Fractional Kinetic Model for First Flush of Stormwater Pollutants

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.