4. RADIONUCLIDE INTERACTION IN SOILS
4.1. Concepts and processes
4.1.1. The solid-liquid distribution coefficient concept
Dissolved radionuclide ions can bind to solid surfaces by a number of processes that are often classified under the broad term of sorption. The behaviour and ultimate radiological impacts of radionuclides in soils are largely controlled by their chemical form and speciation, which strongly affect their mobility, the residence time within the soil rooting zone and uptake by biota.
The degree of radionuclide sorption on the solid phase is often quantified using the solid-liquid distribution coefficient, Kd, which can be used when making assessments of the overall mobility and likely residence times of radionuclides in soils. Kd is the ratio of the concentration of radionuclide sorbed on a specified solid phase to the radionuclide concentration in a specified liquid phase [55]:
(17)
The Kd approach takes no explicit account of sorption mechanisms but assumes that the radionuclide on the solid phase is in equilibrium with the radionuclide in solution and that exchange between these phases is reversible.
Kd = activity concentration in solid phase activity concentrattion in liquid phase
Bq kg
Bq L-- (L kg -Ê
ËÁ
ˆ
¯˜
1
1 1)
However, the time elapsed since the incorporation of the radionuclide in the soil is known to affect the magnitude of Kd, since a fraction of the incorporated radionuclide may become fixed by the solid phase (an aging effect related to sorption dynamics) [56, 57].
Kd values for specific radionuclides are commonly obtained from field and laboratory studies. Since radionuclides in the field may have been present in the soil for a long period of time (e.g. from atmospheric nuclear weapons testing or from the Chernobyl accident), Kd values determined in situ may be higher than those determined in short term laboratory experiments [55].
For some well studied radionuclides the influence of specific co-factors on Kd values can be evaluated. Co-factors are soil properties involved in the mechanisms responsible for radionuclide sorption [58–64], and they can be used to group Kd values and can reduce the variability of these values when the grouping is based on fundamental properties, such as soil texture and organic matter. More details concerning the use of co-factors in Kd grouping are provided in the the accompanying TECDOC [5].
4.1.2. Vertical transfer of radionuclides in undisturbed soil profiles
The basic processes controlling the mobility of radionuclides (and other trace elements) in soil include convective transport by flowing water, dispersion caused by spatial variations of convection velocities, diffusive movement within the fluid, and physicochemical interactions with the soil matrix. In addition to abiotic processes, soil fauna may contribute to the transport of radionuclides in soils [65], and their action under general conditions results in the dispersion of radionuclides within the soil profile [66].
Two approaches are widely applied for modelling the migration of radionuclides in soils:
(1) The serial compartment model;
(2) The convection-dispersion equation (CDE).
Results from the serial compartment models for describing vertical migration in soil are generally expressed as migration rates (cm a–1). In contrast, the CDE approach considers that the input of the radionuclide can be approximated by a single pulse-like function. In this case, for a large time t, the first two moments of the depth distribution function are asymptotically approximated by:
E[z] vs·t (18)
var [z] 2·Ds·t (19) where Ds is the effective (or apparent) dispersion coefficient (cm² a–1), and vs is the convection velocity (cm a–1) [67]. The parameters vs and Ds are estimated from the position of the peak concentration in soil, zM, and the distance, ∆z, between zM and the depth where the concentration reduces to approximately 0.6 = 1/
–
eof its maximum:(20)
(21)
Values of Ds and vs can be used in the CDE for a chosen time t to produce a vertical profile of the radionuclide. In some cases, authors reported not only vs and Ds but also the migration rate, derived from the peak of the vertical distribution (or half-depth, i.e. the soil depth above which 50% of the total activity is present) at a given time t.
This migration rate is directly comparable with that resulting from compartment model calculations. Therefore, both kinds of migration rate may be combined (see Table 16).
4.1.3. Relationship between Kd and other parameters characterizing radionuclide mobility
4.1.3.1. Relationship between Kd and vertical migration
In a porous medium such as soil, the radionuclide diffusion process differs from diffusion in free water. An effective diffusion coefficient, De(m2 s–1), should therefore be defined. Only those pores that contribute to the transport of the dissolved radionuclide species have to be considered, although in most cases (mainly when the relative saturation tends to 1, and for cationic radionuclides), the total porosity, , is an adequate approximation. In the case of radionuclides with significant sorption, an apparent diffusion coefficient, Da (m2 s–1), can be calculated from the diffusion profile of the sample.
v z
s= tM
D z
s=
( )
Dt 2 2The apparent diffusion coefficient takes into account the retardation of the radionuclide due to interactions with the porous material:
(22)
where fret is the retardation factor. If we hypothesize a linear sorption pattern, with a constant Kd in the range of concentrations studied, fret can be defined as:
(23)
where r (kg m–3) is the dry bulk density of the soil.
If sorption of a radionuclide on soil is instantaneous, reversible and independent of its concentration (i.e. the Kd concept applies), this process is reflected in the CDE model by the following relations of the model parameters of a sorbing and a non-sorbing trace substance, respectively:
(24)
(25)
where Ds and vs are respectively the effective dispersion coefficient and the convective velocity of the radionuclide showing sorption, D is the dispersion coefficient of a non-sorbing trace substance, vw is the mean pore water velocity and fret is the retardation factor.
4.1.3.2. Relationship between Kd and root uptake
Soil to plant radionuclide transfer is assessed by measuring the soil to plant transfer factor or concentration factor, Fv, defined as the ratio of the radionuclide content in the plant (or in part of the plant) to that in the soil (Bq kg–1 dry weight plant tissue/Bq kg–1 dry weight soil). The concentration factor can be assumed to be controlled mostly by root uptake, since other sources of plant contamination (i.e. foliar uptake, soil adhesion by resuspension) are often of less significance.
D D
a f e
ret
=
fret= + ÊËÁ ˆ Kd
¯˜◊
1 r
e
D D
s f
ret
=
v v
s fw
ret
=
The radionuclide concentration in the plant, Cv, is assumed to be linearly correlated to the radionuclide level in the soil solution, Css. This relationship is controlled by the selectivity of the plant root system, represented by the bioaccumulation factor, Bp:
Cv = Css ·Bp (26)
where Bp refers to the radionuclide plant to soil solution ratio (Bq kg–1 dry weight plant tissue/Bq L–1 soil solution). The process of ion uptake from the soil solution to the plant by its roots includes physiological aspects of the plant related to nutrient uptake and selectivity, and depends on both the plant and the element considered.
Therefore, the soil solution–plant bioaccumulation factor is assumed to be dependent on the concentrations of radionuclide competitive species in the soil solution [68], as has been fully described for the K-Cs pair [69–71].
Concentrating on soil chemical factors, Css may be written as:
Css = Cs frev /Kd (27)
where Cs is the radionuclide concentration in the soil (Bq kg–1, dry weight soil) and frev is the reversibly sorbed radionuclide fraction (dimensionless), which also refers to the time dependent potential of the soil to fix the radionuclide to the solid phase.
Combining these equations results in the following:
Fv = Cv /Cs = Css · Bp /Cs = frev Bp /Kd (28) Attempts to correlate field data on Fv to any one of the parameters in Eq. (28) should be made with caution and are rarely justified.
However, for a given radionuclide and in the medium term after the contamination event, the reversibly sorbed fraction can be expected to be reasonably similar for a given set of soils, except when the set contains soils of contrasting properties (e.g. high clay content soils and peat soils) [72, 73]. In any case, the range of variation will be much narrower than that of Kd. Therefore, radionuclide availability may be quantified solely in terms of Kd.
To summarize, when comparing the concentration factors in the medium term for a set of similar soils, Eq. (28) may be simplified as follows:
Fv = Bp /Kd (29)
After a log transformation of this equation, the result is:
log Fv = log Bp – log Kd (30)
The resulting log equation has been successfully used to predict radiocaesium and radiostrontium transfer factors from Kd,both measured in contaminated soils and calculated from soil properties [70, 74]. For other radionuclides — for example, actinides and transuranides — this approach may not be valid and should be tested further.