Partial Reversibility of Dispersion in Heterogeneous Porous Media

在过去的四十年里，溶质在非均质多孔介质中的输运一直是研究的热点。溶质扩散测量的是溶质羽流的不规则性增加，而溶质混合测量的是溶质羽流与其周围的质量交换，这一点已经得到了很好的证实。前者先于后者，但只有后者才能促进混合控制的反应。迄今为止，还没有一种理论能很好地预测大规模的非菲克式扩散和溶质混合。对于进行大规模的守恒输运实验来量化溶质混合，两者都没有给出现有理论的实际建议。提议的项目建立在这样一个事实的基础上，即在非均质地层中携带溶质的水包的纯运动学变形是完全可逆的，而扩散混合是不可逆的。在这些地层中，溶质运移中的变形和小规模扩散混合之间的相互作用导致了溶质扩散的部分可逆性：在流动逆转时，溶质羽流的空间范围缩小，但不会恢复到原始状态。该项目将分析非均质多孔介质中溶质羽流的第二中心矩（其中一半的变化率定义了色散系数），这些介质具有均匀的平均流动，并受到流动反转的影响。申请人假定不可逆的分散分数，经过等量的向前和向后运动后，可以作为溶质混合的度量。在非径向推拉实验中，目标量是回溶质在注入/萃取截面上的突破曲线的扩展。该分析是通过三维虚拟域的粒子跟踪随机行走模拟完成的，通过一阶随机摄动方法进行空间矩的理论分析，通过开发一种新的相关连续时间随机行走方法，该方法具有前步记忆和随机交换的平均值，用于分析时间矩。利用折射率匹配流体在约2m × 1m的准二维流域中进行实验，优化光透射成像检测。实验将包括检测返回溶质的突破曲线。假设线性随机理论可以很好地预测具有轻度异质性的情况下的系综和有效矩。增加反psamclet数、非均质性及其各向异性，应增加不可逆色散的比例。第二中心矩预计会在气流逆转时减小，并在羽流中心到达其原始位置之前再次增大。收缩时间和对总色散的可逆贡献应与局部psamclet数成比例。本项目开发了新的理论和实验方法来区分非均质多孔介质中的扩散和混合，这控制了反应性化合物的行为。

Solute transport in heterogeneous porous media has been the topic of intensive research in the last four decades. It is well established that solute spreading, measuring the increasing irregularity of solute plumes, differs from solute mixing, quantifying the mass exchange of a solute plume with its surrounding. The former precedes the latter, but only the latter facilitates mixing-controlled reactions. To date there is no theory that is good in predicting both large-scale non-Fickian spreading and solute mixing. Neither give existing theories practical advice on performing large-scale conservative-transport experiments to quantify solute mixing. The proposed project builds on the fact that purely kinematic deformation of water parcels carrying solutes in heterogeneous formations is fully reversible, whereas diffusive mixing is irreversible. The interaction between deformation and small-scale diffusive mixing in solute transport in such formations cause partial reversibility of solute spreading: Upon flow reversal the spatial extent of a solute plume shrinks, but does not revert to the original initial state. The project will analyze second-central moments of solute plumes (of which half the rate of change define dispersion coefficients) in heterogeneous porous media with uniform-in-the-mean flow subject to flow reversal. The applicant presumes that the irreversible fraction of dispersion, after equal times of forward and backward motion, can be taken as a metric of solute mixing. In non-radial push-pull experiments the target quantity is the spread of the breakthrough curve of the returning solute in the injection/extraction cross-section. The analysis is done by particle-tracking random-walk simulations in 3-D virtual domains, by first-order stochastic-perturbative methods for the theoretical analysis of spatial moments, by the development of a new correlated Continuous-Time Random-Walk approach with memory of preceding steps and random exchange with the mean for the analysis of temporal moments, and by experiments in a ca. 2m × 1m quasi 2-D flow domain using refractive-index matching fluids to optimize detection by light-transmission imaging. The experiments will include detecting the breakthrough curve of the returning solute. It is hypothesized that linear stochastic theory predicts ensemble and effective moments well for cases with mild heterogeneity. Increasing the inverse Péclet number, the degree of heterogeneity, and its anisotropy should increase the irreversible fraction of dispersion. Second-central moments are expected to shrink upon flow reversal and increase again before the plume center reaches its original position. The shrinking time and the reversible contribution to ensemble dispersion should scale with the local Péclet number. This project develops new theoretical and experimental approaches to distinguish spreading and mixing in heterogenous porous media, which controls the behavior of reactive compounds.