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

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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.