Partial Reversibility of Dispersion in Heterogeneous Porous Media

近四十年来，溶质在非均质多孔介质中的运移一直是人们研究的热点。众所周知，溶质扩散不同于溶质混合，它测量的是溶质羽流不断增加的不规则性，它量化了溶质羽流与其周围的质量交换。前者先于后者，但只有后者促进了混合控制反应。到目前为止，还没有一种理论能够很好地预测大规模的非费克扩散和溶质混合。在进行大规模的保守输运实验以量化溶质混合方面，这两个理论都没有给出实际的建议。拟议的项目基于这样一个事实，即在非均质地层中携带溶质的水块的纯运动变形是完全可逆的，而扩散混合是不可逆的。在这种地层中，溶质运移中的变形和小尺度扩散混合之间的相互作用导致了溶质扩散的部分可逆性：当流动逆转时，溶质羽流的空间范围缩小，但不恢复到初始状态。该项目将分析非均质多孔介质中的溶质羽流的第二中心矩(其中一半的变化率定义了弥散系数)，其中平均均匀流动受流动逆转的影响。申请人假定，在前后运动相等次数后，不可逆的弥散分数可以作为溶质混合的度量。在非径向推拉实验中，目标量是返回的溶质在注入/提取截面上的穿透曲线的展开度。分析是通过在3-D虚拟区域中的粒子跟踪随机游动模拟，通过用于空间矩理论分析的一阶随机微扰方法，通过开发具有先前步骤记忆和用于时间矩分析的随机交换的新的相关的连续时间随机游动方法来完成的，以及通过在大约2m×1m的准2-D流动区域中使用折射率匹配流体来优化通过光传输成像进行检测的实验来完成的。实验将包括检测返回的溶质的穿透曲线。假设线性随机理论可以很好地预测具有轻度非均质性的情况下的集合和有效矩。增加逆Péclet数、非均质程度及其各向异性应该会增加弥散的不可逆分数。二次中心力矩预计会在气流逆转时收缩，并在羽流中心到达其原始位置之前再次增加。收缩时间和对系综弥散的可逆贡献应与局域Péclet数成比例。这个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，这控制了活性化合物的行为。

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.