Multifractal scaling of hydraulic conductivity distributions and the effect on plume-scale contaminant transport

A Collaborative NSF Research Project

Fred Molz, PI & Hui Hai Liu (Clemson University)
Chunmiao Zheng (University of Alabama)

From a contaminant transport viewpoint, hydraulic conductivity (K) is the single most important property function. K is highly heterogeneous, and quantifying the K distribution is a prerequisite to understanding contaminant migration. Over the past decade an increasing number of studies have documented the existence of fractal scaling in K distributions. However, the scaling appears to be of a variable nature that is characterized by a special family of PDF's known as Levy-stable processes. Different sets of increments display properties of different members of the Levy-stable class, which suggests a type of fractal known as a universal multi-fractal. It has been shown recently that the universal multi-fractal paradigm, which includes monofractals as a special case, is successful in modeling the fractal scaling in most K data sets, and the desire to exploit this observation fully is the motivation of the present proposal. The 3 objectives are: I) Develop procedures for the generation and data conditioning of 3-D multi-fractal structures; II) Evaluate multi-fractal effects on solute transport by simulating tracer tests conducted at the highly heterogeneous MADE site; and III) Determine the behavior of plume-scale apparent dispersivity involving multi-fractal scaling and compare the results to that derived from conventional statistical theories. Meeting these 3 objectives will increase understanding significantly of fractal scaling in porous media and the effect on contaminant transport.

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Last modified: June 14, 2001