Fractal mobile/immobile solute transport

Fractal mobile/immobile solute transport A fractal mobile/immobile model for solute transport assumes power law waiting times in the immobile zone, leading to a fractional time derivative in the model equations. The equations are equivalent to previous models of mobile/immobile transport with power law memory functions and are the limiting equations that govern continuous time random walks with heavy tailed random waiting times. The solution is gained by performing an integral transform on the solution of any boundary value problem for transport in the absence of an immobile phase. In this regard, the output from a multidimensional numerical model can be transformed to include the effect of a fractal immobile phase. The solutions capture the anomalous behavior of tracer plumes in heterogeneous aquifers, including power law breakthrough curves at late time, and power law decline in the measured mobile mass. The MADE site mobile tritium mass decline is consistent with a fractional time derivative of order γ = 0.33, while 's (2002) stream tracer test is well modeled by a fractional time derivative of order γ = 0.3. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

Fractal mobile/immobile solute transport

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Publisher
Wiley
Copyright
Copyright © 2003 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
D.O.I.
10.1029/2003WR002141
Publisher site
See Article on Publisher Site

Abstract

A fractal mobile/immobile model for solute transport assumes power law waiting times in the immobile zone, leading to a fractional time derivative in the model equations. The equations are equivalent to previous models of mobile/immobile transport with power law memory functions and are the limiting equations that govern continuous time random walks with heavy tailed random waiting times. The solution is gained by performing an integral transform on the solution of any boundary value problem for transport in the absence of an immobile phase. In this regard, the output from a multidimensional numerical model can be transformed to include the effect of a fractal immobile phase. The solutions capture the anomalous behavior of tracer plumes in heterogeneous aquifers, including power law breakthrough curves at late time, and power law decline in the measured mobile mass. The MADE site mobile tritium mass decline is consistent with a fractional time derivative of order γ = 0.33, while 's (2002) stream tracer test is well modeled by a fractional time derivative of order γ = 0.3.

Journal

Water Resources ResearchWiley

Published: Oct 1, 2003

References

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