R. Periäfiez et al. 
Water column 
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Reversible phase of 
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Reversible phase of 
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Environmental Modelling and Software 122 (2019) 104523 
Slow reversible 
phase of 
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Slow reversible 
phase of 
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Fig. 5. Scheme representing exchanges of radionuclides between dissolved and solid (suspended matter and bed sediments) phases (from Maderich et al., 2017). Kinetic rates k, 
and k, describe uptake and release, respectively, for the first fast reaction. Rates k, and k, describe the second, slower, reaction, Only k, and k, are considered in the case ot 
L-step models; the full scheme is applied in 2-step kinetic models. 
Table 1 
'AEA (2004) recommended k&, values (m’kg-1) for open ocean and ocean margins for 
a number of elements. 
Element Open ocean Ocean margin 
1x 1073 1x 10-3 
4x 102 5x 10! 
2x 10° 2x 10% 
5X 10% 1x 10? 
3x 10% 2x 10' 
1x 1077 8x 1073 
| > 1071 ' x 1071 
3x 10° 3x 107 
1x 10° 1x 10° 
x 109 1x 10° 
ix 10° 1x 10° 
1x 10% x 10? 
1x 10% 2x 10° 
bx 10% 2x 10° 
5x 103 3x 10% 
kw 107 'x 10° 
x 102 1x 10? 
102 “W 
‘he sediment is calculated through equation (15). This can be an ade- 
Juate simplification in the long-term assessments usually done with box 
models; however it is clear now for the marine modelling community 
‘hat such is not the case in the near field, in both cases of accidental 
and chronic releases, Carroll et al. (1997) noted that in dynamic 
coastal environments the distribution of radionuclides between water 
and sediment may not reach equilibrium. For instance, in the Amazon 
Shelf the rates between measured concentrations of 2*Th in sediment 
and water varied over two orders of magnitude during a single tidal 
zycle. 
In the case of an accident, radionuclide concentration in the sedi- 
ment would be overestimated in the initial phase and underestimated 
‚ater if equilibrium is assumed. Moreover, as demonstrated in Periäfiez 
‘2003a), Periäfez et al. (2018), equilibrium is never reached in the near 
äeld in the case of chronic releases, even if they are constant in time, 
As a consequence, the state-of-the-art approach involves the use of 
kinetic models, by which adsorption/desorption reactions are described 
in a dynamic way and non-equilibrium situations can be treated in a 
more valid way (Nyffeler et al., 1984; Laissaoui et al., 1998; Periäfez 
et al., 2018). Uptake/release of radionuclides may be considered to be 
described by a single reversible reaction (1-step model, Fig. 5). This 
reaction is described by kinetic rates k, and k, for adsorption and 
release respectively, which are reaction rates measured in s71. 
The differential equations whose solution gives the time evolution 
of activity in water and sediment, Ay and A,, are! 
rn = —kıAwtkzA;s 
5 = kıAn- kA, 
Note that kinetic rates k, and k, operationally include all mecha- 
nisms for adsorption, like electrostatic attraction, ion exchange etc, and 
desorption. Also, in steady-state conditions (time derivatives are equal 
to zero) it is found from Egs. (16) (Periäüez et al., 2018) that: 
1% 
ka zz ni ka) 
where m is the concentration of sediment (mass of sediment per water 
volume unit), Thus, kinetic rates are related with the equilibrium k,. 
Nevertheless, there has been evidence to suggest that uptake takes 
place in two stages: fast surface adsorption followed by slow migration 
of jons to pores and interlattice spacings (Nyffeler et al., 1984; Turner 
et al., 1992; Turner and Millward, 1994; Oughton et al., 1997; Ciffroy 
et al., 2001; El-Mrabet et al., 2001). Thus, a 2-step model (Fig. 5) has 
also been included in some marine radionuclide transport models, A 
2-step model considers that exchanges are governed by two consec- 
utive reversible reactions: surface adsorption is followed by another 
process that may be a slow diffusion of ions into pores and interlattice 
spacings, inner complex formation or a transformation such as an 
oxidation. The forward and backward rates for this second reaction are 
k3 and k, respectively. Thus, radionuclides adsorbed by sediments are 
divided into two phases: a reversible and a slowly reversible fraction. 
It was shown that the 2-step model reproduces both the adsorption 
and release kinetics of !9Cs in the Irish Sea, where it is released 
from Sellafield nuclear fuel reprocessing plant (Periäfiez, 2003b). It was 
also recently included in THREETOX, which is the marine radionuclide 
transport model implemented within the JRODOS decision support 
system (Maderich et al., 2008, 2016). 
Although a kinetic model provides a more realistic description of 
adsorption/desorption processes than a k, model, it requires the speci- 
fication of kinetic rates, Obtaining values of kinetic rates is not easy 
since requires laboratory adsorption experiments with marine water