Modelling the physico-chemical speciation of plutonium in the eastern Irish Sea

Modelling the physico-chemical speciation of plutonium in the eastern Irish Sea R. PeriaH n8 ez Departamento Fn&sica Aplicada, E.U. Ingenier&naTe&cnica Agr&ncola. Universidad de Sevilla. Ctra Utrera km 1, 41013-Sevilla, Spain Abstract A numerical model to simulate the speciation of 239,240Pu in the eastern Irish Sea is presented. The model solves the three dimensional hydrodynamic equations, using normalized p coordinates in the vertical direction. Simultaneously, the equation for suspended matter, that includes advection, di!usion, settling, deposition and erosion of the sediment, is solved too. Thus, the tidal dispersion of non-conservative radionuclides can be simulated. Reduction and oxidation reactions are included in the model; they are described in terms of reaction velocities. It is considered that Pu can be present in solution, suspended matter and bottom sediments. Also, Pu can be in reduced and oxidized forms in each of these three phases. Thus, six equations are solved, whose solutions give the temporal evolution of Pu concentration in each phase for both reduced and oxidized forms. The model has been applied to the eastern Irish sea, where Pu is released from the Sella"eld nuclear fuel reprocessing plant. Observed and computed Pu distributions in water and bottom sediments have been compared. Also, the model gives the percentage of Pu that is reduced and oxidized in each phase. Finally, distribution coe$cients for total Pu (reduced plus oxidized), oxidized and reduced Pu have been calculated over the sea. Results are, in general, in agreement with observations. Keywords: Plutonium; Speciation; Irish Sea; Sella"eld; Modelling 1. Introduction Over recent years, there has been an increasing interest in developing models to simulate the dispersion of non-conservative radionuclides in aquatic environments since these models can be used as predictive instruments that can be applied in the assessment of radioactive contamination following an accidental release of radionuclides. The "rst models for non-conservative radionuclides were long-term dispersion models, in which the transfer of radionuclides between the liquid and solid phases was described in terms of equilibrium distribution coe$cients (Gurbutt, Kershaw & Durance, 1987; Abril & GarcmHa-LeoHn, 1993a). PeriaHn8ez, Abril & GarcmHa-LeoHn (1996a) developed a model to simulate the dispersion of non-conservative radionuclides in tidal waters based upon kinetic transfer coe$cients and thus the model could be used under non-equilibrium conditions. This model was applied to simulate the dispersion of 226Ra, 238U and 232Th in a Spanish estuary (PeriaHn8ez, Abril & GarcmHa-LeoHn, 1996b; PeriaHn8ez & MartmHnez-Aguirre, 1997a). Recently, PeriaHn8ez (in press) developed a three dimensional model to simulate the tidal dispersion of non-conservative radionuclides in the marine environment, also based upon kinetic transfer coe$cients. A similar model was also developed by Margvelashvily, Maderich and Zheleznyak (1997). Abril and GarcmHa-LeoHn (1993b) and PeriaHn8ez (in press) applied their respective models to simulate the dispersion in the Irish Sea of plutonium released from the nuclear fuel reprocessing plant at Sella"eld. However, the behaviour of Pu in aquatic systems is of considerable complexity due to the fact that it can simultaneously exist in di!erent oxidation states. Thus, Pu (III) and Pu (IV) predominate as the reduced and Pu (V) and Pu (VI) as the oxidized forms. The reduced Pu is highly particle-reactive and has been shown to possess a distribution coe$cient that is two orders of magnitude higher than that of the more soluble oxidized Pu (McKay & Pattenden, 1993; Mitchell, Vives i Batlle, Downes, Condren, LeoHn-VintroH& Sanchez-Cabeza, 1995). Hence the values observed in "eld measurements represent the properties of the mixture of oxidation states that is present in the particular sample. To overcome this problem, Abril and GarcmHa-LeoHn (1993b) and PeriaHn8ez (in press) used a mean distribution coe$cient and mean kinetic transfer coe$cients, respectively, in their models. Nevertheless, the main di$culty is that the oxidation state of Pu changes with time: Pu is released in a reduced form and after some days an equilibrium in the partition of Pu between the reduced and oxidized species is achieved (Pentreath, Harvey & Lovett, 1986). The objective of this paper is to present the "rst results on a Pu dispersion model that includes reduction and oxidation (redox) reactions in a simple way. Thus, mean kinetic transfer coe$cients are not used (reduced and oxidized Pu have their corresponding speci"c coe$cients) and the model can also give information on the speciation state of Pu in water, suspended matter and bottom sediments. Moreover, the model calculates total distribution coe$cients and distribution coe$cients for the reduced and oxidized Pu separately. The model solves the three dimensional hydrodynamic equations using normalized pcoordinates in the vertical, so that vertical resolution is not reduced in the shallower regions, the equation for suspended matter, which is also written in pcoordinates and includes advection, di!usion, settling, deposition and erosion of the sediment, and the equations whose solutions give the time evolution of reduced and oxidized Pu in water, suspended matter and bottom sediments. In this way, the tidal dispersion of reduced and oxidized Pu is obtained. The model is presented in the next section. Thereafter, the model results are presented and discussed. Fig. 1. Percentage of oxidized Pu as a function of time from the experiments of Boust et al. (1996) (points) and the result from numerical "tting to Eq. (3) (line). 2. The model 2.1. Redox reactions Redox reactions will be described in terms of reaction velocities. Thus, the rate at which Pu is oxidized is considered to be proportional to the concentration of reduced Pu at each particular point. The proportionality factor is the oxidation velocity b1. Similarly, the rate at which Pu is reduced is considered to be proportional to the concentration of oxidized Pu. The proportionality factor will now be the reduction velocity, denoted as b2. An estimation of the values of b1and b2can be obtained from the laboratory experiments carried out by Boust, Mitchell, Garcia, Condren, LeoHn-VintroHand Leclerc (1996). Filtered sea water was spiked with Pu(IV) at a well known concentration and the oxidation reaction was followed during some 30 d (details can be seen in Boust et al., 1996). The % of oxidized Pu, as a function of time, is given by the points in Fig. 1. In our model, the equations that give the temporal evolution of the concentration of oxidized and reduced Pu, C09 and C3%$ respectively, are: LC3%$ Lt"!b1C3%$#b2C09 (1) LC09 Lt"b1C3%$!b2C09 (2) If these equations are solved, knowing that at t"0, C09"0 and C3%$"C3%$(0), it follows that C09"b1 b1#b2 C3%$(0)(1!e~(b 1 `b 2 )t). (3) b1and b2can be obtained from numerical "tting of Eq. (3) to the experimental points presented in Fig. 1. If numerical "tting is carried out, the following reaction velocities are obtained: b1"1.85]10~6 s~1, b2"4.48]10~7 s~1. The numerical "tting to Eq. (3) is also represented in Fig. 1 as the solid line. It can be seen that the oxidation reaction is almost completed within 15}20 d: 80% of Pu has been converted to the oxidized form. It must be pointed out that redox reactions occur in the three phases considered in the model: water, suspended matter and bottom sediments. It is assumed that reaction velocities in suspended matter and sediments are the same as in water, which is a simpli"cation since reduction/oxidation conditions may be di!erent in the three phases. Of course, this can lead to discrepancies between model predictions and observations, as will be seen. However, our main objective is to present the model formulation and some preliminary results. The model can be further re"ned as b1and b2are better known in the other phases from observations and laboratory experiments. On the other hand, environmental conditions such as light and temperature a!ect the reaction velocities, which is not considered in the model. Thus, the model sensitivity to changes in b1and b2has to be studied (see Section 4) due to the uncertainty in their values. 2.2. Hydrodynamics The three dimensional hydrodynamic equations are transformed to pcoordinates; thus a constant number of layers is used in the vertical at each horizontal grid point and vertical resolution is not reduced in the shallower areas. The transformation to pcoordinates is (see Davies, 1985a, for instance): p"(z#f) (h#f)(4) where his the undisturbed depth of water, fis the sea surface displacement from the mean level due to tidal oscillations measured upwards from the undisturbed level and the zcoordinate is measured from mean sea level to the bottom. The form of the equations, for a homogeneous sea, in pcoordinates has been given previously (Davies, 1985a) and will not be repeated here. Details of the boundary conditions applied at the sea surface and the sea bottom can be seen in PeriaHn8ez (1998a): no wind e!ects are considered since we are mainly interested in testing and tuning the formulation of the three dimensional dispersion model including redox reactions and realistic results are obtained although wind is not included, as will be seen. A linear law for bottom friction has been adopted. Although a quadratic formulation of bottom friction is now more extensively used than the linear law, the latter has been adopted since the tidal regime becomes established faster. Also, there are no appreciable di!erences in the dispersion patterns (for dissolved radionuclides) obtained when the hydrodynamic model is calibrated using linear or quadratic friction (PeriaHn8ez, 1998a). A#ow-dependent eddy viscosity has been used in the model. This formulation gives good results for tidal #ow studies (Jones & Davies, 1996; Davies & Lawrence, 1994; Davies, Kwong & Flather, 1997): N"CNJu62#v62h(5) where CN"0.0025 is a dimensionless experimentally obtained coe$cient and u6and v6are depth mean currents along the xand yaxis respectively. 2.3. Suspended matter dynamics The three dimensional equation for suspended matter has been obtained by transforming the equation proposed by Nicholson and O'Connor (1986) into pcoordinates. Details can be seen in PeriaHn8ez (in press). Such an equation includes advectivedi!usive transport plus vertical fall (settling) of particles. Erosion and sedimentation are incorporated into the sea-bed boundary condition of the equation. Erosion and deposition have been formulated in terms of threshold velocities in such a way that there is erosion only if the sea-bed water velocity is larger that the erosion threshold. Otherwise the erosion term is set to zero. Similarly, there is deposition only if the sea-bed water velocity is smaller than the deposition threshold velocity. Otherwise the deposition term is set to zero. As usual in suspended matter studies, it is considered that only particles with a diameter (62.5 lm can remain in the water column as suspended matter, since larger particles will sink rapidly to the bottom and, as a consequence, their horizontal movement is negligible (Belderson, 1964; Clarke, 1995; PeriaHn8ez, Abril, & GarcmHaLeoHn, 1996c). Indeed, Eisma (1981) has pointed out that for all practical purposes muds can be regarded as synonymous with suspended matter. A standard formula to represent the increase in the settling velocity as the suspended matter concentration increases has been used in the model (Pejrup, 1988; Mehta, 1989; Clarke, 1995; PeriaHn8ez, in press). Also, a source-term is included in the suspended matter equation in those grid cells located along the coastline. This term represents the input of particles from runo!of continental waters. All details can be seen in PeriaHn8ez (in press). 2.4. Radionuclide dispersion The model considers that radionuclides can be present in three phases: solution, suspended matter and active bottom sediments (as denoted by Benes, Cernik & Slavik, 1994), that consist of particles with a diameter (62.5 lm. In each phase, Pu can exist in two oxidation states: reduced and oxidized Pu. Reduction and oxidation processes (that occur in each of the three phases) are governed by the reaction velocities, that were presented above. The transfer of Pu from the solid phase to solution is governed by a kinetic transfer coe$cient k2and the inverse process by a kinetic transfer coe$cient k1. However, these coe$cients will be di!erent for oxidized and reduced Pu. Thus, the model solves six equations whose solution gives the time evolution of the concentration of reduced and oxidized Pu in water, suspended matter and bottom sediments. It is known that actinide adsorption tends to be a surface phenomenon (Ramsay & Raw, 1987) and will depend on the surface of particles per water volume unit into each grid cell. This quantity has been denoted as the exchange surface (PeriaHn8ez et al., 1996a; PeriaHn8ez & MartmHnez-Aguirre, 1997a). Thus (PeriaHn8ez et al., 1996a): k1"s1(Sm#Ss)"k11#k12 (6) where Smand Ssare the exchange surfaces for suspended matter and bottom sediments respectively and s1is a parameter with the dimensions of a velocity. It is denoted as the exchange velocity (PeriaHn8ez et al., 1996a). As a "rst approach, assuming spherical particles and a step function for the grain size distribution of particles, it can be obtained (PeriaHn8ez et al., 1996a) that Sm"3m/oR(7) Ss"3¸//R*p H(8) where mis the suspended matter concentration, ois the suspended matter particle density, Ris the mean radius of the suspended matter and active sediment particles, H"h#fis the total water depth, ¸is the average mixing depth (the distance to which the dissolved phase penetrates the sediment), *p is the spacing in the vertical direction and /is a correction factor that takes into account the fact that not all the mass of the sediment is in contact with the water. This description of the transfer of radionuclides between the dissolved and solid phase has been used successfully in previous modelling works (PeriaHn8ez et al., 1996b; PeriaHn8ez & MartmHnez-Aguirre, 1997a,b, MartmHnez-Aguirre & PeriaHn8ez, 1998). The equations that give the three dimensional dispersion of Pu, including advection, di!usion, settling and deposition of suspended matter, erosion of the sediment and transfers between the liquid and solid phase, presented in PeriaHn8ez (in press), have been modi"ed to take into account the fact that Pu can exist in reduced and oxidized forms. Thus, instead of three equations six must be solved. The form of the six equations is summarized in the Appendix. 2.5. Numerical solution The hydrodynamic equations are solved using an explicit "nite di!erence scheme, although the vertical di!usion term is solved using the Saul'ev implicit scheme to retain stability (Davies, 1985b). At land boundaries, the normal component of the current is set to zero. Along open boundaries, amplitude and phase of the surface elevation at the M2frequency are speci"ed from observations (Howarth, 1990) and the surface current component that is normal to the boundary is obtained from a radiation condition (Kowalick & Murty, 1993). Only the main tidal component, M2, has been used since we are mainly interested in testing the formulation of the three dimensional dispersion of Pu, including chemical reactions. Thus, only the M2tide has been used since realistic results are obtained, as will be shown. However, a result improvement should be expected if weaker components (at least S2and N2) are included. The advection and horizontal di!usion terms are solved using second order accuracy schemes (Kowalick & Murty, 1993) and vertical di!usion is again treated using the Saul'ev method. Along land boundaries, no #uxes of suspended particles and Pu are considered. The open boundary condition described in PeriaHn8ez (1998a,b) has been adopted: Ci"tCi~1 (9) where Cirepresents the concentration of suspended matter and Pu along the boundary and Ci~1 represents the concentration just inside the computational domain. The non-dimensional value t"0.9 is obtained from a calibration exercise (PeriaHn8ez, 1998a,b). A FORTRAN code has been developed to solve the equations involved in the model. It was implemented on a HP SPP-2000 X-Class computer. 3. Model application and results The model domain is presented in Fig. 2, where the location of Sella"eld nuclear fuel reprocessing plant is also shown. The model's horizontal resolution is *x"*y"5000 m. Ten layers are used in the vertical, thus *p"0.1, and the time step is "xed as *t"60 s. Water depths are introduced from bathymetric maps and range from 55 m in the west to a shallower area along the British coast. The values given to all the parameters involved in the model are presented in detail in PeriaHn8ez (in press). The source of virtually all Pu to the Irish Sea is the discharge from Sella"eld through a pipeline that extends 2.5 km beyond high water. The magnitudes of the discharges have been compiled from McKay and Pattenden (1993) and Hunt, Smith and Camplin (1997), and have been used as the Pu input to the model. It has also been reported (Pentreath, 1985) that about 99% of the discharged Pu is associated with particles in a reduced form. The values of the kinetic transfer coe$cient k2and the exchange velocity X1for the reduced and oxidized Pu must be given. Ny!eler, Li and Santschi (1984) measured k2for a wide set of chemical elements and found a very small variation (an order of magnitude), even for elements with a very di!erent geochemical behaviour. Thus, it has been considered that k2has the same value for reduced and oxidized Pu. It has been assumed that k2"1.16]10~5 s~1, the value that has been obtained by Ny!eler et al. (1984) for Cs and Cd. This value of k2has given good results in previous modelling work when it has been used for Ra, U, Th, Cs and Pu (PeriaHn8ez et al., 1996b; PeriaHn8ez & MartmHnez-Aguirre, 1997a; PeriaHn8ez, 1998c, in press). The exchange velocity can be estimated from k2and the distribution coe$cient, k$, since the following Fig. 2. Model domain. Each unit in the xand yaxis is 5000 m (grid element number). The star is the Sella"eld nuclear fuel reprocessing plant. relation holds (PeriaHn8ez et al., 1996b): k$"s1 k2 3 oR. (10) Measured total Pu k$'s in the eastern Irish Sea are of the order of 105lkg ~1 (McKay & Walker, 1990; Mitchell et al., 1995), in agreement with the value recommended by IAEA (1985): 1.0]105lkg ~1. However, the Pu oxidation state has been shown to have a major in#uence on the k$value, being of the order of 106and 104lkg ~1 for the reduced and oxidized Pu respectively (Nelson and Lovett, 1978). The same variations have been observed in the Irish Sea (Mitchell et al., 1995). Thus, it has been considered that k$is 1.0]106and 1.0]104lkg ~1 for the reduced and oxidized Pu respectively. From Eq. (10), the exchange velocities for reduced and oxidized Pu are: s3%$ 1"1.51]10~4 ms ~1, s09 1"1.51]10~6 ms ~1. Fig. 3. Temporal evolution of the percentages of reduced Pu in solution and suspended matter, Cdr and Csr, and oxidized Pu in water and suspended matter, Cdo and Cso. To obtain these values, it has been taken that R"15 lm and o"2600 kg m~3 (PeriaHn8ez et al., 1996b; PeriaHn8ez, in press). Once the exchange velocities are known, kinetic transfer coe$cients k11and k12 for both oxidized and reduced Pu can be obtained from Eqs. (6)}(8). A numerical experiment has been carried out to test the values of the transfer coe$cients and the reaction velocities. Let us consider a volume of sea water that contains a certain concentration of suspended matter particles (1 ppm, which is a typical value for the Irish Sea). A known amount of Pu, associated with suspended matter, in a reduced chemical form is added. The four di!erential equations whose solutions give the temporal evolution of Pu concentrations in water and suspended matter (in both reduced and oxidized forms in each phase) are integrated numerically. These equations include redox reactions in water and suspended matter and transfers of reduced and oxidized Pu between water and suspended matter (they are Eqs. (A1)}(A4) in the Appendix if terms involving advection, di!usion, settling, erosion, deposition and transfers with sediments are removed). The result is presented in Fig. 3, where the time evolution of the % of Pu in reduced and oxidized forms (in both water and suspended matter) is given. It can be seen that equilibrium is reached after some 20 d, as has been reported by other authors (Boust et al., 1996). After 35 d, the amount of Pu associated with solid particles (reduced plus oxidized) is 11.4%. Molero, Sanchez-Cabeza, Merino, Vives i Batlle, Mitchell and Vidal-Cuadras (1995) found that 11% of the total Pu concentration is absorbed onto suspended matter in the Mediterranean Sea. Livingston and Bowen (1977) showed that 30% of Pu was "xed to suspended particles in Atlantic waters. Mitchell, Vives i Batlle, Ryan, Schell, Fig. 8. Measured and computed 239,240Pu speci"c activities in water (a) suspended matter (b) and bottom sediments (c) northwest (positive distances) and southwest (negative distances) from Sella"eld. It should also be commented that, since the model formulation is three dimensional, it can be applied to study vertical variations of parameters like radionuclide concentrations in water and suspended matter and distribution coe$cients. Discussion of this point can be found in PeriaHn8ez (in press) and will not be repeated here. 4. Model sensitivity to b1and b2 The model sensitivity to the choice of boundary conditions for the dispersion equations, di!usion coe$cients, parameters involved in the suspended matter submodel, kinetic transfer coe$cient k2and exchange velocity s1has already been studied (PeriaHn8ez, in press). Results will not be repeated here. The model sensitivity to changes in reaction velocities has been investigated due to the uncertainties associated with these parameters. The numerical experiment described in Section 3 has been repeated for di!erent values of b1and b2. The results are summarized in Table 1, where the percentage of Pu "xed to the solid matter, the Fig. 9. Computed distribution coe$cients (L kg~1): (a) total Pu (]105), (b) reduced Pu (]106), (c) oxidized Pu(]104). percentage of oxidized Pu in the water and the percentage of reduced Pu in the suspended matter are given together with the values of b1and b2in each experiment. Experiment 1 is carried out with the parameters used in the model (experiment presented in Section 3). It can be seen that %ox is in agreement with measurements Table 1 Model sensitivity to the reaction velocities. Experiment b1(s~1)b2(s~1) % solid % ox % red 1 1.85]10~6 4.48]10~7 11.4 88.0 81.0 2 3.70]10~6 4.48]10~7 7.0 93.4 67.2 3 3.70]10~6 2.24]10~7 4.17 96.6 59.5 4 1.85]10~6 8.96]10~7 18.1 78.7 84.2 5 1.85]10~6 1.34]10~6 23.0 70.9 85.6 6 9.25]10~7 8.96]10~7 26.1 65.4 91.5 7 9.25]10~7 1.34]10~6 31.1 55.6 92.2 8 6.17]10~7 1.34]10~6 35.5 45.4 94.8 % solid is the percentage of Pu associated with suspended matter after 35 d, %ox is the percentage of oxidized Pu in solution and %red is the percentage of reduced Pu in suspended matter. (Mitchell et al., 1995), but %red is slightly low when compared with observations (Mitchell et al., 1995). In experiments 2 and 3 oxidation is enhanced by increasing b1 (experiment 2) or increasing b1and simultaneously decreasing b2(experiment 3). In these cases, %ox is still in agreement with observations but too low values for %red occur. In experiments 4}8 reduction is enhanced by increasing b2or by simultaneously increasing b2and decreasing b1. As reduction increases %red shifts to values closer to observations, but too low values for %ox are obtained (see experiment 8). Thus, changes in b1and b2due to changes in environmental conditions may a!ect the distribution of Pu between oxidized and reduced forms. If these variations in reaction velocities and also di!erent values for them in water, suspended matter and bottom sediments are included in the model, results would probably be improved (in particular the Pu distribution between reduced and oxidized forms in suspended matter and bottom sediments). 5. Conclusions A numerical model that simulates the physico-chemical speciation of Pu in the eastern Irish Sea has been developed. The model simultaneously solves the hydrodynamic equations, the suspended matter equation and six equations whose solution gives the temporal evolution of reduced and oxidized Pu concentrations in water, suspended matter and bottom sediments. Reduction and oxidation reactions are described in terms of the reaction velocities, which have been deduced from laboratory experiments. The transfer of radionuclides between water and the solid phase is described in terms of kinetic transfer coe$cients, which have di!erent values for reduced and oxidized Pu. In general, the observed and computed Pu distributions in water and bottom sediments are in agreement. It has been obtained that most Pu in solution is in oxidized form. Also, the Pu distribution between reduced and oxidized forms, in solution, remains rather uniform over the sea, which is in agreement with previous measurements. On the other hand, Pu in suspended matter is mainly in a reduced form, although in a percentage that is lower than observations. Also, it has been found that most Pu in the sediment is in an oxidized form. These two results may be a consequence of the simple model that has been used to describe redox reactions, since probably reaction velocities in the sediment should be di!erent to these in the water column. Computed distribution coe$cients for reduced, oxidized and total Pu are, in general, in agreement with observations. A decrease in the total k$with increasing distance from the Sella"eld discharge point has been obtained, which is in agreement with previous observations. Acknowledgements Work partially supported by EU contract FI4PCT960046, Spanish CICYT contract AMB97-1720-CE and ENRESA. Appendix A A.1. Dissolved phase The equation that gives the temporal evolution of oxidized Pu in solution, C09 d(Bq m~3), is LC09 d Lt"(adv#dif)3D!(k09 11#nk09 12)C09 d#k2AmC09 s#nA09 s¸omf/ *pH]103B !jC09 d#b1C3%$ d!b2C09 d(A.1) where (adv#dif)3Drepresents three dimensional advection plus di!usion of radionuclides. n"0 unless we are solving the equation for the water layer that is in contact with the sediment; in this case n"1 to allow the transfer of radionuclides between water and the bottom sediment. C09 sand A09 sare oxidized Pu concentrations in suspended matter and sediments, both in Bq g~1. The sediment bulk density, om,is expressed in kg m~3 and jis the radioactive decay constant. fgives the fraction of active sediments. The external source should be added to this equation if it exists. A similar equation is deduced for reduced Pu in solution, C3%$ d(Bq m~3): LC3%$ d Lt"(adv#dif)3D!(k3%$ 11 #nk3%$ 12 )C3%$ d#k2AmC3%$ s#nA3%$ s¸omf/ *pH]103B !jC3%$ d#b2C09 d!b1C3%$ d(A.2) with obvious meanings for the notation. A.2. Suspended matter In the case of oxidized Pu, C09 s(Bq g~1): L(mC09 s) Lt"(adv#dif)3D!sett09#n(res09!dep09)#k09 11C09 d!k2mC09 s !jmC09 s#m(b1C3%$ s!b2C09 s) (A.3) where mis the suspended matter concentration in g m~3 and sett, res and dep means settling, resuspension and erosion (see PeriaHn8ez (in press) for details). The equation for reduced Pu is L(mC3%$ s) Lt"(adv#dif)3D!sett3%$#n(res3%$!dep3%$)#k3%$ 11 C3%$ d!k2mC3%$ s !jmC3%$ s#m(b2C09 s!b1C3%$ s) (A.4) A.3. Active bottom sediments Oxidized Pu: LA09 s Lt"k09 12 C09 d(b)H*p ¸omf]10~3!k2A09 s/ #(dep09!res09)!jA09 s#b1A3%$ s!b2A09 s(A.5) where (d) means that this parameter must be evaluated at the deepest water layer (in contact with the sediment). dep and res means deposition and resuspension (see PeriaHn8ez (in press) for details). Reduced Pu: LA3%$ s Lt"k3%$ 12 C3%$ d(b)H*p ¸omf]10~3!k2A3%$ s/ #(dep3%$!res3%$)!jA3%$ s#b2A09 s!b1A3%$ s. (A.6) The total activity (reduced plus oxidized) in the sediment (active plus non active) can be obtained as A"f(A09 s#A3%$ s). (A.7) A.4. Distribution coezcients Oxidized Pu: k09 d"C09 s C09 d (A.8) Reduced Pu: k3%$ d"C3%$ s C3%$ d (A.9) Total k$: k$"(C09 s#C3%$ s) (C09 d#C3%$ d). (A.10) References Abril, J. M., & GarcmHa-LeoHn, M. (1993a). A 2D 4 phase marine dispersion model for radionuclides. Part 1: conceptual and computational model. Journal of Environmental Radioactivity,20,71}88. Abril, J. M., & GarcmHa-LeoHn, M. (1993b). 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