HR: 0800h
AN: H11D-1308    [Abstracts]
TI: On the Predictability of Solute Transport in Fractured Media
AU: * Reeves, D M
EM: mreeves@dri.edu
AF: Desert Research Institue, Division of Hydrologic Sciences 2215 Raggio Parkway, Reno, NV 89512 United States
AU: Benson, D A
EM: dbenson@mines.edu
AF: Colorado School of Mines, Department of Geology and Geological Engineering 1516 Illinois Street , Golden, CO 80401 United States
AU: Meerschaert, M M
EM: mcubed@maths.otago.ac.nz
AF: University of Otago, Department of Mathematics & Statistics P.O. Box 56 , Dunedin, 00000 New Zealand
AB: Predictions of real-world solute transport based on a stochastic advection-dispersion equation rely on at least one assumption of ergodicity. One of these assumptions is that the distribution of solute particles for an individual realization will be equivalent to the ensemble distribution of solute particles after a sufficient number of particle motions have occurred. Under this condition, the solute particles of the individual realization will have experienced all of the velocity variations present in a ground water flow system. In a physical sense, this assumes sufficient mixing of a plume, which depends on the connectivity of flowpaths. Deviations from this ideal are more likely in fractured low-permeability rock. We explore deviations between individual and ensemble solute particle motion in a wide range of fracture network types to explore the validity of the ergodic hypothesis in fractured media. Synthetic plumes are produced from numerical simulations of fluid flow and solute transport through large-scale (2.5km by 2.5km), randomly generated fracture networks. These two-dimensional networks are generated according to statistics obtained from field studies of fracture length, transmissivity, density, and orientation. The ensemble particle motions tend to converge to either operator-stable or multi-Gaussian random vectors, depending on distributions of fracture length and values of spatial density. Although operator-stable and multi-Gaussian densities are the analytic solutions to fractional-order and classical advection-dispersion equations, respectively, these equations assume that a dissolved solute undergoes ergodic transport. Measures of Kolmogorov distance, the largest distance between empirical cumulative distribution functions for ensemble plumes and individual realizations, provide a metric to evaluate deviations of individual realizations from the ensemble. Low values of Kolmogorov distance imply that individual and ensemble particle motions are similar and the ergodic hypothesis is valid, while high values of Kolmogorov distance question the validity of the ergodic hypothesis as significant variability exits between individual and ensemble particle motions. As expected, ensemble and individual particle motions are similar for densely fractured networks dominated by short fractures, while a high degree of variability between individual realizations and the ensemble exists for sparsely fractured networks dominated by very long fractures. This work quantifies the degree to which the individual fractures must be characterized for accurate predictions of transport in fracture networks.
DE: 1832 Groundwater transport
DE: 1847 Modeling
DE: 1869 Stochastic hydrology
DE: 1873 Uncertainty assessment (3275)
DE: 5104 Fracture and flow
SC: Hydrology [H]
MN: Fall Meeting 2005