Oscillatory dynamics of the biologically active zone in in situ bioremediation

In situ bioremediation is a promising biotechnology for removing aqueous phase contaminants from groundwater. The system of three partial differential equations used to model bioremediation has a traveling wave solution which loses stability in a Hopf bifurcation, giving rise to oscillating fronts....

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Bibliographic Details
Published in:Water resources research 2002-10, Vol.38 (10), p.21-1-21-15
Main Authors: Murray, Regan E., Luce, Benjamin P.
Format: Article
Language:English
Subjects:
Approximation
Bifurcations
biodegradation
biologically active zone
Bioremediation
Contaminants
Differential equations
Dynamical systems
Dynamics
Groundwater
Mathematical models
oscillating waves
Oscillations
Partial differential equations
Stability
time-delay differential equations
Traveling waves
Water treatment
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Summary:In situ bioremediation is a promising biotechnology for removing aqueous phase contaminants from groundwater. The system of three partial differential equations used to model bioremediation has a traveling wave solution which loses stability in a Hopf bifurcation, giving rise to oscillating fronts. To understand the origin of these oscillations, we construct a simplified model of the biologically active zone, a time delay differential equation with state‐dependent delay. Despite its simplicity the new model mimics the dynamical characteristics of the bioremediation equations remarkably well and yields an approximate parametric expression for the oscillation onset point.
ISSN:0043-1397
1944-7973
DOI:10.1029/2000WR000206