Prediction uncertainty for tracer migration in random heterogeneities with multifractal character

S. Painter, G. Mahinthakumar

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Travel-time statistics for non-reacting tracers in fractal and multifractal media are addressed through numerical simulations. The logarithm of hydraulic conductivity is modeled using fractional Brownian motion (fBm) and more recently developed multifractal model based on bounded fractional Levy motion (bfLm). These models have been shown previously to accurately reproduce statistical properties of large conductivity datasets. The ensemble-mean travel time increases nearly linearly with travel distance and the variance in the travel time increases nearly parabolically with travel distance. This is consistent with near-field analytical approximations developed for non-fractal media and suggests that these analytical results may have some degree of robustness to non-ideal features in the random-field models. The magnitudes of the travel-time moments are dependent on the system size. For fBm media, this size dependence can be explained using an effective variance that increases with increasing size of the flow system. However, the magnitudes of the travel-time moments are also sensitive to other non-ideal effects such as deviations from Gaussian behavior. This sensitivity illustrates the need for careful aquifer characterization and conditional numerical simulation in practical situations requiring accurate estimates of uncertainty in the plume position.

Original languageEnglish
Pages (from-to)49-57
Number of pages9
JournalAdvances in Water Resources
Volume23
Issue number1
DOIs
StatePublished - Sep 15 1999
Externally publishedYes

Funding

This work was partially supported by a travel grant from the Bilaterial Collaboration Program of the Australian Department of Industry, Science and Tourism. We also acknowledge the support by the Center of Computational Sciences at Oak Ridge National Laboratory for the use of Intel Paragon XP/S 150 supercomputer.

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