Knowing local concentration distributions is important for transport and mixing, particularly in porous media, yet a comprehensive understanding of them remains a challenge. Computing advancements have enabled high-resolution pore-scale simulations, offering an unprecedented opportunity for in-depth investigation of mixing. In this study we use simulation data to examine concentration distributions at the pore scale in the context of longitudinal (pseudo-one-dimensional) solute transport through a porous column. These distributions arise in a single column from heterogeneous flow at the pore-scale, which gets averaged out when upscaled and are not with reference to statistics across multiple random realizations. To measure these distributions, we first devise a semi-analytical approach to estimate the mean effective transport velocity profile for a non-uniform Darcy-scale fluid velocity, which unavoidably occurs due to the presence of lateral boundaries. This development allows sampling micro-scale concentrations over a moving surface that possesses a well defined Darcy-scale mean concentration, enabling empirical computation of the local concentration distribution. As an added benefit we find that our approach allows for the estimation of transverse dispersion coefficients, which is not typical in traditional column experiments. The implemented approach can estimate it via inverse modeling, and it agrees closely with previously published experimental data across the range of Peclet numbers we studied. We found that the measured pore-scale concentration probability density functions are best represented by a beta distribution, thus validating this longstanding hypothesis with direct evidence. Furthermore, we propose a model to describe the temporal and spatial evolution of the local concentration pdf, as well as its Péclet number dependence.

中文翻译：

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孔隙尺度浓度 PDF 的演变以及数值多孔介质柱实验的横向色散估计


了解局部浓度分布对于传输和混合非常重要，特别是在多孔介质中，但全面了解它们仍然是一个挑战。计算的进步实现了高分辨率孔隙尺度模拟，为深入研究混合提供了前所未有的机会。在本研究中，我们使用模拟数据来检查在通过多孔柱的纵向（伪一维）溶质传输的背景下孔隙尺度的浓度分布。这些分布出现在孔隙尺度的非均质流的单列中，在放大时会被平均，并且不参考多个随机实现的统计数据。为了测量这些分布，我们首先设计一种半解析方法来估计非均匀达西尺度流体速度的平均有效传输速度剖面，由于横向边界的存在，这种情况不可避免地发生。这一发展允许在具有明确定义的达西尺度平均浓度的移动表面上对微尺度浓度进行采样，从而能够根据经验计算局部浓度分布。作为一个额外的好处，我们发现我们的方法可以估计横向色散系数，这在传统柱实验中并不常见。所实现的方法可以通过逆向建模来估计它，并且它与我们研究的佩克莱特数范围内先前发布的实验数据非常一致。我们发现，测量的孔隙尺度浓度概率密度函数最好用贝塔分布来表示，从而用直接证据验证了这一长期存在的假设。 此外，我们提出了一个模型来描述局部浓度 pdf 的时间和空间演化及其佩克莱特数依赖性。