CHEN Bin

State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China, E-mail: chenb@bnu.edu.cn

ZENG Li, WU Yi-hong, J? Ping, ZHAO Yi-jun

State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China ?nstitute of Water Resources and Hydropower Research, Beijing 100038, China

(Received May 18, 2012, Revised October 30, 2012)

TRANSPORT OF BICOMPONENT CONTAMINANT IN FREE-SURFACE WETLAND FLOW*

CHEN Bin

State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China, E-mail: chenb@bnu.edu.cn

ZENG Li, WU Yi-hong, J? Ping, ZHAO Yi-jun

State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China ?nstitute of Water Resources and Hydropower Research, Beijing 100038, China

(Received May 18, 2012, Revised October 30, 2012)

This paper presents a theoretical analysis of a pulsed bicomponent contaminant emission into a free-surface wetland flow. The basic equations are for the bicomponent contaminant transport in the wetland flow under the combined action of advection, mass dispersion, and ecological reaction at the phase averaged scale. The effect of the ecological reaction is separated from the hydrodynamic effect via a set of widely used transforms. The analytical solution for the evolution of the depth-averaged concentration is rigorously derived, with a limiting case covering the known solution for the single component contaminant transport. ?t is found that the depth-averaged species concentration of the bicomponent contaminant can approach an equilibrium state determined by the distribution coefficient.

contaminant dispersion, bicomponent contaminant, wetland hydrodynamics, environmental risk assessment

Introduction

The wetlands play a variety of roles in terms of water purification, flood control, drought resistance, and biodiversity conservation[1-9]. For an environmental risk assessment and a restoration program related to the wetlands, the essential issue is to predict the contaminant transport under the combined action of advection, mass dispersion and ecological reaction at the phase average scale[10,11].

With respect to the contaminant transport in a wetland flow, some theoretical studies were carried out based on the Taylor’s classic analysis on the dispersion, the method of concentration moments, and the multi-scale analysis. Lightbody and Nepf proposed a formula for predicting the longitudinal dispersion coefficient for a wetland flow dominated by the emergent vegetation[12,13]. Based on the Taylor’s analysison the dispersion and the method of concentration moments, Chen et al.[10], Zeng et al.[11,14-17]and Wu et al.[18,19]obtained some analytical solutions of the environmental dispersivities for a single zone wetland flow under various conditions. Murphy et al.[20]and Nepf et al.[21]investigated the behavior of the longitudinal dispersion due to the turbulence at different scales. Analytical solutions of the environmental dispersivities were also obtained for a two-layer wetland flow and a two-zone wetland flow[22,23]. However, these analytical solutions concern only the evolution of a single component contaminant, not so much the behavior of the bicomponent contaminant, due to the complexity of the hydraulic dispersion and the ecological reaction[24-28].

For the typical case of a pulsed bicomponent contaminant discharge into a free surface wetland flow, this paper comes up with an analytical solution of the depth-averaged concentration under the conditions of the hydraulic dispersion and the ecological reaction. The specific goals are: (1) to introduce the general equations for the bicomponent contaminant transport in the wetland flow, and (2) to present ananalytical solution for the long time evolution of the depth-averaged concentration of the bicomponent contaminant.

1. Formulation

For a typical wetland flow, the governing equations for mass transport of the bicomponent contaminant can be written as[10,11,29]

where φ is the porosity, t the time,AC the concentration of contaminant A, u the velocity, κ the tortuosity, λ the mass diffusivity, K the mass dispersivity tensor,Ar the ecological reaction rate of contaminant A,dk the distribution coefficient,BC the concentration of contaminant B, andBr the ecological reaction rate of contaminant B. The last term on the right hand side of Eqs.(1) and (2) represents the interaction between pollutants A and B.

Fig.1 Schematic diagram of a free water surface wetland flo w

Consider the bicomponent contaminant transport in a unidirectional free-surface wetland flow in a Cartesian coordinate system with coordinate axes coinciding with the principle axes of the tensor K, the longitudinal x-axis along the flow direction, the vertical z-axis upward, and the origin at the bottom, as shown in Fig.1. The corresponding velocity profile can be expressed as[11]

where U is the depth-averaged velocity, α is a dimensionless parameter representing the combined action of the depth, the vertical momentum dispersion, the microscopic curvature of the flow passage, and the viscous friction of vegetation[11], and H is the depth of the wetland.

Consider a uniform instantaneous emission of the bicomponent contaminant at the cross-section of =x 0 at time =0t, with the initial condition as

where Q is the mass per unit width, and ()xδ is the Dirac delta function.

For the two-dimensional process, Eqs.(1) and (2) reduce to

respectively, whereLK andVK are the longitudinal and the vertical mass dispersivities, respectively. For a finite contaminant discharge, the concentration boundary conditions at =x±∞ are

For the bottom bed at z=0 and the free surface at z=H, the concentration boundary conditions are

With the dimensionless parameters defined as

the governing equations, as well as the boundary and the initial conditions can be rewritten as

where

2. Separation of ecological reaction effect from hydrodynamic effect

The method for solving the second-order constant-coefficient linear parabolic system in Ref.[30] is adopted, with the effect of the ecological reaction being separated from the hydrodynamic effect. With the transform introduced in Ref.[30]

where ε=NB/NA, Eqs.(13) and (14) of an advection-diffusion-reaction type for the concentration become

respectively. Eqs.(17) and (18) represent a physical process of the advection-diffusion with various initial conditions.

The solution of Eqs.(17) and (18) can be rewritten as

Since ψ varies with ζ, it is difficult to obtain the exact analytical solution of Θ. For the environmental risk assessment associated with the wetland flow, the main concern is the long time evolution of the contaminant. According to Zeng and Chen’s results, the depth-averaged concentration satisfies[11]

whereLD is the environmental dispersivity expressed as

The solution of Eq.(21) is[11]

where

3. Results and discussions

The solution for the long time evolution of the depth-averaged concentration of the bicomponent contaminant can be expressed as

Fig.2 Variations of ΨAEand ΨBEwith ξ for τ=15.0, α=1.0, Pex=1.0, φ=0.9, RxK=0.1, NA=1.0, kd=2.0 and ε=0.1, 0.5, 1.0, 2.0, 4.0 and 8.0

This result shows that the species concentration of the bicomponent contaminant will reach an equilibrium state, and the ratio of the depth-averaged concentration of pollutant A to that of pollutant B is determined bydk. Figure 2 shows the variations ofΨAEand ΨBEwith ξ for τ=15.0, α=1.0, Pex= 1.0, φ=0.9,=0.1, NA=1.0, kd=2.0and ε= 0.1, 0.5, 1.0, 2.0, 4.0, and 8.0. ?t is shown that the concentration of pollutant A is just twice that of pollutant B for kd=2.0.

Acknowledgement

This work was supported by the Special Foundation of China ?nstitute of Water Resources and Hydropower Research (Contract No. SJ1239).

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* Project supported by the National Natural Science Foundation of China (Grant Nos. 10972009, 50939001 and 41271543).

Biography: CHEN Bin (1972-), Male, Ph. D., Professor