HR: 10:50h
AN: B32B-03    [Abstracts]
TI: Anomalous Diffusion in 2-Dimensional, Random Euclidean and Prefractal Models of Heterogeneous Porous Media
AU: Kim, J
EM: jwookim@gist.ac.kr
AF: Department of Environmental Science and Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju, 500-712 Korea, Republic of
AU: * Perfect, E
EM: eperfect@utk.edu
AF: Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, TN 37996 United States
AU: Choi, H
EM: hcchoi@gist.ac.kr
AF: Department of Environmental Science and Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju, 500-712 Korea, Republic of
AB: Diffusion in disordered systems is known to deviate from Einstein's classical description and become ``anomalous''. However, the implications of this phenomenon for solute diffusion in water-saturated porous media have not been widely explored. Understanding the relationship between pore-space geometry and anomalous diffusion is important for predicting the kinetics of biogeochemical reactions in applications such as contaminant transport, and nutrient availability to plants and microorganisms. This study reports on numerical simulations of solute diffusion performed within the pore phase of 2-dimensional random Euclidean and prefractal models of heterogeneous porous media. Three classes of prefractal were studied: pore, mass, and pore-solid Sierpinski carpets. The main objectives were to investigate the effects of varying porosity (Φ) and lacunarity (L) on the extent of anomalous diffusion, and to identify the best model for representing natural porous media by relating our results to previously published simulations in digitized soil thin sections. Solute diffusion was simulated using a stochastic cellular automaton model based on the ``myopic ant'' algorithm. The resulting mean squared displacement versus time relations were parameterized by the random walk dimension (d_w), which was > 2 in all of the porous media investigated. Values of d_w > 2 have implications for the scaling of biogeochemical processes since the standard diffusion coefficient is not longer a constant but depends upon the time. The estimates of d_w increased non-linearly with decreasing Φ. The increases were most pronounced for the Euclidean porous media and least pronounced for the pore-solid prefractals and soil thin sections. The presence of large pores was an important factor controlling the extent of anomalous diffusion, and d_w → 2 as L → 1. A power law relationship based on the product of Φ and L explained > 97% of the total variation in d_w regardless of the porous medium considered. Our results suggest that pore-solid prefractals are the closest geometrical model to natural porous media. Further research on solute adsorption and specific surface area scaling in pore-solid prefractals might prove valuable for a variety of biogeochemical applications.
DE: 0412 Biogeochemical kinetics and reaction modeling (0414, 0793, 1615, 4805, 4912)
DE: 1829 Groundwater hydrology
DE: 4440 Fractals and multifractals
SC: Biogeosciences [B]
MN: Fall Meeting 2005