Modelling the Distribution of Radionuclides in Deep Ocean Water Columns. Application to 3H, 13 Cs and 239, 246Pu

Modelling the Distribution of Radionuclides 7 in Deep Ocean Water Columns. Application to 3H, 13 Cs and 239•246Pu R. Periáñez Opto. Física Aplicada, E.U. Ingeniería Técnica Agrícola, Universidad de Sevilla, Ctra. Utrera km 1, 41013- Sevilla, Spain ABSTRACT A one-dimensional model to simulate the dispersion of radionuclides down deep water columns has been developed. The model includes the transfers of radionuclides between water, suspended matter and bottom sediments. Such transfers are formulated in terms of kinetic transfer coefficients. A suspended matter sub-model has also been developed to obtain the suspended matter concentra/ion profile. The dependence of the settling velocity of suspended particles on the salinity profile and the dependence of the vertical turbulent diffusion coefficient on the horizontal water current profile are included in the model. The mode/ has been validated by comparing measured and computed profiles of 3 H, 137 Cs and 239'240 Pu in the Atlantic, the Mediterranean and the Pacific. Sorne predictive studies and sensitivity test have a/so been carried out. INTRODUCTION There has been an increasing interest in measuring radionuclide profiles in water columns in the deep ocean over the last few years (Bowen et al., 1980; Fukai et al., 1980; Livingston et al., 1987; Molero et al., 1995). However, few one-dimensional mathematical models have been developed to study such profiles. The model of Monte et al. (1991) simulates the dispersion of conservative radionuclides (neglecting interactions with suspended matter and bottom sediments) in deep lakes. The water column is divided into three layers: epilimnion, thermocline and hypolimnion. This model reproduces the depth distribution of radionuclide concentrations in sorne lakes, but in other cases, there are discrepancies due to the fact that interaction with sediments 1s an important factor in removing radionuclides from the water. The model of Ribbe et al. (1991) includes the interactions of radionuclides with suspended matter and bottom sediments, and is applied ín a shallow sea (water depth is around 140m). A constant suspended matter distribution in the water column is assumed, as well as a constant vertical turbulent diffusion coefficient. These may be realistic assumptions in shallow waters, but not in the deep ocean (water depths of sorne thousands of meters). Indeed, suspended matter concentrations decrease from the surface to the bottom (Brewer et al., 1976; Eisma, 1993). Also, since the horizontal water velocity is not constant in the water column (Pugh, 1987) and since turbulence is related to the water velocity, the diffusion coefficient will not be constant along the water column. Because of this, the model of Ribbe et al. (1991) <loes not adequately reproduce the radionuclide concentrations in the deepest water layers. In this paper, a one-dimensional dispersion model for both conservative and non-conservative radionuclides is presented and validated by comparing measured and computed vertical profiles of 3H, 137Cs and 239•240Pu in the deep ocean. Toe exchange of radionuclides between water, suspended matter and bottom sediments is described in terms of kinetic transfer coefficients. Thus, a coefficient k1 governs the transfer from water to the solid phase, and a coefficient k2 governs the inverse process. The adsorption of radionuclides on suspended matter, and therefore the transfer coefficient k1, depend on the suspended matter concentration. Thus, a suspended matter sub-model is developed to obtain the suspended matter concentration profile. The vertical diffusion coefficient is written as a function of the horizontal water velocity, which also varíes along the water column. The model is totally general and can be applied to both stratified and non-stratified seas. The salinity along the water column is introduced in the model as input data and so the salinity profile may feature a halocline if necessary. It must be noted that horizontal advection and diffusion of contaminants are not incJuded in the model. This effect can be neglected in the case, for instance, of fallout that is constant over a large area. In the case of a point discharge, horizontal dispersion will be important, and the time that the model computes for the removal of radionuclides from the water column will be longer than the real time, since such horizontal dispersion produces a faster decrease in concentration. Thus, a one-dimensional model must be applied in the case of uniform sources of contamination. In the next section, the suspended matter and the radionuclide dispersion models are presented. In the third section, the model is validated and applied to sorne predictive studies dealing with hypothetical accidents. Finally, sorne sensitivity tests have been performed to study the model response to variations in the parameters involved in the model. MODEL DESCRIPTION Suspended matter sub-model As mentioned in the Introduction, the vertical suspended matter distribution must be known to compute the transfer of radionuclides from water to suspended particles. lt is assumed that, in a steady state situation, the upward diffusion rate of suspended particles is equal to the downward settling rate, which leads to the following equation (Nicholson and O'Connor, 1984; Eisma, 1993): (1) where Kz, m and Wz are, respectively, the vertical diffusion coefficient, the suspended matter concentration and the settling velocity of suspended particles at level z measured from the surface to the bottom. The settling velocity of particles is obtained from Stokes' law: (2) where g is gravity, µ the viscosity of water, d the mean diameter of suspended particles, Ps the density of suspended particles and Pz is the water density at a depth z below the surface. The settling velocity is considered to be independent of m, that is, the eff ects of aggregation and of hindered settling at high values of m have been neglected. This is a reasonable assumption given the low suspended matter concentrations found in the ocean (Jones et al., 1994). The vertical diffusion coefficient, K2, is considered to be proportional to the horizontal water velocity (Nicholson and O'Connor, 1984): (3) where U2 is the horizontal water velocity at depth z. U2 can be related to the surface water velocity, Us, through the relationship (Pugh, 1987): (4) D is the total water depth and n is an integer number that ranges between 5 and 7 (Pugh, 1987). The coefficient rx. in Eq. (3) is obtained from a calibration exercise. Equation (1) is solved numerically to obtain the suspended matter concentration profile. The values for the different parameters will be given later. Dispersion of radionuclides Radionuclides can be dissolved or fixed to solid particles. Ionic exchanges produce a transf er of radionuclides between water and suspended matter. This transfer is described by kinetic transfer coefficients. Radionuclides in the dissolved phase are subject to turbulent mixing, and radionuclides in the particulate phase have a falling velocity equal to the settling velocity of suspended particles. In the water layer that is in contact with the bottom sedimentan ionic exchange between the water and the sediment takes place. Also, radionuclides in suspended matter can be deposited on the sea bed. Resuspension of material from the sea bed is related to the presence of strong bottom currents (Eisma, 1993). This effect has been neglected; thus, the model should be applied only in regions lacking such currents. The water column is divided into a number of layers of thickness �z. The equation whose solution gives the time evolution of radionuclide concentration in water, Cd (Bq m -3), at a given layer is: fJCd fJ ( fJCd) 75t = az Kz az -k, Cd + k2mCs -J..Cd,(5) where Cs is the radionuclide concentration in suspended matter (Bq g-1) and A is the radioactive decay constant. k1 and k2 are the kinetic transfer coefficients. The transfer of radionuclides from water to suspended matter depends on the suspended matter surface per unit water volume, which is denoted as the exchange surface (Periáñez et al., 1996a). Assuming spherical particles and a step function for the grain size distribution of suspended matter, the coefficient k1 can be written as (Periáñez et al., 1996a): 3m k, =x,R Ps (6) where R is the mean radius of suspended particles and Xi is a parameter that depends on the water conditions (salinity, pH, temperature). Since it has dimensions of a velocity, it is denoted the exchange velocity (Periáñez et al., 1996a). The coefficient that governs the transfer of radionuclides from suspended particles to water, k2, is assumed to be constant (Periáñez et al., 1996a). The equation that gives the time evolution of radionuclide concentration in suspended matter is: (7) where k1 is given by Eq. (6). In these equations, the settling velocity of suspended particles and the vertical diffusion coefficient are taken as in the suspended matter sub-model. The deepest water layer also interacts with the bottom sediments. Neglecting resuspension, the equation that gives the time evolution of sediment activity per area unit, As (Bq m-2), is: (8) where '*' means that the respective quantity is evaluated for the deepest water layer. The equations for Cd and C., in this deepest layer are also corrected to take into account interactions with the sediments. In this equation, the transfer coefficient k� will depend on the exchange surface of the sediment. This coefficient can be writen as (Periáñez et al., 1996a): k* _ 3Lfl/J 1 -X1 Ró.z (9) where L gives the mean depth to which the water penetrates the sediment due to its porosity, f is the fraction of active sediment, which is made up of particles with a diameter < 62·5 µm (Benes et al., 1994), R is the mean radius of the active sediment particles and 1/J is a geometrical accessibility factor, which takes into account that, for geometrical reasons, not all the mass of the active sediment is in contact with water. The mean radius of the active sediment particles has been considered to be equal to the mean radius of suspended particles (Periáñez et al., 1996a). The concepts of exchange surface and exchange velocity and the formulation of the transfer coefficient k1 have been successfully applied to simulate the dispersion of 226Ra, 238U, 232Th and 210Po in a tidal estuary in south-west Spain (Periáñez et al., 1996b; Periáñez and Martínez-Aguirre, 1997, in press). MODEL RESULTS Calibration and results The model has been validated by comparing radionuclide profiles measured in the Atlantic Ocean, the Pacific Ocean and the Mediterranean Sea with the computed profiles. First, the suspended matter concentration profile must be obtained by solving Eq. (1). The water column is divided in layers of thickness �z =lOOm. Water viscosity is taken as µ=1·005x10-3Ns m-2 and the mean density of suspended particles is selected as 2600 kgm-3, which is the established value for the density of soil particles (Baver et al., 1972) and has been used in previous modelling work (Periáñez et al., 1996b; Periáñez and Martínez-Aguirre, 1997b). Water salinity, S, is considered to increase linearly with depth from 30gl-1 at the surface to 90gl-1 at the bottom. This is a realistic assumption (see for instance the measurements of Feely et al., 1979). The density of water (kg m-3) increases linearly with salinity following the relation given by Kowalick and Murty (1993): p = 998 · 91(1 + 7 · 5 X 10-4S). (10) Such a salinity profile leads to stable stratification, which is characterized by a Richardson number greater than 1 (Eisma, 1993). Only particles with a diameter less than 62 ·5 µm can be present in the water column as suspended matter; larger particles quickly sink to the bottom (Gurbutt et al., 1987). Thus, the mean diameter of suspended particles is fixed as 30 µm. Using these parameters, the settling velocities of the suspended particles, Wz, are in the order of 10-3 m s-1, which is in agreement with that found by Jones et al. (1994) and Nicholson and O'Connor (1984). The average water velocity at the surface is taken as Us=0·02ms-1 since this is a typical value of the residual current in the open sea (Elliott et al., 1992; Prandle et al., 1993). To obtain the current profile, the mean value 6 was taken for the integer n. Suspended matter concentrations in surface waters in the sea can range from 0·005mg l-1 to the lOO mg l-1 measured in coastal waters (Eisma, 1993). In this work, a surface concentration of 2 mg 1-1 is taken as the boundary condition to numerically solve Eq. (I). In the ocean, there is a more turbid surface layer and a decreasing concentration of suspended particles with depth (Brewer et al., 1976). Thís effect is observed in the solution of Eq. (I). Indeed, a suspended matter concentration of 0· 13 mg 1-1 is obtained for the deepest water layer (if the total water depth is 4000m), which represents 6·5% of the concentration in the surface. This suspended matter profile has been used as input data for the radionuclide dispersion model. A deep nepheloid layer (water close to the sea bottom with a large suspended load) may exist [see, for instance, Biscaye and Eittreim (197 7)). Deep nepheloid layers in the deep ocean are related to the presence of strong bottom currents (Eisma, 1993) that produce resuspension of particles from the sediment. Since resuspension has been neglected, the deep nepheloid layer <loes not appear. Of course, the suspended matter distribution along the water column will not be the same for the Mediterranean, the Atlantic and the Pacific, but the computed distribution can be considered as representative of the real situation in the sea. Indeed, such a profile will be more realistic than assuming a constant suspended matter concentration as in Ribbe et al. (1991). This is confirmed by the fact that results in agreement with measurements are obtained when using this suspended matter profile in modelling the dispersion of non-conservative radionuclides along the water column. The mixing depth in the sediment has been taken as L = 0-1 m following previous modelling work (Abril and García-León, 1993; Periáñez et al., 1996b ). The fraction of active sediments was taken as f = O· 30, which is a common value (Periáñez and Martínez-Aguirre, 1997b), and the geometrical factor is selected as 1/1=0-001 (Periáñez and Martínez Aguirre, 1997b ). The model has been applied to simulate the dispersion of 137Cs, 239•24ºPu and 3H. Thus, the exchange velocity XI and the transfer coefficient k2 must be known for these radionuclides. In the case of 137 Cs they have been obtained from laboratory experiments carried out by Nyffeler et al. (1984): XI =2-10x10-8ms-1 and k2= l-16x10-5s-1. Nyffeler et al. (1984) found a very small variability in k2 (less than an order of magnitude) when they measured this parameter for a wide set of elements (Th, Sn, Hg, Pa, Zn, Sb, Cs, Se, Cd, Ba) with very different chemical behaviours. This small variation makes it possible (Nyffeler et al., 1984) to estimate XI without laboratory experiments. Thus, the k2 of Pu can be taken to be equal to that of Cs. From the coefficient k2 and the mean value of the distribution coefficient, kd, of Pu in the sea, the exchange velocity of Pu can be estimated following the method presented in detail in Periáñez and Martínez-Aguirre (1997a). Indeed, the following relationship between Xi, k2 and kd (Periáñez et al., 1996b) holds: kd = �_2__ (11) k2PsR This method has yielded good results in previous modelling work (Periáñez and Martínez-Aguirre, 1997a, b). The exchange velocity obtained is x1=1-51x10-5ms-I. The exchange velocity of Pu is three orders of magnitude greater than that of Cs, due to the larger affinity of Pu to solid particles. In the case of 3H, interactions with the solid phases are neglected: XI= k2 = O. Once all the parameters involved in the model have been defined, the dispersion equations are solved using a finite difference explicit scheme with a time step b.t = 100 s and taking b.z = 100 m. The actual contamination of the ocean is caused by the fallout resulting from nuclear weapon tests, the Chemobyl accident, releases from nuclear facillities, etc. This fallout has been taking place over severa! decades, and so the model should run over long time scales. To save CPU time, simulations over 2 years are carried out. At t = O, the water column is has no radioactivity, and the fallout starts. The fallout magnitude is amplified in such a way that after 2 years, the actual levels of contamination are reached. Of course, the magnitude of the fallout is not constant in time, but a constant deposition rate of radionulides on the sea surface is considered, which can be taken as a mean deposition. This technique of amplifing the source terms has been used successfully in previous modelling work (Periáñez and Martínez-Aguirre, 1997b). The magnitudes of the deposition rates (used to obtain the actual contamination levels after just 2 years for each radionuclide and for each location where the model is applied) were selected by trial-and-error exercises. Unfortunately, the deposition rates could not be compared with measurements owing to the lack of data at the places in which the model is applied. Measured and computed 137Cs profiles in the Pacific ocean are shown in Fig. lA (Tahiti) and B (Tuamoto Archipelago). Experimental data were taken from Bourlat et al. (1996) and Hamilton et al. (1996), respectively. Units and scales used by the authors of the experimental works have been followed in drawing the figures presented in this paper. As mentioned above, the parameter a in the diffusion coefficient is obtained from a calibration exercise for each location where the model is applied. This calibration consists of selecting, by trial and error, the values of a that produce the results in the best possible agreement with the measurements. lt was taken as O· l in Tahiti and 0-08 in Tuamoto Archipelago. Thus, diffusion coefficients similar, by order of magnitude, to those used by Ribbe et al. (1991) and Monte et al. (1991) are obtained. As can be seen in Fig. 1, model results are in good agreement with the experimental measurements. In Fig. 2A and B, measured and computed pro files of 137 Cs in the Mediterranean Sea and 3H in the Atlantic Ocean, respectively, are shown. The Cs profile was taken from Papucci et al. (1996) and the tritium one from Nyffeler et al. (1996). a was taken as 0-8 in the Atlantic and 0-08 in the Mediterranean sea. Again, the model gives good results for both radionuclides. In Fig. 3, model and experimental results for 239•24ºPu in Tahiti and the Tuamoto Archipelago are shown. Experimental results are taken from Bourlat et al. (1996) and Hamilton et al. (1996). Model results are in agreement with measurements in both profiles. The model shows two interesting features that have been observed: the subsurface maximum 2.5 (a) "model" - "exp• 1-+-l 2 1.5 � Ji 0.5 m lll 111 111 o o 500 1000 1500 2000 2500 depth (m) 10 (b) "model" - "exp • i-+---, ?'" Ji 0.1 0.01 .___���..__�......_�...__�.....__�......___�_._______. O 500 1000 1500 2000 2500 3000 3500 4000 depth (m) Fig. l. Computed and measured 137Cs profiles in water samples (dissolved phase) collected at Tahiti (A) and Tuamoto Archipelago (B). Errors are 2<T in (B). detected around 600 m below the surface and the 'high Pu deep layer' described in Livingston et al. (1987) and Bowen et al. (1980). Indeed, in Fig. 3, a slight increase of dissolved Pu from 1500 m to the bottom can be observed. Thus, in deep water, Pu is released to the dissolved phase by M' M' 0.6 .---"""T""--r-----.----,---,-------.--....-----, 0.5 0.4 0.3 0.2 0.1 o o 90 80 70 60 50 40 30 20 10 o o (a) (b) "time-1" - "time-2" ----· "time-3" ---- "time-4" 500 1000 1500 2000 2500 3000 3500 4000 depth (m) "time-1" - "time-2' ----· "time-3" ---- 'time-4" ····· · 500 1000 1500 2000 2500 3000 3500 4000 depth (m) Fig. 7. Total contents of 137Cs (A) and 239·240Pu (B) 5, 10, 15 and 20days (time!, time 2, time 3 and time 4, respectively) after the deposition. SENSITIVITY TESTS Sorne parameters, such as the surface suspended matter concentration, the surface water velocity and r:i in the diffusion coefficient, are not known for the places where the model is applied. Thus, values that are similar to 3000 ------------...---.--�-�---. "model" - 2500 2000 l1500 1000 500 oL...._.L.__.L-...:::...L--...L--.J--...L--....L.--'----'---' o10 20 30 40 50 60 70 80 90 100 time (days) Fig. 8. Time evolution of 239·240Pu activity in the bottom sediment 0.6 ---------------�------. 0.5 'time-1' - 'time-2' --- 'time-3' ..... 'time-4' ¿;, 0.4 1 0.3 0.2 0.1 o500 1000 1500 2000 2500 3000 3500 4000 depth (m) Fig. 9. Total contents of 137Cs 5, 10, 15 and 20days (time 1, time 2, time 3 and time 4. respectively) after the deposition when a halocline is present. those found in current literature have been selected. Sorne sensitivity tests have been performed to study the model response to changes in these parameters. The tests have been carried out with the 239·24ºPu profile measured at Tuamoto Archipelago. First, the sensitivity of the model to changes in the water layer thickness was studied. The model results do not show any appreciable difference if the thickness of the water layers is taken as �z = 50 m. In a second test, the model response to changes of the surface suspended matter concentration was studied. The result is presented in Fig. 10, where '1' represents the model result when the surface suspended matter concentration is taken as 1 mg 1- 1 and '2' is the model result when such a concentration is taken as 4 mg 1-1• It should be noted that changing the surface suspended matter concentration implies that suspended matter concentrations along the water column also change, since the suspended matter equation is solved again with the new boundary condition. A decrease in suspended matter concentrations leads to an increase in dissolved Pu concentrations (' l' in Fig. 1 O) since the exchange surface is reduced. However, an increase in suspended matter concentration ('2' in Fig. 1 O) produces a decrease in dissolved Pu concentrations since the exchange surface increases. It can be seen that good results are obtained with a surface-suspended matter concentration of 2 mg 1-1 ('model'). In the third test, the model sensitivity to changes in the surface water velocity was studied. The result is presented in Fig. 11, where 'l' represents the model result when the surface water velocity is taken as 0·08 m s- 1, and '2' represents the model result when it is taken as 0-005 m s-1• A larger sub-surface maximum is obtained when the water 20 18 16 M' 14 12 .§. � 10 � 8 6 Q. 4 2 o o 500 'model' - 'exp' � ·1 • ----. ·2· \ ... 1 _________________ f. .. ---·t···· 1000 1500 depth (m) 2000 2500 Fig. 10. Model response to changes in the surface suspended matter concentration. See text for explanation of '1' and '2'. ¿;, .s 12 10 8 6 4 2 500 1000 1500 depth (m) 'model' - 'exp' f-+--1 '1' ·2· . 2000 2500 Fig. 11. Model response to changes in the surface water velocity. See text for explanation of 'I' and '2'. velocity decreases since the diffusion coefficient decreases too. The model is not sensitive from 1500 m to the bottom since water velocities at such depths are very small in all cases (Eq. (4)). Finally, the sensitivity of the model to the parameter IX in the diffusion coefficient is presented in Fig. 12. 'l' represents the model result taking IX= 0-04 and '2' the model result taking IX= O· 16. Again, a decrease in the diffusion coefficient leads to a larger sub-surface maximum. The model is not sensitive from 1500 to the bottom for the mentioned above. The formulation on which the transfer of radionuclides between the dissolved and solid phase is based, is presented in Periáñez et al. (1996a). In Periáñez et al. (1996b), the sensitivity of such formulation to Xi, k2 and the geometrical accessibility factor 1/¡ is studied. CONCLUSIONS A one-dimensional model has been developed to simulate the dispersion of radionuclides along deep water columns. The model includes the transfer of radionuclides between water, suspended matter and bottom sediments. Such transfers are described by means of kinetic transfer coefficients. A suspended matter sub-model is also developed to obtain the suspended matter concentration profile along the water column. The turbulent 14 'model' - 12 'exp' 1-+-----, '1' ... ·2· (') 10 i 8 s 6 4 2 500 1000 1500 2000 2500 depth (m) Fig. 12. Model response to changes in the parameter C< in the diffusion coefficient. See text for explanation of 'I' and '2'. diffusion coefficient and the settling velocity of suspended particles depend on the water depth, which has improved the model results with respect to previous modelling work. Also, the model can be applied to stratified seas since the salinity profile is used as input data. Model results are in good agreement with measured concentration profiles of 137Cs, 3H and 239•240Pu in the Atlantic, the Pacific and the Mediterranean, which show the adequacy of the description of the processes. Once the model has been validated, it has been applied to sorne predictive studies concerning hypothetical nuclear incidents. 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