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Numerical assessment of 3D macrodispersion in heterogeneous porous media

机译：非均质多孔介质中3D宏观分散的数值评估

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摘要

Hydrodynamic dispersion is a key controlling factor of solute transport in heterogeneous porous media. It critically depends on dimensionality. The asymptotic macrodispersion, transverse to the mean velocity direction, vanishes only in 2D and not in 3D. Using the classical Gaussian correlated permeability fields with a lognormal distribution of variance σ_Y~2, the longitudinal and transverse dispersivities are determined numerically as a function of heterogeneity and dimensionality. We show that the transverse macrodispersion steeply increases with σ_Y~2 underlying the essential role of flow lines braiding, a mechanism specific to 3D systems. The transverse macrodispersion remains however at least two orders of magnitude smaller than the longitudinal macrodispersion, which increases even more steeply with σ_Y~2. At moderate to high levels of heterogeneity, the transverse macrodispersion also converges much faster to its asymptotic regime than do the longitudinal macrodispersion. Braiding cannot be thus taken as the sole mechanism responsible for the high longitudinal macrodispersions. It could be either supplemented or superseded by stronger velocity correlations in 3D than in 2D. This assumption is supported by the much larger longitudinal macrodispersions obtained in 3D than in 2D, up to a factor of 7 for σ_Y~2 = 7.56.
机译：流体动力分散是溶质在非均质多孔介质中运移的关键控制因素。关键取决于尺寸。垂直于平均速度方向的渐近宏观色散仅在2D中消失，而在3D中不消失。使用具有对数正态分布σ_Y〜2的经典高斯相关渗透率场，根据异质性和维数在数值上确定纵向和横向离散度。我们显示出横向宏散度随着σ_Y〜2急剧增加，这是流线编织（这是3D系统特有的机制）的基本作用的基础。然而，横向宏观色散至少比纵向宏观色散小两个数量级，后者随着σ_Y〜2的增加甚至更大。在中等到高水平的非均质性下，横向大分散比纵向大分散更收敛到其渐近状态。因此不能将编织物作为造成高纵向大分散的唯一机制。 3D中比2D中更强的速度相关性可以补充或替代它。 3D中获得的纵向宏散度比2D中的大得多，而σ_Y〜2 = 7.56的系数高达7，从而支持了这一假设。

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