Dispersion in Heterogeneous Porous Media Through Advection

通过平流在非均质多孔介质中进行分散

• 批准号: 0810186
• 负责人: Allen Hunt
• 金额: --
• 依托单位: Wright State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-08-01 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0810186&HistoricalAwards=false
• 关键词: Dispersion; Heterogeneous; Porous; Media; Through

We propose a theoretical framework to calculate from first principles the distribution of arrival times, W(t), of non-sorbing solute due to advection in two- and three-dimensional heterogeneous porous media and then compare these theoretical predictions with experimental values. Using the related spatial concentration distribution at a given time, the PIs will then predict the time dependence of the longitudinal dispersion coefficient, Dl(t). The theory, based partly on critical path analysis (using cluster statistics of percolation) and partly on percolation scaling of tortuosity, links existing work of one of the PIs in calculating a distribution of rate-limiting conductances with published work of the Eugene Stanley group at Boston University regarding the scaling of the typical travel time with length. We compare our predictions with particle tracking simulations of flow performed by other researchers on a two-dimensional percolation structure, for which the Navier-Stokes equations were solved numerically. Our results compare very favorably with the numerical simulations. Using parameters appropriate for a very narrow pore size distribution (rmin/rmax=0.7), we are able to fit their data at an early time and, using no new parameters, predict W(t) in a system five times larger. The theoretical results are compatible with experiment as well. We propose to test the theoretical work rigorously on experiments and give hypotheses to guide the tests. The experimental results that we address have been the subject of decades of concentrated study without resolution. Moreover, the results of the simulations have not yet been addressed by anyone. Since traditional modeling of dispersion in porous media yields Gaussian spreading in the direction of transport, and since our method is compatible with the much more commonly observed power-law spreading (Margolin and Berkowitz, 2000), it has the potential to transform the way dispersion is modeled. Understanding dispersion is relevant for modeling radioactive tracers to determine groundwater ages or histories of migrating crustal fluids (and thus constraining models), spreading of contaminant plumes, and for agricultural purposes. Our treatment, which excludes molecular diffusion, is not relevant for flows with very small Peclet numbers, meaning that including effects of diffusion is probably the most important extension we can envision. By carrying out this project we will be providing research opportunities for undergraduate students in the earth and environmental sciences department, acquainting them with the most current status of research in hydrogeology. We will also introduce the students to modern quantitative methods in probability theory

我们提出了一个理论框架，从第一性原理计算二维和三维非均质多孔介质中由于平流引起的非吸附溶质到达时间W(t)的分布，然后将这些理论预测与实验值进行比较。利用给定时间的相关空间浓度分布，pi将预测纵向色散系数Dl(t)的时间依赖性。该理论部分基于关键路径分析（使用渗透的聚类统计），部分基于扭曲度的渗透标度，将一个pi在计算限速电导分布方面的现有工作与波士顿大学尤金·斯坦利（Eugene Stanley）小组关于典型旅行时间与长度标度的已发表工作联系起来。我们将我们的预测与其他研究人员对二维渗流结构进行的颗粒跟踪模拟进行了比较，其中Navier-Stokes方程是用数值方法求解的。我们的结果与数值模拟结果非常吻合。使用适合于非常窄的孔径分布的参数（rmin/rmax=0.7），我们能够在早期拟合他们的数据，并且在不使用新参数的情况下，预测系统中5倍大的W(t)。理论结果与实验结果基本一致。我们建议在实验上严格检验理论工作，并提出假设来指导测试。我们讨论的实验结果是几十年来没有解决的集中研究的主题。此外，模拟的结果还没有得到任何人的解释。由于多孔介质中色散的传统建模在输运方向上产生高斯分布，并且由于我们的方法与更常见的幂律分布兼容（Margolin和Berkowitz， 2000），因此它有可能改变色散的建模方式。了解弥散与放射性示踪剂建模有关，以确定地下水年龄或迁移地壳流体的历史（从而限制模型），污染物羽流的扩散以及农业用途。我们的处理排除了分子扩散，与非常小的佩莱特数的流动无关，这意味着包括扩散效应可能是我们可以想象的最重要的扩展。通过开展本项目，我们将为地球与环境科学系的本科生提供研究机会，使他们了解水文地质研究的最新状况。我们还将向学生介绍概率论中的现代定量方法