Fractional Kinetic Model for First Flush of Stormwater Pollutants
Publication: Journal of Environmental Engineering
Volume 131, Issue 2
Abstract
By generalizing the urban ground as a fractal surface and revising the classical Fick’s formula as a law of dispersion with a fractional-order derivative, a fractional kinetic model is developed for simulation of the first flush phenomenon of urban stormwater pollutants. The model is comprised of (1) a fractional dispersion-advection equation (FADE); (2) the kinematic-wave overland flow equation; and (3) methods for numerical solution of the equations. A split-operator method is proposed for numerical solution of the FADE by means of a newly presented F.3 finite-difference scheme for fractional partial differential equations. The kinematic-wave overland flow equation is solved using the Lax–Wendroff explicit scheme. Under a constant rainstorm the hydrograph displays an initial rising limb followed by a constant flow discharge. The pollutograph exhibits a steep receding limb (the first flush), followed by a long stretched tail (heavy tail process). The agreement between simulated and measured dispersion characteristics is found to be good, demonstrating that the fractional kinetic model is capable of accurately predicting the characteristics of the first flush phenomenon.
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Acknowledgments
The first writer would like to acknowledge the support from the Foundation for Science and Technology of the Portuguese Ministry of Science and Technology, Lisbon, Portugal through the Research Project FCT-SFRH/BPD/11537/2002. During the preparation of this manuscript the first writer was a postdoctoral research fellow in the Department of Civil Engineering of the Faculty of Science and Technology at the University of Coimbra, in Portugal. The writers would also like to express their sincere gratitude to the anonymous reviewers of this paper for their constructive comments and thorough review.
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Information & Authors
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Published In
Journal of Environmental Engineering
Volume 131 • Issue 2 • February 2005
Pages: 232 - 241
Copyright
© 2005 ASCE.
History
Received: May 28, 2003
Accepted: Apr 5, 2004
Published online: Feb 1, 2005
Published in print: Feb 2005
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