Dispersion in Heterogeneous Porous Media Through Advection

我们提出了一个理论框架，从第一性原理计算的到达时间，W（t），由于在二维和三维非均质多孔介质中的平流的非吸附溶质的分布，然后比较这些理论预测与实验值。使用给定时间的相关空间浓度分布，PI将预测纵向扩散系数Dl（t）的时间依赖性。该理论的基础上，部分关键路径分析（使用集群统计的渗透）和部分渗透缩放的曲折，链接现有的工作之一的PI在计算分布的限速电导与发表的工作的尤金斯坦利集团在波士顿大学关于缩放的典型旅行时间的长度。我们比较我们的预测与其他研究人员进行的二维渗流结构，数值求解的Navier-Stokes方程的粒子跟踪模拟流。我们的结果比较非常有利的数值模拟。使用适合于非常窄的孔径分布（rmin/rmax=0.7）的参数，我们能够在早期拟合他们的数据，并且不使用新的参数，在五倍大的系统中预测W（t）。理论计算结果与实验结果也是一致的。我们建议严格的实验测试的理论工作，并给出假设来指导测试。我们讨论的实验结果是几十年来集中研究的主题，但没有解决方案。此外，模拟结果尚未得到任何人的处理。由于传统的多孔介质中的色散模型在传输方向上产生高斯传播，并且由于我们的方法与更常见的幂律传播（Margolin和Berkowitz，2000）兼容，因此它有可能改变色散的建模方式。了解分散是相关的建模放射性示踪剂，以确定地下水的年龄或迁移地壳流体的历史（从而约束模型），污染物羽流的传播，并用于农业目的。我们的处理，其中不包括分子扩散，是不相关的流量非常小的Peclet数，这意味着，包括扩散的影响可能是最重要的扩展，我们可以想象。通过实施该项目，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学研究的最新状况。我们也将向学生介绍概率论中的现代定量方法

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