Anomalous behaviors during infiltration into heterogeneous porous media
Anomalous behaviors during infiltration into heterogeneous porous media
复制标题
渗透到异质多孔介质过程中的异常行为
DOI：
10.1016/j.advwatres.2018.01.010
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发表时间：
2018
影响因子：
4.7
通讯作者：
V. Voller
中科院分区：
文献类型：
--
作者：
F. A. Reis;D. Bolster;V. Voller
非均质多孔介质中的渗流和输运往往表现出反常的行为。一个物理模拟的例子是单向渗透的粘性液体到一个水平取向的Hele-Shaw细胞包含通过厚度流动障碍;一个系统，旨在模仿砾石/砂介质与不可渗透的夹杂物。当不存在障碍物或障碍物形成多重复图案时，渗透长度F随时间t的变化倾向于遵循Fickian样缩放，F t 1 2。当障碍场呈谢尔宾斯基地毯分形分布时，渗透是反常的，即F t n，n <$1/2。在这里，我们研究渗透到这样的海勒-肖细胞。首先，我们研究渗透到一个正方形细胞包含一个分形地毯，并作出观察，这是可能的，产生亚（n< 1/2）和超（n> 1/2）的扩散行为在相同的异质性配置。我们表明，这可以解释的尺度分析的随机行走模拟分形障碍的结果，结果表明，域边界的性质控制的指数n所产生的异常运输。此外，我们调查渗透到一个矩形单元格包含几个重复给定的谢尔宾斯基地毯。在早期，在液体遇到任何障碍之前，渗透是菲克式的。当液体遇到第一个（最小尺度）障碍物时，渗透急剧转变为亚扩散。随后，在液体已经对系统中的所有不均匀长度尺度进行采样的时间附近，存在快速转变回到菲克行为。这第二个过渡的解释是通过开发一个简化的渗透模型的基础上定义的一个代表性的平均导水率。
Flow and transport in heterogeneous porous media often exhibit anomalous behavior. A physical analog example is the uni-directional infiltration of a viscous liquid into a horizontal oriented Hele-Shaw cell containing through thickness flow obstacles; a system designed to mimic a gravel/sand medium with impervious inclusions. When there are no obstacles present or the obstacles form a multi-repeating pattern, the change of the length of infiltration F with time t tends to follow a Fickian like scaling, F∼ t 1 2. In the presence of obstacle fields laid out as Sierpinski carpet fractals, infiltration is anomalous, ie, F∼ t n, n≠ 1/2. Here, we study infiltration into such Hele-Shaw cells. First we investigate infiltration into a square cell containing one fractal carpet and make the observation that it is possible to generate both sub (n< 1/2) and super (n> 1/2) diffusive behaviors within identical heterogeneity configurations. We show that this can be explained in terms of a scaling analysis developed from results of random-walk simulations in fractal obstacles; a result indicating that the nature of the domain boundary controls the exponent n of the resulting anomalous transport. Further, we investigate infiltration into a rectangular cell containing several repeats of a given Sierpinski carpet. At very early times, before the liquid encounters any obstacles, the infiltration is Fickian. When the liquid encounters the first (smallest scale) obstacle the infiltration sharply transitions to sub-diffusive. Subsequently, around the time where the liquid has sampled all of the heterogeneity length scales in the system, there is a rapid transition back to Fickian behavior. An explanation for this second transition is obtained by developing a simplified infiltration model based on the definition of a representative averaged hydraulic conductivity.