Uranium and thorium concentrations in an estuary affected by phosphate fertilizer processing: Experimental results and a modelling study

J. Environ. Radioactivity, Vol. 35, No. 3, pp. 281-304, 1997 0 1997 Published by Elsevier Science Limited All rights reserved. Printed in Ireland ELSEVIER PII: SO265-931X(96)00057-4 0265-931X/97 $17.00 + 0.00 Uranium and Thorium Concentrations in an Estuary Affected by Phosphate Fertilizer Processing: Experimental Results and a Modelling Study R. Perihiiez & A. Martinez-Aguirre Dpto Fisica Aplicada, E.U. Ingenieria Tkcnica Agricola, Universidad de Sevilla, Ctra Utrera km 1, 41014 Sevilla, Spain (Received 16 February 1996; accepted 25 June 1996) ABSTRACT The Odiel river, in southwest Spain, forms an estuarine system which is ujfected by waste disposal from a fertilizer complex. Uranium and thorium concentrations in waters and suspended matter, activity ratios and distribution coefficients, kd, have been measured along the river during two different tidal states. The results have shown that a radioactive impact is being delivered to the river, as well as a signtjiicant variability depending on the sampling point and the tidal state. Thus, a quantitative study of the distribution of radionuclides can be carried out best bq’ means of a mathematical model. The model includes the partition of radiotracers between four phases (water, suspended matter and two sedimentfractions) and has been designedfor non-equilibrium conditions. Thus, radiotracer transfers are described in terms of kinetic transfer coefficients instead of kds. The model simultaneously solves the hydrodynamic equations, the suspended matter equation (including depostion and resuspension processes) and the equations which describe the time evolution of radionuclide concentrations in each one of the four phases. The model has yielded good results in predicting U and Th concentrations in water and suspended matter, distribution coefficients and ThjU mass ratios. o 1997 Published by Elsevier Science Limited. All rights reserved 1 INTRODUCTION The Odiel river is located in the southwest of Spain. At its lowest reaches, it forms a tidal estuarine system which discharges into the Atlantic Ocean. 281 282 R. Periciriez, A. Martinez-Aguirre The estuary is close to a large industrial area in which a phosphate fertilizer processing complex operates. This complex processes around 1.6 MT of phosphate rock per year from Morocco, Senegal and Togo. Part of the waste is released directly into the Odiel river. It is well known (Van der Heijde et al., 1988; Laiche & Scott, 1991) that such wastes contain significant amounts of natural radionuclides: U, Th, Ra and their daughters. The presence of 226Ra and 224Ra in water and suspended matter samples collected from the Odiel river has already been investigated (Periafiez & Garcia-Leon, 1993; Periaiiez et al., 1994a). These studies have revealed that a radioactive impact is being delivered to the river since, for instance, levels up to 670mBq 1-l of 226Ra have been measured in a water sample collected close to the fertilizer complex. Although there are data on the Uand Th-isotope content in the Odiel river water and suspended matter (Martinez-Aguirre et al., 1994a), a more detailed study is reported in this paper. The objective of this work is to understand the U and Th dispersion mechanisms in dynamic aquatic systems, including the distribution between the solid and liquid phases as well as the effect of tidal oscillations. Thus, water samples were collected along the Odiel river at two different tidal states (high and low water) and the Uand Th-isotope contents in water and suspended matter were measured. The distribution coefficients kd were also calculated. A qualitative description of the results is not straightforward as there is significant variability in activity concentrations and kd, depending upon the sampling point and the tidal state. This is a logical result since we are dealing with an open system in which some different effects are taking place at the same time: non-constant input from the source, adsorption of radionuclides on to suspended matter and bottom sedimens, desorption, and water and suspended matter movements due to tides. Thus, a quantitative understanding of the U and Th dispersion can be achieved best by means of mathematical models. A two-dimensional model, that includes the transfer processes between four phases (water, suspended matter and two grain size fractions of bottom sediments), has been applied to the Odiel river. The model simultaneously solves the hydrodynamic equations, the suspended matter dynamic equation (including the resuspension and deposition processes) and the equations that describe the time evolution of radionuclide concentrations into each of the four phases. Although the model has been previously applied to study the dispersion of 226Ra in the Odiel river (Periaiiez et al., 1996a), there are two main objectives in applying it to U and Th: to achieve a quantitative understanding of the experimental results and to provide extra validation of the model, that is, to validate the model for elements with very different geochemical behaviours, such as U and Th. Uranium and thorium in an estuary 283 In the next section, the sampling and experimental methods are described. Next, the experimental results are discussed. The modelling work is described in Section 4. 2 EXPERIMENTAL Water samples were collected in plastic bottles along the Odiel river basin (see Fig. 1) during July 1990. Two samples were collected from each sampling station: one during high water and the other during low water so as to study the influence of tidal oscillations on the results. The water was filtered as soon as possible through previously weighed Nuclepore filters (0.4pm pore size) to separate the suspended matter. The filter was then dried and weighed to calculate the mass of recovered matter. Typical suspended matter concentrations in the Odiel river ranged from 24 to 50ppm, depending on the sampling point and the tidal state during sampling. The filter was then covered with HCI and introduced into an ultrasonic bath for half an hour, during which, the suspended matter was separated from the filter and dissolved. The filter was then washed with Fig, 1. Map of the Odiel river showing the sampling points. The rectangular box is the grid used in the model. 284 R. Pericifiez, A. Martinez-Aguirre HNOs which was added to the HCI to form aqua regia. This solution was slowly heated to dissolve all remaining particles. Uranium-232 and 229Th spikes and Fe carrier were added to the filtered water and to the solution obtained after the dissolution of suspended matter particles. Precipitation of Fe with oxyhydroxides with concentrated amonium then followed. Uraniumand Th-isotopes were extracted from the precipitates by using anion exchange resins (DOWEX AGlX8, HCl form) and electroplated on to stainless steel planchets. Activities were measured with Si ion-implanted detector alpha spectrometry. Details of the radiochemical and measurement methods can be found in Martinez-Aguirre (1991). 3 EXPERIMENTAL RESULTS Water samples are denoted by ‘0’ and suspended matter samples by ‘SO’. The numbers given to each sample identify the sampling stations (see Fig. l), which are distributed along the low reaches of the river, close to the fertilizer complex. Station 1 is, however, far upstream of this area. As it is not believed to be affected by tidal oscillations, only one sample was collected there. The results for low and high water suspended matter samples are presented in Tables 1 and 2, respectively. In the case of the low water samples, there is a high concentration peak at station S04, for both U and Th, revealing the presence of a local source of activity. Up to 86 and 116 pg g-r of U and Th, respectively, have been measured in this sample, values which are much higher than those previously found for suspended matter samples collected from other rivers. Indeed, U concentrations ranging from 1.8 to 2.4 pg gg’ have been detected in the Amazon and Mississippi rivers (Moore, 1967). On the other hand, Th concentrations in these rivers range from some 8 to lOpgg_’ (Moore, 1967). In some Japanese rivers, Th concentrations range from some 2.2 to 6.7 pg g-’ (Miyake et al., 1973). Thus, it seems clear that samples SO4 and S05, collected close to the fertilizer complex, are affected by the waste disposal from the complex. In the case of the high water suspended matter samples, the distribution of Th and U is different. The maximum Th concentration is 0.7pgg-‘, and there is a general homogenization of concentration levels. This could be due to tidal mixing, input of non-contaminated suspended matter from the sea and a non-constant input of contaminants from the source (the fertilizer complex). On the other hand, U concentrations are also lower than during low water, although there is still an important peak in sample Uranium and thorium in an estuary 285 TABLE 1 Concentrations of U and Th (pgg-‘) for the Suspended Matter Samples Collected During Low Water, and Activity Ratios Sample fU1 [Th/ 234 Ui23R U 230Th/232Th ThjU so1 l.lOztO.24 1.2 It 0.3 so2 1.08 f 0.13 0.07 It 0.04 1.27 f 0.14 7*4 0.06 i 0.04 so3 2.03 i 0.24 0.11 f0.05 1.39zto.17 9f4 0.05 xt 0.03 so4 86 It 10 116&6 0.98 f 0.05 5.28 z!z 0.13 1.35f0.17 so5 25.3 zt 1.3 31 f3 1 .OO f 0.07 6.1 f 0.7 1.22zto.13 SO6 13.4 f 1.5 0.052 zt 0.024 1.07 f 0.17 2.4 & 1.4 (3.9 + 1.8) x 1O-3 so7 19.1 It 1.7 1.06 zt 0.06 Errors are la. TABLE 2 Concentrations of U and Th (pg g-‘) for the Suspended Matter Samples Collected During High Water, and Activity Ratios Sample so1 so2 so3 so4 so5 SO6 so7 l.lOztO.24 3.9 * 0.5 2.8 f 0.3 9.ozt 1.0 69 i 3 1.6 IIZ 0.4 2.4 zk 0.4 F”hl 0.12 f 0.07 0.19 zt 0.07 0.27 f 0.13 0.06 f 0.04 0.7 * 0.2 234u1238u 230Th/232Th ThjU 1.2zlco.3 1.12 f 0.16 13f8 0.031 f 0.018 1.09 f 0.10 3.2 f 1.4 0.07 * 0.03 1.24f0.10 1719 0.030 zt 0.015 1.04 * 0.07 0.9 k 0.3 8f5 0.04 f 0.03 0.91 f 0.17 5.1 * 1.9 0.29 k 0.10 Errors are la. S05, which is close to the fertilizer complex. This effect has already been observed for 226Ra (Periafiez et al., 1994a). In general, 234U/238U activity ratios are compatible with the existence of secular equilibrium in samples in which high U concentrations have been detected. This is not a typical feature of rivers, but it is typical of the minerals used for fertilizer production (Martinez-Aguirre et al., 1994a). The secular equilibrium found suggests an external origin for the suspended matter particles, which must be the fertilizer complex. The 230Th/232Th activity ratios are higher than 1 all along the river for both high and low water suspended matter samples. This reveals the high contamination by members of the 238U radioactive chain. The existence of an external source of activity is confirmed from the Th/ U mass ratios. Since U is considerably more soluble than Th, it is often found in deficit with respect to Th in the solid surface environment. Thus, suspended matter in unperturbed rivers usually has ThjU mass ratios 286 R. Peri&ez, A. Martinez-Aguirre above 1. This is not the case with the Odiel river. It can be seen, in Tables 1 and 2, that, with the exception of samples SO4 and SO5 in low water, the Th/U mass ratios are below 1. This confirms the existence of an external source of U contaminated particles to the river. The exceptions mentioned above show ratios above 1, values which are typical of unperturbed rivers’ suspended particles (although they are the most contaminated samples). These results will be discussed further, with the help of the mathematical model. The results for the water samples are presented in Table 3. Unfortunately, only the low water samples could be measured (due to technical problems in the laboratory). Sample 01 shows an anomalously high U concentration with respect to the rest of the data. The very low pH of the water, 2.86 (Periaiiez & Garcia-Leon, 1993) due to local geology conditions (Martinez-Aguirre et al., 1994b), accounts for the enhanced U concentration. The acid waters around station 1 provoke a dissolution of U from the solid phase (suspended matter and bottom sediments) to the liquid phase. This effect has also been observed for Ra-isotopes (Periaiiez & Garcia-Leon, 1993). The pH of waters downstream from station 01 ranges from 6.3 to 7.6; thus, this effect does not take place (Periaiiez & Garcia-Leon, 1993). High U concentrations are also observed all along the studied area with a peak around sample 04, close to the complex. Indeed, U concentrations in river water range from some 0.02 pgll’ in the Amazon river (Bertine et al., 1970) to some 3.5 pgll’ in the Nahe river (Mangini et al., 1979). Similar values were found in some Indian rivers (Bhat & Krishnaswamy, 1969). Thus, it seems that an input of Ucontaminated water is taking place around the sampling station 04. This input is again probably related to the operation of the fertilizer complex. In the case of Th, concentrations at least one order of magnitude higher TABLE 3 Concentrations of U and Th in Water Samples (pgl-‘) Collected During Low Water, and Activity Ratios Sample [VI [Th/ 234 v38 u 230 Th/232 Th Thl U 01 7.5 f 0.3 1.89 f 0.03 02 2.85 f 0.16 0.102 f 0.018 1.09 & 0.05 7.9 f 1.4 0.014 f 0.003 03 3.09 f 0.18 0.147 f 0.020 1.02 f 0.04 7.5 f 1 .o 0.048 & 0.007 04 6.9 & 0.4 8.4 f. 1.0 1 .oo f 0.05 5.4 * 0.02 1.22f0.16 05 5.3 f 0.3 0.58 f 0.19 1.06f0.09 11 zt4 0.11 f0.04 06 4.5 f 0.3 0.29 f 0.05 1.09 &O.ll 5.8 f 1.1 0.064 f 0.012 07 4.98 zt 0.24 0.14 f 0.02 1.08 zt 0.04 7.4 f 1.2 0.028 f 0.004 Errors are la. Uranium and thorium in an estuary 287 than in other non-perturbed world rivers (Moore, 1967; Miyake et al., 1973) have been detected. A high concentration peak (8.4pgl-‘) has been found in sample 04, probably related to the operation of the complex. The 234U/238U activity ratios are, in general, compatible with the existence of secular equilibrium. This is not the typical disequilibrium observed in river waters (Scott, 1982) but is typical of the minerals used for fertilizer production. The high ratio observed in sample 01 must be due to the higher trend of 234U to be dissolved. The 230Th/232Th activity ratio is above unity all along the river, indicating greater contamination by radionuclides of the 238U radioactive chain. Finally, the ThjU mass ratio is, with the exception of sample 04, below unity. This is consistent with the trend of Th being associated with the solid phases in rivers. The exception must be, as in the case of suspended matter, related to the contaminants. This will be discussed later, with the help of modelling. kd distribution coefficients between suspended matter and water for 238~ 232Th and 230Th are presented in Table 4. In the case of 238U, our results are in agreement with the values found in literature. Indeed, kd for U in coastal water can range from 0.2 to 5 lg-‘, the mean value being 1 lg-’ (IAEA, 1985). The kds are very similar for both Th-isotopes, indicating that they are distributed between water and suspended matter in the same way. However, values below the range of variation which can be found in the literature (IAEA, 1985) have been obtained. Nevertheless, a clear conclusion of these results is the large kd variation between different sampling points (up to two orders of magnitude). This variation comes from the kd definition itself: it assumes an equilibrium situation for the exchanges between the solid and liquid phases. This situation is not always achieved when an in-situ measurement of kd is performed, especially in sites where the input into the system is changing with time (man-made pollution). Thus, when a kd measurement is carried out, an extensive TABLE 4 Distribution Coefficients (1 g-‘) for the Low-water Samples Sample 238 I/ 232Th 230Th 01 0.15 zt 0.3 02 0.38 zt 0.05 0.7 It 0.4 0.59 IO.17 03 0.91 * 0.12 0.7 4 0.3 0.91 rt 0.17 04 12.5 zt 1.6 13.8 f 1.8 13.3 Sr 1.6 0.5 4.8 IIZ 0.4 531t 18 30f4 06 3.0 f 0.4 0.2 * 0.1 0.07 xt 0.02 07 3.8 zt 0.4 Errors are lo 288 R. Peririviez, A. Martinez-Aguirre description of the sampling conditions (pH, temperature and salinity) should be made in order to interpret the result. In open dynamic systems, such as in an estuary, equilibrium conditions will probably never be reached. Thus, mathematical models designed for non-equlibrium conditions are important tools to study the dispersion of radionuclides in dynamic aquatic systems. 4 THE MODELLING STUDY 4.1 Model description The first models which were developed to study the dispersion of nonconservative radionuclides in aquatic systems were averaged box models in which the exchanges of radionuclides between the liquid and solid phases were described in terms of kd, assuming complete equilibrium in the system (Howorth and Eggleton, 1988; Abril & Garcia-Leon, 1993). However, in open systems where the input is changing with time (as in the case of man-made pollution) and when studying the dispersion of radionuclides in small coastal regions (such as estuaries), the equilibrium approach will not hold. This is due to the fact that, because of the high spatial and temporal resolutions that are imposed by the numerical scheme, the equilibrium will not be reached in each time step (Periafiez et al., 19966). In these cases, a kinetic approach is more appropriate. Thus, the equilibrium will be the dynamic balance between two opposite chemical reactions (Nyffeler et al., 1984). The model developed to study the dspersion of radionuclides in the Odiel river estuary (which, of course, could be applied to any other site) makes use of this kinetic approach. The model is presented in detail in Periaiiez et al. (1996b); thus, only a brief description of the processes that are included will be given here. The system under study is divided into a number of grid cells or ‘compartments’. Four phases or subcompartments are present in each grid cell, which are water, suspended matter and two sediment grain size fractions. In Fig. 2, a grid cell is shown. Radionuclides can be dissolved or associated with suspended matter. As tides produce a continuous movement of water, radionuclides in both phases will be transported from one grid cell to another by advective and diffusive processes. Only particles with a diameter 4 < 62.5 pm are considered to be present in the water column as suspended matter (Gurbutt et al., 1987): larger particles will rapidly sink to the bottom. In sediments, we will consider two grain size fractions: particles with diameter 4 < 62.5 ,um (small grain size fraction) and particles with 4 > 62.5 pm Uranium and thorium in an estuary 289 advection and diffusion 0 0 Fig. 2. Grid .# ce lame fractions cell in which the radionuclide transfer processes between the four phases are represented. (large grain size fraction). Only the small grain size fraction can be resuspended in the water column and incorporated into suspended matter. On the other hand, when suspended matter is desposited on the estuary bed, it will be incorporated into the small grain size fraction of the sediments. Thus, the deposition and resuspension processes produce an exchange of radionuclides between the suspended matter and the small grain size fraction of the sediment. The water is in contact with the other three phases; thus, adsorption and desorption reactions take place. These reactions are described in terms of kinetic transfer coefficients. Finally, external sources of radionuclides (in dissolved and suspended phases) may exist in each grid cell. We will consider that the adsorption process (transfer from water to the solid phases) is governed by a coefficient kl and the inverse process (desorption towards the liquid phase) by a coefficient k2. The adsorption process is a surface phenomenon and will depend on the surface of particles per water volume unit into the grid cell. This quantity will be denoted the exchange surface. If we now consider only suspended matter as the solid phase (neglecting sediments), we have: kl = xl &> (1) 296 R. Perihiez, A. Martinez-Aguirre 12 - ,' 1 : : I' 10 - ,' : ,jl : 8 2 ,' 8s /' ,' ,/ 6- / ,/:: : IL 4- '! I' I ,I : ,' '\ ,' '-_ 2- --.__.________,,.---_\ ,I' \L_ ,' NC __________________m 0 I 1 I I I I I 0 0 5 10 15 20 25 30 35 40 Fig. 5, Computed (line) and measured (points) distribution coeffkient (I g-‘) for U during low water. general behaviour of the Th/U mass ratios is well reproduced by the model in all cases. It was mentioned in Section 3 that the U excess with respect to Th in suspended matter indicates the existence of an external source of U contaminated particles to the river. There was, however, an E , I I I I 1 1 I 1.4 - exp. 8"s. - - A model susp. ---- model disc -- 1.2 - ,I' \\ l- , ,' : /' : : \. '\ 0.8 - I' \\ : \I : : : : 0.6 - : (1 : \\ : \\ I' \\ 0.4 - : '._\ I' : __--__________ 1' 0.2 - '\ ' \ ' \L__/ __.-. I I I 0 5 IO 15 20 25 30 35 40 Fig. 6. Model results for Th dispersion. (A) Water and suspended matter during high water. (B) Suspended matter during low water. (C) Water during low water. Concentrations are given in pg 1-l and pg g-’ for water and suspended matter samples, respectively. Uranium and thorium in an estuary 297 F 140 1 I 1 I , I b =P. w B model ---- 120 - f 100 I : - I : / / : 80 - : ) : : : , /j ,' : 60 - ,' ,' ,I' ,' 40 - ;p ,/' I 20 - ,' I' : ,' I' \I ,/ : . . 0 5 10 15 20 25 30 35 40 I 9 c 8 exp. - model ---- 10 15 20 25 30 35 40 Fig. 6. Continued. exception (samples SO4 and SO5 which were the most contaminated). Indeed, more Th than U is discharged into the river, in both dissolved and suspended forms. From the second input rates (the first are not indicative because they are used just to create the background), it can be shown that, in solution, ThjU = 2.4, and in suspended matter, Th/U = 1.5. Thus, more Th than U is discharged and, as a consequence, there is an excess of Th in water and suspended matter near the source. However, there is an 298 R. Peribiez, A. Martinez-Aguirre 100 80 20 1 I I I I I I exp. - model ..~_ ,,-- >’ I ‘.\\ ,/- Y_ I’ -._ _______.-._____-I --._________.----.-_ ok ” I I I I I I IA & 1 0 5 10 15 20 25 30 35 40 Fig. 7. Computed (line) and measured (points) distribution coefficient (1 g-‘) for Th during low water. excess of W in the rest of the river in both liquid and suspended phases. It seems clear that the dissolved Th that is released to the river is quickly fixed to solid particles, and these particles (together with the particles that are released from the source and are rich in Th) are deposited on the river 0.25 0.2 3 E 0.15 0.1 5.000000e-02 0 I - _‘.. .__________-..\ ,,.\ ,--’ Y\ ,’ \\,,’ \\ ,,-- ‘\ _‘\ I’ -*_-\ \._,_‘- $I ,I’ 1, , , , ‘, : I’ i : \.-. ,’ ----.__________--- ** i i ( , 0 5 10 15 20 25 30 35 40 Fig. 8. Computed (lines) and measured (points) ThjU mass ratios for suspended matter samples during high water (A), water samples during low water (B), and suspended matter samples during low water (C). Uranium and thorium in an estuary 299 1.4 I I ! exP. 1-41 model ---- l.20 0.6 - I' ,,' /' I' 0.4 - I' I' /' I\ ,' 0.2 - I' ,' : : ,,= ,' I : \\ * /__-' .I_ 0. ____________---- I I ---___ _-----__-- _io___ 0 5 10 15 20 25 30 35 40 1.4c ,’ __-- 4 cup. w model ---- ____-- t, ,/-- 1.2 - ,' I r' ,' '\ l- ,' I I' 0.6 - : 0.6 - ,'\ , I ‘\' I' : ), : >/ 0.4 - : : : II #' : 0.2 - : j\ _____----..___I \\ '. '.. oe 1 I I I I ---___________T---g I I 0 5 10 15 20 25 30 35 40 Fig. 8. Continued. bed near the source. In this way, a U excess would exist in the rest of the river, as confirmed by the experimental and the model results. This hypothesis is also supported by the fact that an excess of Th has been measured in sediments collected close to the fertilizer complex (MartinezAguirre et al., 19946). The sensitivity of the model to the different parameters, the way of creating the background and the magnitude of the source term have already been studied (Periafiez et al., 19943, 1996a,c). 300 R. Pericinez, A. Martinez-Aguirre 5 CONCLUSIONS Uranium and Th concentrations have been measured in water and suspended matter samples in an estuarine system affected by waste disposal from a fertilizer processing complex. Distribution coefficients have also been calculated. The results have shown a radioactive impact and a significant kd variability. In order to perform a quantitative study on the distribution of U and Th, as well as on the kd variability, a modelling study has been carried out. The model includes the partition of radiotracers between four phases, and this partition is based on a kinetic approach. The model solves the hydrodynamic equations, the suspended matter equations and the four equations that govern the time evolution of the radiotracer concentrations in each one of the four phases. The model results are in good agreement with the experimental data for both U and Th, and for both water and suspended matter samples. The kd variability is reproduced by the model, as well as the ThjU mass ratios. This shows the goodness of the description of the transfer processes, since good results are obtained for elements with a very different chemical behaviour (Ra, U, Th) by simply changing the value of a parameter: the exchange velocity. ACKNOWLEDGEMENTS This work was partially supported by ENRESA. The author is indebted to J. M. Abril for help in the modelling work. REFERENCES Abril, J. M. & Garcia-Leon, M. (1993). A 2D-4 phases marine dispersion model for radionuclides. Part 1: conceptual and computational model. J. Environ. Radioact., 20, 71-88. Bertine, K. K., Chan, L. H. & Turekian, K. K. (1970). Uranium determinations in deep-sea sediments and natural waters using fission tracks. Geochim. Cosmochim. Acta, 34, 641-8. Bhat, S. G. & Krishnaswamy, S. (1969). Isotopes of uranium and radium in Indian rivers. Proc. Indian Acad. Sci., 70, 1-17. Flather, R. A. (1994). 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The time derivative must be interpreted as in a forward finite differences scheme. The * means that the corresponding quantity must be evaluated in the new time step. The first term represents the transfer of radionuclides from water to the three solid phases. Thus, kl is given by eqn (3). adv + dif represents advective plus diffusive transport of dissolved radionuclides from one grid cell to another. The third term is the transfer of radionuclides from the two fractions of sediments to water: sed s H* sed I (A21 (A3) where a, and aI are the radionuclide concentrations in the small and the large grain size fraction of the sediments, respectively (mgg-*). The bulk density of the sediment, pm, is given in kgme3. Uranium and thorium in an estuary Suspended matter 303 acs at= m*H* kl x - k2Cs s + (res - dep) + (adv + dif). (-44) As the first term is the transfer of radionuclides from water to just suspended matter, kl is given by the first term of eqn (3). adv + dif is the advective plus diffusive transport of radionuclides in suspended matter. The second term is the transfer of radionuclides from suspended matter to water, and res and dep represent the resuspension and deposition processes: vd C,m dep = - m*H* vrfiws 9 res = ___ m*H’ ( > -- I 103, VC, (A% where vd and v, are the mean deposition and resuspension velocities, vCd and v,, are the critical deposition and resuspension velocities and q is the water flux velocity. Both in the dissolved phase and in the suspended matter equations, the external sources of radionuclides must be included in the grid cells in which they exist. Sediments The equation for the small grain size fraction is: &I, CdH at= kl - P&f lo3 - kza,t,b + (dep - res). (A7) The first term is the transfer from water to the small fraction of the sediment. Thus, kl is given by the second term of eqn (3). The second term is the transfer of radionuclides from the sediment to water and dep - res represents the transfers between the sediment and suspended matter (through deposition and resuspension): dep = (A@ vr a, ( > z-1 res = 7 v,, . (A9) 304 R. Pericir?ez, A. Martinez-Aguirre The equation for the large grain size fraction of the sediment is: 8 al at= (AlO) where the first term is the transfer of radionuclides from water to the sediment [kl is given by the third term of eqn (3)], and the second term represents the inverse process.