A case study for a numerical box model with
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A case study for a numerical box model with lagging argument in order to simulate transportation of pollution in Dnieper reservoirs and Loire River Vladimir P. Sizonenko Institute of General Energy, Antonovicha 172, 03150, Kiev, Ukraine INTRODUCTION The focus of this study was to describe radionuclide pollution transport in the surface water using a box model with lagging argument (UNDBE). The model takes into account the time of transport of polluted water and partial mixing of pollution in the box. It is hypothesized that this model will increase the accuracy of the prediction of pollutant concentration at the outlet of the box. In addition, the complexity of the mathematical model and programming tools are comparable to the simplest of current models for predicting pollution concentrations in rivers. There are no additional requirements to obtain the quantity compared to full-scale measurements. Transportation 90Sr was learned for reservoirs of the Dnieper River (Ukraine). The research of passing of ejections 3H in 350 kilometers channel Loire River (France) on stretch a half-year was made in the framework of the IAEA program EMRAS. MATERIALS AND METHODS A set of models of varying complexities for three-dimensional boxes was developed to simulate transport of radionuclide pollution. The simplest of these box models include one which considers complete mixing and averages volume variables; however, the prediction is less accurate than more advanced models. In addition, the simplest model is less sensitive to the quantity of initial data than the existing more complex 1, 2, or 3-dimensional models. The use of latter models imposes fundamental constraints on the possibility of obtaining accurate predictions because these require large quantities of accurate initial and boundary data, as well as considerable computer time. Model UNDBE takes into account that the transposition flows past in two stages. In the first stage, each portion of the water and pollution moves through the reservoir until the outflow. In the second step only at the end of transportation each portion of water and pollution mixes up in a certain part of compartment volume and interacts there with sediments and bottom depositions as in ordinary box model. This approach takes into account time of transporting of water masses and intermixing of contamination in some part of volume of the camera at the moment of termination of transporting. In addition, all transformations of pollutants during transposition are equivalent to transformations in volume. These assumptions gives a model which is described by a system of the usual differential equations with time lag - time of contamination transposition. The difference between the conventional box model and UNDBE box model is the impulse response to contamination at the inflow of the box. Figure 1 illustrate the impulse of the inflow at the first camera and the outflow response of the joint boxes. The conventional box model gives an immediate response on outflow of the box where it is stipulated that intermixing is instantaneous at the inflow. Whereas, the UNDBE box model with lagging argument accounts for the time of contamination transposition. 0.10 0.10 Inflow Inflow 0.08 1-st box 1-st box 0.08 2-nd box 2-nd box C o n cen tra tio n C o n cen tra tio n 0.06 0.06 0.04 0.04 0.02 0.02 0.00 0.00 27 29 31 33 35 37 39 41 27 29 31 33 35 37 39 41 43 45 47 49 51 Time Time Figure 1. Response of the conventional box model and the box model with lagging argument. Case study reservoir The floodplain areas near the Chernobyl Nuclear Power Plant and surrounding catchments are heavily contaminated with radionucleotides, especially 90Sr. The major fraction of the radionucleotides wash-off comes from the watershed of the Pripyat River, the right-hand tributary of the River Dnepr. The 90Sr run-off from these watersheds is transported to the Black Sea through a system of six reservoirs located along the Dnepr River. The largest part of the annual runoff goes through the reservoirs from March until June during flood season. The upper reservoir is Kiev reservoir which has a capacity of 3.7 km3, the length is 70 km, the maximum depth is 14.5 m, the average depth is 4 m, and there are four main tributaries including Pripyat River. An ice jam took place in the Pripyat River in 1994 and water covered heavily contaminated area and inflow concentration of 90Sr increased rapidly up to 5920 Bq/m3 during the period 10–14 February 1994. At that time water discharge in the Pripyat was low – 520 m3/sec. The spring flood occurred from 27 March to 22 April and concentrations of 90 Sr had increased up to 2553 Bq/m3. Water discharge in the latter period reached 1700 m3/sec. Daily data were used for water discharges and values of concentrations (Voitsekhovitch et al., 1997). One box was used for modeling only. Figure 2 presents conventional box model WATOX (Zheleznyak et al., 1992) results in a comparison with daily data for 90Sr concentrations in the outflow of the Kiev reservoir. The results usage of the new model with lagging argument for the same situation is in Figure 3. The next examples are when high spring flood in the Pripyat River took place during February through June 1991 and 1999. Case study River Loire This study consists in modeling the dispersion of 3H in the Loire River has been done in the framework of EMRAS project (EMRAS, 2006). The testing area is approximately 350 km in length for a period of 6 months from the July 1 through December 31, 1999. This study takes into account water discharges from 4 main tributaries and 3H discharges from 5 nuclear power plants (14 reactors) (by using real hydraulic conditions of the year 1999). The hydraulic boundary conditions and 3H discharges for each nuclear power plant were given with a time step of one hour. Channel of the River Loire in length 350 kilometers, was broken on 33 sequential cameras. The results of the modeling (temporal series of 3H concentration with a time step one hour) were compared to measurements of tritium concentration made in Angers, a city along the Loire river, located downstream of all 3H discharges. The outcomes obtained with the help of the model UNDBE in Angers and compared to measurements, are represented on Figure 4. 1300 Kiev Reservoir Outflow Concen tration Sr (Bq/m ) 3 Mod el WATOX 900 90 500 100 28/02/94 20/03/94 09/04/94 29/04/94 08/06/94 28/06/94 19/05/94 Figure 2. Dynamics of 90Sr concentrations in the outflow of the Kiev reservoir and ordinary box model WATOX predictions. 1300 C once ntratio nSr (Bq/ m ) Kiev R eservo ir O utflow 3 900 Mod el UNDBE 90 500 100 2 8/0 2 /9 4 20/0 3 /9 4 0 9/0 4 /9 4 2 9/0 4 /9 4 1 9/ 05 /9 4 0 8/0 6 /9 4 2 8/0 6 /9 4 Figure 3. Dynamics of 90Sr concentration in the outflow of the Kiev reservoir in 1994 and UNDBE model predictions. RESULTS AND CONCLUSIONS The box model with lagging argument (UNDBE) taking into account time of water transport and partial mixing in box, gives the opportunity to increase the accuracy of the box model without small spatial discretization. The comparison of results shows that box model UNDBE gives good coincidence with measurements. Figure 4. Comparison between calculated and measured tritium concentration at Angers. ACKNOWLEDGEMENT The author kindly thanks to the researchers of Ukrainian Hydrometeorological Institute, the Hydrological Forecasting Department of the HydroMet Center in Kiev, the DIREN Centre and EDF (France) for radiological and hydrological data. REFERENCES Voitsekhovitch O., Kanivets V., Laptev G., 1997. Radioecology of Water Objects the Chernobyl zone, Vol.1, Chernobylinterinform, Kiev, (1997), pp. 60-96. Zheleznyak M., Demchenko R., Khursin S., Kuzmenko Y., Tkalich P., Vitjuk N., 1992. Mathematical Modeling of Radionuclide Dispersion in the Pripyat-Dnieper Aquatic System after the Chernobyl Accident, The Science of the Total Environment, Vol. 112, (1992), pp. 89-114. EMRAS Working Group on Model Validation for Radionuclide Transport in the Aquatic Systems. 2006. http://www-ns.iaea.org/projects/emras/.