ZHANG Wan-shun, ZHAO Yan-xin, XU Yan-hong, WANG Yong-gui

School of Resource and Environmental Science, Wuhan University, Wuhan 430079, China,

E-mail: wszhang@whu.edu.cn

PENG Hong

College of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China XU Gao-hong

Bureau of Hydrology of Changjiang Water Resources Commission, Wuhan 430010, China

(Received January 25, 2012, Revised June 16, 2012)

2-D NUMERICAL SIMULATION OF RADIONUCLIDE TRANSPORT IN THE LOWER YANGTZE RIVER*

ZHANG Wan-shun, ZHAO Yan-xin, XU Yan-hong, WANG Yong-gui

School of Resource and Environmental Science, Wuhan University, Wuhan 430079, China,

E-mail: wszhang@whu.edu.cn

PENG Hong

College of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China XU Gao-hong

Bureau of Hydrology of Changjiang Water Resources Commission, Wuhan 430010, China

(Received January 25, 2012, Revised June 16, 2012)

The assessment of the radiological impact of the liquid discharges from nuclear power plants is a major issue for the environmental protection. In this study, a numerical model for the radionuclide transport in the aquatic environment is built, based on the hydrodynamic equations, including the complete set of Saint-Venant equations, the sediment transport equations, with consideration of several different particle sizes and the deposition and erosion of the suspended sediments, and the radionuclide transport equations. The exchanges of radionuclides between water, suspended matter and bed sediments are described in terms of kinetic transfer coefficients. The model is used to simulate the transport of the radionuclides discharged from a planned nuclear power plant project to be sited along the lower Yangtze River. From the model results, one may see the detailed temporal-spatial evolution of the radionuclide contamination in the solution, in the suspended matter and in the bed sediments. The model can be used as a basic tool for studying the environmental impacts of the liquid discharges from nuclear facilities on a river system.

2-D numerical model, radionuclide, Yangtze River, sediment

Introduction

Nuclear Power Plants (NPPs) may routinely or accidentally release radionuclides into surface waters, where they would become potential environmental hazards for invertebrates[1], fish[2]and human beings[3,4]. Studies show that after radionuclides are discharged, the river systems are the main pathway for the radionuclide transport to locations hundreds of kilometers downstream[5]. Suspended sediments also play an important role as the carriers of radioactive contaminants over long distances. The processes of sedimentation and erosion of contaminated sediments drive a redistribution of the pollutants in the water-bed sediment system[6,7]. Radionuclides can also be accumulated and biomagnified through food chains[8]. Methods used to evaluate the environmental risks caused by artificial radionuclides include the fieldmeasurements and the laboratory experiments[9,10], but they are very costly and time-consuming. Furthermore, it is very difficult to provide the decision makers with some comprehensive information when the monitoring does not have a sufficiently high frequency, especially, before the operation of a NPP.

Over the past decades, there has been growing interest in the development of transport models for radionuclides because they can be applied to the assessment of radiological consequences of existing or planned routine discharges or accidental releases. Thus, models that can simulate the dispersion of radionuclides in the riverine environment were reported[11-13]. A state-of-the-art review was made by Monte et al. for models developed to predict the migration of radionuclides through rivers[14]. These models represent an improvement in the description of the radionuclide dispersion over the earlier box models. However, there is a need for a comprehensive modeling system that can realistically describe significantly different temporal and spatial dispersion pro-cesses[15].

The aim of the present study is to develop a 2-D numerical model that describes the transport of two artificial radionuclides (137Cs,90Sr) in river systems. The model is based on a combination of three modules: a module of river hydrodynamics, a module of sediment transport, and a module of radionuclide transport. It is assumed that the exchanges between water and sediments are governed by first-order, reversible reactions, with unequal rates of desorption and adsorption and different equilibrium distribution coefficients for bottom sediments and suspended sediments. In principle, the radionuclide transport module of the present model is based on the 1-D RIVTOX model[13]. After validation, the model is applied to simulate a hypothetical scenario of a continuous radionuclide release from the planned Pengze NPP, which is located on the Madang Reach of the lower Yangtze River. The simulation results are used to predict the transport of radionuclide pollutants in the aquatic environment of the Yangtze River.

Fig.1 The main processes of radionuclide transport in river systems

1. Mathematical model

Figure 1 shows the main processes governing the radionuclide transport in river systems. The pollutants in the rivers are transported by the water flow (advection processes) under the simultaneous influence of turbulent diffusion processes. At the same time, the dissolved radionuclides can interact with the suspended matter and the upper layer of the bottom sediments. The transfer of radionuclides from water to sediment can occur either through sorption to the charged particles by electrostatic attraction or through ion exchange on the sediment surfaces. Reverse reactions, by which radionuclides can be desorbed, can also occur. The other two main physical exchange mechanisms of radionuclides are the sedimentation of the contaminated suspended matter onto the riverbed and the resuspension of the bed sediments into the water. Thus, the transport of radionuclides in river systems is greatly affected by different hydrological and hydrodynamic conditions throughout the year.

1.1 Module of hydrodynamics

The unsteady water flow dynamics in a channel can be described by the 2-D Saint-Venant equations as follows:

Continuity equation

Momentum equations

where u and v are the depth-averaged velocity components in thex and y directions, respectively, hand zare the flow depth and the elevation of the river flow, respectively,g is the gravity acceleration, γtis the turbulent viscosity coefficient, and n is the roughness coefficient.

1.2 Module of sediment transport

The transport of suspended sediments is described by the 2-D nonequilibrium suspended sediment transport equation, including a sink/source term describing the sedimentation and the resuspension flux of sediments[16].

Continuity equation of suspended sediments

Riverbed deformation equation

whereis andare the depth-averaged concentration and the sediment carrying capacity for the i-th group of suspended sediments, respectively, Z*is the bed elevation, is the turbulent diffusion coeffi-

ε cient,αsis the coefficient of the saturation recovery, and γsis the dry density of the sediment. ωiis the settling velocity for the i-th group of suspended sediments, which can be calculated by using Zhang?s formula[17].

The method employed here to calculate the nonuniform sediment-carrying capacity is as follows:

(1) Determine the sediment carrying capacity of the total suspended sediments by using Zhang?s formula[17]

where Ksand m are empirical coefficients,ω is the average settling velocity of non-uniform suspended sediments, which can be calculated as=in whichPkiS*, and Pkiis the gradation component of the bed material.

(2) Determine the sediment carrying capacity for the i-th group of suspended sediments

1.3 Module of radionuclide transport

The module of the radionuclide transport describes the temporal-spatial transport processes of radionuclides in the river-water environment. The module includes the advection and dispersion equations for the dissolved radionuclides in the aqueous solution (Cw), the radionuclides adsorbed by the suspended sediments(Cs)and the radionuclides in the bottom deposit (Cb). The adsorption and the desorption of radionuclides in the solution-suspended sediment-bed deposition system are described by the equilibrium distribution coefficient (Cd), but in addition, different exchange rates (ai,j) for the forward and the reverse reactions are taken into account in order to provide a more realistic simulation of the geo-chemical behaviour of radionuclides in the aquatic environment. It is implicitly assumed that the adsorptiondesorption processes may occur simultaneously with constant rates on the particle surfaces. The radionuclide transport equations in a river system are as follows[13]:

Fig.2 Sketch of Madang Reach

Transport equation of dissolved radionuclides

Transport equation of radionuclides on the suspended sediments

Transport equation of radionuclides in the bed sediments

where Cwis the radionuclide concentration in the aqueous solution,Csis the radionuclide concentration i n the suspende d s edim ents , Cbis the radionuclideconcentrationinthebedsediments, α12andα21are the adsorption and the desorption rates in the water-suspended sediment system, respectively,α13and α31are the adsorption and the desorption rates in the water-bed sediment system, respectively,Kdsis the distribution coefficient in the water-suspended sediment system, Kdbis the distribution coefficient in the water-bed sediment system,λ is the radionuclide decay constant, and Cmis the radionuclide discharged.

Table 1 Radionuclides released by the Pengze NPP*

Table 2 Concentrations of137Cs and90Sr in surface water, suspended sediments, and bed sediments*

1.4 Boundary conditions

Two types of boundaries are assumed along the boundary of the computational domain in the model, viz., the open and the closed boundaries. For the open boundaries, the distributions of the depth-averaged velocity of the river flow and the depth-averaged concentration of the suspended sediments are given at the upstream boundary, and at the downstream boundary the elevation of the river flow is given. The no-slip condition is considered, where the flow velocity and all fluxes (suspended sediments, radionuclides) are set to zero at the the side banks of the river.

1.5 Numerical discretization and solution

The governing equations are discretized in the framework of the Finite-Volume Method (FVM). The convective flux on non-orthogonal, quadrilateral grids is evaluated using the second-order upwind scheme with a deferred correction, and the diffusive flux is solved by using the central difference scheme[18]. The velocity-pressure coupling relationship is realized by using the SIMPLE algorithm based on the method described by Liu et al.[16].

Fig.3 Topography of the study region

Fig.4 River discharge and suspended sediment concentration during 2006

2. Model application

2.1 Study area and boundary coditionsn

The ongoing Pengze NPP project is located onthe right bank of the Madang Reach of the Yangtze River in Pengze County, Jiangxi Province, a sketch of which is shown in Fig.2. The project consists of two sets of AP1000 PWR reactor, each with a capacity of 1 250 MW. As one of the first three inland NPPs of China, the plant is planned to be put into operation in 2016. In the operation of the two reactors, 0.76 m3/s of wastewater will be discharged into the Yangtze River, including the cooling water and the low-level radioactive liquid waste containing the products of nuclear activation and fission. Table 1 lists the estimated amounts of the main artificial radionuclides that will be generated and released by the NPP.

Table 3 Transport coefficients for radionuclides137Cs and90Sr

5(a) Velocity distribution

Currently, there is no other NPP in the basin of the Yangtze River. A radiological survey was conducted to assess the background radiation levels around the plant site in February 2006. During the survey, three sampling sites, called 0#, 1# and 2#, were chosen in the reach (see Fig.2). The sampling mediums include the water, the suspended matter and the bed sediments. The results show that the concentrations of137Cs and90Sr are extremely low in the aquatic environment of the Madang Reach and do not indicate any contamination. Table 2 lists the measured concentrations of137Cs and90Sr in the water, the suspended sediments, and the bed sediments, as well as the estimated average background concentrations in the Madang Reach. However, the radionuclides discharged by the Pengze NPP could be a potential hazard for the aquatic environment.

The main objective of this study is, therefore, to examine the potential radiological impacts of the Pengze NPP on the Madang Reach of the Yangtze River. The calculation domain is from Penglangji to Dongliu, as shown in Fig.2. The channel length in the longitudinal direction is 40 km, and in the vertical direction, it is about 0.5 km-2.5 km. The topographic map issued in 2005 is used for the simulation, as shown in Fig.3.

5(b) Suspended sediment concentration

The upstream river boundary conditions are determined according to the measurements at the Pengze NPP Gauging Station, and the downstream water level is obtained from the measurements at the Tianxingzhou hydrologic station. Figure 4 shows the hydrological series data in the period January-December 2006. The mean particle diameter is 0.026 mm, and 90% of the suspended particles are finer than 0.0001 m. Suspended sediments are dominant, and there is no need to consider the bed loads in the modeling. The sediment particles are classifiedinto five groups by diameters: d=0m-0.00001m, 0.00001 m-0.00005 m, 0.00005 m-0.0001 m, 0.0001 m-0.00025 m, and 0.00025 m-0.001 m.

5(c)137Cs concentration in water and suspended sediments

2.2 Grid generation and parameters

The whole domain is discretized into 181×41 cells, and more grid cells are allocated in the region of interest than elsewhere. The distance between grid cells varies from 35 to 100 m. The roughness coefficient ranges from 0.028 to 0.030 for the riverbed. The coefficients of the suspended sediment transport are taken as Ks=0.246 and m=0.92. The distribution coefficients and the adsorption/desorption rates of the radionuclides are obtained from Kryshev et al.[13], as listed in Table 3.

5(d)90Sr concentration in water and suspended sedimentsFig.5 Comparison between simulation and field data

2.3 Verification of calculation results

Fig.6137Cs and90Sr concentrations in water, suspended sediments, and bottom sediments on the 60th day

Fig.7137Cs and90Sr concentrations in water, suspended sediments, and bottom sediments on the 210th day

The numerical model is verified by comparing the numerical results with the field data. The hydrographic data in the period Febuary 1-20, 2006, and the radiological measurements during this period are used for the verification. Figure 5(a) shows the comparison of the flow velocity between the model results and the observations at Section 1 and Section 2. Figure 5(b) compares the numerical results with the observed time series of the sediment concentration at the two sections. The calculated time series of concentrations of137Cs and90Sr in the water and the suspended sediments at the two sampling sites (1#, 2#) and the comparison with the measurements (on the 5th, 10th and 15th day) are shown in Fig.5(c) and Fig.5(d). It can be seen that the simulation results agree well with the measurements. Therefore, the model is accurate and can be used to forecast the radionuclide transport in the lower Yangtze River.

2.4 Model simulation and result analysis

Fig.8137Cs and90Sr concentrations in water, suspended sediments, and bottom sediments on the 360th day

In order to assess the radiological impacts on the aquatic environment after the operation of the Pengze NPP, a hypothetical scenario of a continuous release of radionuclides is simulated with the hydrological series data obtained during 2006 (see Fig.4). The initial radionuclide concentrations are set at the natural background levels. Figure 6 shows the prediction of radionuclide concentrations for the 60th day, which is in the dry season. The results show that the highest radionuclide concentrations would be found very near the outlet. The suspended sediment flux goes through this very concentrated plume and can adsorb radionuclide ions that could not be desorbed from the sediment surfaces in a short time. The spatial distribution of the bottom activity shows that the pollution plume has contaminated the bottom sediment by the dual effects of the direct adsorption and deposition of the contaminated suspended sediments. Figure 7 shows the predicted distribution of radionuclides for the 210th day, when the Yangtze River floods. At this time, the pollution plume has decreased its size significantly compared with that during the dry season because the high flow of the Yangtze River favors the transverse and longitudinal dispersions of radionuclides. At the same time, because of the high river flow velocity, the contaminated bed-sediments can be resuspended and removed from the riverbed. Thus, we have observed the minimally contaminated areas during the year. The simulated radionuclide concentrations at the end of the year are shown in Fig.8. The contamination plume is similar to that of the 60th day, as the hydrological and hydrodynamic conditions are both very similar. Comparing the calculation results under different conditions, we suggest that the radionuclide concentrations in the water, the suspended sediments, and the bed deposits after the start of the NPP project will generally be of the same order of magnitude as the background levels. The pollution plume is negligible beyond 2 km from the location of the NPP effluent outlet, due to the high flow discharge of the lower Yangtze River.

3. Conclusions

In this study, a 2-D numerical model is developed to simulate the transport of radionuclides in the lower Yangtze River. The model is based on the combination of the hydrodynamic module, the nonequilibrium sediment-transport module, and the radionuclide transport module. The numerical results are compared with observations in February 2006 and it is shown that this model is applicable to the radionuclide transport in the aquatic environment. The proposed model is then used to simulate a hypothetical scenario of a continuous release of137Cs and90Sr from a planned NPP on the Madang Reach of the lower Yangtze River. The simulation results could reflect the detailed temporal-spatial evolution of radionuclide concentrations in the water, the suspended matter and the bed sediments near the effluent outlet. Generally speaking, the successful results of both applications demonstrate that the model is appropriate for the numerical study of the NPP radionuclide release into the aquatic environment.

It should be noted, however, that because of the complexity of the dynamic radionuclide transport processes, much work remains to be done to improve the model, especially, for determining the adsorption anddesorption parameters in the aquatic environment. For better understanding the transport processes and for more accurately calibrating the model parameters, one needs more observational data and more comprehensive analysis of hydrodynamics, sedimentation, and transport coefficients for radionuclides.

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* Biography: ZHANG Wan-shun (1965-), Ph. D., Professor