Journal article
Non-Fickian dispersion of groundwater age
Water resources research, Vol.48(7), pp.W07508-n/a
07/2012
Handle:
https://hdl.handle.net/2376/104874
PMCID: PMC4070610
PMID: 24976651
Abstract
We expand the governing equation of groundwater age to account for non-Fickian dispersive fluxes using continuous random walks. Groundwater age is included as an additional (fifth) dimension on which the volumetric mass density of water is distributed and we follow the classical random walk derivation now in five dimensions. The general solution of the random walk recovers the previous conventional model of age when the low order moments of the transition density functions remain finite at their limits and describes non-Fickian age distributions when the transition densities diverge. Previously published transition densities are then used to show how the added dimension in age affects the governing differential equations. Depending on which transition densities diverge, the resulting models may be nonlocal in time, space, or age and can describe asymptotic or pre-asymptotic dispersion. A joint distribution function of time and age transitions is developed as a conditional probability and a natural result of this is that time and age must always have identical transition rate functions. This implies that a transition density defined for age can substitute for a density in time and this has implications for transport model parameter estimation. We present examples of simulated age distributions from a geologically based, heterogeneous domain that exhibit non-Fickian behavior and show that the non-Fickian model provides better descriptions of the distributions than the Fickian model.
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Details
- Title
- Non-Fickian dispersion of groundwater age
- Creators
- Nicholas B Engdahl - Department of Land, Air, and Water Resources, University of California, DavisTimothy R Ginn - Civil and Environmental Engineering, University of California, DavisGraham E Fogg - Department of Land, Air, and Water Resources, University of California, Davis
- Publication Details
- Water resources research, Vol.48(7), pp.W07508-n/a
- Academic Unit
- Civil and Environmental Engineering, Department of
- Publisher
- United States
- Grant note
- P42 ES004699 / NIEHS NIH HHS
- Identifiers
- 99900547089701842
- Language
- English
- Resource Type
- Journal article