truncated power-law late-time tails in CuSO4 breakthrough curves. Results show that the tempering parameter in the TS-FADE model generally decreases with an increase of the column length (probably due to the higher probability of long retention processes), while the time index (which is a non-local parameter) remains stable for the uniformly packed columns. Transport in sand columns filled with relatively homogeneous silica sand, therefore, is scale-dependent, and the resultant transient sub-diffusion can be quantified by the TS-FADE model.