HR: 0800h
AN: H11D-1289    [Abstracts]
TI: Effective Hydraulic Conductivity Scaling in a 2-Dimensional Geometrical Multifractal Model for Aquifer Heterogeneity
AU: * Gentry, R W
EM: rgentry@utk.edu
AF: Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN 37996 United States
AU: Perfect, E
EM: eperfect@utk.edu
AF: Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, TN 37996 United States
AU: Sukop, M C
EM: sukopm@fiu.edu
AF: Department of Earth Sciences, Florida International University, Miami, FL 33199 United States
AB: Recent analyses of field data suggest that the spatial variation of hydraulic conductivity, K, within an aquifer may be multifractal. We investigated the implications of this finding for the scaling of effective hydraulic conductivity, <K>, by performing numerical simulations of flow in 2-dimensional geometrical multifractal K fields. A theoretical framework for generating such fields is presented based on the parameters of the truncated binomial distribution, TBD. This leads to an approximate analytical expression showing that <K> increases with increasing length scale as a power law, whose exponent, α, is determined by the TBD parameters. Five geometrical multifractal K fields were generated with different minimum length scales. Each domain was discretized using a block center grid consisting of 59,049 uniformly-spaced nodes. A unit cube aquifer was used for the numerical simulations. The boundary conditions were implemented with constant head (unit gradient) parallel planes, and corresponding zero flux planes on the normal axes. A finite difference simulation model based on MODFLOW 2000 was used, and "zone budget" was employed to calculate the flow balance. The discharge into and out of the unit cube was then used to calculate <K> based on Darcy's law. The numerical simulations produced similar increases in <K> with increasing length scale to those predicted by the analytical model. Nonlinear regression analyses yielded estimates of α from the numerical simulations that were within 10% of the analytical value for these fields. These simulations provide a theoretical explanation for effective hydraulic conductivity scaling in terms of multifractals. The advantage of such an approach is that the α-parameter, which controls the degree of scaling, is physically-based and can potentially be estimated from independent measurements.
DE: 1828 Groundwater hydraulics
DE: 1839 Hydrologic scaling
DE: 4440 Fractals and multifractals
SC: Hydrology [H]
MN: Fall Meeting 2005