Ghanbarian-Alavijeh B, Skinner T E, Hunt A G
Department of Earth and Environmental Sciences, Wright State University, Dayton, Ohio 45324, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066316. doi: 10.1103/PhysRevE.86.066316. Epub 2012 Dec 19.
In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute distributions as a function of time and calculate arrival time distributions as a function of system size. Our previous results correctly predict the range of observed dispersivity values over ten orders of magnitude in experimental length scale, but that theory contains no explicit dependence on porosity or relative saturation. This omission complicates comparisons with experimental results for dispersion, which are often conducted at saturation less than 1. We now make specific comparisons of our predictions for the arrival time distribution with experiments on a single column over a range of saturations. This comparison suggests that the most important predictor of such distributions as a function of saturation is not the value of the saturation per se, but the applicability of either random or invasion percolation models, depending on experimental conditions.
在本研究中，我们利用关键路径分析、渗流的簇统计以及渗流簇的分形标度等概念，开发了一种依赖饱和度的多孔介质中弥散处理方法。我们计算了作为时间函数的空间溶质分布，并计算了作为系统尺寸函数的到达时间分布。我们之前的结果正确地预测了在实验长度尺度上十个数量级范围内观测到的弥散度值范围，但该理论没有明确依赖孔隙率或相对饱和度。这一遗漏使得与弥散实验结果的比较变得复杂，因为这些实验通常在饱和度小于1的情况下进行。我们现在将我们对到达时间分布的预测与在一系列饱和度下对单个柱体进行的实验进行了具体比较。这种比较表明，作为饱和度函数的此类分布的最重要预测因子不是饱和度本身的值，而是随机或入侵渗流模型的适用性，这取决于实验条件。
