Partial Reversibility of Dispersion in Heterogeneous Porous Media

非均质多孔介质中色散的部分可逆性

• 批准号: 506393436
• 负责人: Professor Dr.-Ing. Olaf A. Cirpka
• 金额: --
• 依托单位: Department of Geosciences
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/506393436?language=en
• 关键词: Partial; Reversibility; Dispersion; Heterogeneous; Porous

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.

在过去的四十年中，异质多孔媒体中的溶质运输一直是密集研究的话题。众所周知，可溶性扩散，测量可溶性羽流的不规则性增加，与可溶性混合不同，量化了可溶性羽流的质量交换与周围的周围。前者之前是后者，但后者只有后者有助于混合控制的反应。迄今为止，没有理论在预测大规模的非叉境和固体混合方面都没有良好的理论。都没有提供有关执行大规模保守 - 传输实验以量化固体混合的实用理论建议。拟议的项目建立在以下事实的基础上，即在异质地层中纯净的携带溶剂的水包裹的运动型变形是完全可逆的，而不同的混合是不可逆的。在这种地层中，变形与固体转运中的小尺度分化混合之间的相互作用导致溶质扩散的部分可逆性：在流动逆转时，可溶性羽流的空间范围收缩的空间范围，但并未恢复为原始的初始状态。该项目将分析固体羽毛的第二中心力矩（其中一半的变化率定义了分散系数）在异质的多孔介质中具有均匀的均匀流动流量的均匀流动。在向前和向后运动相等的时间后，不可逆转的分散分数的适用产品可以作为固体混合的度量。在非radial推力实验中，目标数量是注入/提取横截面中回流固体的突破曲线的扩散。分析是通过在3-D虚拟域中的粒子跟踪随机步行模拟，通过一阶随机扰动方法来对空间矩进行理论分析，通过开发新的相关连续时间随机漫游方法，并通过对前面的步骤进行记忆和随机交换，并通过对临时力矩进行分析，以及在CA中进行分析的含义。使用折射率匹配的流体进行2M x 1M准2-D流域，以通过光传输成像来优化检测。实验将包括检测返回固体的突破性曲线。假设线性随机理论预测的集合和有效的矩适合轻度异质性病例。增加逆Péclet数，异质性及其各向异性的程度应增加不可逆的分散分数。预计二次瞬间会在流动逆转后缩小，并在羽流中心达到其原始位置之前再次增加。收缩时间和对集成分散的可逆贡献应随当地的péclet数量而扩展。该项目开发了新的理论和实验方法，以区分异质多孔培养基中的扩散和混合，从而控制反应性化合物的行为。