Field Measurement and Theoretical Study of the Fractal Properties of Hydraulic Conductivity

水力电导率分形特性的现场测量与理论研究

• 批准号: 9405075
• 负责人: Joseph Judkins
• 金额: $ 25.54万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-15 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9405075&HistoricalAwards=false
• 关键词: Field; Measurement; Theoretical; Study; Fractal

19405075 Molz During the past decade, interest in the use of fractal concepts to describe various phenomena in the Earth Sciences, including subsurface hydrology, has been increasing. It has become apparent that many, if not most, porous media posses a hierarchical structure. It is not clear how classical transport theory based on the concept of a representative elementary volume should be applied at the vastly different scales of interest in such natural media. While it is not known how the term "hierarchical structure" should be defined, there is experimental evidence that the hierarchical structure of the three-dimensional hydraulic conductivity function exhibits the spatial structure of certain self-affine, stochastic fractals called Gaussian noise (fGn) and fractional Brownian motion (fBm). This work would develop a fractal-based method for constructing three-dimensional distributions of field-measured K from a limited number of measurements. Three dimensional horizontal K distributions will be obtained at a variety of field sites using the new electromagnetic (EM) borehole flowmeter. Data sets will then be analyzed for the presence of fGn/fBm using rescaled range analysis. This will be followed by the generation of stochastic K interpolations and a study of the distribution properties using modern computer graphics. Finally, an attempt will be made to relate the potential fractal properties of natural porous media to the physics of the probably chaotic processes that determine the property distributions of sediments. From an aquifer transport viewpoint, K is the single most important property function. For any particular aquifer, K varies over one or more orders of magnitude and is highly heterogeneous. Yet making sense of the K distribution is often a prerequisite to understanding the pattern of contaminant migration in polluted aquifers. A tremendous amount of money is spent attempting to characterize aquifers using tools that are not adequate to the task. The proposed work has the potential to lead to the development of new theoretical tools and practical insights that could contribute significantly to the long-term solution of subsurface contamination problems. It will have the potential to establish a new practical framework for transport phenomena at a variety of scales in natural porous media.

小行星19405075 在过去的十年中，在使用分形概念来描述地球科学，包括地下水文学的各种现象的兴趣一直在增加。 很明显，许多（如果不是大多数的话）多孔介质具有分级结构。 目前尚不清楚如何经典的输运理论的基础上的概念，一个代表性的基本体积应适用于在这样的自然介质中的巨大不同规模的利益。 虽然目前还不知道如何定义术语“层次结构”，但有实验证据表明，三维水力传导系数函数的层次结构表现出称为高斯噪声（fGn）和分数布朗运动（fBM）的某些自仿射随机分形的空间结构。 这项工作将开发一种基于分形的方法，用于从有限数量的测量中构建现场测量的K的三维分布。 三维水平K分布将获得在各种现场使用新的电磁（EM）钻孔流量计。 然后使用重新标度的范围分析分析数据集是否存在fGn/fBm。 其次是随机K插值的生成和使用现代计算机图形学的分布特性的研究。 最后，将尝试将天然多孔介质的潜在分形特性与决定沉积物属性分布的可能混沌过程的物理学联系起来。 从含水层输运的角度来看，K是唯一最重要的属性函数。 对于任何特定的含水层，K值的变化超过一个或多个数量级，并且具有高度的异质性。 然而，理解K分布往往是理解污染含水层中污染物迁移模式的先决条件。 人们花费了大量资金试图使用不足以完成任务的工具来描述含水层的特征。 拟议的工作有可能导致新的理论工具和实际的见解，可以大大有助于地下污染问题的长期解决方案的发展。 它将有可能建立一个新的实际框架，在各种规模的天然多孔介质中的传输现象。