Transverse mixing in three‐dimensional nonstationary anisotropic heterogeneous porous media
Transverse mixing in three‐dimensional nonstationary anisotropic heterogeneous porous media
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DOI：
10.1002/2014wr015331
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发表时间：
2015-01
影响因子：
5.4
通讯作者：
O. Cirpka;G. Chiogna;M. Rolle;A. Bellin
中科院分区：
文献类型：
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作者：
O. Cirpka;G. Chiogna;M. Rolle;A. Bellin
来自连续排放源的地下水羽流通常由羽流和环境溶液中的反应物横向混合控制。在二维域中，非均质性只会导致稳态流动中横向混合的微弱增强。在三维域中，可能会出现更复杂的流型，因为流线可能会扭曲。特别是，各向异性在空间上的不同取向可能会导致地下水的稳态漩涡。分析了具有块状各向异性相关结构的三维局部各向同性非均质多孔介质中的稳态溶质运移，其中各向异性的主方向随块间的不同而不同。为此，我们提出了一种基于Voronoi细分的沿流线的平流输送和它们之间的横向弥散质量交换的输送方案。在不考虑非平稳性的情况下，我们将非平稳各向异性对数导水率场的流动和输运结果与具有相同均值、方差和两点相关函数的等效稳态场进行了比较。非平稳各向异性场受平均次级运动的影响，导致相邻流线强烈发散，这种发散可以用平流层横向位移的两粒子半方差函数来量化。流场的一个等效运动学描述符是羽流的平流折叠，它与混合的前兆更相关，而不是拉伸。当考虑局部弥散时，相邻流线的分离增强了横向混合。我们用与通量相关的稀释指数来量化混合，它对于非平稳各向异性电导率场比对于平稳各向异性电导率场大得多。结果表明，关联结构中的非定常各向异性对横向羽流的形变和混合有重要影响。在天然沉积物中，污染物羽流在横向方向的混合很可能比忽略各向异性非平稳性的模型预测的更有效。
Groundwater plumes originating from continuously emitting sources are typically controlled by transverse mixing between the plume and reactants in the ambient solution. In two‐dimensional domains, heterogeneity causes only weak enhancement of transverse mixing in steady‐state flows. In three‐dimensional domains, more complex flow patterns are possible because streamlines can twist. In particular, spatially varying orientation of anisotropy can cause steady‐state groundwater whirls. We analyze steady‐state solute transport in three‐dimensional locally isotropic heterogeneous porous media with blockwise anisotropic correlation structure, in which the principal directions of anisotropy differ from block to block. For this purpose, we propose a transport scheme that relies on advective transport along streamlines and transverse‐dispersive mass exchange between them based on Voronoi tessellation. We compare flow and transport results obtained for a nonstationary anisotropic log‐hydraulic conductivity field to an equivalent stationary field with identical mean, variance, and two‐point correlation function disregarding the nonstationarity. The nonstationary anisotropic field is affected by mean secondary motion and causes neighboring streamlines to strongly diverge, which can be quantified by the two‐particle semivariogram of lateral advective displacements. An equivalent kinematic descriptor of the flow field is the advective folding of plumes, which is more relevant as precursor of mixing than stretching. The separation of neighboring streamlines enhances transverse mixing when considering local dispersion. We quantify mixing by the flux‐related dilution index, which is substantially larger for the nonstationary anisotropic conductivity field than for the stationary one. We conclude that nonstationary anisotropy in the correlation structure has a significant impact on transverse plume deformation and mixing. In natural sediments, contaminant plumes most likely mix more effectively in the transverse directions than predicted by models that neglect the nonstationarity of anisotropy.