HR: 1340h
AN: H23G-1712    [Abstracts]
TI: Power Law Tailing in Air-spargingand Invasion-percolation Model for Calculating Diffusion in the Liquid Phase
AU: * Kawanishi, T
EM: kawanisi@t.kanazawa-u.ac.jp
AF: Kanazawa University, Kakuma-machi, Kanazawa, 920-1302, Japan
AU: Hayashi, Y
EM: yohayasi@t.kanazawa-u.ac.jp
AF: Kanazawa University, Kakuma-machi, Kanazawa, 920-1302, Japan
AB: Power law tailings are often seen in removal of pollutants from soil or ground water. We have found that the power law tailing can also be seen in laboratory scale column air-sparging experiments. For this, we propose the following hypothesis. Introducing gas to the water saturated glass bead column causes some fractal-like gas flow path, which causes the power law distribution of distance that solute has to travel until it reaches the gas- water interface, this causes the power law tailing. In order to prove this, we constructed a model for removal of solute in water by diffusion to gas/water interface based on the invasion percolation. In a simple cubic bond lattice, invasion percolation is performed, assuming that the invading phase is gas and remaining phase is water. Then, set the initial solute concentration in water uniformly unity, set the boundary conditions as the concentration of the solute at the gas/water interfacial nodes is zero (or for random walk, set the interface as absorbing ends). Then diffusion process was calculated with two different methods: finite difference method for solving the partial differential equation based on Fick's law, and the random walk method. The results of two different methods are qualitatively identical. Near the percolation threshold of gaseous phase, the removal rates revealed power law tailing, and the slope in double-log removal late vs. time curves was about -1.0. At higher gaseous content, away from the threshold, this kind of power law behavior was not seen. The removal rate of solute from the lattice filled with water and the top and bottom face are set as zero concentration or absorbing, we got the slope in double-log plot of -0.5, this was in good accordance with the theory. Theoretically, at the threshold of gas phase, water phase in three dimensions is away from threshold, therefore, the water phase cannot be seen as fractal. We consider, in the short range of time, the dangling of water phase contributes to the power-law like distribution of diffusion distance of solute, and thus causes the power law tailing. In the presentation, we discuss the effect of gaseous content, lattice size on the removal rate and the distribution of diffusion distance.
DE: 1831 Groundwater quality
DE: 1847 Modeling
DE: 1849 Numerical approximations and analysis
DE: 1875 Vadose zone
SC: Hydrology [H]
MN: 2007 Fall Meeting